[
    {
        "image_filename": "designv10_5_0000966_tac.2011.2162884-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000966_tac.2011.2162884-Figure1-1.png",
        "caption": "Fig. 1. Examples of admissible and non admissible trajectories.",
        "texts": [
            " Let an orthogonal system of coordinates be defined on the plane and assume that two perfectly rigid and infinitely massive walls constrain the ball to move in the region . Assuming that the control inputs are two forces and directed as the and axes, respectively, the system can be described by , , , , , where , and , , are all zero and are not needed. Note that such a system could have been described using just one mode, if, as suggested in Remark 1, a notation allowing different transitions between the same pair of modes corresponding to different switching surfaces was used. An admissible reference, indicated with in Fig. 1, is described by , , , , being . Letting , it is easy to verify that , , (13a) (13b) (13c) (13d) (13e) satisfy all the requirements 1)\u20136) of Definition 1. Moreover, being such a MIMO hybrid system in the class described in Remark 7, such a reference is also robustly admissible, since (13) are still valid for with the only difference that the input has to be computed by (13b) and (13c) but with replaced by . It is clear that infinitely many robustly admissible trajectories can be defined for the system above. On the other hand, it is also easy to imagine trajectories that are well defined for the system, but are not admissible according to Definition 1; e.g., a trajectory like the one indicated by in Fig. 1, in which the ball \u201chits\u201d the boundary with tangential velocity: trajectory violates condition 4) of Definition 1. Similarly, a trajectory like the one indicated by in Fig. 1 can be imagined (although multiple simultaneous impacts are difficult to model, there is a widely accepted solution for this case) but it would not be admissible according to Definition 1, because condition 5) would be violated. The reason for being so strict, in the requirements for admissible trajectories, is that we want to avoid Zeno behaviour locally around the desired trajectory. The proof of the main result of this paper implies that, for suitably small initial errors, the solutions of the closed-loop system that is proposed cannot exhibit Zeno effects, neither genuine nor chattering (see [47])"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001163_1.4028881-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001163_1.4028881-Figure3-1.png",
        "caption": "Fig. 3 Three types of machined rough surfaces used (from Ref. [33])",
        "texts": [
            " Because the primary objective of this paper is to numerically simulate the entire transition from the full-film and mixed EHL all the way down to boundary lubrication, and to investigate the frictional behaviors in the form of Stribeck curve, a series of cases have been chosen with different types of surface roughness orientations and different contact ellipticity ratios in a wide range of speed, but otherwise under the same operating conditions. Three types of machined rough surfaces used in the present study are illustrated in Fig. 3, representing the major roughness orientation patterns relative to the rolling direction: longitudinal, transverse, and isotropic. It can be seen that the topography of a turned surface consists of either longitudinal or transverse ridges with a rather consistent wavelength, while the shaved surfaces have more random asperities without any apparent direction. In each case, two rough surfaces of the same type and the same RMS roughness are running through the EHL zone, having their original composite RMS roughness fixed to r\u00bc 600 nm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001117_12_2012_168-Figure12-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001117_12_2012_168-Figure12-1.png",
        "caption": "Fig. 12 Schematic representation of deswelling processes of LC gels. Figure taken from [72]",
        "texts": [
            " Only small sample sizes are accessible as quadratic elastomer sheets have to be deformed. Moreover, the strong boundary conditions at the edges allow for a uniform orientation only in the very center of the sample. Not to mention that it is a very delicate operation to clamp a swollen elastomer sample for such a procedure. A more accessible technique to realize uniaxial compression based on anisotropic deswelling has been introduced for cholesteric elastomers and will be discussed in the next section (Fig. 12). Cholesteric LSCEs Since a cholesteric phase is a twisted nematic phase, the local director n is not constant in space but helically arranged perpendicular to an axis, usually referred to as the z-axis. For a nematic polymer with locally a prolate chain conformation, the helicoidal arrangement of n in the z-direction will cause an overall oblate network conformation. As described above for nematic elastomers, a uniaxial compression of the elastomer film can be used to achieve a global network conformation that is consistent with the helicoidal structure of the cholesteric phase. This deformation can be realized experimentally by using an anisotropic deswelling technique as described by Kim et al. (Fig. 12) [72]. Analogous to the classical two-step crosslinking procedure, a lightly crosslinked elastomer film swollen with a solvent is produced by a spin-casting technique. In a second step the solvent is slowly evaporated under centrifugation. Ordinarily, such a deswelling process would be isotropic. The network deswells simultaneously in all dimensions and the spherical shape of the chain conformation of the network strands is not affected. However, during centrifugation in a confined cell the film can only deswell in one direction \u2013 the film thickness (z-direction) \u2013 while the other two dimensions are defined by the experimental setup and remain unchanged"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002707_tie.2017.2764843-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002707_tie.2017.2764843-Figure2-1.png",
        "caption": "Fig. 2. Illustration of the experimental SEA.",
        "texts": [
            " To the best of the authors\u2019 knowledge, only one recent work [31] in the literature addresses the finite-time control problem for the SEA by using a terminal sliding-mode control scheme, where the bothersome chattering issue cannot be avoided. In this section, we will show that the proposed theoretical result will provided a much easier control implementation, and meanwhile significant control performance improvements can be achieved compared with the conventional PD and linear state feedback controllers, while there are not much added complexities of the gain tuning mechanism. In this paper, we use an SEA with a novel design (as depicted by Fig. 2) that gives the actuator different impedances at different force ranges. The actuator has two series elastic elements: a linear spring with a low stiffness and a torsional spring with a high stiffness. In this paper, we verify the proposed controller using only the torsional spring. Fig. 2(a) is a cross section showing the structure of the studied actuator. The motor (Maxon EC-4pole brushless dc motor operating at 200 W) shown is coupled to a ball screw through a torsional spring. Two incremental encoders (Renishaw RM22IC) with resolutions of 2 048 and 1 024 pulses per revolution are used to measure the angular displacement of the motor shaft and lead screw, respectively. Using the analogy of two-mass\u2013spring\u2013damper system, by neglecting the inevitable unmodeled disturbances, one can obtain the nominal mathematical model of the following form [30]: { mm q\u0308m + bm q\u0307m = Fm \u2212 k(qm \u2212 ql) mlq\u0308l + bl q\u0307l = k(qm \u2212 ql) (13) where the description of all involved parameters are listed in Table I"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001090_tmag.2011.2105498-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001090_tmag.2011.2105498-Figure2-1.png",
        "caption": "Fig. 2. Determination of field MMF for on-load SPSG for arbitrary operation mode and on-load condition.",
        "texts": [
            " Furthermore, in the region out of the pole span, flux density decreases considerably due to the large air-gap length. At the same condition flux density at SPSG stator\u2019 teethes at arbitrary rotor position can be determined by the air-gap flux density pattern. In the on-load SPSG, the magnetic field is established by the current in the field winding and by a balanced set of currents in the armature windings . In turn, the field is the result of the joint action of the MMF in the field winding and the MMF of armature winding . In Fig. 2, the directions of the phasors are determined for arbitrary operation mode and on-load condition. Phase angle , depends on the ratio of reactive impedance to resistance as follows: (3) where is the inductive reactance of armature winding, is the reactance of the load, is the resistance of the armature winding and is the resistance of the load. Phase angle , is between zero and , depending on the load parameters. can be resolved into the d-axis component, , and the q-axis component, , as illustrated in Fig. 2, for arbitrary value of . It is observed that the level of resultant MMF phasor in the air gap, , has been decreased in this case compared to resultant MMF at no-load. Therefore, it is anticipated that the flux density pattern of the air gap due to with profile shown in Fig. 2 (full line) has decreased and shifted compared to the case of no-load condition. As seen in Fig. 2, the shift angle can be calculated as follows: (4) The resultant MMF in this condition can be also determined as follows: (5) Using (3)\u2013(5), angles and and the resultant MMF in the no-load and on-load conditions are calculated. Field analysis in real SPSG indicates that the saturation of the stator teeth decreases the flux density in the region of minimum air gap [17]. At the region between the adjacent poles, the effect of saturation in the stator teeth is immaterial, because the air-gap reluctance in this region is large",
            " Based on the above mentioned reasons, a novel air-gap function for the SPSG in the presence of saturation is proposed, as follows: (6) where is the position of the air-gap flux measured from phase a-axis, and is the saturation factor. Variable degree of the saturation in SPSG is determined by saturation factor. This factor varies from 1 to 1.4 in SPSGs in which imply to the unsaturated case. in SPSG can be determined precisely by the procedure introduced in [17] at the no-load and on-load conditions. This procedure is based on the magnetic equivalent circuit method that used B-H curve of the magnetic material to evaluate in which is available. As illustrated in Fig. 2, is equal to . Since angle can be easily calculated using (4), depends on the rotor position in all modes of operating and on-load conditions. Therefore, (6) can be written as follows: (7) which appropriately indicates the dependency of the saturated air-gap function on the level and position of the air-gap flux. The inverse air-gap function of the SPSG in the presence of saturation, , can be calculated using distribution. This is achieved by Fourier series, in which the \u201c \u201d seems to be adequate to fit the Fourier representation of on distribution"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001968_978-94-007-6101-8-Figure4.6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001968_978-94-007-6101-8-Figure4.6-1.png",
        "caption": "Fig. 4.6 Cylindrical robot manipulator with coordinate frames",
        "texts": [
            " This means that the axis can be directed either into the list of paper or out of it. After selecting the x2 axis, we draw into the same direction also the axes x0 and x1. There remains only the coordinate frame at the robot end-point. The 4th exception only requires that the x3 axis is perpendicular to the z2 axis, which does not prevent us to make the robot end-point frame parallel to the precedent frame. The schematic presentation of the cylindrical robot with the appertaining coordinate frames is displayed in Fig. 4.6. We will continue with the table of DH parameters, which as in the previous case has 5 columns and 3 lines. First we shall write into each line a single joint variable \u03d11, d2, and d3. In the first column we have the index i running from 1 to 3 as in the previous example. We insert into the second column the distances between the neighboring coordinate frames ai , running along the xi axes. We can notice at the first sight that the origins of all four coordinate frames lay in the same plane, so that three zeros can be written into the ai column"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001968_978-94-007-6101-8-Figure4.10-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001968_978-94-007-6101-8-Figure4.10-1.png",
        "caption": "Fig. 4.10 Two initial poses od spherical robot manipulator",
        "texts": [
            " After drawing the coordinate frames into the robot mechanism, we left the mechanism in an arbitrary pose. Let us see 4.2 Examples of Geometric Robot Models 71 what is the initial pose of our simple spherical mechanism by considering the second joint. The angle \u03d12 is defined as the angle between the axes x2 and x1 about the z1 axis. From Fig. 4.9 we can see that zero angle occurs when the axes x2 and x1 are superimposed. This is the initial pose of the spherical robot which is shown in the left side of Fig. 4.10. Such initial pose cannot be reached by real industrial robots because of the limitations in joint movements. The producers of robots select such initial poses of robot mechanisms that the robot end-point is above the working area where the robot is supposed to execute its task. In our example of spherical robot such pose can be e.g. the one displayed in the right side of Fig. 4.10. Our minimalistic geometric model can be easily adapted to the required initial pose where the initial angle in the second joint \u03d12 is \u03c0/2. In the DH table we simply exchange \u03d12 by (\u03d12 + \u03c0/2). In the geometric model 0A3 we exchange all s2 with sin(\u03d12 + \u03c0/2), which is equal to c2, and all c2 with cos(\u03d12 + \u03c0/2), which is equal to \u2013s2. 1. Lenarc\u030cic\u030c, J., Bajd, T., & Stani\u0161ic\u0301, M. (2012). Robot mechanisms. Berlin: Springer. 2. Siciliano, B., Sciavico, L., Villani, L., & Oriolo, G. (2009). Robotics\u2013Modelling, planning and control"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002213_j.mechmachtheory.2014.06.006-Figure15-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002213_j.mechmachtheory.2014.06.006-Figure15-1.png",
        "caption": "Fig. 15. State 11 of the derivative queer-square mechanism (\u03b11 N 0, \u03b12 N 0, \u03b211 = \u03b212, \u03b221 \u2260 \u03b222).",
        "texts": [
            " When the links of the combination limb1p are parallel to each other and at the same time the bars in the combination limb2ap are antiparallel to each other, the angle relations of the derivative queer-square mechanism in category 4 are given as \u03b12 \u00bc \u2212\u03b211 \u03b211 \u00bc \u03b212 \u03b12 \u00fe \u03b82 \u00bc 0 : 8< : \u00f040\u00de The limb1s and limb2s have different relative positions with respect to the base and the platform has different relative positions with respect to the limb1p and limb2ap in the last four sub-states. In state 11, both limb1s and limb2s are higher than the base OA1A2 and the platform E1F1E2F2 is higher than limb1p and limb2ap. Fig. 15 offers the diametric view of the derivative queer-square mechanism in state 11 and its angle relations are given as \u03b11N0;\u03b211b0;\u03b212b0 \u03b12N0;\u03b221N0;\u03b222N0 : \u00f041\u00de When it comes to state 12, the angle \u03b12 changes from positive to negative. The dimetric view of the derivative queer-square mechanism in state 12 is illustrated in Fig. 16. As shown in Fig. 16, the relations between the angles of the revolute joints in the derivative queer-square mechanism in state 12 are provided as \u03b11N0;\u03b211N0;\u03b212N0 \u03b12b0;\u03b221N0;\u03b222N0 : \u00f042\u00de The limb1s and limb2s in state 12 have different relative positions compared to the base"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001509_j.apm.2016.07.016-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001509_j.apm.2016.07.016-Figure3-1.png",
        "caption": "Fig. 3. Nonlinear models of the gear-bearing system.",
        "texts": [
            " The time-varying stiffness of tooth pair 2 with period expansion method, which is k h 2 ( t ), can be expressed as the form of Fourier series. And the time-varying stiffness of tooth pair 1 could be derived as k h 1 (t) = k h 2 (t + T 0 ) . So k h 1 ( t ) and k h 2 ( t ) can be expressed as \u23a7 \u23aa \u23a8 \u23aa \u23a9 k h 1 (t) = k m + R \u2211 r=1 k r cos ( \u03c0 rt T 0 \u2212 \u03c6r + r\u03c0 ) , k h 2 (t) = k m + R \u2211 r=1 k r cos ( \u03c0 rt T 0 \u2212 \u03c6r ) , (2) where k m is the average mesh stiffness value, and k r and \u03c6r are the r th Fourier coefficient and phase angle of k h 2 ( t ), respectively. The non-linear dynamic model of a spur gear pair is shown in Fig. 3 . In this model, gears are supported on bearing with rolling elements and are subjected to torque T i ( i = 1, 2). Here, the non-linear effect of the bearing is not considered. I i is the mass moment of inertia; m i is the mass; k h is the nonlinear stiffness and c h is the damping coefficient of the gear mesh. r bi is the radius of base circle; K 1 x and K 1 y are the x and y direction stiffness coefficients of bearing 1, respectively; K 2 x and K 2 y are the x and y direction stiffness coefficients of bearing 2, respectively; x and y represent the vertical gear mesh direction and the mesh direction, respectively",
            " (8) where S ( t ) and S (t) (i = 1 , 2) are the friction moments of the i th tooth pair. 1 i 2 i Please cite this article as: L. Xiang et al., Bifurcation and chaos analysis for multi-freedom gear-bearing system with time- varying stiffness, Applied Mathematical Modelling (2016), http://dx.doi.org/10.1016/j.apm.2016.07.016 The differential equations of coupled transverse-torsional motion of the nonlinear gear-bearing system with time-varying mesh stiffness, friction and gear backlash, as shown in Fig. 3 , can be expressed as: \u23a7 \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23a8 \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23a9 I 1 \u0308\u03b81 + r b1 ( F mesh 1 + F mesh 2 ) + ( \u03bc1 \u03bb1 \u00b7 S 11 (t) \u00b7 F mesh 1 + \u03bc2 \u03bb2 \u00b7 S 12 (t) \u00b7 F mesh 2 ) = T 1 , I 2 \u0308\u03b82 \u2212 r b2 ( F mesh 1 + F mesh 2 ) \u2212 ( \u03bc1 \u03bb1 \u00b7 S 21 (t) \u00b7 F mesh 1 + \u03bc2 \u03bb2 \u00b7 S 22 (t) \u00b7 F mesh 2 ) = \u2212T 2 , m 1 \u0308x o1 + c 1 x \u0307 xo1 + k 1 x x o1 \u2212 ( \u03bc1 \u03bb1 \u00b7 F mesh 1 + \u03bc2 \u03bb2 \u00b7 F mesh 2 ) = F x 1 , m 1 \u0308y o1 + c 1 y \u0307 yo1 + k 1 y y o1 + ( F mesh 1 + F mesh 2 ) = F y 1 , m 2 \u0308x o2 + c 2 x \u0307 xo2 + k 2 x x o2 + ( \u03bc1 \u03bb1 \u00b7 F mesh 1 + \u03bc2 \u03bb2 \u00b7 F mesh 2 ) = \u2212F x 2 , m 2 \u0308y o2 + c 2 y \u0307 yo2 + k 2 y y o2 \u2212 ( F mesh 1 + F mesh 2 ) = \u2212F y 2 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002115_2422295-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002115_2422295-Figure3-1.png",
        "caption": "Fig. 3.-Crow, as in fig. 1, but with Lat. dot., Propat. b., Delt. maj., Tri. scap., E. mets. tad., E. dig. cohm., E. car. ul., Int. do:.J, and F. dig. III wholly or partly temoved. x.6.",
        "texts": [
            " post. and inserts into the posterior end of the humeral feather tract, where it is closely associated with the Serr. sup. met. (fig. 33). When present he Lat. dor. met. helps to tense the metapatagial membrane. This muscle is absent in the Corvidae. M. RHOMBOIDEUS SUPERFICIALIS (Rhom. sup.) Trapezius, No. 53, Shufeldt, 1890, p. 82. Rhomboideus superficialis, No. 65a, Gadow and Selenka, 1891, p. 217. Rhomboideus uperficialis, No. 2, Fiurbringer, 1902, p. 372. Rbomb. superf., Howell, 1937, p. 369; Fig. 3c, p. 373. Rhomboideus superficialis, Fisher, 1946, p. 582. Description (for the crow and raven; figs. 1-3 ).-A thin flat muscle, arising by a tendinous sheet from the spinous processes of the last two cervical, tlhe first wo thoracic vertebrae and the anterior half or more of the third (figs. 11, 15). The fibers are directed antero4laterally to the fleshy insertion on about the anteriotr wo-thirds of the dorso-medial surface of the shaft of the scapula (figs. 11, 14). A short distance from the anterior end of the muscle the insertion is interrupted by blood vessels and nerves emerging from the thorax",
            " californica (one specimen) A. c. californica (one specimen) Pica A. ultramarina Kitta Garrulus Cissolopha yucatanica Corvus Gymnorhinus Nucifraga Cyanocorax Psilorhinus Cissolopha beecheyi Calocitta Cyanolyca M. RHOMBOIDEUS PROFUNDUS (Rhom. pro.) Rhomboideus, No. 54, Shufeldt, 1890, p. 84. Rhomboideus profundus, No. 65b, Gadow and Selenka, 1891, p. 218. Rhomboides profundus, No. 3, Furbringer, 1902, p. 380. Rhomboideus posticoprofundus; Rhomboideus anticosublimnis, Burt, 1930, p. 486. Rhomb. prof., Howell, 1937, p. 369; fig. 3c, p. 373. Rhomb!oideus profundus, Fisher, 1946, p. 582. Description (for the crow and raven; figs. 1-4).-A thin, flat muscle, arising partly fleshy from the spinous processes of the last cervical and anterior four thoracic vertebrae (figs. 11, 15). The insertion is fleshy on about the posterior two-fifths of the dorso. medial border of the shaft of the scapula (figs. 11, 14). Anteriorly the fibers are directed postero-laterally but at the posterior end they pass almost directly laterally. The Rhom"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000150_20080706-5-kr-1001.01098-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000150_20080706-5-kr-1001.01098-Figure1-1.png",
        "caption": "Fig. 1. Body-fixed frame and earth-fixed frame for the quadrotor.",
        "texts": [
            " The objective of our controller is to achieve good tracking of desired positions and yaw angle while maintaining the stability of pitch and roll angles. The paper is outlined as follows. In section II, the dynamic model of the quadrotor helicopter is presented. Then, in section III, the closed-loop stability of the proposed controller is demonstrated. In section IV, some simulation results are carried out to show the efficiency of the controller. Finally, some conclusions are given in section V. The quadrotor, shown in figure 1, has four rotors to generate the propeller forces F1, F2, F3 and F4. Its configuration simplifies the displacement and increases the lift force. On varying the rotor speeds altogether with the same quantity, the lift forces will change, affecting in this case the altitude of the vehicle. The two pairs of rotors (1, 3) and (2, 4) turn in opposite directions in order to 978-3-902661-00-5/08/$20.00 \u00a9 2008 IFAC 6513 10.3182/20080706-5-KR-1001.1353 balance the moments and produce yaw motion as needed. Yaw angle is obtained by speeding up or slowing down the clockwise motors depending on the desired angle direction. The motion direction according to the horizontal plan depends on the sense of yaw angle and tilt angles (pitch and roll), whether they are positives or negatives. The equations describing the altitude and the attitude motions of a quadrotor helicopter are basically those of a rotating rigid body with six degrees of freedom [7]. Let there be two main reference frames (see figure 1): the earth-fixed inertial reference frame Ea(Oa, \u2212\u2192 ea 1 , \u2212\u2192 ea 2 , \u2212\u2192 ea 3) such that \u2212\u2192 ea 3 denotes the vertical direction downwards into the earth and the body-fixed reference frame Eb(Ob, \u2212\u2192 eb 1 , \u2212\u2192 eb 2 , \u2212\u2192 eb 3) fixed at the center of mass of the quadrotor. The absolute position of the quadrotor is described by X = [x, y, z]T and its attitude by the Euler angles \u0398 = [\u03c8, \u03b8, \u03c6]T , used corresponding to aeronautical convention. The attitude angles are respectively called Yaw angle (\u03c8 rotation around zaxis), Pitch angle (\u03b8 rotation around y-axis) and Roll angle (\u03c6 rotation around x-axis)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002735_3242587.3242659-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002735_3242587.3242659-Figure5-1.png",
        "caption": "Figure 5. Design of a single Dynablock.",
        "texts": [],
        "surrounding_texts": [
            "The next key design component is the connection and disconnection mechanism. A switchable connector is the key to allow the material elements to be reusable for reconstructable shape formation. An appropriate design and selection of the connection mechanism is important for several reasons. First, the speed of switching between connection and disconnection significantly affects the entire assembly time because the formation of each layer depends on the switching time. For example, if switching between connection and disconnection takes 10 seconds, constructing each layer takes more than 10 seconds, and therefore it would take N x 10 seconds to build N-layer objects, which is too slow for real-time interaction. Moreover, the connection mechanism would have the greatest impact on the cost and complexity of manufacturing the elements. Thus, the connector design must be carefully considered with regard to speed and manufacturing complexity. A variety of switchable connectors have been proposed in the literature of modular self-reconfigurable robots. We summarize some of these approaches in Table 1. Mechanical latching is the simplest and most common way for reversible connection (e.g., LEGO blocks). While existing systems in modular robots usually achieve mechanical latching with internal motors and actuators [30], past work in digital materials has explored micro-scale mechanical latching by press fitting [4]. As mechanical latching can be achieved with simple mechanical force, elements can be simple to fabricate. However, depending on the design the external assembler can be complicated and switching the connection may be slow. Magnetic force is another option. The simplest connection uses a permanent magnet to connect and uses external force to push or rotate the magnet to disconnect. This approach has been explored in several systems [42, 56]. Electromagnetic connection can be faster as it can switch states by running current, and it can be fabricated with a standard PCB manufacturing [34, 45, 48]. However, one notable disadvantage of using electromagnets is power consumption: The electromagnet requires continuous current to hold the magnetic force. On the other hand, electrostatic and electro-permanent magnetic connection can maintain the connection. For example, an electro-permanent magnet can be switched to the connection state with pulse current without requiring continuous current [19]. Although these connection mechanisms are ap- pealing due to their speed and size, for millimeter scale (e.g., 1 mm [17] to 10 mm [8]), manufacturing complexity presents difficulty for large numbers of elements. Thermal and photochromic bonding are other reversible connection methods. These bonding mechanisms leverage phase change of materials between liquid and solid to bond elements. Similar to soldering, thermal bonding uses heating to change the phase of a material from liquid to solid, and cooling to solidify the bond. For fast phase changing, it is common to use a low-temperature melting metal such as Galium or Field\u2019s metal, which melts at 40-80C degree [20, 29]. Thermal bonding is used in recent work on liquid metal 3D printing [20, 50]. Existing systems use a heater (e.g., resistive heating [29]), but cooling the metal at room temperature takes time. An alternative phase-changing connection is photochromic bonding, which leverages UV or visible light to change the phase of materials such as azobenzene [1] or liquid crystal materials [40]. We also expect that reversible dry adhesion, which can connect elements with Van der Waals force, could be another approach [22, 31]. Although these methods are promising, they have not been substantially explored for connecting modular robots or digital assembly. We prototyped 10 mm blocks with three different connectors (permanent magnet, electro-permanent magnet, and thermal bonding using Field\u2019s metal). We decided to further explore and implement a design using permanent magnetic connectors due to the simple manufacturing and faster speed of connection and disconnection of this approach."
        ]
    },
    {
        "image_filename": "designv10_5_0001945_j.ijheatmasstransfer.2018.06.033-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001945_j.ijheatmasstransfer.2018.06.033-Figure5-1.png",
        "caption": "Fig. 5. Predicted metal-transfer behaviors under different heat inputs: (a) Process No. 3 with AMR grids, (b) Process No. 3, and (c) Process No.",
        "texts": [
            " The difference between the above experiments was the heat input, which was proportional to the beam power divided by the wire feeding speed. Thus, we concluded that the metal-transfer mode changed from liquid bridge to droplet with a decrease in the heat input. On the basis of the aforementioned mathematical model, we systematically simulated the metal-transfer behaviors under different heat input conditions. The simulated processes were the first to the fifth sets of processes listed in Table 1. The experimental results of these processes revealed the phenomenon of the metal-transfer mode transition. Fig. 5 shows the predicted result of Process No. 1. Fig. 5b shows the droplet transition mode. Fig. 5c shows the liquid bridge transition mode. We observed that the use of the proposed model reproduced the two different metal-transfer modes appropriately. In addition, we compared the predicted geometry of the deposit with the experimental one in Fig. 6. The predicted result was close to the experimental one. A quantitative comparison of the width and the remaining height of the deposits is shown in Table 3. The measurements were carried out under the microscope with 0.1 mm index value. For the smooth deposits, the cross-section is chosen randomly",
            " After measured, the average values and the standard deviations of the melt height, width and depth were listed in Table 3. We found that the predicted results were consistent with the experimental results. Thus, we proved that the proposed model could accurately predict the metal-transfer modes under different process parameters. In addition, note that for an accurate and efficient simulation, we used the AMR method. The grid near the molten pool was considerably fine, while that far away from the molten pool was rather tough, as shown in Fig. 5a. A large amount of computing time was saved. More specifically, a set of process simulations could be completed within 12 h. Therefore, we now have an efficient theoretical tool to study the metal-transfer behaviors in the electron beam 3D printing process. Recently, Zhao et al. conducted a high-speed camera study on the wire feeding-based electron beam 3D printing process [12]. Their work also proved that with an increase in the heat input, the transition from the droplet to the liquid bridge occurred"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002260_tmag.2017.2668845-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002260_tmag.2017.2668845-Figure5-1.png",
        "caption": "Fig. 5. Steady-state temperature distributions when 25\u00b0C in ambience. (a) In the whole stator. (b) In stator iron and magnets. (c) In the magnets.",
        "texts": [
            " 0195 3 B. 3D Temperature Distributions by traditional 3D-FEA First of all, an equivalent heat circuit of the 12/10 PMFS motor is given in Fig. 4 with the material properties listed in Table IV. The armature slots are assumed to be fully filled by coils, thus the thermal conductivity and mass density of \u201cCoil\u201d in Table IV is lower than that of copper due to counting in the air and coil isolations in the slots. And the thermal property values may vary slightly considering manufacturing tolerances. Fig. 5 gives the steady-state temperature distributions when Br, Hc, and \u03c1 are obtained at 25\u00b0C, the same with ambience. Generally, the highest and lowest temperature in the stator can be found in coils and stator back iron, respectively. As can be seen in Fig. 5(c), the temperature in the magnet varies from 65\u00b0C to 75.5\u00b0C in both radial and axial directions, which apparently cannot be considered by traditional 2D-FEA. Although this problem can be solved by a using 3D coupled magnetic-thermal fields FEA, a much longer calculating time is required. Hence, an axially segmented FEA model of the PMFS motor is proposed in the following part, which enables the electromagnetic and thermal behaviors to be predicted with satisfied accuracy, but much less time consuming than the traditional 3D coupled-fields FEA model"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003987_tmech.2020.2979027-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003987_tmech.2020.2979027-Figure2-1.png",
        "caption": "Fig. 2. Exploded view of the force sensor CAD model. The assembly of the sensor on the trocar by interference is illustrated on the right.",
        "texts": [
            " Some issues resulting from the evaluation of the sensor prototype are discussed in Section VI. Section VII concluds this article. The innovation of the solution proposed in this article concerns the sensing element that is allocated at the end-tip of the trocar. Fig. 1 shows a sketch of the proposed idea with a zoomed view of the trocar where the sensor is placed. The sensor is composed of a bronze ring that has an inner diameter lower than the inner diameter of the trocar; the bronze ring is glued to a deformable structure (see Fig. 2). The inner diameter of the bronze ring is still greater than the diameter of the instrument shaft. The interaction force between the instrument end-effector and the patient body produces a displacement of the bronze ring, pushed by the instrument shaft, with respect to the trocar axis, which causes the deformation of the elastic frames that compose the sensor. This deformation, which depends on the elasticity of the deformable elements and is measured using four proximity optical sensors mounted in the appropriate way, is proportional to the force applied by the shaft to the ring",
            " Of course, the proposed solution requires that the minimally invasive robotic surgery (MIRS) instruments have a constant diameter and is particularly useful in the case that different Authorized licensed use limited to: University of Exeter. Downloaded on June 22,2020 at 20:21:40 UTC from IEEE Xplore. Restrictions apply. instruments have the same diameter. These limitations are not critical considering that they are verified in the da Vinci surgical robotic system. The exploded view of the computer-aided design (CAD) model of the trocar sensor is shown in Fig. 2. The sensor is composed of three main parts. The top part (g) is attached at the trocar end-tip by interference in order to simplify the assembly (see Fig. 2 right). It is composed of four deformable frames designed with four digs holding flat reflective surfaces; the surgical instrument slides inside a bronze ring (c) that is glued on the four deformable frames. The bronze ring ensures a homogeneous deformation of the four deformable frames when a force is applied by the instrument shaft; moreover, it allows to reduce the sliding friction and to reinforce the overall structure. In order to measure the deformation, four optical sensors are fixed to the bottom part of the sensor (a) in correspondence with the reflective surfaces"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001880_j.applthermaleng.2014.02.008-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001880_j.applthermaleng.2014.02.008-Figure1-1.png",
        "caption": "Fig. 1. The experimental test rig.",
        "texts": [
            " In this paper, we conduct a 3D thermal field computation of an induction motor with a healthy rotor and broken rotors based on the electromagnetism analysis. The influence of the number of broken bars on themotor thermal field is analyzed and validated by experimental approaches. The temperature-rise experiments of the prototype motor under full load are done in three different conditions, which include healthy state, one broken bar fault and two adjacent broken bars fault state. The dedicated experimental test rig has been set up which consists of one inductionmotor and three rotors, as shown in Fig. 1. The three rotors include a healthy one used as the reference and two broken ones by deliberately drilling holes in their bars on all the depth. In the course of the experiment, each drill hole is checked carefully to make sure the bars were totally broken. The basic parameters of the prototype motor are listed in Table 1. In order to evaluate the thermal behavior of the induction motor, a complete thermal evaluation of the prototype motor fitted with thermistor was carried out in the laboratory, and the temperaturerise of the motor in all the spots of interest can be obtained"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003793_j.mechmachtheory.2019.103764-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003793_j.mechmachtheory.2019.103764-Figure6-1.png",
        "caption": "Fig. 6. Relationship of internal and external meshing phase.",
        "texts": [
            " Since the gears of the star gearing system are fixed-axis rotation, an absolute coordinate system OXYZ is established for central floating components (sun gear, ring gear, planet carrier), and coordinate systems o i x i y i z i are built for each star gear, in which the coordinate center is the rotational center of each star gear, the direction of X \u2212 axis is along the radial direction of the floating member, and the Y \u2212 axis is tangential along the center floating member. Fig. 5 (a) shows the schematic diagram of the left end face of the dynamic model of the star gearing system. Fig. 5 (b) is a three-dimensional schematic diagram of the engagement, where the X \u2212 axis is perpendicular to the meshing line of the sun gear and the first star gear, and the counterclockwise direction is the positive direction. Fig. 5 (c) shows coupled dynamics model of star gear and planet carrier. Fig. 6 shows the relationship of internal and external meshing phase. Each side of gear has four degrees of freedom (movement in X, Y, Z direction and rotation around Z axis). Different gears are marked with upper and lower marks. The subscripts s, p, r represent the sun gear, star gears and ring gear respectively. Superscript L, R represent the gear in left end and right end. In the dynamic model of star gearing system, the sun gear and ring gear float axially, assume that all the star gears have same support stiffness and damping"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003235_j.jmapro.2020.04.073-Figure10-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003235_j.jmapro.2020.04.073-Figure10-1.png",
        "caption": "Fig. 10. Schematic illustration of surface modified by oxidation wear.",
        "texts": [
            " At 200 \u00b0C, due to the higher oxidation resistance of the steel, only a small amount of tribo-oxides appeared; the tribo-oxides were sparsely distributed on the partially worn surface since the oxidation occurred preferentially at the contacting asperities. In this case, the tribo-oxides were too thin to fully avoid metal-to-metal adhesion. However, it was found that the wear rate reduced as the temperature increased for most of the test conditions. On the other hand the wear rate increased with increasing temperature and applied load for WAAM processed 347 specimens compared to the 347 substrate. The schematic illustration of the possible surface modified by the oxidation wear is depicted in Fig. 10 and confirmed from the XRD plots and EDS spectra\u2019s. The formation of Fe2O3 and Fe3O4 is observed at elevated temperatures. Fe3O4 occurs above 400 \u00b0C and acts as a self-forming solid lubricant and reduces the friction coefficient for most load conditions (Fig. 9). This wear mechanism reduces the wear rate for all test conditions. During initial break-in period, the rate of wear is higher compared to the wear rate after the break-in period. In this sense, the running-in behavior can be regarded as a transition from a higher to a milder type of wear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002452_tpwrd.2019.2891119-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002452_tpwrd.2019.2891119-Figure1-1.png",
        "caption": "Fig. 1. (a) Schematic diagram of the 500 kV AC transmission line system (b) Front view and (c) Side view of the tower structure (ha, hb, and hc are the heights of phase A, B and C conductors at the tower, L is the span length)",
        "texts": [
            " A scaled down experiment was conducted in the laboratory to verify the effectiveness and robustness of the reconstruction algorithm and the measurement system. The parameter reconstruction of transmission line current is mainly regarded as the inverse problem between the transmission line current and the surrounding magnetic field distribution. Therefore, the forward calculation was firstly implemented under the practical scenarios. The structure of the 500 kV AC transmission line system used in this paper is illustrated in Fig. 1, in which the geometry of three phases and the span length are clearly indicated. The transmission lines usually have sags considering the influence of gravity, which is set as 4.75 m in Fig. 1(c). The transmission line with sag is considered in a catenary shape and satisfies (1).   cosh cosh , 2 2 2 a x kLL a z h a L L L x kL             (1) where L is the span length, h is the height of phase conductor on the transmission tower as shown in Fig. 1(b), a is a catenary constant and set as 0.1. k is an integer and x-kL represents the periodical calculation at different spans. According to the derivation of catenary line equation, the transmission line element dl can be represented by dx as shown in (2).   0 sinh 2 2 a x kL d dx dx L L L x kL            l (2) The magnetic field distribution in vicinity of the transmission lines was obtained based on Biot-Savart law. The calculation is in the magnetostatic regime since the frequency of transmission system is usually 50/60 Hz",
            " In the second stage, the interior point method was utilized to calculate the final optimization results, the initial values of which were the results obtained in the first stage. This comprehensive method avoided the problem when poor initial points often led to a local minimum, and could usually obtain the global optima in a tolerate calculation time simultaneously. The flowchart of the comprehensive reconstruction algorithm is illustrated in Fig. 4. The reconstruction algorithm was interpreted and simulated in the three-phase 500 kV AC transmission system illustrated in Fig. 1. To model the UAV\u2019s patrolling behavior in vicinity of the transmission lines, it was assumed that the height of the UAV was between 16 m and 20 m in one span. Considering a span length with x coordinate from -190 m to 190 m, the measurement points were selected evenly on the horizontal xy planes with heights of 16 m. The y coordinate of the trajectory was from -20 m to 20 m, and the angle between the trajectory and the x coordinate was approximately 80\u00b0, which formed a serpentine shape to simulate the practical trajectory"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003960_j.chaos.2020.110387-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003960_j.chaos.2020.110387-Figure3-1.png",
        "caption": "Fig. 3. Model of the gear profile.",
        "texts": [
            " (t) = b 0 \u2212 R a 1 R ac ( D 1 ) \u2211 + \u221e k =0 \u03bb( D 1 \u22122) k sin ( \u03bbk t) \u2212 R a 2 R ac ( D 2 ) \u2211 + \u221e k =0 \u03bb( D 2 \u22122) k sin ( \u03bbk t) (6) . Dynamic model .1. Time-variant mesh stiffness Single, and double teeth pairs contact alternatively in the proess of gear meshing, leading to the cyclical change of mesh stiffess. Therefore, it is essential to evaluate the mesh stiffness preisely for gear dynamics. Ma [37] proposed a potential energy method to work out the esh stiffness. The gear tooth is regarded as a cantilever beam in is research, as is shown in Fig. 3 . The accuracy of this approach as verified by the finite element method [37] . Therefore, in this K. Huang, Z. Cheng, Y. Xiong et al. Chaos, Solitons and Fractals xxx (xxxx) xxx s n k s s p T n c i 3 o e i a \u03c9 r r a t V t F K tudy, the method proposed by Ma is used for solving mesh stiffess. And the formula is expressed as follows. m = j = 2 \u2211 j = 1 ( 1 k h + 1 k b1 , j + 1 k s 1 , j + 1 k a 1 , j + 1 k f 1 , j + 1 k b2 , j + 1 k s 2 , j + 1 k a 2 , j + 1 k f 2 , j )\u22121 (7) Where k h, k b, k s, k a, k f are Hertzian stiffness, bending stiffness, hear stiffness, axial compressive stiffness, and fillet-foundation tiffness, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002833_tim.2017.2664599-Figure25-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002833_tim.2017.2664599-Figure25-1.png",
        "caption": "Fig. 25. Sketch of the bearing accelerated life test system.",
        "texts": [
            " The computation efficiency of DRS-LMD is lower than EWT, but it is much higher than EEMD and LMD. The accelerated bearing life tester (ABLT-1) is provided by the Hangzhou Bearing Test and Research Center in China illustrated in Fig. 24(a) [6]. The designed tester has four bearings on one shaft driven by an ac motor. The rubber belt is used to connect the ac motor and the shaft using two belt pulleys in Fig. 24(b). The two belt pulleys have the same size with the diameter of 134 mm. A sketch of the bearing accelerated life test system is shown in Fig. 25. In this experiment, single row deep groove ball bearings (model: 6308) are tested in the full life test. Each bearing has eight balls with a 0\u00b0 contact angle. The pitch diameter is 65.5 mm and the ball diameter is 15.081 mm. The outer races were fixed and the corresponding inner races revolved with the shaft. When a rolling bearing fails, the failed bearing is replaced by another new one. The experimental tests were performed at a motor rotational speed of 3000 rpm. A radial load of 20.5 kg was added to the test and then the load was amplified 100 times by an oilpressure amplifying unit. Therefore, the load added on each bearing was 1025 kg (P/2 = ((20.5 \u00d7 100)/2)). Meanwhile, all the bearings were forcibly lubricated by an oil circulation system that controlled the temperature to be around 58\u00b0. The data acquisition system includes four high-sensitivity quartz Kistler 8704B25 ICP accelerometers. The accelerometers were installed on bearing housings and their positions are shown in Fig. 25. A data acquisition and analysis system called LMS SC310-UTP is applied to collect the data. One group of vibration data with 20480 points are collected every 5 min. The sampling frequency is 20480 Hz. The analyzed bearing was confirmed with inner race fault after the accelerated life test. In this paper, RMS index is applied to describe the degradation process of the pitting as shown in Fig. 26. To see the fault increasing process and fault location, Fig. 27 shows the bearing at three stages: normal stage, early fault stage, and severe fault stage"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002213_j.mechmachtheory.2014.06.006-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002213_j.mechmachtheory.2014.06.006-Figure1-1.png",
        "caption": "Fig. 1. Structure of the derivative queer-square mechanism.",
        "texts": [],
        "surrounding_texts": [
            "The derivative queer-squaremechanism is composed of ten rigid links and twelve revolute joints. As illustrated in Figs. 1\u20133, the ten links are denoted from 1 to 10. The length of links 2, 4, 5, 6, 8, 9, the longer part of links 3 and 10 is defined as l3 which equals to l1 + l2. The length of the longer part of links 1 and 7 is equal to l1. The length of the shorter part of links 1 and 3 is l2 / 2, while the length of the shorter part of links 7 and 10 is l2. Link 3 is connected to link 4 by a revolute joint located at a distance of l1 from the intersecting point of the longer and shorter parts of link 3. The revolute joint connecting link 9 and link 10 is located at a distance of l1 from the intersecting point of the longer and shorter parts of link 10. Themechanism is fixed at pointO\u2032, which is the intersecting point of the shorter part and longer part of link 1. Point A1 is on the axis of the revolute joint connected link 1 and link 2. Similarly, point A2 is on the axis of the revolute jointwhich connected link 1 and link 6. The planewhere pointsO\u2032,A1 andA2 are located serves as the base of the derivative queersquare mechanism. The platform is considered as the plane consisting link 10, which is the target plane for mobility analysis in this paper. LInks 2 and 6 are named as Limb1s and Limb2s. When the links 4 and 5 are parallel to each other, their combination is named as Limb1p. When the links 4 and 5 are antiparallel to each other, their combination is named as Limb1ap. Similarly, depending on links 8 and 9 are parallel or antiparallel to each other, their combinations are named as Limb2p and Limb2ap, respectively. For the purpose of analysis, a coordinate system O(x, y, z) is built up as shown in Figs. 2 and 3. The origin point O of the system is located at a distance of l2 / 2 away from point O\u2032 in the direction of A1O0. The x-axis points in the direction of OA1. The z-axis is perpendicular to the plane OA1A2, and points upwards. The y-axis is defined by the right hand rule. All of the angles \u03b11, \u03b81, \u03b211, \u03b212, \u03b12, \u03b82, \u03b221 and \u03b222 are defined by rotating from the extended line of the former bar to the latter bar, as demonstrated in Fig. 3. Each of the twelve revolute joints of the derivative queer-squaremechanism is expressed by a screw, denoted as Si, which belongs to a six-dimension linear vector spacewith transformation features [21]. The unit vector in the direction of the screw axis is presented in the first three components. In some postures, S3, S4, S5 and S6 and S9, S10, S11 and S12 can form two parallelograms. When the derivative queer-square mechanism changes to some other postures, S3, S4, S5 and S6 or S9, S10, S11 and S12 only build up one parallelogram. For the purpose of simplification, s\u03b11, c\u03b11, s\u03b211, c\u03b211, s\u03b212, c\u03b212, s\u03b221, c\u03b221, s\u03b222, c\u03b222, s(\u03b11 + \u03b81), c(\u03b11 + \u03b81), s(\u03b12 + \u03b82) and c(\u03b12 + \u03b82) in the following equations are short hand of sin\u03b11, cos\u03b11, sin\u03b211, cos\u03b211, sin\u03b212, cos\u03b212, sin\u03b221, cos\u03b221, sin\u03b222, cos\u03b222, sin(\u03b11 + \u03b81), cos(\u03b11 + \u03b81), sin(\u03b12 + \u03b82) and cos(\u03b12 + \u03b82), respectively. Twelve screw expressions of twelve revolute joints are given as S1 \u00bc 0 \u22121 0 0 0 \u2212l1\u2212 l2 2 T ; \u00f01\u00de S \u00bc 0 \u22121 0 l2 T ; \u00f02\u00de where and, 2 cs\u03b11 0 \u2212l1\u2212 2 \u2212l3c\u03b11 S3 \u00bc c \u03b11 \u00fe \u03b81\u00f0 \u00de 0 s \u03b11 \u00fe \u03b81\u00f0 \u00de l1s \u03b11 \u00fe \u03b81\u00f0 \u00de l3s\u03b11c \u03b11 \u00fe \u03b81\u00f0 \u00de\u2212 l1 \u00fe l2 2 \u00fe cc\u03b11 s \u03b11 \u00fe \u03b81\u00f0 \u00de \u2212l1c \u03b11 \u00fe \u03b81\u00f0 \u00de T \u00f03\u00de S4 \u00bc c \u03b11 \u00fe \u03b81\u00f0 \u00de 0 s \u03b11 \u00fe \u03b81\u00f0 \u00de l1 \u00fe l3c\u03b211\u00f0 \u00des \u03b11 \u00fe \u03b81\u00f0 \u00de o \u2212 l1 \u00fe l3c\u03b211\u00f0 \u00dec \u03b11 \u00fe \u03b81\u00f0 \u00de\u00bd T; \u00f04\u00de S5 \u00bc c \u03b11 \u00fe \u03b81\u00f0 \u00de 0 s \u03b11 \u00fe \u03b81\u00f0 \u00de l3s \u03b11 \u00fe \u03b81\u00f0 \u00de l3s\u03b11c \u03b11 \u00fe \u03b81\u00f0 \u00de\u2212 l1 \u00fe l2 2 \u00fe l3c\u03b11 s \u03b11 \u00fe \u03b81\u00f0 \u00de \u2212l3c \u03b11 \u00fe \u03b81\u00f0 \u00de T \u00f05\u00de S6 \u00bc c \u03b11 \u00fe \u03b81\u00f0 \u00de 0 s \u03b11 \u00fe \u03b81\u00f0 \u00de l3 \u00fe l3c\u03b212\u00f0 \u00des \u03b11 \u00fe \u03b81\u00f0 \u00de r \u2212 l3 \u00fe l3c\u03b212\u00f0 \u00dec \u03b11 \u00fe \u03b81\u00f0 \u00de\u00bd T; \u00f06\u00de S7 \u00bc \u22121 0 0 0 0 l2 2 T ; \u00f07\u00de S8 \u00bc \u22121 0 0 0 \u2212l3s\u03b12 l2 2 \u00fe l3c\u03b12 T ; \u00f08\u00de S9 \u00bc 0 c \u03b12 \u00fe \u03b82\u00f0 \u00de s \u03b12 \u00fe \u03b82\u00f0 \u00de l2 2 \u00fe l3c\u03b12 s \u03b12 \u00fe \u03b82\u00f0 \u00de\u2212l3s\u03b12c \u03b12 \u00fe \u03b82\u00f0 \u00de 0 0 T ; \u00f09\u00de S10 \u00bc 0 c \u03b12 \u00fe \u03b82\u00f0 \u00de s \u03b12 \u00fe \u03b82\u00f0 \u00de s \u2212l3c\u03b221s \u03b12 \u00fe \u03b82\u00f0 \u00de l3c\u03b221c \u03b12 \u00fe \u03b82\u00f0 \u00de\u00bd T; \u00f010\u00de S11 \u00bc 0 c \u03b12 \u00fe \u03b82\u00f0 \u00de s \u03b12 \u00fe \u03b82\u00f0 \u00de l2 2 \u00fe l3c\u03b12 s \u03b12 \u00fe \u03b82\u00f0 \u00de\u2212l3s\u03b12c \u03b12 \u00fe \u03b82\u00f0 \u00de \u2212l2s \u03b12 \u00fe \u03b82\u00f0 \u00de l2c \u03b12 \u00fe \u03b82\u00f0 \u00de T \u00f011\u00de S12 \u00bc 0 c \u03b12 \u00fe \u03b82\u00f0 \u00de s \u03b12 \u00fe \u03b82\u00f0 \u00de t \u2212 l2 \u00fe l3c\u03b222\u00f0 \u00des \u03b12 \u00fe \u03b82\u00f0 \u00de l2 \u00fe l3c\u03b222\u00f0 \u00dec \u03b12 \u00fe \u03b82\u00f0 \u00de\u00bd T; \u00f012\u00de , o \u00bc l3s\u03b11 \u00fe l3s\u03b211 cos \u03b11 \u00fe \u03b81\u00f0 \u00de\u00bd c \u03b11 \u00fe \u03b81\u00f0 \u00de\u2212 l1 \u00fe l2 2 \u00fe l3c\u03b11\u2212l3s \u03b11 \u00fe \u03b81\u00f0 \u00des\u03b211 s \u03b11 \u00fe \u03b81\u00f0 \u00de; r \u00bc l3s\u03b11 \u00fe l3s\u03b212c \u03b11 \u00fe \u03b81\u00f0 \u00de\u00bd c \u03b11 \u00fe \u03b81\u00f0 \u00de\u2212 l1 \u00fe l2 2 \u00fe l3c\u03b11\u2212l3s \u03b11 \u00fe \u03b81\u00f0 \u00des\u03b212 s \u03b11 \u00fe \u03b81\u00f0 \u00de; s \u00bc l2 2 \u00fe l3c\u03b12\u2212l3s\u03b221s \u03b12 \u00fe \u03b82\u00f0 \u00de s \u03b12 \u00fe \u03b82\u00f0 \u00de\u2212 l3s\u03b12 \u00fe l3s\u03b221c \u03b12 \u00fe \u03b82\u00f0 \u00de\u00bd c \u03b12 \u00fe \u03b82\u00f0 \u00de; t \u00bc l2 2 \u00fe l3c\u03b12\u2212l3s\u03b222s \u03b12 \u00fe \u03b82\u00f0 \u00de s \u03b12 \u00fe \u03b82\u00f0 \u00de\u2212 l3s\u03b12 \u00fe l3s\u03b222c \u03b12 \u00fe \u03b82\u00f0 \u00de\u00bd c \u03b12 \u00fe \u03b82\u00f0 \u00de: One or two parallelograms included in the derivative queer-square mechanism can be regarded as complex joints, which are close-loop sub chains. Equivalent constraints of the complex joints are analysed which are not presented in this paper. Based on the equivalent constraints analysis, relative degrees of freedom between inputs and outputs of complex joint are derived which lead to the constraint analysis of one or two entire branches each as an open chain serially connected by links and joints. According to the platformmotion\u2013screw system [22] of the derivative queer-square mechanism obtained by using equivalent constraints analysis of complex joints, mobility of the platform indicates that this method does not have the ability to reflect the mobility change of the platform since it loses the information of parallel or antiparallel between bars 4 and 5 or between bars 8 and 9. Since the equivalent constraint analysis of the complex joint is not suitable for the case of mobility variation, another method is proposed as follows. Four branch motion\u2013screw systems which span the motion from the base to the platform are used to describe the mechanism. Twelve screws compose four branch motion\u2013screw systems [22]. Specifically, screws S1, S2, S3 and S4 build up the first branch motion\u2013screw system and screws S1, S2, S5 and S6 form the second branch motion\u2013screw system. The third branch motion\u2013screw system is composed by screws S7, S8, S9 and S10, while the fourth branch motion\u2013screw system consists of screws S7, S8, S11 and S12. Four branch motion\u2013screw systems of the derivative queer-square mechanism in arbitrary configurations are derived as Sb1f g \u00bc S1 S2 S3 S4 8>< >: 9>= >; ; \u00f013\u00de S1 8> 9> where Althou genera rocal s Srb1 where d \u00bc \u2212 Srb2 with, e \u00bc \u2212 Srb3 where f \u00bc \u2212 Sb2f g \u00bc S2 S5 S6 < >: = >; ; \u00f014\u00de Sb3f g \u00bc S7 S8 S9 S10 8>< >: 9>= >; ; \u00f015\u00de Sb4f g \u00bc S7 S8 S11 S12 8>< >: 9>= >; ; \u00f016\u00de curly brace {\u22c5} describes the set which possesses the largest linear independent screws of all revolute joints in each branch. gh all of four screw systems belong to four-systems, they have different components. The branch constraint\u2013screw system is ted from the reciprocal screw of the branchmotion\u2013screw system as Sbi\u2218Sbi r \u00bc 0 i \u00bc 1;2;3\u00f0 \u00de\u0394 \u00bc 0 I I 0 . By solving the recip- crews of the branch motion\u2013screw systems of four branches, four branch constraint\u2013screw systems are obtained as \u00bc Sr11 \u00bc cot\u03b11 c\u03b211 c \u03b11 \u00fe \u03b81\u00f0 \u00des\u03b11\u2212s \u03b11 \u00fe \u03b81\u00f0 \u00dec\u03b11\u00bd s\u03b11s\u03b211 1 d \u2212l1\u2212 l2 2 0 T Sr12 \u00bc 0 0 0 \u2212 tan \u03b11 \u00fe \u03b81\u00f0 \u00de 0 1\u00bd T 8< : 9= ;; \u00f017\u00de , l1 \u00fe l3\u00f0 \u00des2 \u03b11 \u00fe \u03b81\u00f0 \u00dec\u03b11c\u03b211 \u00fe 2l3c 2 \u03b11 \u00fe \u03b81\u00f0 \u00dec\u03b211s 2\u03b11 \u00fe 2l3s 2 \u03b11 \u00fe \u03b81\u00f0 \u00dec2\u03b11c\u03b211 \u00fe2l1s 3 \u03b11 \u00fe \u03b81\u00f0 \u00dec\u03b11s\u03b211\u22122l1c 3 \u03b11 \u00fe \u03b81\u00f0 \u00des\u03b11s\u03b211\u22122l1c \u03b11 \u00fe \u03b81\u00f0 \u00des2 \u03b11 \u00fe \u03b81\u00f0 \u00des\u03b11s\u03b211 \u2212 l1 \u00fe l3\u00f0 \u00dec \u03b11 \u00fe \u03b81\u00f0 \u00des \u03b11 \u00fe \u03b81\u00f0 \u00dec\u03b211s\u03b11 \u00fe 2l1c 2 \u03b11 \u00fe \u03b81\u00f0 \u00des \u03b11 \u00fe \u03b81\u00f0 \u00dec\u03b11s\u03b211 \u22124l3c \u03b11 \u00fe \u03b81\u00f0 \u00des \u03b11 \u00fe \u03b81\u00f0 \u00dec\u03b11c\u03b211s\u03b11 0 BBB@ 1 CCCA 2c \u03b11 \u00fe \u03b81\u00f0 \u00des\u03b11s\u03b211 ; \u00bc Sr21 \u00bc 0 0 0 \u2212 tan \u03b11 \u00fe \u03b81\u00f0 \u00de 0 1\u00bd T Sr22 \u00bc cot\u03b11 c\u03b212 c \u03b11 \u00fe \u03b81\u00f0 \u00des\u03b11\u2212s \u03b11 \u00fe \u03b81\u00f0 \u00dec\u03b11\u00bd s\u03b11s\u03b212 1 e \u2212l1\u2212 l2 2 0 T 8< : 9= ;; \u00f018\u00de l1 \u00fe l3\u00f0 \u00des2 \u03b11 \u00fe \u03b81\u00f0 \u00dec\u03b11c\u03b212 \u00fe 2l3s 3 \u03b11 \u00fe \u03b81\u00f0 \u00dec\u03b11s\u03b212\u2212 l1 \u00fe l3\u00f0 \u00dec \u03b11 \u00fe \u03b81\u00f0 \u00des \u03b11 \u00fe \u03b81\u00f0 \u00dec\u03b212s\u03b11 \u00fe2l3s 2 \u03b11 \u00fe \u03b81\u00f0 \u00dec2\u03b11c\u03b212 \u00fe 2l3c 2 \u03b11 \u00fe \u03b81\u00f0 \u00dec\u03b212s 2\u03b11\u22122l3c \u03b11 \u00fe \u03b81\u00f0 \u00des2 \u03b11 \u00fe \u03b81\u00f0 \u00des\u03b11s\u03b212 \u00fe2l3c 2 \u03b11 \u00fe \u03b81\u00f0 \u00des \u03b11 \u00fe \u03b81\u00f0 \u00dec\u03b11s\u03b212\u22124l3c \u03b11 \u00fe \u03b81\u00f0 \u00des \u03b11 \u00fe \u03b81\u00f0 \u00dec\u03b11c\u03b212s\u03b11\u22122l3c 3 \u03b11 \u00fe \u03b81\u00f0 \u00des\u03b11s\u03b212 0 B@ 1 CA 2c \u03b11 \u00fe \u03b81\u00f0 \u00des\u03b11s\u03b212 \u00bc Sr31 \u00bc 0 0 0 0 \u2212 tan \u03b12 \u00fe \u03b82\u00f0 \u00de 1\u00bd T Sr32 \u00bc c\u03b221 c \u03b12 \u00fe \u03b82\u00f0 \u00des\u03b12\u2212s \u03b12 \u00fe \u03b82\u00f0 \u00dec\u03b12\u00bd s\u03b12s\u03b221 cot\u03b12 1 l2 2 f 0 T 8< : 9= ;; \u00f019\u00de , c\u03b221 c \u03b12 \u00fe \u03b82\u00f0 \u00des\u03b12\u2212s \u03b12 \u00fe \u03b82\u00f0 \u00dec\u03b12\u00bd l2s \u03b12 \u00fe \u03b82\u00f0 \u00de\u22122l3c \u03b12 \u00fe \u03b82\u00f0 \u00des\u03b12 \u00fe 2l3s \u03b12 \u00fe \u03b82\u00f0 \u00dec\u03b12\u00bd 2c \u03b12 \u00fe \u03b82\u00f0 \u00des\u03b12s\u03b221 ; Srb4 with, g \u00bc 0 B@ where respec along t from a Sr \u00bc where tem, an with r relatio form m S f n o \u2218 \u00bc Sr41 \u00bc c \u03b12 \u00fe \u03b82\u00f0 \u00dec\u03b222s\u03b12\u2212s \u03b12 \u00fe \u03b82\u00f0 \u00dec\u03b12c\u03b222 s\u03b12s\u03b222 cot\u03b12 1 l2 2 g 0 T Sr42 \u00bc 0 0 0 0 \u2212 tan \u03b11 \u00fe \u03b81\u00f0 \u00de 1\u00bd T 8< : 9= ;; \u00f020\u00de l2s 2 \u03b12 \u00fe \u03b82\u00f0 \u00dec\u03b12c\u03b222 \u00fe 2l2s 3 \u03b12 \u00fe \u03b82\u00f0 \u00dec\u03b12s\u03b222 \u00fe 2l2c 2 \u03b12 \u00fe \u03b82\u00f0 \u00des \u03b12 \u00fe \u03b82\u00f0 \u00dec\u03b12s\u03b222 \u22122l2c \u03b12 \u00fe \u03b82\u00f0 \u00des2 \u03b12 \u00fe \u03b82\u00f0 \u00des\u03b12s\u03b222\u2212l2c \u03b12 \u00fe \u03b82\u00f0 \u00des \u03b12 \u00fe \u03b82\u00f0 \u00dec\u03b222s\u03b12\u22122l2c 3 \u03b12 \u00fe \u03b82\u00f0 \u00des\u03b12s\u03b222 \u22124l3c \u03b12 \u00fe \u03b82\u00f0 \u00des \u03b12 \u00fe \u03b82\u00f0 \u00dec\u03b12c\u03b222s\u03b12 \u00fe 2l3c 2 \u03b12 \u00fe \u03b82\u00f0 \u00dec\u03b222s 2\u03b12 \u00fe 2l3s 2 \u03b12 \u00fe \u03b82\u00f0 \u00dec2\u03b12c\u03b222 1 CA 2c \u03b12 \u00fe \u03b82\u00f0 \u00des\u03b12s\u03b222 , s3(\u03b11 + \u03b81), c3(\u03b11 + \u03b81), s3(\u03b12 + \u03b82) and c3(\u03b12 + \u03b82) stand for sin3(\u03b11 + \u03b81), cos3(\u03b11 + \u03b81), sin3(\u03b12 + \u03b82) and cos3(\u03b12 + \u03b82), tively. Among each constraint screw in branch constraint\u2013screw systems, the first three components demonstrate the force he screw axis and the last three components present the torque. Platform constraint\u2013screw systemof themechanism is generated dding four branch constraint\u2013screw systems as Srb1 \u00fe Srb2 \u00fe Srb3 \u00fe Srb4 ; \u00f021\u00de addition \u201c+\u201d simply combines all components of four branch constraint\u2013screw systems into one platform constraint\u2013screw sysd angle bracket is used to illustrate amultisetwhichmay include repeated components. The constraint andmotionof theplatform espect to the base are represented by platform constraint\u2013screw system and platformmotion\u2013screw system based on the parallel n of four branches. Relative constraint of the platform can be imposed by either branch, while corresponding motion of the platust be allowed by all the branches. Platform motion\u2013screw system is determined as Sr \u00bc 0: \u00f022\u00de With regard to platformmotion\u2013screw system shown in Eq. (22), its cardinal number, which is also equal to the dimension of its spanned subspace, indicates the mobility of the platform. The screws in the platformmotion\u2013screw system reveal the rotation about the screw axis in the first three components and the translation along the screw axis in the last three components. The derivative queer-square mechanism has the same representation of all the screws in different states since there is no joint or component changing when the mechanism changes from one state to another state. All the states of the derivative queer-square mechanism have the same expression of the platformmotion\u2013screw system as presented in Eq. (22). On the other hand, in different states, the mechanism receives distinct geometrical constraints generating from different geometric positions which cause the variation of the mobility and motion type as demonstrated in further sections."
        ]
    },
    {
        "image_filename": "designv10_5_0001474_j.engappai.2013.08.017-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001474_j.engappai.2013.08.017-Figure1-1.png",
        "caption": "Fig. 1. Coordinate systems.",
        "texts": [
            " The system dynamics can be divided into two parts: estimated dynamics \u03c4\u0302 and unknown dynamics ~\u03c4: \u03c4\u00bc \u03c4\u0302\u00fe ~\u03c4 \u00f02\u00de where \u03c4\u0302\u00bc M\u0302 _q\u00fe C\u0302q\u00feD\u0302q\u00fe g\u0302, ~\u03c4 \u00bc ~M _q\u00fe ~Cq\u00fe ~Dq\u00fe ~g\u00few, M\u0302; C\u0302; D\u0302; g\u0302 are estimated terms, ~M ; ~C ; ~D; ~g are the unknown terms, w is the disturbance term. Eq. (2) will be in detailed description in Section 3. In the following, the general control allocation problem will be related with the motion in the horizontal plane. The UUV posture in the horizontal plane can be described in terms of two coordinates x; y and the orientation angle \u03c8 . Fig. 1 shows its structure. The dynamic model (Eqs. (3)\u2013(5)) is decoupled and controllable in 3 DOF (q\u00bc \u00bdu v r ). The coordinate systems considered in the horizontal plane are illustrated in Fig. 1. The following are the reduced dynamic equations for the thruster-powered underwater vehicles \u00f0m X _u\u00de _u\u00feXuu\u00feXuuujuj\u00fe\u00f0W B\u00des\u03b8\u00bc \u03c4X \u00f03\u00de \u00f0m Y _v\u00de_v\u00feYvv\u00feYvvvjvj\u00fe\u00f0W B\u00dec\u03b8s\u03c6\u00bc \u03c4Y \u00f04\u00de \u00f0Iz N_r\u00de_r\u00feNrr\u00feNrrrjrj \u00bc \u03c4N \u00f05\u00de where the symbols c\u03b8, s\u03b8, c\u03c6, s\u03c6 represent cos \u03b8, sin \u03b8, cos \u03c6, sin \u03c6 respectively. The basic control architecture of the system is illustrated in Fig. 2. The design of the hybrid control strategy consists of two parts: (1) an outer loop virtual velocity controller by using position and orientation state errors; (2) an inner loop sliding-mode controller by using velocity state vector"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002213_j.mechmachtheory.2014.06.006-Figure17-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002213_j.mechmachtheory.2014.06.006-Figure17-1.png",
        "caption": "Fig. 17. State 13 of the derivative queer-square mechanism (\u03b11 b 0, \u03b12 N 0, \u03b211 = \u03b212, \u03b221 \u2260 \u03b222).",
        "texts": [
            " 16, the relations between the angles of the revolute joints in the derivative queer-square mechanism in state 12 are provided as \u03b11N0;\u03b211N0;\u03b212N0 \u03b12b0;\u03b221N0;\u03b222N0 : \u00f042\u00de The limb1s and limb2s in state 12 have different relative positions compared to the base. The limb1s and limb1p are higher than the base, and the limb2s and limb2ap are lower than the base. The platform is located in themiddle of the limb1p and limb2ap, in particular it is lower than the limb1p and higher than the limb2ap. The observation of the derivative queer-square mechanism in state 13 is illustrated in Fig. 17 and its angle relations are given as \u03b11b0;\u03b211N0;\u03b212N0 \u03b12N0;\u03b221b0;\u03b222b0 : \u00f043\u00de The diametric view of the derivative queer-square mechanism in state 14 is presented in Fig. 18 and its angle relations are given as \u03b11b0;\u03b211b0;\u03b212b0 \u03b12b0;\u03b221b0;\u03b222b0 : \u00f044\u00de When the derivative queer-square mechanism moves to state 14 as shown in Fig. 18, both limb1s and limb2s are lower than the base OA1A2 and the platform E1F1E2F2 is even lower than the limb1p and limb2ap. By the same approach of the abovementioned states, combining Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001742_0954406214531943-Figure17-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001742_0954406214531943-Figure17-1.png",
        "caption": "Figure 17. The contact force of rolling ball under different loads for the guideway with high preload. (a) P\u00bc 0; (b) P\u00bc 1000 N; (c) P\u00bc 1500 N; (d) P\u00bc 2000 N; (e) P\u00bc 2500 N; (f) P\u00bc 3000 N.",
        "texts": [],
        "surrounding_texts": [
            "The contact model of single ball bearing is modeled based on the Hertz contact theory in this paper. The nonlinear relation between the contact force and deformation is demonstrated, and the contact stiffness of the ball bearing is obtained using the contact model. Furthermore, the statics model of linear at UNIV OF CONNECTICUT on June 15, 2015pic.sagepub.comDownloaded from guideway with four grooves was studied, and the method of correcting analytic model with experimental results was proposed and demonstrated. The statics characteristics of guideway were also studied by FEM. To improve the efficiency of analysis, the component finite element modeling method was proposed and verified with statics experiment, which can attain the same calculation accuracy with the full finite element model. Effects of load and preload on static characteristics of the linear guideway were analyzed using the corrected analytical model and component finite element model. Some important conclusions were drawn. For example, the increased preload can significantly increase the vertical stiffness of guideway. The greater preload will make the rolling balls bear larger contact forces, which will lead to the increment of the friction force and traction force of guideway. Therefore, the suitable preload should be chosen according to the work conditions of guideway."
        ]
    },
    {
        "image_filename": "designv10_5_0000317_1.2890112-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000317_1.2890112-Figure3-1.png",
        "caption": "Fig. 3 Coordinate systems for the G",
        "texts": [
            " The above mathematical model can be applied to simulate both enerating and nongenerating face-hobbing processes, including erlikon\u2019s Spiroflex and Spirac, and Gleason\u2019s TriAC\u00ae cutting ystems. It can also be easily simplified to simulate face-milling utting, including most existing flank modification features. ournal of Mechanical Design om: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/28/201 4 Mathematical Model of the Cartesian-Type Hypoid Generator The DOF of the proposed Cartesian-type hypoid generator is arranged based on the Gleason Phoenix machine, which has six axes: three rectilinear motions Cx ,Cy ,Cz and three rotational motions a , b , c see Fig. 3 . Such a machine configuration is recognized to have a minimum number of movable axes for the operation of spiral bevel gear cutting. Its coordinate systems St xt ,yt ,zt and S1 x1 ,y1 ,z1 , respectively, are rigidly connected to the cutter head and work gear, whose relative positions are described by auxiliary coordinate systems from Sa to Sd. Here, a and c are the rotation angles of the work gear and cutter, respectively, and b denotes the machine root angle. The horizontal motion Cx and the vertical motion Cy are used for cutter positioning, while Cz is the sliding base for controlling cutting depth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001968_978-94-007-6101-8-Figure4.4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001968_978-94-007-6101-8-Figure4.4-1.png",
        "caption": "Fig. 4.4 SCARA robot manipulator with coordinate frames",
        "texts": [
            " According to the 1st exception we shall select the common normal where d3 = 0. The origin of the third frame will be again placed into the center of the joint. As in the case of the second joint, the z2 axis runs along the rotational joint axis. The x2 axis goes with the common normal. There remains only the frame with its origin at the robot end-point. In accordance with the 4th exception we place the x3 axis perpendicular to the z2 axis and the z3 axis parallel to the z2 axis. The SCARA robot with the coordinate frames is shown in Fig. 4.4. Table of DH parameters represents an important step in development of geometric robot model. The table is the essence of the standardized approach to modeling of robot mechanisms. For a roboticist it is sufficient to see the table of DH parameters, and he will know exactly what are the characteristic properties of a robot mechanism designed by another roboticist from a laboratory or company in the other part of the world. The table contains 5 columns which are for practical reasons always written in the same order",
            " There remains only the second column representing the lengths of individual segments. The first segment consists from a vertical column, which is changing its length between 0 and d1 (which was taken into account already in the third column) and horizontal part denoted as the length a1 which must be included into the first line of the ai column. The second and third segments run along the x2 and x3 axes respectively and are as the lengths a2 and a3 written into the second and third line of the same column. The segment lengths a1, a2, and a3 must be inserted also in Fig. 4.4. The correctly written table and the matrices describing the relations between the neighboring coordinate frames are as follows: 64 4 Geometric Robot Model i ai \u03b1i di \u03d1i 1 a1 0 d1 0 2 a2 0 0 \u03d12 3 a3 0 0 \u03d13 0A1 = \u23a1 \u23a2\u23a2\u23a3 1 0 0 a1 0 1 0 0 0 0 1 d1 0 0 0 1 \u23a4 \u23a5\u23a5\u23a6 1A2 = \u23a1 \u23a2\u23a2\u23a3 c2 \u2212s2 0 a2c2 s2 c2 0 a2s2 0 0 1 0 0 0 0 1 \u23a4 \u23a5\u23a5\u23a6 2A3 = \u23a1 \u23a2\u23a2\u23a3 c3 \u2212s3 0 a3c3 s3 c3 0 a3s3 0 0 1 0 0 0 0 1 \u23a4 \u23a5\u23a5\u23a6 The geometric model of SCARA robot mechanism with three degrees of freedom has the following final form: 0A3 = 0A1 1A2 2A3 = \u23a1 \u23a2\u23a2\u23a3 c23 \u2212s23 0 a1 + a2c2+ a3c23 s23 c23 0 a2s2+ a3s23 0 0 1 d1 0 0 0 1 \u23a4 \u23a5\u23a5\u23a6 In the last matrix the following abbreviations sin(\u03d12 + \u03d13) = s23 = s2c3 + c2s3 and cos(\u03d12 + \u03d13) = c23 = c2c3\u2212 s2s3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002468_j.matdes.2019.108018-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002468_j.matdes.2019.108018-Figure5-1.png",
        "caption": "Fig. 5. (a) Schematic representation of the thermocouple substrate design showing the holdin surrounding substrate material. Not scaled. (b) Bottom view of thermocouple substrate showi",
        "texts": [
            " The temperature evolution of reference samples was measured insitu using a bespoke 13 mm-thick thermocouple substrate. The substrate is composed of multiple adjustable bolt-holders that locate the g powder showing D10, D50 and D90 values. (a) powder morphology and (b) cross-sectional density. thermocouple probes at the bottom of the substrate in a fixed position and known distance from the top surface of the substrate. The thermocouple probes are surrounded by the substrate material and are in solid contactwith themeasuring surface. Fig. 5a shows a schematic representation of the temperature measurement approach of a single reference sample and Fig. 5b shows a bottom view of the thermocouple substrate with spatially-defined thermocouple probe bolt-holders. Multiple samples of varying hatch spacing and exposure time were monitored as described in Fig. 4. For proper alignment betweenmeasuringpoints and sample location on substrate, the substrate geometrywas embedded on an STLfile, superposed to the sample array inMagics Software. The samples of interest were located superposed to the substrate measuring points. The substrate geometry was then removed from the STLfile and the sample arraywas built without superposing geometries"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001860_1464419315569621-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001860_1464419315569621-Figure7-1.png",
        "caption": "Figure 7. Roller\u2013race contact geometry.",
        "texts": [
            " The ultimate term on the right-hand side of equation (6) is due to squeeze film motion under oscillating conditions (this is essentially lubricant squeeze as the result of local mutual approach and separation of contacting surfaces). The pressure distribution, p is obtained, when variations in the film thickness, h is known as (Figure 6 shows the elastic film shape in the direction of entraining motion) h X,Y\u00f0 \u00de \u00bc h0 \u00fe s X,Y\u00f0 \u00de \u00fe \u00f0X,Y\u00de \u00f07\u00de The rolling elements used are cylindrical rollers with dub-off end profiles in the axial roller direction (Figure 7). These relief profiles are used to mitigate pressure spikes, which would otherwise form at the roller extremities due to stress discontinuity.26 The undeformed roller conjunctional profile is thus obtained as s X,Y\u00f0 \u00de \u00bc X2 2RZX \u00fe \u00f0ld Y\u00de2 2Rd if Y4ld s X,Y\u00f0 \u00de \u00bc X2 2RZX if ld 5Y5 l ld s X,Y\u00f0 \u00de \u00bc X2 2RZX \u00fe \u00f0Y \u00f0l ld \u00de\u00de 2 2Rd if ld4Y \u00f08\u00de Rzx is the equivalent radii of contact of an ellipsoidal solid against a semi-infinite elastic half-space, representing the instantaneous contact of any rollerto-race in the principal plane of contact ZX as shown in Figure 7 1 RZX \u00bc 1 Rra \u00fe 1 Rro \u00f09\u00de The radii of contact of the roller and the race in the ZY principal plane of contact are considered to be very large (nominally flat), thus: RZY 1. The localised contact deflection (x,y) is obtained by solution of the elasticity potential integral \u00f0X,Y\u00de \u00bc 1 Er Z Z A p X1,Y1\u00f0 \u00dedX1dY1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0X X1\u00de 2 \u00fe \u00f0Y Y1\u00de 2 q \u00f010\u00de where X,Y\u00f0 \u00de represents a point where the deflection of the semi-infinite elastic half-space of reduced elastic modulus Er is calculated due to any arbitrary pressure distribution p X1,Y1\u00f0 \u00de over the contact domain; 2 \u00f0X1,Y1\u00de"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003831_tia.2020.3029997-Figure14-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003831_tia.2020.3029997-Figure14-1.png",
        "caption": "Fig. 14. Stator structure and thermal sensors of analyzed machine.",
        "texts": [
            " The comparison of derived end-winding temperature distributions is given in Appendices. In order to validate the analytical temperature distributions of active- and end-windings, the DC tests are carried out. In the tests, three-phase stator windings are supplied by DC power source (\ud835\udc3c\ud835\udc37\ud835\udc36=18A) parallelly; and the influence of the iron losses and AC losses in the winding can be eliminated. Meanwhile, the rotor is removed to prevent the potential demagnetization of PMs caused by high temperature. The stator structure and the installed thermal sensors are shown in Fig. 14. There are in total 14 K-type probe thermocouples inserted in the active- and end-windings, i.e. seven sensors in the active winding and seven thermocouples in the endwinding, as shown in Fig. 15. When the stator reaches thermal steady state, i.e. temperatures do not vary in five minutes, the 14 temperatures for the active-winding (sensor 1 to 7) and for Authorized licensed use limited to: Carleton University. Downloaded on November 02,2020 at 03:10:25 UTC from IEEE Xplore. Restrictions apply. 0093-9994 (c) 2020 IEEE"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000690_iros.2011.6095168-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000690_iros.2011.6095168-Figure2-1.png",
        "caption": "Fig. 2. Configuration q = (\u03b81, l1, \u03b82, l2, \u03b83, l3) for a concentric tube robot with N = 3 nested tubes.",
        "texts": [
            " Problem Formulation We consider a concentric tube robot with N nested tubes numbered in order of decreasing cross-sectional radius. Each tube i consists of a straight transmission segment of length Li followed by a pre-curved portion of length Ci, i = 1, . . . ,N. The pre-curved portions of the tubes are curved with constant radii of curvature of ri, i = 1, . . . ,N. We assume that the device is inserted at a point xstart in 3D space and oriented along the vector vstart. Each tube contributes two degrees of freedom to the entire concentric tube robot, as shown in Fig. 2. Each tube may be (1) inserted or retracted from the previous tube, and (2) axially rotated. We therefore define a configuration of a concentric tube robot as a 2N dimensional vector q = (\u03b8i, li : i = 1, . . . ,N) where \u03b8i is the axial angle at the base of the i\u2019th tube and li > 0 is the length of insertion of tube i past the tube just before it (and l1 is the length of the first tube past the insertion point xstart). For a given configuration qi, we define the device\u2019s shape using x(q, s) : R2N \u00d7 R 7\u2192 R3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003767_j.conengprac.2019.03.012-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003767_j.conengprac.2019.03.012-Figure3-1.png",
        "caption": "Fig. 3. Pitch gauge indicating the collective blade pitch angle at 60% throttle.",
        "texts": [
            "2 kg, each rotor needs to generate 300 grams of thrust, which is generated at approximately 17\u25e6 pitch angle and the corresponding coefficient of thrust is 0.017 as shown in Fig. 2(b). It should be noted that the rotor is operating at a relatively high thrust coefficient due to a high all up weight but the rotor is not stalled and the quadrotor is able to fly and maneuver reasonably well. Further, at a pitch angle of 19\u25e6 the rotor generates a thrust coefficient of 0.02 which is found to be adequate to perform various maneuvers during both simulations and experiments. Fig. 3 shows that at a hover throttle of 60% given manually via radio control (mode 2), the blade pitch angle is measured to be 17.1\u25e6. This validates the discussion on aerodynamic behavior of each rotor. A performance comparison of the proposed robust backstepping control law and PID in the presence of disturbances is shown through simulations for sinusoidal roll angle tracking as well as sinusoidal tracking in x, y, and z directions in the inertial frame of reference. Since the attitude controller used by default in the PX4 flight stack has a cascaded PID structure and uses geometric methods (Px4 developer guide, 2013\u20132017), the default attitude control law is replaced with traditional PID using Euler angles in simulations and experiments for comparison",
            " Signals to turn the motor on and off can also be sent through the output that is connected to the ESC. In addition to the autopilot board, a 433MHz telemetry module is used for remote communication between the autopilot and the ground station. A FrSky X8R receiver is connected to the PixHawk autopilot to receive manual control inputs (in manual mode) and signals to switch between manual and auto modes. This receiver is paired with a FrSky X9D transmitter which contains the throttle, roll, pitch, and yaw sticks along with mode switches as shown in Fig. 3. A GPS receiver is fixed onboard to provide data for global position feedback. The PixHawk flight controller comes with a firmware called \u2018\u2018PX4 flight stack\u2019\u2019. This provides a modular platform and uses a Unix based approach and a bash-like shell. The microcontroller-based execution environment has a low latency and good hardware connectivity. Such a software structure provides us ample scope to experiment with various control laws. The related details can be found in Meier, Honegger, and Pollefeys (2015)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000331_j.ins.2010.08.046-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000331_j.ins.2010.08.046-Figure2-1.png",
        "caption": "Fig. 2. A DOF robot arm.",
        "texts": [
            " By using the norm inequality and Lemma 3, we have k~x\u00f0t\u00dek 6 C1 \u00fe C2 \u00fe C3k~hf k a 2 \u00fe C4k~hgk a 2 1ffiffiffi a p ; \u00f042\u00de where C1 is a term decaying exponentially to zero with the initial condition, and C2, C3 and C4 are positive computable constants. From (41) and (42), the trajectory k~x\u00f0t\u00dek is UUB if the adaptive parameter estimation errors k~hf k and k~hgk are bounded. This completes the proof. h 4.4. An illustrative example This section gives some simulation results, which were carried out by the proposed observer scheme with two different robust compensation terms. Consider the single-link robot system depicted in Fig. 2. Its motion dynamics can be described as M\u20acq\u00fe 1 2 mglsin\u00f0q\u00de \u00bc s; y \u00bc q; ( \u00f043\u00de where g = 9.8 m/s2 is the acceleration due to gravity, M is the inertia, q is the angle position, _q is the angle velocity, \u20acq is the angle acceleration, l is the length of the link, m is the mass of the link, and s is the control force. Setting x1 = q1, x2 = q2 and u = s, then the above equation can be rewritten in the following state-space form, including external disturbances: _x1 \u00bc x2; _x2 \u00bc u 0:5mglsin\u00f0x1\u00de M \u00fe d; y \u00bc x1: 8><>: \u00f044\u00de In this simulation, we choose m = 1 kg, M = 0",
            " By using the norm inequality and Lemma 3, we have ke\u00f0t\u00dek 6 D1 \u00fe \u00f0D2 \u00fe D3k~hf k a 2 \u00fe D4k~hgk a 2 \u00fe D5k~eka2\u00de 1ffiffiffi a p ; \u00f055\u00de where D1 is a term decaying exponentially to zero with the initial condition, and D2, D3, D4 and D5 are positive and computable constants. From (54) and (55), the trajectory ke(t)k is UUB due to the boundness of the parameter estimation errors k~hf k; k~hgk and k~ek. This completes the proof. h 5.2. Simulation results with comparisons For the single-link robot system depicted in Fig. 2, we present some comparative results of the output-feedback controller with two different observers. One is the following controller with an adaptive fuzzy observer (26): u \u00bc 1 nT g \u00f0x\u0302\u00deh\u0302g nT f \u00f0x\u0302\u00deh\u0302f \u00fe sin\u00f0t\u00de \u00fe cos\u00f0t\u00de 2x\u03021 x\u03022 ua h i ; ua \u00bc 26sign\u00f0x1 x\u03021\u00de: 8<: \u00f056\u00de The other is the same controller (56) with the following high-gain observer (57) _\u0302x1 \u00bc x\u03022 \u00fe 1 e Hp\u00f0x1 x\u03021\u00de; _\u0302x2 \u00bc 1 e2 Hv\u00f0x1 x\u03021\u00de; ( \u00f057\u00de where e = 0.001, Hp = 0.03, and Hv = 0.06. Time responses of state x1 and x2 for output-feedback controllers ((a) and (b): using adaptive fuzzy observer; (c) and (d): using high-gain observer)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001982_j.triboint.2015.09.004-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001982_j.triboint.2015.09.004-Figure2-1.png",
        "caption": "Fig. 2. Roller-raceway contact in SRB.",
        "texts": [
            " All the rollers are revolving on their own axes at \u03c9r. SRBs usually work in low speed and heavily-loaded applications, where the skid between rollers and raceways is negligible, so the motion relationship of the rollerraceway can be regarded as pure rolling [18]. Thus, the average linear velocities of roller-inner raceway contact and roller-outer raceway contact can be expressed as [18], Uij \u00bc 0:5dm 1 \u03b3 \u03c9i \u03c9c\u00f0 \u00de\u00fe D=dm \u03c9r \u00f01\u00de Uoj \u00bc 0:5dm 1\u00fe\u03b3 \u03c9c\u00fe D=dm \u03c9r \u00f02\u00de The roller-raceway contact in an SRB is illustrated in Fig. 2. The radius of the roller's profile is slightly smaller than the radii of the raceways, so the roller-raceway contact in an SRB has the characteristics of point contact when the bearing operating under a moderate load [19]. Houpert [20] derived a formula describing the relationship between elastic deformation and load for rollerraceway point contact: \u03b4 Rx \u00bc 1:7138k 0:2743W2=3 PC \u00f03\u00de where k\u00bc Ry Rx , WPC \u00bc Q E\u2018R2 x , Rx is the equivalent radius of rollerraceway contact in rolling direction, Q is the normal load, E0 is the equivalent elastic modulus of roller-raceway contact, and \u03b4 is the normal elastic deformation of roller-raceway contact"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001115_j.wear.2015.01.047-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001115_j.wear.2015.01.047-Figure9-1.png",
        "caption": "Fig. 9. Configuration of the simulated contact. (a) PRS screw/roller contact, and (b) test rig contact.",
        "texts": [
            " It reveals that the stick magnitude in the contact is strongly dependent on the creep ratio, and varies greatly with the normal pressure and the lubrication condition. For significant creep ratios, the rolling friction is negligible compared to the overall transverse sliding. The PRS single contact is difficult to reproduce experimentally. But it can be reasonably assimilated to the contact of a curved body on a flat surface, with rolling and sliding. A test rig has been developed to simulate this simplified configuration and then study the damage induced by the rolling\u2013sliding motion. It uses a torus and a flat disc as samples (Fig. 9), which represent respectively the roller and the screw profiles. A given PRS of small pitch (pscrew\u00bc2.5 mm) has been chosen as a reference for the design of the two specimens. The aim is to obtain the same characteristics of contact: ellipse size and contact pressure for a given load, same materials and lubrication. The external radius of the torus is 10mm. It corresponds to the pitch radius Rr of the PRS roller. The radius of curvature is set to be 1.5 mm, equal to the roller curved profile. The materials are martensitic stainless steels similar to those of the PRS components"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003199_j.mechmachtheory.2019.103576-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003199_j.mechmachtheory.2019.103576-Figure1-1.png",
        "caption": "Fig. 1. Helical pinion and face-gear with axle offset.",
        "texts": [
            " The typical field of application is gear drives, which are usually realized with bevel gears. Similar to a bevel gear drive, a wide range of shaft angles, axle offsets and helix angles can be achieved. The main advantage of the face-gear is the high tolerable axial clearance of the pinion since the axial movement of the pinion does not have any impact on the contact pattern as long as the pinion is not crowned. This enables advantageous capabilities concerning the design of the gear housing and positioning of bearings. As an example, in Fig. 1 , a face-gear drive with a helical pinion is shown. The content of this manuscript covers three main subjects: \u2022 Face-gear geometry generation \u2022 Face-gear crowning and pinion profile modification \u2022 Determination of quantities of crowning and profile modification for face-gear drives \u2217 Corresponding author. E-mail address: zschippang@inspire.ethz.ch (H.A. Zschippang). https://doi.org/10.1016/j.mechmachtheory.2019.103576 0094-114X/\u00a9 2019 Elsevier Ltd. All rights reserved. Nomenclature \u03b1n Normal pressure angle \u03b1s Pressure angle \u03b1w Working transverse pressure angle pinion/face-gear \u03b1sc Tip clearance angle of shaper cutter \u03b2 Helix angle \u03b2\u2217 Modified helix angle \u03b3 , E , a Alignment errors a ( c ) Shift of shaper to produce the crowning c , c \u2217 Vertical shift of tool to achieve crowning, \u2217"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002053_s40194-018-0567-9-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002053_s40194-018-0567-9-Figure3-1.png",
        "caption": "Fig. 3 Principle of laser ultrasonics inspection",
        "texts": [
            " The brief laser impulse can either lead to a reversible thermoelastic deformation (thermoelastic mode) or at higher energy induce melting and vaporization of the material (ablative mode) which is not nondestructive anymore. Our study ensured that the experiments were performed within the thermoelastic regime. Both surface and volume elastic waves are created (respectively Rayleigh waves and compressional and transversal waves). The interactions of waves with flaws induce surface displacements which can be detected by interferometry. Figure 3 sums up the principle of LU inspection. This technique enables both surface and subsurface inspections and expands the scope of existing monitoring control [2]. Indeed, contrary to other in situ techniques, our aim is to detect porosities and lacks of fusion occurring after the melt pool. With respect to flaw sizes of interest, the wavelength of generated waves must be about 0.1 mm which corresponds to frequencies above 15 MHz for Rayleigh waves. Those values are calculated for steel wave velocities (Rayleigh waves velocity is approximately equals to 2900 m/s in steel at 20 \u00b0C)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002301_j.addma.2018.12.018-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002301_j.addma.2018.12.018-Figure1-1.png",
        "caption": "Fig. 1. Geometric model and mesh for finite element simulation.",
        "texts": [
            " The heat flux distribution was as follows: \ud835\udc5e(r) = \ud835\udf02\ud835\udc48\ud835\udc3c 2\ud835\udf0b\ud835\udc5f0 2 exp (\u2212 \ud835\udc5f2 2\ud835\udc5f0 2) (2) where \u019e is the absorption efficiency, U is the acceleration voltage, I is the current, r0 is the standard deviation for the Gaussian distribution (estimated to be 100 \u03bcm), and r is the distance from the center of the heat source. The heat absorption efficiency in an EBM process is usually high since the atmosphere is a vacuum. The value of \u019e was set to 0.9, as in the literature [22, 23]. The 3D geometric model is shown in Fig. 1. The imposed boundary condition assumes insulation on all free surfaces. The cooling rate and thermal gradient at the onset of solidification have been extracted from the temperature distribution results at various nodal locations [20, 21]. The cooling rate is determined as: ACCEPTED M ANUSCRIP T \ud835\udf15\ud835\udc47 \ud835\udf15\ud835\udc61 = | \ud835\udc47\ud835\udc3f \u2212 \ud835\udc47\ud835\udc46 \ud835\udc61\ud835\udc3f \u2212 \ud835\udc61\ud835\udc46 | (3) where tL and tS are the times at which the temperature reaches the liquidus temperature TL = 1336 \u00b0C and the solidus temperatures TS = 1260 \u00b0C, respectively. The thermal gradient evaluated at the time t = tL is determined directly from the nodal heat flux output, and is obtained from Fourier\u2019s law as: \ud835\udc3a = |",
            " Typical pole figures for the ACCEPTED M ANUSCRIP T three cases are compared in Fig.10c. For all three cases, the grain orientations do not exhibit any preference. The grain orientations of a single bead were inherited from the substrate by epitaxial growth, and the substrate is polycrystalline in all three cases. Therefore, there is no obvious preference for the grain orientation. A moving surface heat source with a Gaussian distribution (expressed by Eq. (1)) was used to simulate the electron beam. The geometric model measured 15 \u00d7 10 \u00d7 2 mm3, as shown in Fig. 1. The temperature-dependent material properties for the bulk material were employed, while the powder bed was not taken into consideration in this simulation. Simulations with various beam powers and scan speeds, corresponding to experimental Cases A and B, were conducted. Figure 11 shows the melt pool shape formation process for the preheated process condition with P = 400 W, v = 300 mm/s, and preheating temperature Tpre = 1025 \u00b0C. The melt pool becomes stable after approximately 2 \u00d7 10-2 s, and eventually a melt pool with an elongated tear drop shape forms"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003386_j.ast.2020.105974-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003386_j.ast.2020.105974-Figure7-1.png",
        "caption": "Fig. 7. Experimental System.",
        "texts": [
            " The control parameters in these two sliding surfaces can be tuned according to PID controller tuning methods. To validate the proposed transportation approach, experiments are conducted using the York University Autonomous Unmanned Vehicle (YU-AUV) facility at the Spacecraft Dynamics Control and Navigation Laboratory (SDCBLab). The YU-AUV facility consists of QDrone quadrotors, the OptiTrack motion capture system and a workstation. For the QDrone quadrotor, the Intel Aero compute board and the onboard BMI160 IMU is used as the onboard computer and sensor, respectively. As shown in Fig. 7, the payload is attached by four cables to the quadrotor. The OptiTrack motion capture system with 16 Flex 3 cameras is used to measure the position and attitude of the quadrotor and the payload. It should be noted that the proposed controller does not need the feedback of the payload state. The information is collected only for validation purpose. The OptiTrack motion capture system can provide the position and attitude information at 100 Hz. Both the desired and measured pose of the quadrotor are broadcast via Wi-Fi"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001232_s1006-706x(11)60014-9-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001232_s1006-706x(11)60014-9-Figure2-1.png",
        "caption": "Fig. 2 Geometric and mesh models",
        "texts": [
            " In or der to make investigative subject clear, a model of laser cladding should be simplified, the assumptions are as follows: 1) Surface of samples is flat, except cladded layer; 2) Materials are isotropic, and their densities and thermal conductivities are depended on the temperature; 3) Influence of liquid flow on the temperature field is ignored; 4) Laser energy density is Gaussian distribution. In order to make simulation accurate, the size of model is the same as the sample. The model is di vided into three-parts, the first is the cladded part whose cross section is a semi-cylinder with a 2 mm radius, the second is the transition zone with a 50 mmX 8 mmX 100 mmX 10-9 cube, the third is the base with a 50 mrnX 10 mm X 100 mm X 10-9 cube. Due to the symmetry of the work-piece, a half of the work-piece is considered in analysis given by Fig. 2 (a). The tem perature changes large in cladding area, so the mesh is fine where more precision is needed. Contrari wise, the mesh is coarse. The mesh of the transition zone is between the cladding and the base given by Fig. 2 (b). The thermal property parameters of H13 are listed in Table 3 and those of P20 are given by Fig. 3. Issue 1 Effect of Laser Power on the Cladding Temperature Field and the Heat Affected Zone \u2022 75 \u2022 2. 2 Results and discussion In practice, laser cladding is carried out by syn chronized powder feeding. So the element which is irradiated by laser is given by Fig. 4 (a). The c1added layer can be set to the surface of thermal convection. To realize a load moving in laser cladding, the continuous movement of space is transformed into discrete time domain using APDL of ANSYS soft ware, and then the moving load is loaded for circular statement at a certain time step"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000325_bi00655a031-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000325_bi00655a031-Figure6-1.png",
        "caption": "FIGURE 6: Proposed structures of CO Fe\"HRP A and C, giving the three ir stretching frequencies uco 1906-1905 cm-I, 1925/1929 cm-I, and 1938/1933 cm-I.",
        "texts": [
            " While the midpoints, 193 1 cm-I, of thedouble bands 1925/1938 and 1929/1933 cm-I for CO H R P A2 and C fit well into the linear relation between Em7 and uco (Figure 5) the two actual values for vco in the doublets correspond to two probability maxima for the position of CO, separated by a potential energy barrier. Transition metal carbonyl complexes commonly have a nearly linear M-C-0 linkage, but this is not necessarily the case for carbonyl heme proteins. X-ray analysis of carbonyl erythrocruorin revealed an Fe-C-0 angle of 145 f 15O, the result of a possible steric interaction between the carbonyl ligand and an isoleucine (Huber and Formanek, 1970). In H R P a similar interaction could allow CO to bind in two geometries (Figure 6). Whatever the nature of the barrier may be, the two probability maxima must have a structural correspondence in two niches for CO of somewhat different character. The difference in energy between CO bound in the two niches is well within the previously mentioned range of vco for variations in polarity 2228 B I O C H E M I S T R Y , V O L . 1 5 , N O . 1 0 , 1 9 7 6 of solvent environment. The two values for the bands centered at 1931 cm-l are split further in H R P A (12 cm-\u2019) than in H R P C (4 cm-\u2019). This may reflect greater differences in polarity for the two sites in HRP A than in HRP C. In each of the HRP\u2019s the niche giving the higher frequency stretching is insensitive to pH and may be less polar in character. The other position of CO produces two communicating stretching frequencies, the intrinsic acidity being decisive in the choice between them. The protonation of a sterically suitable group \u201cX\u201d in the protein would permit the establishment of a hydrogen bond as shown in Figure 6. The energy of the CO stretching frequency is lowered from 1925 and 1929 cm-I for H R P A2 and C, respectively, to 1905 and 1906 cm-\u2019, which is consistent with hydrogen-bond formation. The existence of the hydrogen bond C-0-H-X is substantiated by the dependence of the formation of the 1905- and 1906-cm-\u2019 bands upon a single dissociation constant. Moreover, the large deviation from the linear E,7 vs. YCO relationship in Figure 5 corresponds to a major change in CO bonding not transmitted through the heme iron and thus a result of a direct action on the bound CO"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000560_j.jsv.2009.03.013-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000560_j.jsv.2009.03.013-Figure5-1.png",
        "caption": "Fig. 5. Relative displacement between the inner and the outer ring centers.",
        "texts": [
            " / Journal of Sound and Vibration 325 (2009) 145\u2013160150 with dCc dt \u00bc oc; dX c dt \u00bc VX c; dY c dt \u00bc VY c (14) For the inner ring: mi dVX i dt \u00bc XN j\u00bc1 \u00f0Qij sinCj\u00de F ur sin\u00f0oit\u00de (15) mi dVY i dt \u00bc XN j\u00bc1 \u00f0Qij cosCj\u00de \u00fe F R \u00fe Fur cos\u00f0oit\u00de (16) where F ur \u00bc murEX uro2 i and with dX i dt \u00bc VX i; dY i dt \u00bc VY i (17) One equation is added for each roller: 0 \u00bc FC2j FC1j \u00feQij Qoj \u00fe F c (18) where F c \u00bc mRdmo2 j =2. Two geometric relations must be added to describe the relative displacement between the inner and the outer ring centers (Fig. 5) and the lubricant film thickness between the roller and the cage pocket. The first relation includes the elastohydrodynamic lubrication (EHL) film thickness at the roller/race contacts h, the ARTICLE IN PRESS A. Leblanc et al. / Journal of Sound and Vibration 325 (2009) 145\u2013160 151 contact deformations d, the radial clearance Jd and the structural deformations u: Jd 2 \u00fe dij \u00fe doj hij hoj \u00fe uij \u00fe uoj \u00bc Y i cosCj X i sinCj (19) The lubricant film between the roller and the cage (Fig. 6) is given by H1j \u00bc dm 2 Ccj arctan 2Rr dm arctan X c EX cosCcj \u00fe Y c EX sinCcj Rc EX X c EX sinCcj Y c EX cosCcj Cj 0 BB@ 1 CCA 0 BB@ 1 CCA (20) where Ccj \u00bc Cc \u00fe 2p\u00f0j 1\u00de=N"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002260_tmag.2017.2668845-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002260_tmag.2017.2668845-Figure1-1.png",
        "caption": "Fig. 1. Configuration of the three-phase 12-stator-slot/10-rotor-pole (12/10) PMFS motor and the water cooling system. (a) Machine topology. (b) The water cooling system.",
        "texts": [
            " It is found that when the cooling water is injected, the temperature distribution in magnets varies greatly along the axial direction, since the magnets are located between the water cooling system and armature windings, which carries the heat generated by copper loss. Considering the performances of magnets (e.g. NdFeB) and consequently the machines are directly related to temperature, an axially segmented magnetic-thermal coupled-fields FEA model is proposed to take into account the variations of temperature distributions in the axial directions based on a three-phase 12-stator-slot/10rotor-pole PMFS motor employing NdFeB as given in Fig. 1 and Table I, where the cooling water is injected into the stator shell/housing. In the proposed FEA model, the PMFS motor is divided into segments along the axial direction according to different temperature in PM. By combining both 2D and 3D FEA methods, the proposed coupled-fields model enables the electromagnetic and thermal behaviors to be predicted more accurately than a 2D model, meanwhile requires much less time consuming than a traditional synchronous 3D one in which the electromagnetic behavior and thermal behavior are calculated simultaneously"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003776_j.isatra.2019.07.003-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003776_j.isatra.2019.07.003-Figure1-1.png",
        "caption": "Fig. 1. The architecture of two-link robotic manipulator.",
        "texts": [
            " However, this function has sharp corners as \u03c4 = \u03c4max which is undesirable for practical application. Recently, in [48,49] Rahimi et al. have proposed a smooth hyperbolic tangent function \u0393 = \u03c4max tanh (\u03c4/\u03c4max) to have all functions being differentiable. Inspired by this idea, we propose here a new algorithm for actuator saturation avoidance using the following smooth saturation function \u0393 = \u03c4max \u03c4 |\u03c4 |+\u03c4max . To demonstrate the benefits of the proposed algorithm, a simulation study was carried out using a planar 2 DOF robot manipulators (see Fig. 1). The dynamic equation of the system can be described by[ m11(q2) m12(q2) m21(q2) m22 ][ q\u03081 q\u03082 ] + [ \u2212c(q2)q\u03071 \u22122.c(q2)q\u03071 0 c(q2)q\u03072 ][ q\u03071 q\u03072 ] + g [ g1(q1, q2) g2(q1, q2) ] = [ \u03c41 \u03c42 ] (74) where m11(q2) = (m1 + m2) L21 + m2L22 + 2m2L1L2 cos(q2) + J1 m12(q2) = m21(q2) = m2L22 + m2L1L2 cos(q2) m22 = m2L22 + J2 c(q2) = m2L1L2 sin(q2) g1(q1, q2) = (m1 + m2) L1 cos(q2) + m2L2 cos(q1 + q2) g2(q1, q2) = m2L2 cos(q1 + q2) where mi is the mass of link i, Li is the length of link i, Ii is the inertia of link i (i = 1, 2)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003867_j.matdes.2020.108691-Figure25-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003867_j.matdes.2020.108691-Figure25-1.png",
        "caption": "Fig. 25. Chip formation of the simulated milling process of Cut 1: (a) cone supports; (b) block supports.",
        "texts": [
            " Therefore, compared with the cone support structure, milling the block support structure has less tool wear. During themilling process, since the tool was rotating at high speed, when the cutting edge of the tool cut into the workpiece, the chips always flow irregularly in all directions [27]. Fig. 24 shows the morphologies of the chips collected after each cut. Cut 1 only cut the supports, resulting in fragmented chips. The chip formation of Cut 1 can be seen from the simulated milling process, as shown in Fig. 25. At the onset of cutting, chips began to be generated by the tool edge on the end of the supports. When cutting the cone supports, the tilting-effect consists of elastic and plastic deformations causing the uncut chip layer not to be entirely removed by the tool. The connected pillar, which is integrated by five arrayed sub-pillars, has better resistance of tilting and the stable structure makes the uncut chip layer easier to be removed integrally. Therefore, the integral chips and fragmentary chips are produced, as shown in Fig. 25(a). However, when cutting the block supports, the stress is distributed evenly over the whole support structures and the chips can be removed continuously. Hence, continuous chips are generated, as shown in Fig. 25(b). The chip is fragile and easily broken, although some chips are collected, they are different in length and shape, and many of them are broken chips. However, from Figs. 24 (a) and (b) in the red dotted circle, a circular notch is observed from the chips of theworkpiece with cone supports and is likely to be caused by the stubble left on theworkpiece surface after Cut 2 and Cut 3. In addition, the morphology of the chips from Fig. 24(a) demonstrated that Cut 2 did cut into the surface of the workpiece"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002838_978-3-319-54169-3-Figure2.6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002838_978-3-319-54169-3-Figure2.6-1.png",
        "caption": "Fig. 2.6 Analogy of the resonance frequency in the ramp path (Goncalves et al. 2014)",
        "texts": [
            "1 Simple Degree of Freedom Oscillator Coupled with a Non-ideal \u2026 19 Fig. 2.5b is used to represent the motor with resistive torque where it is more difficult to reach the energy level 0. The rate of velocity changing is no longer linear. When the motor is mounted on a flexible base, its motion is described with Eq. (2.40). It is clear that the angular acceleration is also a function of the cart motion x .Besides, themotion of the cart is a function of the acceleration and angular velocity of the motor (2.7). In Fig. 2.6 a system which is analog with the motor mounted on a flexible base is represented. Similar to Fig. 2.5a, wheel must climb a ramp to reach the level of energy defined by 0. In this case the ramp path is modified by the cart resonance frequency \u03c90. The resonance frequency is represented by the valley in the ramp path. The deep and the width of the valley in the ramp are related to the amplitude of the motion of the cart and in some cases the wheel can get stuck inside the valley in the ramp path. Numerical simulation is done for frequencies around the cart resonance frequency \u03c90"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003913_s00170-019-04908-3-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003913_s00170-019-04908-3-Figure2-1.png",
        "caption": "Fig. 2 a Produced single tracks on printed substrates. b Schematic of printed single tracks and the substrate",
        "texts": [
            "5 \u00d7 5 mm were printed from the same material (Hastelloy X) by using the default EOS process parameters (laser power 195W, scanning speed 1150 mm/s with hatch distance of 90 \u03bcm). Then, an additional layer thickness of powder was spread on top of the printed substrate to manufacture the single tracks with specified process parameters. For this study, various process parameters such as laser power and laser scanning speed were considered. The range of laser power and scanning speed are listed in (Table 2) which are used for validation of the numerical model. Figure 2 shows the produced single tracks at different process parameters. The distance between every single track was 2.5 mm. Then, the printed specimens were removed from the build plate and cut perpendicular to single tracks using a Buehler ISOMET 1000 (Buehler, IL, USA) precision cutter with 5 mm distance from the side of samples. Afterward, the specimens were mounted and polished before etching with a Glyceregia solution [15]. Finally, in order to measure the single tracks melt pool geometries, a Keyence VK-X250 confocal laser microscope (Keyence Corporation, Osaka, Japan) was used"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000593_1.4023300-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000593_1.4023300-Figure2-1.png",
        "caption": "Fig. 2 Gear tooth crack model at tooth root [35]",
        "texts": [
            " Then, the total equivalent mesh stiffness of one tooth pair in mesh can be obtained by [35], Ke \u00bc 1 1 Kb1 \u00fe 1 Ks1 \u00fe 1 Ka1 \u00fe 1 Kf 1 \u00fe 1 Kb2 \u00fe 1 Ks2 \u00fe 1 Ka2 \u00fe 1 Kf 2 \u00fe 1 Kh (13) Here, the subscript 1 means pinion and 2 is the gear. 2.2.2 Tooth Crack With Variant Crack Depth Along Tooth Width. The gear mesh stiffness calculation model with consideration of tooth crack propagating along tooth width was proposed in Ref. [35], which can eliminate the assumption that the tooth crack is through the tooth width with a constant depth like the models applied in Refs. [43\u201345]. Dividing a gear tooth into some independent thin pieces like the shaded area shown in Fig. 2, so that the crack length along tooth width for each piece can be regarded as a constant which is reasonable when the thickness of the piece dx is very small. Stiffness of each piece, namely Kp (x), can be calculated with taking tooth bending, shear, and axial compress into account based on Eqs. (8)\u2013(10). Kp (x) can be obtained by [35], Kp\u00f0x\u00de \u00bc 1 1 Kb\u00f0x\u00de \u00fe 1 Ks\u00f0x\u00de \u00fe 1 Ka\u00f0x\u00de (14) Kb\u00f0x\u00de, Ks\u00f0x\u00de, Ka\u00f0x\u00de are the stiffness under consideration of the effect of tooth bending, shear, and axial compress for one piece of tooth",
            " Then, the stiffness of the whole tooth can be obtained by integration of Kp(x) along tooth width [35], Journal of Vibration and Acoustics JUNE 2013, Vol. 135 / 031004-3 Downloaded From: http://vibrationacoustics.asmedigitalcollection.asme.org/ on 01/23/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use Kt \u00bc \u00f0W 0 Kp\u00f0x\u00de (15) With the effect of fillet-foundation deflection in Eq. (12) and Hertzian contact in Eq. (11), the equivalent mesh stiffness can be calculated by [35], Ke \u00bc 1 1 Kt1 \u00fe 1 Kf 1 \u00fe 1 Kt2 \u00fe 1 Kf 2 \u00fe 1 Kh (16) The crack depth can be described as a function of its position along tooth width in Fig. 2. That means [35], q\u00f0x\u00de \u00bc f \u00f0x\u00de (17) The tooth crack profile in Ref. [35] where the crack depth was assumed to distribute along tooth width as a parabolic function is also utilized in this paper and shown in Fig. 3. Moreover, the assumed crack function with regard to the position x along the tooth width can be written as [35], For the solid curve where Wc<W and q2\u00bc 0, q\u00f0x\u00de \u00bc q0 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x\u00feWc W Wc r ; x 2 W Wc W\u00bd q\u00f0x\u00de \u00bc 0; x 2 0 W Wc\u00bd 8< : (18) For the dashed curve where Wc\u00bcW, q\u00f0x\u00de \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi q2 0 q2 2 W r x\u00fe q2 2 (19) In this paper, the severity of the gear tooth crack is defined as Crack(q0, Wc/W, q2,ac) which will be used in the definition of the gear tooth crack in Table 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000733_j.proeng.2010.09.125-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000733_j.proeng.2010.09.125-Figure2-1.png",
        "caption": "Fig. 2: Nyquist plots of impedance spectra for creatinine-imprinted in poly(ethylene-co-vinyl alcohol) (EVAL) films at various urea concentrations on 5 mM of PBS buffer : from 0.1 \u00b5g/mL to 3 \u00b5g/mL, with -600 mV potential",
        "texts": [
            "4 the characteristic peak of C=N shifts to lower frequencies, demonstrating the existence of H-bonding related to electron donor property of nitrogen atom. For urea, the characteristic peak of C=O shifts to lower frequencies (1676 to 1663 cm-1) proving the existence of weak interactions between polymer matrix and target molecule. W a v e n u m b e r (c m -1 ) A b s o r b a n c e 1 6 6 8 c m - 1 C = N Fig. 1. FTIR spectra a) EVAL; b) 0.5% creatinine in EVAL film before rinsing; c) 0.5% creatinine in EVAL film after rinsing; d)pure creatinine Fig. 1 and Fig. 2 show the impedance change with different urea and creatinine concentrations. Urea and creatinine was injected to a stirred 5 mM of PBS buffer pH 7.5, from 0.1 \u00b5g/mL to 3 \u00b5g/mL for each substrate. It could be seen that the impedance decreased with increasing urea, and with increasing creatinine concentration. This change was more obvious in the low frequency region. Each curve was registered when the signal did not change with time, it required about a 20 mins. When the concentration exceeds 3.5 \u00b5g/mL for urea and 3 \u00b5g/mL for creatinine, there is no obvious impedance change in the whole frequency range, which means the saturation and no imprint sites were left"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003686_tie.2019.2959504-Figure15-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003686_tie.2019.2959504-Figure15-1.png",
        "caption": "Fig. 15. Armature reaction field distributions of DF-FPSM machine. (a) Is = 2.98 A, Ir = 0 A, stator current angle = 0 elec. deg. (b) Is = 0 A, Ir = 1.78 A, rotor current angle = 0 elec. deg. (c) Is = 0 A, Ir = 1.78 A, rotor current angle = 30 elec. deg. (d) Is = 0 A, Ir = 1.78 A, rotor current angle = -30 elec. deg.",
        "texts": [
            "98A, 0A sr s r s r s r T T I I T I I T I I          (5) where the PMs are removed. The three items on the right of (5) represent the total torque produced by armature reaction fields, the rotor reluctance torque, and the stator reluctance torque, respectively. It can be seen that Tsr is zero when the stator and rotor current angles (the angle between current vector and q-axis) are almost equal, while it is positive or negative if the stator current angle is lager or smaller than the rotor current angle. As shown in Fig. 15(a) and (b), both the stator and rotor armature reaction field distributions are symmetrical with reference to the stator pole SP1 when the stator and rotor current angles are zero, thus Tsr is zero. However, if the rotor current angle is larger (smaller) than the stator current angle, the stator armature reaction field leads (lags behind) the rotor armature reaction field and thus Tsr is positive (negative), as shown in Fig. 15(c) and (d). Tsr reaches positive and negative maximum when the stator current angle minus rotor current angle is equal to 90 and -90 elec. deg. However, as shown in Fig. 16, the maximum total torque of DF-FSPM machine is achieved when both the stator and rotor current angles are approximately 0 elec. deg. As shown in Fig. 17, the torque-speed characteristics of the DF-FSPM and FSPM machines are calculated when the maximum phase voltages are set to be 60 V, while the maximum phase currents are set to be same with the rated phase currents shown in Table I"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001443_ls.1271-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001443_ls.1271-Figure6-1.png",
        "caption": "Figure 6. Two common types of rolling-sliding contact for elastohydrodynamic friction measurement.",
        "texts": [
            "30 Thus, to predict shear stress at high pressure, viscosity\u2013pressure data are needed over the whole pressure range up to the maximum contact pressure. In practice, all of the previous means that it is presently much simpler to measure lubricant EHD friction properties in a test machine and apply these directly or via a simple curve-fitting exercise to predict of the EHD friction in machine components. This is described in the next section. Elastohydrodynamic friction is generally measured using two types of device, a disc machine or a ball on rotating flat machine. These are shown schematically in Figure 6. In the ball on rotating flat, the ball shaft is tilted to intercept the top surface of the flat at its rotating centre so as to minimise spin in the contact. The key to both of these types of device is that the two bodies are rotated one against the other at different and variable speeds, u1 and u2, so any combination of sliding and rolling speed can be achieved. This enables friction to be studied as a function of sliding speed (and thus strain rate) at a fixed entrainment speed and thus EHD film thickness, which would not be possible if one body was held stationary with u2 = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003199_j.mechmachtheory.2019.103576-Figure19-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003199_j.mechmachtheory.2019.103576-Figure19-1.png",
        "caption": "Fig. 19. Curve for plunging of tool (schematic).",
        "texts": [
            " This function is also used for modification of the root fillet surfaces and the surfaces generated by the shaper front edge. In the following, this crowning method is explained for a face-gear with similar design parameters as listed in Table 3 , but with the same number of teeth of pinion and shaper. The modified design parameters (Var. d) are listed in Table 4 . The plunging curve is realized by two circle segments with radii to reach approximately 50 \u03bcm of crowning inside and outside of the tooth. This curve c ( u s ) is shown schematically in Fig. 19 . Its mathematical formulation is given by c(u s ) = | u s \u2212 l 0 c | cos \u03b3 \u2212 R sin \u03b3 1 + cos 2 \u03b3 + \u221a ( | u s \u2212 l 0 c | cos \u03b3 \u2212 R sin \u03b3 1 + cos 2 \u03b3 )2 \u2212 (u s \u2212 l 0 c ) 2 1 + cos 2 \u03b3 with R = { R c i , u s \u2264 l 0 c R c a , u s > l 0 c (61) Distance l 0 c marks the distance u s at where no plunging of the tool occurs. Radii R c i and R c a define the inner and outer part of the plunging curve, defined as two circle segments beside distance l 0 c . Fig. 20 shows the plunging curve in detail and the resulting crowning along the face-gear width"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000940_j.aca.2011.11.053-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000940_j.aca.2011.11.053-Figure2-1.png",
        "caption": "Fig. 2. Experimental setup for the measurement of l-lactate with our biosensor.",
        "texts": [
            " CV experiments were performed with and without l-lactate solution; the potential range used was \u22120.4/+0.6 V, at a scan rate of 10 mV s\u22121. The amperometric experiments were carried out by applying a constant potential to the working electrode of the biosensor. After the transient current had settled (t = 150 s), 10 L aliquots of known concentrations of l-lactate standard solutions were injected into the sampling unit by micropipette and the sensor response was measured until the resulting current reached a steady state value. The experimental setup is depicted in Fig. 2. 2.3. Synthesis of mesoporous silica powder (FSM8.0) Mesoporous silica (MPS) powder, FSM8.0, with a pore diameter of 8.0 nm, was prepared from sodium silicate using dococyltrimethylammonium chloride and 1,3,5-triisopropylbenzene (TIPB) as we previously reported [41]. 16 g of C22TMA was added to 200 mL of water at 70 \u25e6C, and to this mixture was added 60 g of TIPB; the resultant mixture was vigorously stirred for 30 min at 70 \u25e6C. It was then added to 200 mL of water at 80 \u25e6C in the presence 116 T"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001070_j.optlaseng.2011.10.017-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001070_j.optlaseng.2011.10.017-Figure3-1.png",
        "caption": "Fig. 3. Schematic of the observation system and methods: (a) observation",
        "texts": [
            " The schematic of the first method is shown in Fig. 2. A high speed camera is placed perpendicular to the moving direction of the powder flow. The high-power magnesium light illuminates the powder flow, and the angle between the light and the high speed camera is less than 901. Using this method, the moving powder particle will be captured by the camera with appropriate exposure time (2 10 4 s in this study) due to the reflections from the powder particles. This method will be used for the measurement of the powder particle speed. Fig. 3 shows the schematic of the powder flow concentration observation. The zone illuminated by the light sheet can be imaged Fig. 1. Schematic of the LSF process. in the camera with an exposure time of 0.5 s. In Fig. 3(a) and (b) (top view), the light sheet illuminates the powder flow along the two symmetrical planes, respectively, so the images of the powder flow through two symmetrical planes can be obtained. In addition, some experiments of single-layer deposition were performed to investigate the influences of the powder feed behaviors on the deposited layer quality. The LSF system consists of a 4 kW continuous wave CO2 laser, a powder delivery unit, a four-axis CNC machine and an inert gas chamber. Fig. 4 is a diagram of the LSF system",
            " Based on the assumption that the powder mass concentration in the nozzle tube is uniform and is the same as that near the nozzle exit, the powder mass concentration near the nozzle exit c0 can be expressed approximately as c0 \u00bc mp vp0pd2 0 \u00f07\u00de where mp denotes the powder feed rate, vp0 is the average speed of the powder particles near the nozzle exit (can be obtained from Eq. (1)) and d0 stands for the diameter of the nozzle tube (in this case, d0\u00bc1.5 mm). The gray value k0 can be extracted from the powder flow image near the nozzle exit (obtained by the method shown in Fig. 3(b)), and the constant C can be calculated (C\u00bcc0/(rp k0)). In this study, the constant C with te\u00bc0.5 s can be calculated as C0.5 s\u00bc1.01 10 6. Finally, the powder mass concentration can be obtained from Eq. (6). Fig. 9 shows the average speed of the powder particles with different carrier gas flow rates. It can be seen that average speed of the powder particles increases from 3500 mm s 1 to 7300 mm s 1 with the carrier gas flow rate increases from 150 L h 1 to 400 L h 1. Fig. 10 shows the powder flow images obtained by the observation method in Fig. 3(a) with the exposure time te\u00bc0.5 s. From Fig. 10, it can be found that the brightness of the powder flow decreases with the increase of the carrier gas flow rate. As the powder flow images in Fig. 10 were preprocessed, the powder mass concentration of the powder flow can be obtained. Fig. 11(a) and (b) show the powder mass concentrations on the vertical symmetry axis and the horizontal axis at S\u00bc13.5 mm below the nozzle exit plane, respectively. It can be seen that the powder mass concentration decreases with the increase of the carrier gas flow rate, the powder mass concentration along the vertical symmetry axis increases rapidly at first and then decreases slowly with the increase of the distance S from the nozzle exit plane, and the powder mass concentrations at S\u00bc13",
            " Average speed of the powder particles with different carrier gas flow rates. Fig. 12 shows the average speed of the powder particles with different powder feed rates. It can be seen that the average speed of the powder particles is almost constant with the change of the powder feed rate. This implies that the particles account for a very small volume fraction in the powder flow so that the increase of the particle number in the powder flow has little effect on the movement of the particles. Fig. 13 shows the powder flow images obtained by the observation method in Fig. 3(a) with an exposure time of te\u00bc0.5 s and powder feed rates of 0.052 g s 1, 0.07 g s 1 and 0.088 g s 1. It can be found that the brightness of the powder flow increases with the increase of the powder feed rate. Fig. 14(a) and (b) show the powder mass concentrations on the vertical symmetry axis and the horizontal axis at S\u00bc13.5 mm below the nozzle exit plane, respectively. It can be seen that the powder mass concentration increases with the increase of the powder feed rate, and the powder mass distributions with different powder feed rates are similar to each other"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002200_admt.201800486-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002200_admt.201800486-Figure3-1.png",
        "caption": "Figure 3. a) Schematic diagram showing the fabrication process of polymer microtubes with structured inner surface. b) Optical image during the rolling of the tubes. c) Optical image of a transparent polymer microtube with visible inner structure. Adapted with permission.[49] Copyright 2005, Wiley-VCH.",
        "texts": [
            " Technol. 2019, 4, 1800486 www.advancedsciencenews.com \u00a9 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim1800486 (4 of 26) www.advmattechnol.de also be generated inside membranes system upon the change in environment. In the case of swelling strain, the rolling process is not confined to inorganic materials. Strain can also be introduced in organic membranes system and microtubes can also be formed utilizing different swelling properties of chemically dissimilar polymers in selective solvents.[49] Figure 3 demonstrates a bilayer polymer system which consists of polystyrene (PS) and poly(4-vinylpyridline) (P4VP). PS forms a stiff hydrophobic layer upon exposure to water due to its low water uptake, while P4VP is less hydrophobic and thus swells in acid aqueous solutions. When putting the bilayer system into contact with acid aqueous solutions, the two layers present an unequal change in volume, resulting in the lateral forces which eventually create the bending moment for rolling process. Recently, such approach has also been widely applied to the construction of 4D mesostructures"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003869_j.ins.2020.03.068-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003869_j.ins.2020.03.068-Figure1-1.png",
        "caption": "Fig. 1. Schematic of the offshore ship-mounted crane system.",
        "texts": [
            " Different from the results in [1] , in the proposed method, the estimated fault and disturbance values are utilized to design the compensator, which contributes to attenuating the disturbance and to compensating for the actuator fault. The remainder of this paper contains four sections. In Section 2 , the problem formulation of the crane system and FLS are given. In Section 3 , the construction of the proposed method is presented. In Section 4 , the simulation results are listed and, we conclude the study in Section 5 . C 2. Problem formulation 2.1. System statement The schematic of the ship crane system is shown in Fig. 1 , where \u03d5, l and \u03b8 represent the trolley position, the length of wire and the payload swing angle respectively. \u03b1( t ) denotes the rolling angle of the ship, m and m l are the payload mass and the trolley mass. The dynamics of the ship crane system can be developed in the following manner [7] , M ( q ) \u0308q + C ( q, \u02d9 q) \u0307 q = F \u03c4 + F \u03be + F g + ( t ) (1) where q = [ \u03d5 l \u03b8 ] T is the generalized position, M ( q ) and C ( q, \u02d9 q) denote the inertial and Coriolis-centripetal matrix, respectively. F \u03c4 is the control input signal, F \u03be denotes the external disturbance, F g is a gravity vector, ( t ) represents the unknown dynamics which can denote the sea waves or winds and friction forces"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003686_tie.2019.2959504-Figure18-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003686_tie.2019.2959504-Figure18-1.png",
        "caption": "Fig. 18. Prototype machine. (a) Machine components. (b) Laminations. (c) Assembled machine.",
        "texts": [
            " The power factors are calculated from the phase difference between FE predicted phase voltage and phase current with zero d-axis current. TABLE III COMPARISON OF EFFICIENCY AND POWER FACTOR Parameter DF-FSPM FSPM Stator Rotor Total Stator Rotor Total Core loss (W) 0.8 1.1 1.9 0.9 0.7 1.6 Copper loss (W) 15 9 24 24 0 24 Efficiency (%) 87.2 82.5 Power factor 0.95 0.99 0.91 V. EXPERIMENTAL VALIDATION A 3-stator-phase/5-rotor-phase and 12-stator-pole/10-rotor-tooth DF-FSPM machine is manufactured and tested to validate the theoretical analyses, whose structure and main parameters are shown in Fig. 18 and Table IV. As shown in Fig. 18 (b), a 0.5mm iron bridge is employed to connect the individual stator iron segments in order to facilitate the manufacture. The rotor winding terminal wires are connected to the slip ring outside the machine through the groove on the shaft. TABLE IV MAIN PARAMETERS OF PROTOTYPE MACHINE Parameter Value Stator outer radius (mm) 50 Stator inner radius (mm) 35.25 Active axial length (mm) 50 Stator tooth arc to pole pitch ratio 0.28 Magnet arc to stator pole pitch ratio 0.24 Stator yoke thickness to tooth arc ratio 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002325_icra.2015.7139915-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002325_icra.2015.7139915-Figure3-1.png",
        "caption": "Fig. 3. An example foot trajectory during a stride.",
        "texts": [
            " For clarity of discussion, we consider the operation of the robot in statically stable modes. The dimensions of the robot (Fig. 2) are given by the body length LB and the body widths WA and WB (lower and upper bounds on the width). The forward direction corresponds to the positive x axis and up corresponds to the positive z axis forming a right handed coordinate frame. The lengths of the femur and the tibia links are given by LF and LT , respectively. The stride length is given by S. A typical triangular foot trajectory is shown in Fig. 3, and corresponds to the motion T1 \u2192 T2 \u2192 T3. Smoother trajectories can be defined by interpolating over a larger number of points (for example, T1 \u2192 T4 \u2192 T2 \u2192 T5 \u2192 T3). Similar to insects, hexapod robots achieve locomotion by repeatedly executing a \u201cgait pattern\u201d. This involves a set of legs pushing back with their feet on the ground thrusting the body forward while the rest of the legs swing forward with their feet off the ground [16]. The legs with feet on the ground are said to be in \u201cstance phase\u201d while the legs swinging forward are in \u201cswing phase\u201d"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002276_tsmc.2017.2744676-Figure12-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002276_tsmc.2017.2744676-Figure12-1.png",
        "caption": "Fig. 12. Tripled inverted pendulums connected by springs.",
        "texts": [
            " It should be pointed out that large control gains might leading to unexpected large control input signals at the initial stage and actuators might be suffered from abrupt lash within short period, which is not be of permission from a practical point of view. For the sake of space limitation, we omit these simulation results and readers interested in this aspect may do it by themselves. It indicates that we should make a compromise between the control performance and control signals. All the above provide constructive and suggestive tuning procedures for the designed gains. B. Example 2 Consider another practical issue that the stabilization problem of the tripled inverted pendulums. The system is shown in Fig. 12 and described by \u23a7 \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a9 \u03b8\u03071 = g l sin \u03b81 + T 1 u1+ k1a2 m1l2 (sin \u03b82 cos \u03b82\u2212sin \u03b81 cos \u03b81) \u03b8\u03072 = g l sin \u03b82+ T 2 u2+ k1a2 m2l2 (sin \u03b81 cos \u03b81\u2212sin \u03b82 cos \u03b82) + k2a2 m2l2 (sin \u03b83 cos \u03b83\u2212sin \u03b82 cos \u03b82) \u03b8\u03073 = g l sin \u03b83+ T 3 u3+ k2a2 m3l2 (sin \u03b82 cos \u03b82\u2212sin \u03b83 cos \u03b83) where \u03b8i, mi, and l are the angle position of the ith pendulum, the mass of the ith rod, and the length of the rod, respectively. ki is the spring constant of the connected spring, i = 1, 2. We denote that \u03b8i = xi,1 and \u03b8\u0307i = xi,2, i = 1, 2, 3, and the equation of the system can be rewritten as \u23a7 \u23aa\u23aa\u23a8 \u23aa\u23aa\u23a9 x\u0307i,1 = xi,2 + i,1(y1, y2, y3) x\u0307i,2 = g l sin xi,1+ T i ui+ i,2(y1, y2, y3) yi = xi,1 where i,1(y1, y2, y3) = 0, 1,2(y1, y2, y3) = [(k1a2)/(m1l2)](sin y2 cos y2 \u2212 sin y1 cos y1), 2,2(y1, y2, y3) = [(k1a2)/(m2l2)](sin y1 cos y1 \u2212 sin y2 cos y2) + [(k2a2)/(m2l2)](sin y3 cos y3 \u2212 sin y2 cos y2), 3,2(y1, y2, y3) = [(k2a2)/(m3l2)](sin y2 cos y2 \u2212 sin y3 cos y3), i,j = 1, and ui = [ ui,1, ui,2 ]T"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000807_j.mechmachtheory.2013.06.013-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000807_j.mechmachtheory.2013.06.013-Figure8-1.png",
        "caption": "Fig. 8. Coordinate systems for simulation of meshing.",
        "texts": [
            " where Since the contact line is a symmetric distribution in the tooth surfaces of the face-gear, it is easy for us to obtain the value of \u03c8\u2032 s max\u00f0 \u00de \u00bc \u2212\u03c8s min\u00f0 \u00de and \u03c8\u2032 s min\u00f0 \u00de \u00bc \u2212\u03c8s max\u00f0 \u00de (see Fig. 6(b)). TCA is designated for the simulation of meshing and contact of surfaces \u22111 and \u22112 of pinion and face-gear respectively, which provides a way to investigate the influence of errors of alignment on transmission errors and shift of bearing contact. The TCA procedure is based on the application of coordinate systems shown in Fig. 8. S1, S2 and Sf are fixed to pinion, face-gear and the frame of machine respectively. Sq, Se and Sd are auxiliary coordinate systems as in Fig. 8. Parameters, \u0394E, B and B cot \u03b3 simulate the location of Sq with respect to Sf. \u0394E is used to simulate the alignment error of the crossed displacement between axes of pinion and face gear. \u0394\u03b3 is set up to simulate the angular alignment error between axes of pinion and face-gear. The variable \u0394q along the axis of face gear represents the alignment error of Se to Sq. The pinion and the face-gear rotate around the axes of z1 and z2 respectively. The output of TCA of proposed geometry (see Table 2) is illustrated in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001968_978-94-007-6101-8-Figure2.1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001968_978-94-007-6101-8-Figure2.1-1.png",
        "caption": "Fig. 2.1 Rotation of a point about arbitrary axis",
        "texts": [
            " Chapter 2 Abstract Rotation about an arbitrary axis is described by the use of Rodrigues\u2019s formula. Orientation of a coordinate frame with respect to another frame is expressed with the rotation matrix. Orientation of a robot gripper is determined by the use of rotation matrix, RPY and Euler angles, and quaternions. A brief introduction to quaternions is also given in this chapter. Rotation represents circular movement about an axis [1]. The point P1 is rotated for an angle \u03d1 in positive direction about an arbitrary axis, running through the origin of a fixed coordinate frame (Fig. 2.1). Positive rotation around a selected axis in a cartesian frame is defined by the right-hand rule (the thumb is placed in direction of the axis, while the index of the right hand is rotated towards the palm). In a right-handed frame the positive rotations are counter-clockwise. When determining the direction of rotation we must look from the positive end of the axis towards the origin of the frame. The direction of running of athletes on a stadium is also an example of positive rotation. After positive rotation the point comes into a new position P2",
            " The position of the point P1 can be denoted by the vector: r1 = OP1 After rotation the point comes into position P2: r2 = OP2 The direction of rotation is denoted by the unit vector s: s = [sx , sy, sz]T T. Bajd et al., Introduction to Robotics, SpringerBriefs in Applied Sciences 9 and Technology, DOI: 10.1007/978-94-007-6101-8_2, \u00a9 The Author(s) 2013 10 2 Rotation and Orientation s The vector s describes the axis of rotation. By equating the following two scalar products, we have: rT 1 s = r1 cos\u03b1 = rT 2 s = r2 cos\u03b1 = |OSp| (2.1) In Eq. (2.1) \u03b1 represents the angle between the vectors r1 and s or r2 and s. The following difference of the vectors can be seen from Fig. 2.1: SpP1 = r1 \u2212 OSp From where we can write the Eq. (2.2): SpP1 = r1 \u2212 (rT 1 s)s (2.2) SpP2 = r2 \u2212 (rT 2 s)s The relation between the unit vector s and the vector r1, describing the absolute value of the cross product, can also be found from Fig. 2.1: |s\u00d7 r1| = |SpP1| = r1 sin \u03b1 2.1 Rotation 11 P2 Let us now look at the plane, where the rotation between the points P1 and P2 took place. It is perpendicular to the rotation axis (Fig. 2.2). The point, where the plane and the rotation axis intersect, will be denoted as Sp. There also holds: NP2 \u22a5 SpP1 As the points P1 and P2 are on the same circular line, we have: |SpP1| = |SpP2| from Fig. 2.2 we can see: |SpN| = |SpP2|c\u03d1 = |SpP1|c\u03d1 In robotics we prefer shorter notation of trigonometric functions c\u03d1 = cos\u03d1 and s\u03d1 = sin \u03d1 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000807_j.mechmachtheory.2013.06.013-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000807_j.mechmachtheory.2013.06.013-Figure2-1.png",
        "caption": "Fig. 2. (a) Profile of parabolic rack cutter As, (b) profile of parabolic rack cutter A1.",
        "texts": [
            " (3) The simulation processing test based on Vericut is presented and its results have verified the feasibility and correctness of the mentioned method. The following section mainly shows schematically steps of the generation of tooth surfaces of rack-cutters, shaper, pinion and profile-modified spur face-gear: (1) Rack-cutters A1 and As are provided by mismatched parabolic profiles that deviate from the straight line profiles of reference rack-cutter A0. Fig. 1 shows an exaggerated deviation of A1 and As from A0 schematically. The parabolic profiles of one tooth side of rack-cutters As and A1 for one tooth side are shown in Fig. 2(a) and (b) schematically. (2) The tooth surfaces \u2211s and \u22111 of the shaper and the pinion are generated by rack-cutters As and A1 respectively. (3) The tooth surface \u22112 of the profile-modified spur face-gear is generated by the shaper. Fig. 2(a) represents the rack cutter's straight line profile of Aswhich is substituted by a parabolic profile applied for the generation of the shaper. Both of the coordinate systems St and Sr are located in the transversal section of the rack cutter. S0 = 0.5\u03c0m represents the space or the tooth width of the rack cutter, ad is the normal pressure angle, ur is the rack cutter surface \u2211r parameter, as is the parabola coefficient, and parameter fd controls the point of tangency of the parabolic profile to the traditional straight-flank surface",
            " Finally, we represent the shaper surface by a vector function rs ur; \u03b8r ;\u03c8r ur\u00f0 \u00de\u00f0 \u00de \u00bc Rs ur; \u03b8r\u00f0 \u00de: \u00f04\u00de The normal to the shaper is represented in coordinate system Ss as: Ns ur ;\u03c8r ur\u00f0 \u00de\u00f0 \u00de \u00bc Lsr \u03c8r ur\u00f0 \u00de\u00f0 \u00deNr ur\u00f0 \u00de \u00f05\u00de the matrix Lsr(\u03c8r) is the 3 \u00d7 3 order sub matrix of matrix Msr. where In order to ensure that the height distribution of the shaper is consistent with the standard gear cutter with involute teeth (the geometry of the rack-cutter A0), we need to calculate the two limit values ur1 and ur2 of the parameter ur (Fig. 2(a)). Using Eq. (4), and assume rs ur; \u03b8r\u00f0 \u00de \u00bc xs; ys; zs;1\u00f0 \u00de: \u00f06\u00de The values of ur1 and ur2 are represented as: ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x2s ur1\u00f0 \u00de \u00fe y2s ur1\u00f0 \u00de q \u2212rsa \u00bc 0ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x2s ur2\u00f0 \u00de \u00fe y2s ur2\u00f0 \u00de q \u2212rsm \u00bc 0 8< : \u00f07\u00de rsa and rsm are the radius of addendum circle and the root circle radius of the standard gear cutter with involute teeth where respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000577_j.nucengdes.2010.05.040-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000577_j.nucengdes.2010.05.040-Figure2-1.png",
        "caption": "Fig. 2. Schematic of friction and wear tests.",
        "texts": [],
        "surrounding_texts": [
            "L H a b c\na\nA R R A\n1\ng T t\na m c r S 2 S X 2\nw c\np\n0 d\nContents lists available at ScienceDirect\nNuclear Engineering and Design\njourna l homepage: www.e lsev ier .com/ locate /nucengdes\naser cladding of Colmonoy 6 powder on AISI316L austenitic stainless steel\n. Zhanga,\u2217, Y. Shia, M. Kutsunab, G.J. Xuc\nDepartment of Mechanical Engineering, Changchun University of Science and Technology, No. 7089 Weixing-lu, Changchun 130022, Jilin, PR China Advanced Laser Technology Research Center Co. Ltd., 40-7 Hiromi, Anjo-cho 446-0026, Anjo-shi, Aichi-ken, Japan School of Materials Science and Engineering, Shenyang University of Technology, No. 111 Shenliaoxilu, Shenyang 110178, PR China\nr t i c l e i n f o\nrticle history: eceived 9 October 2009 eceived in revised form 4 March 2010 ccepted 8 May 2010\na b s t r a c t\nStainless steels are widely used in nuclear power plant due to their good corrosion resistance, but their wear resistance is relatively low. Therefore, it is very important to improve this property by surface treatment. This paper investigates cladding Colmonoy 6 powder on AISI316L austenitic stainless steel by CO2 laser. It is found that preheating is necessary for preventing cracking in the laser cladding procedure \u25e6 and 450 C is the proper preheating temperature. The effects of laser power, traveling speed, defocusing distance, powder feed rate on the bead height, bead width, penetration depth and dilution are investigated. The friction and wear test results show that the friction coefficient of specimens with laser cladding is lower than that of specimens without laser cladding, and the wear resistance of specimens has been increased 53 times after laser cladding, which reveals that laser cladding layer plays roles on wear resistance. The microstructures of laser cladding layer are composed of Ni-rich austenitic, boride and carbide.\n. Introduction\nStainless steel is widely used in nuclear power plant due to its ood corrosion resistance, but its wear resistance is relatively low. herefore, it is very important to improve this property by surface reatment.\nLaser cladding minimizes the heat affected zone and creates true metallurgical bond between the two materials, forming a uch finer microstructure than hand or arc welding. The proess increases surface hardness, improves corrosion resistance and esults in little or no distortion (Ming et al., 1998; Lim et al., 1998; un et al., 2000; Kathuria, 2000; Wong et al., 2000; Zhang et al., 001; Conde et al., 2002; Jendrzejewski et al., 2004; Li et al., 2004; un et al., 2005; Dutta Majumdar et al., 2005; Fern\u00e1ndez et al., 2005; u et al., 2006a,b,c; Tobar et al., 2006; Navas et al., 2006; St-Georges, 007; Chen et al., 2008).\nColmonoy 6 powder is self-fluxing Ni\u2013Cr\u2013B\u2013Si system alloy, hich is an industry mainstay because of its good welding and wear haracteristics. The aim of this paper is to investigate cladding Colmonoy 6 owder on AISI316L austenitic stainless steel by CO2 laser.\n\u2217 Corresponding author. Tel.: +86 431 85582286; fax: +86 431 85383815. E-mail address: h zhang@cust.edu.cn (H. Zhang).\n029-5493/$ \u2013 see front matter \u00a9 2010 Elsevier B.V. All rights reserved. oi:10.1016/j.nucengdes.2010.05.040\n\u00a9 2010 Elsevier B.V. All rights reserved.\n2. Experimental details\n2.1. Materials\nThe base material is AISI316L austenitic stainless steel, the powder is Colmonoy 6, and their chemical compositions and mechanical properties are given in Tables 1\u20133 respectively. The geometry of specimens used in the experiments is 80 mm \u00d7 30 mm \u00d7 10 mm.\n2.2. Laser cladding setup\nThe arrangement for laser cladding is shown in Fig. 1. The laser generator is DAIHEN ELA-2001 axial-flow laser. The wave length is 10.6 m, the beam mode is TEM01\n*, and the beam divergence is less than 2 mrad. The powder was delivered by SULZER METCO TWIN10-SPG powder feeding machine, argon was used as powder carrier gas. Argon was also served as center shielding gas, its purity was 99.9% and its flux was set at 25 l/min. Before laser cladding, the surface of specimens was cleaned by acetone.\n2.3. Characterization of the effects induced by laser cladding\nFor macro-observations and micro-observations, the specimens were transversely sectioned, polished, and chemically etched with a mixture of HNO3:HCI = 1:3.\nAKASHI MVK-E hardness tester with a load of 50 g and a holding time of 15 s was used to measure the Vickers hardness of cladding layer. HITACHI H-800 scanning electron microscope was used to",
            "laser power of 2.3 kW, travel speed of 500 mm/min, powder feed rate of 25 g/min, spot diameter is 2 mm, overlapping of 28%. After laser cladding, the specimens were ground and were cut into 14 mm \u00d7 10 mm \u00d7 10 mm for friction and wear tests. Three specimens were tested and the average value was taken as the final results. The normal load was 98 N, the sliding speed was 1 m/s, the test time was 30 min. The friction coefficient was calculated by the following:\n= M\nRP\nwhere M is the friction moment, R is the radius of counterpart, and P is the normal load on the specimen. The method of weight loss was used to evaluate the wear resistance of specimens. Before and after test, the specimens were cleaned by ethanol and were weighed by an electronic balance TG328B with accuracy of 0.1 mg.\n3. Results and discussions\n3.1. Effect of preheating on crack in the laser cladding\nThe cracks are often generated in single pass and multi-pass laser cladding process without preheating. The generation of crack is mainly due to different thermal expansion coefficients of the cladding powder and the base material, a large temperature gradient produced and thermal stresses generated by different alloying elements during the solidification process.\nIn order to prevent cracking, preheating the base material has been taken into account in the experiment. A torch was used to heat the specimens, and a thermometer was used to measure the surface preheating temperature of specimens. The relation between the number of cracks and the preheating temperature is shown in Fig. 3. It can be seen that with increasing the preheating temperature, the number of cracks decrease. It is also noted that when the preheating temperature reaches 450 \u25e6C, crack does not generate again. Therefore, 450 \u25e6C is the proper preheating temperature for laser cladding Colmonoy 6 powder on AISI316L austenitic stainless steel.\n3.2. Effects of defocusing distance on bead height, bead width, penetration depth and dilution\nThe cross-sectional profile of a single clad pass is a description of the geometrical dimensions of the bead, is shown in Fig. 4, where h is the bead height, W is the bead width, H is the penetration depth, A is the clad metal area, and B is the base material area. In our experiments, single pass laser cladding was used to investigate the effect of the laser cladding parameters on the bead height, bead width, penetration depth and dilution.\nIn condition of laser power of 2.0 kW, travel speed of 700 mm/min, powder feed rate of 17.5 g/min, and preheating temperature of 450 \u25e6C, the relations between the defocusing distance and bead height, bead width, penetration depth, and dilution are shown in Fig. 5. It can be seen that bead height and bead width increase with increasing the defocusing distance, however, the penetration depth and dilution decrease.\nIn fact, in the laser cladding process, the energy from laser can be divided into two parts, one for building up the bead, and another",
            "file of\nf t b d l\n3 p\n2 a b c d\nd m t\nF a\nor heating the base material. When increasing the defocusing disance, the beam size gets larger, so the bead height and bead width ecome bigger. On the other hand, when increasing the defocusing istance, the energy density per unit of clad pass available becomes ess, thus the penetration depth and dilution decrease.\n.3. Effects of laser power on bead height, bead width, enetration depth and dilution\nIn the case of travel speed of 500 mm/min, powder feed rate of 5 g/min, defocusing distance of +15 mm, and preheating temperture of 450 \u25e6C, the relations between laser power and bead height, ead width, penetration depth and dilution are shown in Fig. 6. It an be seen that bead height, bead width, penetration depth and ilution increase with increasing laser power.\nThe reason is that when increasing the laser power, the energy ensity used both for building up the bead and heating the base aterial gets much more, thus the bead height, bead width, peneration depth and dilution become larger.\nig. 5. Effects of defocusing distance on bead height, bead width, penetration depth nd dilution.\nsingle pass laser cladding.\n3.4. Effects of travel speed on bead height, bead width, penetration depth and dilution\nIn condition of laser power of 2.3 kW, powder feed rate of 25 g/min, defocusing distance of +15 mm, and preheating temperature of 450 \u25e6C, the relations between travel speed and bead height, bead width, penetration depth and dilution are given in Fig. 7. We can see that bead height and bead width decrease with increasing the travel speed, however, penetration depth and dilution increase.\nIn reality, when increasing the travel speed, the energy used for building up the bead gets less, so the bead height and bead width decrease. However, at the same time, the energy for heating the base material becomes much more, thus the penetration depth and dilution increase.\n3.5. Effects of powder feed rate on bead height, bead width, penetration depth and dilution\nIn the case of laser power of 2.3 kW, travel speed of 500 mm/min, defocusing distance of +15 mm, and preheating temperature of"
        ]
    },
    {
        "image_filename": "designv10_5_0000236_j.mechmachtheory.2010.06.004-Figure13-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000236_j.mechmachtheory.2010.06.004-Figure13-1.png",
        "caption": "Fig. 13. Close-up of the stress concentration zone for the optimized gear (\u03b1c=34\u00b0, \u03b1d=20\u00b0, \u03b7=1.57 and \u03bc=0.07). The stress is reduced with 23.2% as compared to the ISO profile.",
        "texts": [
            " The price we pay in this design relative to the original ISO tooth is a smaller contact ratio but this can be fixed through a possible longer tooth since the tooth top thickness is not near the limit. Alternatively to this we fix the drive side pressure angle at \u03b1d=20\u00b0 resulting in the same contact ratio as the ISO gear. Result of this optimization is presented in Figs. 12 and 13. The optimized design in Fig. 12 has the following design parameters \u03b1c=34\u00b0, \u03b1d=20\u00b0, \u03b7=1.57 and \u03bc=0.07. Stress is reduced with 23.2% as compared to the ISO profile. In Fig. 13 a close-up of the interesting tooth part is given. Overall the improvements in the bending stresses are large. The largest stress improvement is possible with \u03b1dN\u03b1c, here we find almost twice the improvement found when \u03b1db\u03b1c. The improvement of 39.2% and 23.2% should be compared to the result in Ref. [1] where thebestdesigngavea stress reductionof12.2%, so the influence fromtheenlarged tooth root thickness is clear. The choiceof\u03b1dN\u03b1c is similar towhat is found in e.g. Ref. [10]while\u03b1db\u03b1c corresponds to the choice in e"
        ],
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    },
    {
        "image_filename": "designv10_5_0003487_j.tafmec.2020.102634-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003487_j.tafmec.2020.102634-Figure2-1.png",
        "caption": "Fig. 2. (a) Fatigue sample fabricated along the three different building directions defined by the angle between building direction and sample longitudinal axis. (b) Misalignment of two heads.",
        "texts": [
            " Cylindrical fatigue samples were fabricated using MCP HEK REALIZER II, which is a laser powder bed fusion machine, utilizing a Nd:YAG laser source. Fig. 1 shows the schematic of the adopted scanning strategy, i.e., the alternate-hatching pattern. To minimize oxidation, scanning was performed in high-purity argon atmosphere with an oxygen content lower than 0.6%. Energy density (Ed, see Eq. (1)) was set as 200 J/mm3. The fatigue samples were built along three different directions defined by the angle between the building direction and sample longitudinal axis (Fig. 2a). The values of the angles were 0\u00b0, 45\u00b0, and 90\u00b0. The geometry was compliant with ASTM E466-15, and a uniform gage section was provided to critically stress a significant amount of material. In this manner, the impact of the microstructure and defectiveness on the fatigue behavior could be captured more effectively compared to common hourglass samples. As-built samples were double-tempered at 650 \u00b0C for 2 h (i.e., 2 \u00d7 2 h, 650 \u00b0C) in a vacuum furnace (TAV Minijet). To correct the distortion resulting in a misalignment (\u0394f) of up to ~ 0.4 mm (see Fig. 2b), the samples surface was completely turned to achieve concentricity between the two heads and the central part below 0.01 mm. The samples were further milled till the cylindrical central part. The removal of more than 0.1 mm material, practically deleted any influence of the original surface finishing/defectiveness and reduced the surface roughness. The roughness of as-built and machined samples was measured, after machining using a portable profilometer (Marsurf PS1). Density was measured using the Archimedes principle, according to ASTM EB962"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003720_j.addma.2020.101491-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003720_j.addma.2020.101491-Figure8-1.png",
        "caption": "Fig. 8. Spatiotemporal variations of temperature fields during ten-layer laser DED for the 1st, 8th, 9th, and 10th layers, respectively. Laser power 1500W, scanning speed 8mm/s, mass feed rate 20 g/min, bidirectional scanning. (a) the 10th layer with scanned distance 25mm, (b) the 9th layer scanned distance 30mm, (c) the 8th layer scanned distance 35mm, (d) the 1st layer scanned distance 5mm.",
        "texts": [
            " 7(d) indicates that the local fluid flow in the rear region of the molten pool is mainly driven by the Marangoni stress resulting from the gradient distribution of surface tension [52,53]. Such a flow pattern drives the liquid metal to the rear of the molten pool, spreading on the preceding layer. In a recent article [23], a prominent bulge at the beginning part of a single track was observed. Similarly, the protrusion at the track head was observed in single track laser powder bed fusion samples [54]. Thus, an accumulation of the liquid metal is generated at the starting zone of each layer during multi-layer DED. Fig. 8 shows the spatiotemporal variations of temperature fields during ten-layer laser DED for the 1st, 8th, 9th, and 10th layers, respectively. Significantly lager molten pools for upper layers compared with those for lower layers can be observed. Similar experimental observations have also been reported for thin wall structure printing using laser wire DED [37,55]. As demonstrated in Fig. 8(c), a declining zone which has progressively smaller build height was generated at the end of the 8th layer. The 9th layer subsequently started from this zone. Although the molten pool metal flows in a similar pattern as described for Fig. 7(d), the starting condition for the bidirectional scanning case changed layer wisely compared with the unidirectional case shown in Fig. 7. Thus, the different features of the starting and ending zones are counteracted via the opposite scanning directions of adjacent layers for the bidirectional scanning cases"
        ],
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    },
    {
        "image_filename": "designv10_5_0002424_j.mechmachtheory.2017.12.003-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002424_j.mechmachtheory.2017.12.003-Figure2-1.png",
        "caption": "Fig. 2. Tooth flank point coordinates: (a) parametric expression; (b) CMM measurement.",
        "texts": [
            " Different from previous studies [10,11] that the initial value is artificially given, the gear and pinion initial points are directly calculated as a set of the accurate initial values, respectively. The identified initial value can make it easy to get the solutions of initial contact point and relative TCA evaluation results, even though the established TCA equation set is of the strong nonlinearity. An accurate geometric analytical arrangement in this work is firstly proposed to identify the initial point on gear flank after the parametric expression of the gear tooth flank with respect to \u03c62 and \u03b82 . It is needed to make a parameterization of tooth flank. Fig. 2 (a) shows coordinates r 2 and L 2 of the tooth flank point. Generally, tooth flank coordinate regularization can be obtained by referring to the measurement with the coordinate measuring machines (CMMs). Fig. 2 (b) represents the parametric tooth flank grid. Too often, the tooth flank is made discretization by a typical 5 \u00d7 9 points grid, which selects 9 data points along the face width (FW) direction and 5 data points along the tooth height (TH) direction according to the Gleason measurement rule [14,16] , respectively. An accurate analytical method is developed to calculate the gear initial point coordinates by simulating the actual measurement. Referring to descriptions in the paper [10] , in establishments of the basic coordinate system { i , j , k }, there are i = [1 0 0 ] , j = [0 1 0 ] , k = [0 0 1 ] (7) Here, p i is the function with respect to \u03b4M "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002564_tie.2017.2760246-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002564_tie.2017.2760246-Figure2-1.png",
        "caption": "Fig. 2. Axes of the HSV.",
        "texts": [],
        "surrounding_texts": [
            "Output-Redefinition-Based Dynamic Inversion Control for a Nonminimum Phase\nHypersonic Vehicle Linqi Ye, Qun Zong, Member, IEEE, John L. Crassidis , and Bailing Tian , Member, IEEE\nAbstract\u2014Output-redefinition-based dynamic inversion (ORDI) control is proposed for a nonminimum phase hypersonic vehicle (HSV). When velocity and altitude are selected as control outputs, an HSV exhibits nonminimum phase behavior, preventing the application of standard dynamic inversion control due to the unstable zero dynamics. This problem is solved by the ORDI control architecture, where output redefinition is utilized at first to render the modified zero dynamics stable, and then, dynamic inversion is used to stabilize the new external dynamics. Three kinds of ORDI controllers with different choices of new control output are investigated. The first takes the internal variable as the control output, which exhibits good robustness but with restricted performance. The second utilizes a synthetic output, which is a linear combination of the system output and internal variable, making the zero dynamics adjustable, and thus improves the tracking performance. The third adds an integral item to the synthetic output, and thus ensures zero steady-state error even with model uncertainties. A systematic way is proposed to determine the combination coefficient to achieve zero dynamics assignment by using the root locus method. The efficiency of the method is illustrated by numerical simulations.\nIndex Terms\u2014Dynamic inversion, hypersonic vehicle (HSV), nonminimum phase, output redefinition, zero dynamics assignment.\nI. INTRODUCTION\nHYPERSONIC vehicles (HSVs) refer to vehicles that travels at velocity greater than Mach 5. This is regarded as one of the most promising technology for achieving cost effective and reliable access to space. One of the most difficult challenges encountered in designing flight control systems for\nManuscript received February 27, 2017; revised June 11, 2017 and August 10, 2017; accepted September 7, 2017. Date of publication October 6, 2017; date of current version January 5, 2018. This work was supported in part by the National Natural Science Foundation of China under Grant 61673294, Grant 61503323, and Grant 61773278; in part by the China Scholarship Council under Grant 201606250160; and in part by the Ministry of Education Equipment Development Fund under Grant 6141A02033311. (Corresponding author: Bailing Tian.)\nL. Ye, Q. Zong, and B. Tian are with the School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China (e-mail: yelinqi@tju.edu.cn; zongqun@tju.edu.cn; bailing_tian@tju.edu.cn).\nJ. L. Crassidis is with the Department of Mechanical and Aerospace Engineering, University at Buffalo, The State University of New York, Amherst, NY 14260-4400 USA (e-mail: johnc@buffalo.edu).\nColor versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org.\nDigital Object Identifier 10.1109/TIE.2017.2760246\nHSVs is the nonminimum phase problem due to elevator-tolift coupling [1]. When the nonlinear control method, dynamic inversion, is straightforwardly applied to nonminimum phase systems, it results in exact tracking but the unstable zero dynamics remains an unstable part in the closed-loop system. Therefore, the nonminimum phase character of an HSV prevents the application of standard dynamic inversion and all of its invariants, bringing great challenges to nonlinear controller design for these vehicles.\nThe nonminimum phase problem of HSV can be avoided by adding a canard. Since the elevator-to-lift coupling is canceled by the canard, the nonminimum phase behavior is removed. Many nonlinear methods are applied to the canard configured HSV, such as sliding mode control [2]\u2013[4], dynamic surface control [5]\u2013[7], and feedback linearization control [8], [9], to name a few. Although a canard is beneficial to avoid the nonminimum phase problem, it is a problem for the vehicle structure since the canard must withstand a large thermal stress at hypersonic speeds. Therefore, it is of great significance to investigate the control problem of an HSV without a canard, which means that a controller must be designed directly based on the nonminimum phase HSV model. This issue has received more and more attention in recent years but only a few new control methods have been proposed [1], [10]\u2013[15].\nThough the nonminimum phase character of an HSV limits the application of classical nonlinear control methods, linear control methods are still available. In [10], a linear controller is developed for an HSV by the pole assignment method. As an improvement, a stable inversion approach [16], [17] was applied to an HSV in [11]. It achieves exact tracking by imbedding the ideal internal dynamics into a linear feedback controller. However, this method is noncausal and greatly depends on exact model knowledge.\nIn addition, some nonlinear control methods are proposed for a nonminimum phase HSV. One typical method is approximate feedback linearization [12], [13]. By strategically ignoring the elevator-to-lift coupling and resorting to dynamic extension at the input side, an approximate model with full vector relative degree is obtained. Then, standard dynamic inversion can be applied to the approximate model, resulting in approximate linearization of the original model. Other methods can also be used to the approximate model, such as backstepping [14]. This method works mainly because the approximate model has higher relative degree so that the internal variables are included in the\n0278-0046 \u00a9 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information.",
            "control loop. However, this method only works when the coupling is weak enough, i.e., a \u201cslightly\u201d nonminimum phase system [18]. The control law designed by the approximate model will result in instability when applied to the model with stronger nonminimum phase behavior [13].\nAnother nonlinear control method focuses on the redefinition of the zero dynamics. In [1], a preliminary feedback transformation is used to convert the model into the interconnection of systems with feedforward and feedback form, respectively. Then, the original output is converted into a state trajectory of new zero dynamics. Hence, additional control effort is not required for stabilizing the internal dynamics. In [15], with the definition of two separate nested zero dynamics subsystems, the elevator is treated as the primary effector to control the regulated output and the stabilization of the internal dynamics as a secondary objective.\nThe idea of the two aforementioned papers is very similar to the output redefinition method [19], whose main concept is: first, to perform an output redefinition such that the zero dynamics with respect to the new output are acceptable; and second, to define a modified desired trajectory for the new output to track such that the original output tracks the original desired trajectory asymptotically. Since the second step can be realized by stable inversion [16], [17], the main difficulty lies in how to find a minimum phase output. In [19], the new output is constructed through the B-I norm form. But it is nontrivial to implement in practice since the B-I norm form of a complex system is usually difficult to obtain. In [20], the flatness-based approach is proposed, where a variable with full relative degree is selected as the control output. This variable is called by the flat output, and there is no zero dynamics corresponding to it. However, no systemic way is provided to find such a flat output, which limits the application of this method. Another method is statically equivalent output [21], [22], where the new output is computed on the basis of the solution of a singular partial differential equation to induce the prescribed zero dynamics.\nInspired by [1] and [19], an output-redefinition-based dynamic inversion (ORDI) control method is developed to achieve stable tracking control for a nonminimum phase HSV. The ORDI method combines the advantage of linear and nonlinear control. In the first step, the zero dynamics are stabilized by constructing a synthetic output, which is a linear combination of the system output, an internal variable and integral tracking error, whose effect is very similar to Proportional-Integral (PI) control. In the second step, the external dynamics are stabilized by dynamic inversion, which takes advantage of nonlinear control. As a result, the closed-loop system becomes an asymptotic stable linear system cascaded with a locally stable nonlinear zero dynamics. Based on the ORDI control architecture, three kinds of ORDI controllers are developed for the HSV with different choices of the new output definitions.\nThe main contributions of this paper are twofold. First, for the nonminimum phase system control theory, a systematic way is proposed to construct a minimum phase output. By selecting the new output as a linear combination of the system output, an internal variable and integral tracking error, and using the root locus method to determine the combination coefficient,\nan effective way is proposed to achieve zero dynamics assignment. Compared to the methods in the aforementioned references [19]\u2013[22], the proposed method is based on the original coordinate and the classical root locus method, making it much easier to be carried out, especially for complex systems. Second, for the HSV control problem, the ORDI method is successfully applied to solve the nonminimum phase problem. The proposed method has advantages over the existing ones [1], [10]\u2013[15]. Compared to the linear methods [10], [11], the developed method is nonlinear, which takes advantage of dynamic inversion control. Compared to [12]\u2013[14], this method is able to deal with stronger nonminimum phase behavior due to the inclusion of the zero dynamics assignment process. Finally, compared to [1] and [15], this method transfers the high-order control problem into two control problems of lower order, which greatly simplifies the control design.\nThe remainder of this paper is organized as follows. In Section II, the HSV model and its zero dynamics analysis are presented. The main idea of ORDI control is provided in Section III. Then, the ORDI controllers for an HSV will be developed in Sections IV and V. Next, simulations and discussions are given in Section VI. Finally, the conclusions are summarized in Section VII.\nThe model considered in this paper is the rigid-body longitudinal model of an air-breathing HSV, which is developed in [1] to verify the control algorithm for HSV with nonminimum phase characteristics. The model is based on NASA\u2019s scramjetpowered X-43A, as shown in Figs. 1 and 2.\nThe model comprises five state variables x = [V, h, \u03b3, \u03b8,Q]T , representing velocity, altitude, flight path angle, pitch angle, and pitch rate, respectively. There are two control inputs u = [\u03c6, \u03b4e ]T , representing fuel to air ratio into the scramjet combustor and the elevator deflection angle, respectively. The control inputs indirectly affect the dynamics of the aircraft through the forces and moments: T , D, L, and M .",
            "The angle of attack \u03b1 satisfies \u03b1 = \u03b8 \u2212 \u03b3. The dynamic pressure q\u0304 is calculated by q\u0304 = \u03c1(h)V 2/2 with \u03c1(h) = \u03c10e\u2212(h\u2212h0 )/hs being the atmospheric density. All the parameter values in the model are shown in Tables I and II [1], [23].\nThe system outputs are [V, h]T and the admissible flight range is \u039ey :={7500\u2264V \u226411 000(ft/s), 70 000\u2264h\u2264135 000(ft)}. The control objective is to design a control law u = [\u03c6, \u03b4e ]T such that the system outputs track the given constant commands V \u2217, h\u2217 asymptotically in the admissible flight range \u039ey .\nDynamic Inversion\nIn standard dynamic inversion, the system outputs [V, h]T are employed as control outputs. According to [24], zero dynamics are the remaining dynamics when the outputs are identically zero. Denote the tracking errors as eV = V \u2212 V \u2217, eh = h \u2212 h\u2217.\nC\u03b1 D \u22120.074020 rad\u22121 C\u03c6\u03b1 3 T \u221214.038 rad\u22123 C 1 T 0.037275 rad\u22121 C 0 D \u22120.019880 rad\u22122 C\u03c6\u03b1 2 T \u22121.5839 rad\u22121 C 0 T \u22120.021635\nSince the commands V \u2217, h\u2217 are nonzero, the tracking errors [eV , eh ]T will be used as regulated outputs to analyze the zero dynamics.\nFor the convenience of zero dynamics analysis and control design, the HSV model (4) is rewritten in an affine form as\n\u23a7 \u23aa\u23aa\u23aa\u23aa\u23a8\n\u23aa\u23aa\u23aa\u23aa\u23a9\nV\u0307 = fV + gV \u03c6 h\u0307 = V sin \u03b3 \u03b3\u0307 = f\u03b3 + g\u03b3\u03c6\u03c6 + g\u03b3\u03b4 \u03b4e \u03b8\u0307 = Q Q\u0307 = fq + gq\u03c6\u03c6 + gq\u03b4 \u03b4e\n(4)\nwhere\nfV = (q\u0304SCT (\u03b1) cos \u03b1 \u2212 q\u0304SCD (\u03b1) \u2212 mg sin \u03b3) /m\ngV = q\u0304SCT \u03c6 (\u03b1) cos \u03b1/m\nf\u03b3 = (q\u0304SCL (\u03b1) + q\u0304SCT (\u03b1) sin \u03b1 \u2212 mg cos \u03b3) / (mV )\ng\u03b3\u03c6 = q\u0304SCT \u03c6 (\u03b1) sin\u03b1/ (mV ) , g\u03b3\u03b4 = q\u0304SC\u03b4e L / (mV )\nfq = (zT q\u0304SCT (\u03b1) + q\u0304c\u0304SCM (\u03b1)) /Iyy\ngq\u03c6 = zT q\u0304SCT \u03c6 (\u03b1) /Iyy , gq\u03b4 = q\u0304c\u0304SC\u03b4e M /Iyy . (5)\nWith the regulated outputs y = [eV , eh ]T , the external dynamics are\n[ e\u0307V\ne\u0308h\n]\n=\n[ fV\nfh\n]\n+\n[ gV 0\ngh\u03c6 gh\u03b4\n][ \u03c6\n\u03b4e\n]\n(6)\nwhere\nfh = fV sin \u03b3 + f\u03b3 V cos \u03b3\ngh\u03c6 = gV sin \u03b3 + g\u03b3\u03c6V cos \u03b3\ngh\u03b4 = g\u03b3\u03b4V cos \u03b3. (7)\nWhen the regulated outputs are identically zero, the inputs can be derived by setting the right side of (6) to zero, which are\n[ \u03c60\n\u03b40 e\n]\n=\n[ gV 0\ngh\u03c6 gh\u03b4\n]\u22121 [ \u2212fV\n\u2212fh\n]\n. (8)\nSubstituting (8) into the \u03b8,Q dynamics yields\n\u03b8\u0307 = Q\nQ\u0307 = fq + gq\u03c6\u03c60 + gq\u03b4 \u03b4 0 e . (9)\nThis is the zero dynamics corresponding to the regulated outputs y = [eV , eh ]T , which represents the remaining dynamics"
        ]
    },
    {
        "image_filename": "designv10_5_0002754_j.jfranklin.2019.04.017-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002754_j.jfranklin.2019.04.017-Figure1-1.png",
        "caption": "Fig. 1. The directed graphs of a group of one leader L and four followers F1 to F4.",
        "texts": [
            " The communication ranges 0 = 15 (m), R 1 = 9 (m), R 2 = 9 . 5 (m), R 3 = 6 (m), and R 4 = 5 (m), avoidance ranges A = 1 (m), nd avoidance preparation ranges P 1 = 8 . 75 (m) and P 4 = 5 . 4(m) of USVs are adopted. The nitial postures of networked USVs are chosen as q 0, 1 (0) = [0, 0, 0] , q 1 , 1 (0) = [0, \u221210, 0] , 2, 1 (0) = [0, 10, 0] , q 3 , 1 (0) = [ \u22125 , \u221215 , 0] , and q 4, 1 (0) = [ \u22125 , 15 , 0] . From the comunication ranges and initial postures, the initial communication topology is described by he directed graph shown in Fig. 1 (a). Then, the trajectory of the leader is generated by u 4 a [ L k 1 o a f i s a 0 = 0. 2, v\u0304 0 = 0, and r 0 = 0 for 0 \u2264 t < 40(s), u 0 = 0. 2, v\u0304 0 = 0, and r 0 = 0. 1 sin (\u03c0t/ 20) for 0 \u2264 t < 80(s), and u 0 = 0. 2, v\u0304 0 = 0, and r 0 = 0 for t \u226580(s). The desired distances and angles re taken from Park and Yoo [14] . These simulation environments are the same as those of 14] . The design parameters for the proposed output-feedback formation tracker are chosen as i, 1 = diag [2, 2, 5] , L i, 2 = diag [20, 20, 10] , L i, 3 = diag [1 , 1 , 1] , k i, 1 = 0",
            " 2 (b), we can see that there are collisions between F1 and F2 and between F3 nd F4. Since the connection algorithm (24) is not considered for the collision avoidance, the initially non-connected USVs cannot communicate even within the avoidance preparation ranges and their collision avoidance cannot be ensured while achieving the desired formation tracking shown in Fig. 2 (a). Case 2: The proposed output-feedback formation tracker is implemented with the link connectivity algorithm (24) for the initially non-connected USVs. Thus, the initial directed graph ( Fig. 1 (a)) is changed to the directed graph ( Fig. 1 (b)) during the desired formation tracking. Since by using Eq. (24) , the communication links of the initially non-connected USVs are provided within the avoidance preparation ranges, they avoid the collision. The formation tracking results are depicted in Figs. 3\u20136 . From Fig. 3 (a) and (b), one can see that the initially non-connected USVs do not violate their minimum avoidance ranges (i.e., the condition (II) of Problem 1 is achieved). Fig. 4 (a) and (b) show the relative distances between the initially connected USVs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003722_s10846-020-01237-6-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003722_s10846-020-01237-6-Figure1-1.png",
        "caption": "Fig. 1 Free body diagram of a CR model by Cosserat rod",
        "texts": [
            " In section 5, the application of the controller using the CR model is discussed, and simulation results are presented. In this section, the design of experiments based on the Taguchi method and evolutionary algorithms are used to obtain the values for learning parameters and fuzzy membership structures, respectively. The conclusion of the paper is presented in section 5. All the symbols used have been defined in the Appendix (Nomenclature). Although a model-free control policy is presented, a mechanical model is required to initiate the process. The Cosserat rod model (Fig. 1) [6] will be used due to its accuracy and the straightforward computational procedure. The principle equations in this method are n 0 s\u00f0 \u00de \u00bc 0; m 0 s\u00f0 \u00de \u00fe P 0 s\u00f0 \u00de n s\u00f0 \u00de \u00bc 0; \u00f01\u00de where n, m, and P indicate force, moment, and final position vectors of the CR, respectively. A complete nomenclature is presented in the Appendix. The prime operation shows a derivative with respect to the length of the robot [50] (Fig. 1). The forward kinematics of the CR can be described as follows, n1 0 \u00fe k2n3\u2212\u03c4n2 \u00bc 0; n2 0 \u2212k1n3 \u00fe \u03c4n1 \u00bc 0; n3 0 \u2212k2n1 \u00fe k1n2 \u00bc 0; m1 0 \u00fe k2m3\u2212\u03c4m2\u2212n2 \u00bc 0; m2 0 \u2212k1m3 \u00fe \u03c4m1 \u00fe n1 \u00bc 0; m3 0 \u00fe k1m2\u2212k2m1 \u00bc 0; \u00f02\u00de EI2k2 0 \u00fe EI2\u2212GJ\u00f0 \u00dek1\u03c4\u2212EI1\u03c4u1 \u00fe k1GJu3 \u00fe n1 \u00bc 0; EI2k2 0 \u00fe EI2\u2212GJ\u00f0 \u00dek1\u03c4\u2212EI1\u03c4u1 \u00fe k1GJu3 \u00fe n1 \u00bc 0; GJ\u03c4 0 \u00fe EI2\u2212EI1\u00f0 \u00dek1k2 \u00fe EI1k2u1\u2212EI2k1u2 \u00bc 0; \u00f03\u00de \u03b8 0 \u03c8 0 \u03c6 0 24 35 \u00bc cos\u03c6 \u2212sin\u03c6 0 sin\u03c6=cos\u03b8 cos\u03c6=cos\u03b8 0 sin\u03c6tan\u03b8 cos\u03c6tan\u03b8 1 24 35 k1 k2 \u03c4 24 35; x 0 y 0 z 0 24 35 \u00bc \u2212cos\u03c6sin\u03c8\u00fe sin\u03c6sin\u03b8cos\u03c8 sin\u03c6sin\u03c8\u00fe cos\u03c6sin\u03b8cos\u03c8 cos\u03b8cos\u03c8 24 35: \u00f04\u00de Fig. 5 Control effort strategy of a 2-DOF CR at the end of learning for the second controller (u3) In (2) to (4), the Darboux vector is specified by\u03c9(S) = [k1 k2 \u03c4]Tas shown in Fig. 1, and the Euler angles are represented by \u03b8, \u03c8, and \u03c6. Later on in this paper, the initial values of k1, k2, and \u03c4 (three main curvatures) are considered as u1, u2,and u3 as the control parameters. As it will be shown in Fig. 2, these control outputs will be converted to tendon tension parameters by the tendon driver. The constant parameters used in this paper are given in Table 1 (with the parameters defined in the Appendix and units are all metric unless specified otherwise). In any RL-based control design, there is a trade-off between the accuracy and efficiency of reaching NE [45, 46]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000492_tie.2011.2168795-Figure32-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000492_tie.2011.2168795-Figure32-1.png",
        "caption": "Fig. 32. Positions of points at which the trajectories of vector B are shown in Fig. 33.",
        "texts": [],
        "surrounding_texts": [
            "This paper has presented a no-load core loss analysis of three-phase energy-saving small-size induction motors fed by sinusoidal voltage, using a combination of the timestepping FEM and an analytical approach, which offers rapid computation. In this field-circuit approach, the distribution and changes in magnetic flux densities of the motor are computed using a time-stepping FEM. A DFT is then used to analyze the magnetic flux density waveforms in each element of the model obtained from several snapshots taken over a voltage cycle of the time-stepping solution. Rotational aspects of the field are accounted for by introducing a correction to the first harmonic of the alternating losses. The core losses in each element are evaluated using the specific core loss expression, in which the frequency-dependent parameters and flux are derived from a test conducted on a sample laminated ring core. The results are compared with measurements, and good agreement is observed for both methods. However, the field-circuit timestepping method is quite time consuming, so for optimization, the rapid analytical method is to be recommended. APPENDIX A FLUX DENSITY HARMONICS See Figs. 25\u201327. APPENDIX B CORE LOSS SPECTRUM See Figs. 28 and 29."
        ]
    },
    {
        "image_filename": "designv10_5_0003624_j.aej.2020.09.059-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003624_j.aej.2020.09.059-Figure8-1.png",
        "caption": "Fig. 8 Residual errors of the ITFCZNN and OZNN with periodic noise n(t) = 1.5cost.",
        "texts": [],
        "surrounding_texts": [
            "A new ITFCZNN model for finding the inversion of DMI (1) is designed in Section 3, and detailed analysis of the ITFCZNN model with various interference and noises is introduced in Section 4. In this section, two numerical simulation verifications of the ITFCZNN for finding finding the inversion of DMI and one robotic application are presented. In addition, the OZNN activated by three commonly used AFs in (5)\u2013(7) (LAF, PSAF and SBPAF) for solving DMI problems are also provided for comparison purposes. Example 1. Second-order dynamic matrix inversion (DMI) In order not to lose generality, the time-varying coefficients of the DMI (1) are set as follows: A\u00f0t\u00de \u00bc cos3t sin3t sin3t cos3t B\u00f0t\u00de \u00bc 1 0 0 1 Starting from an arbitrary initial state X(0) 2 [ 1.5, 1.5]2 2, the ITFCZNN (10) and the OZNN (4) activated by other three commonly used AFs in (5\u20137) are applied to compute the above SODMI (1) with four different interference and noises in Table 1. Fig. 1 is the neural state solutions X(t) generated by the ITFCZNN (10) and the OZNN (4) activated by other three commonly used AFs in (5)\u2013(7) for solving SODMI (1) with constant noise n(t) = 1.5. Fig. 2 is the simulated residual errors k A\u00f0t\u00deX\u00f0t\u00de I kFof the ITFCZNN and OZNN for solving SODMI (1) with constant noise n(t) = 1.5. Figs. 3\u20135 present the simulated residual errorsk A\u00f0t\u00deX\u00f0t\u00de I kFof the Fig.2 Residual errors of the ITFCZNN and OZNN with constant noise n(t) = 1.5. Please cite this article in press as: J. Jin, J. Gong, An interference-tolerant fast convergence zeroing neural network for dynamic matrix inversion and its application to mobile manipulator path tracking, Alexandria Eng. J. (2020), https://doi.org/10.1016/j.aej.2020.09.059 ITFCZNN (10) and the OZNN model (4) for solving SODMI (1) with the following three other types of noises: PN n (t) = 1.5cost, VN n(t) = exp(-t) and NVN n(t) = 0.1 t. Following Figs. 1\u20135, it can be observed that the external noises seriously deteriorate the convergence performance of the OZNN model (5), and they cannot obtain the accurate solutions of the SODMI (1) when attacked by external noises. However, the ITFCZNN (10) always converges very quickly to the theoretical solutions of the SODMI (1) under various noise disturbances, which demonstrates the better robustness and accurateness of the ITFCZNN (10). Example 2. Third-order dynamic matrix inversion (TODMI) In order to further verify and compare the effectiveness and robustness of the ITFCZNN (10) and the OZNN (4) activated by other three commonly used AFs in (5)\u2013(7) for solving high-order DMI, the following TODMI is considered, and the dynamic coefficient matrices of DMI (1) are simply set below: Please cite this article in press as: J. Jin, J. Gong, An interference-tolerant fast converg mobile manipulator path tracking, Alexandria Eng. J. (2020), https://doi.org/10.10 A\u00f0t\u00de \u00bc 6\u00fe sin2t sin2t 0:5sin2t cos2t 6\u00fe sin2t sin2t 0:5cos2t cos2t 6\u00fe sin2t 0 B@ 1 CAB\u00f0t\u00de \u00bc 1 0 0 0 1 0 0 0 1 0 B@ 1 CA Starting from an arbitrary initial state X(0) 2 [ 1.5, 1.5]2 2, the ITFCZNN (10) and the OZNN (4) activated by other three commonly used AFs in (5\u20137) are applied to compute the above TODMI (1) with four different interference and noises in Table 1. Fig. 6 is the neural state solutions X(t) generated by the ITFCZNN (10) and the OZNN (4) activated by other three commonly used AFs in (5)\u2013(7) for solving TODMI (1) with constant noise n(t) = 1.5. Fig. 7 is the simulated residual errors k A\u00f0t\u00deX\u00f0t\u00de I kFof the ITFCZNN and OZNN for solving SODMI (1) with constant noise n(t) = 1.5.Figs. 8\u201310 present the simulated residual errorsk A\u00f0t\u00deX\u00f0t\u00de I kFof the ITFCZNN (10) and the OZNN model (4) for solving TODMI (1) with the following three other types of noises: PN n (t) = 1.5cost, VN n(t) = exp(-t) and NVN n(t) = 0.1 t. N (4) activated by other three commonly used AFs in (5)\u2013(7) for ence zeroing neural network for dynamic matrix inversion and its application to 16/j.aej.2020.09.059 Following Figs. 6\u201310, it can be also observed that the external noises seriously deteriorate the convergence performance of the OZNN model (4), and they cannot obtain the accurate solutions of the TODMI (1) when attacked by external interference and noises. However, the ITFCZNN (10) always converges very quickly to the theoretical solutions of the TODMI (1) under various noise disturbances, which further demonstrates the better robustness and accurateness of the ITFCZNN (10). In summary, based on the above two simulation examples, we can conclude that the presented ITFCZNN (10) are effective on solving DMI problems. More importantly, comparing with the OZNN models, the ITFCZNN (10) has the advantages of better robustness, effectiveness and fixed-time convergence. Example 3. Movable robotic manipulator (MRM) application Please cite this article in press as: J. Jin, J. Gong, An interference-tolerant fast converg mobile manipulator path tracking, Alexandria Eng. J. (2020), https://doi.org/10.10 In order to further validate the applicability of the proposed ITFCZNN model, positioning control of a MRM is provided in this part. The geometric model of the MRM was introduced in Ref. [39]. According to Ref. [39], the position level kinematics equation of the MRM is presented as follow: R\u00f0t\u00de \u00bc n\u00f0H\u00f0t\u00de\u00de \u00f018\u00de According to Eq. (18), the velocity level kinematics equation of the MRM can be depicted as: R \u00f0t\u00de \u00bc J\u00f0H\u00deH \u00f0t\u00de \u00f019\u00de where R(t) represents the position vector of the end-effector, n ( ) is a mapping function, matrix H (H = [u,hT]T) 2 Rn+2 consists of the angle vector of the platform u (u = [u1,ur] T) and the joint space vector h (h = [h1,h2,. . .. . .,hn] T, and the Jacobian matrix J(H)=\u0259n(H)/\u0259H. ence zeroing neural network for dynamic matrix inversion and its application to 16/j.aej.2020.09.059 Generally, R \u00f0t\u00deis known, and H \u00f0t\u00de is unknown in (19), which means when the motion tracking task of the endeffector is allocated, the positioning control of MRM can be realized by solving a inverse kinematic equation in (19). Eq. (19) can be seen as a time-varying LME (TVLME), and the proposed ITFCZNN can be applied to solve this TVLME. The ITFCZNN model (10) and the OZNN activated by SPBAF are both applied to the positioning control of MRM. The positioning control model are shown as follows: J\u00f0H\u00f0t\u00de\u00deH \u00bc R \u00f0t\u00de cU\u00f0R\u00f0t\u00de f\u00f0H\u00f0t\u00de\u00de\u00de \u00fe n\u00f0t\u00de \u00f020\u00de J\u00f0H\u00f0t\u00de\u00deH \u00bc R \u00f0t\u00de cC\u00f0R\u00f0t\u00de f\u00f0H\u00f0t\u00de\u00de\u00de \u00fe n\u00f0t\u00de \u00f021\u00de Eqs. (20) and (21) are the positioning control models of the MRM using the RFCZNN and OZNN activated by SPBAF, respectively. n(t) = 0.05 t stands for non-vanishing noise. Let us allocate a double circle for the MRM to track, and the initial state of the MRM is set as H(0) = [0, 0, p/6, p/3, p/6, p/3, p/3, p/3]T, and task duration is 30 s. The experiment results are displayed in Figs. 11 and 12. Figs. 11 and 12 are the trajectory tracking results of MRM generated by the proposed RFCZNN (20) and the OZNN (21) with non-vanishing noise n(t) = 0.05 t, respectively. Following Figs. 11 and 12, it is clear that the end-effector of the MRM controlled by the proposed ITFCZNN completes the Please cite this article in press as: J. Jin, J. Gong, An interference-tolerant fast converg mobile manipulator path tracking, Alexandria Eng. J. (2020), https://doi.org/10.10 circle path tracking exactly, and its tracking errors are less than 0.09 10 5 m with non-vanishing noise disturbance, while the the end-effector of the MRM controlled by the OZNN fails to finish the circle path tracking task. The successful circle-tracking task further validates the robustness and effectiveness of the proposed ITFCZNN."
        ]
    },
    {
        "image_filename": "designv10_5_0000509_1.4005952-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000509_1.4005952-Figure3-1.png",
        "caption": "Fig. 3 Geometry of a typical roller",
        "texts": [
            " In the same way the original gap between the two surfaces can be given roughly by f \u00f0x; y; t\u00de \u00bc x2 2Rx \u00fe y2 2Ry (2) However, in reality the contact geometry of mechanical components is often more complicated. Typical \u201cline contact\u201d components, such as gear teeth and bearing rollers, are usually designed to have a crown along the contact length direction in order to accommodate possible misalignment, fabrication errors, and nonuniform load distribution. Also, the contact length is always finite with round corners or chamfers at its two ends to minimize edge stress concentration. Therefore, the roller contact geometry illustrated in Fig. 3 appears to be more generic, precise, and practical. The mathematic simplification based on the Taylor expansion series may not be necessary because the realistic geometry is already sufficiently simple and easy to model. Definitions of relevant geometric parameters can also be found in Fig. 3. In the present study a roller in contact with a plane is assumed. Contact between two rollers can be readily handled in a similar way. It is important to note that both idealized line contact and point contact shown in Figs. 1 and 2 are actually special cases of the roller contact illustrated in Fig. 3. The roller contact EHL model is a modification of the deterministic mixed EHL model originally presented by Zhu and Hu [19], and Hu and Zhu [20], and continuously modified by Wang et al. [21], Liu et al. [22], Zhu [23], and others. Most recently, it has been further improved by Zhu et al. [24] to consider possible surface evolution due to wear, and by Ren et al. to take into account the effect of plastic deformation when necessary [25,26]. The model is capable of simulating the entire spectrum of lubrication regimes, from full-film and mixed lubrication to dry contact, with a unified formulation and numerical approach",
            " (4). More precisely defined contact geometry is certainly needed in the EHL modeling. Note that the original geometry, f(x, y, t), consists of simple shapes and their combination, to be used and shown in later sections. Its detailed mathematic descriptions for various types of roller geometry are sufficiently simple in nature but possibly lengthy, so we will not present them all here. However, giving a typical example may still be a good idea. For a crowned roller with rounded end corners (see Fig. 3), one can have f \u00f0x; y; t\u00de \u00bc Rx ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi D2 x2 p (10) where D \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 y y2 q \u00f0Ry Rx\u00de; if yj j L 2 lc or D \u00bc Rc \u00fe ffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2 d2 p d \u00bc yj j yc yc \u00bc L 2 lc 1 r Ry Rc \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0Ry r\u00de2 y2 c q \u00f0Ry Rx\u00de if L 2 lc < yj j L 2 Figure 4 demonstrates a numerical example according to Eqs. (4) and (10), in which the machined surface RMS roughness is 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003929_j.apsusc.2020.146393-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003929_j.apsusc.2020.146393-Figure6-1.png",
        "caption": "Fig. 6. (a) Schematic of the process principle and (b) sinusiodal laser power modulation.",
        "texts": [
            " To produce these samples, discs are cut off from a larger rod so that all samples come from the same batch of material. These rectangular discs are then milled and on both sides to achieve a plane parallelism in the order of 10 \u00b5m. The distance between milling grooves is approx. 90 \u00b5m (Fig. 5). Relevant thermo-physical properties of AISI H11 that are used for material related calculations in this work are listed as followed in Table 2. The laser power is modulated sinusoidally at the mean laser power PM with a laser power amplitude of PA and a spatial wavelength \u03bb (Fig. 6b). Simultaneously to the laser power modulation, a 3D laser scanning system guides a focused laser beam with a diameter of dL over a workpiece surface. The laser beam travels unidirectionally over the surface at a defined scanning velocity vscan. To achieve an areal surface structuring subsequent laser tracks are positioned parallel to each other in the distance of the track offset dy, which is usually significantly smaller than the laser beam diameter (Fig. 6a). The wavelength \u03bb of the laser power modulation is equivalent to the spatial wavelength \u03bb of the resulting surface structures [16]. The main process parameters for the WaveShape process are laser power amplitude PA, laser beam diameter dL and wavelength of laser power modulation \u03bb. The most important parameter for characterization is structure height h. The interrelationship of laser power amplitude and structure height was investigated as they depend on wavelength, laser beam diameter and number of repetitions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000749_tmag.2011.2169805-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000749_tmag.2011.2169805-Figure6-1.png",
        "caption": "Fig. 6. 3-D model of the proposed 24/32-pole DSEG.",
        "texts": [
            " In a load condition, the excitation winding inductance is slightly smaller due to the magnetic saturation. Fig. 5 shows the air-gap flux density distribution of the 24/32- pole DSEG with different excitation currents in the no-load condition. When the excitation current is increased to 10 A, the maximum air-gap flux density reaches almost 1.4 T. B. 3-D FEA In order to provide a more accurate calculation and verification, the 3-D FEA model of the 24/32-pole DSEG is also established. We develop the quarter FEA model by setting a master-slave boundary, as shown in Fig. 6, so the computational complexity is reduced. Fig. 7 shows the 3-D meshed model of the proposed DSEG. Fig. 8 presents the flux density vector in stator and rotor when the electrical MMF is 1000 A.T, and shows the distinct flux path and saturated condition of the magnetic core. When the DSEG is used as a direct-driven wind turbine generator, many more turns of armature windings are needed because of the low operation speed, which should cause higher inductance and resistance of phase windings, and it may negatively affect the output capability of the DSEG"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003082_lra.2020.2983681-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003082_lra.2020.2983681-Figure2-1.png",
        "caption": "Fig. 2. Parameters for the theoretical analysis and two actuation modes. A: geometric parameters for a single pouch, B: the angular motion when the pouch is pasted to the PET film. C: the linear motion of serially connected pouches. Pouches were driven with a heat gun in B and C.",
        "texts": [
            " 1 left, the actuator at the low temperature is in a thin sheet shape. When the temperature gets higher than 34 \u25e6C, in turn, the liquid evaporates inside the pouch and thereby the whole structure inflates in the same way as Pouch Motors, as shown in Fig. 1 right. By sealing a pneumatic port conventionally connected to the pneumatic channel, the actuators can be driven by diverse heat sources without bulky tubes. Next, we show two basic actuation modes (linear and angular motion) of our proposed actuators inheriting from Pouch Motors in Fig. 2. The volume V , linear force F , and the angular torque M in Fig. 2B, C have already been analyzed theoretically in [1], [2] as V (\u03b8) = L0 2D 2 ( \u03b8 \u2212 cos \u03b8 sin \u03b8 \u03b82 ) (1) M(\u03b8) = L2 0DP cos \u03b8(sin \u03b8 \u2212 \u03b8 cos \u03b8) 2\u03b83 (2) F (\u03b8) = L0DP cos \u03b8 \u03b8 (3) These equations are also valid for Liquid Pouch Motors. From them, we will derive a suitable amount of liquid in the next section. In this section, we describe two fabrication processes of Liquid Pouch Motors, along with the suitable material selection. Our methods allow both highly customizable prototyping and mass production of rectangular actuators"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000755_s00170-013-5102-y-Figure10-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000755_s00170-013-5102-y-Figure10-1.png",
        "caption": "Fig. 10 a\u2013f The temperature field evolution in weld-based additive manufacturing",
        "texts": [
            " The thermal cycles show a good agreement both for peak temperature and cooling rate. The maximum errors occur around the troughs of the thermal cycle curves, all <30 \u00b0C. The large errors around troughs are due to the deviation of the convection coefficient. As known, natural convection is geometry dependent. The prediction accuracy is apparently improved compared with the published studies on weldbased additive manufacturing [4, 19]. The comparison of the calculated temperature field evolution with the measured result is another demonstration of prediction accuracy. Figure 10a\u2013c depicts the measured temperature distributions 1 s after arc extinguishment in the 5th, 10th, and 15th layers, respectively, while Fig. 10d\u2013f depicts the corresponding calculated temperature distribution in the 5th, 10th, and 15th layers, respectively. A good agreement can be found between the measured and the calculated temperature fields. The deviations of maximum temperature and the sizes of each temperature zone are attributed to two factors: weld beads slightly collapse at the start and end of each layer and measuring error rises at the interface between metal and air due to limited image resolution. A new approach based on inverse analysis and the application of IR imaging is proposed to calibrate input parameters of thermal simulation for weld-based additive manufacturing, thereby improving prediction accuracy"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001225_j.technovation.2011.09.007-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001225_j.technovation.2011.09.007-Figure4-1.png",
        "caption": "Fig. 4. Prototype of the",
        "texts": [
            " The system is designed as a wireless powered active RFID Tag (Tesoriero et al., 2008; Lin et al., 2007) where the inductively coupled link, generated by the implantable and the external antenna, is able to supply enough energy to power the entire system and to provide wireless bidirectional communication through the human skin. Thus it can transmit the information obtained by the nanobiosensor and receive data from the external reader who in turn can configure the implanted electronics and read the data acquired. Fig. 4 shows the final product focusing on its size, main components and the interaction in/out-body. able front-end architecture. implantable device. The availability of in-vivo biomedical devices, such as the one described above, is closely linked to advances in nanobiotechnology. Nanotechnology is expected to have a rapid impact on society (Roco and Bainbridge, 2005): creating future economic scenarios, stimulating productivity and competitiveness, converging technologies, and promoting new education and human development"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000874_j.wear.2013.01.047-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000874_j.wear.2013.01.047-Figure6-1.png",
        "caption": "Fig. 6. Developed running and test system with a loading function for the linear guide.",
        "texts": [
            " 5(c), the simulation result of the turning stiffness has a similar change trend as that of the measured turning stiffness; however, the turning stiffness of the simulation result is slightly larger than the measurement data because deformation of the slider\u2019s opening portion appears inevitably under the action of lateral turning torque. According to Fig. 5(a)\u2013(c), the proposed stiffness calculation of the model is correct and can describe well the contact stiffness of the roller linear guide. The wear experiments of the roller linear guide are performed by using the developed running and test system with loading function. This running and test system is mainly composed of the framework, guide rail, drive unit, loading device, and control cabinet (Fig. 6). The basic working principle of the running and test system is as follows: after exerting the load on the measured linear guide by using the loading device, the drive unit will drive the slider back and forth on the rail of the measured linear guide. This procedure is conducted at regular intervals to measure the height of the upper surface of the slider and obtain the changes in the magnitude of displacement in the Y-axis direction DdV for further analysis on the wear situation of the measured linear guide"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003247_j.isatra.2020.10.039-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003247_j.isatra.2020.10.039-Figure2-1.png",
        "caption": "Fig. 2. 3-D trajectory tracking profile for quadrotors using the developed trategy.",
        "texts": [
            " Additionally, controller parameters are selected as below, such that a smooth and fast profile can be obtained. Kp = diag{0.2, 0.2, 0.2}, Kv = diag{0.5, 0.5, 0.5},K\u0398 = diag{25, 25, 25}, K\u2126 = diag{10, 10, 10}, \u03b11 = 0.8, \u03b12 = 0.7 , \u03b5 = 0.01 Besides, to guarantee an error bounded estimation, the parameters of FTESO are chosen as Lv = 15, L\u2126 = 10, Tu = 0.1, \u03ba1 = \u03ba2 = \u03ba3 = \u03ba4 = \u03ba5 = \u03ba6 = 15, \u03b4 = 0.1. Scenario 1: Feasibility of the developed controller. Simulation results of trajectory tracking under the present module for quadrotors are illustrated in Figs. 2\u20138. Fig. 2 depicts the 3-D ascending flight trajectory tracking results for quadrotors with different initial position cases, and the corresponding 2- D trajectory tracking profiles are plotted in Fig. 3, it follows from Figs. 2\u20133 that the preassigned command can be followed accurately for quadrotors irrespective of disturbances and various initial positions. Furthermore, time responses of position loop for quadrotors under different cases are shown in Fig. 4. It is clearly discerned that the settling times of quadrotors are almost the same no matter whether the initial positions of quadrotors are leaving away from the desired path, indicating that the convergence rate of proposed algorithm is weak related with initial positions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003530_j.addma.2019.01.010-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003530_j.addma.2019.01.010-Figure1-1.png",
        "caption": "Fig. 1. Specimen geometry for a) fatigue and b) tensile tests.",
        "texts": [
            " In addition, to investigate the influence of the surface roughness on the fatigue performance six additional specimens with PBF-surface were tested without further post processing via surface machining. Just the support structures were removed. For this specimens a pattern with stripes with a 10mm width was used and rotated with 79\u00b0 for every new layer. For all specimens no further heat treatment was performed. The process parameters of the rough specimens are displayed in Table 1 as well. The geometry of the tensile and fatigue specimens are displayed in Fig. 1. The resulting density for the used process parameters was examined via metallurgical cross sections of cubes samples as well as with measurements according to the Archimedes method with a density determination kit YDK01 from Sartorius. An exemplary result for the present microstructure was done with etched metallurgical cross section. The hardness measurement was performed according to Vickers (HV1) with a LV-700 AT testing device from LECO with a 10\u00d710 data point matrix. The surface roughness was obtained by means of a 3D Laser Scanning Microscope VK-9700 from Keyence and expressed by the arithmetical mean height Sa of the scale-limited surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001860_1464419315569621-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001860_1464419315569621-Figure1-1.png",
        "caption": "Figure 1. Two-DOF bearing dynamic model.",
        "texts": [
            " The oscillatory nature of the contact load leads to the rolling elements being subjected to squeeze film motion as well as rolling, sliding and tilting motions. Hence, even with a nominally fixed applied dominant radial bearing load, the rolling elements are subject to transient loading. Therefore, a bearing dynamic model is a pre-requisite for the determination of in situ instantaneous contact conditions. With a dominant radially applied bearing load a 2-DOF bearing dynamics model suffices.17 Under this condition any misalignment of rolling elements is ignored in the current analysis. A 2-DOF bearing dynamic model (Figure 1) takes into account the lateral radial excursions of the supported shaft centre from the nominal geometric centre of the bearing. This creates a loaded region in the bearing, where the orbiting rolling elements are subjected to increased loading and contact deformation. Any emerging clearances (unloaded regions) can result in the deviation of roller-to-races contacts from elastohydrodynamic regime of lubrication, which can cause roller\u2013cage collisions, roller skewing and excessive sliding in the contact region. Suitable preloading and/or interference fitting of bearings can guard against these phenomena by yielding a widely spread loaded region. An initial dynamics model can indicate the extent of load share per rolling element at Kungl Tekniska Hogskolan / Royal Institute of Technology on September 10, 2015pik.sagepub.comDownloaded from and aid correct preloading to avoid deviation from elastohydrodynamic conditions. The equations of motion for the 2-DOF bearing model (Figure 1) are M \u20acx \u00bc Xm i\u00bc1 Wicos i \" # Mg\u00fe Fx M \u20acy \u00bc Xm i\u00bc1 Wisin i \" # \u00fe Fy \u00f01\u00de where, i \u00bc 2 fct\u00fe i 2 m , i \u00bc 1! m. These equations ignore the mass of rolling elements, as in most analyses.1,8,11,13,17,18 Otherwise, an m-DOF model would be required with discretisation of the supported shaft mass proportionately to these radial degrees of freedom. In the equations of motion, Fx and Fy are the external excitation forces and i is the instantaneous circumferential angular position of a rolling element i, whilst Wi is its instantaneous contact load"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001902_17452759.2016.1210483-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001902_17452759.2016.1210483-Figure2-1.png",
        "caption": "Figure 2. (a) Image of the block and curved parts with varying fin thicknesses of 1, 5, 10 and 20 mm. (b) Schematic showing the various locations in which the microstructure observation and Vickers microhardness measurements were conducted.",
        "texts": [
            " All parts made in this study were fabricated using the powder bed fusion AM system (A2XX, Arcam AB).The STL data were generated and prepared using Magics, a commercial STL software, and were sliced using the Build Assembler software by Arcam AB. A schematic of the system is shown in Figure 1. The build conditions are: pre-heating stainless steel start plate to 600\u2013650\u00b0C, a controlled vacuum pressure of \u223c2e-3 mBar and build layers of 50 \u00b5m. High-purity helium was used to regulate the vacuum and to prevent powder charging due to the electronbased process. Figure 2 shows the two parts with different 2D-planar geometries, namely the block part and the curve part, respectively. The built height of these two parts is \u223c30 mm. Each part has a fin structure with thicknesses of 1 mm, 5, 10 and 20 mm, respectively. Figure 2 shows a schematic of the built layout and the measurement points that are taken at the same height. The fins of the straight-finned structure were spaced 5 mm apart from one another to minimise the thermal interactions (which is further than 1 mm which was used in a previous study (Hrabe and Quinn 2013) to isolate each part thermally.) The measurement points are located along the fin structures of the two parts. For the straight-finned part, locations 1, 2, 3 and 4 are located 0, 7, 14 and 20 mm away from the main block, respectively",
            " Metallographic and microhardness testing protocol Metallographic measurements were conducted using an optical microscope (OM; ZEISS Axioskop 2 MAT) and a scanning electron microscope (SEM; JEOL JMS-6700F; 20 kV). The quantitative image analysis on the prior \u03b2 columnar grain width and \u03b2 interspacing was carried out using the Image J software. A sampling size of 30 is used for the \u03b2 interspacing and the prior \u03b2 columnar grain width as is statistically needed to obtain a standard normal distribution. SEM samples were sliced into smaller pieces based on different positions as shown in Figure 2 and then hot mounted with phenolic resin. Grinding and polishing were carried out with a Struers Tegramin 25 with the following protocol: a 280# silicon carbide was used for rough grinding followed by a Struers MD-Largo disc with a Struers Allegro/Largo 9 \u00b5m suspension for fine grinding; a chemical polishing process is also used with a Struers MD-Chem disc and a Struers OP-S active oxide polishing suspension; the polished surface is etched in Kroll\u2019s reagent (1\u20133% HF, 2\u20136% HNO3, and 91\u201397% H2O) for 10 s before it is observed using OM and SEM"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000648_978-3-642-17531-2-Figure8.26-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000648_978-3-642-17531-2-Figure8.26-1.png",
        "caption": "Fig. 8.26. Reluctance stepper motor with three phases (on the stator) and four poles (on the rotor): a) schematic configuration (only one set of electrical windings 'A A shown, windings 'B B and 'C C configured equivalently, mechanical step angle S ), initial position with energized coils 'B B , b) final position for energized coils 'A A (magnetic flux flow indicated)",
        "texts": [
            " Layout and principle of operation The toothed armature and pole shoe structure presented in the previous section can be advantageously combined with a temporally and spatially phase-shifted electrical drive. Such configurations with an non-suspended, kinematically guided, toothed reluctance rotor (armature) are known as reluctance stepper motors and have been very successfully adopted with a large variety of implementations in many application areas (Hughes 2006). The electrical excitation can occur in either the stator or the rotor. 550 8 Functional Realization: Electromagnetically-Acting Transducers Fig. 8.26a shows the schematic configuration for a rotational reluctance stepper motors with three electric phases and four rotor teeth. In the example depicted, the stator consists of pairs of poles with field coils connected in series, each pair being independently electrically driven; these are termed electric phases (windings shown for phase 'A A , not shown for phases ', 'B B C C ). The rotor poles (teeth) are spatially arranged such that at any point in time, only one pair of poles can fully overlap a pair of poles on the stator (in the initial position here: poles 2 4 overlap 'B B ). Single-phase drive If, given no current in coils 'B B and 'C C , a current A i is imposed on coils 'A A , this current induces the previously described tangential reluctance forces at rotor poles 1 and 3, respectively directed towards stator poles A and 'A . This then causes the rotor to move in the direction shown by an angle S \u2014the step angle\u2014until poles 1 3 fully overlap 'A A (final position in Fig. 8.26b). Given a sustained current flow A i , this pole position represents a stable rest posi- tion, as further displacement causes the rotor poles to be pulled back into the original pole position. In this rest position, there is a braking moment which depends on the current A i as described by Eq. (8.80). Thus, in this mode of operation, only one phase at a time is supplied with current. The current ( ) A i t \u2014upon whose temporal profile, remarkably, no particular demands need be placed\u2014thus induces a self-controlled step-wise motion of the rotor by a clearly-defined step length S , leading to the self-explanatory term stepper motor. Reference configuration For the mathematical description of the dynamics, consider the configuration shown in Fig. 8.27. This configuration can be interpreted either as the spatially unrolled stator and rotor of the rotational stepper motor in Fig. 8.26 or as the schematic configuration for a linear stepper motor. For a generalized description, thus let the generalized motion coordinate x be introduces, the corresponding assignment for a rotating motor is obvious. Step angle The step angle of a stepper motor depends on the spatial electromechanical layout of the stator and rotor. The mechanical step angle (step length) is given by the following relation (Kallenbach et al. 2008), (Kreuth 1988), (Ogata 1992) S phase RT x N N , (8.85) where is the rotor perimeter (for rotating motors, 2 or 360\u00b0 ), phase N is the number of electrical phases, and RT N is the number of rotor teeth12. 12 For the stepper motor in Fig. 8.26, given 3, 4, 360 phase RT N N , a mechanical step angle 30 S results. 552 8 Functional Realization: Electromagnetically-Acting Transducers Position-dependent force evolution Table 8.1, Type G, already presented the fundamental relationship between rotor position and inductance or force/moment evolution. The considerations below draw upon the situation depicted in Fig. 8.27 for dynamic analysis. At switching cycle [i-1], the rotor is engaged at poles 4 ', 2B B . During the next switching cycle [i], coils 'A A are to be energized",
            " Multi-phase drive One common option for improving the operating dynamics of reluctance stepper motors employs synchronous, coordinated drive of multiple phases, a multi-phase drive. For one, this makes available additional rotor rest positions. Additionally, there is the possibility of passive or active damping of the rotor resonance. This principle has been investigated and implemented in countless varieties (Krishnan 2001), (Miller 2002), (Ogata 1992). Fig. 8.28 shows an example of two-phase drive of the reluctance motor in Fig. 8.26. With a simultaneous energizing of two phases, the magnetic flux forms loops as shown, making available the depicted rest positions. Since, in such cases, there are two reluctance force components acting on the rotor, suitable variation of the phase currents , A B i i at the rest position can be used to generate damping corrective forces, leading to active damping (Krishnan 2001), (Middleton and Cantoni 1986). 556 8 Functional Realization: Electromagnetically-Acting Transducers Another method producing coordinated switching of the field coils consists of a single-phase drive and simultaneous shunting with impedance feedback in other phase windings, known as passive electromagnetic damping (Hughes and Lawrenson 1975), (Russell and Pickup 1996)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000679_j.ymssp.2010.02.003-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000679_j.ymssp.2010.02.003-Figure2-1.png",
        "caption": "Fig. 2. Free body diagram of the force components acting on the gears, in the case of meshing contact along the DLA.",
        "texts": [
            " The known input of the model is the coordinate y0, representing the angular displacement of the electrical drive, assumed to rotate at constant speed. Coordinate y0 is connected to y1 by a torsional spring-damper element that represents the dynamic behaviour of the shaft. The force components acting on each gear are the resultant forces and momentum of the pressure distribution fpxk, fpyk, Mpk, the meshing force fmg, the bearing reactions fbxk, fbyk and the motor driving torque Mm. Thus, in the case of meshing contact along the DLA, the free body diagram of the force components is shown in Fig. 2 and the equations of motion in reference frames OkXkYk, are as follows: m1 \u20acx1 \u00bc fbx1\u00fe fpx1 m1 \u20acy1 \u00bc fby1\u00fe fpy1\u00fe fmg J1 \u20acy1 \u00bc rb1fmg Mp1\u00feMm m2 \u20acx2 \u00bc fbx2\u00fe fpx2 m2 \u20acy2 \u00bc fby2\u00fe fpy2 fmg J2 \u20acy2 \u00bc rb2fmg Mp2 8>>>>>< >>>>>: \u00f0126\u00de In the following sections, the formulations concerning pressure distribution, pressure forces and torques and journal bearing reactions are presented. The pressure rise in the travel from the low to the high pressure region is more or less progressive but it is really conditioned by several dimensional and operational parameters such as the clearances in the radial and axial direction, oil viscosity, outlet pressure and shaft speed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000328_elan.200804529-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000328_elan.200804529-Figure2-1.png",
        "caption": "Fig. 2. Chemical structures of the monomers: a) phenylenediamine (PPD) and b) Nickel tetrasulfonated phthalocyanine (NiTSPc).",
        "texts": [
            " Then on the six electrodes kept for the present study we estimated, considering sensitivity and determination limit parameters, a deviation from the norm/ mean at 10%. MPT was purchased from Sigma-Aldrich, and their 10.000 mg L 1 stock solutions were prepared in acetonitrile and PNP from Fluka as a powder with analytical grade. A 0.2 mol/L of acetate buffer (pH 5.2) was used as the supporting electrolyte. MPT and PNP acetate buffer solutions were prepared in a concentration range between 0.01 to 10 mg L 1. PPD (para-phenylenediamine dihydrochloride) (see Fig. 2a) and NiTSPc (see Fig. 2b) (batch n820526KA) monomers were purchased by Sigma and used as received. Deionized water was obtained from a Elga Labwater ultrapure-water system (Purelab-UVF, Elga, France). A carbon fiber microelectrode was immerged into acetate buffer solution containing the desired concentration of OPs (MPT and/or PNP) in the 10 mL electrochemical cell. A typical cyclic voltammogram of a MPT solution in acetate buffer is reported in the Figure 3. Square-wave voltammetry (SWV) scanning was performed from 1.1 to\u00fe0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002848_s00773-017-0486-2-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002848_s00773-017-0486-2-Figure2-1.png",
        "caption": "Fig. 2 Motion coordinate systems for an underactuated surface vessel. Adapted from [18]",
        "texts": [
            " Many kinds of surface vessel models have been used in path following in different applications. Kinematics and kinetics models from one to six DOFs with environmental disturbance forces and moments have been derived and elaborated in [7]. These models can be used in applications such as course keeping, dynamic positioning, trajectory tracking, and path following. In this section, we focus on models that can be used for path following. The inertial motion coordinate is defined as {n} = {xn, yn}, and the body-fixed coordinate system is defined as {b} = {xb, yb}, as shown in Fig.\u00a02, where U and are the velocity and course in {n}, respectively; and r stand for the vessel heading angle and yaw rate in system {n}, respectively; ( r) and n ( u) stand for rudder angle (rudder torque) and propeller rotation speed (thrust force), respectively. Note that the heading angle is different from the vessel course and = + . The drift angle is equal to 0 only when the sway velocity v = 0 and there is no current. A 6 DOF model for an surface vessel can be denoted as follows [7]: where = [u, v,w, p, q, r]T i s the ve loci ty vector of surge, sway, heave, roll, pitch, and yaw in {b}; r = [ur, vr,wr, pr, qr, rr] T is the relative velocity vector between ship hull and the fluid; = [x, y, z, , , ]T is the position/Euler angles; the model matrices MRB and MA, CRB( ) and CA( ), and D( ) denote inertia, Coriolis, and damping, respectively; is the system input vector of forces and moments; wind and wave are the vectors of forces and moments generated by wind and wave, respectively; g( ) is the vector of gravitational and buoyancy forces; and g0 is the static restoring forces and moments"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000821_j.triboint.2010.02.002-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000821_j.triboint.2010.02.002-Figure2-1.png",
        "caption": "Fig. 2. Apparatus for creation of textures on roller.",
        "texts": [
            " For these conditions the lubrication parameter L, defined as the ratio of minimum film thickness within the smooth contact to reduced surface roughness, is between 0.4 and 0.6. All experiments were carried out at 33 1C. The level of the vibration of the roller was monitored and apparatus was automatically shut off once the vibration level corresponding to the surface damage was reached. One test specimen (roller) can be used up to 12 measurements (one measurement corresponds to one track, see Fig. 1). The roller surface is indented mechanically using a Rockwell indenter (Fig. 2) to obtain micro-dents with well-defined shapes. The indenter had an angle of a cone 1201 and radius of a diamond tip 0.2 mm. The indentation process was fully controlled by a PC with appropriate software. A vertical movement of the indenter was controlled by a step motor whereas the desired load was checked using a strain guage. Rotation of the roller was also controlled by step motor through a clutch. Such a configuration Fig. 3. Types of created textures on ground surfaces of rollers before RCF test"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003304_j.jsv.2019.01.048-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003304_j.jsv.2019.01.048-Figure2-1.png",
        "caption": "Fig. 2. The dynamic model of ball bearing and the definition of angular parameters.",
        "texts": [
            "1(b), the rolling element impacts point Awhen it enters the fault area, and impacts point D when it exits the fault area. The effective circumference angle of faulty region qd is calculated by the fault length L and the bearing geometric parameters. The maximum displacement of the impact excitation DH is calculated by the size of the fault and the bearing geometric parameters, DH0 is the theoretic value of the maximum displacement determined by the relationship between the rolling element and the fault. The dynamic model of ball bearing and the angular parameters are illustrated in Fig. 2, where 4d represents the angle between the fault location and X-axis, q1 is the initial angle between the defined first rolling element and X-axis, and qi indicates the real-time angular position of the i-th rolling element. DH \u00bc DH0 DH0 <H H DH0 H (1) DH0 \u00bc 0:5d \u00f00:5d\u00de2 \u00f00:5min\u00f0L;B\u00de\u00de2 0:5 (2) where d is diameter of the rolling element. Suppose that there is a surface defect on the bearing raceway, the rolling element would produce additional shock vibrationwhen it passes through the defect. Fig",
            " (6) and (7): 8>>>>>>>>>>>>>>>< >>>>>>>>>>>>>>>: 4do 0:5qdo mod\u00f0qi;2p\u00de<4do hi \u00bc DHor sin p qdo \u00f0mod\u00f0qi;2p\u00de 4do \u00fe 0:5qdo\u00de a hj \u00bc hi cos 2\u00f0i z\u00dep z ; j2\u00bd1; z and jsi 4do mod\u00f0qi;2p\u00de 4do \u00fe 0:5qdo hi \u00bc DHor sin p qdo \u00f0mod\u00f0qi;2p\u00de 4do \u00fe 0:5qdo\u00de b hj \u00bc hi cos 2\u00f0i z\u00dep z ; j2\u00bd1; z and jsi otherwise hi \u00bc 0 (11) In order to analyze the dynamic characteristics of the faulty ball bearing, its nonlinear dynamic model is established, where the rolling elements are considered as nonlinear elastic contact elements [27]. According to the coordinate and model of ball bearing shown in Fig. 2, a nonlinear dynamic model of the faulty ball bearing is built based on the two-degree-offreedom dynamic model [23,33]: m\u20acx\u00fe c _x\u00fe Fx \u00bc Qx m\u20acy\u00fe c _y\u00fe Fy \u00bc Qy (12) The interaction force between the rolling elements and the race is derived from the Hertz contact theory [15]: 8>>< >>: Fx \u00bc K Xz i\u00bc1 mi\u00f0X cos qi \u00fe Y sin qi g hi\u00de1:5 cos qi Fy \u00bc K Xz i\u00bc1 mi\u00f0X cos qi \u00fe Y sin qi g hi\u00de1:5 sin qi (13) where g is the initial clearance of the bearing, K is the force-deformation coefficient of normal bearing computed by the Harris's method [35,36], and mi is the judgment factor of the valid contact area of the i-th rolling element which is defined as mi \u00bc 1 X cos qi \u00fe Y sin qi g\u00fe hi 0 X cos qi \u00fe Y sin qi <g\u00fe hi (14) Solving the Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001742_0954406214531943-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001742_0954406214531943-Figure1-1.png",
        "caption": "Figure 1. Schematic of the linear guideway.",
        "texts": [
            " To improve the efficiency of analysis, the full finite element model of guideway was replaced by the component finite element model in this section. At last, the created analytical and component finite element models were applied to analyze the effect of load and preload on the statics characteristics of single ball and whole guideway system. Statics experiments of linear guideway The SHS-35R linear guideway with middle preload was used in the statics experiment to obtain the vertical stiffness of guideway in this section. The guideway is shown in Figure 1 and consists of rail, carriage, retainer, balls, and other accessories. There are four grooves in the guideway. According to the handbook of guideway provided by THK Corporation,11 the relative parameters guideway are listed in Table 1. These parameters will be used in analytical and finite element analysis in the next sections. The test instruments are shown in Figure 2, including a universal testing machine, two dial indicators, and accessories. First, the linear guideway is fixed on the bed of testing machine"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000050_nme.2959-Figure23-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000050_nme.2959-Figure23-1.png",
        "caption": "Figure 23. Experimental y-displacement measurement.",
        "texts": [
            " The computed longitudinal stress field z during welding and after cooling is shown in Figures 20, 21 and 22. These stress maps show that a compressive stress is formed in front of the fusion zone, Copyright 2010 John Wiley & Sons, Ltd. Int. J. Numer. Meth. Engng 2011; 85:84\u2013106 DOI: 10.1002/nme whereas a tensile stress is developed at the back of the fusion zone, and is mainly determined by the thermal expansion effects. The residual y-displacement observed in the plate after the experiment is shown in Figure 23, where flatness measures at the top face are given. This measure can be compared with results from computations given in Figure 24. The value of 0.7 mm observed experimentally can be compared with the value of 0.5 mm calculated by simulation. Very good agreement between the FEM Copyright 2010 John Wiley & Sons, Ltd. Int. J. Numer. Meth. Engng 2011; 85:84\u2013106 DOI: 10.1002/nme results and experimental measurements was observed, which gives confidence in the proposed FE model. In this section, the simulation of the construction of a titanium wall by SMD is presented"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003881_j.mechmachtheory.2020.104047-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003881_j.mechmachtheory.2020.104047-Figure1-1.png",
        "caption": "Fig. 1. The coordinate systems for the dynamic analysis of bearing.",
        "texts": [
            " Meanwhile, we assume that the rolling bearing suffers the combination of axial and radial forces. By solving the proposed multiple-degree-of-freedom (11 DOFs) dynamic model under different situations, we obtain the corresponding vibration response, and analyze the effect of localized defect on the cage and other components. Finally, the correctness and effectiveness of the proposed model is verified by the experimental data. In order to better describe the motion of the rolling elements, two coordinate systems are set up, as shown in the Fig. 1 . One coordinate system ( o - xyz ) is fixed at the mass center of the bearing, and the inner race rotates around the z-axis with the speed of \u03c9 i . In regard to the inner race, its torsional degree of freedom is ignored, while three translational degrees of freedom about the x -axis, y -axis, and z -axis, two rotations degrees of freedom about x -axis and y -axis are considered. The other coordinate system ( o b - x b y b z b ) moves with the rolling element, where z b -axis is parallel with the z-axis of bearing and the coordinate origin ( o ) is attached to the center of rolling elements"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001130_j.jsv.2011.12.025-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001130_j.jsv.2011.12.025-Figure6-1.png",
        "caption": "Fig. 6. Estimation of dimension a in contact loss period.",
        "texts": [
            " While the values set in Refs. [21,22] may be plausible, constant amplitudes represent average contributions. In the present work, the dimension a, which by extension of the Hertz\u2019s theory corresponds to the half-width of the active area, is calculated as the shortest distance between the virtual contact radius (rc) and the tip radius (Rt) of the teeth in contact. Hence, the approach accounts for the variation in the virtual contact position along the tooth profiles and leakage of the lubricant at the tooth tip. Fig. 6 illustrates the calculation of the a dimension during the no-load condition. The variable h0 corresponds to the tooth separation during contact disappearance. Actually, this distance is determined by the dynamic response of the gear set. Therefore, the real problem is the estimation of the lower limit of h0. Calculations not included in this paper demonstrated the drastic influence of this limit on the resulting damping, and thus, the importance of a realistic estimation. Determining the h0 low limit can be seen as a lubricated impact problem"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001842_s00170-015-7647-4-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001842_s00170-015-7647-4-Figure1-1.png",
        "caption": "Fig. 1 Die setup for hot aluminum extrusion for the manufacturing of a hollow profile: a extrusion die consisting of a die cap and a mandrel and b material flow into the die, schematic (according to [3])",
        "texts": [
            "2367 (X40CrMoV5-3) with strengths of more than 1000 MPa during extrusion temperature [1]. The layout of the die opening depends on the geometry of the desired cross section of the profile. Extrusion dies for the direct extrusion can be divided in flat dies, porthole dies, or bridge dies [2]. Flat dies are the simplest form of dies. Here, the shaping die opening forms the negative of the profile\u2019s cross section. Porthole and bridge dies are geometrically most complex and used for the manufacturing of hollow profiles. These dies consist of a mandrel and a die cap (Fig. 1a). Within the bridge die, the material flow is divided in front of the supporting bridge and the material flows through the feeders. The individual material streams are then rejoined in the welding chamber, and the profile exits the extrusion die (Fig. 1b). In hot metal extrusion, the exit temperature of the extrudate increases immediately after starting the process due to the forming heat and the heat generated by friction and shear in the outer zone of the billet (Fig. 2a) [4]. With increasing extrusion speed or higher extrusion ratio, the temperature increases additionally. If the solidus temperature is exceeded, surface defects like hot cracks occur (Fig. 2b). Especially at high-strength alloys that must be extruded at higher temperatures in order to decrease the flow stress, the melting temperature is significantly lower"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003394_j.compstruct.2020.112698-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003394_j.compstruct.2020.112698-Figure7-1.png",
        "caption": "Fig. 7. Discretization of the geometric model using bidimensional (shell181) elements.",
        "texts": [
            " One IP was employed per layer, providing accurate results for in\u2010 plane failures [52]. One IP was also employed per layer interface with the scope of considering out\u2010of\u2010plane phenomena such as delamination (Fig. 6). Discussion of this approach and comparison with alternatives is provided in [53,54], where a significant reduction in mesh complexity is reported, with good overall precision especially in detecting in\u2010 plane failures. Two\u2010dimensional (shell) elements with dimensions in the range 5\u201330 mm were used, with a total of 36,388 elements and 37,794 nodes (Fig. 7). SHELL181 elements characterized by 4 nodes and 6 degrees of freedom (dof) per node were employed due to their suitability in applications where large rotations or large deformations emerge. Furthermore, SHELL181 elements have also been shown to be appropriate in situations where layers must be discretized, as in the case of modeling composite shells or sandwich constructions [55\u201357]. Specifically, each lay\u2010up was discretized by one specific FE layer. Convergence tests, carried out by progressively increasing the number of discretization layers and elements, exhibited stable outputs, with numerical results in terms of deformation changing by no >3% within the most sensitive areas"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002930_j.triboint.2016.03.017-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002930_j.triboint.2016.03.017-Figure4-1.png",
        "caption": "Fig. 4. Parameters of the ellipsoid and contact zone.",
        "texts": [
            " Therefore, an arbitrary velocity vector at the contact zone can be obtained by this experimental setup. The lubricant parameters in this experiment are: kinematic viscosity 45.8 mm2/s (40 \u00b0C); viscosity \u03b70 0.08 Pa s, and pressure-viscosity coefficient 21.8 GPa 1. The following empirical formulae [9] is employed for the calculation of \u03c4L and G1: G1\u00f0p; T\u00de \u00bc 1:2p 2:52\u00fe0:024T 10 9 \u03c4L\u00f0p; T\u00de \u00bc 0:25G1 \u00f012\u00de The boundary friction coefficient is 0.13 measured by experiment. The experiments were carried out with ellipsoid producing k\u00bc2 (Fig. 4a) by applying a load of 100 N, which gives maximum Hertzian pressures of Ph\u00bc0.73 GPa. Both the disc and ellipsoid are made of steel, and the modulus of elasticity and Poisson's ratio are E\u00bc210 GPa and 0.3, respectively. The machined surface profiles of the ellipsoid and disk measured by white-light interferometer are shown in Fig. 5, which are used in the mixed EHL model for predicting the friction coefficient. The solution domain in the numerical study is defined as 2rXr2 and 2rYr2. The computational grid covering the domain consists of 321 321 nodes equally spaced, corresponding to dimensionless mesh spacing of \u0394x1\u00bc0.0125, \u0394y1\u00bc0.0125. The obtained comparison results are summarized in Fig. 6. In Fig. 6 (a), the value of surface velocity of ellipsoid v is equal to the velocity of disk u, and the value of entraining velocity ue with fixed direction \u03b8\u00bc22.5\u00b0 (as shown in Fig. 4b) is changed in a wide range from 0.1 m/s to 10 m/s. In Fig. 6(b), the directions of v and u remain unchanged, the value of entraining velocity ue is fixed at 1 m/s but the direction angle \u03b8 varies from 7.5\u00b0 to 37.5\u00b0. And in Fig. 6(a) and (b), the red line represents the simulation results through the friction calculation model and the dots are the results obtained by experiment. The friction coefficient f under each operating condition was measured three times. It is observed that, as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000035_tie.2010.2095392-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000035_tie.2010.2095392-Figure7-1.png",
        "caption": "Fig. 7. Schematic of posture control.",
        "texts": [
            " Some of the previous methods require information on the pipes to move; this information is collected using vision sensors or the electrical load of the motor [10], [12]. However, PAROYS-II does not require any information about the curved pipe for its locomotion. The posture control allows the robot to balance itself while moving through any pipe, including curved pipes. When the robot moves through a straight pipe and each track has the same velocity, the posture of the robot is aligned. However, if the robot must overcome obstacles or moves through a curved pipe, the posture of the robot is not aligned, as shown in Fig. 7. Although the posture of PAROYS-II is misaligned, revolute joints keep the tracks in contact with the inner walls of the pipes. The amount of misalignment is determined by the rotation angle of the track module, as described in Section III-A. The robot compares the rotation angle \u03c6 of each track. The tracks move at different velocities until all of the rotating angles \u03c6 are identical, indicating that the posture of PAROYS-II is aligned. For instance, the track behind the center module has faster velocity than that of the leading track in Fig. 7. These different velocities are maintained until the posture of the robot is aligned. C. Inclination of Pipe Estimation The center module of PAROYS-II is not always parallel to the pipe, as mentioned before. Because the accelerometer is attached to the center module, its detection of the pipe\u2019s inclination with respect to the ground is impossible when the posture is misaligned. That is why estimating the relative orientation of the robot to the pipe is necessary. Section P crosses the three contact points and the center of the robot, as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003601_j.ast.2020.105995-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003601_j.ast.2020.105995-Figure1-1.png",
        "caption": "Fig. 1. Two quadrotor slung load system.",
        "texts": [
            " In this case, the five bodies are the two quadrotors, the two rigid bars connecting the quadrotors to the load and the load itself; the four joints are spherical joints through which the bars connect the quadrotors to the load. The mathematical model presents a realistic full nonlinear 3-D model of the entire system, as the quadrotors, rigid bars and load all have masses and inertias. The suspension point in the mathematical model is also not at the centre of mass of the quadrotors. The bars are also connected to the load at two separate points through spherical joints. Fig. 1. In modelling the quadrotor slung load system, it is assumed that the bars connecting the load to the quadrotors are stiff. Spherical joints connect the bars to the quadrotor and load and thus the joint torques are assumed to be zero. The rotational equations for the two quadrotors in their own respective quadrotor fixed reference frame can be written as [27]: J1\u03c9\u03071 = T 1 + T S 1 \u2212 \u03c9\u00d7 1 J1\u03c91 + r\u00d7 1 C1 N F S 1 J2\u03c9\u03072 = T 2 \u2212 C2 c2 T S 4 \u2212 r\u00d7 2 C2 N F S 4 \u2212 \u03c9\u00d7 2 J2\u03c92 (1) Similarly, the rotational equations of motion of the load and cables in their own respective load and cable fixed frame of reference can be written as: Jc1\u03c9\u0307c1 =T c1 \u2212 Cc1 1 T S1 \u2212 r\u00d7 c11 Cc1 N F S1 + T s2 + r\u00d7 c12 Cc1 N F S2 \u2212 \u03c9\u00d7 c1 Jc1\u03c9c1 J L\u03c9\u0307L =T L \u2212 C L c1 T s2 \u2212 r\u00d7 L1 C L N F S2 + T s3 + r\u00d7 L2 C L N F S3 \u2212 \u03c9\u00d7 L J L\u03c9 L Jc2\u03c9\u0307c2 =T c2 \u2212 Cc2 L T S3 \u2212 r\u00d7 c21 Cc2 N F S3 + T s4 + r\u00d7 c22 Cc2 N F S4 \u2212 \u03c9\u00d7 c2 Jc2\u03c9c2 (2) The translational equations written in the inertial frame of reference are: m1v\u0307 1 = F 1 + F S1 mc1 v\u0307 c1 = F c1 + F s2 \u2212 F S1 mLv\u0307 L = F L + F S3 \u2212 F S2 mc2 v\u0307 c2 = F c2 + F S4 \u2212 F S3 m2v\u0307 2 = F 2 \u2212 F S4 (3) The constraint equations can then be obtained by equating the joint accelerations: v S1 = v 1 + \u03c9\u00d7 1 r1 = v c1 + \u03c9\u00d7 c1 rc11 v\u0307 1 + C N 1 \u03c9\u0307\u00d7 1 r1 + C N 1 \u03c9\u00d7\u00d7 1 r1 = v\u0307 c1 + C N c1 \u03c9\u0307\u00d7 c1 rc11 + C N c1 \u03c9\u00d7\u00d7 c1 rc11 \u21d2 v\u0307 c1 \u2212 v\u0307 1 = C N 1 \u03c9\u0307\u00d7 1 r1 + C N 1 \u03c9\u00d7\u00d7 1 r1 \u2212 C N c1 \u03c9\u0307\u00d7 c1 rc11 \u2212 C N c1 \u03c9\u00d7\u00d7 c1 rc11 v S2 = v c1 + \u03c9\u00d7 c1 rc12 = v L + \u03c9\u00d7 L r L1 v\u0307 c1 + C N c1 \u03c9\u0307\u00d7 c1 rc12 + C N c1 \u03c9\u00d7\u00d7 c1 rc12 = v\u0307 L + C N L \u03c9\u0307\u00d7 L r L1 + C N L \u03c9\u00d7\u00d7 L r L1 \u21d2 v\u0307 L \u2212 v\u0307 c1=C N c1 \u03c9\u0307\u00d7 c1 rc12+C N c1 \u03c9\u00d7\u00d7 c1 rc12 \u2212 C N L \u03c9\u0307\u00d7 L r L1 \u2212 C N L \u03c9\u00d7\u00d7 L r L1 v S3 = v L + \u03c9\u00d7 L r L2 = v c2 + \u03c9\u00d7 c2 rc21 v\u0307 L + C N L \u03c9\u0307\u00d7 L r L2 + C N L \u03c9\u00d7\u00d7 L r L2 = v\u0307 c2 + C N c2 \u03c9\u0307\u00d7 c2 rc21 + C N c2 \u03c9\u00d7\u00d7 c2 rc21 \u21d2 v\u0307 c2 \u2212 v\u0307 L=C N L \u03c9\u0307\u00d7 L r L2+C N L \u03c9\u00d7\u00d7 L r L2 \u2212 C N c2 \u03c9\u0307\u00d7 c2 rc21 \u2212 C N c2 \u03c9\u00d7\u00d7 c2 rc21 v S4 = v c2 + \u03c9\u00d7 c2 rc22 = v 2 + \u03c9\u00d7 2 r2 v\u0307 c2 + C N c2 \u03c9\u0307\u00d7 c2 rc22 + C N c2 \u03c9\u00d7\u00d7 c2 rc22 = v\u0307 2 + C N 2 \u03c9\u0307\u00d7 2 r2 + C N 2 \u03c9\u00d7\u00d7 2 r2 \u21d2 v\u0307 2 \u2212 v\u0307 c2 = C N c2 \u03c9\u0307\u00d7 c2 rc22 + C N c2 \u03c9\u00d7\u00d7 c2 rc22 \u2212 C N 2 \u03c9\u0307\u00d7 2 r2 \u2212 C N 2 \u03c9\u00d7\u00d7 2 r2 (4) In vector-matrix form, all the above equations may be written as: \u23a1 \u23a3 A 0 R 0 M U RT U T 0 \u23a4 \u23a6 \u23a7\u23a8 \u23a9 x\u0307 y\u0307 f \u23ab\u23ac \u23ad = \u23a7\u23aa\u23a8 \u23aa\u23a9 \u03c4 \u03c5 \u03d1 \u23ab\u23aa\u23ac \u23aa\u23ad (5) where A = \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 J1 0 0 0 0 0 0 Jc1 0 0 0 0 0 0 J L 0 0 0 0 0 0 Jc2 0 0 0 0 0 0 J2 0 0 0 0 0 0 m1 I \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 , R = \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 \u2212r\u00d7 1 C1 N 0 0 0 r\u00d7 c11 Cc1 N \u2212r\u00d7 c12 Cc1 N 0 0 0 r\u00d7 L1 C L N \u2212r\u00d7 L2 C L N 0 0 0 r\u00d7 c21 Cc2 N r\u00d7 c22 Cc2 N 0 0 0 r\u00d7 2 C2 N \u2212I 0 0 0 \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 (6) M = \u23a1 \u23a2\u23a2\u23a2\u23a3 mc1 I 0 0 0 0 mL I 0 0 0 0 mc2 I 0 0 0 0 m2 I \u23a4 \u23a5\u23a5\u23a5\u23a6 , U = \u23a1 \u23a2\u23a2\u23a3 I \u2212I 0 0 0 I \u2212I 0 0 0 I \u2212I 0 0 0 I \u23a4 \u23a5\u23a5\u23a6 (7) \u03c4 = \u23a7\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a9 T 1 \u2212 \u03c9\u00d7 1 J1\u03c91 + T S 1 T c1 \u2212 \u03c9\u00d7 c1 Jc1\u03c9c1 \u2212 Cc1 1 T S1 + T s2 T L \u2212 \u03c9\u00d7 L J L\u03c9L \u2212 C L c1 T s2 + T s3 T c2 \u2212 \u03c9\u00d7 c2 Jc2\u03c9c2 \u2212 Cc2 L T S3 + T s4 T 2 \u2212 \u03c9\u00d7 2 J2\u03c92 \u2212 C2 c2 T S 4 F1 \u23ab\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23ac \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23ad , \u03c5 = \u23a7\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23a9 F c1 F L F c2 F 2 \u23ab\u23aa\u23aa\u23aa\u23ac \u23aa\u23aa\u23aa\u23ad , \u03d1 = \u23a7\u23aa\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23aa\u23a9 C N 1 \u03c9\u00d7\u00d7 1 r1 \u2212 C N c1 \u03c9\u00d7\u00d7 c1 rc11 C N c1 \u03c9\u00d7\u00d7 c1 rc12 \u2212 C N L \u03c9\u00d7\u00d7 L r L1 C N L \u03c9\u00d7\u00d7 L r L2 \u2212 C N c2 \u03c9\u00d7\u00d7 c2 rc21 C N c2 \u03c9\u00d7\u00d7 c2 rc22 \u2212 C N 2 \u03c9\u00d7\u00d7 2 r2 \u23ab\u23aa\u23aa\u23aa\u23aa\u23aa\u23ac \u23aa\u23aa\u23aa\u23aa\u23aa\u23ad (8) x\u0307 = \u23a7\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a9 \u03c9\u03071 \u03c9\u0307c1 \u03c9\u0307L \u03c9\u0307c2 \u03c9\u03072 v\u0307 1 \u23ab\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23ac \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23ad , y\u0307 = \u23a7\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23a9 v\u0307 c1 v\u0307 L v\u0307 c2 v\u0307 2 \u23ab\u23aa\u23aa\u23aa\u23ac \u23aa\u23aa\u23aa\u23ad , f = \u23a7\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23a9 F S1 F s2 F S3 F S4 \u23ab\u23aa\u23aa\u23aa\u23ac \u23aa\u23aa\u23aa\u23ad (9) x\u0307, y\u0307 and f can be decoupled in Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003199_j.mechmachtheory.2019.103576-Figure15-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003199_j.mechmachtheory.2019.103576-Figure15-1.png",
        "caption": "Fig. 15. Calculation of an arbitrary point on the usable flank of the face-gear: (a) Points on existing flank lines ( \u03b8s i = const, i = 1 . . . k ) are used as start values for determination of point at defined distance to face-gear axis l \u22172 and z-coordinate z \u22172 ; (b) 3D surface mesh; (c) Measurement grid.",
        "texts": [
            " l \u22172 = \u23a7 \u23a8 \u23a9 \u221a r 2 2 x + r 2 2 y , \u03b3 = 90 \u25e6 cos \u03b3 ( r 2 z + tan \u03b3 \u221a r 2 2 x + r 2 2 y ) , \u03b3 = 90 \u25e6 z \u22172 = r 2 z with r 2 (\u03b8 \u2217 s , \u03c6 \u2217 s ) = (r 2 x , r 2 y , r 2 z ) T , i = 1 . . . k (50) In case of a helical shaper, one part of the concave flank side is calculated by finding the first root of Eq. (19) of meshing and the second root defines the second part. The root which should be used to determine the required point on the usable flank can be judged on the roots used by the adjacent points. If the algorithm does not converge, the other root has to be used. In Fig. 15 , the approach is illustrated on the left side. The possible range of the z-coordinate z \u22172 is given by the adjacent tooth surfaces as well as by the user-defined tooth tip, e.g. in this case, the lower limit is given by the root fillet. Finally, structured surface meshes and measurement grids can be generated efficiently and with the highest accuracy. 3. Face-gear crowning and pinion profile modification Considering the theoretical case of pure rigid body motion, without crowning there will be line contact between the pinion and the face-gear at every instant, but even small alignment errors will cause edge contact during meshing of the gear pair"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000559_icar.2011.6088631-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000559_icar.2011.6088631-Figure1-1.png",
        "caption": "Fig. 1. UAV Flight Mode Conversion Operational Usefulness",
        "texts": [
            " The active tracking of a progressing phenomenon in unknown, unstructured large areas (wildfire surveillance, identification of victims caused by natural disasters such as earthquakes or tsunamis) and the ability to take immediate action in case of an incident, such as the provision of medium-sized items (pharmaceutical The authors are with the Electrical and Computer Engineering Department, University of Patras, Greece papachric@ece.upatras.gr equipment, clean air supplies, etc.), can greatly aid in saving lives in emergency situations. Towards this goal, a special UAV design, enabling the vehicle to execute flight mode conversion manoeuvres, from rotorcraft hovering mode to fixed-wing longitudinal flight mode and conversely as shown in Figure 1, has been selected to be the candidate of our experimental procedure. The vehicle has the ability to modify the angle of its rotors relative to its airframe by rotating them perpendicular to the wing axis. This small-scale Tilt-Rotor (TR) prototype shown in Figure 2, assembled in our laboratory, has been designed with special attention given to its ability to perform full cyclic tilting of the rotors. In this article, the problem of attitude control of the aforementioned vehicle in Bi-Rotor Hovering flight mode is addressed through an experimental procedure"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001117_12_2012_168-Figure17-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001117_12_2012_168-Figure17-1.png",
        "caption": "Fig. 17 Smectic-C elastomer with uniformly aligned director but conical layer distribution subjected to shear strain perpendicular to the director [117] (a) and corresponding reorientation process that produces an SC monodomain (b). Reprinted with permission from [87]. Copyright (2008) American Chemical Society",
        "texts": [
            " A mechanical deformation that is consistent with the biaxial SC phase symmetry and that is able to induce a macroscopic orientation of the layer normal and the director is a shear mechanical field. Hiraoka et al. prepared side chain SC* LSCEs by applying a shear deformation perpendicular to the director followed by chemical crosslinking [117, 118]. For this, the uniaxially aligned elastomer with uniformly oriented director but conical layer distribution is mounted into a mechanical shear setup (Fig. 17a). The elastomer is sheared stepwise at room temperature until the shear angle is consistent with the tilt angle of the SC phase structure. Between each shear step a sufficiently high relaxation time should be maintained to avoid damaging the sample. The mechanical field induces a continuous reorientation of the SC phase structure where the director rotates towards the shear diagonal, while the layer normal takes up the position perpendicular to the shear mechanical field (Fig. 17b). This multi-step orientation process can take up to several hours. It must be avoided that the chemical crosslinking reaction is completed before a macroscopic orientation is induced. If a hydrosilylation reaction is used, the reaction speed is rather slow at ambient temperature. However, it might be advisable to cool the sample during the orientation process to slow down the crosslinking process and to provide enough time for a successful alignment. The sheared state which corresponds to an SC monodomain structure can be fixed permanently by completing the chemical crosslinking reaction at elevated temperatures \u2013 completely analogous to nematic elastomers"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003199_j.mechmachtheory.2019.103576-Figure33-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003199_j.mechmachtheory.2019.103576-Figure33-1.png",
        "caption": "Fig. 33. Face-gear with helical pinion as example for geometry optimization.",
        "texts": [
            " All contact ellipses should be completely within the usable flank of the teeth in order to avoid edge contact. If some contact ellipses are beyond the face-gear inner or outer diameter, face-gear crowning must be increased. Edge contact at the tooth tip can be avoided by increasing the reliefs at the tip or root of the pinion. To illustrate the effect of face-gear crowning and pinion profile modifications on the resulting contact patterns, the optimization for a face-gear drive with helical pinion is performed as an example. This face-gear drive is shown in Fig. 33 . The datasets for the base geometries as well as the optimized face-gear drives are listed in Table 8 . For the base geometries, the pinion is not modified and the initial face-gear crowning is realized by a shaper which has one tooth more than the pinion. The shift of the shaper a ( c ) has been set to reach a working transverse pressure angle of \u03b1w = 30 \u25e6. This is an appropriate value that shifts the contact path in an area that provides space for changes in the path that occur due to alignment errors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002154_1.4037570-Figure14-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002154_1.4037570-Figure14-1.png",
        "caption": "Fig. 14 Optimum build orientation part 2",
        "texts": [
            " A multi-objective was adopted to simultaneously optimize the different objective using normalized importance weights. This research provides a useful tool for the user to decide the build orientation of a part for selective laser melting according to a given load direction and different requirements. The proposed software provides also different visualization and evaluation tools and offers a great freedom to the user as almost all the optimization factors are customizable. Table 8 Optimization results part 2 (see Fig. 14) Dimension 122 128 93 mm Weight 0.288 kg Volume 65,483.58 mm3 YS \u00fe44.67% UTS \u00fe41.1% Elongation 74.28% Ra 10.75 lm BTF 1.1 Build time 16.36 h Build cost 414.17 $ 111011-8 / Vol. 139, NOVEMBER 2017 Transactions of the ASME Downloaded From: http://manufacturingscience.asmedigitalcollection.asme.org/ on 09/14/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use The author is grateful to the \u201cConsortium de recherche et innovation en a eronautique du Qu ebec\u201d (CRIAQ), McGill University, and the Ecole Polytechnique de Montr eal, as well as Bell Helicopter Textron Canada, Bombardier, Edmit, GE Aviation, H eroux-Devtek, Liburdi, MDA and Pratt Whitney Canada for their collaboration and involvement in project MANU601"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001310_s00170-012-3922-9-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001310_s00170-012-3922-9-Figure7-1.png",
        "caption": "Fig. 7 Molding of engine impeller whose shape of every layer changes a lot",
        "texts": [
            " The model with more sophisticated designs and cavities inside is used whose shape of every layer changes a lot. The model comes from the molding with a practical application. As for the model, the design is very complicated, the height is big and the size is also very big, and every layer is complex shape which contains few rings or slender canyon and so on. The model is processed by the helix scanning strategy and the progressive scanning strategy. In the fourth group of experiment, the model in Fig. 7 is the molding of engine impeller. Below the model, supported structures which can make the model were found, and the base plate melted tightly. The length of the model is three times more than the width of the model, and the height of the model is three times more than the width of the model. Inside the model, there are some apertures and cavities. The shape of every layer of the model changes a lot, and every layer is a complex shape which contains many rings or slender canyon and so on. The model is processed by the helix scanning strategy and the progressive scanning strategy"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000807_j.mechmachtheory.2013.06.013-Figure15-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000807_j.mechmachtheory.2013.06.013-Figure15-1.png",
        "caption": "Fig. 15. The simplified model of PHOENIX\u00ae 800G Bevel Gear Grinding Machine.",
        "texts": [
            " Finally, the translational range of lw can be represented as where R1\u2212d\u2264\u0394lw\u2264R2 \u00fe d \u00f022\u00de R1, R2 are the inner radius and the outer radius of the face-gear, respectively (see Fig. 7). Usually d = 2 ~ 5. The following is a simulation processing test that illustrates the application of the mentioned grinding method. The design parameters of face-gear drive considered for this test are represented in Table 3. The results of swing angle and radial feed range represented in Table 3 are obtained considering ur2 \u2264 ur \u2264 ur1 and Eqs. (21) and (22). The PHOENIX\u00ae 800G Bevel Gear Grinding Machine is chosen as the processing equipment (shown in Fig. 15), which can meet the requirements of face-gear grinding movement based on the disk wheel as mentioned above. However, a disk-shaped grinding wheel cannot be installed based on the original structure of the machine. Therefore, a tool slide should be added to install the disk wheel. As shown in Fig. 15, a tool slide is funded on the machine and the installation solutions for grinding face-gear based on the disk wheel are mentioned above. The range of swing angle \u0394\u03c8w of the disk wheel is [\u2212 \u03c8w \u2217 ,\u03c8w \u2217 ] combined with Eq. (21). Whereas, the movement of B-axis of PHOENIX\u00ae 800G Bevel Gear Grinding Machine is limited to [0, 90]. Therefore, the whole process is implemented in two steps: (1) Move the disk wheel to the process station of station 1, where tooth surfaces 1 of face-gear is in-process (shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000937_icma.2012.6282874-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000937_icma.2012.6282874-Figure1-1.png",
        "caption": "Fig. 1. Configuration of a quadrotor",
        "texts": [
            " The dynamic behavior of a quadrotor has been described in a variety of publications to varying degrees of complexity, see for example [11]\u2013[14]. The following derivation is roughly based upon [8], but extends its mathematical description by the full consideration of nonlinear coupling between the axes as well as by a quaternion-based representation. Aerodynamic side effects and elastic deformations play a minor role at slow speeds, sufficient stiffness and realistic flight maneuvers and are therefore omitted. The basis of the model is Fig. 1 which shows a freely moving quadrotor in three-dimensional space. The origin of the body-fixed frame (CS)B (basis vectors e1B , e2B , e3B) is located at the center of gravity whose position in earth-fixed inertial frame (CS)I (basis vectors e1I , e2I , e3I ) is given by the vector (I)r = (x, y, z)T . The orientation of the quadrotor is first described by three Euler angles (roll angle \u03c6, pitch angle \u03b8, yaw angle \u03c8) combined in the vector \u03a9 = (\u03c6, \u03b8, \u03c8)T . A rotation from (CS)I to (CS)B is realized by three consecutive elementary rotations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000648_978-3-642-17531-2-Figure8.31-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000648_978-3-642-17531-2-Figure8.31-1.png",
        "caption": "Fig. 8.31. Electrodynamic force generation with a rectangular coil, LORENTZ forces on coil wires: cancellation of collinear coil forces with antiparallel current flows",
        "texts": [
            " The LORENTZ force has two notable properties differing from the reluctance force discussed in previous sections: , ( ) ed Q T F i is independent of the coil displacement x , and is linearly dependent on the coil current T i . The configuration in Fig. 8.30 thus permits feedback-free, linear, bipolar force generation at the mechanically attached armature. Cancellation of LORENTZ force components The fact that only a vertical electrodynamic force ed F results for the coil configuration in Fig. 8.30 can be easily illustrated with the representation depicted in Fig. 8.31. Naturally, LORENTZ forces ,1 ,3 , ed ed F F also act on the vertical wire sections. However, due to the antiparallel current direction, these forces cancel each other out, so that only the force ,2ed F acting on the upper wire contributes to the electrodynamic force on the coil. Energy storage vs. energy transformation The electrodynamic transducer has one interesting and not readily apparent property with respect to energy storage. Closer inspection of the energy functions reveals that only the coil inductance C L stores energy; the external magnetic field 0 B does not contribute to storage and only serves to transform the energy"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003012_s00170-018-2107-6-Figure18-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003012_s00170-018-2107-6-Figure18-1.png",
        "caption": "Fig. 18 3D influence curve on dilution by interaction of scanning speed and laser power",
        "texts": [
            " Table 7 reveals that dilution is primarily affected by laser power, gas flow, the interaction between laser power and scanning speed, the interaction between laser power and gas flow, and overlapping rate square. Figures 15 and 16 indicate a remarkable model fitting and prediction on dilution. In Fig. 17, dilution shows the increasing trend with increased laser power and decreased gas flow, because lower gas flow will reduce the amount of powder feed onto substrate, while increased laser power will create larger molten pool, causing a larger dilution. Indicated by Fig. 18, increasing laser power and increasing scanning speed will lead to increased dilution. A larger power creates a larger area of molten pool for cladding between powder and substrate. With the increasing of scanning speed, the energy for melting powder and substrate is reduced in the same interval time frame, which would create reduced clad area and reduced melt area. On the other hand, the blocking effect from cladding powder is reduced, leading to an increased interaction between laser and substrate, causing an enlarged melt area due to increased laser irradiation energy onto the substrate"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002226_s11837-015-1299-6-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002226_s11837-015-1299-6-Figure1-1.png",
        "caption": "Fig. 1. Illustration of UAM process: (a) welding of aluminum tape and (b) periodic machining operations.",
        "texts": [
            " In this work, the potential to overcome these difficulties and realize the potential of metals AM for heat exchangers is demonstrated using ultrasonic sheet lamination of metal foils using ultrasonic additive manufacturing (UAM) technology produced by Fabrisonic (Columbus, OH). The UAM process involves building up solid metal objects through ultrasonically welding a succession of metal tapes into a 3D shape, with periodic machining operations to create the detailed features of the resultant object.5 Thus, Fig. 1a shows a rolling ultrasonic welding system, consisting of an DOI: 10.1007/s11837-015-1299-6 2015 The Minerals, Metals & Materials Society ultrasonic transducer, a booster, a (welding) horn, and a \u2018\u2018dummy\u2019\u2019 booster. The vibrations of the transducer are transmitted through the booster section to the disk-shaped welding horn, which in turn creates an ultrasonic solid-state weld between the thin metal tape and base plate. The continuous rolling of the horn over the plate welds the entire tape to the plate. This is the essential building block of UAM. It is to be noted that the \u2018\u2018horn\u2019\u2019 shown in Fig. 1a is a single, solid piece of metal that must be acoustically designed so that it resonates at the ultrasonic frequency of the system (typically at 20 kHz). Through welding a succession of tapes, first sideby-side and then one on top of the other (but staggered in the manner of bricks in a wall so that seams do not overlap), it is possible to build a solid metal part, as shown in Fig. 1b. During the build, periodic machining operations add features to the part, as suggested by the slot in Fig. 1b, to remove excess tape material and true up the top surface for the next stage of welds. Thus, the so-called \u2018\u2018additive manufacturing\u2019\u2019 involves both additive and subtractive steps in arriving at a final part shape. The solid-state nature of Fabrisonic\u2019s welding process allows UAM to readily bond aluminums (2xxx, 3xxx, 5xxx, 6xxx, 7xxx) and coppers. Additionally, all Fabrisonic\u2019s SonicLayer machines are based on traditional three-axis CNC mills. Thus, the welding process can be stopped at any point and 3D channels can be machined"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002988_j.jmbbm.2017.11.009-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002988_j.jmbbm.2017.11.009-Figure2-1.png",
        "caption": "Fig. 2. (a) CAD model of fatigue specimen, (b) cross section of the CAD data, (c) 3D finite element model and (d) Gaussian laser power density.",
        "texts": [
            " Following the fatigue test, the fracture surfaces were observed by scanning electron microscopy (SEM) (S-3400NX, Hitachi, Japan) under an accelerating voltage of 15 kV and an emission current of 65 \u00b5A. In addition, the clasp arm was cut parallel to the fracture surface and polished according to the conditions described previously. Then, the grain sizes were examined using SEM and EBSD. A commercial finite element analysis software (ANSYS) was used to investigate the difference in the thermal conduction behavior depending on the surrounding material, support structure (solid part), or powder bed. Fig. 2 shows the 3D finite element model of clasp arm part, which was designed using the cross section of the CAD model for the fatigue specimen. The model consists of 58,207 elements and 223,651 nodes. In order to improve the calculation accuracy and reduce the computational cost, the elements that interact with the laser beam were finely meshed, and a coarser mesh was used for the surrounding area. A Gaussian heat flux source was used to simulate the moving laser beam during the SLM process. The simulation was conducted when the heat source moved along the dotted line (Fig. 2c). Some thermally dependent physical properties of the MP1 solid parts were taken from the official material data sheet, and those in an unknown range were determined by assuming that they change linearly. The specific heat capacity was assumed to be 450 J/kg \u00b0C, which was assumed to be a thermally independent property because of the lack of information (Henry, 2009). The thermal conductivity of the powder was measured to be 0.20379 W/m \u00b0C at room temperature using a thermal constants analyzer (Hot Disk TPS 500 S, Hot Disk AB, G\u00f6teborg, Sweden)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000679_j.ymssp.2010.02.003-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000679_j.ymssp.2010.02.003-Figure9-1.png",
        "caption": "Fig. 9. Different number of isolated tooth spaces during the rotation of one pitch (gear 1).",
        "texts": [
            " the pressure in all the control volumes can be calculated. Due to the geometric periodicity, such a system has to be solved for an angle variation equal to the angular pitch (yp=2p/zk). It is worth noting that the number of isolated spaces changes during one pitch rotation: thus, two different systems must be integrated: one for N and one for N 1 equations, where N is the maximum number of isolated spaces. The initial position in the integration procedure is chosen as the position when a tooth space becomes isolated at the inlet side as shown in Fig. 9(a) for gear 1: in such a condition the number of isolated spaces is the maximum (N). Then, when the gear arrives in the position represented by Fig. 9(b), the last tooth space begins to communicate with the outlet chamber and the number of isolated space is reduced to N 1; therefore, the number of equations must be modified. Finally the starting situation is repeated when a new tooth tip arrives at the initial position and a new tooth space is isolated from the inlet chamber (Fig. 9(c)); the number of isolated spaces becomes maximum again. Moreover, in order to solve the equation system, an initial value of the pressure distribution has to be known; hence the pressure values obtained at the end of one integration step are used as initial values for a new integration cycle. After several cycles the solution for the pressure distribution is obtained. In order to completely define the pressure distribution acting on a gear, the pressure in the inlet chamber and outlet one is assumed as constant and equal to the atmospheric pressure and the output pressure, respectively",
            " In both operational conditions the gear eccentricity is close to the maximum value allowed by the clearance, but the influence of different operational conditions is important in eccentricity modulus as well as in direction. In particular, in the condition of lower speed and higher pressure the eccentricity modulus is higher, as expected. The pressure distribution on gear 1 is presented in Fig. 20; more precisely, it deals with the pressure evolution in a space between teeth during a complete gear rotation, normalized with the outlet pressure and calculated in the SEP. The initial position is the one in which the tooth space becomes isolated from the inlet chamber, as shown in Fig. 9(a). In the first part where the tooth space is isolated, corresponding to about 2211, the pressure evolution is obtained using the results pi(y) of the numerical integration of the differential equation system (21) over one pitch: the pressure evolutions concerning all the isolated tooth spaces are consecutively plotted in order to represent the complete evolution. For the remaining part of the gear rotation, where the tooth spaces are not isolated, the pressure evolution is plotted in agreement with the model hypotheses: constant pressure in the outlet and inlet chambers and linear pressure transition from high to low pressure"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002064_s11661-018-4788-8-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002064_s11661-018-4788-8-Figure1-1.png",
        "caption": "Fig. 1\u2014Optical micrographs of the X to Z section of all cylindrical samples and crack regions with different overhang geometries: Overviews of the parts with the angles of (a) 30 deg, (b) 40 deg, (c) 45 deg, and (d) 50 deg are shown. The magnified images of samples tilted at (e) 30 deg and (f) 50 deg show consistent cracking only on the left side.",
        "texts": [
            " The powder particle is in size range of 40 to 120 lm. The layer thickness was 50 lm. The preheat temperature was 1298 K. A standard raster beam scan pattern was used. Since the values of process parameters are often considered as intellectual property by many industries, the values are given as a range in this study. The process parameters of beam current (30 to 40 mA), scan velocity (4.53 m/s), and hatch spacing (70 to 125 lm) were used to fabricate the Mar-M247 parts. The cylindrical parts (see Figure 1) were built at angles of 30, 40, 45, and 50 deg with reference to the build direction (z-direction) with identical process parameters for the builds. A support structure in the shape of a cone 8 mm in height was built first and then the cylinder 42 mm in height was built on top of it. As a part of our standard qualification route, the cylindrical part was sectioned parallel to the build direction at the center of the part and characterized with an optical microscope. Interestingly, the un-etched surfaces showed consistent cracking only on the left side of the cylindrical parts with a clear distinction between crack and crack-free regions",
            " Therefore, in this research, a low-fidelity heat transfer model is implemented based on the numerical solution of heat conduction equation using Python library code, FEniCs.[36] The code solves partial differential equation (PDE) using finite element method (FEM) on a predefined mesh and assume heat transfer purely through conduction and ignore the fluid flow, latent heat absorption or release, and temperature-dependent material properties. Three-dimensional thermal simulation using FEniCs is implemented to describe the cylindrical parts with angles shown in Figure 1. The geometry and meshes were created using the built-in Python library, DOLFIN.[37] The computation domain with dimensions of 7.5 mm (diameter) 3 mm (height) is discretized into 35,000 tetrahedral cells with 140,000 nodes. The governing equation is given by Eq. [1] [38]: qCp @T @t \u00bc r \u00f0hrT\u00de \u00fe _Es; \u00bd1 where q is density, Cp is specific heat, T is temperature, t is time, h is thermal conductivity, and _E is energy input deposited by the heat source. The thermal energy to fuse powder comes from the focused electron beam"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003303_j.addma.2019.02.006-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003303_j.addma.2019.02.006-Figure5-1.png",
        "caption": "Fig. 5. (a) Representative mesh of the powder model and (b) thermal boundary conditions.",
        "texts": [
            " Thermal losses from the top of the substrate are set by the global convection value, (h_global). Heat that dissipates through the substrate is subject to the same convection boundary conditions at the substrate sides (h_sub_side) and bottom (h_sub_bottom). For both models, the convection coefficient values for the top surface of the part and powder bed, the substrate side, and the substrate bottom surfaces are fixed at 25W/m2/\u00b0C with a sink temperature of 25 \u00b0C [24]. In the powder model, the convection coefficient values for the powder bed side surfaces (h_sub_side, see Fig. 5(b)) are set from 0 to 100W/m2/\u00b0C to investigate the effect of heat conduction loss through powder bed side surfaces to the machine components. In real practice, for instance, EOSINT M280M system has a 14.6mm thick aluminum cylinder to hold the powder bed. The actual convection coefficient on the powder bed side surface is unknown but this range of values is a reasonable estimation [24]. In the convection approximation model, the convection coefficient values tested for the part side surfaces are also within the maximum range of 0\u2013100W/m2/\u00b0C"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001786_s00170-017-0546-0-Figure19-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001786_s00170-017-0546-0-Figure19-1.png",
        "caption": "Fig. 19 V-shaped specimen before and after EP: a EP-specimen (nominal dimensions and roughness), b L-PBF-built specimen (nominal dimensions + EP allowances + process tolerances); dimensions are in mm and EP allowances are shown in a 5:1 scale, for better visibility",
        "texts": [
            " 18, the thickness reductions (EP allowances) resulting from 9000 Jt polishing can be determined as follows: \u2013 0.16 mm for the 0\u00b0-oriented surface; \u2013 Between 0.16 and 0.18 mm for the 45\u00b0- and 90\u00b0-oriented surfaces (maximum values considered); \u2013 0.21 mm for the 135\u00b0-oriented surface. Let us now design a component to be built by L-PBF and electropolished (as an example, we use here a V-shaped anode from this study). We need to start from the design requirements, which comprise the nominal part\u2019s dimensions and surface roughness (Fig. 19a). Next, we need to take into account the processing tolerances of \u00b140 \u03bcm for small IN625 components built with an EOS M280 400 W [16]. Note that smaller L-PBF tolerances (\u00b15\u201330 \u03bcm) were found in the context of this study bymeasuring the thickness of the as-built 90\u00b0 wall of the V-shaped specimen. Finally, considering the EP allowances (Fig. 18) and processing tolerances of \u00b140 \u03bcm, the dimensions of the rough LPBF-built component can be determined (Fig. 19b). It should be noted that the numbers presented are strongly technologyspecific and should be re-evaluated in the case of any change in the L-PBF and EP technologies. In this paper, process of electropolishing has been optimized with an objective to obtain a uniform surface finish of L-PBFbuilt IN625 components, regardless of their build orientation. Additionally, an original methodology for the determination of the build orientation-dependent allowances and polishing time leading to a specified roughness of L-PBF-built IN625 components has been proposed and validated"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001237_1.3671411-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001237_1.3671411-Figure1-1.png",
        "caption": "FIG. 1. (Color online) The proposed MNS divided into (a) Part I and (b)",
        "texts": [
            " showed that the magnetic gradient generated from a rotatory MNS can axially translate a cylindrical microrobot on a surface.4 However, the helical and translational motions required for a microrobot have not been generated with one MNS due to the magnetic and structural restrictions of conventional MNSs.1\u20136 Combination of helical and translational motion capabilities would greatly improve the maneuverability of a microrobot in complex human blood vessels. Here we propose a novel type of MNS to achieve both helical and translational motions of a microrobot within one compact structure (Fig. 1). The MNS can be divided into Parts I and II, according to the type of magnetic field generation. Part I [Fig. 1(a)] is composed of one Helmholtz coil (HC) and two uniform saddle coils (USCs) capable of generating the rotating magnetic field, while Part II [Fig. 1(b)] is composed of one Maxwell coil (MC) and one gradient saddle coil (GSC) to generate the magnetic gradient.2 Part II is inserted into Part I. In this paper, we calculate the input voltages of Part I to generate a precise rotating magnetic field by considering the frequency effect on the MNS. We also calculate the current relationship of the MC and GSC to translate the microrobot on a three-dimensional surface. Finally, we conduct several experiments to verify the efficacy of the proposed MNS"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000031_s11044-007-9082-2-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000031_s11044-007-9082-2-Figure4-1.png",
        "caption": "Fig. 4 A 3R planar robot at its home and its post-loaded (dashed) postures",
        "texts": [
            " (46) Moreover, at the unloaded posture, displayed with dashed lines, the joint angles are all off from the above values by an angle \u03b8 = +\u03c0/100. In order to carry the robot from its unloaded posture s0 to its HP s1 we need to apply a wrench w10 to its EE, which is calculated from its Cartesian stiffness matrix KC , as given by (23). The purpose of the example is to calculate this wrench, then a wrench w21 that takes the robot to a second loaded posture s2 that we term post-loaded. The robot is depicted at both its preloaded and its post-loaded postures in Fig. 4, the former displayed with continuous lines, the latter with dashed lines. Finally, we calculate the incremental wrench from the preloaded to the post-loaded postures with respect to the operation point in both its current position at the post-loaded posture and its position at the HP. We show that the latter is associated with an asymmetric matrix. In (23), we need both the joint stiffness matrix K and the Jacobian-inverse. The former is known to be diagonal, and assumed to have the numerical values K = k diag(3,2,1) Nm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002420_s00170-017-1455-y-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002420_s00170-017-1455-y-Figure1-1.png",
        "caption": "Fig. 1 Schematic diagram of laser-aided direct metal deposition process",
        "texts": [
            "eywords Direct metal deposition . Repair . Reverse engineering . Additivemanufacturing . Tool steel Laser-aided direct metal deposition (DMD) is an additive manufacturing (AM) process that can build fully dense complex parts according to their 3D models layer by layer following a user-defined tool path [1]. The process requires using a high-power laser to create a molten pool by melting substrate surfaces and filler metal particles that delivered into the molten zone (Fig. 1). The addingmaterial solidifies to form a layer of the part to be fabricated, forming a good bond between two materials [2, 3]. The DMD process has shown great applications in fields of near-net-shape part fabrication [4\u20136] and surface coating [7\u20139] to enhance hardness, wear, and corrosion resistance. For H13 tool steel that broadly used to fabricate die, mold, and cutting tools, reinforcing surfaces to withstand wear and corrosion is always desired. Generally, hard surfacing alloys can be cladded on tool steel to enhance wear and corrosion resistance or tool steel matrix can be reinforced by hard phases such as WC or TiC"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000648_978-3-642-17531-2-Figure8.16-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000648_978-3-642-17531-2-Figure8.16-1.png",
        "caption": "Fig. 8.16. Lossy current drive electromagnetic (EM) transducer with variable working air gap (parallel resistance, coil losses): a) schematic configuration (working air gap and magnetic flux guide not shown), b) signal-flow diagram for electrical gate ( /u i",
        "texts": [
            " Once again, for increasing rest displacement, the applied mechanical power climbs as well. However, electromagnetic softening also renders the transducer increasingly unstable. Thus, in order to prevent pull-in, large coupling factors are only possible within a strictly limited range of motion. 8.3 Generic EM Transducer: Variable Reluctance 529 Passive damping via parallel resistance As previously explained, using a resistance in parallel with the current source in a current drive EM transducer (a shunt, see Fig. 8.16a), passive damping of mechanical subsystem oscillations can be achieved (see also the general presentation in Sec. 5.5 or the analogous electrostatic transducer in Sec. 6.4.3). Thus, a parallel resistance can again be considered among the important design degrees of freedom. Steady-state dynamics without coil losses In the steady state with a finite R , there is only a current flowing in the inductance\u2014its resistance is nearly nonexistent. Thus, rest position conditions identical to those of the lossless transducer result",
            "59) As in the case of the electrostatic (ES) transducer, the maximum achievable damping of the transducer eigenfrequency depends solely on the relative motion geometry of the transducer, and increases with increasing rest position R x (or R X ), as shown in Fig. 8.17a for 0 0F . 0 0F , b) optimal conductivity for maximum damping Eq. (8.59) for 0 0F The corresponding optimal conductivity max max1/Y R in Eq. (8.59) is plotted in Fig. 8.17b as a function of the rest displacement, again for 0 0F (cf. Fig. 6.13). Coil losses Non-negligible resistive losses in the windings\u2014the coil losses C R \u2014have only a limited effect with current drive. In normal operation without shunting ( 0Y in Fig. 8.16a), there is no effect on the imposed transducer current T S i i , and the transfer charac- teristics remain unchanged (see Sec. 5.5). In particular, the series resistance T R cannot effect passive electromechanical damping. If this latter is required, an additional finite shunting resistance 0Y must be introduced. This modifies the rest current to be 0 0 / (1 ) T T I I YR , and this latter should be substituted into the rest position condition (8.48) in place of 0 I . For dynamic small-signal operation, the block diagram shown in Fig. 8.16b describes the electric feedback. Some intermediate calculations give the characteristic polynomial of the transducer with feedback: 2 3 , 2 3 , ( ) ( )( ) ( ) 1 1 ( ) . C em I R C R C C em I R R s R R k k kL s R R m s mL s YR YR k k kL s m s mL s Y Y (8.60) 532 8 Functional Realization: Electromagnetically-Acting Transducers A comparison with the previous case without coil losses shows that the selection rules (8.58) and (8.59) can be adopted unchanged if, in place of 1/R Y , the total resistance ( ) C R R or the equivalent conductiv- ity / (1 ) C Y YR is used"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001758_jrproc.1956.275102-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001758_jrproc.1956.275102-Figure2-1.png",
        "caption": "Fig. 2-Setting the transfluxor to a level in a continuous range.",
        "texts": [
            " This force in the magnetic material is greatest at the periphery of the hole and diminishes gradually with distance. In the case of a circular aperture it is inversely proportional to the radius. Therefore, for the given selected amplitude of the setting current pulse, there will be a critical circle separating an inner zone, in which the magnetizing force is larger than the threshold magnetizing force H, required to reverse the sense of flux flow, and an outer zone, where this field is smaller than the threshold value. These two zones are shown in Fig. 2. Consider now the alternating magnetomotive force on leg 3 produced by an indefinitely long sequence of pulses of alternating polarity. The first pulse, applied to leg 3 in a direction to produce downward magnetization in leg 2, can change only that part of the flux in leg 2 which is directed upwards, namely that part which has been \"set\" or \"trapped\" into that leg by the setting pulse. This changing part of the flux will flow through leg 3 until leg 2 reaches its original downward saturation. The amount not affect leg 3 which will remain saturated downward"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001115_j.wear.2015.01.047-Figure11-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001115_j.wear.2015.01.047-Figure11-1.png",
        "caption": "Fig. 11. Generation of the transverse sliding component. (a) Top view of pure rolling position \u0394\u00bc0. (b) Top view of rolling\u2013sliding position \u0394a0.",
        "texts": [
            " It is thickened withMicrogels and it contains anti-wear and high-pressure additives. A specific test rig has been developed to reproduce the PRS kinematics. The roller is mounted on a small shaft that rolls freely on small ball bearings inside a holder. The holder is fixed to a shaft that loads the assembly on the rotating disc (Fig. 10). Tangential force and rolling speed are measured and recorded. The transverse sliding component is generated by moving the contact perpendicularly to the radius of the disc (Fig. 11). The axial shift \u0394 between the roller axis and the disc axis is controlled with precision and creates a radial sliding component. As a result, it generates a tangential force Ft. The creep ratio \u03c4 is defined by \u03c4\u00bc \u00f0Vsliding=Vrolling\u00de \u00bc tan \u03b8. Hence \u0394 is calculated as follows: \u0394\u00bc R sin \u03b8\u00bc R sin \u00f0a tan \u03c4\u00de, where R is the radius of track on the disc. First, the test rig can be used to plot continuous traction curve by varying the axial shift \u0394 during one single test. Then, wear tests can be conducted with continuous or alternative rotation to reproduce the PRS contact kinematics"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001130_j.jsv.2011.12.025-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001130_j.jsv.2011.12.025-Figure2-1.png",
        "caption": "Fig. 2. Lumped model.",
        "texts": [
            " [15,16] is also employed; the vibration excitation inherent to the tooth meshing is generated as the gears roll and the instant stiffness changes. Moreover, to reduce the calculation times, a new tooth stiffness function is proposed. Furthermore, because of the literature survey and additional verifications not included in this paper, the model is based on the assumption that during the tooth separation periods, the iso-viscous hydrodynamic lubrication contribution to the mesh damping is negligible, as compared to the oil squeeze effects. Fig. 2 and Eqs. (4)\u2013(7) describe the model, while Fig. 3 illustrates some of the variables J1 \u20acy1\u00feR1 cosf 1\u00fe 1 Nc XNc i \u00bc 1 wiSiA1i ! Wdyn\u00feC1 _y1 \u00bc T1 (4a) J2 \u20acy2\u00feR1 cosf mg\u00fe 1 Nc XNc i \u00bc 1 wiSiA2i ! Wdyn\u00feC2 _y2 \u00bc T2 (4b) Wdyn \u00bc Km y1R1 cosf\u00fey2R2 cosf \u00feCm _y1R1 cosf\u00fe _y2R2 cosf h i C2 1 mgR1 cosf _y2 (5) A1\u00f01\u00de \u00bc \u00f0x\u00feDxmc\u00de (6a) A1\u00f02\u00de \u00bc x (6b) A1\u00f03\u00de \u00bc \u00f0x Dxmc\u00de (6c) A2\u00f0i\u00de \u00bc f\u00f01\u00femg\u00detanf A1ig (6d) S\u00bc 1 if xioA1\u00f0i\u00deotanf 0 if A1\u00f0i\u00de \u00bc tanf 1 if tanfoA1\u00f0i\u00deoxo 8>< >: (6e) Dxmc \u00bc 2p N1 (7a) xi \u00bc t1m R1 cosf (7b) xo \u00bc t1n R1 cosf (7c) where x, xi,xo are the roll angle, the roll angle at mesh beginning, the roll angle at mesh end (rad), Dxmc is the angular pitch (rad), yj, _yj, \u20acyj are the angular position (rad), velocity (rad s 1) and acceleration (rad s 2) of wheel j, f is the operating pressure angle (deg",
            " (4) thus consider the individual contribution of three potential meshing tooth pairs by means of the Si Aj(i) combinations. The central tooth pair in mesh is designated by 2, while numbers 1 and 3 represent the preceding and the following tooth pairs, respectively. Eqs. (4) clearly indicate that the churning losses on both gear wheels contribute to the efficiency reduction. On the other hand, the dynamic force (Eq. (5)) is affected solely by the churning loss active on the output gear 2. The Voigt model employed in Fig. 2 for the mesh and damping stiffness parallel action is a simplified representation. However, because of the very small fluid film thickness and the assumption of a liquid lubrication, the approach is appropriate. The composition of Km and Cm are then given below Km \u00bc XNc i \u00bc 1 1 Kf 1 \u00fe 1 Kf 2 \u00fe 1 KH \u00fe 1 K lub 1 i (8) Cm \u00bc Csys\u00feCcont (9) Ccont \u00bc XNc i \u00bc 1 1 Chys \u00fe 1 Club 1 i loaded condition \u00bc XNc i \u00bc 1 \u00f0Club\u00dei no-load condition (10) Chys \u00bc 1 Chys,1 \u00fe 1 Chys,2 \u00fe 1 Chys,H 1 (11) where Ccont is the total damping produced by the tooth pairs, Chys is the global hysteresis damping of tooth pair I, Chys,j is the hysteresis damping generated by the flexion of tooth j of pair i, Chys,H is the contact hysteresis damping of tooth pair i, Club is the lubricant damping (oil squeeze effect) of tooth pair i, Csys is the system damping (contributions not properly related to the teeth), Kf,j is the flexural rigidity of tooth j of pair i, KH is the Hertz contact rigidity of tooth pair i, and Klub is the lubricant rigidity (oil squeeze effect)",
            " The transition between the value sets is determined by a critical Reynolds number (Rec). Recr6000 refers to the low speed formulation, whereas RecZ9000 requires a high speed representation. The authors of the reference suggested a linear interpolation for Rec between the limits. Rec\u00bc _yRF u (40) The model solution initially assumes that the active tooth flanks are in contact. Consequently, the contact condition and mesh rigidity are controlled by the normal approach of the flanks (Ap (mm)) Eq. (41). Fig. 8 illustrates this variable. Considering the coordinate systems shown in Fig. 2, a positive value of Ap corresponds to a positive load between the active flanks (Wdyn40). Conversely, a negative normal approach with amplitude exceeding the backlash (2B cos f) causes a back flank contact (Wdyno0). Any other negative value of Ap corresponds to a no-contact situation. The relative position of the teeth then fixes the side (active or back) bearing the lubricant influence; the lubricant is assumed to be trapped on the thinnest gap side. These conditions are summarized below Ap\u00bc \u00f0R1y1\u00feR2y2\u00decosf (41) The following possibilities lead to the mesh rigidity and contact conditions: ApZ0 teeth touch on their active flanks and Km given by Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002213_j.mechmachtheory.2014.06.006-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002213_j.mechmachtheory.2014.06.006-Figure8-1.png",
        "caption": "Fig. 8. State 4 of the derivative queer-square mechanism (\u03b11 N 0, \u03b12 b 0, \u03b211 = \u03b212, \u03b221 = \u03b222).",
        "texts": [
            " Besides the angle ranges in the presented equations, the angle ranges of \u03b11, \u03b12, \u03b211, \u03b212, \u03b221 and \u03b222 can be extendedmore than \u03c0 2 until two or more bars geometrically touching where the angles are always smaller than \u03c0. Fig. 7 offers the observation of the derivative queer-square mechanism in state 3. Fig. 7 indicates that the limb1s, limb2s, limb1p and limb2p all have higher locations compared to the base OA1A2 of the derivative queer-square mechanism, and the platform E1F1E2F2 is higher than the limb1s, limb2s, limb1p and limb2p. By rotating a positive angle \u03b11 and a negative angle \u03b12 from the singular position, as illustrated in Fig. 8, the derivativemechanism changes to state 4 whose angle ranges satisfy \u03b11N0;\u03b211 \u00bc \u03b212b0 \u03b12b0;\u03b221 \u00bc \u03b222N0 : \u00f029\u00de It can be observed from Fig. 8 that limb1s has a relatively higher position, limb2s has a relatively lower position compared to the base OA1A2 and the platform E1F1E2F2 is lower than limb1p and higher than limb2p in state 4. Through rotating a negative angle \u03b11 and positive angle \u03b12 from the singular position, the derivative queer-square mechanism achieves state 5. The schematic diagram of state 5 is shown in Fig. 9. The angle ranges of state 5, which also satisfies the angle relation in Eq. (27), are illustrated as \u03b11b0;\u03b211 \u00bc \u03b212N0 \u03b12N0;\u03b221 \u00bc \u03b222b0 : \u00f030\u00de In state 5, limb1s is lower than the base OA1A2, limb2s is higher than the base and the platform E1F1E2F2 locates in the position higher than limb1p but lower than limb2p"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001233_s11071-011-0309-7-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001233_s11071-011-0309-7-Figure1-1.png",
        "caption": "Fig. 1 A schematic diagram of rolling element bearing",
        "texts": [
            " The rolling elements are positioned symmetrically so that their moving parts are in synchronization. Since the nonlinear bearing forces act on the system, implicit type numerical integration techniques Newmark-\u03b2 with the Newton\u2013Raphson method have been used to solve the nonlinear differential equations iteratively. The results have been presented in the form of bifurcation diagrams, Fast Fourier Transformation (FFT), and Poincar\u00e9 maps. A schematic diagram of rolling element bearing is shown in Fig. 1. Geometrical parameters of a radial ball bearing are selected as shown in Table 1. To analyze the structural vibrations in rolling element bearings, a model is developed in which the outer race of the bearing is fixed in a rigid support and the inner race is fixed rigidly to the shaft. A constant radial vertical force is assumed act on to the bearing. Elastic deformation between the race and ball produces a nonlinear force deformation relation, which is obtained by using Hertzian theory. Other sources of variation are the positive internal radial clearance, the finite number of balls whose position change periodically and the defects at the inner and outer race"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001310_s00170-012-3922-9-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001310_s00170-012-3922-9-Figure6-1.png",
        "caption": "Fig. 6 The model is the molding of blade of aviation engine with more sophisticated designs and cavum inside are used whose shape of every layer changes a lot",
        "texts": [
            " 5); The length of X direction dimension is the length of diameter of the model, the length of Y direction dimension is the width of the model, the length of X direction dimension is large than the length of Y direction dimension, the length of X direction dimension is equal to length of Z direction dimension and the length of Z direction dimension is also the length of diameter of the (c)(b) (a)Fig. 3 a\u2013c Calculation of helix scan paths with the model layer model. As for the model, the model is processed by the helix scanning strategy and the progressive scanning strategy. In the third group of experiment, the model in Fig. 6 is the molding of blade of aviation engine. The model with more sophisticated designs and cavities inside is used whose shape of every layer changes a lot. The model comes from the molding with a practical application. As for the model, the design is very complicated, the height is big and the size is also very big, and every layer is complex shape which contains few rings or slender canyon and so on. The model is processed by the helix scanning strategy and the progressive scanning strategy. In the fourth group of experiment, the model in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003868_13621718.2020.1743927-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003868_13621718.2020.1743927-Figure6-1.png",
        "caption": "Figure 6. Generation of the distortion negative from the simulated results. The calculated distortions (left) are inverted to create the geometric distortion-negative. Baseplate hidden for clarity.",
        "texts": [
            " is exhausted, distortion still forms at a lowered magnitude. Distortion-compensation is a valid option to reduce distortions significantly by changing the geometry itself and keeping the process parameters constant. The idea is to superimpose the process distortions with the distortion-negative in order to generate a distortion-free build, i.e. to build a \u2018wrong\u2019 geometry that distorts during buildup in such a way as to result in the desired shape. The generation of the distortionnegative is visible in Figure 6: Calculated distortions are inverted so that all positive distortions are turned into negatives of the same magnitude and vice versa. This method is expected to lead to an optimised final geometry if distortions occur close to the position causing the displacement. Based on the hypothesis that distortions in the compensated part form in a similar or near-similar manner as in the original part, the compensationwill lead to a zero distortion part as compared with CAD. After extracting the distortion-negative, a new pathplanning is created according to the changed geometry and imported into the simulation tool",
            "14mm larger than for the original part forms at point 1, leading to the residual distortion in comparison with CAD after compensation. Especially for highly stressed areas, the distortions are non-linear and geometry-dependent so that the linear superposition of process distortion with the inverted distortion-negative geometry is not fully applicable. If this remaining deformation is considered to be nonnegligible, another distortion-compensation iteration could be conducted by adding the negative residual distortions from Figure 7 to the distortion-compensated geometry from Figure 6. In summary, it could be demonstrated that transient numerical simulation presents a valid approach to determine and reduce distortions in industry-scale DED builds. \u2022 An optimised hybrid deactivated/quiet-element boundary condition is proposed for fully transient, moving heat source simulation of DED components. \u2022 The 80-layer, 17.4m weld-length turbine blade is built with DED and bulging distortions form especially in low-stiffness areas. \u2022 The buildup could be simulated using a transient thermomechanical approach"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001461_icra.2013.6631355-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001461_icra.2013.6631355-Figure3-1.png",
        "caption": "Fig. 3. Hovering\u2013Translation Control Principles and Coordinate Frames",
        "texts": [
            " It is equipped with high-efficiency Electronic Speed Controllers (ESCs) driving the BLDC motors, which have been reprogrammed with a special firmware allowing the immediate change of the motor-driving energizing pulses. This has a significant advantageous impact on rotor dynamics (rotor is used to imply the assembled subsystem consisting of the ESC, the BLDC and the direct-drive, fixed-pitch Propeller), as presented in Subsection III-B. The UPAT-TTR\u2019s translational hovering mode operation principles are depicted in Figure 3, along with the BodyFixed coordinates Frame (BFF) B = {Bx, By, Bz} and the North-East-Down (NED) [4] Local Tangential coordinates Plane (LTP) E = {N, E, D}. Let \u0398 = {\u03c6 , \u03b8 , \u03c8} be the LTP-based rotation angles vector, and XW = {x, y, z} the LTP-based position vector. For the system\u2019s rotational (attitude) control, the roll (\u03c6 ) is controlled via the differential thrusting of the main rotors, the pitch (\u03b8 ) via the differential thrusting of the front and tail rotors, and the yaw (\u03c8) via the tilting of the tail rotor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000911_tmech.2014.2311382-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000911_tmech.2014.2311382-Figure1-1.png",
        "caption": "Fig. 1. Exploded view of a harmonic drive showing the three components.",
        "texts": [
            " The harmonic drive mechanism is described in Section II, the proposed harmonic drive model is presented in Section III, parameter estimation is described in Section IV, experimental results are discussed in Section V, and concluding remarks are given in Section VI. 1083-4435 \u00a9 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information. Harmonic drives consist of three main components as shown in Fig. 1. The wave generator is connected to a motor, the circular spline is connected to the joint base, and the flexspline is sandwiched in between the circular spline and the wave generator and connected to the joint output. The wave generator consists of an elliptical disk, called wave generator plug, and an outer raced ball-bearing assembly. The wave generator plug is inserted into the ball-bearing assembly, thereby giving the bearing an elliptical shape as well. The flexspline is a thin cylindrical cup with external teeth at the open end of the cup having a slightly smaller pitch diameter than the internal teeth of the circular spline"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003375_j.actaastro.2020.04.016-Figure11-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003375_j.actaastro.2020.04.016-Figure11-1.png",
        "caption": "Fig. 11. Stereo camera unit, which has approx. 1 m extendable mast (STEM) and stereo camera system [31].",
        "texts": [],
        "surrounding_texts": [
            "In order to accomplish the three missions, satellite and ground station systems were designed. Table 1 shows basic specifications of the CubeSat. Fig. 2 shows the on-board components and Fig. 3 shows the system diagram of OrigamiSat-1. The system consists of four major subsystems: (i) membrane deployment unit, (ii) stereo camera unit, (iii) bus, and (iv) ground station. For the bus, most components are composed of purchased CubeSat components, which are made of commercial off-theshelf (COTS) components. Three circuit boards are developed in-house. This design aims at facilitating future space technology demonstrations in various sectors. Finally, Fig. 4 shows the mission sequence. (1) the CubeSat is released from a rocket, (2) the deployable antennas are deployed, (3) the extendable mast is extended to enable taking pictures/movies of the deployable membrane, and finally (4) the multifunctional membrane is deployed. In the following subsection, each of the satellite subsystems is described."
        ]
    },
    {
        "image_filename": "designv10_5_0002453_s11071-019-04780-6-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002453_s11071-019-04780-6-Figure2-1.png",
        "caption": "Fig. 2 Gear geometry",
        "texts": [
            " The combined stiffness is deduced from the stiffness of both the gear tooth and oil film, while the combined damping is derived from the damping of these parts. Effects of oil film stiffness and damping in normal and tangential directions on spur gear dynamics are investigated. Finally, the comparison of dynamic response between the developedmodel and the conventional model is discussed. 2.1 Enhanced dynamic model for spur gear pairs The dynamic model for a spur gear pair is sketched in Fig. 1, and the gear geometry is shown in Fig. 2. In the present study, an enhanced dynamic model for spur gear pairs including the backlash and static transmission error and stimulatingly incorporating the combined stiffness in the normal direction as well as the combined damping both in normal and tangential directions is developed from a conventional model [6,7]. And the conventional model refers to the spur gear dynamicmodel inwhich theoil filmstiffness anddamping are not considered and the friction is not included as well. The combined stiffness and damping are derived from the counterparts of gear pair and oil film",
            " The equations of torsional motion of 2-degree-of-freedom model for a spur gear pair neglecting the effects of tangential stiffness of oil film and gear pair, and of shift as well as bearing are written as: Ip \u03b8\u0308p + Rpcm ( t\u0304 ) ( Rp \u03b8\u0307p \u2212 Rg \u03b8\u0307g \u2212 e\u0307 ( t\u0304 )) + tan \u03d5Racn ( t\u0304 ) ( Rp \u03b8\u0307p \u2212 Rg \u03b8\u0307g \u2212 e\u0307 ( t\u0304 )) + Rpkm ( t\u0304 ) f ( Rp\u03b8p \u2212 Rg\u03b8g \u2212 e ( t\u0304 )) = Tp (1) Ig \u03b8\u0308g \u2212 Rgcm ( t\u0304 ) ( Rp \u03b8\u0307p \u2212 Rg \u03b8\u0307g \u2212 e ( t\u0304 )) \u2212 tan \u03d5Rbcn ( t\u0304 ) ( Rp \u03b8\u0307p \u2212 Rg \u03b8\u0307g \u2212 e ( t\u0304 )) \u2212 Rgkm ( t\u0304 ) f ( Rp\u03b8p \u2212 Rg\u03b8g \u2212 e ( t\u0304 )) = \u2212Tg (2) where \u03b8p and \u03b8g denote the angular displacements of pinion and gear, respectively. Rp and Rg are the base circle radii of gears, Ip and Ig are the mass moment of inertia of gears. km and cm represent the combined normal stiffness and damping respectively. cn denotes the combined tangential damping. Ra and Rb shown in Fig. 2 are the acting arms of tangential forces on the pinion and gear respectively, which are the distances between the mesh point and points N1 and N2 respectively and they vary along LOA. N1and N2 are the tangent points where the action line is tangent to the base circles of pinion and gear, respectively. \u03d5 is the pressure angle. f is the backlash function ande denotes the static transmission error. Tp and Tg are the external torques acting on the pinion and gear, respectively. t\u0304 denotes the time. For simplifying dynamics equations, introducing the dynamic transmission error expressed as x\u0304 ( t\u0304 ) = Rp\u03b8p ( t\u0304 ) \u2212 Rg\u03b8g ( t\u0304 ) \u2212 e ( t\u0304 ) (3) Substituting Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000200_1.3197187-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000200_1.3197187-Figure9-1.png",
        "caption": "Fig. 9. The angle is the angle the velocity vector makes with the horizontal.",
        "texts": [
            " We use Eqs. 5 \u2013 7 to write Eq. 8 as a = v2 \u2212 CDv\u0302 + CL\u0302 + CS \u0302 v\u0302 + g , 9 where = A /2m 0.0530 m\u22121. Equation 9 is a second-order coupled nonlinear differential equation. After choosing a coordinate system, Eq. 9 must be solved numerically for the trajectory. Consider the case for which a soccer ball is launched with no sidespin so that CS=0 in Eq. 9 . It may have topspin, backspin, or no spin. The motion is thus confined to the x-z plane in Fig. 2. The unit vectors v\u0302 and \u0302 are determined easily from Fig. 9 and are 1023 Am. J. Phys., Vol. 77, No. 11, November 2009 Downloaded 28 Oct 2012 to 142.103.160.110. Redistribution subject to AAPT v\u0302 = cos x\u0302 + sin z\u0302 = vx v x\u0302 + vz v z\u0302 , 10 and \u0302 = \u2212 sin x\u0302 + cos z\u0302 = \u2212 vz v x\u0302 + vx v z\u0302 , 11 where vx and vz are the x and z components, respectively, of the velocity vector. With g =\u2212gz\u0302, Eq. 9 may be written as ax = \u2212 v CDvx + CLvz , 12 and az = v \u2212 CDvz + CLvx \u2212 g . 13 If the trajectory is known, the velocity and acceleration can be determined and Eqs. 12 and 13 may be solved for CD and CL, giving CD = \u2212 az + g vz + axvx v3 , 14 and CL = az + g vx \u2212 axvz v3 , 15 where v2=vx 2+vz 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003953_j.engfailanal.2020.104907-Figure12-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003953_j.engfailanal.2020.104907-Figure12-1.png",
        "caption": "Fig. 12. Experimental geared rotor system.",
        "texts": [
            " The effective contact area of the tooth surface reaches the maximum when the gear center distance is the minimum, and the double tooth meshing area reaches the maximum. The high stress zone at the middle of the gear tooth is the single tooth contact area. The addendum and root of the tooth are excessive stress areas because of the excessively small length of the contact line. The parameters of experimental test rig are shown in Table 3. The structural schematic of the experimental geared rotor system is shown in Fig. 12. No localized defects (crack or spalling) can be found for the gears applied in this experiment and there are spline shafts in the assembly of the experimental gear system. The non-loaded transmission error is inevitable in the machining process [7] and the geometric eccentricities are easily caused by the spline assembling error and the manufacturing error resulting that the gear center distance is time-varying with the frequency of fr. The geometric eccentricities of the pinion and gear are determined to be 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001232_s1006-706x(11)60014-9-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001232_s1006-706x(11)60014-9-Figure1-1.png",
        "caption": "Fig. 1 Sketch of laser cladding",
        "texts": [
            " In this paper, the in fluence of laser processing parameters on the clad ding temperature field and the heat affected zone IS tested and simulated by finite element method. 1 Test Method In order to know the relationships among the laser power, the temperature field and the heat affected zone of the cladded layer, the plastic die steel P20 is selected as the base material, and the sample is a 100 mmX 50 mmX 10 mmX 10-9 block. H13 powder is cladded on the base through synchronous powder feeding as shown in Fig. 1. The chemical composition of P20 and H13 are shown in Table 1 and Table 2, respec tively. Set the scanning speed v as O. 006 m/s , the di ameter of laser spot as O. 004 m and the laser power P as 1. 2, 1. 8 and 2. 2 kW, respectively. 2 Building Model and Analysis 2. 1 Building model Laser cladding is a complex process which has a lot of process parameters and include the heat con duction, thermal radiation, melting and solidifying of metals, the stress and deformation of cladded lay er and other physics and chemistry phenomena"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000679_j.ymssp.2010.02.003-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000679_j.ymssp.2010.02.003-Figure1-1.png",
        "caption": "Fig. 1. (a) Diagram of the gear pump and (b) reference frames.",
        "texts": [
            " They are simple and robust devices that can work at a wide range of pressures and rotational speeds, providing at the same time a high reliability. Their main applications can be found as lubrication pumps in machine tools, as oil pumps in engines or in fluid power transfer units. Depending on the application, several designs are available; nevertheless the most usual configuration uses twin gears, which are assembled by a couple of floating bearing blocks that act as seals for the lateral ends. Fig. 1(a) presents a sketch highlighting the clearances between the core elements of the pump. This is the type of pump studied in this work, used in automotive applications, such as in steering systems, and operating at relatively high speed (from 1500 to 3400 rpm) and low pressure (from 3.5 to 100 bar). The bearing blocks are hydraulically balanced and act as supports for the gear shafts by means of two hydrodynamic bearings, which use the same operational oil. Gear 1 is the driving one, while gear 2 is driven. The driving gear shaft is connected to an electrical motor by an Oldham coupling, allowing some misalignments between them. This is necessary because the shaft centreline can move with respect to the bearing blocks describing an orbit that will be a function of the working pressure and speed. The operating principle of external gear pumps is very simple. The fluid is carried around the outside of each gear from the intake to the discharge side (from left to the right in Fig. 1(b)) within the spaces included between two subsequent gear teeth, the case and the floating bearing blocks. As the gears turn in the directions indicated by y1 and y2 in Fig. 1(b), these isolated spaces increase progressively their pressure up to the high pressure. In the gear meshing area, when two tooth pairs come in contact, a trapped volume arises and could undergo a sudden volume reduction and consequently a violent change in its pressure. To avoid this, the trapped volume is put in communication with the high or low pressure chambers. That is the role of the relief grooves milled in the internal face of bearing blocks whose shape and location are so important in the resulting dynamic behaviour",
            " In fact, during this process, the gears can dig their optimal groove in the case; moreover, because of the pressure difference between the inlet and outlet chamber, gears come in contact with the case in a zone near the low pressure chamber and a certain amount of material is removed due to the different hardness of gear and case materials. As known, the tooth meshing contact can take place along two different lines of action. The direct line of action (DLA) is defined as the line where the force from gear 1 to gear 2 causes a momentum in agreement with the direction of rotation y2, and the inverse line of action (ILA) as the line where the force from gear 1 to gear 2 causes a momentum in the opposite direction of rotation (Fig. 1(b)). In normal working conditions the meshing contact is along the DLA because the meshing force from gear 1 to gear 2 must balance the pressure torque on gear 2, which is opposite to the direction of rotation. The model takes into account only transversal plane dynamics: it is a planar model with 6 degrees of freedom, as presented in Fig. 1(b). Two different reference frames for each gear are used, both having their origins on the axis of the cylindrical cavities housing the gears; in reference frames O1X1Y1 and O2X2Y2, the Y-axis is parallel to the DLA and the X-axis is perpendicular. On the other hand, in reference frames O1X1 0 Y1 0 and O2X2 0 Y2 0 , the Y0-axis is along the line connecting the centres of the gears, directed from O2 towards O1, and the X0-axis is orthogonal. For each gear, the degrees of freedom are the displacements along the directions X and Y and the angular displacement: coordinates x1, y1, and y1 are relative to gear 1 (driving), while coordinates x2, y2, and y2 are relative to gear 2 (driven)",
            " Once the pressure distribution around each gear was obtained, the resultant pressure force and torque can be determined. The pressure force is calculated as the vectorial sum of the pressure around the gear multiplied by the involved area; in particular, taking as reference Fig. 10, the pressure force in tooth space q, having direction as the symmetric axis of the space itself, can be calculated as follows: fp q \u00bc 2 Z yp=2 0 pqcos\u00f0y\u00debkrextdy\u00bc 2pqsin\u00f0yp=2\u00debkrext \u00f022\u00de Such a pressure force has to be reduced in the reference frames OkXkYk of Fig. 1(b) and considering the contribution of the zk spaces between teeth, the following relations for gears 1 and 2 can be written: fpx1 \u00bc Xzk q \u00bc 1 fpqcos\u00f0j1q \u00de fpy1 \u00bc Xzk q \u00bc 1 fpqsin\u00f0j1q \u00de 8>>>< >>>: \u00f023\u00de fpx2 \u00bc Xzk q \u00bc 1 fpqcos\u00f0j2q \u00de fpy2 \u00bc Xzk q \u00bc 1 fpqsin\u00f0j2q \u00de 8>>>< >>>: \u00f024\u00de where jkq is the angular position of the axis of tooth space q for gear k with respect to the Xk-axis. The pressure forces depend on the same quantities as the pressure distribution around the gears, namely, the axis eccentric position (coordinates xk and yk) that influences the radial clearances between tooth tips and case, the gear angular position yk over one pitch, and the gear angular speed (see Eq",
            " The relationship between the journal-bearing block eccentricity and the gear-case one is evaluated on the basis of this assumption. Based on the above-described formulation, the bearing reactions depend on the gear centre position and velocity as well as the gear angular velocity. In order to introduce these reactions in the equations of motion (1)\u2013(6), expressions (28) have to be multiplied by two, since each gear is supported by two bearings, and finally the reactions have to be reduced in the reference frames OkXkYk of Fig. 1(b), obtaining the reaction components in directions X and Y for each gear: fbxk \u00bc fbxk\u00f0xk; yk; _xk; _yk; _yk\u00de fbyk \u00bc fbyk\u00f0xk; yk; _xk; _yk; _yk\u00de \u00f038\u00de In steady-state operational conditions, several force components in the equations of motion (1)\u2013(6) exhibit a periodical variation. In details, Sections 4 and 5 have illustrated as the pressure forces and torques are intrinsically periodic with periodicity corresponding to the gear pitch. On the other hand, the gear meshing force exhibits the same periodicity, due to the periodic variation of the meshing stiffness and the profile errors, under the hypothesis that these errors are identical for all the teeth and other gear errors are negligible",
            " This section presents some simulation results about the gear SEP, the pressure distribution and the pressure forces and torques, concerning a pump with twin gears of 12 teeth, module of 1.15 mm, pressure angle in working condition of 27.7271 and relief groove dimension of 2.9 mm; other pump parameters are reported in Table 1. These results refer to two typical operational conditions for this type of gear pump, in terms of outlet pressure and rotational speed, namely 20 bar and 3350 rpm in the first case, and 90 bar and 2000 rpm in the second one. Fig. 19 depicts the SEP in the two mentioned operational conditions in reference frames Ok 0 Xk 0 Yk 0 of Fig. 1(b); the circle represents the maximum displacement of gear axis, allowed by the nominal clearance hrn of 0.0245 mm between gears and pump case. In both operational conditions the gear eccentricity is close to the maximum value allowed by the clearance, but the influence of different operational conditions is important in eccentricity modulus as well as in direction. In particular, in the condition of lower speed and higher pressure the eccentricity modulus is higher, as expected. The pressure distribution on gear 1 is presented in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002168_j.prostr.2017.11.063-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002168_j.prostr.2017.11.063-Figure1-1.png",
        "caption": "Figure 1: (a) Schematic representation of the building strategy of the XY and Z bars from which fatigue specimens are removed, (b) Position and orientation of bar, (c) Fatigue test specimen machined by fine turning from previous bars",
        "texts": [
            " In order to relax the stress due to the process, a post processing heat treatment have been performed during one hour at 160\u00b0C. The P1 specimens were tested on a rotative bending machine. The results of the P1 production tests were analyzed and used as a reference for the study. Julius N. Domfang Ngnekou et Al./ Structural Integrity Procedia 00 (2017) 000\u2013000 3 Secondly, the P2 samples were built using EOS M290 machine and EOS powder. This machine is equipped with a standard DIN EN 1706:2010. P2 samples have been built in two directions, namely XY and Z as in figure 1-a. Fatigue specimens test have been machined (MA) from the produced bars by fine turning. Fatigue test specimens geometry is given on figure 1-c. After machining, some specimens have been subjected to heat treatment T6 with specific conditions in table 1. As it is shown on table 2, and depending on production number, orientation and T6 or not, different designation for fatigue specimen is used in this paper. Production Orientation Treatment Designation P1 XY Without P1-XY-MA P2 XY Without P2-XY-MA T6 P2-XY-MA-T6 Z Without P1-Z-MA T6 P2-Z-MA-T6 78 Julius N. Domfang Ngnekou et al. / Procedia Structural Integrity 7 (2017) 75\u201383 Julius N. Domfang Ngnekou et Al",
            " The droplets then cover unmelted particles and increase the energy required to melt them as the unmelted particles below. X-ray tomography were also used to characterize porosity. Avizo software were use to analyse images with a voxel size of 5\u00b5m. Defect were reconstitute as it is shown on figure 4-a. Figure 4-b shows the defect size distribution. 80 Julius N. Domfang Ngnekou et al. / Procedia Structural Integrity 7 (2017) 75\u201383 Julius N. Domfang Ngnekou et Al./ Structural Integrity Procedia 00 (2017) 000\u2013000 6 In this study cylindrical specimens were used as shown on figure 1-c. Fatigue tests have been performed at room temperature on resonance machine with a load ratio R=-1. The frequency was in the range of 80 to 82 Hz. The fatigue limit have been defined at one million cycles. A step by step method described by Iben Houria [4] were used as it is the only way to evaluate the fatigue limit for a natural defect. It is assumed that no significant damage is introduced in the loading as shown by Roy et al [11] for cast alloy A356. The failure is define by a 5Hz drop of frequency",
            " The effect of anisotropy induced by the building strategy (XY versus Z) will be examined on the basis of S-N curves for machined and machined plus size on fatigue limit. Julius N. Domfang Ngnekou et al. / Procedia Structural Integrity 7 (2017) 75\u201383 81 Julius N. Domfang Ngnekou et Al./ Structural Integrity Procedia 00 (2017) 000\u2013000 6 Figure 4: (a) Characterization of the defect induced by the SLM process, using X-ray tomography with a resolution of 5\u00b5m per voxel (b) defect size distribution In this study cylindrical specimens were used as shown on figure 1-c. Fatigue tests have been performed at room temperature on resonance machine with a load ratio R=-1. The frequency was in the range of 80 to 82 Hz. The fatigue limit have been defined at one million cycles. A step by step method described by Iben Houria [4] were used as it is the only way to evaluate the fatigue limit for a natural defect. It is assumed that no significant damage is introduced in the loading as shown by Roy et al [11] for cast alloy A356. The failure is define by a 5Hz drop of frequency"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001742_0954406214531943-Figure12-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001742_0954406214531943-Figure12-1.png",
        "caption": "Figure 12. The idea of modeling the component finite element model. (a) The linear guideway; (b) The component finite element model.",
        "texts": [
            " In this study, it takes 59 h to complete the calculation by using DELL workstation. This computational efficiency is unacceptable. Therefore, a new finite element modeling method should be developed, which can both achieve high-calculation accuracy and complete the calculation efficiently. Modeling of the component finite element model of guideway To improve the calculation efficiency, the component finite element model is proposed in this section. The idea of creating the component finite element model is shown in Figure 12. The guideway is considered as consisting of several components, and each component contains rail slice, carriage slice, and some rolling balls. Because only the statics characteristics of vertical direction of guideway are studied in this work, the component finite element model can simulate the statics characteristics of whole guideway. When the load P is applied on the upper surface of carriage, the force of applying on the component finite element model is P/n. Under the load of P/n, the relative deformation H0 can be obtained by using the component finite element model. Then the vertical stiffness K0F of guideway is computed according to K0F P H0 \u00f026\u00de Compared with the full finite element model, the number of element and node of component finite element model is very small. In the model of Figure 12(b), there are 120,474 elements and 117,697 nodes, and during which, there are 7776 contact elements and 1152 target elements. Using the component finite element model and the same DELL workstation, the statics of guideway is recalculated, and the calculation results are also listed in Figure 11. As shown in Figure 11, the results obtained by the component finite element at UNIV OF CONNECTICUT on June 15, 2015pic.sagepub.comDownloaded from model are also consistent with the experiment. So, the correctness of the proposed method is proved"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002170_tec.2017.2789322-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002170_tec.2017.2789322-Figure8-1.png",
        "caption": "Fig. 8: FE model of a 12/10 surface PM motor used for comparison with CM-MEC method",
        "texts": [
            " For calculation of saturated inductance Lq and crosscoupling inductance Lqd, the instantaneous armature winding phase currents are set to values which will place the current vector in the q axis and the permanent magnet currents are set to zero. After obtaining the field solution using iterative CM-MEC method, inductances can be calculated as Lq = \u03a8q Iq (36) Lqd = \u03a8d Iq (37) where \u03a8d and \u03a8q are the d and q axis flux linkages when the armature current space vector I is located in the q axis (Id = 0). The proposed CM-MEC method has been implemented on a surface permanent magnet machine with 12 slots and 10 poles (Fig. 8). In Table I parameters and rated data of the analysed machine are shown. Comparisons have been made with 2D nonlinear time-stepping FEM calculations. In order to emphasize the importance of modelling magnetic saturation, comparisons have also been made with FEM calculations of an infinitely permeable 12/10 machine. Table II shows maximum flux densities that are obtained in both no-load and on-load FEM simulations to indicate high saturation levels in the core. Fig. 9 to Fig. 14 show comparisons of air-gap flux densities, back EMF and torque for no-load and rated load simulations with the initial position of the rotor corresponding to the one shown in Fig. 8. Flux density waveforms (Figs. 9 and 10) have higher values in the infinitely permeable FE model in comparison to both saturated FE and CM-MEC models, which consequently has an influence on all other quantities such as back EMF and 0885-8969 (c) 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. torque. Models that do not include saturation effect into account cannot accurately predict back EMF and torque waveforms which is especially evident in the case of on-load condition where back EMF (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001564_j.triboint.2013.06.017-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001564_j.triboint.2013.06.017-Figure5-1.png",
        "caption": "Fig. 5. Positions of the ball centre and raceway groove curvature centres at angular position \u03c8 j .",
        "texts": [
            " Under an applied load of P2, the distance between the inner and outer raceway groove curvature centres increases by the contact deformation \u03b4i and \u03b4o, as shown in Fig. 4(a). Fig. 4(b) shows the relative angular position (azimuth) of each ball in the bearing. Under an applied axial load, a centrifugal force acts on the ball. Because the ball-inner and ball-outer raceway contact angles are dissimilar, the line of action between the raceway groove curvature centres is not collinear with BD [22]. Instead, it is discontinuous, as indicated in Fig. 5. It is assumed in Fig. 5 that the outer raceway groove curvature centre is fixed in space, and the inner raceway groove curvature centre moves relative to that fixed centre. Moreover, the ball centre shifts by virtue of the dissimilar contact angles. In accordance with the relative axial displacement of the inner and outer rings da, the axial distance between the loci of inner and outer raceway groove curvature centres at angular position \u03c8 j is A1j \u00bc BD sin \u03b1o \u00fe da \u00f03\u00de The radial displacement between the loci of the groove curvature centres at each ball location is A2j \u00bc BD cos \u03b1o \u00f04\u00de Jones [23] found it convenient to introduce new variables X1j and X2j. Using the Pythagorean Theorem, it can be seen from Fig. 5 that cos \u03b1oj \u00bc X2j \u00f0f o 0:5\u00deD\u00fe\u03b4oj sin \u03b1oj \u00bc X1j \u00f0f o 0:5\u00deD\u00fe\u03b4oj cos \u03b1ij \u00bc A2j X2j \u00f0f i 0:5\u00deD\u00fe\u03b4ij sin \u03b1ij \u00bc A1j X1j \u00f0f i 0:5\u00deD\u00fe\u03b4ij 8>>>>< >>>>: \u00f05\u00de and X2 1j \u00fe X2 2j \u00bc \u00bd\u00f0f o 0:5\u00deD\u00fe \u03b4oj 2 \u00f06\u00de \u00f0A1j X1j\u00de2 \u00fe \u00f0A2j X2j\u00de2 \u00bc \u00bd\u00f0f i 0:5\u00deD\u00fe \u03b4ij 2 \u00f07\u00de Consider a plane passing through the bearing axis with the centre of a ball located at any azimuth. If \u201couter raceway control\u201d is approximated at a given ball location, the ball gyroscopic moment is resisted entirely by friction force at the ball-outer raceway contacts and, in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000369_iros.2010.5649095-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000369_iros.2010.5649095-Figure1-1.png",
        "caption": "Fig. 1. Joints of the Barrett WAM",
        "texts": [
            " It is shown that all possible geometric poses can be completely defined by three circles in the Cartesian space. This can be parameterised by a single angle parameter running over one of the circles. The usable limits on the redundancy circle have also been determined for some of the joint variables. In this approach a specific solution can be selected from the null space of solutions through specification of the elbow position. The Barrett WAM is a 7 DOF manipulator that has only revolute joints. A schematic with all the joint variables is shown in Figure 1. The first two variables specify the azimuth (J1) and the elevation (J2) of the lower arm from the base 978-1-4244-6676-4/10/$25.00 \u00a92010 IEEE 2976 position. The third variable is a twist DOF of the lower arm (J3). The fourth variable corresponds to the forearm (upper arm) elevation (J4) from the joint, or elbow angle. The fifth and the sixth variables set wrist azimuth (J5) and elevation (J6) from the forearm. The seventh variable sets the hand rotation (J7). The forward kinematics for a manipulator is easily expressed in the D-H convention, which offers a simple way to find out the end-tool position and orientation, given the seven joint variables [\u03b81, \u03b82, \u03b83, \u03b84, \u03b85, \u03b86, \u03b87]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001070_j.optlaseng.2011.10.017-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001070_j.optlaseng.2011.10.017-Figure2-1.png",
        "caption": "Fig. 2. Schematic of the first method.",
        "texts": [
            "5 mm below the nozzle exit plane (Fig. 1). The angle of each nozzle tip is 251 to the laser beam. The diameter d0 of the nozzle tube is 1.5 mm. The spherical pure titanium powder was chosen as the feeding material, which was delivered by the argon gas. The powder particle diameter was limited to a small range from 0.065 to 0.075 mm using the molecular sieves. To simplify the analysis, the equivalent diameter of the powders can be considered as 0.07 mm in this study. The schematic of the first method is shown in Fig. 2. A high speed camera is placed perpendicular to the moving direction of the powder flow. The high-power magnesium light illuminates the powder flow, and the angle between the light and the high speed camera is less than 901. Using this method, the moving powder particle will be captured by the camera with appropriate exposure time (2 10 4 s in this study) due to the reflections from the powder particles. This method will be used for the measurement of the powder particle speed. Fig. 3 shows the schematic of the powder flow concentration observation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001357_iros.2013.6696696-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001357_iros.2013.6696696-Figure1-1.png",
        "caption": "Fig. 1. Schematic representation of a six-rotor UAV platform. Inertial frame with origin O is denoted I and the body-fixed frame with origin G is denoted B.",
        "texts": [
            " The most basic multirotor helicopter configuration consists of a rigid airframe with two pairs of counter-rotating rigid propellers attached to it. Control of this platform is achieved by varying the rotational speed of the rotors. While such a four-rotor configuration already allows for full actuation of the vehicle\u2019s attitude, this configuration can be scaled up to an arbitrary number of rotors, however, the configuration should always consist of a multiple of counter-rotating rotor pairs for torque balancing reasons. In Fig. 1, a schematic of the Flybox hexacopter, used for the experimental validation of the proposed control scheme, is depicted. First, the following notation is introduced (see Fig. 1). The vehicle\u2019s center of mass (CoM) is denoted as G, its mass m, 978-1-4673-6358-7/13/$31.00 \u00a92013 IEEE 2419 and its inertia matrix J. Let I = {O;\u2212\u2192\u0131 o, \u2212\u2192 o, \u2212\u2192 k o} and B = {G;\u2212\u2192\u0131 ,\u2212\u2192 , \u2212\u2192 k } denote the inertial frame (i.e. world frame) and the frame attached to the vehicle (i.e. bodyfixed frame), respectively. Let \u03be \u2208 R 3 denote the position of the vehicle\u2019s CoM expressed in I. The rotation matrix representing the orientation of the frame B relatively to the frame I is R \u2208 SO(3). The vehicle\u2019s velocity and the wind velocity are both expressed in the frame I are denoted as \u03be\u0307 \u2208 R 3 and \u03be\u0307w \u2208 R 3, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000069_ichr.2005.1573583-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000069_ichr.2005.1573583-Figure1-1.png",
        "caption": "Fig. 1. Our inverse pendulum model, closely related to the \u2018Simplest Walking Model\u2019 of [5].",
        "texts": [
            " We use a Poincare\u0301 map analysis of a simple point-mass model (Section II). The results are shown in Section III, including a peculiar asymmetric gait that is more stable than any of the symmetric solutions. Section IV reports that the results are also valid for a model with a more realistic mass distribution. The discussion and conclusion are presented in Sections V and VI. The research in this paper is performed with an inverted pendulum model consisting of two straight and massless legs (no body) and a single point mass at the hip joint, see Fig. 1. Straight legged (\u2018compass gait\u2019) models are widely used as an approximation for dynamic walking [7], [6], [9], [8], [5]. The stance leg is modeled as a simple inverted pendulum of length 1 (m) and mass 1 (kg) (Fig. 1). It undergoes 0-7803-9320-1/05/$20.00 \u00a92005 IEEE 295 gravitational acceleration of 1 (m/s2) at an angle of \u03b3 following the common approach to model a downhill slope in passive dynamic walking. It has one degree of freedom denoted by \u03b8, see Fig. 1. The foot is a point and there is no torque between the foot and the floor. The equation of motion for the stance leg is: \u03b8\u0308 = sin(\u03b8 \u2212 \u03b3) (1) which is integrated forward using a 4th order Runge-Kutta integration routine with a time step of 0.001 (s). The swing leg is modeled as having negligible mass. Its motion does not affect the hip motion, except at the end of the step where it determines the initial conditions for the next step. A possible swing leg motion is depicted in Fig. 2 with a dashed line. As is standard with compass gait walkers, we ignore the brief but inevitable foot scuffing at midstance. The swing leg motion at the end of the step is a function of time which we construct in two stages. First we choose at which relative swing leg angle \u03c6 (See Fig. 1) heel strike should take place, \u03c6lc. This is used to find a limit cycle (an equilibrium gait), which provides the appropriate step time, Tlc. Second, we choose a retraction speed \u03c6\u0307. The swing leg angle \u03c6 is then created as a linear function of time going through the point {Tlc, \u03c6lc} with slope \u03c6\u0307. The simulation transitions from one step to the next when heel strike is detected, which is the case when \u03c6 = \u22122\u03b8. An additional requirement is that the foot must make a downward motion, resulting in an upper limit for the forward swing leg velocity \u03c6\u0307 < \u22122\u03b8\u0307 (note that \u03b8\u0307 is always negative in normal walking, and note that swing leg retraction happens when \u03c6\u0307 < 0)",
            " A benefit of this effect is that a downhill slope is no longer required, but the question is whether it breaks the stabilizing effect of swing leg retraction. Or, even if it does still help stability, whether the stability gain outweighs the added energetic cost for accelerating the swing leg. We study these questions using a model with a more realistic mass distribution, based on a prototype we are currently experimenting with [1] (Fig 9). The swing leg trajectory is optimized both for stability and for efficiency. The model (Fig. 9) has the same topology as our initial model (Fig. 1). However, instead of a single point mass at the hip, the model now has a distributed mass over the legs, see Table II. The swing leg follows the desired trajectory with reasonable accuracy using a PD controller on the hip torque: T = k(\u03c6 \u2212 \u03c6des(t)) + d\u03c6\u0307 (4) with gain values k = 1500 and d = 10. The swing leg trajectory is parameterized with two knot points defining the start and the end of the retraction phase (Fig. 10). The trajectory before the first knot point is a third order spline which starts with the actual swing leg angle and velocity just after heel strike"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001742_0954406214531943-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001742_0954406214531943-Figure9-1.png",
        "caption": "Figure 9. The finite element model of single ball bearing.",
        "texts": [
            " To improve the efficiency of analysis, a component finite element modeling method is proposed, which can attain the same calculation accuracy as the full finite element model. Finite element modeling of the single ball bearing To obtain the statics characteristics of whole guideway by FEM, the single ball bearing should be analyzed first. Here, two mass blocks are chosen to simulate the contact between rolling ball and rail or carriage, and the created finite element model of single ball bearing is shown in Figure 9. In the model, the rolling ball and two mass blocks are modeled with Solid45 element, and the contacts between rolling ball and grooves are modeled with Conta174 contact element and Targe170 target element, respectively. As a whole, the model consists of 29,972 elements and 29,163 nodes. To exclude the impact of mesh density on the results, the contact areas are refined, where the amounts of contact elements and target elements are 1944 and 480, respectively. The uniform load PA \u00bc F=A is applied on the surface of upper mass block, where A is the area of active surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002958_j.ins.2016.12.006-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002958_j.ins.2016.12.006-Figure2-1.png",
        "caption": "Fig. 2. The curves of sin ( x 1 ), x 1 , and 2 \u03c0 x 1 .",
        "texts": [
            " 35) ( u + d ) \u02d9 x2 = \u2212 sin (x 1 ) \u2212 x 2 y = x 1 } (54) where \u2212\u03c0/ 2 \u2264 x 1 \u2264 \u03c0/ 2 , and d represents the lumped disturbance given as follows: d(t) = { 0 . 8 , 3 < t \u2264 4 \u22120 . 8 , 6 < t \u2264 7 0 , otherwise . (55) Without control and disturbance, i.e., u = 0 and d = 0 , the x 1 \u2212 x 2 phase plane is shown in Fig. 1 , where circles denote the initial points and the squares denote the end points. It is observed that the system is unstable when starting from a few initial points such as (1, 4). Except for monomials in (54) , sin ( x 1 ) is the only part that is nonlinear. As shown in Fig. 2 , the curve of sin ( x 1 ) is sandwiched between the lines of x 1 and 2 \u03c0 x 1 when \u2212\u03c0/ 2 \u2264 x 1 \u2264 \u03c0/ 2 . Following the concept of sector nonlinearity [34] , sin ( x 1 ) can be expressed as follows: sin (x 1 ) = N 1 (y ) y + N 2 (y ) 2 y (56) \u03c0 where N 1 (y ) + N 2 (y ) = 1 and y = x 1 . This results in the following membership functions: N 1 (y ) = sin (y ) \u2212 2 \u03c0 y ( 1 \u2212 2 \u03c0 ) y N 2 (y ) = y \u2212 sin (y ) ( 1 \u2212 2 \u03c0 ) y \u23ab \u23aa \u23aa \u23ac \u23aa \u23aa \u23ad (57) Additionally, the nonlinear system can be represented by the following polynomial fuzzy model: Rule i : If y is N i (y ) , Then \u02d9 x = A i (x ) x + B i (x ) ( u + d ) where i = 1 , 2 , x = [ x , x ] T , and 1 2 A 1 (x ) = [ \u22121 + x 1 + x 2 1 + x 1 x 2 \u2212 x 2 2 1 \u22121 \u22121 ] A 2 (x ) = [ \u22121 + x 1 + x 2 1 + x 1 x 2 \u2212 x 2 2 1 \u2212 2 \u03c0 \u22121 ] B 1 (x ) = [ x 1 + 1 ",
            " (66) Without the control and disturbance, the x 1 \u2212 x 2 phase plane is shown in Fig. 13 , where the circles correspond to the initial points. It is clear that the system is unstable in the absence of a controller. With respect to the nonlinear system (65) , sin ( x 1 ) is the only part that is not monomial. Therefore, it is essential to deal with the part to convert (65) into a polynomial fuzzy model form. However, unlike Example 1 where x 1 is assumed as \u2212\u03c0/ 2 \u2264 x 1 \u2264 \u03c0/ 2 , sin ( x 1 ) is no longer sandwiched between the lines of x 1 and 2 \u03c0 x 1 as shown in Fig. 2 . However, according to Fig. 14 , sin ( x 1 ) is between the lines of x 1 and \u22120 . 2172 x 1 in the whole region, and finally sin ( x 1 ) is expressed as follows: sin (x 1 ) = N 1 (y ) y \u2212 N 2 (y )0 . 2172 y (67) where N 1 (y ) + N 2 (y ) = 1 and y = x 1 . This results in the following membership functions: N 1 (y ) = sin (y ) + 0 . 2172 y 1 . 2172 y N 2 (y ) = y \u2212 sin (y ) 1 . 2172 y \u23ab \u23aa \u23ac \u23aa \u23ad (68) Additionally, the nonlinear system can be represented by the following polynomial fuzzy model: Rule i : If y is N i (y ) , Then \u02d9 x = A i (x ) x + B i (x ) ( u + d ) where i = 1 , 2 , x = [ x 1 , x 2 ] T , and A 1 (x ) = [ 1 \u22120 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002476_j.ymssp.2019.106342-Figure12-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002476_j.ymssp.2019.106342-Figure12-1.png",
        "caption": "Fig. 12. UofA experimental setup: (a) Gearbox test rig in University of Alberta, (b) Schematic of the 2nd stage Speed-up gearbox, (c) Four sensor locations.",
        "texts": [
            " Noticeably, the res-spa can detect F2 whereas the res-con failed. We conclude that an improved modeling accuracy ensures the residual to contain more fault induced features, and hence benefits the health state assessment of a gearbox under TVS in early detection of faults and better assessment the severities of faults. This section evaluates the proposed sparse FP-AR model using two independent experimental datasets. This experimental dataset is collected at the University of Alberta (UofA), Canada. Fig. 12(a) shows the gearbox test rig which includes a drive motor, bevel gearbox, 1st stage planetary gearbox, 2nd stage planetary gearbox, 1st stage speedup gearbox, 2nd stage speed-up gearbox, and load motor. We choose the 2nd stage speed-up gearbox as the target of the experiment. Fig. 12(b) shows the schematic of the 2nd gearbox which has two spur gear mesh pairs. The gear and pinion of the first mesh pair have 48 and 18 teeth, respectively, whereas the second mesh pair have 64 and 24 teeth. Fig. 12(c) shows the locations of four accelerometers (1000 [mV/g] sensitivity). Without loss of generality, we analyze the vibration signals from vertical accelerometer installed on the bearing cab (Sensor #2). Furthermore, load torque and rotational speed are acquired using strain gauge sensor and encoder, respectively. We configure the speed profiles similar as the profile in simulation study. Load motor generates a constant load level of 80Nm during the experiment. Fig. 13 shows two segments of baseline vibration, as well as their corresponding speed profiles acquired by an encoder"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003394_j.compstruct.2020.112698-Figure15-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003394_j.compstruct.2020.112698-Figure15-1.png",
        "caption": "Fig. 15. Effect of local changes in the geometry on maximum principal stresses.",
        "texts": [
            " - even if the total deformation is comparable in both cases, with values in the range 20\u201330 mm, the metal roll bar exhibits dangerous deformation that is primarily in the Y direction, with 17\u201326 mm at the intersection between the central vertical bar and the front seat; practically at the back of the passenger. This situation does not take place for the CFRP safety cage, where the higher stiffness of the central pillars and top rail compared to the tubular central and top bars, respectively, eliminates the requirement for vertical reinforcing elements joined to the front seats. It must be noted that the numerical simulation was carried out with a slight modification to the real geometry. This difference, shown in Fig. 15, mainly relates to the absence of a roof rail segment over the central pillow. This \u2018window\u2019 was opened to allow better investigation into one of the most critically stress zones. This modification allowed some of the discontinuities present in the composite structure (i.e. the joining of three orthogonal composite elements) to be studied in greater detail. In terms of failure criteria, ANSYS Workbench Ver. 18.2 provides Maximum Stress,Maximum Strain and Tsai\u2010Wu Failure as standard criteria [70,71]",
            " The IRF, in particular, represents a dimensionless inverse margin to failure that is normalized against the load, where IRF> 1 means failure and IRF much lower than 1 (e.g. 0.5) means safety. As undertaken in the present study, each criterion must be considered separately for structural validation as each can cause maximum IRF for different staking sequences. Based on the numerically calculated stress states within the present study, the modeled composite structure met all safety requirements for each of the selected failure criteria (i.e. IRF < 0.50), with the exception of a single critical zone, the joint displayed in Fig. 15. Discretization and element codes for each FE within this zone are presented in Fig. 16. For this preliminary analysis and discussion of results, the Hashin criterion was utilized. This condition takes into account matrix failure due to simultaneous axial and shear stress, allowing differentiation between fiber breakage, to be avoided, and matrix failure, which can be allowed as an extreme case in the event of overturning. Fig. 17 displays the IRF map based on the Hashin criterion. For each FE, the most stressed layer (highest IRF) is also reported in brackets"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002139_b978-0-08-100433-3.00004-x-Figure4.3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002139_b978-0-08-100433-3.00004-x-Figure4.3-1.png",
        "caption": "Figure 4.3 Standard specimens to assess surface roughness versus inclination angle, f. a and b refer to the perpendicular direction of roughness measurement.",
        "texts": [
            " Numerous measures of roughness have been proposed [27]. To be compatible with other contributions in this field, the arithmetic average roughness, Ra, is used, where Ra measures the arithmetic average deviation of the measured profile from the centre line of the measured profile (Eq. (4.1)): Ra \u00bc 1 n Xn i\u00bc1 yj (4.1) where yj is the vertical distance from the mean line to the jth data point and i is the facet of interest. Specimens were fabricated to quantify the roughness of a commercial SLM method versus inclination angle1 (Table 4.2, Fig. 4.3). Optical macroscopy was recorded (Fig. 4.5) and Ra recorded for the upper and lower surfaces (Fig. 4.6). Inspection of the sample macroscopy (Fig. 4.5) and measured surface roughness (Fig. 4.6) identifies distinct topology regions associated with the inclination angle F: \u2022 For inclinations approaching horizontal (f/ 0 degree), staircase effects dominate, and the observed roughness asymptotes towards peak values. For inclinations below the 1 Note, the inclination angle, f, used in this work seems to be the most common nomenclature reported in the literature; however, q \u00bc p/2 f, for example, is also used [8]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001968_978-94-007-6101-8-Figure3.7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001968_978-94-007-6101-8-Figure3.7-1.png",
        "caption": "Fig. 3.7 Displacement with respect to reference coordinate frame",
        "texts": [
            "21) describes a displacement with respect to the relative coordinate frame. Let us examine both displacements by the help of simple example. Let us select an initial pose of a coordinate frame: P = \u23a1 \u23a2\u23a2\u23a3 1 0 0 20 0 0 \u22121 0 0 1 0 0 0 0 0 1 \u23a4 \u23a5\u23a5\u23a6 (3.22) 3.3 Displacement 47 The displacement consists from translation and rotation: D = T rans(0, 20, 0)Rot (z, 90\u25e6) = \u23a1 \u23a2\u23a2\u23a3 0 \u22121 0 0 1 0 0 20 0 0 1 0 0 0 0 1 \u23a4 \u23a5\u23a5\u23a6 (3.23) After premultiplication (3.20) the new pose is obtained: X = \u23a1 \u23a2\u23a2\u23a3 0 0 1 0 1 0 0 40 0 1 0 0 0 0 0 1 \u23a4 \u23a5\u23a5\u23a6 which is shown in Fig. 3.7. The expression for displacement (3.23) was read in the reverse order, which means, that translation with respect to the reference frame was performed after rotation. Postmultiplication of a pose by displacement D means a displacement with respect to the relative coordinate frame. After multiplication (3.21) the following new pose is obtained: Y = \u23a1 \u23a2\u23a2\u23a3 0 \u22121 0 20 0 0 \u22121 0 1 0 0 20 0 0 0 1 \u23a4 \u23a5\u23a5\u23a6 which is shown in Fig. 3.8. Here, the expression for displacement (3.23) was read in usual order (from left to right), which means that rotation was performed after translation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000035_tie.2010.2095392-Figure14-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000035_tie.2010.2095392-Figure14-1.png",
        "caption": "Fig. 14. Case of losing contact in a branched pipe.",
        "texts": [
            " The suggested method for estimating the inclination of pipes works well and enables the robot to reduce its power consumption and the stresses on its components by properly controlling the normal force. PAROYS-II can contribute to the expansion of the applicable field of in-pipe robots into various environments. The experimental results have demonstrated that the presented in-pipe robot adapts to most geometric changes other than branched pipes. In-pipe robots with three driving modules, like PAROYS-II, can face contact loss problems when they meet direction changes in a branched pipe. As shown in Fig. 14, if the robot hits a T-shaped branched pipe, one of its track modules may hang in open space opposite the desired moving direction, preventing further motion. This case has been referred to as a \u201cmotion singularity\u201d [8]. Solutions to this problem include auxiliary devices, like a wheel rotating along the circumferential direction [9] or connecting several individual robots [8]. Future research will focus on a fully autonomous in-pipe robot and a multimodule system to allow for pipeline explorations without any external aid or remote control and for applications in branched pipelines"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002283_j.rcim.2017.10.003-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002283_j.rcim.2017.10.003-Figure1-1.png",
        "caption": "Fig. 1. A closed-loop 3M system of collaborative manufacturing for hypoid gears.",
        "texts": [
            " ith state-of-the-art CNC technology [1] , the gear design and manufacuring have been closely linked each other to form a unified closed-loop eedback system. To this end, the system should be a data-driven eedback with the manufacturing requiring the high geometric and hysical performances. Here, considering the accuracy and efficiency, n advanced computer support cooperative system is proposed based on AD/CAM/CAE/CAPP (computer aided design (CAD), computer aided anufacturing (CAM), computer aided engineering (CAE), computer ided process planning (CAPP)) integrated methods. Fig. 1 represents n advanced collaborative manufacturing for hypoid gear which is a losed-loop 3 M system including the following parts: (i) Manufacturing of hypoid gear with given initial machine settings, (ii) Measurement of tooth flank after manufacturing to described a ease-off as a basic premise for modification, and (iii) Modification of machine setting to obtain the accurate machine settings providing the actual manufacturing. It is worth notation that the above three parts involves some HCIs nd are needed to be integrated by the data-driven programming",
            " Undisputedly, the core of this system is data-driven rogramming of HCI 3 for the machine setting modification. In the proosed modification, in addition to conventional geometric performance, he contact strength analysis is used to evaluate physical performance. .2. Data communication architecture From a technical perspective, the data transfer and exchange is lways an important stage to achieve the required production in odern industrial practice [27\u201328] . In the establishment of data-driven ollaborative system (as Fig. 1 ), a data communication system is stablished to realize the effective information operation in whole c i d n s e d c h d a T s i e i 2 [ X a s o i s f i p n p X i t p m f c F S X b 3 w g d m c a m t p a U i t i i t c u w o m a W p r omplex process. Here, the information integrated operation model n networked manufacturing for hypoid gear [27] is applied in the ata-driven programming system. Fig. 2 shows the global data commuication architecture for programming the HCIs. In some application ystems for the collaborative manufacturing, such as the manufacturing xecution system (MES), enterprise resource planning (ERP), product ata management (PDM), a web services-based integration is used to omplete the integration and transformation of data information for ypoid gear manufacturing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003304_j.jsv.2019.01.048-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003304_j.jsv.2019.01.048-Figure4-1.png",
        "caption": "Fig. 4. The diagram of bearing zone.",
        "texts": [
            " 3, the rectangular function is applicable to constant displacement excitation; the half-sine function is applicable to time-varying displacement excitation; the segmented function is applicable to time-varying and constant displacement excitation simultaneously. According to the analysis in section 3.1, the improved displacement excitation function is based on the half-sine function. According to the kinetic characteristics of the deep groove ball bearing, there are several rolling elements that bear the load at the same time when the bearing running, and the bearing region is symmetrical along the direction of the external load, as shown in Fig. 4. The number of the load-bearing rolling elements and the load-bearing range increase with the external load and the number of rolling elements. Due to the mechanical characteristics of ball bearings, the uniform distribution of rolling elements and the principle of force balance, the force condition of the all bearing rolling elements are coupled with each other in the bearing area. Hence, the force conditionwill change when there are impacts or other changes of force condition on one of the bearing rolling elements",
            " However, the measured acceleration response of fault bearing appears obvious impact with symmetrical amplitudes at the failure position, as shown in Fig. 9(b). Thus, those traditional faulty bearing dynamic models cannot express the dynamic response accurately. It follows that the bearing dynamic model with improved displacement excitation function is proposed. For better mathematical calculation and consideration of timevarying displacement excitation, the improved displacement excitation function is based on the half-sine function. The rolling elements contact with raceway only in a certain angle range according to Fig. 4 and Eq. (14). Therefore, when the rolling element is outside of the valid contact area, the Hertz contact force between it and the raceway is 0. The Hertz contact force between the single rolling element and the raceway is derived from Eq. (13): Fyi \u00bc Kmi\u00f0X cos qi \u00fe Y sin qi g hi\u00de1:5 (15) With the above equation, the Hertz contact force between the single rolling element and raceway can be numerically calculated. The force response results of the bearing with faults of 1, 5 or 9 listed in Table 1 are illustrated in Figs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002270_tmag.2017.2706764-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002270_tmag.2017.2706764-Figure1-1.png",
        "caption": "Fig. 1 Cross section of the series hybrid VFM machine.",
        "texts": [
            " However, due to the distinct PMs located on the alternate poles, the magnetic unbalance occurs in the proposed series hybrid VFM machine, which causes unipolar z-axis leakage flux [12]. The z-axis leakage flux not only decreases torque output but also poses threats to the mechanical components, such as bearing life. In this paper, the characteristics of the series connected PMs are investigated, then the rule of achieving balanced field in the series hybrid VFM machines is revealed. As illustrated in [11], the cross section of the series hybrid VFM machine is shown in Fig. 1. The 48-stator-slot/8-rotor pole configuration equipped with distributed windings to obtain reluctance torque is employed, which is identical to the commercial Prius2010 IPM machine. Moreover, the VPMs and CPMs are alternately accommodated on the adjacent rotor poles to achieve the series connection, where all VPMs have the same polarity while all CPMs have the opposite one. The major demagnetization curves of the CPM and VPM, which are NdFeB and SmCo respectively, are shown in Fig. 2. It can be seen that the VPM has a relatively low coercive force (Hc), and its knee point, the point beyond which the demagnetization curve becomes nonlinear, is high in Quadrant II"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001711_s1560354713060166-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001711_s1560354713060166-Figure7-1.png",
        "caption": "Fig. 7. The region of positive definiteness of a drift on the plane of first integrals (indicated by inclined shading).",
        "texts": [
            " The Region of Positive Definite Drift Consider the following problem, which can be solved by purely topological methods: find the values of first integrals of a system for which the function Vx on the invariant torus is positive definite. As discussed above, the boundary of this region is defined by min Vx = 0. Let us fix the values of first integrals of the system as follows \u03b32 = 1, M2 = C, (M,\u03b3) = M\u03b3 , 2E = E . (4.2) We show that the following theorem holds for the Chaplygin ball. Theorem 1. Let M \u2226 \u03b3, I3 < I2 < I1, then the velocity of the contact point Vx is positive definite on the invariant torus if the constants of the first integrals satisfy the conditions (see Fig. 7): M2 \u03b3 C > (I1 + I3) EM2 \u03b3 C2 \u2212 I1I3 E2 C2 , E \u2208 ( M2 \u03b3 I1 , M2 \u03b3 I2 ) \u222a ( M2 \u03b3 I2 , M2 \u03b3 I3 ) . (4.3) REGULAR AND CHAOTIC DYNAMICS Vol. 18 No. 6 2013 Proof. It follows from (4.1) that the extrema of the function Vx on the invariant tori coincide with those of the function Z = (AM ,\u03b3) D\u22121 \u2212 (\u03b3,A\u03b3) . (4.4) In the previous section it was shown that if such functions are explicitly restricted to a torus, they are very cumbersome (particularly for M\u03b3 = 0), therefore, to find the critical points of Z, we make use of the method of undetermined multipliers and seek the extrema of the function \u03a6 = Z + \u03bb0(\u03b32 \u2212 1) + \u03bb1(M2 \u2212 C) + \u03bb2 ( (M ,\u03b3) \u2212 M\u03b3 ) + \u03bbH ( E \u2212 1 2 E ) , (4",
            " Solving these equations for \u03c8k and Vk, which we shall assume to be free parameters, we obtain three families of solutions: M\u03b3 = ( cos 2\u03c8k + Ii + Ij Ii \u2212 Ij ) Vk, C = (I2 i \u2212 I2 j ) cos 2\u03c8k + I2 i + I2 j (Ii \u2212 Ij)2 2V 2 k , E = (Ii \u2212 Ij) cos 2\u03c8k + Ii + Ij (Ii \u2212 Ij)2 2V 2 k , Uk = Ii + Ij Ii \u2212 Ij Vk. Eliminating \u03c8k and Vk, we obtain equations for the surfaces \u03c3ij in explicit form in the space of values of the first integrals, for which the velocity of the contact point vanishes at one of the points of the extremum on the invariant torus: \u03c3ij : E2IiIj \u2212 EM2 \u03b3 (Ii + Ij) + CM2 \u03b3 = 0, E \u2208 ( c2 Ii , c2 Ij ) . (4.12) Rewriting this relation for the constants h = ED C and g = M\u03b3\u221a C , we obtain D\u22122IiIjh 2 \u2212D\u22121(Ii + Ij)hg2 + g2 = 0 and show the corresponding curves on the bifurcation diagram (see Fig. 7). We can see that in the case I3 < I2 < I1 the curve \u03c313 is closer to the axis g = 0 than the others, hence, the velocity Vx vanishes on it, i.e., it corresponds to the condition minVx = 0. Taking into account the possible motion on the plane (g, h) and eliminating the solution corresponding to the bifurcation curve \u03c32, we obtain inequalities (4.3). Remark. The position of critical points of the function Z on the invariant torus depending on the values of first integrals can be defined as follows",
            " detB1 = detB2 = detB3 = 0 (all three multipliers vanish simultaneously). Expressing \u03bb1 and \u03bbH from two equations detBi = detBj = 0 by the formulae (4.9) and substituting into the third equation, we obtain detBk = AiAj A2 k (Ai \u2212 Ak)(Aj \u2212 Ak). Hence, in the case of a dynamically asymmetric ball detBk = 0, therefore, this condition cannot be realized. Thus, the region of positive definiteness of Vx is defined only by inequalities (4.3), and a drift in the direction of Ox always occurs for values of the integrals which correspond to the shaded region in Fig. 7. Analysis of the drift for other values of the first integrals (the unshaded area on the diagram, Fig. 7) requires application of the analytical approach (see the Appendix). First of all, it is necessary to calculate the drift velocity averaged over the invariant torus \u3008Vx\u3009. Computer experiments suggest the following. Hypothesis. The average velocity \u3008Vx\u3009 is strictly positive for M \u2226 \u03b3 and \u3008Vx\u3009 = 0 for M \u2016 \u03b3. 4.2. Bifurcation Analysis and the Types of Trajectories of the Contact Point Figure 8 shows examples of dependences of Vx(t) for the initial conditions from various regions in Fig. 7 and the corresponding traces of the contact point. As seen in the figures, one part of the minima of the function Vx(t) in the region between the curves \u03c312, \u03c323 and \u03c313 lies above zero and the other part lies below zero. Each segment of negative velocity corresponds to a typical loop on the trajectory of the contact point. Thus, in this region of the diagram on the trajectory of the contact point, loops appear only in the part of the maxima of the curve y(x). In the region between the curves \u03c312 and \u03c34 (or \u03c323 and \u03c34) all minima of the function Vx(t) lie below zero and, consequently, loops appear on all maxima of the curve y(x)",
            " \u2013 For the Chaplygin ball with axisymmetric mass distribution, we have proved the absence of transverse drift, and the boundedness of motion in the case M \u2016 \u03b3. REGULAR AND CHAOTIC DYNAMICS Vol. 18 No. 6 2013 Among the unresolved issues relating to the problem considered we mention 1. Proof of the hypothesis of boundedness of the motion of a ball in the case M \u2016 \u03b3 for arbitrary moments of inertia. 2. Proof of the positiveness of longitudinal drift outside the region of positive definiteness of velocity Vx (see Fig. 7). 3. Calculation of the value of longitudinal drift depending on the values of first integrals of the system. 4. Proof of the fact that for resonant tori which do not satisfy the conditions of Proposition 2 there always exists a transverse drift (i.e., proof of sufficiency of the condition of Proposition 2). 5. Proof of existence or nonexistence of nonresonant tori with an unbounded amplitude of oscillations in the axis Oy (i.e., proof of nonuniform convergence of the Fourier series for the coordinate y)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000911_tmech.2014.2311382-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000911_tmech.2014.2311382-Figure2-1.png",
        "caption": "Fig. 2. Typical stiffness and hysteresis curve of a harmonic drive. (a) Stiffness and hysteresis curve. (b) Straight lines approximation.",
        "texts": [
            " To represent the nonlinear stiffness, the manufacturer suggests using piecewise linear approximations [19], while several researchers have used a cubic polynomial approximation [2], [6]. The nonlinear flexspline output torque TF is approximated by a third-order polynomial function of the torsional angle as TF = a1 \u03b8 + a3( \u03b8)3 (10) where \u03b8 is the torsional angle of the harmonic drive, a1 and a3 are constants to be determined. Another method of estimating the torsional angle is described in [19], where \u03b8 is approximated by a piecewise linear function of the output torque as shown in Fig. 2(b). The piecewise linear function is given by \u03b8 = \u23a7 \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a9 TF K1 , TF \u2264 T1 T1 K1 + TF \u2212 T1 K2 , T1 < TF < T2 T1 K1 + T2 \u2212 T1 K2 + TF \u2212 T2 K3 , TF \u2265 T2 (11) where K1 , K2 , K3 , T1 , and T2 are given by the manufacturer. When the harmonic drive torsion is assumed to be caused by flexspline only, the torsional angle can also be determined as \u03b8 = \u03b8F o \u2212 \u03b8F i (12) where \u03b8F o denotes the flexspline angular position at the load side which is measured using the link-side encoder. In general, only the wave generator input position (motor\u2019s angle) and flexible output position (joint\u2019s angle) are measurable",
            " This misalignment is dependent on the magnitude of the torque applied to the wave generator plug as well as the load torque. This compliance of the wave generator needs to be taken into account when modeling the harmonic drive compliance. In this section, a model of the compliance of the flexspline and the wave generator is derived first, and then the complete compliance model of the harmonic drive is given. Remark 1: The compliance of wave generator can be readily understood by observing the curve shown in Fig. 2(a). The torsional angle could have a value between B and B\u2019 at zero flexspline torque, which clearly indicates that this torsion is not due to flexspline flexibility. This deformation is due to the torque at the wave generator and cannot reach zero because of the hysteresis. The following assumption is made for deriving the model for the harmonic drive. Assumption 1: The angle at the flexspline input (gear-toothed circumference) is assumed to be equal to the angle of the wave generator output (outer rim of the ball bearing)",
            " When F > Ff r , spring (b) is compressed by (F \u2212 Ff r ), and the displacement \u0394X can be described by X = Fa/Ka + Fb/Kb . Moreover, spring-mass systems exhibit friction-induced hysteresis behavior which is similar to that observed in harmonic drives [24]\u2013[27]. Therefore, the two- spring system describes the stiffness and hysteresis behavior of the harmonic drive transmission. To study the analogy of this system to the harmonic drive, simulations were used to compare the typical stiffness curve of the harmonic drive, shown in Fig. 2(a), to that of the two-spring system. Fig. 5 shows the force of spring (b) Fb versus the force applied to spring (a) Fa ; and Fig. 6 shows the stiffness curve and the hysteresis loss caused by friction for the harmonic drive and the two-spring system. From Fig. 6, it is clear that the two-spring system stiffness curve replicates the shape of harmonic drive typical stiffness and hysteresis curve. The mismatch between these two shapes stems from the fact that the spring\u2019s stiffness is assumed linear whereas the harmonic drive stiffness is nonlinear",
            " (21) Equations (10) and (11) describe the nonlinear compliance of the flexspline, but are inconvenient to use in control system design. Equation (11) has discontinuity and is not accurate as the curve was approximated by three straight lines. Equation (10) does not have discontinuity, but not convenient to use as the inverse is required. It is more suitable to describe the torsional angle as a function of the torque, especially for control purposes. By observing (10) and the stiffness curve in Fig. 2(a), it is clear that the local elastic coefficient increases as TF increases. Let us define, the local elastic coefficient KF L as KF L = dTF d \u03b8F . Considering the symmetric property of the harmonic drive stiffness and using Taylor expansion, the local elastic coefficient can be approximated by KF L = KF 0 ( 1 + (CF TF )2) (22) where KF 0 and CF are constants to be determined. If KF 0 = 0, then the flexspline torsion can be calculated as \u03b8F = \u222b TF 0 dTF KF L . (23) By substituting the expression for KF L in (22) into (23), one can obtain the following expression: \u03b8F = arctan(CF TF ) CF KF 0 (24) where arctan(",
            " (27) Finally, the total deformation of the harmonic drive is obtained by substituting the flexspline and wave generator deformation given in (24) and (27) into (21) \u03b8 = arctan(CF TF ) CF KF 0 \u2212 sign (Tw ) Cw NKw0 (1 \u2212 e\u2212Cw |Tw |). (28) Remark 2: Information about motion-reversal points is implicit in (28) due to the fact that Tw incorporates information about the direction-dependent friction torque. In this section, a systematic way of estimating the parameters of the proposed harmonic drive model is described. The typical stiffness and hysteresis curve of the harmonic drive, as provided by manufacturer\u2019s specification sheet [19], is depicted in Fig. 2. From the stiffness and hysteresis curve shown in Fig. 2(b), the local elastic coefficients at torque T1/2 and (T1 + T2)/2 are K1 and K2 , respectively. These local elastic coefficients can be calculated using (22), as follows: K1 = KF 0 ( 1 + (CF T1/2)2) (29) K2 = KF 0(1 + (CF (T1 + T2)/2)2). (30) By solving (29) and (30) for KF 0 and CF , one can obtain the following: KF 0 = K1 + (K1 \u2212 K2)T 2 1 (T1 + T2)2 \u2212 T 2 1 (31) CF = 2 \u221a K2 \u2212 K1 K1(T1 + T2)2 \u2212 K2T 2 1 . (32) From the typical stiffness and hysteresis curve shown in Fig. 2(b), the stiffness of the wave generator at zero output torque can be estimated using the following relation: Kw0 = 2Tf s N\u03a8 (33) where \u03a8 denotes the hysteresis loss and Tf s is the harmonic drive\u2019s starting torque. From (27), the maximum torsion of the wave generator at one direction is 1/(Cw NKw0). It is also evident from Fig. 2 that the total deformation due to the wave generator compliance at one direction is half of the hysteresis loss \u03a8. Therefore, one can write 0.5\u03a8 = 1 Cw NKw0 . (34) Solving (34), one can obtain Cw = 2 NKw0\u03a8 . (35) To investigate the behavior of harmonic drive systems, a test station is set up as shown in Fig. 9. In this experimental setup, the harmonic drive is driven by a brushed DC motor from Maxon, model 218014. Its weight is 480 g, with maximum rated torque of 188 mNm, and torque constant of 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001488_piee.1965.0386-Figure12-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001488_piee.1965.0386-Figure12-1.png",
        "caption": "Fig. 12 Effective skew",
        "texts": [
            " 12, DECEMBER 1965 Variation ofkdi with frequency The factor kdN is shown plotted against frequency in Fig. 10, with permeability j i i a sa variable parameter. The Figure applies to laminations of thickness 0-635 mm used in the experimental rotors. The choice of permeability is explained in the next Section. 2.4 Core losses in rotor teeth 2.4.1 Damping of the tooth flux In a squirrel cage, each rotor tooth has a low-impedance loop surrounding it, and therefore circulating currents can be induced in this loop to oppose the flux penetration into the tooth. By considering the analogous system of Fig. 12, it can be 2323 easily shown that the ratio of tooth fluxes, with and without the current i2 flowing, is (36) where M is the mutual flux and l2 the secondary leakage. Although the differential harmonic reactance x2dv is normally considered as a leakage for calculations of torque from the equivalent circuit, in the context of the present discussion it cannot be so considered, since it is directly the result of the harmonic currents induced in the squirrel-cage bars by the air-gap harmonic fields",
            " in calculating kdh) should be the average incremental permeability, given by &B A n of 900 was chosen for the numerical calculations, and this was based on the experimental results of Spooner18 and Ball.15 2324 2.5 Effective skew Since the flux density in the air gap of a machine does not vary in the axial direction, the currents induced in the rotor would flow axially if allowed to do so. Thus, if the bars of a squirrel cage are skewed, the currents will not flow parallel to the centre line of the bar, but in a direction more nearly axial, as shown in Fig. 12. The current density at the end of the bar would be much higher at the extreme right-hand corner (Fig. 12) than at the left-hand tip. The current density at the left-hand corner is therefore assumed to be zero, and the density distribution across the bar width is arbitrarily taken to be linear, as shown in Fig. 13. With this assumption, the effective skew can be calculated as (4D where A\u0302 is the geometrical skew, and w2e is the effective width of the bar. For a coffin-shaped bar, w2e can be taken as the mean width w2. 3 Experimental investigation 3.1 Description of machines All experimental work described in this paper was performed on 7^hp 3-phase squirrel-cage induction motors with cast aluminium rotors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000467_0954406212470363-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000467_0954406212470363-Figure1-1.png",
        "caption": "Figure 1. Generic experimental geometry considered for the simulation.",
        "texts": [
            " Direct laser deposition, laser cladding, laser deposition, finite element analysis modelling, numerical simulation Date received: 4 May 2012; accepted: 12 November 2012 Currently, aero-engine components are produced by combined manufacturing processes that include forging, rolling and subtractive CNC mechanical machining.1 Use of these processes in the machining of certain components from solid blocks can lead to massive wastage of material2 and high cycle time. Evidence of this is with the aero-engine component shown in Figure 1, whose CNC machining out of an axisymmetric forged and preformed component of Inconel 718 led to a material wastage of about 85%. The direct laser deposition (DLD) process has on the other hand, demonstrated its capability in the production of parts with complex three-dimensional (3D) geometries.3 Over the past few years, this process has gained increasing attention in the industry for the rapid manufacture, repair and modification of high-cost material such as super alloy components.4\u20137 Towards increasing the efficiency of material utilisation involved in the manufacture of the aeroengine component of the complex shape in Figure 1, the highlighted attributes of the DLD process stand out to recommend its capabilities in that respect and thus its exploration in the current research. Despite the widely recognised merits of the DLD process in the manufacture of components in general, a negative aspect with it is the high thermal gradients generated during laser heating process and the subsequent residual stress generation during cooling.8\u201311 1School of Mechanical, Aerospace and Civil Engineering, Laser Processing Research Centre, University of Manchester, UK 2Near Net and Fusion Welding Group, Rolls-Royce plc, UK 3The Welding Institute, TWI Technology Centre (Yorkshire), UK Corresponding author: S Marimuthu, Wolfson School of Mechanical and Manufacturing, Loughborough University, Loughborough, LE11 3TU, UK. Email: S.Marimuthu@lboro.ac.uk at University of Ulster Library on April 28, 2015pic.sagepub.comDownloaded from This often causes permanent distortion in components,6,12\u201315 which may sometimes lead to unacceptable tolerance and crack formation. With regard to the manufacture of the aero-engine component shown in Figure 1, the initial trials with the process resulted in high axial distortion of the base plate. This effect was speculated to be caused by the relatively thin substrate (base plate) compared to the laser deposited clad layers. Recovering such residual stress induced distortion in components through post-heat treatment is difficult.16 Consequently, strategies of minimising distortion in the substrate need to be identified. In that respect, laser cladding simulations have been investigated by various researches although most previous works, however, involve studies of laser cladding on simple flat geometries9,17,18 that are deposited with a few layers of cladding",
            " The modelling of metal deposition processes is highly complex as it generally includes phenomena such as mass transfer, phase transformation, heat transfer by conduction, convection and radiation; all of which occurring at the same time. Accurate modelling of at University of Ulster Library on April 28, 2015pic.sagepub.comDownloaded from the process involving physics from such interacting fields requires the solution of a highly non-linear problem. Full-fledged FE modelling of a complex 3D geometry (as shown in Figure 1) is impractical and every efforts have been made to choose appropriate and useful assumptions which helps to simulate the laser cladding process close to reality. The following are the specific assumptions considered in the current analysis: 1. Distortion in the DLD processes is a consequence of generated stresses.4 The stress is caused primarily by the thermal gradient20,21,23,24 induced by the laser heating. 2. The laser deposition process is simulated by adding prescribed amount (one segment per time step as shown in Figure 3(b)) of material at specific temperature and time"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002731_iet-est.2018.5050-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002731_iet-est.2018.5050-Figure5-1.png",
        "caption": "Fig. 5 Rotor slot dimensions",
        "texts": [
            " It can be controlled by various high-performance control techniques. However, from (14) it can be observed that the breakdown torque depends on rotor leakage inductance which in turn depends on the rotor slot permeance and rotor slot dimensions. It is given by [30] \u03bbu = hr4 3br2 + hr3 br2 + hr1 br1 + hr2 br2 \u2212 br1 lnbr2 br1 . (17) To observe the pattern of breakdown torque, efficiency and power factor with the variation of rotor slot dimension, a parametric study on the rotor slot shape is performed. Fig. 5 shows the proposed IET Electr. Syst. Transp. \u00a9 The Institution of Engineering and Technology 2018 3 rotor slot shape for the analytical study. Rotor slot width br2 and height hr4 are varied keeping all other dimensions fixed. The dimensions of the rotor slot are given in Table 4. The dimensions of the rotor slot are varied to a limit such that the rotor bar current density and rotor tooth width are within the standard design limits. Figs. 6a and b show the rotor leakage inductance and breakdown torque with variation in rotor slot parameter, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002055_s00170-018-1913-1-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002055_s00170-018-1913-1-Figure1-1.png",
        "caption": "Fig. 1 a Strut 0.7 mm, hexagon; b strut 0.55 mm, circle; c strut 0.6 mm, square",
        "texts": [
            " The sample is fabricated using the EOSINT M270 adapting the laser-sintering framework with improved parameters to acquire the full thickness of laser-sintered parts. In this work, the sample was fabricated with an open cellular structure with four controlled parameters. Ti6Al4V powder with a mean particle size of 30 \u03bcm is used in this investigation. The powder quality is imperative to lessen the substance of debasements (oxygen, hydrogen, and nitrogen), which may influence mechanical properties of laser-sintered parts. Design of experiments is used to develop the experiment table. The parameters were divided into three levels, as shown in Table 2. Figure 1 shows the strut designs that were drawn using CAD software. Based on the design, their volume porosity is determined to be 70, 75, 80, 85, 90, and 95%, respectively. Total numbers of samples fabricated is 13 with 5 replications for each parameter. All of the samples Table 1 Composition of the Ti6AL4V powder Materials Aluminum Vanadium Carbon Nitrogen Oxygen Hydrogen Iron Yttrium Other Titanium % 6.75 4.50 0.08 0.05 0.2 0.0125 0.3 0.005 0.1 Remainder were successfully built with optimum machine setting parameter"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000679_j.ymssp.2010.02.003-Figure13-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000679_j.ymssp.2010.02.003-Figure13-1.png",
        "caption": "Fig. 13. Gear position when the second tooth pair comes in contact and the pressure in the trapped volume equals the outlet pressure.",
        "texts": [
            " 12 depicts the length of action, highlighting some important points in the calculus of the pressure torque; in particular, points I and F are the starting and the ending points of the length of action, while points B and A represent the positions where the number of meshing tooth pairs changes, in B from two to one and in A from one to two. When a new tooth pair starts the contact in I, the antecedent one is in contact in A, see Figs. 12 and 13. As the contact point of the new subsequent tooth pair (second pair in Fig. 13) moves from I to B, the contact point of the antecedent tooth pair (first pair in Fig. 13) moves from A to F, ending its contact in F. Then, from B to A only one tooth pair exists. When two tooth pairs are in contact, a trapped volume between them is created, so the trapped volume exists only along IB and AF . Points C and D in Figs. 12 and 13 denote the intersections of the profile of the relief grooves with the line of action, so CD is the \u2018seal line\u2019 due to the relief grooves. The situation of ideal \u2018seal line\u2019 is firstly considered, in which it equals the base pitch, i.e. CD \u00bc Wprbk. Therefore, the trapped volume will be connected through the relief grooves to the outlet chamber when the contact point moves along IC , and to the inlet chamber along DF , but not to both at the same time. Since the two gears have equal geometrical parameters and the relief grooves are symmetric with respect to the line connecting the gear centres, the result is IC AD \u00bc IB=2\u00bc AF=2\u00bc yprbk\u00f0e 1\u00de=2. When the subsequent tooth pair comes into contact in point I (Fig. 13), the contact point that actually separates the outlet and inlet volumes is point A; therefore, the pressure inside the trapped volume equals the outlet pressure and the only unbalanced space refers to the first contact point A. This condition remains the same when the contact point moves along IC for the subsequent tooth pair and along AD for the antecedent tooth pair, while the time increases from 0 to T\u00f0e 1\u00de=2. Therefore, in this time interval, the radii of the contact point in the pressure torque expressions (26) refer to the antecedent tooth pair in contact"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001908_j.procs.2017.01.046-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001908_j.procs.2017.01.046-Figure4-1.png",
        "caption": "Figure 4 shows the closed-loop system with L1 adaptive controller. The controller includes a reference model and a lowpass filter C(s). Adding the low-pass filter C(s) does two important things. First, it limits the bandwidth of the control signal u being sent to the plant. Second, the portion of that gets sent into the reference model is the highfrequency portion.",
        "texts": [
            " Equation of Movement Assume a common factor of proportionality k and F T , each equation of movement for quadcopter has written down below: 1 4 2 3 1 2 3 4(( ) ( ))k k k k k 1 2 3 4 1 2 3 4(( ) ( ))k k k k k 1 3 2 4 1 2 3 4(( ) ( ))k k k k k 1 2 3 4 1 2 3 4(( ))F k k k k k by using matrices: 1 2 3 4 k k k k k k k k k k k k k k k k F (7) 1 1 2 2 3 3 4 4 k k k k k k k k Kk k k k k k k k F (8) According to equation (8), controlling the four input forces (roll, pitch, yaw, thrust) can be write down as below, 1 12 3 4 k k k k k k k kK k k k k k k k k F F , (9) Closed-loop response 1 y s H s C s r s H s C s d s , (10) Response to reference r(s) Response to disturbance d(s) where 1 A s M s H s C s A s C s M s (11) Adaptive function and controller: : _ _ ( ),C xxx rate controller e that is: 0 ( ) ( ) : ( ) ( ) ( ) t p i d de t c t K e t K e d K dt , (12) In a discrete world (at kth sampling instant): 0 ( ) ( 1) ( ) : ( ) ( ) k p i d j e k e k C k K e k K e j T K T , (13) Fig.4 L1 adaptive feedback control block diagram. Fig.5 Full block diagram of the L1 adaptive control system of quadcopter. 4. Simulation Results Numerical results obtained in figures 3-4 approved that effects from [6-8] which were called \u201careas of linear behavior\u201d and \u201careas of closing\u201d could be obtained and for queueing system with retrial. Also from these chart can be seen that changing retrial probability for both types of packets can be used as one more effective way of loss control in queueing model"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000603_s11460-009-0065-3-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000603_s11460-009-0065-3-Figure5-1.png",
        "caption": "Fig. 5 Type I RC rotorcraft. (a) Rmax; (b) ZALA 421-02; (c) Schiebel S-100; (d) Dragon Warrior",
        "texts": [
            "howto = 22&page = 1 view, the RC rotorcraft can be further categorized into three types based on its size and characteristics. 1) Type I includes the monsters of the RC rotorcraft. It is generally and relatively large in size and rotorspan. As summarized in Table 1, it has top-level engine power, flight endurance and payload. This type of RC rotorcraft includes Rmax1) from Yamaha, ZALA 421-022) from ZALA Aero, Schiebel S-1003) from Schiebel, and Dragon Warrior4) from the US Naval Research Lab (see Fig. 5). Because it is large in size, its aerodynamics is relatively more stable and some of its members adopt a configuration without the stabilizer bar. Compared with the other two types below, Type I rotorcraft is more suitable for long-endurance flight missions. 2) Type II covers the main stream of the RC rotorcraft, and it is specially designed for the RC-hobby purpose. Over 100 brands of Type II rotorcraft are currently available in the market. Shown in Fig. 6 are Raptor 90 SE5) of Thunder Tiger, Dauphin6) of Hirobo, Maxi-Joker 27) of Joker-USA, and Observer-Twin8)of Bergen, to name a few"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000857_j.cma.2013.12.017-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000857_j.cma.2013.12.017-Figure8-1.png",
        "caption": "Fig. 8. shaft an",
        "texts": [
            " This algorithm for tooth contact analysis does not depend on the precondition that the surfaces are in point contact or the solution of any system of nonlinear equations as the existing approaches, and can be applied for tooth contact analysis of gear drives in point, lineal, or edge contact as it will be shown below. All TCA analyses are conducted under rigid body assumptions so that no elastic tooth deformation due to actual loading is considered when TCA results are shown. Relative positioning of the wheel with respect to the pinion is considered in order to investigate the sensitivity of the contact patterns and function of transmission errors when errors of alignment occur. The errors of alignment considered are: (i) DA2 as the axial displacement of the wheel with respect to the pinion (Fig. 8(a)), (ii) DC as the center distance error (Fig. 8(b)), (iii) DV as the intersecting shaft angle error (Fig. 8(c)), and (iv) DH as the crossing shaft angle error (Fig. 8(d)). Fig. 9 represents the applied coordinate systems for tooth contact analysis (TCA) and simulation of transmission errors. The following auxiliary coordinate systems have been defined: Parameter PINION WHEEL Number of teeth, N 24 34 Module, m [mm] 2 Face width, FW [mm] 20 Young\u2019s Modulus, E [GPa] 210 Poisson\u2019s ratio, m 0.3 Nominal torque applied, T [Nm] 150 \u2013 Angles /1 and /2 are the angles of rotation of the pinion and wheel, respectively. The common basic geometric design data for all examples of design investigated are shown in Table 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000501_s10311-010-0289-8-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000501_s10311-010-0289-8-Figure2-1.png",
        "caption": "Fig. 2 Cyclic voltammograms of a carbon paste electrode in 0.1 M PBS (pH 7.0) at scan rate 20 mV s-1 and b as (a) ? 200 lM phenylhydrazine; (c) as (a) and (d) as (b) at the surface of ferrocenemodified carbon paste electrode and carbon nanotube paste electrode, respectively. Also, (e) and (f) as (b) at the surface of ferrocenemodified paste electrode and ferrocene-modified carbon nanotube paste electrode, respectively",
        "texts": [
            " The antifouling properties of modified electrode toward phenylhydrazine and its oxidation product were investigated by recording the cyclic voltammograms of this modified electrode before and after using in the presence of phenylhydrazine. The cyclic voltammetry of phenylhydrazine at the surface of modified electrode after 15 repetition cycles at a scan rate 20 mVs-1 shows the oxidation peak potential of phenylhydrazine was not changed, and the anodic peak current was decreased by less than 3.35%. However, we regenerated the surface of modified electrode before each experiment. Electrochemistry of phenylhydrazine at modified electrode Figure 2 depicts the cyclic voltammetric responses from the electrochemical oxidation of 200 lM phenylhydrazine at ferrocene-modified carbon nanotube paste electrode (curve f), ferrocene-modified carbon paste electrode (curve e), carbon nanotube paste electrode (curve d), and bare carbon paste electrode (curve a). As can be seen, the anodic peak potential for the oxidation of phenylhydrazine at ferrocene-modified carbon nanotube paste electrode (curve f) and ferrocene-modified carbon paste electrode (curve e) is about 370 mV, while at the CNPE (curve d) peak potential is about 700 mV, and at the bare carbon paste electrode (curve b) peak potential is about 755 mV for phenylhydrazine"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000014_j.triboint.2008.11.003-Figure11-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000014_j.triboint.2008.11.003-Figure11-1.png",
        "caption": "Fig. 11. Dismounted and disassambled ball bearing.",
        "texts": [
            " The spectrum at 1412 h shows the outer defect in the ball bearing as well as inner and ball defects. When the planned test set is completed, both bearings are dismounted and then they are disassembled by cutting their outer rings and cages using EDM. Rolling raceways surfaces of outer and the inner rings as well as the surfaces of rolling elements are Fig. 12. Outer ri investigated using an Olympus GX71F microscope system equipped with a digital camera and a capture program. The picture of one of the dismounted ball bearings is given in Fig. 11. Fig. 12 shows the different sections of the outer ring rolling surfaces. Different stages of fatigue due to cyclic contact force are seen in this figure. The general form of surface wear is generally pitting. However, denting of the particle, which is probably spalled from other surface sections, is also visible in Figs. 12a and b. In Fig. 12c, spall progress is also visible in the upper right of the figure in the direction of rolling. In Fig. 12b, the surface is blistered and new spalls are about to occur"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001843_s00170-015-7697-7-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001843_s00170-015-7697-7-Figure1-1.png",
        "caption": "Fig. 1 Deposition of multiple layers during additive manufacturing",
        "texts": [
            "hin walls can be successfully processed by additive manufacturing using plasma transferred arc. Keywords Additivemanufacturing . Plasma transferred arc (PTA) . Nickel-based superalloys . Microstructure Additivemanufacturing (AM) refers to the production of components by deposition of multiple layers to obtain the desired 3D geometry. The process is based on CAD models, which divide the component or area to be restored into various layers so that the deposition path and sequence can be planned. The layers are produced by a deposition process supported by a CNC positioning system (Fig. 1). The most frequently found AM parts are processed by laser. However, arc deposition processes, such as gas metal arc welding (GMAW) and gas tungsten arc welding (GTAW), and plasma processes have become the subject of increasing attention in the international literature [2]. AM is also known as 3D printing, additive processing, and free-form fabrication [2]. The main advantages of AM are the freedom of design it allows and the possibility of manufacturing complex shapes and with a wide variety of materials"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003486_j.ijmecsci.2020.105665-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003486_j.ijmecsci.2020.105665-Figure5-1.png",
        "caption": "Fig. 5. Definition of the critical plane under a multi-axial stress state.",
        "texts": [
            " Since the critical plane at ach material point is unknown, the shear strain, the normal strain and he normal stress at each candidate plane should be calculated based pon the time-varying stress components extracted from the finite eleent simulation [36 , 37] : \ud835\udf03 = \ud835\udf0e\ud835\udc65 cos 2 \ud835\udf03 + \ud835\udf0e\ud835\udc67 sin 2 \ud835\udf03 + 2 \ud835\udf0fxz sin \ud835\udf03 cos \ud835\udf03 \ud835\udf00 \ud835\udf03 = \ud835\udf00 \ud835\udc65 cos 2 \ud835\udf03 + \ud835\udf00 \ud835\udc67 sin 2 \ud835\udf03 + \ud835\udefexz sin \ud835\udf03 cos \ud835\udf03 \ud835\udefe\ud835\udf03 = \ud835\udefe\ud835\udc65 ( cos 2 \ud835\udf03 \u2212 sin 2 \ud835\udf03 ) + 2 ( \ud835\udf00 \ud835\udc67 \u2212 \ud835\udf00 \ud835\udc65 ) sin \ud835\udf03 cos \ud835\udf03 (5) here \ud835\udf0e\ud835\udf03 is the normal stress, \ud835\udf00 \ud835\udf03 is the normal strain, \ud835\udefe\ud835\udf03 is the shear train, and \ud835\udf03 is the angle of an arbitrary plane, as shown in Fig. 5 . The mean stress is considerably large in a non-conformal contact roblem [33] . Besides, when the lubrication effect is taken into account, he fatigue limit stress of POM could be increased by 1~1.2 times emirically, thus, this enhancement impact is indicated as the parameter \ud835\udf06 n the fatigue criterion. Finally, the Brown-Miller fatigue model describng the polymer gear contact fatigue, modified with the mean stress and he lubrication effect, can be expressed as: \u0394\ud835\udefe\ud835\udc5a\ud835\udc4e\ud835\udc65 2 + \u0394\ud835\udf00 \ud835\udc5b 2 = \ud835\udc36 1 \ud835\udf06\ud835\udf0e\u2032\ud835\udc53 \u2212 \ud835\udf0e\ud835\udc5a \ud835\udc38 ( 2 \ud835\udc41 \ud835\udc53 ,\ud835\udc3b )\ud835\udc4f + \ud835\udc36 2 \ud835\udf00 \u2032 \ud835\udc53 ( 2 \ud835\udc41 \ud835\udc53 ,\ud835\udc3b )\ud835\udc50 (6) here \u0394\ud835\udefemax /2 is the amplitude of the maximum shear strain, \u0394\ud835\udf00 n /2 is he normal strain amplitude on the critical plane, \ud835\udf0em is the mean stress n the critical plane, \ud835\udf0e\u2032 f and \ud835\udf00 \u2032 f denote the fatigue strength coefficient nd the fatigue ductile coefficient, respectively, \ud835\udf06 is the lubrication cofficient, b is the fatigue strength exponent, c is the fatigue ductile exonent, 2 N f,H is the contact fatigue life of this specific material point, and C are two material constants"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000323_j.jsv.2008.08.021-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000323_j.jsv.2008.08.021-Figure1-1.png",
        "caption": "Fig. 1. (a) Mesh forces A and B are contact positions of the two tooth pairs. (b) Dynamic model of two gears with tooth friction.",
        "texts": [
            " Extending that derivation to include friction perpendicular to the line of action gives the total deflection of a pair of loaded gear teeth as W \u00bc gc cos jc gs sin jc EI \u00fe 1 kr N1;i \u00fe gc sin jc gs cos jc EI \u00fe 1 kr f 1;i, (1) where N1,i and f1,i are contact and friction forces of tooth pair i, respectively; jc is the pressure angle at the current mesh position; EI denotes tooth bending rigidity; gc and gs are tooth geometric factors based on parameters defined in Ref. [27]; and kr is the effective rotational stiffness of the gear flank as reduced from Lee et al. [27], which is assumed the same for both forces. Although the compliance for N1,i is softer than that for f1,i, they are of the same order. To demonstrate the significance of the friction bending effect, a pilot study static analysis is conducted on a pair of spur gears in Fig. 1a. Gear 1 is loaded with torque T1 and gear 2 is fixed. The equilibrium conditions ARTICLE IN PRESS G. Liu, R.G. Parker / Journal of Sound and Vibration 320 (2009) 1039\u20131063 1041 yield the resultant contact and friction forces N1 \u00bc Xz i\u00bc1 N1;i \u00bc T1 r1 Pz i\u00bc1sgn\u00f0vi\u00demiliai ; f 1 \u00bc Xz i\u00bc1 f 1;i \u00bc N1 Xz i\u00bc1 sgn\u00f0vi\u00demiai, (2) ARTICLE IN PRESS G. Liu, R.G. Parker / Journal of Sound and Vibration 320 (2009) 1039\u201310631042 where r1,2 denotes gear base radii; z is the number of tooth pairs in contact; vi, mi and li are sliding velocities, friction coefficients and friction force moment arms (Fig. 1b), respectively; and ai \u00bc N1,i/N1 are load sharing factors between the z tooth pairs. The contact force of tooth pair i is aiN1 and the friction force is miaiN1 according to Coulomb friction. The friction moments about the gear centers depend on the position of the contact points. The moment arms of friction forces f1,i in Fig. 1a are shown in Fig. 2a. The difference between the two moment arms is a base pitch and r0 \u00bc r1 tanj, r1 \u00bc r0\u20132pgr1, and r2 \u00bc r0+2p(c 1)r1, where j is the pressure angle at the pitch point and c is the contact ratio. g denotes the position in a mesh period where double-tooth contact starts. Contact force variations results from the friction force. These variations relative to the frictionless condition are DN1 \u00bc N1 T1 r1 \u00bc N1 Xz i\u00bc1 sgn\u00f0vi\u00demiaili=r1; Df 1 \u00bc N1 Xz i\u00bc1 sgn\u00f0vi\u00demiai, (3) ( the first tooth pair; - - the second tooth pair)",
            " The mesh stiffnesses normalized by k\u0304 are Segment 1 : k1=k\u0304 \u00bc k1 \u00bc \u00f01 b\u00de\u00bd1\u00fe \u00f01 c\u00de ; k2 \u00bc 0 Segment 2 : k1=k\u0304 varies linearly from k2 to k3; k2=k\u0304 varies linearly from k3 to k2 k2 \u00bc a\u00f01 b\u00de\u00bd1\u00fe \u00f02 c\u00de ; k3 \u00bc \u00f01 a\u00de\u00f01\u00fe b\u00de\u00bd1\u00fe \u00f02 c\u00de Segment 3 : k1 \u00bc 0; k2=k\u0304 \u00bc k4 \u00bc \u00f01\u00fe b\u00de\u00bd1\u00fe \u00f01 c\u00de , (5) where b \u00bc ~bm is the friction bending factor. The frictional mesh stiffnesses in segments 1 and 3 are reduced and increased by b, respectively, due to the friction bending effect. The mesh stiffnesses of high contact ratio gears (c42) can be treated in a similar way. 3.2. Dynamic model of gear pair with tooth friction Referring to Fig. 1a, the dynamic normal forces Nz,i and friction forces fz,i act at the mesh positions A and B. Elasticity of each tooth pair is captured by the variable mesh stiffnesses k1,2 in Fig. 1b. To visually emphasize the parallel connection of stiffnesses for the individual tooth pairs, each elastic mesh element is artificially shifted slightly in the x direction. The normal forces and mesh stiffnesses, however, are actually collinear along the line of action. The gear translations are constrained by bearings with lateral stiffnesses kxz and kyz. J1,2 are polar moments of inertia. y1,2 are vibratory gear rotations. T1 and T2 are the input torque and load, respectively. Dynamic transmission error u \u00bc r1y1+r2y2 is introduced to remove the rigid body mode"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002115_2422295-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002115_2422295-Figure1-1.png",
        "caption": "Fig. 1.-Crow (Corvus brachyrhynchos). Dorsal view of wing with skin and feathers removed. X.6.",
        "texts": [],
        "surrounding_texts": [
            "LATISSIMUS DORSI ANTERIOR (Lat. dor. ant.; figs. 1-3) This thin flat sheet arises mostly tendinous from the spinous processes of the last cervical vertebra, the first horacic vertebra nd thie anterior tip of the second and the ligaments between them (figs. 11, 15). It passes antero-laterally, and a little more than halfway its course disappears between the scapular and humeral heads of the triceps. It inserts fleshy on the upper surface of the distal portion of the Cris. lat. hum., adjacent to the insertion of the Delt. maj. (figs. 11, 16a). LATISSIMUS DORSI POSTERIOR (Lat. dor. post.; figs. 1-3) This is also a thin flat muscle and is somewhat wider than the preceding. It arises directly behind the Lat. dor. ant. by a thin, tendinous heet from the spinous processes of the posterior part of the second, the third and the fourth thoracic vertebrae (figs. 11, 15). About four-fifths of the way toward the insertion it passes beneath the Lat. dor. ant. and inserts by a short, narrow tendon on the posterior surface of the humerus, a short distance behind the postero-proximal edge of the insertion of the Lat. dor. ant. The insertion of"
        ]
    },
    {
        "image_filename": "designv10_5_0001442_romoco.2015.7219710-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001442_romoco.2015.7219710-Figure8-1.png",
        "caption": "Fig. 8. Screenshots from motion planning with end-effector constraints. The carried box had to be kept in the horizontal position during the motion.",
        "texts": [
            " This version is referred to as Servicenone in the rest of the paper. The planners were tested with and without end-effector pose constraints (denoted Con=0/1 in the tables). The constraint Con=1 means that the carried box has to be kept in the horizontal position, and Con=0 allows arbitrary orientation of the box. The RRT planner was run 20 times for each combination of service and pose constraints. The maximum number of allowed planning iterations was set to Kmax = 150000. Examples of computed plans are depicted in Fig. 8. The tables show two types of time information: Process time, showing the total time the process spent on the processor, and Real time, which shows the real time before the planner delivers a solution. The real time and process time are similar in the case of Servicenone variant, as all the computations are realized on a single process. In the case of service-based planning (Servicelinks, Servicearm and Serviceangles), the process time is less than real time, as part of the computations is realized on a different computer"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002991_j.optlastec.2017.10.035-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002991_j.optlastec.2017.10.035-Figure5-1.png",
        "caption": "Fig. 5. Arc-shaped outline.",
        "texts": [
            " [22] suggested that in order to form a dense cladding layer, the contact angle h must be smaller than 80 . So in this paper, only the cladding layer with the outline shown in Fig. 3(a) was discussed and calculated. By checking the samples from the experiments, the outline of the track\u2019s cross section was very close to an arc shape with a radius R (shown as Fig. 4). In this paper, the geometry characteristics of the single cladding layer were defined by its width W, and the height H and the cross section area S (see Fig. 5). As shown in Fig. 5, the center of the arc was at the downside of the substrate, and its distance to the surface of the substrate wasffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 \u00f0W=2\u00de2 q . The cross section area was then given as: S \u00bc R2 arcsinW 2R 1 2 W\u00f0R H\u00de \u00f01\u00de Meanwhile the max height H of the cladding layer could also be calculated by the arc radius R and the width of the cladding layer W: H \u00bc R ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 \u00f0W=2\u00de2 q \u00f02\u00de 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000992_j.epsr.2012.08.002-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000992_j.epsr.2012.08.002-Figure4-1.png",
        "caption": "Fig. 4. Machi",
        "texts": [
            " / Electric Power Systems Research 95 (2013) 28\u2013 37 ne slo m g t t P t t \u2264 w s t p o w p \u02c7 w a d F e m e 1)\u00d7(nn X] nb\u00d7 otion, the sections of the flux tubes vary and consequently the air ap permeances are updated at every rotor angular relative posiion. Following [11], the permeance Pi,jwhich connects the ith stator ooth to the jth rotor tooth reads: i,j = \u23a7\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23a9 Pmax if 0 \u2264 \u2264 t1 and 2 \u2212 t1 \u2264 \u2264 2 Pmax ( 1 + cos ( ( \u2212 t1 ) / ( t \u2212 t1 ))) /2 if t1 \u2264 \u2264 Pmax ( 1 + cos ( ( \u2212 2 + t1 ) / ( t \u2212 t1 ))) /2 if 2 \u2212 0 otherwise here Pmax, t and t1 will be defined below with respect to the bar kewing angle. When the rotor bars are skewed (Fig. 4a), the cross sections of he air gap flux tubes are not rectangular and their corresponding ermeances are modified. The various parameters Pmax, t and t1 f the air gap permeances function (4) are therefore recalculated ith respect to the skewing angle  \u030c (Fig. 4a) and the geometrical arameter of the machine (Fig. 4b). Regardless of the skewing angle , the parameter t of Eq. (4) is given by [11]: t = ( Lst + Lrt + oss + orr + Lm tan \u02c7 ) /Dag (5) here Lst and Lrt are the stator and rotor tooth width, oss and orr re the stator and rotor slot opening, and Dag is the average air gap iameter (Fig. 4b). On the other hand, according to the possible cases detailed in ig. 4a, the parameters Pmax and t1 are given by the following quations: Case i: 0 \u2264 tan  \u030c \u2264 (Lt max \u2212 Lt min)/Lm with Lt max = ax (Lst, Lrt) and Lt min = min (Lst, Lrt) t1 = ( Lt max \u2212 Lt min \u2212 Lm tan \u02c7 ) /Dag and Pmax = ( 0 Lm Lt min)/e (6) { br } nb\u00d71 = [ [Y]nb\u00d7nb \u00b7 [A]Tnb\u00d7(nn\u22121) \u00b7 [Ybus] \u22121 (nn\u2212\ufe38 [ where 0 is the air permeability, Lm is the machine length and is the air gap length. Case ii: (Lt max \u2212 Lt min)/Lm \u2264 tan  \u030c \u2264 (Lt max + Lt min)/Lm t1 = 0 and Pmax = 0 4e (2Lm (Lt max + Lt min) \u2212 ( L2 m tan \u02c7 ) \u2212 (Lt max \u2212 Lt min)2/ tan \u02c7 ) (7) ts and teeth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002012_1350650114522452-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002012_1350650114522452-Figure3-1.png",
        "caption": "Figure 3. (a) Standard NTN-SNR endurance bearing test rig; (b) cross sections schematic.",
        "texts": [
            "2 In this study, WEC have been reproduced on a standard bearing test rig with and without hydrogen charging. It highlights that, despite similar WEC propagation aspect, hydrogen charging seems to modify WEC initiation mechanisms. Hence, WEC surface initiation and propagation possible mechanisms are proposed based on fractographs, optical micrographs and SEM analyses, identifying different influent drivers. Fatigue tests have been performed on standard ball bearings of mean diameter Dm\u00bc 43.5mm with a minimalist endurance test bench (Figure 3). Operating conditions correspond to a moderate constant rotational speed, as in Paulin et al.,31 and a 3400MPa maximum Hertz pressure for the most loaded ball/ inner ring contact. Contact theoretical stresses and kinematics computed by NTN-SNR software SHARCLAB are detailed in Table 1 and Figure 4. The bearings were tested by pairs under fully jet lubricated conditions using fully formulated commercial ISO 46 gearbox oil at ambient temperature in a neutral environment (no oil contamination, no electrical current, no corrosion, no acceleration/deceleration transient effects, no vibrations, etc",
            " All other bearings were either stopped due to inner ring spalling, presenting an axial cracking aspect (Figure 6(a)), or suspended. All hydrogen precharged bearings that ran under the same operating conditions failed at shorter time, before 104 h, corresponding to 8 106 cycles, due to premature spalling of the inner rings with a similar axial aspect than the ones that were not hydrogen precharged (Figure 6(b)). On each inner ring, with and without apparent surface damage, circumferential and axial optical micrographs (OM) with Nital 2% etching (Figure 3(b)) as well as fractographs based on the protocol detailed thereafter revealed large WEC networks with similar propagation aspect on standard and hydrogenated inner rings (Figure 7). Hence, WEC have been reproduced repeatedly on a standard bearing test rig both with and without hydrogen charging of the inner rings and under the same operating conditions. Characterization of white etching cracks WEC apparent morphology depending on the metallographic cross section Different cross sections have been made to reveal WEC networks on all the tested rings"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002189_s40194-018-0609-3-Figure23-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002189_s40194-018-0609-3-Figure23-1.png",
        "caption": "Fig. 23 X-ray tomography slice (Courtesy of VisiConsult X-ray Systems & Solutions GmbH and IFW - G\u00fcnter-K\u00f6hler-Institut f\u00fcr F\u00fcgetechnik und Werkstoffpr\u00fcfung GmbH)",
        "texts": [],
        "surrounding_texts": [
            "will ensure that the quality of the parts will remain in the acceptable level avoiding applying 100 % NDT on the produced parts, thus reducing production cost.\nIdeal techniques/sensors in process monitoring should provide the right information without:\n& Being disturbed by the process & Introducing malfunctions of the process\nAccording to visibility/accessibility of the building scene, the sensors may receive either direct or indirect information. The sensors can be used in passive or active mode.\nSeveral techniques may be used to collect direct information:\n& Visual observations with or without processing. Lighting shall be carefully adapted to get the optimal information & 2D or 3D reconstruction of the building scene; laser profilometry is often used for that purpose & Thermal measurement due to variation of the extent/shape of typical hot spot generated by the process & Eddy current & Sound and ultrasound & X-rays\nW. J. Seufzer et al. [31] used thermal measurements to control EBF3 process. They also compared the advantages of the possible regulation loops to apply.\nIndirect information may also be collected due to:\n& Thermal variations: as a wide range of processes is based on heat transfer, monitoring the heat exchanged through one constitutive material may be correlated to something wrong happening in the building scene. & Mechanical stress (force or local pressure) or deformation may be transmitted through a component used in the process and may provide interesting hints related to process drift. & Ultrasonic/acoustic wave generation or modification may be transmitted outside the building scene and be used as good hints of process deviation.\nH. Rieder et al. [32] used ultrasound with sensors set underneath the building platform in order to monitor the SLM process.\nThe information provided by a sensor can be used either in a close-loop or as an independent control measurement. In an operational close loop, the value of the sensor should fit a setpoint and has therefore no more interest than checking the settings and stability. However, the actuator level in the close loop is seldom recorded and is often a good indicator of a process drift. The sensor choice and location has also to be taken into account according to the using mode. A passive monitoring sensor can be closer to the material to be transformed and more\nsensitive to variations without disturbing the long-term stability of process. An active/passive sensor couple is also very useful for information redundancy helping to detect possible sensor drift or damage.\nStructural health monitoring (SHM) can be defined as a discipline aiming at surveying continuously the integrity of a structure. To do so, sensors/actuators should be set permanently with the said structure during its full life. An easy-to-use software can be used to automatize the monitoring. Decision to use this software is based on thresholds which are closely related to the collected database. The collected data are unfortunately vulnerable to environmental and operational changes (EOC), which can cause false alarms. Reducing these EOC effects is a challenging task and needs the development of algorithms either analytical or statistical (Table 7).\nM. El Mountassir et al. [33] have made a review of these EOC factors, their associated effects and the various strategies to compensate for or eliminate these effects.\nAnalytical strategies may be used, based on optimisation algorithms that rely on the minimisation of the residual error between the baseline signal and the current signal (which may contain information related to damage). Other strategies are based on using statistical methods which seem to be more reliable and can be easily implemented.\nThese methods can be divided into two categories: supervised and unsupervised learning algorithms:\n& Supervised learning is used when different damage levels and scenarios are available. It can be used for the identification of the type and the damage severity. But in general, data from the damaged structure are not usually available. & Unsupervised learning does not need an a priori on the structure, due to its behaviour with time, damage characteristics (shape, dimensions, orientation, type, location, etc.).\nAn example of application of such algorithms is given in \u00a710.",
            "A nozzle was manufactured by a laser beam melting with a SLM 250 HL (from SLM Solutions GmbH). The material used is a Ti-alloy (TiAl6V4). A section of this nozzle is presented in Fig. 22 where the internal channels are shown. The internal channels are used for some cooling medium (e.g. air or water).\nA nozzle as built was investigated by CT investigations. The x-ray-images and the CT-scan were taken with a XRH222-S equipment.\nThe main settings are:\n& Acceleration voltage: 225 kV & X-ray current intensity: 3,6 mA & Used filter for beam-hardening: 0.5 mm Cu & Pixel size of the detector 139 \u03bcm & CT-scan:\n\u2013 1600 steps\u2014duration of the scan: 3.5 h \u2013 voxel size: 95.4 \u03bcm \u2013 magnification \u00d7 1.4\nNo soundness imperfections were detected. The benefit of CT to investigate this kind of part is also in its capability to measure the internal channels dimensions (Figs. 22 and 23).\nThe presence of austenitic weld metal can seriously affect the ultrasonic testing of a part because of:\n& Distorted wave propagation within the weld material & Reflection of ultrasound at the fusion boundary between\nthe parent material and the weld\nUT procedures have to deal with [34]:\nAnisotropy: the properties of the melted material, e.g. ultrasonic sound velocity, vary with the direction in which they are measured. Choice of appropriate type of wave and ultrasound angle beam generation may limit this effect Beam deviation: Beam deviation is said to occur when an ultrasonic beam propagates in a direction which is not perpendicular to the wave front. This phenomenon can cause unexpected changes in beam direction and shape. Using focus beam generally limits this effect. Scattering: Welds in austenitic materials have coarse macrostructures which cause significant scattering of ultrasonic beam that even may occur at relatively low frequencies, e.g. 2MHz. This can lead to very low signal-tonoise ratios for some ultrasonic testing.\nThat is why UT testing of austenitic welds should follow the recommended flow chart (Fig. 24) [35].\nThe following case study, reported by S.Demonte et al. [31], deals with the testing of nozzle butt welds of high pressure vessels, DN 50 and 75, thickness 25mm+ 3mm weld overlay SS 316. The filler material is inconel 625. The construction code refers to EN1714 (now ISO 17640 [32]). ISO 22825 [33] was used as guidelines. Basic modelling (Fig. 25) was carried out to define appropriate scan plans able to meet the testing zones coverage requirements (Figs. 26 and 27).\nThe main benefits of using PAUT compared to RT are the following:\n& A better detection of critical imperfections: all joints were acceptable by RT, 5 joints were rejected by PAUT. Several",
            "rejectable indications were discovered on the same joints. Defects not detected on RT films were mainly side wall or inter-run lack of fusion).\n& the examination time is reduced:\n\u2013 RT requires 5 h shooting time (Ir 192-1 TBq)\n\u2013 PAUT ranges from 1 to 2 h depending on the number of indications detected\n& PAUT results are given in real time (no offline analysis), defect location directly marked on the weld, allowing immediate repair."
        ]
    },
    {
        "image_filename": "designv10_5_0003301_j.mechmachtheory.2019.01.014-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003301_j.mechmachtheory.2019.01.014-Figure6-1.png",
        "caption": "Fig. 6. Relationship between deformation and displacement of ball screw under load: (a) deformation of rolling ball, (b) centers\u2019 position of grooves.",
        "texts": [
            " With the increase of displacement, the stiffness of linear guide first decreases and then increases. In this analysis, the dynamic model is constructed by considering the coupling of three dimensional forces and two moments on the vibration of the feed system. Fig. 5 shows a single-nut ball screw under load; this is applied preload by a variable lead. The displacement of screw-nut along the X axis is caused by the elastic deformation of balls between screw-shaft and screw-nut. The deformation of ball is shown in Fig. 6 , and the contact force can be calculated using the Hertz contact theory F n = ( \u03b5 n \u22121 \u03b4n ) 3 2 (16) where \u03b5n is the Hertzian contact constant between balls and ball screw. To obtain the contact force, the relationship between contact deformation and contact load can be derived as shown in Fig. 7 . The initial distance A 0 n between the groove curvature centers of screw-nut and screw-shaft is A 0 n = r s + r n \u2212 D w +2 \u03b40 n = ( 2 f \u2212 1 ) D w +2 \u03b40 n (17) where r s and r n are the groove radius of screw-nut and screw-shaft, respectively; these are assumed to be equal. f is the conformity ratio between groove curvature radius and ball, D w is the ball diameter and \u03b40 n is the initial deformation of a rolling ball under preload. When the screw-nut is under load as shown in Fig. 6 , the change trends of deformation of right and left balls are opposite. A 1 and A 1 \u2032 are the distances between curvature centers of screw-nut and screw-shaft, which can be expressed as follows: A 1 = \u221a ( A 0 s cos \u03b10 + x ns ) 2 + ( A 0 s sin \u03b10 ) 2 (18) A 1 \u2032 = \u221a ( A 0 s cos \u03b10 \u2212 x ns ) 2 + ( A 0 s sin \u03b10 ) 2 (19) where \u03b10 is the initial contact angle and x ns is the relative displacement between screw-nut and screw-shaft, which is obtained as x ns = x \u2212 x s . Then, the new contact angels of right and left rolling balls can be obtained as follows: tan \u03b11 = A 0 s sin \u03b10 A cos \u03b1 + x (20) 0 s 0 ns tan \u03b11 \u2032 = A 0 s sin \u03b10 A 0 s cos \u03b10 \u2212 x ns (21) The total elastic deformations \u03b4n and \u03b4n \u2032 of rolling balls can be given by 2 \u03b4n = A 1 \u2212 A 0 n (22) 2 \u03b4n \u2032 = A 1 \u2032 \u2212 A 0 n (23) The contact forces of rolling balls in the left and right sections along the X axis can calculated as follows: F n = ( \u03b5 n \u22121 \u03b4n ) 3 2 cos \u03b11 = ( \u03b5 n \u22121 \u03b4n ) 3 2 ( A 0 n cos \u03b10 + x ns ) \u221a ( A 0 n sin \u03b10 ) 2 + ( A 0 n cos \u03b10 + x ns ) 2 (24) F n \u2032 = ( \u03b5 n \u22121 \u03b4n \u2032 ) 3 2 cos \u03b11 \u2032 = ( \u03b5 n \u22121 \u03b4n \u2032 ) 3 2 ( A 0 s cos \u03b10 \u2212 x ns ) \u221a ( A 0 s sin \u03b10 ) 2 + ( A 0 s cos \u03b10 \u2212 x ns ) 2 (25) The interface force acting on the worktable is the sum of contact force of the balls in the right and left grooves, which is a piecewise function about the relative displacements"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002880_tte.2018.2887338-Figure19-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002880_tte.2018.2887338-Figure19-1.png",
        "caption": "Fig. 19: Radial force density over a complete electrical cycle for the four-phase 8/6 SRM.",
        "texts": [
            " 7, the forcing frequency ff pq 12, circ 4q has symmetric components in all four quadrants. Thus, a standing wave with crest, nodes, and troughs, at a fixed position of the stator geometry, excites the vibrating mode 4 at the frequency of ff q fmech, where q |u|. A similar effect occurs for the forcing frequency ff pu 24, \u03bd 8q. The four-phase 8/6 SRM used in this analysis is rated at 5 kW, 300 V, peak current of 30 A, base speed of 6000 rpm, rated torque of 8.2 Nm and stack length of 90 mm. The crosssection view and the geometric parameters of the 8/6 SRM are shown in Fig. 18. Fig. 19 shows the radial force density over one electrical cycle along with the phase current waveforms. The number of magnetic poles is equal to 2 pNs{Nphq since there are two geometrical opposite stator poles simultaneously excited by each phase. Thus, at each point in time, there are two radial force density pulses along the circumferential position axis. In the same figure, the phase current waveforms are shown to illustrate its direct influence over the radial force. Therefore, over a full electrical cycle, all four phases will conduct resulting in eight peaks of radial force density"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000710_j.jsv.2011.04.008-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000710_j.jsv.2011.04.008-Figure3-1.png",
        "caption": "Fig. 3. Physical scheme for gear rattle modeling: (a) correct contact, (b) separation and (c) incorrect contact.",
        "texts": [
            " 2a) the almost sinusoidal motion of the driving gear due to the good quality of the controller. In the driven gear motion, instead (Fig. 2b), a different slop during the rising and the falling ramps can be noted due to the inertia of the driven gear. Finally, in Fig. 2c the relative angular motion, computed according with Eq. (1), is shown. Following a classic approach in this field, the relative gear motion is described by a single degree-of-freedom lumped parameter model, considering the driven gear forced to vibrate by a motion imposed on the driving gear [6,12]. Fig. 3 shows the physical model of the gear pair where the subscript 1 indicates the driving gear. The mathematical model is then m \u20acx\u00feF\u00f0x, _x,W1\u00de\u00fe fr \u00bc m \u20acX (5) where m is the mass of the driven gear, x\u00bcr2y2\u2013r1y1 is the relative displacement between the teeth, X\u00bcr1y1 is the absolute motion of the driving gear. In Eq. (5), the force F\u00f0x, _x,W1\u00de may assume different expressions depending on the actual value of the relative displacement x: F\u00f0x, _x,W1\u00de \u00bc K\u00f0X\u00de\u00f0x bI\u00f0W1\u00de\u00de if x4bI\u00f0W1\u00de K\u00f0X\u00de\u00f0x bC\u00f0W1\u00de\u00de if xobC\u00f0W1\u00de ( F\u00f0x, _x,W1\u00de \u00bc S\u00f0x,W1\u00de _x if \u00f0bC\u00f0W1\u00de\u00fehmin\u00derxr\u00f0bI\u00f0W1\u00de hmin\u00de F\u00f0x, _x,W1\u00de \u00bc Smax _x if bC\u00f0W1\u00deoxo \u00f0bC\u00f0W1\u00de\u00fehmin\u00de or \u00f0bI\u00f0W1\u00de hmin\u00deoxobI\u00f0W1\u00de (6) The terms bC(W1) and bI(W1) represent the actual values of the relative displacement x where the contact between the meshing teeth takes place. The subscript \u2018\u2018C\u2019\u2019 refers to a correct contact where the gear 1 drives the gear 2, the subscript \u2018\u2018I\u2019\u2019 refers to an incorrect contact (i.e. the gear 2 drives the gear 1). The term hmin represents the film thickness of the oil layer that remains adsorbed on the tooth surface during the contact phase (Fig. 3a and c) and Smax\u00bcS(hmin) is a saturation value of the squeeze damping coefficient (see Appendix). During the contact phases, a nonlinear elastic force K(X) x acts on the driven gear. Such elastic force is given by the sum of the contributes due to the n teeth pairs that are in contact at the same time. Each teeth pair contributes with a stiffness term [30]: Ki\u00f0X\u00de \u00bc kp exp Ca X eXz=2 1:125eaXz 3 ! (7) where e and ea are the total contact ratio and the transverse contact ratio, respectively, and Xz is the transverse base pitch. For a complete meshing cycle, X starts from 0 and ends at eXz. Finally, kp indicates the stiffness at the pitch point that depends on the tooth parameters along with the Ca coefficient. The elastic force is consequently the sum of n periodic functions shifted each other of a transverse base pitch Xz. The contacts can occur either on the driving or on the driven side of the tooth. During the approach phase when the teeth are separated through an oil layer (Fig. 3: case b), the oil squeeze effect gives a nonlinear damping force S x,W1\u00f0 \u00de _x. In Appendix such a squeeze coefficient is described as S\u00f0x,W1\u00de \u00bc 3R3=2mZ \u00bda\u00f0a2 Rx\u00de ffiffiffiffiffi Rx p \u00fe\u00f0a2\u00feRx\u00de2 arctan\u00f0a= ffiffiffiffiffi Rx p \u00de x3=2 \u00f0a2\u00feRx\u00de2 (8) with x\u00bc bI\u00f0W1\u00de x if _x40 9bC\u00f0W1\u00de9\u00fex if _xo0 ( (9) in which m is the absolute viscosity, Z indicates the axial width of the gear pair, R is the relative curvature radius of the teeth and a denotes the semi-length of the oil film along the tooth surfaces related to the lubrication conditions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000127_nme.1620100603-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000127_nme.1620100603-Figure2-1.png",
        "caption": "Figure 2. Second-order Rayleigh-Timoshenko differential beam element of length dx' displaced by w and u, strained by y and K, stressed by T and M, and externally loaded by W and V (and H)",
        "texts": [
            " In addition to the translatory inertia m and the bending flexibility 1/EZ included in the BernoulliEuler theory, rotatory inertia mr2, shear flexibility l/kGA and static axial load H (causing second-order bending moments and shear forces in the beam member 12 in Figure 1) can optionally be considered in PFVIBAT. New elements Fij in the 6 x 6 member stiffness matrix F in (1) are derived from the following theory : The transverse translation w = w(x\u2019), clockwise rotation u = u(x\u2019), shear deformation y = y(x\u2019), bending deformation IC = ~(x\u2019), shear force T = T(x\u2019) and bending moment M = M(x\u2019) of a generic beam lamina dx\u2019 (Figure 2) are collected in three column matrices (Figure 3). The external transverse and moment loads are W and I/. The external static axial load is H and is counted positive when compressive. The mass centre axis is supposed to coincide with the centre of the stress-carrying cross-sectional area. The kinematic compatibility operator G, the constitutive operator Sd and the dynamic compatibility operator G\u201d of the differential beam element (Figure 2) are (Figure 3) The two matrix differential operators G and G\" in (4a,c) are seen to be each other's adjoints (as was anticipated by the superscript a). They contain the same geometric information (which they should do in a consistent linear theory). The general matrix differential equation governing w and u of a non-uniform beam is easily found by the three-step transformation chain G\"SdG (Figure 3) as 1 W - mw - Hw\" GaSdG[r] = [ V - mr2v ( 5 ) where primes and dots denote differentiation with respect to the local length co-ordinate x' (Figure 1) and the time t , respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002825_j.mechmachtheory.2016.11.007-Figure11-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002825_j.mechmachtheory.2016.11.007-Figure11-1.png",
        "caption": "Fig. 11. The assembly error for the spiral bevel gear.",
        "texts": [
            " It is worth notation that the fast convergence performance can be obtained only when we set the reasonable error range, and it will be difficult if the error is too large. The result of the initial contact point is also affected by errors. As represented in Fig. 8, in the consideration of the error items for ETCA, there are two main items, namely the assembly error of gear axis [5,14] and spatial geometric error of machine tool [24] are always mentioned in previous literature. Here, the assembly error as a major error source is considered in ETCA. Fig. 11 represents the geometric relation of the assembly error for the spiral bevel gear. As defined in Ref. [5], E is the vertical displacement of the pinion along the bias direction; P is the horizontal displacement of the pinion along the axis line; G is the vertical displacement of the gear along the bias direction and \u03b1 is the shaft angle between the gear and the pinion, which is set as zero in this paper. Fig. 12 shows the changes of the profile direction and the face-width direction at the initial contact position M"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000083_j.mechmachtheory.2009.01.010-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000083_j.mechmachtheory.2009.01.010-Figure8-1.png",
        "caption": "Fig. 8. (a) Influence coefficient for tooth bending deflection and (b) dimensions for calculation of the tooth bending deflection.",
        "texts": [
            " ; n \u00f044\u00de with the general function g\u00f0x; y\u00de \u00bc xln ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0x\u00de2 \u00fe \u00f0y\u00de2 q \u00fe y \u00fe yln ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0x\u00de2 \u00fe \u00f0y\u00de2 q \u00fe x ; \u00f045\u00de where x; y indicate the relative coordinates of any point j with respect to the considered point k, x \u00bc xj xk; y \u00bc yj yk. The bending deflection at a specified point on the tooth flank that arises due to a concentrated force acting on the neighboring section can be determined with the aid of the influence function E1 for deflection and the flexibility qB of the segment on which the force acts [21]. As illustrated in Fig. 8a, the general influence function E1 for the case of infinite face-width describes the change in deflection at the same height across the face-width of a cantilever tooth due to the concentrated force F. The deflection wB,k of point k can be determined by combining the general influence function E1with the deflection wB,m at point m , at which the force F acts in normal-section, i.e., wB;k \u00bc wB;m E1: \u00f046\u00de However, this relation is only valid for the case of infinite face-width. The effect of the face-width on the bending deflection can be determined by mirroring the deflections outside of the face-width, with the end of face of the tooth acting as the mirror plane",
            " The deflection wB,k can thus be obtained by superpositioning both the deflections wB;k \u00bc wB;m \u00f0E1 \u00fe DE1\u00de: \u00f047\u00de From the results of FEM for involute cylindrical gears, Linke [21] derived the influence function E1 E1\u00f0n k\u00de \u00bc 0:291 e 0:385 n k ffiffiffi n k p ; n k \u00bc jnkj mn ; \u00f048\u00de where nk denotes the relative position of point k to point m. The mirrored influence function DE1 can be defined as DE1\u00f0n k\u00de \u00bc E1\u00f0n D\u00de; n D \u00bc j2nF nkj mn ; \u00f049\u00de where nF is the relative distance from point m to the end of face of the tooth. The positive or negative value of the relative position is in agreement with the defined face-width; see Fig. 8a. For conical gears with a small cone angle, the effect of the cross-sections on E1 can be ignored, and Eq. (47) can be applied to calculate the deflection. The deflection wB,m of the tooth segment at point m arising due to a concentrated load Fj at point j is determined with aid of the flexibility qB,mj, wB;m \u00bc qB;mj Fj: The profile of each individual tooth segment of a conical gear is different. The flexibility qB,mj is not only related to the position of the load but also to the geometric dimensions of each individual tooth segment; see Fig. 8b. The flexibility qB,mj is determined based on the equation for the deflection curve of a cantilever beam with variable cross-sections Sy(y) [21]; see Fig. 8b, q00B;mj\u00f0y\u00de \u00bc cos2 aF\u00f01 t2\u00de E \u00f0yF y\u00de Db S3 y\u00f0y\u00de=12 : \u00f050\u00de Eq. (50) can also be expressed in integrated form qB;mj\u00f0y\u00de \u00bc Z yF 0 cos2 aF\u00f01 t2\u00de E Z yF 0 12 \u00f0yF y\u00de Db S3 y\u00f0y\u00de dy\u00fe C1 \" # dy\u00fe C2; \u00f051\u00de where the integration constants C1 and C2 are determined according to the boundary conditions q0B;mj\u00f00\u00de \u00bc 0, and qB,mj(0) = 0. It is suitable to solve Eq. (51) with the aid of numerical methods [26]. Assuming that the general influence function for bending deflection is independent of the tooth geometry, the total elastic bending deflection wB,kj at point k due to the concentrated force Fj acting at point j can thus be considered wB;kj \u00bc \u00f0E1 \u00fe DE1\u00de \u00f0qB1;mj \u00fe qB2;mj\u00de Fj: \u00f052\u00de Given the area s at which each discrete point acts, we may obtain the influence coefficients fB,kj for the tooth bending deflection fB;kj \u00bc s \u00f0E1 \u00fe DE1\u00de \u00f0qB1;mj \u00fe qB2;mj\u00de: \u00f053\u00de According to the presented method, not only can we obtain the contact stress pj and the relative approach d, but also the actual form and size of the contact region"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003960_j.chaos.2020.110387-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003960_j.chaos.2020.110387-Figure6-1.png",
        "caption": "Fig. 6. Dynamic model of the gear pair system.",
        "texts": [
            " = sign ( V s ) (11) Based on Coulomb\u2019s friction law, the friction force is defined as ollows. f = \u03b7\u03bcF mesh (12) Where F mesh is the dynamic mesh force and \u03bc is the friction oefficient. In this study, Buckingham model [38] is adopted to calulate the friction factor, which could be written as follows: = 0 . 05 e \u22120 . 125 | V s | + 0 . 002 \u221a | V s | (13) Then, the friction torque of Gear i ( i = 1,2) is deduced as fol- ows. f i = \u03b7\u03bcF mesh K N i (14) .3. Dynamic equations A multiple degrees of freedom lumped parameter model of a ear pair system is presented in Fig. 6 . Here, m i is the equivalent ass; I i is the moment of inertia; \u03b8 i is the nominal angular dis- lacement; T i is the torsional torque; d i is the base circle diameter; h denotes the damping coefficient; k ( \u03c4 ) represents comprehensive esh stiffness. K. Huang, Z. Cheng, Y. Xiong et al. Chaos, Solitons and Fractals xxx (xxxx) xxx a I I t n s The dynamic differential equation of the system is established s follows. 1 \u0308\u03b81 + F mesh r b1 + M f 1 = T 1 2 \u0308\u03b82 \u2212 F mesh r b2 \u2212 M f 2 = \u2212T 2 (15) However, using Runge-Kutta method to solve the motion equaions is not easy because of gear backlash"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000362_0045-7906(78)90018-6-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000362_0045-7906(78)90018-6-Figure1-1.png",
        "caption": "Fig. 1. A double inverted pundulum.",
        "texts": [
            " This paper also presents a method to design a first order linear functional observer for general mechanical systems. 2. SYSTEM DESCRIPTION AND LINEARIZED MODEL As mentioned in the introduction, the objective of this paper is to design and to construct a controller for stabilization of a double inverted pendulum, which aims to establish a systematic procedure for control system design based on the state space approach. The double inverted pendulum in the controlled state is shown in Photo I, and is presented with dimension in Fig. 1. The system of the double inverted pendulum treated consists of (1) a cart movable on a straight monorail of the length 1.01(m), (2) the lower pendulum of the length 0.49 (m) made of aluminium pinned to the cart using ball bearings so that its motion is smooth and restricted to Photo I. A double inverled pendulum stabilized at the upright position. the vertical plane containing the line of monorail, and the upper pendulum connected to the lower one in the similar way that the lower one is connected to the cart, and (3) a cart-driving system consisting of 50W d"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000509_1.4005952-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000509_1.4005952-Figure5-1.png",
        "caption": "Fig. 5 Five different types of roller contact (H \u2013 film thickness contour, P \u2013 pressure contour)",
        "texts": [
            " Corresponding dimensionless EHL parameters are G*\u00bc 4000, W*\u00bc 1.842 10 4 and U*\u00bc 1.433 10 11. The solution domain is determined as 3:1 X 1:3 and 1:05 Y 1:05. The computational grid covering the domain consists of 257*257 nodes equally spaced. This corresponds to a spatial mesh size of DX\u00bc 0.01719 and DY\u00bc 0.008203. The progressive mesh densification (PMD) method is used to speed up the solution process, and its description can be found in Ref. [23]. The descriptions and obtained results are summarized in Table 1 and Fig. 5. Note that in the preliminary study the plastic deformation and the surface wear are not considered in the analyses in order to avoid excessive complexity. Plastic deformation and wear can be computed when needed, and their numerical methods have been clearly described in Refs. [24\u201326]. Also, Case (a) is for the corresponding infinitely long straight cylinder contact at the same Hertzian pressure as a comparison reference, Case (b) is a straight roller contact with a finite nominal length of 5 mm, Case (c) is a straight roller with the same finite length but the two ends are rounded and the corner radius is r\u00bc 12",
            "7 mm, Case (d) is the same as Case (c) but a crown of Ry\u00bc 254 mm is added, and Case (e) is the same as Case (d) but the round corners are changed to chamfers of h\u00bc 15 degree. Note that the use of the model system presented in this paper is for a relative comparison, and the error when using Eq. (5) for rollers with sharp edges is not considered. The values of the maximum pressure peak and von Mises stress, as well as the film thickness at the contact center, are also given in Table 1 for comparison. This set of cases covers a good variety of roller contact types so that the results are representative. It should be indicated that in Fig. 5 the first row of the graphs is the film thickness and pressure contours for the five cases, the second row is the film thickness and pressure distributions along the y-axis perpendicular to the direction of motion, and the third row is the subsurface von Mises stress fields on the y-z plane. This figure reveals that the infinitely long straight roller, Type (a), yields the lowest pressure peak and von Mises stress values, but, unfortunately, this type of roller hardly exists in reality. Type (b) is the straight 011504-4 / Vol"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001765_tcyb.2015.2509863-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001765_tcyb.2015.2509863-Figure1-1.png",
        "caption": "Fig. 1. Description of the measurement of the joint positions and applied torque for the Furuta pendulum.",
        "texts": [
            " The notations \u03bbmin{A} and \u03bbmax{A} denote the minimum and maximum eigenvalues of a symmetric positive definite matrix A \u2208 IRn\u00d7n, respectively. The superscript \u201c \u201d denotes the operation transpose, i.e., x denotes the transposed vector x \u2208 IRn and A denotes the transposed matrix A \u2208 IRn\u00d7n. \u2016x\u2016 = \u221a x x denotes the norm of the vector x \u2208 IRn. \u2016B\u2016 =\u221a \u03bbmax{B B} denotes the induced norm of a matrix B(x) \u2208 IRm\u00d7n for all x \u2208 IRn. The Furuta pendulum is a two-degree-of-freedom underactuated mechanical system with an actuator in the first joint. Fig. 1 shows a description of the joint positions and applied torque. The dynamic model of the Furuta pendulum in Euler\u2013Lagrange form [8], [43] can be written as M(q)q\u0308 + C(q, q\u0307)q\u0307 + gm(q) + f (q\u0307) = u (1) where q = [q1 q2] \u2208 IR2 is a vector of joint positions, M(q) \u2208 IR2\u00d72 is the symmetric positive definite inertia matrix, C(q, q\u0307)q\u0307 \u2208 IR2 is the vector of centripetal and Coriolis torques, gm(q) \u2208 IR2 is the vector of gravitational torques, f (q\u0307) \u2208 IR2 is the vector of friction torques, and u = [\u03c4 0] \u2208 IR2 is the vector of input torques, with \u03c4 \u2208 IR being the torque applied to the arm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001770_j.apsusc.2016.09.009-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001770_j.apsusc.2016.09.009-Figure1-1.png",
        "caption": "Fig. 1 Spur HCR gear geometry used for calculation of curvatures and surface velocities The distance between the mesh point and gear center is a function of the pressure angle of the corresponding point and base radius:",
        "texts": [
            " High precision tooth surfaces are costly while low precision surfaces display wear and noise and can lower operating life. The specific objective of this paper is as follows: improve the typical MDOF model for HCR gear by introducing fractal theory in terms of STE, employ an EHL-based friction coefficient to calculate the friction force, and then research system response in the view of DTE, motion in OLOA direction, and friction force influenced by tooth surface roughness. The meshing process of HCR gears is more complex than that of NCR gears. An example of an HCR gear set, as shown in Fig. 1(a), with a contact ratio of approximately 2.19 has design parameters as listed in Table 1. Moments of inertia (kg\u2219m2 ) 0.003 Elasticity modulus(Gpa) 205 Poisson ratio 0.3 The teeth come into ( ) contact at point A and go out ( ) of contact at point D in one mesh cycle. During this time, the absolute value of sliding velocity decreases and then increases. It is assumed that no sliding occurs at point P and the sliding force has a reversal, as shown in Fig. 1(b) and Fig. 1(c). Here, the teeth pair with a contact point located between point A and point B is defined as pair #1, the teeth pair with a contact point located between point B and point C is defined as pair #2, and the teeth pair with a contact point located between point C and point D is defined as pair #3. Thus, a mating teeth pair will experience thrice triple teeth pairs contact and twice double teeth pairs contact in a mesh cycle, resulting in a time-varying formulation. On the base principle of an involute gear and its property, the relationship between pressure angle and operating speed can be expressed as \ud835\udc4e\ud835\udc5b \ud835\udefc\ud835\udc5d\ud835\udc61 \u2212 \ud835\udc4e\ud835\udc5b \ud835\udefc\ud835\udc5d\ud835\udc4e = \ud835\udc64\ud835\udc5d (1) \ud835\udc4e\ud835\udc5b \ud835\udefc\ud835\udc54\ud835\udc4e \u2212 \ud835\udc4e\ud835\udc5b \ud835\udefc\ud835\udc54\ud835\udc61 = \ud835\udc64\ud835\udc54 (2) \ud835\udc5f\ud835\udc5d\ud835\udc61 = \ud835\udc5f\ud835\udc4f\ud835\udc5d \ud835\udc50\ud835\udc5c\ud835\udc60 \ud835\udefc\ud835\udc5d\ud835\udc61 (3) \ud835\udc5f\ud835\udc54\ud835\udc61 = \ud835\udc5f\ud835\udc4f\ud835\udc54 \ud835\udc50\ud835\udc5c\ud835\udc60 \ud835\udefc\ud835\udc54\ud835\udc61 (4) Then, the surface velocities at a contact point are given as \ud835\udf08\ud835\udc5d\ud835\udc61 = \ud835\udc5f\ud835\udc4f\ud835\udc5d\ud835\udc64\ud835\udc5d \ud835\udc50\ud835\udc5c\ud835\udc60( \ud835\udc4e\ud835\udc5b\u22121(\ud835\udc64\ud835\udc5d + \ud835\udc4e\ud835\udc5b \ud835\udefc\ud835\udc5d\ud835\udc4e)) (5) \ud835\udf08\ud835\udc54\ud835\udc61 = \ud835\udc5f\ud835\udc4f\ud835\udc54\ud835\udc64\ud835\udc54 \ud835\udc50\ud835\udc5c\ud835\udc60( \ud835\udc4e\ud835\udc5b\u22121( \ud835\udc4e\ud835\udc5b \ud835\udefc\ud835\udc54\ud835\udc4e \u2212 \ud835\udc64\ud835\udc54 )) (6) \ud835\udf08\ud835\udc5d,\ud835\udc54 \ud835\udc3f\ud835\udc42\ud835\udc34 = \ud835\udc5f\ud835\udc4f\ud835\udc5d\ud835\udc64\ud835\udc5d = \ud835\udc5f\ud835\udc4f\ud835\udc54\ud835\udc64\ud835\udc54 (a constant) (7) \ud835\udf08\ud835\udc5d\ud835\udc61 \ud835\udc42\ud835\udc3f\ud835\udc42\ud835\udc34 = \ud835\udf08\ud835\udc5d,\ud835\udc54 \ud835\udc3f\ud835\udc42\ud835\udc34(\ud835\udc64\ud835\udc5d + \ud835\udc4e\ud835\udc5b \ud835\udefc\ud835\udc5d\ud835\udc4e) (8) \ud835\udf08\ud835\udc54\ud835\udc61 \ud835\udc42\ud835\udc3f\ud835\udc42\ud835\udc34 = \ud835\udf08\ud835\udc5d,\ud835\udc54 \ud835\udc3f\ud835\udc42\ud835\udc34( \ud835\udc4e\ud835\udc5b \ud835\udefc\ud835\udc54\ud835\udc4e \u2212 \ud835\udc64\ud835\udc54 ) (9) Thus, the sliding velocity and entraining velocity can be deduced as \ud835\udf08\ud835\udc60\ud835\udc61 = |\ud835\udf08\ud835\udc5d\ud835\udc61 \ud835\udc42\ud835\udc3f\ud835\udc42\ud835\udc39 \u2212 \ud835\udf08\ud835\udc54\ud835\udc61 \ud835\udc42\ud835\udc3f\ud835\udc42\ud835\udc39| = |\ud835\udf08\ud835\udc5d,\ud835\udc54 \ud835\udc3f\ud835\udc42\ud835\udc34 ((\ud835\udc64\ud835\udc5d + \ud835\udc64\ud835\udc54) + \ud835\udc4e\ud835\udc5b \ud835\udefc\ud835\udc5d\ud835\udc4e \u2212 \ud835\udc4e\ud835\udc5b \ud835\udefc\ud835\udc54\ud835\udc4e)| (10) \ud835\udf08\ud835\udc52\ud835\udc61 = |\ud835\udf08\ud835\udc5d\ud835\udc61 \ud835\udc42\ud835\udc3f\ud835\udc42\ud835\udc39 + \ud835\udf08\ud835\udc54\ud835\udc61 \ud835\udc42\ud835\udc3f\ud835\udc42\ud835\udc39|/ = |\ud835\udf08\ud835\udc5d,\ud835\udc54 \ud835\udc3f\ud835\udc42\ud835\udc34( \ud835\udc4e\ud835\udc5b \ud835\udefc\ud835\udc5d\ud835\udc4e + \ud835\udc4e\ud835\udc5b \ud835\udefc\ud835\udc54\ud835\udc4e + (\ud835\udc64\ud835\udc5d \u2212 \ud835\udc64\ud835\udc54) )|/ (11) Then, the slide to roll ratio \ud835\udc46\ud835\udc45 can be defined as \ud835\udc46\ud835\udc45 = \ud835\udf08\ud835\udc60\ud835\udc61 \ud835\udf08\ud835\udc52\ud835\udc61 = | (\ud835\udc64\ud835\udc5d + \ud835\udc64\ud835\udc54) + \ud835\udc4e\ud835\udc5b \ud835\udefc\ud835\udc5d\ud835\udc4e \u2212 \ud835\udc4e\ud835\udc5b \ud835\udefc\ud835\udc54\ud835\udc4e \ud835\udc4e\ud835\udc5b \ud835\udefc\ud835\udc5d\ud835\udc4e + \ud835\udc4e\ud835\udc5b \ud835\udefc\ud835\udc54\ud835\udc4e + (\ud835\udc64\ud835\udc5d \u2212 \ud835\udc64\ud835\udc54) | (12) The friction moment arms and equivalent radius of curvature are \ud835\udc3f\ud835\udc5d\ud835\udc61 = \ud835\udc5f\ud835\udc4f\ud835\udc5d \ud835\udc4e\ud835\udc5b \ud835\udefc\ud835\udc5d\ud835\udc4e + \ud835\udc5f\ud835\udc4f\ud835\udc5d\ud835\udc64\ud835\udc5d (13) \ud835\udc3f\ud835\udc54\ud835\udc61 = (\ud835\udc5f\ud835\udc4f\ud835\udc5d + \ud835\udc5f\ud835\udc4f\ud835\udc54) \ud835\udc4e\ud835\udc5b \ud835\udefc\ud835\udc5b \u2212 \ud835\udc3f\ud835\udc5d\ud835\udc61 (14) \ud835\udc45\ud835\udc61 = \ud835\udc3f\ud835\udc5d\ud835\udc61\ud835\udc3f\ud835\udc54\ud835\udc61 \ud835\udc3f\ud835\udc5d\ud835\udc61 + \ud835\udc3f\ud835\udc54\ud835\udc61 (15) And the Hertzian pressure \ud835\udc43\u210e on the contact point can be formulated as \ud835\udc43\u210e = \u221a \ud835\udc39 \ud835\udc35 ( 1 \ud835\udc3f\ud835\udc54\ud835\udc61 + 1 \ud835\udc3f\ud835\udc54\ud835\udc61 ) \ud835\udf0b ( 1 \u2212 \ud835\udf101 2 \ud835\udc381 + 1 \u2212 \ud835\udf102 2 \ud835\udc382 ) (16) where, \ud835\udc39/\ud835\udc35 is the load per length, \ud835\udc381, \ud835\udc382is the modulus of elasticity and \ud835\udf101, \ud835\udf102 is Poisson\u2019s ratio"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001091_1.4003357-Figure10-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001091_1.4003357-Figure10-1.png",
        "caption": "Fig. 10 Outlet-area section and width",
        "texts": [
            " 9, it is found that the volumetric flow rate passing through the intertooth spaces varies almost linearly with both the rotational speed and the intertooth volume, suggesting a possible analogy with centrifugal pumps. However, the volumetric flow rate ejected by Transactions of the ASME 6 Terms of Use: http://www.asme.org/about-asme/terms-of-use t s m c x r o r x z o z T F M J Downloaded Fr he moving teeth is not constant over the entire outlet area. Conidering, for example, the outlet area defined in Fig. 10, the voluetric flow rate is not uniform across the face width Fig. 11 and onsequently, the radial velocity varies with the axial coordinate b. In this figure, the horizontal lines represent the total volumetic flow rates expelled from one intertooth volume, whereas the ther curves represent the evolution of the partial volumetric flow ates calculated by integrating the outlet radial velocity from 0 to b. Compared with the average flow rate materialized by the horiontal lines, it is found that more air is expelled in the central part f the face width and near the edges while, in the intermediate one, air is aspired the radial velocity changes sign, see Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000898_j.mechmachtheory.2011.08.010-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000898_j.mechmachtheory.2011.08.010-Figure2-1.png",
        "caption": "Fig. 2. Geometry of a four contact-point rolling bearing defined by vectors and all possible contact forces acting on the raceways.",
        "texts": [
            " The calculation of a load distribution presented here is based on the following assumptions: a) the external loads acting on the bearing are in static equilibrium with the contact forces acting on the raceway, b) the bearing rings are ideally stiff, thus taking into account only elastic contact deformations, c) the procedure for calculation of contact forces is based on the Hertz contact theory, and d) the internal ring is fixed, while external ring can move in x, y and z directions, and rotate about x and y axes, as shown in Fig. 2. The system is in static equilibrium when the outer ring is in such position that external bearing loads F and M are in static equilibriumwith the contact forces Q1 and Q2 acting on the top and bottom outer ring raceways, as shown in Fig. 2. The directions of contact forces depend on the relative position of the inner and outer rings, which are defined by points Cit, Cib, Cot and Cob. After applying external loads to a bearing, an outer ring moves, hence its position can be defined by multiplying vectors of curvature centres' initial positions by transformation matrix T: rCot ;T \u00bc T\u00b7rCot and rCob ;T \u00bc T\u00b7rCob : \u00f01\u00de The directions of contact forces in the initial position can be defined by unit vectors eQ1 and eQ2 . After applying the transformation these can be written as: eQ1 ;T \u00bc rCib\u2212rCot ;T \u2016rCib\u2212rCot ;T\u2016 and eQ2 ;T \u00bc rCit \u2212rCob ;T \u2016rCit \u2212rCob ;T\u2016 : \u00f02\u00de By taking into account small rotations, such that sin(\u03c6)\u2248\u03c6, and cos(\u03c6)\u22481, and due to the static analysis, which means that the rotation about axis z is 0, the transformation matrix T can be written as: T\u2248 1 \u03c6x\u00b7\u03c6y \u03c6y u 0 1 \u2212\u03c6x v \u2212\u03c6y \u03c6x 1 w 0 0 0 1 2 664 3 775: \u00f03\u00de The magnitudes of the contact forces depend on the contact deformations between the balls and the bearing raceways, which are directly connected to the relative movements of the bearing rings, i",
            " The maximum contact force and the contact pressure acting on the inner raceway in relation to different geometries are given in Table 2. In addition to the distribution of the contact forces in case of bearing with and without clearance the influence of ideal, i.e. flat, and non-ideal, i.e. twisted in axial direction, the geometry of the bearing has also been investigated. The non-ideal geometry of the bearing was defined by sine function as f \u03c8\u00f0 \u00de \u00bc A1sin A2\u03c8\u2212\u03c0=2\u00f0 \u00de: \u00f022\u00de This equation was used to describe geometry of the centre points of the outer raceways, i.e. axial position of points Cob and Cot in Fig. 2. Hence, different geometries were specified by sine functions with different amplitudes and wavenumbers, which were defined by parameters A1 and A2, as given in Table 2. In Figs. 7 and 8 the geometry of the outer raceways is schematically shown with a dashed line. As it can be seen from Fig. 7a and b, in case of an irregular geometry defined by 1 sine wave (A2=1), the load distribution does not depend on the amplitude of the deformation. In fact, the load distribution and the maximum contact loads are the same as in case of an ideal geometry with clearance"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001711_s1560354713060166-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001711_s1560354713060166-Figure3-1.png",
        "caption": "Fig. 3. Rolling motion of a ball in a straight line in the case \u03c9 \u2016 ei.",
        "texts": [
            " The trajectories in the phase space T SO(3) which correspond to the fixed values of the integrals are a pair of closed curves for which (see [6] for more details): M = Miei + \u221a C \u2212 M2 i (cos \u03d5ej + sin \u03d5ek), \u03b3 = \u03b3iei + \u221a 1 \u2212 \u03b32 i (cos \u03d5ej + sin\u03d5ek), \u03c9 = \u039bAiei, where the constant values Mi, \u03b3i,\u039b expressed in terms of the values of the first integrals are \u039b = \u00b1 \u221a C + 2D\u22121 \u2212 Ai D\u22121 \u2212 Ai M2 \u03b3 , Mi = \u039b\u22121 ( C + Ai D\u22121 \u2212 Ai M2 \u03b3 ) , \u03b3i = \u039b\u22121D\u22121 D\u22121 \u2212 Ai M\u03b3 . According to (2.5) and (2.6), the velocity of the contact point is x\u0307 = bAi \u221a C \u2212 M2 \u03b3 , y\u0307 = 0. Thus, for these periodic (in M, \u03b3) solutions the ball rolls in a straight line perpendicular to the plane of the vectors M, \u03b3 with constant velocity, and the angular velocity makes an angle \u03d5i = arccos \u03b3i with the vertical (see Fig. 3). 3. THE FLOW ON TORI AND THE VELOCITY OF THE CONTACT POINT IN THE GENERIC POSITION CASE For fixed values of the first integrals (2.2) in the generic position case the vectors M, \u03c9, \u03b3 and, consequently, the velocities of the contact point (2.6) may be regarded as functions given on the invariant tori of the reduced system. In this section we explicitly calculate these functions and obtain equations of motion on the invariant tori. To this end we use one of the modifications of spheroconical coordinates, which are separating variables for the equations of the reduced system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000031_s11044-007-9082-2-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000031_s11044-007-9082-2-Figure1-1.png",
        "caption": "Fig. 1 Two elastically coupled rigid bodies",
        "texts": [
            " It is worthwhile recalling again that the elastic potential energy function and the generalized forces arising from it depend only on the configuration of the system. Therefore, if we study two distinct configurations of the system that are connected via some finite or infinitesimal changes in the generalized coordinates, the value of the elastic potential energy and the associated conservative forces in the two configurations do not depend on the path of how the system moved from one configuration to the other. Based on the foregoing general considerations, let us now study the case of two rigid bodies coupled via an elastic structure, as depicted in Fig. 1. Our analysis primarily concerns the study of static equilibrium configurations to gain insight into the stiffness properties of the connection. Therefore, without loss of generality, we can assume that one of the bodies represents our stationary reference system, and the displacement of the other body relative to this reference system will induce the force and moment, referred to as the wrench, originating from the elastic structure coupling the two bodies. The configuration of the moving body relative to its stationary counterpart can be represented by a set of variables which generally include a combination of Cartesian and non-Cartesian coordinates",
            " For example, the simplest of such compliant structures is a linear translational spring whose spring-joint coordinates are the components of the vector giving the relative elongation of the spring along its line of action. Another example can be a nonredundant robotic mechanical system with locked joints, as discussed above. In that case \u03b7i will represent the joint coordinates \u03b8 i of the robotic mechanical system. Let us now consider an arbitrary configuration of the two-body system indicated by B0 in Fig. 1. The system is in equilibrium in this configuration: the elastic wrench developed by the structure is balanced by an applied wrench exerted on the moving body. Consider a small rigid-body displacement of the moving body relative to this reference configuration. This can be represented, as per (6), by sA = tA t . This small displacement takes the system into another configuration B1, which is also under static equilibrium. However, we have to notice that equilibrium configurations B0 and B1 are not simultaneous; they are separated in time by t "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000234_02678290903062994-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000234_02678290903062994-Figure5-1.png",
        "caption": "Figure 5. Application of an elongation perpendicular to the initial director induces the distribution of chains to rotate. Along with shears, the elongation is achieved simply by rearrangement rather than distortion. Soft response ceases on rotation by 90 where the long axis of the distribution is already aligned with the elongation.",
        "texts": [
            " If we insert such a deformation into the Trace formula, as well as its transpose T, equivalent to , 1=2 o WT ,1=2 since the , are symmetric, we obtain Fel \u00bc 1 2 Tr , o , 1=2 o W T ,1=2 , 1 ,1=2|fflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflffl} W , 1=2 o ; 1 2 Tr \u00bc 3 2 : \u00f013\u00de The middle section ,1=2 , 1 ,1=2 gives the unit matrix , by definition. The rotation matrix W then meets its transpose to also give unity: WT W \u00bc . Likewise disposing of the , o terms, one obtains the final value Fel \u00bc 3 2 . This is identical to the free energy of an undistorted network. The non-trivial set of distortions of the form Equation (12) has not raised the energy of the nematic elastomer! Figure 5 explains the principle. Large strain and rotation experiments confirm this picture by following stress and director in response to an elongation applied perpendicular to the original director. The director rotates in response to present a longer dimension of the network to the strain direction (see Figure 6). Rotation starts and ends in a singular fashion (13) as required by the soft deformation formula above. The characteristic forms shared by all samples collapses on to a master curve when appropriately reduced"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001091_1.4003357-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001091_1.4003357-Figure7-1.png",
        "caption": "Fig. 7 3D computational domain",
        "texts": [
            " In this section, three-dimensional models are used in order to reproduce the experimentally observed flows. The corresponding domains of the study are made up of i a gear sector with one or two intertooth spaces and the associated fraction of the blank and ii the surrounding air. On account of the system symmetry, only half of the face width is considered while the other boundary conditions are similar to those used in 2D simulations. The resulting generic model is schematically represented in Fig. 7. The corresponding results in Fig. 8 exhibit a complex flow pattern independent of gear geometry and speed: The air is drawn axially in the intertooth volumes, circulation then takes place over the entire volume, and finally, the flow is expelled by centrifugal effects. These findings are close to the qualitative description in Sec. 5.2 and the 3D numerical results of Ref. 13 , which, in terms of WPL, compare well with the measurements of Ref. 3 . As illustrated in Fig. 9, it is found that the volumetric flow rate passing through the intertooth spaces varies almost linearly with both the rotational speed and the intertooth volume, suggesting a possible analogy with centrifugal pumps"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001564_j.triboint.2013.06.017-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001564_j.triboint.2013.06.017-Figure4-1.png",
        "caption": "Fig. 4. Ball raceway contact after a static load is applied and",
        "texts": [
            " Qi \u00bc P3 sin \u03b1o sin \u00f0\u03b1i \u03b1o\u00de \u00f01\u00de Qo \u00bc P3 sin \u03b1i sin \u00f0\u03b1i \u03b1o\u00de \u00f02\u00de To determine the internal load distribution in ball bearings, consider Fig. 2(b), which shows the displacement of a ball bearing inner ring relative to the outer ring due to the axial load P2. earing rings preloaded by an axial load (b). Under zero loads, the centres of the raceway groove curvature radii are separated by a distance BD\u00bc ri \u00fe ro 2rb. Under an applied load of P2, the distance between the inner and outer raceway groove curvature centres increases by the contact deformation \u03b4i and \u03b4o, as shown in Fig. 4(a). Fig. 4(b) shows the relative angular position (azimuth) of each ball in the bearing. Under an applied axial load, a centrifugal force acts on the ball. Because the ball-inner and ball-outer raceway contact angles are dissimilar, the line of action between the raceway groove curvature centres is not collinear with BD [22]. Instead, it is discontinuous, as indicated in Fig. 5. It is assumed in Fig. 5 that the outer raceway groove curvature centre is fixed in space, and the inner raceway groove curvature centre moves relative to that fixed centre"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001880_j.applthermaleng.2014.02.008-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001880_j.applthermaleng.2014.02.008-Figure9-1.png",
        "caption": "Fig. 9. The temperature distribution of the stator winding (unit: C).",
        "texts": [
            " Therefore the broken-bar fault has an unobvious effect on the overall temperature distribution of the motor. Due to the role of the fan and connecting box, the motor temperature distribution along the axial and radial is not symmetrical. Temperature-rise in the stator winding is caused by power loss in the winding and the rotor bar, stator core loss and the mechanical loss, in which the main contribution comes from the current flowing through the stator winding. The temperature distribution of the stator winding with healthy cage is shown as Fig. 9(a). Because the connecting box and the fan in the motor model are considered, the temperature of the stator winding closed to the junction box is higher, and the highest temperature is not in the midpoint of the winding, but slightly a little close to load side. Fig. 9(b), (c) are the temperature distribution of stator windingwith broken bar fault. Compared to the healthy motor, we can know that the temperature increases in the case of broken bar fault. Fig. 10(a)e(c) are the steady rotor temperature distributions at the above three states. The temperature of the rotor with broken bars increases obviously comparedwith the healthy rotor. The rotor temperature distribution is also not complete symmetry. From the electromagnetic field analysis, we can know that no currents pass though the broken bars and no losses are generated, and the currents of the bars near to the broken bars are dramatically increased and the losses of the bars are increased a lot"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003694_rcs.2081-Figure10-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003694_rcs.2081-Figure10-1.png",
        "caption": "Figure 10. Fabrication of the variable-stiffness module for the continuum manipulator. (a) The continuum structure without the variable stiffness sheath. (b) The SMA-based sheath for variable stiffness. (c) The single module integrated with the sheath",
        "texts": [
            " In addition, during the cooling procedure, the wire still holds the wavy memorized shape under no external stress, but the phase of SMA gradually transforms from austenite into martensite, along with the decrease in elastic modulus. Fabrication of the single module Components of the variable-stiffness module of the continuum manipulator are a continuum structure and a SMA-based sheath. The continuum structure is composed of a silicone shell with a 12-mm-diameter lumen, a SMA core column (SMA-1), four ABS plastic connectors and guiding disks, three circumferentially distributed dyneema cables and two copper wires, as shown in Figure 10(a). The SMA-based sheath for variable stiffness is woven by eight SMA wires (SMA-2), which have a memorized shape of a wavy line, as shown in Figure 10(b). Then, the module of the variable-stiffness continuum manipulator is obtained by integrating the sheath with the continuum structure, as shown in Figure 10(c). This article is protected by copyright. All rights reserved. Thermo-electric behavior of the SMA In order to verify the relationship between the elastic modulus and voltage of SMA wire on the basis of the elastic modulus model and the thermo-electric model (Equation (5) and (8)), the thermo-electric behavior of the SMA wire is experimentally characterized by applying different voltages on both ends of the wire. The setup for this experimental characterization is shown in Figure 11. A SMA wire (SMA-2) is selected for this characterization"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002776_j.jmapro.2019.09.012-Figure12-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002776_j.jmapro.2019.09.012-Figure12-1.png",
        "caption": "Fig. 12. CT images of a 2Cone-0.25 Ti64 sample (12.5mm diameter) positioned differently in the micro-CT scanner: (a) vertically and (b) horizontally.",
        "texts": [
            " This implies a gap between the internal powder and the top shell, making it virtually insulated with no heat flow through. On the other hand, the designed simple cone features are effective in mitigate the insulating issue and appropriate to the overall combined experimental-numerical method for powder thermal conductivity analysis. To determine the possibility of powder settling and air gaps several samples were measured using x-ray computed tomography (XCT). Air gaps would inhibit heat transfer into and out of the powder and elicit greater effective contact conductance (kt and kb) values in the FE model. Fig. 12 below shows the XCT images of a 2Cone-0.25 sample scanned, positioned vertically and horizontally, using a Bruker SkyScan 1173micro XCT scanner1. The sample, fabricated using Ti64 powder, has a small diameter of 12.5mm in order to be fully transmitted by the x-ray of the scanner, limited by the voltage capacity (130 kV). From the vertical position scan (Fig. 12(a)), a gap (dark area) at the top, between the powder (gray area) and the shell (light area), is clearly noticed (in coronal and sagittal views). On the other hand, when the sample is at a horizontal position during the scan, the contact between the powder and the top shell appears continuous, without noting dark areas except around the very outer circumference (corresponding to gas/void). This again demonstrates (1) the significance of a potential gap that resulted from fabricating the cone structure and may result in thermal insulation, and (2) the effectiveness of the internal cones for powder and solid contacts that improve heat transfer through the powder and ensure the testing and the simulation are meaningful"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003596_tmech.2020.2995138-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003596_tmech.2020.2995138-Figure2-1.png",
        "caption": "Fig. 2. Schematic of the transportation system with motion variables defined.",
        "texts": [
            " 2 distance of two corresponding attachment points on the quadcopter and the payload is limited to the length of the associated cable, li \u2208 R+, i.e, \u2016qi \u2212 qL \u2212RLri\u2016 \u2264 li (4) where qi, qL \u2208 R3 are the COM positions of ith quad-copter and the payload, respectively, expressed in the world frame. The rotation matrix RL \u2208 SO(3) relates the body-fixed frame of the object to the world frame. The variable ri \u2208 R3 is a vector from COM of the payload to the attachment point of the cables, expressed in the body-fixed frame of the object. Figure 2 depicts a schematic of the system with the definition of relevant variables. Provided that cable masses are negligible, the equations of motion of quad-copters with cable-suspended payload are given as, miq\u0308i = fiR(\u03b7i)z \u2212migz + TiRLei +Di1(t) (5) M(\u03b7i)\u03b7\u0308i + C(\u03b7i, \u03b7\u0307i)\u03b7\u0307i = \u03a8(\u03b7i) T\u03c4i +Di2(t) (6) mLq\u0308L = \u2212 n\u2211 i=1 TiRLei \u2212mLgz +D3(t) (7) JL\u2126\u0307L + \u2126\u00d7LJL\u2126L = n\u2211 i=1 r\u00d7i (\u2212Tiei) +D4(t) (8) where mi, g \u2208 R+ and Ji \u2208 R3\u00d73 stand for mass, gravitational acceleration and the moment of inertia expressed in the bodyfixed frame of the drone, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003867_j.matdes.2020.108691-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003867_j.matdes.2020.108691-Figure9-1.png",
        "caption": "Fig. 9. Illustration of hardness decreasing zone and stable zone.",
        "texts": [
            " Moreover, whether it is cone supports or block supports, their hardness distributions are well-regulated regardless of the front surface or side surface, that is, the microhardness near the support structures is the highest, and then gradually decreases; until the distance to the edge of the support structures exceeds 2.5 mm, the microhardness tends to be stable. In other words, the support structures have little influence on hardness in this region. The two regions are defined as hardness decreasing zone and hardness stable zone, as illustrated in Fig. 9. Furthermore, it can be seen that when the hardness value is stable, it is maintained at about 250.7 \u00b1 3.2 HV. Compared with the maximum hardness value, it is reduced by 15.3%. Themelt pools observed on the side surface with block supports are shown in Fig. 10. The optical microscope images revealed that the smaller size of melt pool appeared near the supports, as shown in Fig. 10(a). Far away from the supports, the size of melt pool is relatively larger and more in-depth, as shown in Fig. 10(b)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000620_j.triboint.2012.11.007-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000620_j.triboint.2012.11.007-Figure3-1.png",
        "caption": "Fig. 3. (a) A ball specimen with an example three-dimensional roughness profile, a",
        "texts": [
            " In this experiment, a fully formulated turbine oil Mil-PRF23699 was used as the lubricant. The polyol ester formulation ) T1 and (f) T2 for test I at the last loading stage of ph\u00bc2.47 GPa. includes an anti-wear additive, tricresyl phosphate (TCP). The oil was supplied into the oil slinger and pushed through the small radial holes in the oil slinger towards the contact track by the centrifugal force as shown in Fig. 2(a). Examples of the measured three-dimensional roughness profiles of the ball and disk specimens are shown in Fig. 3. The disk surfaces were textured in the radial direction with the intention of simulating actual ground gear surface roughness (allowing the surface velocities to be perpendicular to the roughness lay direction), while the ball surfaces had a smoother, isotropic texture. The composite root\u2013mean\u2013square (RMS) roughness amplitude of the ball\u2013disk pair shown in Fig. 3 is Rq\u00bc0.53 mm. The test conditions in terms of the rolling velocity and the slideto-roll ratio SR\u00bc us=ur are listed in Table 1. The inlet oil temperature was set at 121 3C . For a complete scuffing test, the normal load was increased incrementally from 18 N (corresponding to Hertzian pressure of ph\u00bc0.76 GPa) to 623 N (corresponding to Hertzian pressure of ph\u00bc2.47 GPa) in 30 constant load steps with one minute of test for each loading step. The scuffing failures were detected through the sudden increase in the measured friction coefficient due to the start of surface welding",
            " The temperature\u2013 viscosity coefficient and the thermal expansion coefficient are assumed to be j\u00bc0.03 and b\u00bc7.42 10 4, respectively. The pressure dependence of the Eyring fluid reference stress is defined the same way as in Ref. [26]. For the convective cooling of the ball, the oil volume ratio in air is assumed to be w\u00bc0.05 and the ambient temperature is estimated as Tamb \u00bc 110 3C . The six tests (2 no-failure tests and 4 scuffed tests) operating under the conditions as defined in Table 1 are analyzed with the after run-in surface roughness profiles shown in Fig. 3 to minimize the effect of roughness profile change due to mild surface wear. The predicted friction coefficient m time histories are compared with the measurements in Fig. 7 for all six tests. Similarly, the predicted ball surface bulk temperature Tb1 time histories are compared to the measured ones in Fig. 8. It is seen the measured and predicted m and Tb1 values agree well for all test conditions. Comparing the two speed levels of ur\u00bc10 m/s (left column in Figs. 7 and 8) and ur\u00bc20 m/s (right column in Figs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001968_978-94-007-6101-8-Figure4.8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001968_978-94-007-6101-8-Figure4.8-1.png",
        "caption": "Fig. 4.8 Spherical robot manipulator",
        "texts": [
            "7, while the third element is evident from Figs. 4.5 or 4.6. In this way the same matrix was obtained as after multiplying the three DH matrices. Of course, this is only possible with such simple mechanism as the cylindrical robot. When developing geometric model of a robot with six degrees freedom, the Denavit-Hartenberg approach is advantageous. From this example we have clearly learned the meaning of the geometric model of a robot mechanism. As the third example we shall consider a spherical robot mechanism shown in Fig. 4.8. The first and the second joint are rotational with the joint variables \u03d11 and \u03d12, while the last joint is translational. Its displacement is described by the distance variable d3. First we draw the coordinate frames into the schematic presentation of the spherical robot. As in both previous examples, we place the origin of the base coordinate frame into the center of the first joint. The z0 axis runs along the rotational axis. We shall again wait with the x0 axis. First we shall determine the direction of the x1 axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003890_j.ymssp.2020.107280-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003890_j.ymssp.2020.107280-Figure1-1.png",
        "caption": "Fig. 1. Model of a single-stage spur gear system.",
        "texts": [
            " Section 2 establishes the dynamic model of a single-stage gear system, and improves the interval analysis approach based on the Chebyshev inclusion function and the matrix form of the least square method. Section 3 uses the proposed approach to examine the effects of different uncertain parameters on dynamic responses of the gear system. Section 4 sets up a gear vibration test rig, and validates experimentally the proposed approach through qualitative analysis. Finally, Section 5 ends the manuscript with the concluding remarks. The dynamic model of a single-stage gear transmission system is shown in Fig. 1. The transmission system is mainly composed of a motor, a pinion, a gear and a load. As illustrated in Fig. 1, the pinion is connected to the traction motor, which provides driving torque of the system. The gear is connected to the load which is applied on the transmission system. In this model, the motor and the load are modeled as rigid wheels. The pinion and the gear are represented by rigid wheels which are connected to each other along the line of action through the periodically time-varying mesh stiffness km. The pinion and the gear are supported elastically in both the x and y directions by springs. The support stiffness is expressed as kx1 and ky1 in the x and y directions for the pinion, kx2 and ky2 for the gear. The x and y directions are orthogonal to the wheels axis of rotation. The torsional stiffness of the driving shaft and the driven shaft are expressed by kc1 and kc2, respectively. The dampers and the excitations which are not plotted in Fig. 1 will be given in the differential equations. Newton\u2019s second law of motions and the differential equations of fixed-axis rotation yield the dynamic model of the gear system m1\u20acx1 \u00fe cx1 _x1 \u00fe kx1x1 cm _d12sina12 kmd12sina12 \u00bc 0 m1\u20acy1 \u00fe cy1 _y1 \u00fe ky1y1 cm _d12cosa12 kmd12cosa12 \u00bc 0 Im\u20achm \u00fe cc1 _hm _h1 \u00fe kc1 hm h1\u00f0 \u00de \u00bc Tin I1\u20ach1 \u00fe cc1 _h1 _hm \u00fe kc1 h1 hm\u00f0 \u00de \u00fe r1cm _d12 \u00fe r1kmd12 \u00bc 0 m2\u20acx2 \u00fe cx2 _x2 \u00fe kx2x2 \u00fe cm _d12sina12 \u00fe kmd12sina12 \u00bc 0 m2\u20acy2 \u00fe cy2 _y2 \u00fe ky2y2 \u00fe cm _d12cosa12 \u00fe kmd12cosa12 \u00bc 0 IL\u20achL \u00fe cc2 _hL _h2 \u00fe kc2 hL h2\u00f0 \u00de \u00bc Tout I2\u20ach2 \u00fe cc2 _h2 _hL \u00fe kc2 h2 hL\u00f0 \u00de r2cm _d12 r2kmd12 \u00bc 0 8>>>>>>>>>>>>< >>>>>>>>>>>: \u00f01\u00de where Im, I1, I2 and IL are moments of inertia of the motor, the pinion, the gear and the load, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001418_j.mechmachtheory.2017.02.006-Figure13-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001418_j.mechmachtheory.2017.02.006-Figure13-1.png",
        "caption": "Fig. 13. FEA mesh model for LTCA of hypoid gear.",
        "texts": [
            " There are n = 7 machine settings K p R aOPT , m = 5 different load conditions, and 35 design schemes. The proportion K p is set as K 1 = 1.010, K 2 = 1.050, K 3 = 1.025, K 3 = 1.0 0 0, K 5 = 0.975 K 6 = 0.950 and K 7 = 0.900; the load condition t is set as t 1 = 200 N m, t 2 = 400 N m, t 3 = 600 N m, t 4 = 800 N m and t 5 = 10 0 0 N m. With the above basic design parameters mainly including the basic blank and machine settings, an FEA mesh model can be established for LTCA of the spiral bevel gear [26] , as shown in Fig. 13 , where the mesh selects a hexahedron style and is dense in the contact area of the tooth flank in order to indicate the tooth contact priority. There are five pairs of tooth flank in LTCA are used to conduct performance analysis. Fig. 14 represents the numerical result of maximum tooth contact pressure by extraction approach based on the LTCA. On the whole, the contact stress increases with the increase of tooth surface load. Under any loads, the closer to 1 K p is, the smaller CP MAX ( K p R aOPT ) will be; under the same variations of K p R aOPT , the influence of its increment on CP MAX is smaller than that of its decrement, and under a same load, K p \u2208 [1,1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001822_j.promfg.2018.07.112-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001822_j.promfg.2018.07.112-Figure8-1.png",
        "caption": "Fig. 8. Thermal adjusted mode implementation. (a) STL plot of a bridge structure. (b) Geometric conductivity factor (GCF) model constructed from the scan path.",
        "texts": [
            " Similarly, thermal adjusted mode can also be implemented based on local geometry and heat conduction (section 4.3). The usage of laser power keyword L is further illustrated in path 6 (Fig. 7), where L200 (laser power = 200 W) was set for all linear moves and L100 was set for the connection arcs. The thermal adjusted mode demonstrated in Fig. 6-7 is based on a single layer residual heat compensation model. The similar concept can be extended to more complicated multiple-layer builds such as the overhanging structure (a bridge) shown in Fig. 8a. Overhanging structure is problematic to build because the large variation in thermal conductivities between powder and solidified regions. Traditionally this is addressed by either adding support structures to improve the local thermal conductivity [15], or changing the structure design itself [16]. The thermal adjusted mode proposed here provides a framework to handle such issues through fine tuning of laser power 876 H. Yeung et al. / Procedia Manufacturing 26 (2018) 871\u2013879 H. Yeung et al./ Procedia Manufacturing 00 (2018) 000\u2013000 6 and velocity at each scan point. Since it operates at Gcode interpretation level, it is independent of the structure design, and hence a more generic solution. A unitless geometric-based thermal conduction factor (GCF) is developed in the interpreter which is conceptually demonstrated in Fig. 8. The x-y scan positions generated by the G-code interpreter for the part in Fig. 8a are used to create a layer-wise bitmap for the \u2018melted\u2019 pixels. A pixel is \u2018melted\u2019 if it is within a specified distance of the laser spot center at a \u2018laser on\u2019 scan point. Depending on the pixel size defined (10 \u00b5m by 10 \u00b5m pixel is used here), a relatively precise cross section of the part being built can be modeled. These bitmap layers are then added up layer by layer, and a GCF value is assigned to the current pixel based on the weighted GCF value of the already-built pixels (from previous layer and its same layer neighbors) with immediate contact to it. Pixels on the base plate (0th layer) have a full GCF value. A weighing factor is based on a hypothetical cylinder with diameter approximately equal to melt pool width, and depth equal to powder layer. For example, a 100 \u00b5m melt-pool and 25 \u00b5m layer results in a 50 % weight to the previous layer since ratio of the bottom surface area to side surface area is about 50 : 50. A multi-layer GCF model (or a three-dimensional GCF lookup table) can hence be built. Fig. 8b shows such a model for the object in Fig. 8a. Once this model is built, the laser power at each scan point can be adjusted according to the GCF value at that location. A linear function L = Lo (aX+b) can be used to adjust the laser power, where L is the adjusted laser power, Lo is the original laser power, X is the normalized GCF, a and b are constants which can be optimized from experiments. Figure 9 shows the adjusted laser power at different layers for the bridge structure in Fig. 8. Note the gradually decreasing power level when approaching the overhanging region. A key signature characteristic in LPBF AM processes is the melt-pool geometry. It is used to compare the effects of different scan strategies in this study. In-situ high-speed coaxial imaging is used to measure the melt-pool image area, and ex-situ confocal microscopy is used to measure the surface topology of the solidified melt-pool (scan track). The paths planned in Fig. 6-7 were scanned on a stainless-steel plate",
            " The variation of track height is mainly due to the laser power switching on and off, which is the most frequent and drastic (while the laser is travelling at full speed) in constant build speed mode. The variation of H. Yeung et al./ Procedia Manufacturing 00 (2018) 000\u2013000 6 and velocity at each scan point. Since it operates at Gcode interpretation level, it is independent of the structure design, and hence a more generic solution. A unitless geometric-based thermal conduction factor (GCF) is developed in the interpreter which is conceptually demonstrated in Fig. 8. Fig. 8. Thermal adjusted mode implementation. (a) STL plot of a bridge structure. (b) Geometric conductivity factor (GCF) model constructed from the scan path. Fig. 9. Scan power at (a) 200th layer. (b) 250th layer. The laser power is reduced gradually at the overhanging area. The x-y scan positions generated by the G-code interpreter for the part in Fig. 8a are used to create a layer-wise bitmap for the \u2018melted\u2019 pixels. A pixel is \u2018melted\u2019 if it is within a specified distance of the laser spot center at a \u2018laser on\u2019 scan point. Depending on the pixel size defined (10 \u00b5m by 10 \u00b5m pixel is used here), a relatively precise cross section of the part being built can be modeled. These bitmap layers are then added up layer by layer, and a GCF value is assigned to the current pixel based on the weighted GCF value of the already-built pixels (from previous layer and its same layer neighbors) with immediate contact to it. Pixels on the base plate (0th layer) have a full GCF value. A weighing factor is based on a hypothetical cylinder with diameter approximately equal to melt pool width, and depth equal to powder layer. For example, a 100 \u00b5m melt-pool and 25 \u00b5m layer results in a 50 % weight to the previous layer since ratio of the bottom surface area to side surface area is about 50 : 50. A multi-layer GCF model (or a three-dimensional GCF lookup table) can hence be built. Fig. 8b shows such a model for the object in Fig. 8a. Once this model is built, the laser power at each scan point can be adjusted according to the GCF value at that location. A linear function L = Lo (aX+b) can be used to adjust the laser power, where L is the adjusted laser power, Lo is the original laser power, X is the normalized GCF, a and b are constants which can be optimized from experiments. Figure 9 shows the adjusted laser power at different layers for the bridge structure in Fig. 8. Note the gradually decreasing power level when approaching the overhanging region. 5. Comparison of different scan strategies A key signature characteristic in LPBF AM processes is the melt-pool geometry. It is used to compare the effects of different scan strategies in this study. In-situ high-speed coaxial imaging is used to measure the melt-pool image area, and ex-situ confocal microscopy is used to measure the surface topology of the solidified melt-pool (scan track). 5.1. Melt-pool image area Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003867_j.matdes.2020.108691-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003867_j.matdes.2020.108691-Figure7-1.png",
        "caption": "Fig. 7. FEM models for cutting two types of supports: (a) cone supports; (b) block supports.",
        "texts": [
            " The detailed descriptions are as illustrated in Fig. 6. 2.6. Modelling and simulation with finite element method To investigate the influence of support structures on the cutting performance in the milling process, a 3D finite element method (FEM) model was conducted in ABAQUS/Explicit software. Cone and block support structures were built as 3D deformable solids, and the dimension parameters were corresponded to the measured results (see Fig. 2). Two support arrays were extruded with section shapes on a cuboid base, as shown in Fig. 7. The base representing the finally obtained workpiece was meshed with 23,922 C3D8R elements, and the cone and block support structures were meshed with 194,769 C3D8R and 757,450 C3D10M elements, respectively. The cutting tool was built as a rigid bodywith a sharp cutting edge. The rake angle and the clearance angle were both 10\u00b0, corresponding to the real tool geometries in the milling process. Encastre boundary condition was initially imposed on the bottom of the workpiece and the tool was defined to move lengthwise with a linear speed of 400 mm/min, corresponding to the linear cutting speed in the experiment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003367_00207543.2020.1733126-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003367_00207543.2020.1733126-Figure3-1.png",
        "caption": "Figure 3. The components manufactured from (a) three-dimensional models to (b) finished parts.",
        "texts": [
            " Two case studies were performed in Xi\u2019an Ruite 3D Technology Company to validate the proposed method. A group of components were used as the first case study (case 1). There are 17 components of different shapes and heights and both full dense parts and support structures are fabricated in this case study. The other case study (case 2) employs three components with internal cooling channels. The parts in both case studies were fabricated using aluminium AlSi10Mg powder on an SLM 280HL facility, SLM Solutions GmbH, Germany (see Figure 3). The machine is equipped with two 400 W fibre lasers with a focal laser beam diameter of 80 \u00b5m. During the fabricating process, two lasers are working together, and the product design and process parameters are shown in Table 1. The parts were fabricated at an average room temperature of 27.0\u00b0C and 5\u00b0C for case 1 and case 2, respectively. The part fabrication was conducted in an inert gas atmosphere. Before the building process began, the oxygen level was reduced from 21% in air to below 0.1% to prevent oxidation and reactions of the AlSi10Mg powder",
            " The total time consumed is 16 h 27 min and 3 h 21 min, during which the machine consumed 50.79 and 8.87 kWh for case 1 and case 2, respectively. The power fluctuates due to the intermittent operation of water-cooling system and lasers. The building phase dominates the energy consumption of the SLM process, accounting for 91.79% and 57.53% of total energy use, followed by the cooling down phase at 5.13% and 23.19%, and the warming up phase at 3.08% and 19.28% for case 1 and case 2, respectively. The results of the experiments to manufacture the part shown in Figure 3 using process parameters in Table 1 are summarised in Table 3. The predicted times in the warming up and cooling down phases for case 1 are very close to the measured times. For case 2, the measured time is longer than the predicted time in the warming up and shorter than the predicted time in the cooling down phase due to low ambient temperature of 5\u00b0C. For both cases, the measured time in the building process is over 20% longer than the predicted time. This could be explained by that the laser jump time being not included in the prediction model and the unsynchronised operating of the two lasers"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000840_sav-2011-0656-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000840_sav-2011-0656-Figure1-1.png",
        "caption": "Fig. 1. Spur gear transmission modeling.",
        "texts": [
            " The adopted model is a lumped parameters one with eight degrees of freedom which offers a global description of the dynamics of the transmission. The torque-speed characteristic of the driving motor is taken into account in order to compute the instantaneous rotational speed of the motor which is related to the load value. Dynamic response of the system is computed and the influence of the loading conditions is identified using Smoothed Wigner-Ville Distribution. The obtained results are compared with experimental results. A one-stage spur gear model is considered [9]. It is divided into two rigid blocks as presented in Fig. 1. Each block has four degrees of freedom (two translations and two rotations). Pinion (12) with Z1 teeth and gear (21) with Z2 teeth are assumed to be rigid bodies and the shafts with torsional rigidity. Shafts are supported by rolling elements bearings modeled each one by two linear spring having constant stiffness. For the case of low contact ratio (c < 2), a fluctuation one pair-two pairs of teeth in contact is observed. This yields to a time varying gearmesh stiffness Kg (t) acting along the line of action of the meshing teeth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000679_j.ymssp.2010.02.003-Figure10-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000679_j.ymssp.2010.02.003-Figure10-1.png",
        "caption": "Fig. 10. Pressure force in a space between teeth.",
        "texts": [
            "5/100 of the meshing period, the trapped volume is simultaneously put in communication with the inlet and outlet volumes due to the shape and dimension of the relief grooves. During this time interval a linear decrease of the pressure in the trapped volume from the outlet to the inlet value was assumed. Once the pressure distribution around each gear was obtained, the resultant pressure force and torque can be determined. The pressure force is calculated as the vectorial sum of the pressure around the gear multiplied by the involved area; in particular, taking as reference Fig. 10, the pressure force in tooth space q, having direction as the symmetric axis of the space itself, can be calculated as follows: fp q \u00bc 2 Z yp=2 0 pqcos\u00f0y\u00debkrextdy\u00bc 2pqsin\u00f0yp=2\u00debkrext \u00f022\u00de Such a pressure force has to be reduced in the reference frames OkXkYk of Fig. 1(b) and considering the contribution of the zk spaces between teeth, the following relations for gears 1 and 2 can be written: fpx1 \u00bc Xzk q \u00bc 1 fpqcos\u00f0j1q \u00de fpy1 \u00bc Xzk q \u00bc 1 fpqsin\u00f0j1q \u00de 8>>>< >>>: \u00f023\u00de fpx2 \u00bc Xzk q \u00bc 1 fpqcos\u00f0j2q \u00de fpy2 \u00bc Xzk q \u00bc 1 fpqsin\u00f0j2q \u00de 8>>>< >>>: \u00f024\u00de where jkq is the angular position of the axis of tooth space q for gear k with respect to the Xk-axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001115_j.wear.2015.01.047-Figure10-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001115_j.wear.2015.01.047-Figure10-1.png",
        "caption": "Fig. 10. Tribometer.",
        "texts": [
            " Surfaces are grinded to obtain RaE0.15 mm. Some samples are also polished (Rao0.005 mm). Some experiments will be made in presence of the grease generally used for PRS. It is thickened withMicrogels and it contains anti-wear and high-pressure additives. A specific test rig has been developed to reproduce the PRS kinematics. The roller is mounted on a small shaft that rolls freely on small ball bearings inside a holder. The holder is fixed to a shaft that loads the assembly on the rotating disc (Fig. 10). Tangential force and rolling speed are measured and recorded. The transverse sliding component is generated by moving the contact perpendicularly to the radius of the disc (Fig. 11). The axial shift \u0394 between the roller axis and the disc axis is controlled with precision and creates a radial sliding component. As a result, it generates a tangential force Ft. The creep ratio \u03c4 is defined by \u03c4\u00bc \u00f0Vsliding=Vrolling\u00de \u00bc tan \u03b8. Hence \u0394 is calculated as follows: \u0394\u00bc R sin \u03b8\u00bc R sin \u00f0a tan \u03c4\u00de, where R is the radius of track on the disc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002784_j.jmrt.2019.11.063-Figure22-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002784_j.jmrt.2019.11.063-Figure22-1.png",
        "caption": "Fig. 22 \u2013 Macrostructure of the Ti6Al4V material resulting from the DMLS additive manufacturing method taken from: (a) samples along the Z axis, (b) sample gripping part, (c) distribution of force lines in the sample during tensile force; I \u2013 the area of significant changes in the material structure",
        "texts": [
            " 12a and 13 a) delivered in the form of an annealed drawn bar does not show significant changes after tensile force action. The macrostructure of the unloaded DMLS sample (Specimen DMLS-1) shows no structural changes in the cross-section and longitudinal section (Figs. 14a and 15 a). In the case of DMLS sample subjected to load (Specimen DMLS-2), the macroscopic images (Figs. 16a and 17 a) demonstrate structural changes resulting from external load. Their precise analysis allows to specify three areas (Fig. 22): I \u2013 the area of significant changes in the material structure resulting from the tensile force action, II \u2013 transitional area, III \u2013 area with limited impact of tensile force. In area I there were large plastic deformations due to the action of the tensile force, and the directionality of the structure (Fig. 22a) is as a function of deformation degree [18]. related to the arrangement of the force lines (Fig. 22c). There is a transition zone between area I and area III (area II), which is indicated in Fig. 22(a and b). Area III is an area in which plastic deformation occurred with a much lower value than in area I. The macrostructure analysis of the samples used in the research indicates that the tensile load causes significant changes in the structure of objects produced by the use of DMLS additive manufacturing method. It may result from additive technology, process implementation parameters, arrangement of material layers in relation to the expected direction of loading. The samples used in the tests were produced along the Z axis, i",
            " Analysis of the macrostructure of the samples used in the tests indicates that the tensile load causes significant changes in the structure of objects produced by the additive DMLS method. It may result from additive technology, process implementation parameters, arrangement of material layers in relation to the expected direction of loading. Comparison of the macrostructure of the sample made by the additive method before and after loading indicates that the implementation of the load introduces plastic deformations, which are visible in the sample photos shown in the Fig. 22. The change in structure is associated with deformations resulting from the load line onflict of interests he authors declare that they have no known competing financial nterests or personal relationships that could have appeared to influnce the work reported in this paper. e f e r e n c e s [1] Murr LE, Martinez E, Amato KN, Gaytan SM, Hernandez J, Ramirez DA, et al. Fabrication of metal and alloy components by additive manufacturing: examples of 3D materials science. J Mater Res Technol 2012;1(1):42\u201354"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000386_iecon.2008.4758270-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000386_iecon.2008.4758270-Figure2-1.png",
        "caption": "Fig. 2. SynRM mounted on the test bench.",
        "texts": [
            " 1) can lead to a critical punching process; \u2022 flux weakening capabilities (required in spindle and traction applications); \u2022 absence of rotor losses, with a cooler motor respect to the induction motor, where the rotor joule losses play an important role on the machine thermal behavior. II. INDUCTION VS. SYNCHRONOUS RELUCTANCE MOTORS (ANALYTICAL APPROACH) In order to understand the advantages of the SynRM with respect to the induction motor, from the thermal point of view, in this paper a direct comparison between the two motor typologies has been done. The analyzed motors are in TEFC (Totally Enclosed Fan Cooled) frame as shown in Fig.2. All the motors are produced by the same company; the induction motors are general-purpose induction motors, while the SynRMs are built putting a reluctance rotor inside stators extracted from the induction motor production line. As a consequence, the SynRMs and the induction motors employed in the analysis have the same windings and stator lamination, while the rotors are obviously different. The motor stators are equal and the differences are due to the unavoidable process tolerances. The induction motors nameplate data rated 380 V, 50 Hz, 4 poles, 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002120_j.mechmachtheory.2015.09.010-Figure20-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002120_j.mechmachtheory.2015.09.010-Figure20-1.png",
        "caption": "Fig. 20. Contact state of the two gears.",
        "texts": [
            " Here, the second method was taken: the cutting processes were implemented with the help of a numerical control gear shaping machine based on the SINUMERIK 840D system. Fig. 18 shows the processing of the drive gear (a) and the driven gear (b). Fig. 19 shows the finished drive gear (a) and driven gear (b), where the tooth profile of each finished gear is the same as the corresponding tooth profile shown in Fig. 17. The surface roughness of the finished gears seems fine in Fig. 19, while the manufacturing precision still needs further investigation. Fig. 20 shows that the two gears are in a good contact state and they could roughly meet the design requirement. However, further research of an effective test method is needed. In combination with the principles of shaping non-circular gears, kinematic relation of the machine, and the manufacturing processes, this paper presented a 3-linkage model with an equal arc-length cutting method involving feed. Additionally, the feeding parameter settings, stock design method, retracting interpolation, and cutter datum presetting relating to the process were discussed in this paper"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003652_j.ymssp.2019.04.029-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003652_j.ymssp.2019.04.029-Figure4-1.png",
        "caption": "Fig. 4. Distribution of pits on the tooth surface.",
        "texts": [
            " It is found that pitting caused by surface fatigue usually extends from a narrow band below the pitch line to both sides, and the pitting will cross the pitch line as the pitting expands. The fatigue gear tests were performed in [31] at a rotational speed of 745 rpm and torques of 220, 147 and 73 Nm, respectively. Fig. 5 shows the distribution of pitting center based on data given in Appendix in [31]. It is found in Fig. 5 that the centers of pitting are always in a narrow area below the pitch line. The boundary 1 and boundary 2 in Fig. 5 correspond to the xmin and xmax (xmin \u00bcmin\u00f0da c \u00fe b 2\u00de; xmax \u00bc max\u00f0da c \u00fe b 2\u00de, where b and c can be found in [31]) in Fig. 4(a), respectively. In this study, the pits are modeled as cylindrical illustrated in Figs. 6\u20138. The pitting center is modeled as a two-dimensional random variable. The probability distribution of the central position of the model follows a Gaussian distribution N2 along tooth height, and uniform distribution along tooth width, as illustrated in Fig. 4(a). Therefore, C : \u00f0Xi;j;k;c;Yi;j;k;c\u00de satisfies Eqs. (2) and (3). The L denotes the tooth width of the spur gear. In addition, for the normal distribution function given in Eq. (2), the 3r criterion is used to describe the distribution area of the pits. That is to say, in the direction of tooth height, there are 99.73% pits in the area of l 3r 6 Xi;1;1;c 6 l\u00fe 3r. Therefore, l and r can be calculated by Eq. (4), where xmax and xmin are the coordinate value of boundary of pitting center as shown in Fig. 4. In the x direction, xmin and xmax are separately determined by the boundary of pitting center as shown in Figs. 4 and 5. The values of \u00f0Xi;j;k;c;Yi;j;k;c\u00de are set the same as \u00f0Xi;1;1;c;Yi;1;1;c\u00de. Xi;1;1;c N2\u00f0l;r\u00de \u00f02\u00de Yi;1;1;c U\u00f00; L\u00de \u00f03\u00de l \u00bc xmax \u00fe xmin 2 ; r \u00bc xmax xmin 6 \u00f04\u00de Therefore, l1i;j and l2i;j in Eq. (1) are subject to Eqs. (2) and (3), respectively. Then, Eqs. (5) and (6) are obtained. Besides, the correlation coefficient q is set to be 0 in this work. The projection of the two-dimensional Gaussian distribution in the plane of X1Z1 and Y1Z1 in Fig. 4(b) is Gaussian distribution. Referring to the 3r principle of Gaussian distribution, the probability of 2D Gaussian distribution in the ellipse with a long axis radius of 3r1 and a short axis radius of 3r 2 is 98.7%. Then a minimum ellipse whose long axis is parallel with the Y axis and the short axis is parallel with the X axis is used to cover the over 98.7% of pitting area. The length of long half axis of the ellipse is denoted as a, while the short half axis is denoted as b. r1i;j and r2i;j can be derived from Eqs",
            " The ratio of the pitting area to the total area of tooth surface is Pw;w \u00bc 1;2;3;4, which is used to indicate the degree of damage corresponding to the pitting of the four stages, and the radius and number of the simulated pits at each stage are shown in Table 1. Sk (k \u00bc 2;3;4) is the average area of a single pit of kind A, B, C on the tooth surface, respectively. Sk and nw can be calculated via Eqs. (11) and (12). H means the tooth height between base circle and addendum circle in direction X as shown in Fig. 4. Sk \u00bc p\u00f0c2k \u00fe d2 k \u00fe ckdk\u00de=3 \u00f011\u00de nw \u00bc 0 w \u00bc 1 HLPw S2 w \u00bc 2 HLPw Pw 1 v\u00bc2 nw v\u00fe1Sv\u00fe1 S2 w P 3 8>< >: \u00f012\u00de In this paper, the TVMS of a gear system with pitting is also deduced by using potential energy method [20,24]. Since it is assumed that the gear system has no friction and manufacturing error in [20,24], this hypothesis will be used in this work. A cantilever model is used to evaluate the mesh stiffness of gears, as shown in Figs. 9 and 10. Four variables \u00f0u;v ; r; d\u00de are used to describe the location and size of a pits where r is the radius of the pit circle and the \u00f0d\u00de is the depth of the pit, u and v are used to describe the position of the pit as shown in Figs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002424_j.mechmachtheory.2017.12.003-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002424_j.mechmachtheory.2017.12.003-Figure4-1.png",
        "caption": "Fig. 4. Misalignment condition setup: (a) assembly error and (b) instantaneous transmission ratio.",
        "texts": [
            " Referring to descriptions in the paper [10] , in establishments of the basic coordinate system { i , j , k }, there are i = [1 0 0 ] , j = [0 1 0 ] , k = [0 0 1 ] (7) Here, p i is the function with respect to \u03b4M . There is p i = [ cos \u03b4M 0 sin \u03b4M ] ( i j k ) (i = 1 , 2) . (8) In the consideration of pinion initial point, the setup of misalignments condition mainly includes: i) assembly error, which mainly includes four items E, P, G, \u03b1; ii) instantaneous transmission ratio, which constrains the gear motion in the initial contact state. A schematic representation of the misalignment condition setup including the assembly error and instantaneous transmission ratio is depicted in Fig. 4 . Here, in the conventional definition of gear assembly error items [6,7] , there are three main items, namely H, P and G , in addition to their crossed axis angle \u03b1 which is generally considered as the constant 90 \u00b0 or ignored its error. In the transmission process, it is well known that the gear transmission ratio is not very constant, which is a main reason for the low carry capacity, high vibration and noise. The most recent decades, gear designers have been trying to make tooth contact state within a propitiate boundary scope",
            " For instance, the tooth contact pattern required to maintain the middle area and avoid the edge or corner contact. In particular, in the initial contact state, the transmission error of initial tooth contact point can directly affect the vibration and noise of whole process. Therefore, the instantaneous transmission ratio in the initial contact constant is significant step to identify the initial tooth contact point for TCA. After obtaining the initial values of gear initial point, the pinion initial point can be identified by considering misalignments condition which is the constraints for TCA. Fig. 4 shows the analytical geometry arrangement of misalignments condition. Where, the gear and pinion are assembled together in accordance with the design requirements. While the gear rotates around the axis p 1 , the pinion rotates around the axis p 2 , the misalignments can be represented as P = [( D O p O g \u00d7 p 1 ) \u00b7 j ] / [ \u2212( p 1 \u00d7 p 2 ) \u00b7 j ] (16) E = D O p O g \u00d7 j (17) Considering the influence of misalignments on tooth contact performances, a new TCA approach is proposed by computing the geometric kinematic transformation relations in tooth contact process"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003793_j.mechmachtheory.2019.103764-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003793_j.mechmachtheory.2019.103764-Figure2-1.png",
        "caption": "Fig. 2. Double-helical gear transmission structure for GTF aero-engine.",
        "texts": [
            " The fan rotor is not directly connected to the low-pressure rotor, but is cantilevered on two juxtaposed tapered roller bearings. The low-pressure rotor adopts a 2-point support of 0-1- 1. The roller bearing behind the low-pressure turbine is supported on the rear bearing of turbine housing, the low-pressure rotor is supported on the ball bearing, and the rear shaft of the low-pressure compressor is connected to the low-pressure rotor through the transition short shaft. 2.2. Double-helical star gearing system Fig. 2 shows the double-helical gear transmission structure for GTF aero-engine, the fan-driven gearbox adopts a five-way shunting herringbone gear transmission structure, which mainly includes the sun gear, star gear, ring gear, planet carrier, input and output shaft. The sun gear is a floating part, which is splined with the input shaft and meshes with five circumferentially evenly distributed star gears. The star gears are designed with gear-bearing integration [24] . The star gears are internally supported by bearing and meshed with the ring gear, which is a semi-floating component and taken as the output end of the gear train, connected to the output shaft by bolts; the gravity of the entire gear box and the torque generated by the gear meshing is carried through planet carrier supported by elastic base"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000728_14763141.2011.650187-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000728_14763141.2011.650187-Figure1-1.png",
        "caption": "Figure 1. A model of an ideal kinematic sequence for a golf swing, highlighting four body segments: hips, shoulders (trunk), wrists, and clubhead.",
        "texts": [
            " Further golf research is needed to assess the importance of variability in the sequence of the transition into the downswing and the temporal nature of segment release to achieve maximal clubhead velocity. It is precisely this sort of research that can allow identification of the variability tolerance within the macro-kinematics that affects the critical factors (i.e. the impact factors). Whilst there is still uncertainty in our understanding of the swing, research is beginning to identify some interesting data to suggest that there is an optimal sequencing of peak segmental angular velocities in the golfer\u2019s kinematic sequence (Figure 1; see Cheetham et al., 2008 for a full discussion). There is little information currently available on the tolerable variation within the velocities and timings of the sequence present and how the sequence differs across the spectrum of abilities and between genders. Cheetham et al. (2008) compared novice amateurs and professionals, finding amateurs demonstrate poorer coordination presented through timing variability of the peak segmental rotational speeds prior to impact. This variability was shown by the standard deviations of the mean timing of the peak segmental (pelvis, thorax, arm) rotational speeds before impact"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002213_j.mechmachtheory.2014.06.006-Figure18-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002213_j.mechmachtheory.2014.06.006-Figure18-1.png",
        "caption": "Fig. 18. State 14 of the derivative queer-square mechanism (\u03b11 b 0, \u03b12 b 0, \u03b211 = \u03b212, \u03b221 \u2260 \u03b222).",
        "texts": [
            " 16, the relations between the angles of the revolute joints in the derivative queer-square mechanism in state 12 are provided as \u03b11N0;\u03b211N0;\u03b212N0 \u03b12b0;\u03b221N0;\u03b222N0 : \u00f042\u00de The limb1s and limb2s in state 12 have different relative positions compared to the base. The limb1s and limb1p are higher than the base, and the limb2s and limb2ap are lower than the base. The platform is located in themiddle of the limb1p and limb2ap, in particular it is lower than the limb1p and higher than the limb2ap. The observation of the derivative queer-square mechanism in state 13 is illustrated in Fig. 17 and its angle relations are given as \u03b11b0;\u03b211N0;\u03b212N0 \u03b12N0;\u03b221b0;\u03b222b0 : \u00f043\u00de The diametric view of the derivative queer-square mechanism in state 14 is presented in Fig. 18 and its angle relations are given as \u03b11b0;\u03b211b0;\u03b212b0 \u03b12b0;\u03b221b0;\u03b222b0 : \u00f044\u00de When the derivative queer-square mechanism moves to state 14 as shown in Fig. 18, both limb1s and limb2s are lower than the base OA1A2 and the platform E1F1E2F2 is even lower than the limb1p and limb2ap. By the same approach of the abovementioned states, combining Eqs. (17)\u2013(22) and Eq. (40), the platformmotion\u2013screw system, when the derivative queer-square mechanism moves into the regions of states 11\u201314, is illustrated as and S f n o \u00bc S f1 \u00bc 0 u 0 v 1 w\u00bd T n o ; \u00f045\u00de with, u \u00bc 2c\u03b12 s\u03b221c\u03b222\u2212s\u03b222c\u03b221\u00f0 \u00de s \u03b11 \u00fe \u03b81\u00f0 \u00dec\u03b11\u2212s\u03b11\u2212c \u03b11 \u00fe \u03b81\u00f0 \u00des\u03b11\u00bd s\u03b12 2l1s\u03b11s\u03b221c\u03b222\u22122l1s\u03b11s\u03b222c\u03b221 \u00fe l2s\u03b11s\u03b221c\u03b222\u22122l2s\u03b222c\u03b11s\u03b221 \u00fe2l3c\u03b11s\u03b12s\u03b221c\u03b222\u22122l3c\u03b11s\u03b12s\u03b222c\u03b221 \u00fe l2s\u03b11s\u03b222c\u03b221 ; v \u00bc \u2212 2c\u03b12 l2s\u03b221s\u03b222c \u03b11 \u00fe \u03b81\u00f0 \u00des\u03b11\u2212l2s\u03b221s\u03b222s \u03b11 \u00fe \u03b81\u00f0 \u00dec\u03b11 \u00fe l2s\u03b12c\u03b222s \u03b11 \u00fe \u03b81\u00f0 \u00des\u03b221c\u03b11 \u2212l3s\u03b11s\u03b12s\u03b221c\u03b222 \u00fe l3s\u03b11s\u03b12c\u03b221s\u03b222\u2212l3s\u03b12c\u03b221s\u03b222s \u03b11 \u00fe \u03b81\u00f0 \u00dec\u03b11 \u00fel2s\u03b11s\u03b221s\u03b222\u2212l3s\u03b12c\u03b222s\u03b221c \u03b11 \u00fe \u03b81\u00f0 \u00des\u03b11 \u00fe l3s\u03b12c\u03b221s\u03b222c \u03b11 \u00fe \u03b81\u00f0 \u00des\u03b11 0 @ 1 A s\u03b12 l2s\u03b11c\u03b222s\u03b221\u22122l3c\u03b11s\u03b12s\u03b222c\u03b221 \u00fe 2l3c\u03b11s\u03b12s\u03b221c\u03b222 \u00fel2s\u03b11s\u03b222c\u03b221\u22122l2s\u03b222c\u03b11s\u03b221\u22122l1s\u03b11s\u03b222c\u03b221 \u00fe 2l1s\u03b11c\u03b222s\u03b221 ; w \u00bc \u2212 c\u03b12 2l3c\u03b11s\u03b12s\u03b221c\u03b222\u22122l3c\u03b11s\u03b12s\u03b222c\u03b221\u22122l1s\u03b11s\u03b222c\u03b221 \u22122l2s\u03b221s\u03b222c\u03b11 \u00fe 2l1s\u03b11s\u03b221c\u03b222\u2212l2s\u03b11s\u03b222c\u03b221 \u00fe l2s\u03b11s\u03b221c\u03b222 \u00fe2l2s\u03b222s \u03b11 \u00fe \u03b81\u00f0 \u00dec\u03b11c\u03b221\u22122l2s\u03b222c \u03b11 \u00fe \u03b81\u00f0 \u00des\u03b11c\u03b221 0 @ 1 A s\u03b12 2l3c\u03b11s\u03b12s\u03b221c\u03b222\u22122l3c\u03b11s\u03b12s\u03b222c\u03b221\u22122l1s\u03b11s\u03b222c\u03b221 \u00fe2l1s\u03b11s\u03b221c\u03b222 \u00fe l2s\u03b11s\u03b222c\u03b221 \u00fe l2s\u03b11s\u03b221c\u03b222\u22122l2c\u03b11s\u03b222s\u03b221 : The cardinal number which also equals to the dimension of the spanned subspace of the platform motion\u2013screw system indicates that the platform changes its mobility to one degree of freedomwhen the derivative queer-square mechanism changes to states 11\u201314 by passing through the singular posture"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001983_j.jtbi.2014.06.034-Figure11-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001983_j.jtbi.2014.06.034-Figure11-1.png",
        "caption": "Fig. 11. The trajectory associated with a hyperactivated virtual sperm for a human shaped head and a hyperactivated beat pattern, given by Eq. (2.6) with the hyperactivated parameters of Table 1. The hyperactivated sperm circles clockwise repeatedly when viewed from above due to the asymmetry of the beat pattern; even though the cell starts close to the surface (z\u00bc0.3 in units of flagellar length), it also reaches large distances from the surface (z43) indicating escape to regions where surface effects are minimal and in reality likely to be dominated by other effects that are not modelled, such as other cells.",
        "texts": [
            " Changes of the mammalian flagellar waveform with hyperactivation have been closely studied due to the importance of hyperactivation in the final stages of the sperm's approach to the egg in the female reproductive tract (Suarez and Pacey, 2006), and are typically characterised by large-amplitude, low-wavenumber and asymmetric beat patterns (Ohmuro and Ishijima, 2006). We therefore briefly consider the impact of such changes in the flagellar waveform by considering a sperm with a human shaped head, a rigid connection between the sperm head and the flagellum and a flagellar waveform given by Eq. (2.6) with the hyperactivated parameters of Table 1. The resulting trajectory is plotted in Fig. 11, showing circling trajectories, reflecting the beat asymmetry. Despite starting close to the surface (z\u00bc0.3 in units of flagellar length), these trajectories also reach large distances from the boundary (z43) where surface effects are minimal, indicating hyperactivated sperm do surface escape. This is in contrast to the cell accumulation often observed for the non-hyperactivated beat with accumulation heights of zno1 (Figs. 8\u201310), demonstrating fundamental changes in sperm\u2013boundary interactions with hyperactivation",
            ", 2009; Tam and Hosoi, 2011) even though a complicated, and thus most likely biological, relationship is observed in practice between sperm morphology and swimming speed (Simpson et al., 2014). Furthermore, on considering hyperactivated waveforms we also observe a loss of surface swimming stability which is consistent with the predictions concerning tethered sperm by Curtis et al. (2012). Furthermore, the modelling presented here yields a prediction of trajectories that oscillate back and forth from the surface, without overall progression (Fig. 11), which may assist in search strategies for the egg, though additional cues and flagellar waveform modulation, such as rheotaxis (Miki and Clapham, 2013), would be required for the sperm to progress along the female reproductive tract. In summary, we have found that stable surface swimming is a robust aspect of sperm motility, holding for many different cell morphologies and waveforms, highlighting that the observations of stable surface swimming across many species do not require detailed regulation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002466_j.optlastec.2019.105666-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002466_j.optlastec.2019.105666-Figure2-1.png",
        "caption": "Fig. 2. The 3D profile of transient temperature distribution (a) and temperature contour plots of the center of the TiB2 layer (point 2) (b); the 3D profile of transient temperature distribution (c) and temperature contour plots of the center of the Ti6Al4V layer (point 1) (d) during the SLM process when laser irradiated the center of the second TiB2 powder layer (point 2) (P=400W, \u03bd=600mm/s).",
        "texts": [
            " The applied process parameters were same as those used in the simulations (Table 1). The fabricated samples for metallurgical examinations were cut, grounded and polished according to standard procedures and then etched with a solution composing of distilled water, HNO3, and HF with a volume ratio of 50:3:1 for 30 s. The characteristic cross-section morphologies study of the SLM-processed such as the metallurgical bonding and defects were conducted by a field emission scanning electron microscopy (FESEM). Fig. 2 depicts the transient temperature distribution of TiB2 layer and Ti6Al4V layer when the laser beam reached point 2 (Fig. 2a) with the P of 400W and \u03bd of 600mm/s. It can be seen in Fig. 2a that an elongated horizontal contour emerged when laser beam moved along the X-axis. The maximum temperature was higher than the melting temperature of the TiB2 (2980 \u00b0C), which slightly fell behind the center of the laser spot. As shown in Fig. 2c, the isotherm curves on the surface of TiB2 layer were a series of ellipses and the fore part of which was more intensive compared with those at the tailed region. The dashed line circle presented in the temperature contour plot was the isotherm of the melting point of the TiB2 (2980 \u00b0C), which led to a small molten pool. The predicted temperature deceased from 3169 \u00b0C in the center of the molten pool to 2980 \u00b0C at the edge of the molten pool. Owing to the heat conduction from the TiB2 layer to the as-fabricated Ti6Al4V layer, the Ti6Al4V layer would remelt as the temperature exceeded the melting point of the Ti6Al4V (1650 \u00b0C). The remelting phenomenon at the as-fabricated Ti6Al4V layer resulted in a remolten pool as shown in Fig. 2d. The operative SLM temperature decreased from 2559 \u00b0C in the center of the remolten pool to the 1650 \u00b0C at the edge of the remolten pool and the maximum temperature was lower than the evaporation point (2976 \u00b0C). It can be found that the size of the molten pool on the surface of the as-fabricated Ti6Al4V layer reached 125 \u03bcm in length and 95 \u03bcm in width respectively, which was much larger than that of the TiB2 layer and the depth of the TiB2 layer with the value of 11.9 \u00b5m was also much smaller than that of the Ti6Al4V layer with the dimension of 16"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001652_s00170-017-0760-9-Figure10-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001652_s00170-017-0760-9-Figure10-1.png",
        "caption": "Fig. 10 For a multiple bead specimen sectioned in the middle, the temperature contours while depositing the second bead a before the torch reaches the mid-section and b when the torch is at the mid-section",
        "texts": [
            " The variation of temperature along the bead when the laser beam is moving on top of the bead for the single-track cladded specimen is shown in Fig. 9a, b for the laser power of 2.5 kW, the feed rate of 20 g/min, and laser speed of 10mm/s. The start and end points are in transient regions, and the middle node is in the steady-state region. The temperature rises rapidly and then falls quickly during heating, while the cooling process due to the convection and radiation heat transfer is relatively slow. The peak temperature of the middle node reaches 2100 \u00b0C at 2.8 s and then falls to 300 \u00b0C at 4 s. Figure 10 depicts the temperature contour on the multi-track cladded specimen in two time steps for the laser power of 2.5 kW, the feed rate of 20 g/min, and laser speed of 10 mm/s. Figure 11a compares the melt pool and HAZ from the simulation and experiment for a single-track specimen that demonstrates the quality of the matching regions. The violet area represents the melted material in the melt pool with a temperature higher than 1500 \u00b0C (melting temperature of the substrate and clad material). Figure 11b depicts the melt pool on the polished and etched surface of the experimental specimen and simulated model for the multi-track cladded specimen"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002213_j.mechmachtheory.2014.06.006-Figure11-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002213_j.mechmachtheory.2014.06.006-Figure11-1.png",
        "caption": "Fig. 11. State 7 of the derivative queer-square mechanism (\u03b11 N 0, \u03b12 N 0, \u03b211 \u2260 \u03b212, \u03b221 = \u03b222).",
        "texts": [
            " According to the positive or negative angles \u03b11 and \u03b12, category 3 is further separated to four states: state 7 where limb1s and limb2s have a relatively higher position compared to the base (\u03b11 N 0, \u03b12 N 0), state 8 where limb1s has a higher and limb2s has a relatively lower position compared to the base (\u03b11 N 0, \u03b12 b 0), state 9 where limb1s is lower and limb2s is relatively higher than the base (\u03b11 b 0, \u03b12 N 0), state 10 where limb1s and limb2s both have a relatively lower position compared to the base (\u03b11 b 0, \u03b12 b 0). The derivative queer-squaremechanism in state 5 is demonstrated in Fig. 11 and the angle ranges of state 5 are expressed as \u03b11N0;\u03b211N0;\u03b212N0 \u03b12N0;\u03b221b0;\u03b222b0 : \u00f034\u00de It is obvious to notice that limb1s and limb2s are higher than the base OA1A2 and the platform E1F1E2F2 is higher than limb1ap and limb2p in state 7. Fig. 12 offers an observation of the derivative queer-square mechanism in state 8. The geometrical ranges of the revolute angles of the derivative queer-square mechanism in state 8 are illustrated as \u03b11N0;\u03b211b0;\u03b212b0 \u03b12b0;\u03b221b0;\u03b222b0 : \u00f035\u00de In state 8, limb1s is located in the higher position and limb2s is located in the lower positionwith respect to the baseOA1A2, and the platform E1F1E2F2 is located relatively lower than limb1ap and higher than limb2p"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000857_j.cma.2013.12.017-Figure14-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000857_j.cma.2013.12.017-Figure14-1.png",
        "caption": "Fig. 14. Finite element model for stress analysis.",
        "texts": [
            " Stress analysis has been carried out by the application of the finite element method, which allows determination of the evolution of contact and bending stresses along the cycle of meshing, investigation of the formation of the bearing contact, and detection of areas of severe contact stress (edge contact). The development of finite-element models of curvilinear cylindrical gears has been accomplished according to the ideas represented in [11]. Finite element models of five pairs of teeth have been used in order to keep boundary conditions far enough from the tooth loaded areas and to study the influence of the load sharing on the bearing contact on the pinion and wheel tooth surfaces. Fig. 14 shows the finite element model of the curvilinear gear set. The wheel actives tooth surfaces have been considered as master surfaces and the pinion actives tooth surfaces as slave surfaces. Three-dimensional solid elements type C3D8I [12] has been used. Elements C3D8I are hexahedral first order elements enhanced by incompatible deformation modes to improve their bending behavior. The total number of elements of the model is 128030 with 154260 nodes. The material is steel with the properties of Young\u2019s module E \u00bc 2:1 105MPa and Poisson\u2019s ratio 0:30"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003881_j.mechmachtheory.2020.104047-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003881_j.mechmachtheory.2020.104047-Figure3-1.png",
        "caption": "Fig. 3. The relative position between the ball center and groove curvature centers of raceways.",
        "texts": [
            " The details can be seen in Ref. [11] , and the half-sine displacement excitation function is given by: { h k = H sin ( \u03c0 \u03d5 2 \u2212\u03d5 1 ( mod ( \u03c6k , 2 \u03c0) \u2212 \u03d5 1 ) ) , \u03d5 1 \u2264 mod ( \u03c6k , 2 \u03c0) \u2264 \u03d5 2 h k = 0 , otherwise (5) where h k is the displacement excitation of the k th ball, \u03d51 and \u03d52 are respectively the central angle of the initial position and that of the final position in the defect area. Suppose that the outer raceway is fixed, and the inner raceway rotates round z -axis at a constant speed \u03c9 i . Fig. 3 shows the position change of ball center and raceway groove curvature centers before and after loading. In this figure, o o represents the groove curvature of outer raceway; o b and o i respectively represent the initial ball center and the initial groove curvature center of inner raceway, while o \u2032 b and o \u2032 i respectively represent the final ball center and the final groove curvature center of inner raceway. When the external load is equal to zero, the outer raceway curvature center, inner raceway curvature center and the ball center are in a straight line",
            " In such case, the contact angle of angular contact ball bearing is equal to the initial contact angle \u03b10 , and the distances between the raceway curvature centers and ball center are defined as: { d ib = r i \u2212 0 . 5 D \u2212 c i d ob = r o \u2212 0 . 5 D \u2212 c o (6) where r i denotes the groove curvature radius of inner raceway; r o denotes the groove curvature radius of outer raceway; c i is the clearance of inner ring; c o is the clearance of outer ring; D is diameter of the rolling element. When the external load is applied, the position of the inner raceway groove curvature center and ball center will change, as show in Fig. 3 . y b and z b denote the displacement of the rolling element along y b -axis and z b -axis direction respectively. According to the geometric relationship, the contact angles \u03b1ik and \u03b1ok between ball and raceways can be respectively written as { \u03b1ik = arctan ( d ib sin \u03b10 + z ib \u2212h k sin ( \u03b10 ) \u2212z b d ib cos \u03b10 + y ib \u2212h k cos ( \u03b10 ) \u2212y b ) \u03b1ok = arctan ( d ob sin \u03b10 + z b d ob cos \u03b10 + y b ) (7) Then the distances D ib and D ob between the rolling element and the raceway groove curvature centers are obtained as:{ D ib = ( d ib sin \u03b1o + z ib \u2212 h k sin ( \u03b10 ) \u2212 z b ) / sin \u03b1ik D ob = ( d ob sin \u03b1o + z b ) / sin \u03b1ok (8) Using Hertz theory, we are able to calculate the contact deformations and contact forces between ball and raceways as: { \u03b4ik = D ib \u2212 d ib \u2212 c i \u03b4ok = D ob \u2212 d ob \u2212 c o (9){ Q ik = \u03beik K ik \u03b4 3 / 2 ik Q ok = \u03beok K ok \u03b4 3 / 2 ok (10) where K ik and K ok are the load-deformation coefficients, and they can be simplified according to Refs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000705_s10846-013-9934-3-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000705_s10846-013-9934-3-Figure1-1.png",
        "caption": "Fig. 1 a simulated model of hex-rotor vehicle, b a prototype robot with 3-dof manipulator in development, c diagram of a typical multi-body aerial system, d an imaginary scenario where aerial agility could play a key role",
        "texts": [
            " The key point is the Lyapunov function V2 is positive definite while the proposed control law renders its time-derivative (51) negative definite. Note that the two assumptions are natural and do not impose practical limitations: 1.) when u = 0 the vehicle looses controllability and, as expected, the vehicle enters free-fall; 2.) the rotation RT d R has an angle exactly \u03c0 almost never since the set {\u03c0} is obviously measure-zero. Since the state is determined by an imperfect sensor and always has small variations, the ill-posedness of the retraction maps at \u03c0 is not an issue in practice. The hexrotor shown in Fig. 1 has three pairs of propellers fixed onto three spokes at 120\u25e6. A twolink manipulator with a low-cost gripper is suspended from the vehicle and can extend forward between the two forward-facing spokes. Such an arrangement enables the manipulator tip to extend beyond the vehicle perimeter which enables interesting reaching maneuvers. Ignoring the gripper motor, the manipulator has two degrees of freedom, i.e. r = (r1, r2). The forward kinematics are given by g01(r) = \u239b \u239c\u239c\u239c\u239c\u239c\u239d c1 0 s1 \u2212 l1 2 s1 0 1 0 0 \u2212s1 0 c1 \u2212 l1 2 c1 0 0 0 1 \u239e \u239f\u239f\u239f\u239f\u239f\u23a0 , (54) g02(r) = \u239b \u239c\u239c\u239c\u239c\u239c\u239d c12 0 s12 \u2212 l2 2 s12 \u2212 l1s1 0 1 0 0 \u2212s12 0 c12 \u2212 l2 2 c12 \u2212 l1c1 0 0 0 1 \u239e \u239f\u239f\u239f\u239f\u239f\u23a0 , (55) g0t(r) = \u239b \u239c\u239c\u239d c12 0 s12 \u2212l2s12 \u2212 l1s1 0 1 0 0 \u2212s12 0 c12 \u2212l2c12 \u2212 l1c1 0 0 0 1 \u239e \u239f\u239f\u23a0 , (56) using the shorthand notation ci := cos ri, si := sin ri for i = 1, 2 and c12 := cos(r1 + r2), s12 := sin(r1 + r2)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003809_j.addma.2020.101252-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003809_j.addma.2020.101252-Figure9-1.png",
        "caption": "Figure 9. \u03b1m phase fraction distribution at the cross-section along the middle of the L2 side at the end of the DED process taken from the FE simulation.",
        "texts": [
            " As shown in the figure, the \u03b1m and \u03b1B phase fractions are zero at the regions close to the heat source where the local temperature exceeds \ud835\udc47\u03b2 \ud835\udc61\ud835\udc5f\ud835\udc4e\ud835\udc5b\ud835\udc60, while \u03b2 phase fraction is approximately unity. On the other hand, away from the heat source, the fraction of alpha phases return to their equilibrium values. Jo ur na l P r -p ro of Figure 8. (a) Temperatures in \u00b0C, (b) \u03b1m, (c) \u03b1B, and (d) \u03b2 phase fraction evolutions during layer-by-layer deposition. The process starts from S1 side and ends with the deposition of the fifth layer on L2 side. Figure 9 presents the \u03b1m phase fraction distribution along a cross-section from the middle of the L2 side (refer to Figure 4) at the end of the DED process. Solid-state phase transformations also take place within the substrate during the deposition process, where the ellipsoidal high \u03b1m phase region inside the substrate is an indication of the heat-affected zone (HAZ). As shown in the figure, the \u03b1m content of the substrate starts to increase J ur na l P re -p ro of significantly from the lower bound of HAZ and reaches about 0",
            " It should be noted that the S1 and L2 represent the sides that show the most significant difference in thermal history when the laser processing stops with the deposition of the last layer of L2. At the S1 side, where the deposition process starts, the \ud835\udc4b\ud835\udefc\ud835\udc4a value is approximately 15% higher than that of the L2 Jo ur na l P side. Correspondingly, \ud835\udc4b\ud835\udefc\ud835\udc5a value is proportionally lower than that of L2 side. The reason behind this is that the L2 side, at which the deposition ends up, experiences higher cooling rates with the cease of laser heat input [45]. The trends for the change of \ud835\udc4b\ud835\udefc\ud835\udc5a with respect to the distance for both sides of the rectangle are similar to the trend discussed for Figure 9. The hardness of a single-phase material depends on several microstructural features such as grain size, \u03b1-colony/lamella size, dislocation density, etc. since different hardening mechanisms could be active [40]. For multiphase alloys like steel and Ti6Al4V, the volumetric fraction and distribution of each phase show different hardness values and thus are the dominant factors in determining the general trend in the spatial hardness distribution in the sample. Ideally, the highest hardness is achieved by the formation of a fully martensitic microstructure [44]",
            " On the other hand, abrupt variations in hardness cannot be predicted since several assumptions and idealizations have been made in the microstructure \u2013 process model. Namely, many physical events (i.e., laser/powder interactions, melt pool/laser interaction, solidification, etc.) are combined and the effects of the mechanical Jo ur na l P re -p ro of field are ignored, and thus local changes in thermal history and geometry are not fully captured. For instance, an ideal rectangular geometry with a constant cross-section and layer thickness is assumed in the FE model (see Figure 9); however, as shown in Figure 11, the sample cross-section, as well as layer thickness, varies significantly. Similarly, high hardness observed in the Ti6Al4V deposit near the substrate in the HAZ may be due to high cooling rates and other complex microstructural changes caused by the substrate, powder, laser and melt pool interactions, and cannot be fully captured by the proposed FEbased approach. Furthermore, the present microstructure model does not contain any information on stress-induced phase transformations, grain structure, imperfections, etc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000979_c2an36035g-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000979_c2an36035g-Figure6-1.png",
        "caption": "Fig. 6 Stern\u2013Volmer plot of P0/P vs.DA concentration under optimized experimental conditions, over a concentration range of 0\u2013100 mM.",
        "texts": [
            " As mentioned above, the PL spectra of the proposed CdTe QD\u2013Lac nanobiosensor displayed a gradual decrease in fluorescence at 537 nm with increasing DA concentration. Thus, in the next step, we established a calibration graph, under optimized experimental conditions, according to the well-known Stern\u2013Volmer equation: P0/P \u00bc 1 + KSV[Q], where P0 and P are the PL intensities of the QDs before and after adding analyte, respectively, and KSV is the Stern\u2013Volmer quenching constant. Accordingly, a plot of P0/P vs. [DA] gave a calibration curve in the range of 0.3 to 100 mM (Fig. 6) with a regression equation of P0/P \u00bc 0.82 + 1.94 105 [DA] and correlation coefficient (R2) of 0.9961. The limit of detection (LOD) of the method, calculated as 3Sb/m, was evaluated to be 0.16 mM. The good reproducibility of the system was also confirmed by obtaining a RSD (for n \u00bc 7) of 3.7% at a DA level of 6.0 mM. In Table 1 are compared the response characteristics of the proposed method with those of some different physico-chemical methods, including spectrophotometric detection using surface plasmon resonance band of silver nanoparticles,5 capillary electrophoresis with amperometry,6 QD-enhanced chemiluminescence detection,7 graphene oxide-based fluorescent biosensing,9 calcein blue\u2013Fe2+ complex based fluorescence,10 and electrochemical detection on modified electrodes such as carbon electrode-poly(dibromofluorescein)12 Au\u2013NiHCF\u2013poly(1-naphthol),13 DMS (disordered mesoporous silica)-(ensal)2Cu, 14 Au\u2013 mercaptopropionic acid\u2013Lac,15 and CILE\u2013Ni/Al based LDH"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002915_s11665-019-04435-y-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002915_s11665-019-04435-y-Figure2-1.png",
        "caption": "Fig. 2 Exemplary plot of powder bed generation with different sized particles",
        "texts": [
            " The particle motion has been solved using Newton s second law of motion. The powder size (diameter) distribution used was from experimental measurement of L-PBF powders. To simulate the creation of the powder bed, a moving blade was utilized to spread one layer of powder particles with a given layer thickness after a cloud of powder particles was freely dropped upon the powder container. The detailed DEM modeling process can be found in (Ref 13, 14). The geometrical information of the powder layer will then be used for the melt pool dynamics simulation. Figure 2 shows the exemplary plot of the generation of one layer of powder. Journal of Materials Engineering and Performance 2.2.1 Thermal and Fluid Flow Simulation Mathematical Model. A microscale multi-physics CFD finite volume method (FVM) model was applied using the commercial software FLOW3D to study the melt pool characteristics. The melted material was assumed to be incompressible, laminar and Newtonian. FLOW3D software numerically solved the conservation equations of mass, momentum and energy (Ref 13): Mass: r ~v \u00bc 0 \u00f0Eq 1\u00de Momentum: @~v @t \u00fe ~v r\u00f0 \u00de~v \u00bc 1 q rP\u00fe lr2~v\u00fe~g \u00fe Fb \u00f0Eq 2\u00de Energy: @h @t \u00fe ~v r\u00f0 \u00deh \u00bc 1 q r krT\u00f0 \u00de \u00fe _q \u00f0Eq 3\u00de where ~v is the molten fluid velocity, t is the time, P is the pressure, q is the material density, l is the fluid viscosity, ~g is the gravitational acceleration, Fb is the body force in the system, h is the enthalpy, k is the conductivity, and T is the temperature, _q is the external heat source"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000064_s00170-005-0318-0-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000064_s00170-005-0318-0-Figure3-1.png",
        "caption": "Fig. 3 Clad formation. a First stage: liquid clad, solid substrate. b Final stage: liquid clad and substrate",
        "texts": [
            "1 Step 1: estimation of liquid clad volume per unit length For estimation of the liquid clad volume per unit length, a number of assumptions were defined so as to simplify the problem. These assumptions include: (a) The substrate material is solid and the added powder is liquefied through the laser beam as it reaches the solid substrate. This assumption, though not realistic, does not spoil the validity of the proposed methodology since it is only used for estimation of the powder volume, that it is liquefied and for the wetting of the substrate. (b) The liquid clad forms a circular section explained by Young\u2019s law (Fig. 3a). (c) For all process speeds only a fraction \u03bb of the supplied powder contributes to the clad formation. This means that only this fraction of the powder reaches the melted substrate, although at this stage the substrate is considered solid. The remaining powder impinges out of the melt pool and is blown away by the gas flow. Applying the surface tension theory, the contact angle \u03b8 of a drop of liquid placed on the substrate (Fig. 3a) can be calculated, by using Young\u2019s equation, with [25]: cos \u03b8\u00f0 \u00de \u00bc \u03b3ss \u03b3ss;lc \u03b3lc (1) where \u03b8 is the contact angle, \u03b3ss is the surface tension (surface free energy) of the solid substrate, \u03b3lc is the surface tension of the liquid clad and \u03b3ss,lc is the interfacial tension between the coating and the solid substrate [25, 26]. Since \u03b3ss,lc values are typically lower, they can be neglected [27], and Eq. 1 becomes: \u03b8 \u00bc arccos \u03b3ss \u03b3lc (2) The volume per unit length (V/l) of the clad can be derived from Fig. 3a by the following equation: V=l\u00f0 \u00de \u00bc R2 \u03b8 sin \u03b8 cos \u03b8\u00f0 \u00de (3) The powder feed rate m : , contributing to the clad formation, is a function of the cladding material density \u03c1c, the process speed u and the clad volume per unit length (V/l) as shown in the following equation: m : \u00bc \u03bb m: f \u00bc \u03bb m t \u00bc \u03bb \u03c1c V t \u00bc \u03bb \u03c1c u V=l\u00f0 \u00de (4) where \u03bb is the fraction of the powder that contributes to the laser clad formation as pointed out in assumption (c) and m : f is the actual powder feed rate that the feeder provides to the process",
            " 3 and 4, the radius of the first stage cycle is provided as indicated in the following equation: R \u00bc m : \u03bb u \u03c1c \u03b8 sin \u03b8 cos \u03b8\u00f0 \u00de 1=2 (5) Wetting, which is expressed in terms of the contact angle \u03b8, plays a dominant role in the formation of the clad width w along with the amount of powder being supplied to the process per unit coating length. The liquid clad has wetted the substrate at a width (AB): AB\u00f0 \u00de \u00bc 2 R sin \u03b8 (6) 2.2 Step 2: estimation of laser clad geometry For the second stage of the model, it is considered that the substrate material starts melting, thus, the molten pool is formed along with a curvature due to the cladding material whilst the clad is created (Fig. 3b). A number of assumptions have been made for the modelling of this stage: (a) The energy supplied to the process exceeds the second threshold limit as suggested in [10], and consequently, all powder reaching the melted substrate is already liquefied. Hence, the clad formed is under a quasi- static loading as it sinks into the molten pool at minimal velocity. (b) The top and bottom part of the clad can be approximated by circular sectors in different diameters. (c) Dilution is negligible, as it is true in the case of laser cladding (less than 10%)",
            " (d) The surface tension of any liquid is a function of the temperature [28] and the rule of thumb is that as the temperature increases the surface tension decreases. As the powder feed rate is increased more energy is attenuated by the powder cloud and thus less energy reaches the substrate. Therefore, the temperature of the liquid clad is increased, whereas the temperature of the liquid substrate is reduced. Subsequently, the surface tension of the liquid clad \u03b3lc decreases and that of the liquid substrate \u03b3ls slightly increases. The coating material that has wetted the substrate at the first stage between points A and B (Fig. 3a) now sinks between these limits without advancing or receding as it is usually 3 to 4 times denser than the substrate\u2019s material. So, points A\u2032, B\u2032 (Fig. 3b) coincide with points A and B, respectively. Thereby, the clad width can be calculated as follows: w \u00bc A0B0\u00f0 \u00de \u00bc AB\u00f0 \u00de (7) Equations 5, 6 and 7 indicate that when the \u03b8 angle values are small, the liquid clad wets well the substrate\u2019s surface resulting in an increased clad width. That is, the liquid clad expands better on the substrate producing more oblong clad tracks. The opposite happens when the contact angle increases. Moreover, the width of the clad increases not only by attaining good wetting of the substrate but also by increasing the powder feed rate m : or by decreasing the process speed u, as more clad material is being supplied per unit length, as would be expected. The bottom part of the clad, which is the molten pool\u2019s curvature since dilution is negligible, is approximated by an arc of circle (Kb, Rb). From the geometry of Fig. 3b, we obtain the following relations: A0B0\u00f0 \u00de \u00bc 2Ru sin\u03c9 \u00bc 2Rb sin\u03c6 ) Rb \u00bc Ru sin\u03c9 sin\u03c6 (8) Also, by utilizing the fact that the liquid powder after wetting the substrate between points A, B will immerse between them, the following two relations can be extracted: A0B0\u00f0 \u00de \u00bc AB\u00f0 \u00de ) Ru \u00bc R sin \u03b8 sin\u03c9 (9) A0B0\u00f0 \u00de \u00bc AB\u00f0 \u00de ) Rb \u00bc R sin \u03b8 sin\u03c6 (10) The volume per unit length (V/l) of the clad in the second stage is derived from Fig. 3b and is given by equation: V=l\u00f0 \u00de \u00bc R2 u \u03c9 sin\u03c9 cos\u03c9\u00f0 \u00de \u00fe R2 b \u03c6 sin\u03c6 cos\u03c6\u00f0 \u00de (11) The volume per unit length of the clad in the first stage (Fig. 3a) equals the volume per unit length in the second stage (Fig. 3b). Hence, we can equate Eqs. 3 and 11 and combine them with Eqs. 9 and 10 and thus the following relationship can be derived: \u03b8 sin\u03b8 cos \u03b8\u00f0 \u00de sin \u03b8 sin\u03c9 2 \u03c9 sin\u03c9 cos\u03c9\u00f0 \u00de sin \u03b8 sin\u03c6 2 \u03c6 sin\u03c6 cos\u03c6\u00f0 \u00de \u00bc 0 (12) If a clad material, which is usually denser than the substrate\u2019s molten pool, is placed on the surface of the molten pool, what happens next depends greatly on its nature. If the clad material is soluble in the liquid substrate and reacts with it, the molecules at their interface are attracted",
            " The elastic membrane that the surface tension of the molten pool forms on its surface is made more resistant and elastic as the surface tension increases. At the specific moment that the surface tension of the substrate, along with the buoyancy force, balance the weight of the clad, the latter is under a quasi-static loading that is being preserved until the substrate solidifies again. At the equilibrium condition Eq. 13 applies. It should be noted that the quasi-static loading is per unit clad length (two-dimensional) and it only calculates forces acting on the normal to (A\u2019B\u2019) in Fig. 3b: Wc \u00bc A\u00fe Tpool (13) where Wc is the weight of the clad, Tpool is the surface tension force of the molten pool and A is the buoyancy force applied to the clad. By substituting the corresponding factors in Eq. 13 the following is obtained: \u03c1cgR 2 \u03b8 sin \u03b8 cos \u03b8\u00f0 \u00de \u00bc\u03c1sgr 2 \u03c6 sin\u03c6 cos\u03c6\u00f0 \u00de \u00fe 2\u03b3ls sin\u03c6 (14) Combining Eqs. 10 and 14, the following relationship is derived: \u03c1cgR 2 \u03b8 sin \u03b8 cos \u03b8\u00f0 \u00de \u03c1sgR 2 sin \u03b8 sin\u03c6 2 \u03c6 sin\u03c6 cos\u03c6\u00f0 \u00de 2\u03b3ls sin\u03c6 \u00bc 0 (15) where \u03c1s is the density of the substrate, \u03c1c is the density of the cladding material, g is the gravitational acceleration and \u03b3ls is the surface tension of the liquid substrate that is different from \u03b3ss in Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002763_j.apm.2019.07.008-Figure11-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002763_j.apm.2019.07.008-Figure11-1.png",
        "caption": "Fig. 11. Comparison of Riemann sum to the adaptive integration algorithm for a moving heat source with a constant velocity and direction for (a) selective laser melting of AlSi10Mg with a laser velocity of 1.5 m/s and (b) electron beam melting of IN718 with a beam velocity of 3 m/s.",
        "texts": [
            " 0 Next, the two integration approaches were compared for a moving heat source with a constant velocity as the thermal field approaches a quasi-static solution with reference to the heat source motion. This situation was computed for AlSi10Mg with a laser velocity of 1.5 m/s, a spot size of 80 \u03bcm, an absorbed power of 87.5 W, and no preheat, and for IN718 with a velocity of 3 m/s, spot size of 200 \u03bcm, absorbed power of 750 W, and 10 0 0 \u00b0C preheat. The corresponding nondimensional velocities are 1.69 and 100.84, respectively. The temperature field and melt pool isotherms are shown in Fig. 11 . Note the dramatic difference in the diffusiveness of the thermal field around the heat source caused by the change in thermal properties and preheat temperature. The resulting change in melt pool shape is significant, with AlSi10Mg exhibiting a short elliptical melt pool, while the melt pool for IN718 is narrow and elongated. For the standard Riemann sum technique, dramatic differences in the integration step size and integration step dilation factor were required. For the highly diffusive AlSi10Mg case, a small integration step was required ( t \u2032 0 = 10 \u22127 s ), but a larger dilation factor was found to be acceptable ( \u03bb= 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000911_tmech.2014.2311382-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000911_tmech.2014.2311382-Figure3-1.png",
        "caption": "Fig. 3. (a) Wave generator axes displacement. (b) Free body diagrams.",
        "texts": [
            " It will be shown that a high fidelity harmonic drive model able to capture the hysteresis loss is achieved by modeling the compliance of the wave generator in addition to the compliance of the flexspline. As explained about the harmonic drive mechanism in Section II, when the wave generator\u2019s rigid elliptical inner-race is rotated, the flexspline molds into the rotating elliptical shape but does not rotate with it. The axes of these two elliptical shapes (Wave generator inner-race and flexspline) are not always aligned, as depicted in Fig. 3. The reason behind this misalignment is the compliance of the wave generator, namely, the ball bearing [23]. This misalignment is dependent on the magnitude of the torque applied to the wave generator plug as well as the load torque. This compliance of the wave generator needs to be taken into account when modeling the harmonic drive compliance. In this section, a model of the compliance of the flexspline and the wave generator is derived first, and then the complete compliance model of the harmonic drive is given"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001314_j.rcim.2013.09.005-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001314_j.rcim.2013.09.005-Figure1-1.png",
        "caption": "Fig. 1. The three-DOF robot.",
        "texts": [
            " To this end, first note that, since M 1\u00f0x1\u00feqd\u00de and C\u00f0x1\u00feqd; x2\u00de are smooth [15,28] and \u03bao0, we have lim \u03b5-0 M 1\u00f0\u03b5r1x1\u00feqd\u00de\u00bd\u00f0C\u00f0\u03b5r1x1\u00feqd; \u03b5r2x2\u00de\u00feC\u00f0\u03b5r1x1\u00feqd; _qd\u00de\u00de\u03b5r2x2\u00feD\u03b5r2x2 \u03b5\u03ba\u00fe r2 \u00bc M 1\u00f0qd\u00de\u00f0C\u00f0qd; 0\u00de\u00feC\u00f0qd; _qd\u00de\u00feD\u00dex2lim \u03b5-0 \u03b5 \u03ba \u00bc 0: \u00f043\u00de Upon applying the mean value theorem to each entry of ~M\u00f0x1; qd\u00de, it follows that [15,28] ~M\u00f0\u03b5r1x1; qd\u00de \u00bcM 1\u00f0\u03b5r1x1\u00feqd\u00de M 1\u00f0qd\u00de \u00bc \u03bf\u00f0\u03b5r1 \u00de: \u00f044\u00de Thus, we have lim \u03b5-0 ~M\u00f0\u03b5r1x1; qd\u00de\u00bdKpSat\u00f0\u03b5r1x1\u00de\u03b11 \u00feKdSat\u00f0\u03b5r2x2\u00de\u03b12 \u03b5\u03ba\u00fe r2 \u00bc lim \u03b5-0 \u03bf\u00f0\u03b5r1 \u03ba r2 \u00de\u00bdKpSat\u00f0\u03b5r1x1\u00de\u03b11 \u00feKdSat\u00f0\u03b5r2x2\u00de\u03b12 \u00bc 0 \u00f045\u00de Note that in the derivations of (43) and (45) we have used the facts that \u03ba \u00bc 1 \u03b1140, r1 \u03ba r2 \u00bc 2\u00f01 \u03b11\u00de40 for 0o\u03b11o1. As a result, for any fixed x\u00bc \u00f0xT1 xT2\u00deT A\u211c2n, we get lim \u03b5-0 f\u0302 2\u00f0\u03b5r1x1; \u03b5r2x2\u00de \u03b5\u03ba\u00fe r2 \u00bc 0: \u00f046\u00de Therefore, according to Lemma 1, we have the local finite-time stability of the closed-loop system (33). Finally, by invoking Lemma 2, we get the semi-global finite-time stability of (33) (i.e. (23)). This completes the proof. Simulations on a three-DOF robot were conducted to illustrate the improved performance of the proposed SFT control. The used three-DOF robot is illustrated in Fig. 1. The robot dynamics are given in Appendix. The desired trajectories were selected as follows: qd\u00f0t\u00de \u00bc \u00f02 sin \u00f0t\u00de; cos \u00f0t\u00de;0:5 sin \u00f02t\u00de\u00deT \u00f0rad\u00de: \u00f048\u00de The actuator constraints were set as \u03c4max \u00bc \u00bd50;100;70 TNm. Inserting the system parameters and (48) into (2), (3), (6) and (12), respectively, we get the upper bounds required to determine the gains of the proposed controller M2 \u00bc 8:9; C2 \u00bc 3:5; dM \u00bc 0; \u03bag1 \u00bc 0; \u03bag2 \u00bc 40; \u03bag3 \u00bc 12:2; VM \u00bc 1:3949; AM \u00bc 2:2219: \u00f049\u00de With these bounds, Ti; M defined by (14) are determined as Tmax \u00bc \u00bd26;66;38 TNm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000648_978-3-642-17531-2-Figure6.22-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000648_978-3-642-17531-2-Figure6.22-1.png",
        "caption": "Fig. 6.22. Axisymmetric double-comb transducer with push-pull control: a) schematic diagram, b) electrically equivalent circuit",
        "texts": [
            " However, it is possible to combine the advantages of push-pull control with the advantages of a transverse comb transducer with a slight change to the structure. For push-pull operation, two transverse push-push comb transducers A, B are used and their two armatures are rigidly coupled. The electrodes of the two sub-transducers A, B are arranged to be geometrically axisymmetric so as to result in equally directed forces to achieve push-pull operation. Electrically, the two sub-transducers A, B are asymmetrically controlled for the push-pull arrangement (Horsley et al. 1998), (Horsley et al. 1999). Fig. 6.22 depicts such a configuration in the form of an axisymmetric double-comb transducer. 436 6 Functional Realization: Electrostatic Transducers Configuration equations For the axisymmetric double-comb transducer depicted in Fig. 6.22, the following configuration equations result ( 0 A ): transducer capacitance , , , , 1 1 ( ) 1 1 ( ) ( ) ( ) ( ), , , T A T B T T A T B C x N x x C x N x x C x C x C x (6.67) transducer force 2 , , , 2 2 2 , , , 2 2 , , , , , , 1 1 ( , ) 2 1 1 ( , ) 2 ( , , ) ( , ) ( , ) . , , el A T A T A el B T B T B el T A T B el A T A el B T B F x u N u x x F x u N u x x F x u u F x u F x u (6.68) Due to the axisymmetric geometric configuration, the stable rest position is found to be 0 R x , for 0 0U and 0 pull in U U , with pull-in vol- tage 3 3 32 1pull in k U "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001849_s00170-014-6708-4-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001849_s00170-014-6708-4-Figure3-1.png",
        "caption": "Fig. 3 Fabricated specimen and sectioning scheme to demonstrate grain size control where the red faces are the sections whosemicrostructure was analyzed",
        "texts": [
            " To obtain a part containing a grain size gradient, the time the specimen was heated prior to melting was doubled (from an 11-s heating cycle each layer to 22-s heating cycle each layer) at 20 to 40 mm, and the extra pre-heating time was removed at 40 mm for the rest of the build. Thus, under the rationale that increased temperature conditions for a longer time span produce coarse grains, the added heating time would help increase grain size, and when heating was removed, grain size would be reduced. After fabrication, the cylinders were cut using an IsoMet 400 Precision Saw (Buehler, Lake Bluff, IL) into three sections (Fig. 3), including a section from the bottom corresponding to a standard heating time of 11 s per layer (\u223c10 mm from the bottom), a middle section with an elevated heating time of 22 s per layer (\u223c30 mm from the bottom), and a top section that was exposed to the standard heating time (\u223c50 mm from the bottom). After cutting, the sectioned pieces were mounted with a KoldMount (CMP Industries, Inc., Albany, NY) specimen mounting resin. Samples were prepared for light optical microscopy through the use of metallographic grinding papers in a sequence of increasing grit value: 80 grit, 120 grit, 220 grit, 320 grit, 500 grit, 800 grit"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000200_1.3197187-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000200_1.3197187-Figure5-1.png",
        "caption": "Fig. 5. The forces on a soccer ball. The gravitational force points down, the drag force is opposite the ball\u2019s velocity, the lift force is perpendicular to the ball\u2019s velocity and in the plane formed by the velocity and the ball\u2019s weight, and the sideways force not shown is into the page.",
        "texts": [
            " If we want the derivative of a function f t at t0 and we know the value of f t at t0, t1, and t2, where t1= t0+ t and t2= t0+2 t for a step size t, then the Richardson extrapolation gives for the first derivative at t0 f t0 \u2212 3f t0 + 4f t1 \u2212 f t2 2 t , 4 where the error is of order t 2. The spin rate was determined by following a given point on the ball as the ball turned either a half turn for slow spins or a full turn for fast spins . We achieved initial spin rates in the range from no spin to about 180 rad/s more than 1700 rpm , though most tests were carried out for spin rates less than 125 rad/s. The forces on projectiles moving through air have been discussed in many articles33 and books.34 Figure 5 shows the various forces on the ball. We assume the soccer ball\u2019s trajectory to be close enough to the surface of the Earth so that the gravitational force on the ball, mg , is constant. The mass of the ball is m=0.424 kg. The air exerts a force on the soccer ball. The contribution to the air\u2019s force from buoyancy is small 0.07 N and is ignored. A scale used to determine weight will have that small force subtracted off anyway. The major contributions 1021John Eric Goff and Matt J. Carr\u00e9 license or copyright; see http://ajp"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002139_b978-0-08-100433-3.00004-x-Figure4.7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002139_b978-0-08-100433-3.00004-x-Figure4.7-1.png",
        "caption": "Figure 4.7 Standard spatial rotations, a1 and a2, used to define the rotation of a component\u2019s geometry in space [24].",
        "texts": [
            " The rationale for this observation is that heat transfer through the inclined specimen causes elevated temperatures at downward-facing (lower) surfaces, resulting in greater thermal distortion and particle adhesion. Surface damage to downward-facing surfaces can also occur where supporting structures are physically removed from the surface, although no supporting structures were used to generate the coupons used in this research. By accommodating these observations of surface roughness versus surface inclination and by rotating the intended component according to the spatial rotations shown in Fig. 4.7, the associated surface finish can be optimised for the specific design objectives. To achieve robust surface roughness outcomes in AM, it is critically important to apply a surface roughness objective that is appropriate for the intended functional and aesthetic objectives. In addition to the area-weighted average roughness, Ra_ave, that is reported in the literature, this section presents a series of novel surface roughness objectives that are of specific relevance to AM. Average roughness, Ra_ave, refers to the area-weighted average roughness of each facet within the component geometry (Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000236_j.mechmachtheory.2010.06.004-Figure14-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000236_j.mechmachtheory.2010.06.004-Figure14-1.png",
        "caption": "Fig. 14. a) Close-up of the stress concentration zone for the optimized gear with 34 teeth, the design parameters shown are \u03b1c=20\u00b0, \u03b1d=36\u00b0, \u03b7=1.8 and \u03bc=\u03bcmin. The stress is reduced with 41.2% as compared to the ISO profile. b) Close-up of the stress concentration zone for the optimized gear with 34 teeth, the design parameters shown are \u03b1c=34\u00b0, \u03b1d=20\u00b0, \u03b7=1.7 and \u03bc=0.09. The stress is reduced with 20.1% as compared to the ISO profile.",
        "texts": [
            " It is not the present paper's intent to comment on these matters but instead focus directly on the possible bending stress improvements. In Ref. [1] it was found that the size of the possible stress improvement depends on the number of teeth. The largest improvements were found when the number of teeth is low. To examine if this is also the case for an asymmetric gear and for a direct comparison with the results reported in Ref. [14] the next examples are with a gear with z=34. Optimization results are presented in Fig. 14. In Fig. 14a theoptimized result forfixed coast sidepressure angle\u03b1c=20\u00b0 shows that the designparameters are\u03b1c=20\u00b0,\u03b1d=36\u00b0, \u03b7=1.8 and \u03bc=\u03bcmin. Improvement in thebending stress as compared to the ISOprofile is 41.2%. In Fig. 14b the result forfixeddrive side pressure angle \u03b1c=20\u00b0 shows that the design parameters are \u03b1c=34\u00b0, \u03b1d=20\u00b0, \u03b7=1.7 and \u03bc=0.09. Improvement in the bending stress as compared to the ISO profile is 20.1%. In both examples the stress along the boundaries of the stress concentration is relatively constant indicating that an optimal or close to optimal result is obtainedwith this simple cutting tool parameterization. In Ref. [14] the reported improvement in the bending stress is 17% which can be compared directly with the 20"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001842_s00170-015-7647-4-Figure15-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001842_s00170-015-7647-4-Figure15-1.png",
        "caption": "Fig. 15 Mandrel with isolated coolant supply and cap, side from the billet",
        "texts": [
            " The turned specimen (#10) has compared to the samples with the additively manufactured surface (rough surface, not mechanically refinished, #9) little higher strength (+120 MPa) [5]. Since in the previously mentioned investigations, basically, a sufficient joining strength was proven, the concept of a hybrid extrusion die described in Sect. 3 was realized. The top of the mandrel with inner cooling channels (480 layers, each 30 \u03bcm) made of 1.2709 was additively manufactured on a die bridge conventionally fabricated from bulk material by machining (Fig. 14). Subsequently, the die was heat treated. Figure 15 shows the mandrel manufactured conventionally together with the cap (side from the billet) and the brass tube which is installed with an air gap in order to supply and to dissipate the coolant through the bridges. Through the isolating gap, also the thermocouples were guided through the die bridges up to the top of the mandrel. The previously described die was tested in experimental trials in combination with a conventionally fabricated die cap for the manufacturing of a squared hollow profile (18\u00d7 18\u00d71 mm)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002208_j.procir.2015.08.052-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002208_j.procir.2015.08.052-Figure1-1.png",
        "caption": "Fig. 1. Generic HPC Blisk for the case study [EMAG]",
        "texts": [
            " Technological analysis For the assessed technologies reachable material removal rates and cutting rates are presented in this section. The data are either based on literature reviews or results of own machining experiments. Subsequently, seven promising process chains are derived. 2.1. Blisk for the case study The generic nickel-based high pressure compressor (HPC) blisk geometry regarded in the case study was provided by EMAG ECM GmbH. The 72 blade blisk is manufactured from Inconel 718. As shown in Figure 1 the cross section is tolerated with 50 \u03bcm and the required surface roughness is Ra 0.4 \u03bcm. 2.2. Milling from solid Today, milling from solid of forged discs is the most common technology for the manufacture of blisks. The main reasons are a high flexibility, the availability of many affordable standard tools and the existence of a great knowledge base with most manufactures. Drawbacks of the technology lie in a high tool wear during roughing, long machining times during finishing and the dynamic excitation of the workpiece"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001923_icra.2017.7989452-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001923_icra.2017.7989452-Figure5-1.png",
        "caption": "Fig. 5. Aerodynamic force and moment",
        "texts": [
            " Fg \u2208 R 3 is gravity in inertial frame and Fg = [ 0 0 mg ]T , R \u2208 R 3\u00d73 is the rotation matrix from body frame to inertial frame, the hat map \u00b7\u0302 is defined such that x\u0302y = x \u00d7 y for any x, y \u2208 R 3. Here we neglect the motor gyroscopic effect and motor acceleration and deceleration terms as they are usually very small. As the transition flight takes place in longitudinal direction, we will focus on the longitudinal equations of motion in this paper. The aerodynamic force and moment in the longitudinal direction (as shown in Fig. 5) can be written as Faero = [\u2212 cos (\u03b1x) sin (\u03b1x) \u2212 sin (\u03b1x) \u2212 cos (\u03b1x) ] [ D L ] Maero = M (5) Where \u03b1x is the angle of attack. D and L are respectively drag and lift force represented in the stability frame [12]. M is pitch moment represented in body frame. They can be written as D = 1 2 \u03c1V 2SCD (\u03b1x) L = 1 2 \u03c1V 2SCL (\u03b1x) M = 1 2 \u03c1V 2SCm (\u03b1x) c\u0304 (6) where \u03c1 is the air density, S is the reference area, c\u0304 is the mean aerodynamic chord. The airspeed V and angle of attack \u03b1x are defined as V = \u2016u\u2016 \u03b1x = arctan ( uz ux ) (7) where u = [ ux uy uz ]T \u2208 R 3 is airspeed vector in body frame"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001474_j.engappai.2013.08.017-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001474_j.engappai.2013.08.017-Figure3-1.png",
        "caption": "Fig. 3. Coordinate conversion.",
        "texts": [
            " For UUV the horizontal plane motion control, the desired state of a reference vehicle is described as \u03b7d \u00bc \u00bd xd yd \u03c8d T qd \u00bc \u00bdud vd rd T \u00f06\u00de where qd \u00bc \u00bdud vd rd T is the desired velocity in the body-fixed frame, \u03b7d \u00bc \u00bd xd yd \u03c8d T is the desired state of UUV in the inertial frame, (xd; yd) is coordinate of desired path in global Cartesian workspace (the inertial frame), \u03c8d is the tangent degree of UUV taken counter-clockwise from the X-axis. The actual state of UUV is represented by \u03b7\u00bc \u00bd x y \u03c8 T , q\u00bc \u00bdu v r T . The detailed description can be seen in Fig. 3. The objective of the path tracking controllers is to make UUV follow the known path by controlling the forward and angular velocities. So, the error e\u00bc \u00bd ex ey e\u03c8 T between desired state and actual state converges to zero. Here e\u00bc \u03b7d \u03b7\u00bc \u00bd ex ey e\u03c8 T is the tracking error in the inertial frame. E\u00bc \u00bd e1 e2 e3 T \u00bc JT e\u00bc JT \u00bd ex ey e\u03c8 T \u00f07\u00de is the tracking error in the body-fixed frame, J \u00bc cos \u03c8 sin \u03c8 0 sin \u03c8 cos \u03c8 0 0 0 1 2 64 3 75: The virtual velocity controller based on the backstepping approach can be defined as: qc \u00bc uc vc rc 2 64 3 75\u00bc k\u00f0ex cos \u03c8\u00feey sin \u03c8\u00de\u00fe\u00f0ud cos e\u03c8 vd sin e\u03c8 \u00de k\u00f0 ex sin \u03c8\u00feey cos \u03c8\u00de\u00fe\u00f0ud sin e\u03c8 \u00fevd cos e\u03c8 \u00de rd\u00fek\u03c8e\u03c8 2 64 3 75 \u00f08\u00de here, uc; vc; rc is the virtual surge, sway and yaw motion speed of the tracking UUV that should generate ex cos \u03c8\u00feey sin \u03c8 and ex sin \u03c8\u00feey cos \u03c8 means the tracking error transformed from inertial frame to the body fixed frame, k; k\u03c8 are constant coefficients, qd \u00bc \u00bdud vd rd T is the desired velocity in the body-fixed frame, ud cos e\u03c8 vd sin e\u03c8 , ud sin e\u03c8 \u00fevd cos e\u03c8 represents the desired velocity frame transformed to the actual velocity frame seen in Fig. 3. In-depth analysis of Eq. (8), the virtual speed can be found directly related to the tracking errors. As mentioned in Section 1, this typical backstepping method will undoubtedly produce sharp speed jumps. In order to resolve the speed jump and control constraint problem, a bio-inspired model is added in the controller to design the virtual velocity. Bio-inspired neural dynamics model was first developed by Grossberg (1988). It can describe an on-line adaptive behavior of individuals. It was originally derived based on the membrane model proposed by Hodgkin and Huxley (1952) for a patch of membrane using electrical elements"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003618_s00170-020-05980-w-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003618_s00170-020-05980-w-Figure3-1.png",
        "caption": "Fig. 3 Microhardness measurement procedure. a Longitudinal (y-direction) 0.5-mm interval. b Longitudinal (y-direction) between 10 layers with 0.25- mm interval. c Transverse (x-direction)",
        "texts": [
            " However, a substantial increase in YS is found for the 2-h hold time. The elongation (%El) also follows the same path as YS. However, for 1-h heat treatment, the ductility decreases more than the 30-min heat treatment. The mechanism of this behavior of UTS, YS, and %El will be discussed later in this study. The measurement of microhardness of the Inconel 625 parts was carried out in three ways: microhardness along the (1) longitudinal (y-axis) direction, (2) longitudinal in a single layer, and (3) transverse (x-axis) direction. Figure 3 a\u2013c schematically describes how the microhardness is measured for all the cases. Figure 4 presents the result of the microhardness for longitudinal and transverse directions. The overall transverse and longitudinal microhardness do not show any significant trend; see Fig. 4a\u2013b). The microhardness seems to vary in a range (220\u2013 240 VHN approximately) without following any trend (increasing or decreasing). The anisotropic microstructure even after heat treatment found in previous studies can cause this behavior"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002235_1.g001439-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002235_1.g001439-Figure1-1.png",
        "caption": "Fig. 1 Quadrotor reference frames and positive rotations.",
        "texts": [
            " The linear velocities in the body-fixed frame are denoted by V u; v;w T in the x, y, and z directions, respectively. The body-fixed angular velocities are denoted as \u03c9 p; q; r T , where p t is the roll rate about the x axis, q t is the pitch rate about the y axis, and r t is the yaw rate about the z axis. If the pitch angle \u03b8 t \u2208 \u2212\u03c0\u22152; \u03c0\u22152 for all t, the Euler angle derivatives can be related to the body-fixed angular velocities by 2 4 _\u03d5 _\u03b8 _\u03c8 3 5 2 4 1 s\u03d5t\u03b8 c\u03d5t\u03b8 0 c\u03d5 \u2212s\u03d5 0 s\u03d5\u2215c\u03b8 c\u03d5\u2215c\u03b8 3 5\"p q r # (2) Figure 1, obtained from Footnote 1 and annotated,\u2021 presents the body (x, y, z) and inertial (N, E, D) frames, their corresponding positive rotations, and the positive rotor rotations \u03a9i. Using the Newton\u2013Euler method, the product of the mass and inertial acceleration equals the sum of the forces on the quadrotor, namely, the weight mg, total thrust T, and drag Fw, m \u03be mG RI bT Fw2 664 N E D 3 775 g 2 664 0 0 1 3 775 \u2212 T m RI b 2 664 0 0 1 3 775 \u2212 1 m 2 664 ks _N \u2212wN j _N \u2212wN j ks _E \u2212wE j _E \u2212 wEj ku _D \u2212wD j _D \u2212wDj 3 775 (3) where m is the quadrotor\u2019s mass, g is the gravitational acceleration, and T is the thrust in the \u2212z direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001164_j.triboint.2015.02.012-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001164_j.triboint.2015.02.012-Figure2-1.png",
        "caption": "Fig. 2. Location of the rolling element and curvature centers of the groove.",
        "texts": [
            " between the rolling element and the ring groove, \u03b10 denotes the initial contact angle between the rolling element and the ring groove, \u03b1 denotes the actual contact angle between the rolling element and the ring groove, Mg denotes the gyroscopic torque on the rolling element, and Fc denotes the centrifugal force. Subscript i indicates that the rolling element is related to the inner ring groove, subscript e indicates that the rolling element is related to the outer ring groove, and q shows the number of rolling elements. In Fig. 2, E and E' denote the initial and final positions, respectively, of the rolling element sphere center, m and m' denote the initial and final positions, respectively, of the inner ring groove curvature center, \u03c8 is the position angle of the rolling element along the circumference of the bearing ring, \u03b4a and \u03b4r denote the circumferential and radial displacements of the bearing inner ring, respectively, and n is the center of the outer ring groove curvature. The quasi-statics model of the properties of the angular contact ball bearing at high speed can be solved according to Figs",
            " (1) Equilibrium equation of the rolling element Qiq sin \u03b1iq Qeq sin \u03b1eq Mgq Dw \u00f0\u03bbiq cos \u03b1iq \u03bbeq cos \u03b1eq\u00de \u00bc 0 \u00f01\u00de and Qiq cos \u03b1iq Qeq cos \u03b1eq Mgq Dw \u00f0\u03bbiq sin \u03b1iq \u03bbeq sin \u03b1eq\u00de\u00feFeq \u00bc 0 \u00f02\u00de where \u03bb is the control parameter of the groove and Dw is the diameter of the rolling element. (2) Geometric equation \u03b4iq \u00bc \u00f0V2 xq\u00feV2 zq\u00de1=2 \u00f0f i 0:5\u00deDw \u00f03\u00de and \u03b4eq \u00bc \u00bd\u00f0Axq Vzq\u00de2\u00fe\u00f0Azq Vzq\u00de2 1=2 \u00f0f e 0:5\u00deDw \u00f04\u00de where \u03b4 is the contact deformation between the rolling element and the inner and outer rings, and f is the radius coefficient of the ring groove curvature. The geometric quantities Vxq, Vzq, Axq, and Azq are shown in Fig. 2. (3) Equilibrium equation of the ring The equilibrium equations of axial force, radial force, and external torque on the inner ring can be derived as follows according to the force balance on the rolling element: Fa Xz q \u00bc 1 Qiq sin \u03b1iq Mgq Dw \u03bbiq cos \u03b1iq \u00bc 0 \u00f05\u00de and Fr Xz q \u00bc 1 Qiq cos \u03b1iq\u00fe Mgq Dw \u03bbiq sin \u03b1iq cos \u03b1iq \u00bc 0 \u00f06\u00de where Fa and Fr are the axial and radial loads on the bearing, respectively. (4) Contact load equation Qiq \u00bc kiq\u03b4 1:5 iq \u00f07\u00de and Qeq \u00bc keq\u03b4 1:5 eq \u00f08\u00de where k is the contact stiffness between the steel ball and the groove"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001565_j.mechmachtheory.2014.12.019-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001565_j.mechmachtheory.2014.12.019-Figure4-1.png",
        "caption": "Fig. 4. Roll contact model between the balls.",
        "texts": [
            " (12a)\u2013(12c), the vertical creep ratio (\u03beeB), horizontal creep ratio (\u03befB) and spin ratio (\u03c6B) can be written as: \u03beeB \u00bc VbSe\u2212VSe VrB \u00bc 2 \u03c9rm\u2212 rb\u2212\u03b4S\u00f0 \u00de \u03c9R cos\u03b2 cos\u03b20 cos\u03b2B \u00fe\u03c9R sin\u03b2 sin\u03b2B \u00fe\u03c9 cos\u03b2B \u03c9rm \u00fe rb\u2212\u03b4S\u00f0 \u00de \u03c9R cos\u03b2 cos\u03b20 cos\u03b2B \u00fe\u03c9R sin\u03b2 sin\u03b2B\u2212\u03c9 cos\u03b2B\u00f0 \u00de \u00f014a\u00de \u03be f B \u00bc VbS f\u2212VSf VrB \u00bc 2 \u2212 rb\u2212\u03b4S\u00f0 \u00de\u03c9R cos\u03b2 sin\u03b20 \u03c9rm \u00fe rb\u2212\u03b4S\u00f0 \u00de \u03c9R cos\u03b2 cos\u03b20 cos\u03b2B \u00fe\u03c9R sin\u03b2 sin\u03b2B\u2212\u03c9 cos\u03b2B\u00f0 \u00de \u00f014b\u00de \u03c6B \u00bc \u03c9bSg\u2212\u03c9Sg VrB \u00bc 2 \u03c9R cos\u03b2 cos\u03b20 sin\u03b2B\u2212\u03c9R sin\u03b2 cos\u03b2B \u00fe\u03c9 sin\u03b2B \u03c9rm \u00fe rb\u2212\u03b4S\u00f0 \u00de \u03c9R cos\u03b2 cos\u03b20 cos\u03b2B \u00fe\u03c9R sin\u03b2 sin\u03b2B\u2212\u03c9 cos\u03b2B\u00f0 \u00de : \u00f014c\u00de Considering the differential slipping caused by surface warpage of screw raceway, the components of slipping velocity in the eBand fB-directions [12] can be stated as: CeB \u00bc \u03beeB\u2212 f B\u03c6B\u2212\u03beh f B\u00f0 \u00de \u00f015a\u00de C fB \u00bc \u03be f B \u00fe eB\u03c6B: \u00f015b\u00de \u03beh(fB) is the slipping item of Heathcote, which can be obtained as: \u03beh f B\u00f0 \u00de \u00bc 1\u00fe \u03c9 cos\u03b2B \u03c9R cos\u03b2 cos\u03b20 cos\u03b2B \u00fe\u03c9R sin\u03b2 sin\u03b2B f B 2 2rb 2 : \u00f016\u00de The roll contact model between balls is shown in Fig. 4. The contact coordinate system between the balls (em, fm, gm) is fixed at the contact point. The tangential direction at the contact point and fm axis form a space angle (\u03b1). The angle between the line o1 0m (or o2 0m) and t1-axis(or t2-axis) is also \u03b1 which has the same value of helix angle. As shown in Fig. 4, the three axial components of the spin angular velocity of the ball 1 (\u03c9R1) in the em- , fm- , and gm-directions can be stated as: Vme1 \u00bc rb\u2212\u03b4m\u00f0 \u00de \u03c9n1 cos\u03b1 \u00fe\u03c9b1 sin\u03b1\u00f0 \u00de \u00f017a\u00de Vmf1 \u00bc \u03c9t1 rb\u2212\u03b4m\u00f0 \u00de \u00f017b\u00de \u03c9mg1 \u00bc \u03c9b1 cos\u03b1\u2212\u03c9n1 sin\u03b1: \u00f017c\u00de \u03b4m is the normal elastic deformation between the balls, which can be calculated based on Hertz contact theory. In the sameway, three axial components of the ball's spin angular velocity (\u03c9R) in the em- , fm- , and gm-directions can be expressed as: Vme2 \u00bc \u2212 rb\u2212\u03b4m\u00f0 \u00de \u03c9n2 cos\u03b1 \u00fe\u03c9b2 sin\u03b1\u00f0 \u00de \u00f018a\u00de Vmf2 \u00bc \u2212\u03c9t2 rb\u2212\u03b4m\u00f0 \u00de \u00f018b\u00de \u03c9mg2 \u00bc \u03c9n2 sin\u03b1\u2212\u03c9b2 cos\u03b1 \u00f018c\u00de where \u03c9R1 and \u03c9R2 can be obtained based on \u03c9R using homogeneous coordinate transformations (Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000749_tmag.2011.2169805-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000749_tmag.2011.2169805-Figure2-1.png",
        "caption": "Fig. 2. Cross-section of three-phase 12/8-pole DSEG and three-phase 6/8-pole DSEG. (a) 12/8-pole DSEG; (b) 6/8-pole DSEG.",
        "texts": [
            " And, the area of the stator slot where both armature windings and excitation windings are placed can be calculated from the following formula: (6) Similarly, the two different stator slot area of the 3N/4N-pole DSEG are respectively given by (7) (8) From (5)\u2013(8), it can be seen that the stator slot area of the 3N/4N-pole DSEG is almost three times as large as that of the conventional one. So, the excitation winding turns can be multiplied so that the electrical MMF is enough. The armature winding turns per pole can be similarly increased. The slot leakage flux is effectively weakened because of the distance increase of the adjacent stator poles. Fig. 2 shows the typical structure of a 6N/4N-pole DSEG and a 3N/4N-pole DSEG, respectively. A. 2-D FEA The magnetic field distribution and steady-state performance of the machine are analyzed by using 2-D FEM. In the 24/32-pole DSEG, the stator pole-width is no longer equal to the stator slot-width, which is different from the conventional DSEG. Table I gives key parameters of the generator. . Fig. 3 shows the electromagnetic field distribution of the DSEG with different rotor positions when the excitation current is 8 A"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000857_j.cma.2013.12.017-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000857_j.cma.2013.12.017-Figure3-1.png",
        "caption": "Fig. 3. Description of generating mechanism of curvilinear cylindrical gears.",
        "texts": [
            " In this case, the generation processes of concave and convex gear tooth surfaces become independent, the radii of the cutters can be optimized according of the sought-for type of contact, and in this way, generated curvilinear gears might be in line or localized point contact. The main drawback for this type of generation is that manufacturing time will be increased. Fig. 2 shows a scheme of the cross section of a fixed-setting cutter provided with outer cutting blades for generation of the concave side of the gear tooth surfaces (Fig. 2(a)) fixed-setting cutter provided with inner cutting blades for generation of the convex side of the gear tooth surfaces (Fig. 2(b)). Fig. 3 shows the generating process for curvilinear gears no matter whether fixed-setting or spread-blade face-milling cutters are considered. During the generation process, the face-milling cutter is translated with lineal velocity vc perpendicular to the rotation axis of the gear blank whereas the gear blank is rotated with angular velocity xgb. The face-milling cutter pitch plane remains tangent to gear pitch cylinder. Finally, the gear tooth surfaces are generated as the envelope to the family of positions of the face-milling cutter blades in his rolling without sliding relative movement over the gear pitch cylinder"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003199_j.mechmachtheory.2019.103576-Figure17-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003199_j.mechmachtheory.2019.103576-Figure17-1.png",
        "caption": "Fig. 17. Face-gear crowning due to different number of teeth pinion/shaper, variants of Table 3 , N 1 = 14 , N s = 16 : (left) shift between pinion and shaper; (right) resulting crowning of face-gear tooth; (a) a (c) = 0 mm , \u03b1w = 20 \u25e6; (b) a (c) = 0 . 297 mm , \u03b1w = 30 \u25e6; (c) a (c) = 0 . 793 mm , \u03b1w = 40 \u25e6 .",
        "texts": [
            " The resulting crowning of the face-gear leads to minimum backlash between pinion and usable face-gear flank at the location where the working transverse pressure angle is identical to the applied normal pressure angle of the pinion/shaper. This location is typically quite close to the inner diameter and can be influenced by a further shift a ( c ) of the shaper relative to the pinion; hence, both pitch circles will not touch any further. The relative shift of the shaper to the face-gear and the resulting effect on the face-gear geometry is illustrated in Fig. 17 . Moving the shaper more away from the face-gear leads to a movement of the position of minimum backlash to the outside of the face-gear. This movement also leads to smaller distances between the face-gear teeth; hence, the overall clearance of a pinion tooth between the face-gear teeth is reduced. If the clearance becomes smaller than zero, clamping of the pinion occurs. Moving the shaper towards the face-gear in the direction of face-gear rotation axis moves the position of minimum backlash towards a smaller diameter and the clearance increases",
            " a d = r s \u2212 r 1 = (N s \u2212 N 1 ) m n 2 cos \u03b2 (51) According to the standard DIN 3960 [22] the centre distance a for a given working transverse pressure angle \u03b1w is calculated by a = a d cos \u03b1s cos \u03b1w (52) The resulting shift is calculated by a (c) = a \u2212 a d = m n (N s \u2212 N 1 )( cos \u03b1s \u2212 cos \u03b1w ) 2 cos \u03b2 cos \u03b1w (53) The corresponding shaper profile shift coefficient for the crowned geometry is given by x (c) s = x s + (N s \u2212 N 1 )(in v \u03b1w \u2212 in v \u03b1s ) 2 tan \u03b1n (54) According to Ripphausen [25] , the relationship between working transverse pressure angle \u03b1w and the face-gear radius R 2 for a drive with a shaft angle of \u03b3 = 90 \u25e6 and no axle offset is given by cos \u03b1w = N 2 m n cos \u03b1s 2 R 2 cos \u03b2 (55) In case of axle offset, the helix angle \u03b2 must be replaced by the modified helix angle \u03b2\u2217 \u03b2\u2217 = \u03b2 \u2212 asin ( E R 2 ) (56) From this, the working transverse pressure angle can be estimated for the general case by cos \u03b1w = N 2 m n cos \u03b1\u2217 s 2 R 2 cos \u03b2\u2217 with \u03b1\u2217 s = atan ( tan \u03b1n cos\u03b2\u2217 ) (57) where the representative face-gear radius R 2 for an arbitrary shaft angle can be approximated by R 2 = l 2 sin \u03b3 \u2212 r s cos \u03b3 (58) The relationship between R and l is illustrated in Fig. 16 . 2 2 The influence of a different number of teeth between pinion and shaper, the shift a ( c ) and modification of profile shift is illustrated in Fig. 17 . The design parameters are listed in Table 3 . The diagram of Fig. 18 shows the resulting crowning distribution. In the given examples, the difference of the number of teeth between pinion and shaper has been set to two (N s \u2212 N 1 = 2) . Variation of a ( c ) shifts the position of minimum backlash while the profile shift coefficient needs to be adapted to keep the overall clearance of the pinion tooth between the face-gear teeth constant. Although the position of minimum crowning can be adjusted easily, the amount of crowning and the distribution gener- ally can not be freely influenced"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000815_j.rcim.2010.07.001-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000815_j.rcim.2010.07.001-Figure1-1.png",
        "caption": "Fig. 1. Inverse kinematic model of 4-RRR and 3-RRR manipul",
        "texts": [
            " [4] the 4-RRR and 3-RRR manipulators should be symmetric. Thus, the base platforms and moving platforms of the two mechanisms are square or equilateral triangle. The 2-RRR mechanism discussed in this paper is constructed by removing two legs of the 4-RRR mechanism and adding an actuator to the second joint of one residual leg. In order to reduce the inertia of the mobile body, the actuator is fixed on the base and then the second joint is driven by transmission belt. 2.1. Kinematics of 4-RRR manipulator The base coordinate system O XY shown in Fig. 1 is fixed on joint point A1, and a moving coordinate system ON XNYN is attached on the center of the moving platform. Let a and h denote the width of the base platform and the moving platform, the position vector of point Bi in the base coordinate system can be expressed as rBi \u00bc rAi \u00fe l1 cosyi sinyi \" # , i\u00bc 1,2,3,4 \u00f01\u00de where rAi and rBi are the position vectors of joint points Ai and Bi, and l1 and yi are the length and rotation angle of link AiBi, respectively. The position vector of Ci can be written as rCi \u00bc rON \u00feRUrN Ci \u00bc rBi \u00fe l2 cosbi sinbi \" # \u00f02\u00de where rON is the position vector of ON in O XY, rN Ci is the position vector of Ci in ON XNYN, R is the rotation matrix from coordinate system ON XNYN to O XY and R\u00bc cosa sina sina cosa , a is the rotation angle of the moving platform, and bi is the rotation angle of link BiCi",
            " (4), the inverse kinematic solution for the 4-RRR mechanism can be expressed as yi \u00bc 2tan 1 e1i7 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi e2 1i\u00fee2 2i e2 3i q e3i e2i , i\u00bc 1,2,3,4 \u00f05\u00de where e11 \u00bc 2l1 y hsina 2 hcosa 2 , e21 \u00bc 2l1 x\u00fe hsina 2 hcosa 2 e31 \u00bc x\u00fe hsina 2 hcosa 2 2 \u00fe y hsina 2 hcosa 2 2 \u00fe l21 l22 e12 \u00bc 2l1 y\u00fe hsina 2 hcosa 2 , e22 \u00bc 2l1 x\u00fe hsina 2 \u00fe hcosa 2 a e32 \u00bc x\u00fe hsina 2 \u00fe hcosa 2 a 2 \u00fe y\u00fe hsina 2 hcosa 2 2 \u00fe l21 l22 e13 \u00bc 2l1 y\u00fe hsina 2 \u00fe hcosa 2 a , e23 \u00bc 2l1 x hsina 2 \u00fe hcosa 2 a e33 \u00bc x hsina 2 \u00fe hcosa 2 a 2 \u00fe y\u00fe hsina 2 \u00fe hcosa 2 a 2 \u00fe l21 l22 e14 \u00bc 2l1 y hsina 2 \u00fe hcosa 2 a , e24 \u00bc 2l1 x hsina 2 hcosa 2 e34 \u00bc x hsina 2 hcosa 2 2 \u00fe y hsina 2 \u00fe hcosa 2 a 2 \u00fe l21 l22 2.2. Inverse kinematics of 3-RRR manipulator The kinematic model of the 3-RRR manipulator is shown in Fig. 1(b). The widths of the base platform and moving platform of the 3-RRR manipulator are the same as those of the 4-RRR manipulator. In the same way, the inverse kinematic solution for the 3-RRR mechanism can be written as yi \u00bc 2tan 1 E1i7 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E2 1i\u00feE2 2i E2 3i q E3i E2i , i\u00bc 1,2,3 \u00f06\u00de where E11 \u00bc 2l1 y hsina 2 ffiffi 3 p hcosa 6 , E21 \u00bc 2l1 x hcosa 2 \u00fe ffiffi 3 p hsina 6 E31 \u00bc x hcosa 2 \u00fe ffiffiffi 3 p hsina 6 !2 \u00fe y hsina 2 ffiffiffi 3 p hcosa 6 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001496_tcst.2015.2454445-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001496_tcst.2015.2454445-Figure2-1.png",
        "caption": "Fig. 2. Quadrotor operating modes. (a) FF. (b) Takeoff-and-landing and takeoff-and-landing sliding (TL/TLs). (c) Landed and landed sliding (LL/LLs).",
        "texts": [
            " For the development of the quadrotor hybrid automaton, we consider five operating modes, corresponding each mode to the different dynamics that the vehicle is subject to. The modes are distinguished by the number of contact points of the landing gear with the ground and the existence of relative movement between the contact point and the ground. The operating modes are defined as follows. 1) FF: In this operating mode, the quadrotor is in FF and no contact with the landing slope occurs. 2) Takeoff and Landing (TL and TLs): In a takeoff-andlanding situation, there exists a single contact point between the quadrotor and the ground, shown as A in Fig. 2(b). The shorthand notation TL denotes the nonsliding situation and TLs the takeoff-and-landing mode where sliding exists between the quadrotor and the ground. In this paper, we focus on landings where point A hits the ground first and acts as pivot, since it leads to more natural landing maneuvers. Landing situations where B is the first point of impact with the landings slope are dealt analogously within the proposed framework as they correspond to considering a landing with point A as pivot where the slope angle \u03b2 is negative. 3) Landed (LL and LLs): In the landed operating mode, the landing gear is in full contact with the ground, with both points A and B touching the landing slope, as observed in Fig. 2(c). The shorthand notation LL denotes the nonsliding situation and LLs the landing operative mode where the quadrotor slides on the ground. The quadrotor presents different dynamics in each operating mode. These were derived in [25] and are presented in the discussion of the hybrid automata model for completion. In determining the discrete jumps between operating states during the landing maneuver, we assume that the collisions are inelastic. A description of the overall quadrotor dynamics is obtained by means of a hybrid automaton whose states correspond to the operating modes described above",
            " Disturbances in the angle dynamics fit within the proposed model but are not considered because they are, in general, negligible. To support the use of a simplified dynamical model, such as the one described above, the FF controller is designed to be robust to external disturbances, which can encompass wind disturbances and modeling uncertainties, up to a given limit. b) Partial interaction with the ground: In the TL and TLs modes of operation, there is only one contact point of the quadrotor with the ground, as evidenced in Fig. 2(b). The vehicle\u2019s motion is restricted to a rotation around the contact point A and translation of the contact point along the slope. The friction coefficient \u03bc between the landing gear and the glide slope materials influences these dynamics, and we assume that the static and dynamic coefficients are equal. In general, only a rough estimate of the friction coefficient is known and, as such, the controller are nominally designed for \u03bc = \u03bc0 but are \u03b5-robust for a range of \u03bc values. The slope is assumed to be sufficiently smooth and cleared of obstacles so that the quadrotor is able to slide without getting stuck"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002447_tie.2018.2878131-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002447_tie.2018.2878131-Figure7-1.png",
        "caption": "Fig. 7. Magnetic flux line and magnetic flux density of the DWPMM with phase-A short-circuit fault. (a) Magnetic flux line of the DWPMM. (b) Magnetic flux density of the DWPMM.",
        "texts": [
            " Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. capacitance. In order to avoid the over-voltage problem, it need adopt the four-quadrant fault-tolerant operation control strategy. Motor phase winding\u2019s terminal short-circuit fault is a common fault in electric drive system for aerospace applications [9]-[11], [23]. So, this paper will mainly investigate the terminal short-circuit fault of the DWPMM phase winding. Fig.7 (a) shows the magnetic flux line of the DWPMM with phase-A short-circuit fault. It can be observed from Fig.7 (a) that each phase winding has almost no the coupling of the magnetic flux line, and the phase-A shortcircuit winding has nearly no magnetic flux line. The DWPMM has good magnetic isolation ability. The magnetic flux density of the DWPMM with phase-A short-circuit fault is shown in Fig.7 (b). The maximum magnetic flux density of the stator teeth and yoke is 1.7 T and it will not outstrip the saturation value of silicon steel sheet. When the phase-A winding happens short-circuit fault, the phase-A voltage vector will become zero. However, the voltage vector of phase-B and the phase-C are not equal to zero. The three phase voltages of ABC windings are asymmetric and it is the asymmetric short-circuit failure. According to the symmetrical component method, the system will appear negative-sequence current and produce a opposing rotating magnetic field, which maybe burn out the DWPMM [9]-[13]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000648_978-3-642-17531-2-Figure8.30-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000648_978-3-642-17531-2-Figure8.30-1.png",
        "caption": "Fig. 8.30. Schematic configuration for a generic translational electrodynamic (ED) transducer with one mechanical degree of freedom (armature moves in one dimension, rigidly connected to a moving rectangular coil in a homogeneous, stationary magnetic field: electrodynamic\u2014LORENTZ\u2014force generation); dashed lines indicate the external loading with voltage/current source and elastic suspension",
        "texts": [
            " Mechanical damping The damping achievable with simple electrical means is naturally insufficient for practical operation of the stepper motor. As a comparison, in Fig. 8.29, Curve 2 traces the transient behavior with an additional viscous damping of 310 Nmsb . Only here is a useful dynamic stepping behavior achieved. 558 8 Functional Realization: Electromagnetically-Acting Transducers Coil moving in a magnetic field Electrodynamic (ED) transducers exploit the LORENTZ force introduced in Eq. (8.22), i.e. the force on an electrical conductor in a magnetic field. Fig. 8.30 shows a schematic implementation where the conductor takes the form of a coil rigidly coupled to an elastically-suspended load mass m (here with one mechanical degree of freedom, i.e. one-dimensional translation). It is characteristic of an electrodynamic (ED) transducer to have a (generally constant) magnetic field 0 B acting on the coil, which is induced either electrically or with a permanent magnet. 8.4 Generic ED Transducer: Lorentz Force 559 Electrodynamic constitutive basic equations The fundamental physical quantity in electromagnetic transduction is the flux linkage of the reference configuration depicted in Fig. 8.30. According to Eq. (8.17), the flux linkage has two components16 ( , ) ( ) ( ) T T ed T x i x i F . (8.96) The first component ( ) ed x describes the magnetic flux linked to the coil via the externally induced magnetic field 0 B . It is obvious that this flux depends on the relative geometry between the coil and magnetic field. This variable geometry is parameterized here with the variable location x of the upper coil edge. The second component, ( )i F , describes the magnetic flux generated in the magnetic circuit of the coil by the magnetomotive force T NiF fol- lowing Eq. (8.18). This coil-induced magnetic field practically only propagates outside the iron core, and is thus largely independent of coil position, as Eqs. (8.13) and (8.20) give a coil inductance 22 0 . C m N AN L const R . For an electrically linear magnetic circuit and the reference configuration shown in Fig. 8.30, Eq. (8.96) gives the basic electrodynamic constitutive equation in Q-coordinates ( , ) T T ED C T x i K x L i , (8.97) with coil inductance C L and ED force constant defined by 0 : ED K N B b [N/A] , (8.98) where N is the turns count of the coil, 0 B is the magnetic flux density of the externally induced magnetic field, and b is the width of the assumed homogeneous magnetic flux field. The electrodynamic constitutive basic equation in PSI-coordinates equivalent to Eq. (8.97) is obtained via a simple rearranging of terms 1 ( , ) ED T T T C C K i x x L L ",
            "102) with imposed coil current T i represents precisely the LORENTZ force from Eq. (8.22) acting on the current-carrying upper coil wires , 0 ( ) ed Q T T F i Nb i B . (8.104) The applicable length of conductor in the magnetic field is l N b and the force direction follows the cross product in Eq. (8.22). The LORENTZ force has two notable properties differing from the reluctance force discussed in previous sections: , ( ) ed Q T F i is independent of the coil displacement x , and is linearly dependent on the coil current T i . The configuration in Fig. 8.30 thus permits feedback-free, linear, bipolar force generation at the mechanically attached armature. Cancellation of LORENTZ force components The fact that only a vertical electrodynamic force ed F results for the coil configuration in Fig. 8.30 can be easily illustrated with the representation depicted in Fig. 8.31. Naturally, LORENTZ forces ,1 ,3 , ed ed F F also act on the vertical wire sections. However, due to the antiparallel current direction, these forces cancel each other out, so that only the force ,2ed F acting on the upper wire contributes to the electrodynamic force on the coil. Energy storage vs. energy transformation The electrodynamic transducer has one interesting and not readily apparent property with respect to energy storage",
            " maximum torque independ- ent of displacement (and constant transducer parameters with 0 R in Eq. (8.119)). Furthermore, the significantly smaller air gap as compared to Fig. 8.34a results in a noticeably greater flux density 0 B , enabling higher torque for the same electrical and magnetic parameters. Electrodynamic voice coil transducer Translational transducers, configuration One of the most widely distributed electrodynamic transducer types is the voice coil transducer. Fig. 8.35 shows a schematic configuration with vertical motion. Compared to the reference configuration in Fig. 8.30, the voice coil configuration makes much better use of space. The cylindrical magnetic field ensures maximum flux linkage with the coil. The minimum air gap is limited only by the winding wire width and the need for a small amount of clearance. This results in a high magnetic air gap flux density 0 B and thus a large ED force constant 0 0 0 2 ED B K N B r , (8.120) where 0BN represents the number of coil windings linked to the magnetic flux of the pole shoes. The transducer model is given precisely by Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003440_s11071-019-05056-9-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003440_s11071-019-05056-9-Figure4-1.png",
        "caption": "Fig. 4 Gear-bearing models established by different kinds of methods. The changing contact conditions between bearing rollers and races, as well as that between gear tooth, are modeled by the FE/CM method. a FE/CM model with full contact bearing; b FE/CM model with stiffness matrix bearing; c analytical model in which the bearing stiffness is modeled as either constant or time-varying",
        "texts": [
            " 3 Time-varying bearing stiffness under different external loads Fr in the radial direction calculated by FE/CMmodel. The curves with marks of circle and square correspond to Fr = 9500 N and Fr = 33,500 N, respectively. The regions A, B, C, and D represent conditions with different numbers of rollers in contact. A: four bearing rollers in contact; B: three rollers in contact; C: two rollers in contact; D: three rollers in contact system contains a sun gear (Gear 1) that has only rotational vibration and a bearing-supported pinion gear (Gear 2) that is able to move translationally and rotate, as shown in Fig. 4. The inner surfaces of both gears, i.e., the innermost surfaces of the gears in Fig. 4b, are assumed as rigid. Gear 2 is supported by a cylindrical roller bearing whose outer race is attached to the inner surface of the gear rim. The inner surface of Gear 1 is assumed as rigid and stays circular. The FE/CMmodel and an analytical model are used to analyze the gear-bearing system. Some previous gear dynamics research has compared the results of FE/CMand analyticalmodels andobtainedgood agreement [15,36,37]. Comparisons between FE/CM and experimental results have also shown good agreement [11,34,35,38\u201341],which further validates the accuracy of the FE/CMmethod for the prediction of gear system dynamic response",
            " Thus, the validated FE/CMmethod is used as the benchmark to verify the accuracy of the analytical model for the coupled gear-bearing system. The influences of non-constant bearing stiffness due to the orbital motion of the bearing rollers are investigated by comparing the results of different gearbearing models with either constant or time-varying bearing stiffnesses. Based on the FE/CM method, a gear-bearing model is built with a full contact finite element bearing model, in which the bearing stiffness fluctuates due to the variation of bearing roller positions, as shown in Fig. 4a. Such a model does not use pre-specified bearing or mesh stiffnesses but instead uses full FE/CM contact models at the roller/race and gear tooth surfaces to analyze the instantaneous contact conditions. As a contrast, a bearing model with pre-specified constant bearing stiffness is used in the FE/CM gear-bearing system shown by Fig. 4b. In the FE/CMmodels of Fig. 4a, b, the gear tooth contact uses a full FE/CM contact model that updates as the gears rotate, as opposed to a pre-specified fluctuating mesh stiffness. In order to focus on the bearing influence, in these two FE/CM models Gear 1 is restricted to have only rotational vibration, while Gear 2 has rotational and vertical (i.e., along the line-of-action (LOA)) translational vibration. Correspondingly, an analytical gearbearing model is also built, as shown in Fig. 4c, where Gear 2 is supported in the vertical direction by a bearing with time-varying stiffness as shown in Fig. 3. The time-varying mesh stiffness km(t) acts along the LOA. Its stiffness variation is determined from the FE/CM model and shown in Fig. 5. The equations of motion of the analytical gearbearing model in Fig. 4c are Mu\u0308 + Ku = F, (1) M = \u23a1 \u23a3 J1 J2 J1r22 + J2r21 0 0 m2 \u23a4 \u23a6 , (2) K = [ km(t) km(t) km(t) km(t) + kb(t) ] , (3) F = [ km(t)(u\u03b80 + ur0), km(t)(u\u03b80 + ur0) \u2212 T2 r2 ]T , (4) whereu = {u\u03b8 , ur }T is the displacement vector, including the relative gear mesh deflection in the rotational direction u\u03b8 = r1\u03b81 + r2\u03b82 and the translational displacement ur of Gear 2. F is the external force vector where u\u03b80 and ur0 are the static rotational and translational displacements from the steady torque T2 [42]. kb(t) is the periodic bearing stiffness obtained in the previous section shown in Fig",
            " The variation of mesh stiffness is calculated over one mesh cycle, and the results under the working load condition in Table 2 are shown in Fig. 5. Based on the models established in the previous section, dynamic simulations of the gear-bearing system are conducted. Firstly, themodal characteristics are calculated. Subsequently, the dynamic response under different rotational speeds is analyzed to detect the phenomena caused by the time-varying mesh stiffness and the influences of time-varying bearing stiffness. Table 3 Natural frequencies of the gear-bearing system (Fig. 4) computed by FE/CM and analytical models for the applied torque T2 = 421.1 N m. fn (n = 1, 2) refers to the nth natural frequency Mode FE/CM model with full contact bearing FE/CM model with stiffness matrix bearing Analytical model 1st f1 4871 Hz 4786 Hz 4869 Hz Error \u2013 1.75% 0.04% 2nd f2 9224 Hz 9190 Hz 9127 Hz Error \u2013 0.37% 1.05% 4.1 Modal analysis of the gear-bearing system For the analytical gear-bearing model, the natural frequencies are obtained by solving the eigenvalue problem. In this process, the time-varyingmesh and bearing stiffnesses are replaced by average stiffnesses over one mesh cycle and one ball pass cycle, respectively",
            " The mathematical explanation of these resonances is given in the following section. The foregoing simulations demonstrate that the timevarying bearing stiffness significantly influences the dynamic response. It is a second periodic excitation for the gear-bearing system, in addition to the wellestablished periodic mesh stiffness. Both excitations are parametric, that is, they involve fluctuations of a stiffness on the left-hand side of the differential equa- Fig. 9 Frequency spectra of the steady-state dynamic transmission errors calculated by: a FE/CM model shown in Fig. 4a, and b analytical model shown in Fig. 4c with time-varying bearing stiffness. The parameters of the gear-bearing system are listed in Table 2 (a) (b) Fig. 10 RMS of the steady-state DTE calculated by the analytical gear-bearing model shown in Fig. 4c (parameters are shown in Table 2) over a wide range of mesh frequency. The dashed curve (red) represents the results of the gear-bearing systemwith constant bearing stiffness model; the solid curve (black) represents the results of the gear-bearing system with time-varying bearing stiffness model tions, rather than direct force excitation on the righthand side. Parametric excitation induces large amplitude vibration when parametric instability occurs. Perturbation is a suitable method to analyze parametric instability problems [43,45]",
            " The resonant unstable cases determined by Floquet theory are marked as discrete dots in Fig. 11. The comparisons show that the analytically calculated boundaries for the instability regions agree with the numerical results from the Floquet theory. For the example system, the instability regions excited by coupled excitations are much smaller compared with the individual excitation instability regions. (a) (b) (d) (f) (c) (e) (g) Fig. 11 Instability regions calculated by the method of multiple scales and Floquet theory for the gear-bearing system shown in Fig. 4c with time-varying bearing stiffness. The parameters R = 5, \u03b4 = 0.438. Other structure parameters of the system are listed in Tables 1 and 2. Solid curves represent the analytical instability boundaries; discrete dots represent numerical unstable response regions calculated by Floquet theory. The results shown in a are caused by a single excitation, i.e., the time-varying mesh stiffness or bearing stiffness; the results shown in b\u2013g are caused by combined mesh stiffness and bearing stiffness excitations 5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001653_tie.2017.2733442-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001653_tie.2017.2733442-Figure2-1.png",
        "caption": "Fig. 2 The open-circuit flux density distributions. (a) SPM-FS machine. (b) RPM-FS machine",
        "texts": [
            " TOPOLOGIES OF RPM-FS MACHINES The topology of a conventional 12-slots 10-poles (12s/10p) SPM-FS machine is shown in Fig. 1(a). It can be found that a modular stator cell is composed of two adjacent stator cores and a sandwiched magnet, which is wound by a concentrated armature winding. The PMs mounted in stator result in a significant influence on armature winding slot area, and then the electrical loading is significantly reduced. Furthermore, the magnetic saturation in stator teeth is serious due to the co-existence of electrical and magnetic loadings in the stator as shown in Fig. 2. To address the above issues, the magnets are moved from stator to rotor to constitute the modular rotor cells as shown in Fig. 1(b). It can be found that each modular cell includes a pair of rotor teeth and a piece of sandwiched magnet, which is similar to the structure of modular stator cell in SPM-FS machines. However, the 12 concentrated armature windings are still remained in the stator and wound around the merged stator-teeth as shown in Fig. 1(b). To provide a flux-path and inherit the flux-switching principle, the fault-tolerant teeth are mounted and sandwiched between adjacent armature windings",
            " Because if the PMs are magnetized in opposite directions, the open-circuit back-EMF waveform of individual coil will not be a sinusoidal or rectangular waveform, which is not suitable for the brushless AC (BLAC) or brushless DC (BLDC) control mode. Compared with the SPM-FS machine, the end-part length of the armature coil in the RPM-FS machine can be obviously reduced due to the absent magnet, and the ratio of winding end-part copper loss to total copper loss decreases, which contributes to improve the efficiency. The open-circuit flux density distribution of two PM machines have been shown in Fig. 2, and it can be found that the flux density due to magnets only in the stator teeth of the SPM-FS machine is about 2T, which is more saturated than that of the RPM-FS machine. The flux-switching principle in the RPM-FS machine has been illustrated in [9]. Based on the magnetic circuit of the RPM-FS machine, the PM flux-linkage linking an individual coil at different special positions is shown in Fig. 3(a). It can be found that the PM flux of the individual coil switches periodically as the rotor rotates continually, and both the polarities and magnitudes of the PM flux-linkage of the individual coil will also change periodically, which is similar to the PM flux switching process in SPM-FS machines as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000648_978-3-642-17531-2-Figure4.24-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000648_978-3-642-17531-2-Figure4.24-1.png",
        "caption": "Fig. 4.24. Zeros of non-dissipative multibody systems: a) migration loci, b) double zero at s=0, c) pair of zeros cancels pair of poles, d) pole/zero swap, e) pair of zeros at s j and pair of real zeros s b",
        "texts": [
            "71), namely, that the bodies at the measurement and actuation locations are dynamically held stationary by the remaining, resonantly oscillating substructures (zeros resonances of the substructures antiresonance frequencies). Zero positions For a non-dissipative multibody system, the numerator of any arbitrary transfer function 2 2( 1) 2 0 2 2( 1) 2 ... ( ) ( ) M M M M G b b s b s b s G s s , 1 DOF M N in the MBS transfer matrix contains only even powers of s . This implies that the zeros of the transfer function must lie symmetrically about the imaginary axis, i.e. they lie either on the imaginary axis (imaginary pairs of zeros, see Fig. 4.24a, type A) or they are axially symmetric real pairs of zeros (see Fig. 4.24a, type B). In the case of dissipative systems with small damping, a similar situation results, the imaginary zeros simply move slightly into the left half-plane. Parameters affecting MBS zeros The locations of zeros of an MBS transfer function fundamentally depend on both configuration parameters 4.7 Measurement and Actuation Locations 269 (geometry, masses, stiffnesses), and the excitation and observation points (cf. Eq. (4.61)). In contrast, the locations of poles of the transfer function are independent of these points and depend only on the configuration parameters. For this reason, it is to be expected that both changes in the configuration parameters (desired or undesired) and variations in the measurement and actuation locations will induce a migration of the zeros. Migration possibilities for MBS zeros The principal possible forms of migration of the zeros are indicated in Fig. 4.24a: symmetrically along the imaginary axis and symmetrically along the real axis. In the process, different, varying configurations of the zeros with respect to the locations of poles can appear. These configurations have fundamental effects on the response characteristics and control characteristics of the system. Typical configurations The following typical configurations can occur: 1. double zero at 0s , Fig. 4.24b, 2. pair of zeros canceling pair of poles, Fig. 4.24c, 3. pole/zero swap given small parameter changes, Fig. 4.24d, 4. pair of zeros at s j , Fig. 4.24e, 5. pair of real zeros s b , Fig. 4.24e. 270 4 Functional Realization: Multibody Dynamics Double zero at 0s This case occurs when an acceleration sensor is used for the measurement, see Eq. (4.65). If there is also a double pole at 0s (i.e. the rigid-body mode of a free multibody system), there is exact canceling. Thus, in this case, the rigid-body mode is unobservable and uncontrollable. Pole/zero cancellation If the pair of imaginary zeros exactly cancels a pair of imaginary poles pi s j , then the eigenfrequency pi no longer ap- pears in the transfer function. Thus, this eigenmode is also unobservable and uncontrollable. Natural oscillations induced by disturbances in this mode can not be affected by a controller. Pole/zero swap A particularly serious case occurs when, for small parameter changes in the MBS configuration, the relative locations of poles and zeros change (Fig. 4.24d). The dramatic effects of this situation can be much better recognized in the frequency response. This situation produces a phase uncertainty of 360\u00b0 , as, for the migration shown in Fig. 4.24d, instead of the original +180\u00b0 phase jump due to the zero, the \u2013180\u00b0 phase jump comes first in the alternate configuration. This completely reverses the stability conditions and can only be managed using gain stabilization (with small gain) in this frequency range. Fortunately, this behavior only appears in non-collocated configurations. Pair of infinite zeros For certain parameter configurations, the zeros can go to infinity, resulting in a reduction in order of the numerator. This creates an (additional) set of neighboring pairs of poles without a separating zero, and the disadvantageous property of having a double \u2013180\u00b0 phase jump. Pair of real zeros: non-minimum phase behavior As a sort of continuous perpetuation of the variation in behavior induced by the presence of imaginary infinite zeros, pairs of zeros can migrate in from infinity along the real axis (Fig. 4.24a, dashed arc). This results in a symmetric pair of real zeros at s b . Due to the existence of a zero in the right half-plan, this results in so-called non-minimum phase behavior with challenging properties for control (Ogata 2010), (Horowitz 1963). Generalized free two-mass oscillator In order to gain some engineering intuition for the various zero configurations, consider the generalized unsuspended two-mass oscillator shown in Fig. 4.25. This example is sufficiently simple to permit the use of analytical relations, while demonstrating all important configurations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002061_j.measurement.2018.06.035-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002061_j.measurement.2018.06.035-Figure5-1.png",
        "caption": "Fig. 5. Gear pair arrangement and LDS position for measuring the deflection of the gear tooth.",
        "texts": [
            " The proposed methodology is explained in Section 2. The methodology proposed to estimate the mesh stiffness of healthy and cracked tooth case is shown by flow chart as given in Fig. 1. In this experimental method, the deflection is measured along the LOA (line of action) of a gear pair. The position of LDS is an important to measure the deflection in the direction of force. The LDS should be placed in such a way that the laser beam should coincide with the LOA of a given gear pair. To understand the position of LDS, see the Fig. 5. The factors on which the position of LDS depends are that how far the reflector is placed from the LDS and the laser beam should be perpendicular to the reflector. The distance between LDS and reflector should be within the range as given in Section 3. The stiffness is calculated with the help of this deflection. Now the individual tooth stiffness of one pair and Hertzian contact stiffness are connected in series and calculated the equivalent mesh stiffness of first and second pair separately. The Hertzian contact stiffness is calculated analytically",
            " The LSF for STCP is one that shows the total force shared by the single pair. In Fig. 4, HPSTC is the highest point of STCP and LPSTC is the lowest point of STCP. Force shared by pair during DTCP can be written as [40] = \u00d7F LSF Fi (9) where Fi and F are the forces shared by the pair and the total force respectively. The deflection of the tooth should be measured along the LOA because this is the direction of force. For measuring the deflection along the direction of force or along the LOA an experimental approach is illustrated in Fig. 5. In this approach, a LDS is used to measure the gear tooth deflection. For this, the laser beam is directed along the LOA so that the gear tooth deflection which can be measured directly along the LOA. The LOA can be drawn by a common tangent between two base circles of gear 1 and gear 2. A reflector is a small rectangular thin plate and is attached to the centre line joining the tooth top and centre of the gear and it is perpendicular to the LOA as shown in Fig. 5. The experiment is conducted under static condition. The reflector is attached at a particular angular position of gears on the desired tooth. At this angular position, the deflection of that tooth can be measured on which the reflector is attached. During the experiments the LDS\u2019s position is kept such that the laser beam is always directed along the LOA; the reflector position will change for next angular position of gear. In the present study, an FE analysis was performed to estimate the mesh stiffness as reported in the literature [17,19]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000603_s11460-009-0065-3-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000603_s11460-009-0065-3-Figure3-1.png",
        "caption": "Fig. 3 Typical hardware configuration of single-rotor RC helicopter",
        "texts": [
            " Interested readers are referred to more acrobatic flight demonstrations on the RC-hobby-related websites (see, for example, Flight Video Gallery1\u20133)). The operation of the single-rotor RC helicopter is generally similar to that of its full-sized counterpart. Smallsized digital or analog servo actuators from well-known vendors, such as Futaba4) and JR-Propo5), are equipped to drive the helicopter mechanically. The standard configuration adopted in the RC circle involves five servo actuators as shown in Fig. 3: 1) The aileron and elevator servos are in charge of tilting the swash plate to realize the rolling motion, pitching motion and translational movement. 2) The collective pitch servo is utilized to change the collective pitch angle of the main rotor, which further generates the heave motion. However, there is no such freedom for a small group of low-end fixed-pitch RC helicopters (see, for example, Electric RC Helicopters Community6)). 3) The throttle servo, cooperating with an engine governor, controls the engine power, which is the second source of heave motion change. 4) The rudder servo, generally possessing higher speed and precision, is employed to realize yaw motion control. It is commonly equipped with an additional piezo-electronic yaw rate gyro to facilitate the servo to overcome the over-sensitive dynamics in the bare yaw channel. The configuration for a typical yaw channel is shown in Fig. 4. We note that a Bell-Hiller stabilizer bar7), which is the most distinguished feature of the RC helicopter (also shown in Fig. 3), is very often employed for ease to achieve desired stabilization. From the practical point of 1) Flight Video Gallery. http://www.model-helicopters.com/main2_f.php 2) Flight Video Gallery. http://www.rcgroups.com/rc-video-gallery-271/ 3) Flight Video Gallery. http://runryder.com/helicopter/galleries/ 4) Futaba Servo Actuators. http://www.futaba-rc.com/servos/index.html 5) JR Servo Actuators. http://www.jrradios.com/Products/Servos-Air.aspx 6) Electric RC Helicopters Community. http://www.electric-rc-helicopter"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001843_s00170-015-7697-7-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001843_s00170-015-7697-7-Figure7-1.png",
        "caption": "Fig. 7 Microstructure of the solid-solution-hardened alloy: a longitudinal section of the top layer; b longitudinal cross section of the first layer; and c images of a transverse cross section, longitudinal cross section, and plane section of the third layer",
        "texts": [],
        "surrounding_texts": [
            "The characterization of the deposited layers started with nondestructive tests with a dye penetrant to identify any defects that might compromise the integrity of the walls. These tests failed to indicate any surface cracks in the deposited layers. Analysis of total and effective thicknesses according to the procedures previously described resulted in the data shown in Table 4. Walls processed without preheating required machining of similar amounts of material to obtain the effective thickness. However, the solid-solution-hardened alloy allowed a thinner wall to be processed (2.3 mm) than the precipitationhardened alloy (2.8 mm). It is interesting to note that material removal in the former mainly relates to differences in thickness between the first layer and superimposed layers, suggesting that processing parts with this alloy should be very efficient since the first layer is removed during final machining. However, special care is required in repair operations, where the first layer is responsible for the bond with the part being repaired. Processing with preheating resulted in changes in the amount of material removed for each of the alloys processed. The small increase in the wettability of the layers deposited with the precipitation-hardened alloy reduced the percentage of the overall area removed (20.2 %) although the effective thickness increased (3 mm). The impact of preheating was more significant on the geometry of walls processed with the solid-solution-hardened alloy. The increase in wettability resulted in a greater difference in thickness between the first and last layers, so that more material had to be removed to achieve a uniform width. Therefore, the amount of material removed increased significantly (28.3 %) although the effective thickness did not change, suggesting that processing parameters could be further optimized to minimize material waste. These results confirm that a thin wall can be produced by AM using PTA and indicate that effective thickness depends on the composition of the alloy. They complement the findings of Martina [4], who used PTA to process walls with an effective thickness of 16 mm, showing that this process can be used in components with a wide range of geometries. Furthermore, microscopic analysis of transverse cross sections did not identify any cracks, showing that thermal cycles during deposition of multiple layers allow stresses generated during processing to be accommodated. Together with the findings of the dye penetrant evaluation, this result attests the soundness of the thin walls produced by AM using PTA. Analysis of the microstructure at a transverse cross section of the multiple layers (Figs. 6 and 7) revealed a fine dendritic solidification structure like those observed for laser deposition [12, 13]. The walls made with precipitation-hardened alloy showed epitaxial growth from the interface with the substrate to the top layer, while in the solid-solution-hardened alloy, epitaxial growth was only observed at the interface between the layers. Epitaxial growth is favored by the similar chemical composition and crystal structures, accounting for the continuity observed between the precipitation-hardened alloy and the substrate with a similar chemical composition. This phenomenon is considered beneficial in welding as it promotes continuity of the grain from the base material to the deposited alloy, leading to fewer, smaller interfaces and, consequently, fewer stress concentrators [14]. Independently of the chemical composition of the alloy used to build the wall, a change in the direction of dendrite growth can be observed in the top layer (Figs. 6c and 7a). The details of the microstructure were analyzed using electron scanning microscopy. The effect of the interaction between the deposited layer and the substrate varied depending on the composition of the alloy. In the precipitation-hardened alloy, deposition resulted in the formation of Ti precipitates throughout the height of the wall when processed both with and without preheating (Fig. 8a). EDS analysis of these precipitates reveals the presence of Ti, C, andMo, suggesting that carbides of the typeMC andM23C7 (M=Mo, Ti) have formed. Banding of areas with and without nanometric \u03b3\u2032 precipitates was also observed and was associated with the impact of deposition thermal cycles (Fig. 8b). In the wall built with the solid-solution-hardened alloy, a region extending through the first two layers where dilution with the substrate had occurred could be observed. It can be seen from Fig. 9, which shows the chemical composition profile of this wall, that there is a greater percentage of Ti in these layers, allowing precipitates to form. However, in accordance with the Ti profile in Fig. 9, these precipitates were not observed in the third or subsequent layers. This variation in composition causes the properties to change along the transverse cross section of the wall processed with the solid-solution-hardened alloy, as shown by the hardness profile (Fig. 10). The first layers are influenced by the chemical composition of the substrate, which changes the alloying elements in the solid solution, causing precipitation of compounds not expected in the original alloy. As the number of superimposed layers increases, the influence of the substrate is reduced and the mean hardness approaches the expected value for the deposited alloy. Preheating does not change the hardness profile although an increase in hardness in the first two layers was observed, suggesting that the substrate has a greater influence on the amount of precipitates in this region. Hardness profiles measured at the transverse cross section of the wall processed with the precipitation-hardened alloy exhibited fluctuations (Fig. 11) which are associated with the observed banding. The peaks of these fluctuations corresponded to areas with precipitates. Preheating did not change the hardness profile as the temperature used was not high enough to have a significant effect on the precipitation caused by the thermal cycles during the superimposed deposition of the layers. This result indicates that although preheating might be required to minimize stresses during deposition, post-deposition heat treatment is required to ensure uniform properties across a transverse cross section. The impact of post-deposition heat treatment on the microstructure of the wal l processed with the precipitation-hardened alloy can be observed in Fig. 12. Besides the precipitate banding mentioned earlier, the as-deposited microstructure reveals the presence of carbides in a Ni-rich matrix (Fig. 12a). Following post-deposition heat treatment, a fine distribution of \u03b3\u2032 can be identified together with finer carbides, probably partially solubilized during the initial steps of the heat treatment cycle. Post-deposition heat treatment also has an impact on the hardness profile across the transverse cross section of the wall (Fig. 13). A lower, more uniform hardness profile was observed, indicating that adequate selection of heat treatment parameters is required to optimize the properties of parts produced by AM using PTA. As expected for a solid-solutionhardened alloy, post-deposition heat treatment did not have a significant impact on the microstructure or the hardness profile measured at the transverse cross section of the five-layer wall (Fig. 14)."
        ]
    },
    {
        "image_filename": "designv10_5_0001394_tec.2016.2597059-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001394_tec.2016.2597059-Figure1-1.png",
        "caption": "Fig. 1. One stator of the proof-of-concept machine.",
        "texts": [
            " A single rotor of the machine consists of ten poles excited by NdFeB magnets, which parameters are gathered in table II. used and the winding insulation material. TABLE III MAXIMUM TEMPERATURES OF MATERIALS UTILIZED IN PROTOTYPING Material Max. Temperature (\u00b0C) Neodymium magnets, 40SH-type 120 Winding Insulation material 155 To reduce rotor eddy current losses, each magnet in the pole was divided into 12 equal segments, and the magnets were embedded below laminated iron parts supported by a composite rotor frame. The rotor has a yokeless structure. Fig. 1 illustrates the construction of one stator. The twelve tooth coils are configured as six pairs forming half of a phase winding each. Each pair has a single inlet and outlet cooling conduit. Fig. 2 shows how the stainless steel cooling conduit arrays pass through the motor housing. Because the proof-of-concept machine was a retrofit into an existing machine, this rudimentary approach was necessary. Table IV summarizes the main dimensions and parameters for the electrical machine. Parameter Value Stack (physical) iron length re-ri = lFe [mm] 70 Total stack length ltot [mm] 70 Stator inner diameter Dsi [mm] 250 Stator outer diameter Dse [mm] 390 Original rotor tangential tension stan (at rated torque) [kPa] 28"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000492_tie.2011.2168795-Figure24-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000492_tie.2011.2168795-Figure24-1.png",
        "caption": "Fig. 24. Test stand. (1) Synchronous generator. (2) Current transducer. (3) Voltage transducer. (4) Test induction machine. (5) Torque transducer. (6) Data acquisition and processing unit. (7) Additional driving motor for mechanical no-load loss test.",
        "texts": [
            " One aspect of the measurement departed from the standard, namely, the mechanical no-load losses were measured for the entire range of rotor speeds [14], [33] using an accurate torque transducer placed between the tested unsupplied driven motor and an additional driving motor. This allowed for a more accurate measurement of the mechanical loss. During tests, the motor fan was removed to reduce the mechanical losses. The setup for the core loss measurements on the test induction motor is shown in Fig. 24. At 50-Hz frequency, the basic no-load core losses, calculated using the analytical method, for motor A were 7.3 W in the stator teeth and 18.6 W in the stator yoke. For motor B, similar results were 2.2 W in the stator teeth and 5.4 W in the stator yoke. The percentage errors of total no-load core losses between the calculated and measured values in relation to the measurement at 50-Hz frequency are as follows: 1) for motor A: a) 0.8% for the field-circuit method; b) 3.1% for the analytical method; 2) for motor B: a) 9% for the field-circuit method; b) 7% for the analytical method"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000047_j.robot.2007.08.001-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000047_j.robot.2007.08.001-Figure2-1.png",
        "caption": "Fig. 2. Examples for stable and unstable support polygons.",
        "texts": [
            " As a result, in one iteration, considering two units of advancement, transitions from 0 to 3, 4, or 5 are possible. A leg in state 0 can stay in return position, so the transition from 0 to 0 is also possible. The leg-states of the six legs, together, construct the state of the robot. There are 66 = 46 656 possible states for the robot. The supporting legs in any state of the robot correspond to a supporting polygon. For the state to be statically stable, the projection of the center of gravity of the robot on the horizontal plane should remain within this supporting polygon (Fig. 2). The stability margin of a support polygon, and that of the corresponding state of the robot, is defined as the minimum of the front and rear stability margins. Theoretically, a state is stable if this stability margin is greater than zero. However, with the actual Robot-EA308 used for this paper, the minimum margin for a stable walk is 2 cm. Therefore, throughout the paper the minimum stability margin will be taken as 2 cm, rather than zero. In Figs. 2 and 3 the convention of numbering the legs throughout the paper is revealed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002983_b978-0-12-811820-7.00008-2-Figure6.4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002983_b978-0-12-811820-7.00008-2-Figure6.4-1.png",
        "caption": "FIGURE 6.4 Connection between the thermal model and the grain growth phase-field model: representative longitudinal section and wall section for grain growth simulation, as well as the interpolated temperature distribution data for phase-field simulations in the two sections.",
        "texts": [
            " 3) It is assumed that the temperature in the newly added layer is uniform, and the process of applying the uniform temperature is instantaneous; 4) It is assumed that the temperature gradient is fixed after the heat source left, and the direction of maximum heat flux always keeps vertical upward. With these assumptions, the grain growth behaviors during AM in the longitudinal and wall sections of the build are investigated, due to their distinct temperature distributions. One representative region in each section is selected for the grain growth simulations, as shown in Figure 6.4. To obtain simulated grain morphology with acceptable resolution, the required mesh size for the phase-field simulations (\u223c\u00b5m) should be much less than that of the thermal calculations (\u223c10 \u00b5m). Therefore, the interpolation method is used to fit the temperature distribution data from the thermal calculations, as shown in Figure 6.4, for both longitudinal and wall sections. With the temperature distribution and history available from the thermal calculations, 2D/3D phase-field grain growth simulations are performed. With randomly distributed grains as the initial state, new layers with adjustable thickness are introduced into the system at adjustable time intervals to mimic the AM process. In the longitudinal section, since the temperature gradient is along the building direction and perpendicular to the layers, columnar grains parallel to the building direction are observed (Figure 6.5A2). In the wall section, since the temperature gradient is not uniform as shown in Figure 6.4, grains grow along the local temperature gradient direction to form the columnar grains in the middle and small grains near the edges of the section (Figure 6.5B2). These simulated grain microstructures can well reproduce the experimentally observed ones in both the longitudinal section [37] and the wall section [17], as shown in Figure 6.5, which confirms the effect of temperature distribution during AM on the grain texture development.The simulated grain width, with an average value of 0.21mm, lies within the experimental ranges (0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003831_tia.2020.3029997-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003831_tia.2020.3029997-Figure1-1.png",
        "caption": "Fig. 1. Structure of studied IPMSM.",
        "texts": [
            " In section II, the studied totally enclosed forced convection (TEFC) interior PM (IPM) machine and the proposed thermal model with 3- D winding thermal modelling are described and developed. The 2-D simplified analytical active-winding (SAW) and end-winding (SEW) models are derived and verified by 2-D FEA method in section III. In section IV, the proposed thermal model is validated experimentally. Finally, the conclusion is drawn in section V. The detailed mathematical derivation is given in Appendices. A 12-slot/10-pole TEFC IPMSM, as shown in Fig. 1, is used for thermal analysis and its geometric parameters are listed in Table I. The proposed LPTN is presented in Fig. 2, in which the main parts are included. In order to restrain the overestimated error caused by simplified \u201cI-type\u201d thermal network, the LPTN is modelled based on the \u201cT-type\u201d elementary network. The detailed description of the thermal model is tabulated in Table II. The active-winding region is built by the homogeneous composite 3-D hollow cylinder segment, including copper, impregnation and wire insulation, in which the heat flow path in axial (\ud835\udc67-), radial (\ud835\udc5f-) and circumferential (\ud835\udf03-) directions are taken account"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002120_j.mechmachtheory.2015.09.010-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002120_j.mechmachtheory.2015.09.010-Figure2-1.png",
        "caption": "Fig. 2. The configuration of CNC shaping machine tool.",
        "texts": [
            " The tangential velocity along with the tangent of the pitch curve is: vt \u00bc t0: \u00f019\u00de Supposing that the cutter's angular velocity along its rotational axis is \u03c92, then, the velocity at a point on the cutter's tooth profile can be presented as [27]: v2 \u00bc \u03c92 r2 \u00bc 0 0 d\u03b8 dt 2 64 3 75 x2 t\u00f0 \u00de y2 t\u00f0 \u00de 0 2 4 3 5 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r \u03c6\u00f0 \u00de2 \u00fe r0 \u03c6\u00f0 \u00de\u00bd 2 q ro \u2212y2 t\u00f0 \u00de x2 t\u00f0 \u00de 0 2 4 3 5: \u00f020\u00de The velocity of the cutter can be represented by: vr \u00bc vt \u00fe v2 \u00bc r0 \u03c6\u00f0 \u00de cos \u03c6\u00f0 \u00de\u2212r \u03c6\u00f0 \u00de sin \u03c6\u00f0 \u00de\u2212y2 t\u00f0 \u00de ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r0 \u03c6\u00f0 \u00de\u00bd 2 \u00fe r \u03c6\u00f0 \u00de2 q ro r0 \u03c6\u00f0 \u00de sin \u03c6\u00f0 \u00de \u00fe r \u03c6\u00f0 \u00de cos \u03c6\u00f0 \u00de \u00fe x2 t\u00f0 \u00de ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r0 \u03c6\u00f0 \u00de\u00bd 2 \u00fe r \u03c6\u00f0 \u00de2 q ro 2 666664 3 777775: \u00f021\u00de By substituting Eqs. (21) and (18) into the meshing equation (Eq. (17)), and then combining Eq. (17) and the envelope equation (Eq. (16)), the tooth profile of the non-circular gear can be solved. Fig. 2 shows the configuration of the 3-linkage CNC shaping machine tool in which the A-axis is the revolving axis of the work piece (shaped gear); the B-axis is the revolving axis of the shape cutter; the X-axis is the linear axis of the center distance between the cutter and the gear; Sp is the spindle of the machine tool, which implements the reciprocal cutting motion of the cutter. A-axis, B-axis, and X-axis are three linkage axes with interpolation. In terms of the mathematical model above, when the cutter and gear are perfectly meshed, the positional equation of each linkage axis is as follows: X \u03c6\u00f0 \u00de \u00bc E \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r \u03c6\u00f0 \u00de2 \u00fe ro 2 \u00fe 2ror \u03c6\u00f0 \u00deffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r \u03c6\u00f0 \u00de2 \u00fe r0 \u03c6\u00f0 \u00de\u00bd 2 q vuut A \u03c6\u00f0 \u00de \u00bc \u03b3\u2212\u03c6 \u00bc a tan ro \u2212r \u03c6\u00f0 \u00de sin\u03c6\u00fe r0 \u03c6\u00f0 \u00de cos\u03c6 \u00fe r \u03c6\u00f0 \u00de sin\u03c6 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r \u03c6\u00f0 \u00de2 \u00fe r0 \u03c6\u00f0 \u00de\u00bd 2 q ro \u2212r \u03c6\u00f0 \u00de cos\u03c6\u2212r0 \u03c6\u00f0 \u00de sin\u03c6\u00bd \u00fe r \u03c6\u00f0 \u00de cos\u03c6 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r \u03c6\u00f0 \u00de2 \u00fe r0 \u03c6\u00f0 \u00de\u00bd 2 q 8>< >: 9>= >;\u2212\u03c6 B \u03c6\u00f0 \u00de \u00bc \u03b8\u2212\u03b1 \u00bc Z\u03c6 0 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r \u03c6\u00f0 \u00de2 \u00fe r0 \u03c6\u00f0 \u00de\u00bd 2 q d\u03c6 ro \u2212a cos ro \u00fe r \u03c6\u00f0 \u00de2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r \u03c6\u00f0 \u00de2 \u00fe r0 \u03c6\u00f0 \u00de\u00bd 2 q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r \u03c6\u00f0 \u00de2 \u00fe ro 2 \u00fe 2ror \u03c6\u00f0 \u00deffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r \u03c6\u00f0 \u00de2 \u00fe r0 \u03c6\u00f0 \u00de\u00bd 2 q vuut 8>>>>>>>>>>< >>>>>>>>>>: : \u00f022\u00de According to the coordinate transformation, the transformation matrix between A-axis and X-axis is: MXA \u00bc cos A \u03c6\u00f0 \u00de\u00bd \u2212 sin A \u03c6\u00f0 \u00de\u00bd 0 sin A \u03c6\u00f0 \u00de\u00bd cos A \u03c6\u00f0 \u00de\u00bd 0 0 0 1 2 4 3 5: \u00f023\u00de The transformation matrix between the X-axis and the machine base can be expressed as: MX0 \u00bc 1 1 X \u03c6\u00f0 \u00de 0 0 0 0 0 1 2 4 3 5: \u00f024\u00de The transformation matrix between the machine base and the B-axis can be expressed as: MB0 \u00bc cos B \u03c6\u00f0 \u00de\u00bd sin B \u03c6\u00f0 \u00de\u00bd 0 \u2212 sin B \u03c6\u00f0 \u00de\u00bd cos B \u03c6\u00f0 \u00de\u00bd 0 0 0 1 2 4 3 5: \u00f025\u00de Thus, the envelope equation of the cutter is: r\u00bcMB0MX0MXAr2: \u00f026\u00de Although Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002896_j.jmapro.2019.04.018-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002896_j.jmapro.2019.04.018-Figure2-1.png",
        "caption": "Fig. 2. Scanning arrangement and Scanning and User Coordinate Systems.",
        "texts": [
            "05mm in precision in the scanned volume. The accuracy of the scanner and its repeatability have been verified through the measurement of a physical standard. The scanner was placed in a fixed position, with a field of view that allowed the top layer to be scanned throughout the process. Point cloud processing and the control strategy were executed by an application developed with Matlab. The process is stopped after a group of layers has been deposited and then the upper layer is scanned. As shown in Fig. 2, the coordinates corresponding to each scanning point are initially defined in a Scanning Coordinate System, SCS. This coordinate system depends on the position and orientation of the scanner. In order to determine the height of Table 1 Setup characteristics of the LMD cells for powder and wire supply. Industrial robot Material Material feeding unit Laser source Maximum laser power ABB IRB4400-60 Sulzer Metco 42C stainless steel powder Sulzer Metco Twin-10C powder feeder Rofin DY022 2.2kW ABB IRB4600-45 316LSi stainless steel 0",
            "8mm diameter wire DINSE wire feeder IPG YLS4000 S2T 4 kW a part, the coordinates of the points based on a new coordinate system called User Coordinate System (UCS) must be expressed. In this coordinate system, two of the components, x and y, form a plane that contains the base of the part, whereas the third component, z, is normal relative to this plane and corresponds to the direction in which the part grows. In order to identify base points only, a volume is established in which the points of the base are searched in every scan (see Fig. 2) once settings have been completed with regard to the position and orientation of the scanning equipment at the beginning of a deposition. Since the real height of the part should be similar to its theoretical growth, the determination of the height of the last deposited layer can also be limited to those points whose z component lies within a range close to the expected height. This searching volume is updated for every group of layers scan. To obtain the base of the UCS, a plane is fitted to the point cloud of the base by means of Principal Component Analysis (PCA)",
            " Rotation, moreover, also referred to as basis change, defines the z-axis as the direction for part growth, and places the x and y axes on the base plane. = \u2219 \u2212p V p b[ ] [ \u00af ]i UCS T i SCS (2) where: p[ ]i UCS are all the points acquired in a scan, as defined in the UCS. \u2212p b[ \u00af ]i SCS is the translation of the scan points in the SCS. V T is the rotation or change of the basis matrix. p[ ]i SCS are all the points acquired in a scan, as defined in the SCS. The height of the layer can be then determined by the mean value or the z component mode of points inside the last layer height searching volume (Fig. 2). Fig. 3a shows the point cloud of the last layer with the deviation in height from the theoretical growth. In Fig. 3b the histogram of the point cloud heights and the average and mode values obtained can be observed. In this procedure, a coordinate system has been calculated based on the points of the base for each scan. Compared to using the same coordinate system for all scans, it has improved scanning accuracy as a result of differences between scans caused by minor movements involving certain parts of the measuring equipment or thermal effects"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002213_j.mechmachtheory.2014.06.006-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002213_j.mechmachtheory.2014.06.006-Figure7-1.png",
        "caption": "Fig. 7. State 3 of the derivative queer-square mechanism (\u03b11 N 0, \u03b12 N 0, \u03b211 = \u03b212, \u03b221 = \u03b222).",
        "texts": [
            " In state 3, by rotating the positive angles \u03b11 and \u03b12, limb1s and limb2s have a relatively higher position compared to the base. Angle ranges of state 3 satisfy \u03b11N0;\u03b211 \u00bc \u03b212N0 \u03b12N0;\u03b221 \u00bc \u03b222N0 : \u00f028\u00de Within the above ranges, the mechanism moves arbitrarily with the allowable motion. Besides the angle ranges in the presented equations, the angle ranges of \u03b11, \u03b12, \u03b211, \u03b212, \u03b221 and \u03b222 can be extendedmore than \u03c0 2 until two or more bars geometrically touching where the angles are always smaller than \u03c0. Fig. 7 offers the observation of the derivative queer-square mechanism in state 3. Fig. 7 indicates that the limb1s, limb2s, limb1p and limb2p all have higher locations compared to the base OA1A2 of the derivative queer-square mechanism, and the platform E1F1E2F2 is higher than the limb1s, limb2s, limb1p and limb2p. By rotating a positive angle \u03b11 and a negative angle \u03b12 from the singular position, as illustrated in Fig. 8, the derivativemechanism changes to state 4 whose angle ranges satisfy \u03b11N0;\u03b211 \u00bc \u03b212b0 \u03b12b0;\u03b221 \u00bc \u03b222N0 : \u00f029\u00de It can be observed from Fig. 8 that limb1s has a relatively higher position, limb2s has a relatively lower position compared to the base OA1A2 and the platform E1F1E2F2 is lower than limb1p and higher than limb2p in state 4"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000241_tmag.2009.2025047-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000241_tmag.2009.2025047-Figure1-1.png",
        "caption": "Fig. 1. Magnet configuration.",
        "texts": [
            " By combination with the parallel case, the force for any magnetization direction and for any magnet position can be calculated by analytical expression [9]\u2013[11]. The torque calculation is an innovative step. The three torque components between two magnets can be fully written with analytical expressions. Now all the interactions (interaction energy, force, and torque components) between two cuboidal magnets can be analytically calculated by relatively simple analytical expressions. The interactions between two parallelepiped magnets are studied. Their edges are, respectively, parallel (see Fig. 1). The magnetizations and are supposed to be rigid and uniform in each magnet. The dimensions of the first magnet are 2a 2b 2c, and its polarization is . Its center is , the origin of the axes Oxyz. For the second magnet, the dimensions are 2A 2B 2C, its polarization is , and the coordinates of its center are . The side 2a is parallel to the side 2A, and so on. The magnet dimensions are given in Table I. The magnetization directions shown in Fig. 1 correspond to the case when the polarizations and have the same direction, parallel to the side 2c. Note that the calculation stays valid when they are in opposite direction; only the expression sign is reversed. The polarizations and are supposed to be rigid and uniform. They can be replaced by distributions of magnetic charges 0018-9464/$26.00 \u00a9 2009 IEEE In the example of Fig. 1, since is perpendicular to the surfaces 2a 2b and oriented to the top, these polar faces wear the density on the upper face (North Pole), and on the lower face (South Pole). All the analytical calculations have been made by successive integrals, to calculate the interaction energy for the two-magnets system. The forces and the torques can be obtained by linear and angular derivation. The analytical calculation of the interaction energy in 3-D is made by four successive integrations. The first one gives a logarithm function"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003758_j.ijhydene.2019.02.031-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003758_j.ijhydene.2019.02.031-Figure2-1.png",
        "caption": "Fig. 2 e Schematic structure of a DGAFC used in this study.",
        "texts": [
            " The blank control group was made by using the above-mentioned procedure, without adding catalyst. All the cathodes used in this work were Cu2OeCu modified activated carbon prepared by a laser irradiation method [18]. The DGAFC device used in this study was a polymethyl methacrylate (PMMA) based single-chamber fuel cell, which were assembled according to the previously reported procedures [2,18,19]. It mainly included an anode plate, a cylindrical chamber (volume of 14 mL) and a cathode plate (Fig. 2). Both AC anode and Cu2OeCu-AC cathode had an effective paration of FCO-modified AC anode. area of 7.065 cm2. The electrolyte used was a mixture of 1 M glucose and 3 M KOH. The power density curves and polarization curves of DGAFCs were measured by using a ZX-21 resistance box (Dongmao, Shanghai, China). The external resistance of DGAFCs was varied from 9000 U to 4 U and the corresponding voltage was acquired using amultimeter (VICTOR8145B, Shenzhen, China) when the reading stabilized. Electrochemical testing of anodes was performed on a CHI660E electrochemical workstation (CHI Instrument Co"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000236_j.mechmachtheory.2010.06.004-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000236_j.mechmachtheory.2010.06.004-Figure4-1.png",
        "caption": "Fig. 4. T circle ra",
        "texts": [
            " \u2022 The involute part of the tooth must not be penetrated on the drive side. That the tool tip height is kept fixed is applied in order to allow for the same clearance in the optimized gears as is the case for the ISO gears. The involute part should be kept unchanged to allow the optimized gears to have the same functional qualities as the original involute gears. A distinction is made between the tool top part that cuts the tooth root of the drive side (drive top) and the other part that cuts the tooth root of the coast side (coast top). As indicated in Fig. 4 the coast side top is a simple circle (part of a full circle). The radius of the circle is given as \u03c1c = \u03baM = 4\u03bc + \u03c0\u22125tan\u00f0\u03b1c\u00de 4\u00f0cos\u00f0\u03b1c\u00de\u2212\u00f0sin\u00f0\u03b1c\u00de\u22121\u00detan\u00f0\u03b1c\u00de\u00de M \u00f09\u00de ight be greater than or smaller than the ISO standard \u03c1\u22480.38 M (see Fig. 1). This also means that the involute on the costs and m sidemight not be as long as it would have been using the ISO cutting tooth, but this is ignored because of the unidirectional loading assumption. he design domain for the optimization shown as the hatched part. The coast side pressure angle and drive side pressure angle are shown together with the dius on the cutting tool coast side. Final part to be parameterized is the drive top, this is done by a modified super elliptic shape. The design domain is shown as the hatched part in Fig. 4 and enlarged in Fig. 5. As seen in Fig. 4 the design domain size is variable and controlled through the parameter \u03bc, with the restrictions from the boundaries this parameter must fulfill. where \u03bcmin = \u2212\u03c0 4 + 5 4 tan\u00f0\u03b1c\u00de\u2266 \u03bc \u2266\u03c0 4 \u22125 4 tan\u00f0\u03b1d\u00de = \u03bcmax \u00f010\u00de From the optimization presented in Ref. [1] it was found that in order to minimize the stress concentration it is important that the parameterization includes a straight part before entering the elliptical shape, but in that paper the tooth were symmetric. The idea used in the present paper is instead that the design domain can change size through the design parameter \u03bc "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000498_978-3-642-00196-3_56-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000498_978-3-642-00196-3_56-Figure1-1.png",
        "caption": "Fig. 1. A: The \u201clinks,\u201d or regions of overlap between component tube transition points, of a three-tube cannula composed of tubes with an initial straight section and a final curved section. Links start and end at transition points, and the jth link is between Tj and Tj+1. In this configuration, the largest tube transitions from straight to the left of T1 to curved to the right. The same is true of the middle tube at T2 and the smallest tube at T4. B: The arc parameters of a curved link consist of curvature (\u03baj), equilibrium plane angle (\u03c6j), and arc length ( j), as shown. Figures reprinted from [9].",
        "texts": [
            " For reader convenience, we review the basic notation used in the derivation of the forward kinematics of an active cannula, reported in detail in [10]. Active cannula joint space is parametrized by axial rotations, \u03b1, and translations, \u03c1, applied at tube bases, namely q = (\u03b11, \u03c11, . . . , \u03b1n, \u03c1n). In what follows, the subscript i \u2208 {1, . . . , n} refers to tube number, while j \u2208 {1, . . . , m} refers to link number. Cannula links are circular segments described by the arc parameters curvature, plane, and arc length (\u03baj , \u03c6j , j), as shown in Figure 1. The kinematics of continuum robots can be decomposed into a mapping from joint space to arc parameters, and a mapping from arc parameters to shape. Consider an active cannula where each component tube has an initial straight section and a circularly precurved tip. The shape of the active cannula is then defined by a sequence of unique overlap regions (\u201clinks\u201d) between transition points Tj, as shown in Figure 1. Each of these remains circular, although bending planes, \u03c6(q), and curvatures, \u03ba(q), change as tubes are axially rotated in order to minimize the stored elastic energy, U . As described in [9], the energy functional can be expressed as a function of the angles, \u03c8, of the tubes at the end of the straight transmission (at T1). The link lengths, (q), are readily determined from the transition point positions in terms of arc length. They are functions of tube base translations, \u03c1, and the lengths of the straight and curved sections of each tube; an example is given in [10]",
            " We take derivatives of \u03c8\u2217 with respect to q as follows. We have \u2207U = F (q,\u03c8\u2217) = 0, and hence DqF = D1F + (D2F ) (Dq\u03c8\u2217) = 0, where D1F and D2F denote the Jacobian matrix of F with respect to the first and second arguments, respectively. If the Hessian (Dq\u03c8\u2217) is invertible, Dq\u03c8 \u2217 = \u2212(D2F )\u22121(D1F ). Finally, the computation of \u0307j is straightforward. Suppose that a transition point on tube a \u2208 {1, . . . , n} defines the start of link j and a transition point on tube b \u2208 {1, . . . , n} defines the end of link j (see Figure 1). Then, the time derivatives of the arc parameters are given by \u03ba\u0307j = \u2212\u2202\u03baj \u2202\u03c8 ( \u2202F \u2202\u03c8\u2217 )\u22121 \u2202F \u2202q q\u0307, \u03c6\u0307j = \u2212\u2202\u03c6j \u2202\u03c8 ( \u2202F \u2202\u03c8\u2217 )\u22121 \u2202F \u2202q q\u0307, \u0307j = \u03c1\u0307b \u2212 \u03c1\u0307a. (7) Recalling that \u0394\u03c6j = \u03c6j \u2212\u03c6j\u22121, the total Jacobian matrix Js st in the expression V s st = Js stq\u0307 (8) is found by combining (6) and (7). Since our initial concern is with linear end effector velocities, we simplify V s st = ( g\u0307g\u22121 )\u2228 = Js stq\u0307 to obtain an expression for linear velocity, p\u0307, of the cannula tip in world coordinates, as follows"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000360_12.786940-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000360_12.786940-Figure1-1.png",
        "caption": "Fig. 1. Experimental setup for Infra-Red camera and pyrometer monitoring of Selective Laser Melting on Phenix PM100TM machine",
        "texts": [
            " 6985, 698505, (2008) \u00b7 0277-786X/08/$18 \u00b7 doi: 10.1117/12.786940 Proc. of SPIE Vol. 6985 698505-1 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/26/2013 Terms of Use: http://spiedl.org/terms 2. EXPERIMENTAL SETUP Visualisation of the SLM process was carried out by an infra-red camera FLIR Phoenix RDASTM with InSb sensor: 3 to 5 \u00b5m band pass arranged on 320x256 pixels array cooled down to 77K. The camera was placed inside the furnace of the Phenix PM100TM SLM system according to the following setup (see Fig. 1). A 25 mm objective was used, coupled to ring lengthening piece in order to increase magnification and improve spatial resolution. In the experimental setup given on Fig. 1, one pixel of camera is found to correspond to 100 \u00b5m. Laser spot size for SLM is estimated to be near 80 \u00b5m. Proc. of SPIE Vol. 6985 698505-2 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 08/26/2013 Terms of Use: http://spiedl.org/terms The integration time was set to 0.05 ms with neutral density filter (attenuation factor = 100). The acquisition frequency can be varied from 2031 Hz up to 3556 Hz by reducing the size of the imaging window, from 136x64 down to 136x32. The pyrometer system comprises: a separated optical head connected to an electronic unit by optical fibre providing the possibility of installing the pyrometer optical head directly into the laser optical head; an internal microprocessor intended to control the instrument operating modes: calibration, measuring (choice of the acquisition period and total duration of the measurements, minimum and maximum temperature values, etc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002983_b978-0-12-811820-7.00008-2-Figure6.3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002983_b978-0-12-811820-7.00008-2-Figure6.3-1.png",
        "caption": "FIGURE 6.3 Calculation results of the thermal model: (A) temperature distribution (in \u00b0C) during AM; (B) temperature history of selected RVEs (nodes).",
        "texts": [
            "3) where U represents the electron beam acceleration voltage, I is the electron beam current, \u03b7 represents the absorption efficiency, fs represents the process scaling factor, x, y and z are the local coordinates of the heat source, a1, b1 and c1 are the transverse, depth, and longitudinal dimensions of the ellipsoid, respectively, vQ represents scanning speed of the heat source, and t is the scanning time. The resulting temperature distribution within the build during the AM process and the thermal history in a selected representative volume element (RVE) are shown in Figure 6.3. With the temperature distribution and history at hand, the \u03b2 grain growth behavior during AM is then investigated using a grain-scale phase-field model. In this model, the texture (crystallographic orientation of each grain) in a simulation cell is specified by a set of continuous order parameters. The total free energy of a polycrystalline microstructure system can be described as follows [65,66] F = \u222b [ f0(\u03c61, \u03c62, ..., \u03c6Q) + Q\u2211 q=1 \u03baq 2 (\u2207\u03c6q)2 ] dr (6.4) where {\u03baq} are positive gradient energy coefficients, and f0({\u03c6q}) is the local free energy density, which is defined as f0 ({\u03c6q}) = \u2212\u03b1 2 Q\u2211 q=1 \u03c62 q + \u03b2 4 ( Q\u2211 q=1 \u03c62 q )2 + ( \u03b3 \u2212 \u03b2 2 ) Q\u2211 q=1 Q\u2211 s>q \u03c62 q\u03c62 s (6",
            " Under low cooling rates (1 K/s), the system can stay at the hightemperature regime for a sufficiently long time, so that the \u03b1 nuclei can grow larger, which, on the other hand, retards the further nucleation of \u03b1 products. For a specific RVE in the macroscopic thermal model, its thermal history during AM involves multiple cooling/heating cycles with non-constant cooling/heating rates. Based on the thermal history calculations, the cooling/heating rates increase significantly when the RVE is near the heat source, and the overall effect for the multiple thermal cycles is a cooling process, as shown in Figure 6.3B. Therefore, in a RVE of the thermal model, below the \u03b2 transus, after each cooling/heating cycle, the \u03b1 products will form and dissolve, while the overall effect is the formation of certain amount of \u03b1 products without dissolution. The \u03b1 products left over after a cooling/heating cycle are generally the ones formed at the earlier stages during the previous cooling process, which will also affect the formation of subsequent \u03b1 products. Therefore, it is critical to understand the formation and growth sequence of \u03b1 products during cooling, especially in polycrystals",
            " The sub-grain microstructure evolution varies with the specific material systems. The current sub-grain phase-field model focuses on the \u03b2 \u2192 \u03b1 transformations, which is the major cause for microstructure evolution during AM of Ti-6Al-4V. Specifically for this system, the phase-field model has been extended for non-isothermal simulations. However, it is still numerically challenging to consider the realistic thermal history of a RVE using the current model due to the rapid thermal cycles (e.g., cooling/heating rates \u223c5000 K/s in Figure 6.3B). The extension of the current model to these extreme cases would definitely be worthwhile pursuing for the understanding of sub-grain microstructure evolution during AM. For other materials systems, the phase transformations in sub-grain scale can become more complicated. For example, during AM of superalloy IN718, different types of precipitates can appear at GBs and/or inside grains, including the Laves phase, \u03b4-Ni3Nb, \u03b3 \u2032-Ni3Al and \u03b3 \u2032\u2032-Ni3Nb precipitates, which have different effects on the mechanical properties of the build"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001565_j.mechmachtheory.2014.12.019-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001565_j.mechmachtheory.2014.12.019-Figure2-1.png",
        "caption": "Fig. 2. Coordinate transformation.",
        "texts": [
            " The homogeneous coordinate transformations between the two coordinates (t, n, b) and (x, y, z) can be obtained through three transformations. One, the origin of the global coordinate system is translated to the intersection pointH along the helix line, which ismarked as Trans(rm cos \u03b8, rm sin \u03b8, rm\u03b8 tan\u03b1). Two, the global coordinate system is rotated around the z axis by (\u03b8+ \u03c0/2)-degree to make x and y axes coincident with t\u2032 and n\u2032 axes which are the projections of t and n axes on the x \u2212 y plane, and is marked as Rot(z, \u03b8 + \u03c0/2), as shown in Fig. 2(a). Three, the global coordinate system is rotated around y axis by (2\u03c0 \u2212 \u03b1)-degree, which is marked as Rot(y, 2\u03c0 \u2212 \u03b1), as shown in Fig. 2(b). According to the homogeneous coordinate transformation, the relation between two coordinates (t, n, b) and (x, y, z) is given as: x y z 1 2 664 3 775 \u00bc Trans rm cos\u03b8; rm\u03b8 tan\u03b1\u00f0 \u00deRot z; \u03b8\u00fe \u03c0=2\u00f0 \u00deRot y;2\u03c0\u2212\u03b1\u00f0 \u00de \u00bc 1 0 0 rm cos\u03b8 0 1 0 rm sin\u03b8 0 0 1 rm\u03b8 tan\u03b1 0 0 0 1 2 664 3 775 cos\u03b8 \u00fe\u03c0=2\u00f0 \u00de \u2212 sin\u03b8 \u00fe\u03c0=2\u00f0 \u00de 0 0 sin\u03b8 \u00fe\u03c0=2\u00f0 \u00de cos\u03b8 \u00fe\u03c0=2\u00f0 \u00de 0 0 0 0 1 0 0 0 0 1 2 664 3 775 cos2 \u03c0\u2212\u03b1\u00f0 \u00de 0 sin2 \u03c0\u2212\u03b1\u00f0 \u00de 0 0 1 0 0 \u2212 sin2 \u03c0\u2212\u03b1\u00f0 \u00de 0 cos2 \u03c0\u2212\u03b1\u00f0 \u00de 0 0 0 0 1 2 664 3 775 \u00bc \u2212 cos\u03b1 sin\u03b8 \u2212 cos\u03b8 sin\u03b1 sin\u03b8 rm cos\u03b8 cos\u03b1 cos\u03b8 \u2212 sin\u03b8 \u2212 sin\u03b1 cos\u03b8 rm sin\u03b8 sin\u03b1 0 cos\u03b1 \u03b8L 2\u03c0 0 0 0 1 2 6664 3 7775 t n b 1 2 664 3 775 \u00f01\u00de where the L is the length of the screw's pitch"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000656_1.58028-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000656_1.58028-Figure2-1.png",
        "caption": "Fig. 2 The Georgia Institute of Technology Twinstar UAS: the GT Twinstar is a fixed wing foam-built UAS designed for FTC work.",
        "texts": [
            " VI, and flight-test results with MRAC under structural faults are presented in Sec. VII. The adaptive-loop transfer recoverymethod is introduced in Section VIII, and flight-test results with injected actuator time delays are presented in Sec. VIII. The paper is concluded in Sec. IX. Flight testing of FTC algorithms for safe flight in the presence of severe structural faults has been performed at the UAV Research Facility at theGeorgia Institute of Technology. These flight tests were performed on the GT Twinstar fixed wing unmanned aerial system (UAS). The GT Twinstar (Fig. 2) is a foam-built, twin engine aircraft based on the Multiplex Twin Star II model airplane. It has been equipped with an off-the-shelf autopilot system. The control algorithms discussed in this paper were implemented on the autopilot system through custom-developed software. The autopilot system comes with an integrated navigation solution that fuses information using an extendedKalman filter from six degrees-of-freedom inertial measurement sensors, Global Positioning System, air data sensor, and magnetometer to provide accurate state information [27]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002453_s11071-019-04780-6-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002453_s11071-019-04780-6-Figure4-1.png",
        "caption": "Fig. 4 Equivalent spring model of the oil film normal stiffness",
        "texts": [
            " At each mesh position of the spur gear mesh cycle, the film pressure, p(x, t), is obtained by solving Eq. (13), and the film thickness, h(x, t), is obtained by using Eq. (15). If an applied load increment, w(t), that is derived from the known quasisteady state load spectrum of a spur gear transmission [22] is given, the film pressure increment, p(x, t), and the compression deformation increment of the film thickness, h(x, t), can be obtained. As the viscouselastic fluid, the oil film between the meshing gear pair is modeled as a massless spring element shown in Fig. 4. Hence, the oil film normal stiffness is derived as [22], ko (t) = Fn h = B \u00d7 k \u2211n i=1 p (x, t) 1 n \u2211n i=1 h (x, t) (23) where B denotes the face width. denotes increment and k represents the grid size in the rolling direction. n is the nodal numberwithin the nominal contact domain. 3.3 Oil film normal damping In one mesh cycle of spur gear transmission, both the fluid pressure and film thickness in transient elastohydrodynamic contact are re-calculated at each mesh position along LOA, which makes it possible to gain the compression speed of the oil film in the direction across film thickness"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001471_j.mechmachtheory.2014.07.013-Figure11-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001471_j.mechmachtheory.2014.07.013-Figure11-1.png",
        "caption": "Fig. 11. Profile error.",
        "texts": [
            "fe \u00b1 f1. Fig. 10 represents the spectral of dynamic component Y1 on the first stage for the resulting eccentricity e12 = 50 \u03bcm. This figure shows that the response of the first stage (Y1) is characterized by the appearance of sidebands around the meshing frequency (fe1) excited by the fault and its harmonics. These bands are located at frequencies nfe1 \u00b1 f1. 7.2. Modeling of profile error Profile errors are representative of discrepancies between the theoretical profile and the real tooth profile (Fig. 11); the theoretical profile may be involute, parabolic form or have a body if it has been corrected. These errors may be generated duringmanufacture or during operation by thewear and tear of the profiles. It can be repeated from one tooth to the other or it can be located on a number of teeth. In the following, we supposed that the wheel (12) has a uniform profile error on all teeth. The error in profile is modeled by deformations normal to the surface: W1.n [9] W1 u12; r12\u00f0 \u00de \u00bc A1 cos B1:Ac u12\u00f0 \u00de \u00fe r12\u00f0 \u00de:C1\u00f0 \u00de: \u00f040\u00de A1 is the amplitude parameter of the function, B1 is the orientation parameter and C1 define their period"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002120_j.mechmachtheory.2015.09.010-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002120_j.mechmachtheory.2015.09.010-Figure8-1.png",
        "caption": "Fig. 8. Presetting position of drive gear.",
        "texts": [
            " 6 shows the stock profile in which (a) is the stock profile of the drive gear and (b) is the stock profile of the driven gear. Both the stock and its corresponding fixture were fabricated and assembled as exhibited in Fig. 7. To avoid undercutting and pointed teeth, the parameters of the shape cutter were set in term of Ref. [15]. Table 2 presents the parameters of the shape cutter. The presetting position of each axis was calculated using Eqs. (48), (49), (50), and (51) (as shown in Table 3). Fig. 8 illustrates the shape of the cutter and the presetting position of the drive gear. Because of a linear interpolation method of the CNC system, theoretical errors depend on the processing step setting [30], regardless if the error was caused by the cutter, machine or material. Taking the drive gear as an example, the total processing steps were set as Ne \u00bc 5000: Thus the step length of equal-polar angle cutting obtained for the maximal polar angle of drive gear is 2\u03c0. \u0394\u03c6 \u00bc 2\u03c0=Ne \u00bc 0:00126rad \u00bc 0:072deg While the step length with equal-polar angle cutting is obtained in term of Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000648_978-3-642-17531-2-Figure4.26-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000648_978-3-642-17531-2-Figure4.26-1.png",
        "caption": "Fig. 4.26. Concrete implementational variants of the generalized free two-mass oscillator: a) longitudinally vibrating rod, b) torsion rod, c) drive train with elastic gearbox and load, d) two-arm manipulator with elastic Joint 2",
        "texts": [
            " Generalized measurement variable Deeper insight into the migration pattern of the zeros is achieved by considering a linear combination of the generalized coordinates of the two bodies as a generalized measurement variable: 1 1 2 2 z y y . (4.78) With a suitable choice of 1 2 , , a variety of measurement principles can be modeled: variable measurement location: 1 2 (1 )z L y y , 0 1 , 1 1 , 2 , see Fig. 4.25, relative measurement: 1 2 z y y , 1 2 1, 1 . Implementation example of variable measurement location By varying the parameter , the measurement location can be continuously varied between Body 1 and Body 2. Physically, such a case is present in linearly elastic longitudinally vibrating rods (Fig. 4.26a), torsion rods (Fig. 4.26b) or elastic gearboxes (Fig. 4.26c). Over the length of the rods, there is a linearly increasing deformation of the form 1 2 1 1 2 (1 ) y y z y L y y L , which can be measured with a position sensor attached at the location y L (Miu 1993). Implementation example of coupled mass matrix In translational and rotational oscillator chains, there is always a decoupled (diagonal) mass matrix. However, considering, for example, a two-arm manipulator (see Example 4.2 and Fig. 4.26d), coupling terms 12 0m also come into play, cf. Eq. (4.35). Parametric response characteristics Using Eqs. (4.76) and (4.78), the generalized response given excitation by 1 F can be calculated: 1 2 / 1 2 1 11 22 12 0 ( ) ( ) ( ) 2 z z F Z s G s F s m m m s . (4.79) The antiresonance frequency which results is 2 1 2 1 22 2 12 z k m m . (4.80) 274 4 Functional Realization: Multibody Dynamics Parametric analysis of zeros: variable measurement location With the substitution for 1 2 , given above, 1 2 1 , so that it holds for the antiresonance frequency that 2 22 22 12 1 ( )z k m m m "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003237_j.matdes.2020.108824-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003237_j.matdes.2020.108824-Figure7-1.png",
        "caption": "Fig. 7. Residual stress distribution along trajectory pom: (a) the path definition, (b) the longitudinal stress, (c) the transverse stress.",
        "texts": [
            " The radial compressive stress in some areas of the coating is transformed into radial tensile stress in the case with SSPT. This may be caused by self-balancing stress in three directions. The stress reduction of the coating in X direction and Z direction will make the coating to shrink inward in these two directions. Meanwhile, the coating expands outward in Y direction to form tensile stress in Y direction. In order to further confirm the influence of SSPT on stress distribution, the transverse stress and longitudinal stress of the path pom in Fig. 7 (a) are extracted. Fig. 7 (a), (b) and (c) respectively show the path pom, the longitudinal stress and the transverse stress along the trajectory pom. When SSPT is considered, the longitudinal residual stress of the coating is obviously reduced and changes from tensile stress to compressive stress on both sides of the coating. The longitudinal residual compressive stress on the substrate is also slightly reduced. The stress distribution with SSPT is more consistent with the experimental value in Fig. 7 (b). Fig. 7 (c) shows that the surface of the substrate is basically in a low transverse stress state and gradually transits to tensile stress towards the coating. The tensile stress reaches the maximum at the junction of the substrate and the coating, and begins to decrease toward the middle of the coating. From the above, SSPT has an obvious effect on the final stress distribution of laser cladding Fe-Mn-Si-Cr-Ni alloy coating. The above simulation results have shown that the stress-induced transformation of austenite to martensite can reduce the residual stress generated in laser cladding, but the microstructure of coating isn\u2019t clear and the evidence of stress release isn\u2019t insufficient"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000004_iros.2010.5650416-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000004_iros.2010.5650416-Figure4-1.png",
        "caption": "Fig. 4: When pd, the CoP corresponding to the desired GRF fd (dotted arrow), is outside the support base, it is not admissible. When the CoP is made admissible by moving it within the support surface, the robot cannot satisfy both linear and angular momenta objectives. Two extreme solutions are illustrated. One is to fully respect linear momentum objective by sacrificing angular momentum (left) and the other is the opposite (right). One can choose a solution between the two extremes.",
        "texts": [
            " While GRF and CoP are uniquely determined from the desired rates of changes of linear and angular momenta during single support, there can be infinitely many solutions for double support. Hence we consider each case separately. 1) Single Support Case: When GRF and CoP computed from the desired momentum rate change (eqs. (1) and (2)) are admissible, we can directly use them. If not, it means that we cannot simultaneously satisfy both l\u0307d and k\u0307d, and hence we need to find an optimal GRF and CoP that will create admissible momentum rate change as close as possible to the desired values. Fig. 4 shows two extreme cases for determining f and p. The first case, left, fully respects linear momentum by laterally shifting the GRF without changing its direction, i.e., the robot puts higher priority to controlling CoM position (related to linear momentum) over body pose (related to angular momentum). As a result, given a large perturbation, rapid rotation can be generated to keep linear momentum under control. This strategy can be seen from humans when they rotate the trunk or arms forward to maintain balance given a forward push. Fig. 4 at right, after the lateral shift, the GRF line of action is rotated to fully respect angular momentum such that p and f satisfy k\u0307d = (p \u2212 rG) \u00d7 f . However, linear momentum is no longer respected, i.e., the robot puts higher priority to keep the desired pose (angular momentum) over its desired location (CoM). In this case, the uncontrolled linear momentum can make CoM to go too far, making it necessary to take a step in order to avoid a fall. In this paper, we choose the first strategy to increase the capability of postural balance controller"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000351_09544062jmes1844-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000351_09544062jmes1844-Figure4-1.png",
        "caption": "Fig. 4 (a) Main points of the mesh cycle along the line of action and long linear/circular PM and (b) qualitative sketch of a tooth with (exaggerated) tip PM",
        "texts": [
            " After each static analysis (practically, the rotation of the gear is applied as a ramp; this rotation is subdivided into increments, each of which corresponds to a static analysis), the constraints that prevent the gear rotation and the torque are removed; then a predetermined rotation is applied to the gear only, since the pinion will be dragged; the system will then move to the position for the next analysis. The constraints are then re-established, and the system is ready for a new static analysis. This procedure is automatically completed by ABAQUS/STANDARD. Following this procedure, it is possible to analyse the whole meshing of a teeth pair (from point A to point D of Fig. 4), analysing it in any position. It is worth noting that these analyses are static, and then they do not include any dynamic effect. On the other hand, if a dynamic analysis is performed considering the gear set only, it will not supply reliable information about the dynamic behaviour of the actual gear mounted in a transmission, since this behaviour is greatly influenced by the inertia, stiffness and damping of the other components of the transmission (shafts, bearings, etc.). In order to reduce the computational effort, therefore, one of the more common practices consists in first determining the static TE (i",
            " Figure 7 shows the load sharing during the theoretical meshing cycle of a teeth pair of the gear set without PM. The load transfer from a tooth pair to the next is not smooth: PMs are the common solution to solve this problem. Hence, a new model with PM has been developed. In order to better reveal the differences between the different shapes of PM, the connection between the modified and the unmodified tooth flank zones has not been rounded, even though this round is always present in practical PM. A long PM [22] has been introduced (Fig. 4). The modifications have been applied to the tip of the gear and of the pinion teeth. Both pinion and gear modifications have been designed for a torque of 100 Nm, corresponding to the working condition where noise emission has to be limited, but that is lower than the maximum admissible torque of the gear itself. The amounts of the modifications (Ca = Ca\u2032 = 6 \u00b5m, Fig. 4) have been calculated by means of the following relationship [23] Ca = Ca\u2032 = Fbt c\u03b3 (1) where Fbt is the load acting on the tooth along the line of action in the transverse section and c\u03b3 is the meshing stiffness computed according to the ISO standards [24]. Figure 8 shows the TE for the theoretical meshing cycle of a teeth pair at several loads. As expected, the TE at the PM design torque is approximately constant, while at the other loads the TE oscillates around the mean value: these oscillations, depending on the system dynamic response, could become the source of vibrations and noise. Let us now proceed to analyse and discuss circular modifications (Fig. 4). In order to evaluate the influence of the shape only, the starting point and the amount will not vary. Figure 9 shows the resulting TE. It can be easily noticed that the TE curve with minimal oscillations does not correspond to the PM design load (100 Nm), but to a lower load: this consideration can be generalized stating that equation (1) (with meshing stiffness computed according to ISO standards) is not always suitable for computing the amount of non-linear PM. To better understand this phenomenon, several models have been analysed",
            " The maximum contact pressure (extracted from the CPRESS output variable) is presented and is used to compare gears with linear or circular PM; therefore the contact pressure presented hereafter are not intended to be an indicator of gear surface resistance. The main data of the sample gear set are listed in Table 1, while Table 2 summarizes the microgeometries that have been analysed. Figures 11 to 15 show some of the results of the analysis during the theoretical meshing cycle of one teeth pair (from point A to point D of Fig. 4). Figure 11 shows the maximum contact pressure and maximum principal stress of a gear without any PM: these results are the baseline for evaluating the performance of modified gears. Amount 6 \u00b5m 15 \u00b5m None NOPM Linear LLPM6 LLPM15 Circular CLPM6 CLPM15 Figures 12 and 13 show a comparison between the maximum contact stress and the maximum principal stress of a gear with 6 \u00b5m linear and circular PMs. Figures 14 and 15 show a similar comparison for gears with 15 \u00b5m PM. The contact pressure peaks that occur in gear sets with linear PM during the transition from the two meshing pairs to the one meshing pair and vice versa (since long PMs have been adopted, these zones correspond to points B and C of Fig. 4) are mainly due to the profile tangency discontinuity introduced with linear PM shaped as depicted in Fig. 4. These peaks are practically avoided by rounding the transition between the modified and the unmodified zones of the tooth flank. The beneficial effects of PM are quite evident; in particular, the load transfer from one tooth pair to the next is smoother. Even though this consideration cannot be immediately generalized, a comparison between maximum Proc. IMechE Vol. 224 Part C: J. Mechanical Engineering Science JMES1844 at CARLETON UNIV on May 10, 2015pic.sagepub.comDownloaded from principal stress and contact pressure of gear sets with linear and circular PMs of the same amount do not highlight any notable differences"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002838_978-3-319-54169-3-Figure5.1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002838_978-3-319-54169-3-Figure5.1-1.png",
        "caption": "Fig. 5.1 Model of the cutting mechanism",
        "texts": [
            " The steady-state motion of the system with ideal and non-ideal forcing is also analyzed. The chapter ends with conclusion. 5.1 Structural Synthesis of the Cutting Mechanism 143 The structure of cutting mechanism is required to satisfy the following: \u2022 the mechanism has to transform the input rotating motion into the translator one \u2022 the cutting element has to move translatory \u2022 the cutting process has to be duringmotion of the cutting element from up to down. To fulfil these requirements, in this Chapter a device which contains two slidercrank mechanisms is suggested (see Fig. 5.1). The system is designed to have an eccentric O1AB and a simple O2DE slider-crank mechanism which are connected with a rod BC . The leading element of the mechanism is the crankshaft O1A, while the slider is the cutting tool at the point E . The suggested mechanism converts the rotating motion of the crankshaft O1A into a straight-line motion of the slider E . Mechanism has the following elements: O1A = a, AB = b, BC = c, O2C = r , O2D = g, DE = h. The position of the slider B of the eccentric slider-crank mechanism O1AB (see Fig. 5.1) is given with the coordinates 144 5 Dynamics of Polymer Sheets Cutting Mechanism Eliminating \u03b8 in Eqs. (5.1) and (5.2) we obtain the position of the slider B as a function of the leading angle \u03d5 yB = \u2212a sin\u03d5 + b \u221a 1 \u2212 ( l \u2212 a cos\u03d5 b )2 . (5.3) For the simple slider-crank mechanism O2DE (see Fig. 5.1) the translatory motion of the slider is described as O2E = g cos \u03b3 + h cos\u03c8, (5.4) where the relation between the angles \u03b3 and \u03c8 is given with the expression g sin \u03b3 = h sin\u03c8. (5.5) Substituting Eq. (5.5) into Eq. (5.4) we have O2E = g cos \u03b3 + h \u221a( 1 \u2212 g2 h2 ) + g2 h2 cos2 \u03b3. (5.6) which describes the position of the slider E as a function of the leading angle \u03b3 of the slider-crank mechanism O2DE . Let us make the connection between these two slider-crank mechanisms. Due to the fact that after connection with the rod BC the two slider-crank mechanism remains an one-degree-of-freedom system (as it was the case for the simple and eccentric slider-crank mechanisms), we have to determine the relation between the position of the slider E and leading angle \u03d5 of the crankshaft O1A. From Fig. 5.1 it is evident that the position of the slider E in the coordinate system xO1y is yE = p + O2E . (5.7) Moreover, w = c cos\u03c7 + r sin \u03b3, (5.8) yB + c sin\u03c7 = p + r cos \u03b3. (5.9) Eliminating \u03c7 in Eqs. (5.8) and (5.9) the yB \u2212 \u03b3 i.e., \u03d5 \u2212 \u03b3 expression is obtained as ( c2 \u2212 w2 \u2212 r2 \u2212 (p \u2212 yB)2 \u2212 2r(p \u2212 yB) cos \u03b3 )2 = 4w2r2(1 \u2212 cos2 \u03b3), (5.10) i.e., A2 cos 2 \u03b3 \u2212 A1 cos \u03b3 + A0 = 0, (5.11) 5.1 Structural Synthesis of the Cutting Mechanism 145 where A = c2 \u2212 w2 \u2212 r2 \u2212 (p \u2212 yB)2, A0 = A2 \u2212 4w2r2, A1 = 4Ar(p \u2212 yB), A2 = 4r2 ( (p \u2212 yB)2 + w2 ) , (5",
            " In our consideration the common assumption used for comparing the three mechanisms is that the cutting depth has to be equal and the cutting angle is calculated from the lowest position of the slider. In Fig. 5.2 the full line indicates the motion of the slider in the sheet (where the shaded area is for cutting) and the dotted line shows the 146 5 Dynamics of Polymer Sheets Cutting Mechanism Fig. 5.3 yB \u2212 \u03d5 diagrams for a simple slider-crank mechanism (Fig. 5.2a), b eccentric slider-crank mechanism (Fig. 5.2b), and c yE \u2212 \u03d5 diagram for two-joined slider-crank mechanism (Fig.5.1) with following notation: shaded area - cutting, dotted line - slider in the sheet, full line-slider out of sheet motion of the slider out of the sheet. Comparing the diagrams in Fig. 5.3, it can be concluded: 1. Cutting lasts more longer with the simple and eccentric slider-crank mechanism than with the two joined slider-crank mechanism. 2. The interval in which the slider (cutting tool) is above the cutting object is much longer for the two joined slider-crankmechanism than for the simple and eccentric one"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001982_j.triboint.2015.09.004-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001982_j.triboint.2015.09.004-Figure6-1.png",
        "caption": "Fig. 6. Diagram of the test rig.",
        "texts": [
            " Therefore, the temperature value of each node at any moment can be numerically solved when the ambient temperature value and the time step \u0394t are initially defined [30]. A type of 24013 double-row spherical roller bearing is chosen as the theoretical calculating model and testing bearing, with its main parameters listed in Table 1. The bearing is lubricated with Al-complex lubricating grease manufactured by SINOPEC, with its main parameters listed in Table 2. In order to validate the model proposed in this paper, a test rig is design to measure the outer ring temperature rise of a greaselubricated spherical roller bearing, shown in Fig. 6. The testing bearing 4 with the main shaft 2 is mounted in the bearing housing 5. The testing bearing 4 is filled with a certain quantity of Alcomplex grease, while the bearing housing 5 is also filled with some grease. The testing bearing 4 is driven by a motor 8 via the coupling 7. The rotating speed of motor 8 is adjusted by a frequency converter, while its speed is monitored by an infrared velocimeter 6. The dead weight of the weights 12 as the radial load is applied to the test bearing via the lever 11 and the loading component 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001198_j.ijsolstr.2014.06.023-Figure18-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001198_j.ijsolstr.2014.06.023-Figure18-1.png",
        "caption": "Fig. 18. Film/Sub III under the second step of compression along the y direction. The left column shows a sequence of wrinkling modes Dv corresponding to its critical load determined by bifurcation indicators. The right column presents the associated instability modes Dv3 at the line Y \u00bc 0:5Ly: (b) the 1st mode, (d) the 2nd mode.",
        "texts": [
            " The sequence of wrinkling modes Dv corresponding to the bifurcation loads and their associated instability modes Dv3 are illustrated in Fig. 17. The first mode is modulated in a sinusoidal way while the second one corresponds to a quasi-uniformly distributed oscillation. During the second step of compression along the y direction, two bifurcations have been captured by computing bifurcation indicators (see Fig. 16(b)). The erboard pattern v in the final step, (b) the final shape v3. first mode shows aperiodic wrinkles (see Fig. 18(a) and Fig. 18(b)), where the perfect periodicity in Fig. 17(d) has been broken by the new bifurcation. Such a loss of periodicity had been previously discussed in Sun et al. (2012), Cao and Hutchinson (2012a,b), Cao et al. (2012), Zang et al. (2012) and Xu et al. (submitted for publication), where period-doubling or even period-quadrupling is observed. Here, the periodicity is broken by the appearance of 3D wrinkling patterns and one can wonder in which cases the sinusoidal modes lose their stabilities by the occurrence of period-doubling or 3D wrinkling modes. The herringbone mode (see Fig. 17(d) and olumn shows a sequence of wrinkling modes Dv corresponding to its critical load ty modes Dv3 at the line Y \u00bc 0:5Ly: (b) the 1st mode, (d) the 2nd mode. Fig. 18(d)) appears around the second bifurcation with an in-plane wave occurring along the y direction in order to satisfy the minimum energy states (Chen and Hutchinson, 2004; Audoly and Boudaoud, 2008b). Apparently, the wavelength ky is larger than the sinusoidal wavelength kx, which is consistent with the experimental results in Yin et al. (2012). A symmetric phase shifting can be obviously seen in the final step (see Fig. 19), which justifies that the new in-plane wave spreads along the y direction while oscillates in the x direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003049_s12555-018-0720-7-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003049_s12555-018-0720-7-Figure1-1.png",
        "caption": "Fig. 1. Quadrotor architecture [24].",
        "texts": [
            " Section 4 presents simulations results for position trajectory tracking, whereas the conclusions are presented in Section 5. 2. MATHEMATICAL MODEL 2.1. Equations of motion In this section, a description of the main mathematical equations for the quadrotor are explained. The equations of motion for the quadrotor were derived by relying on two reference frames: the Earth inertial reference frame (Rb) is defined by axes (Xb,Yb,Zb) with Zb axis pointing upward, and the body-fixed reference frame (Rm) is defined by axes (Xm,Ym,Zm) in Fig. 1. The angular position (or attitude) of the quadrotor is defined by the orientation of the Rm with respect to the Rb by the rotational matrix R, whereas position p is defined on the Rb . In order to understand the model dynamics developed in this work, the hypotheses presented in [25] was adopted \u2022 The structure of the quadrotor is assumed to be rigid and symmetric. \u2022 The propellers are rigid \u2022 Thrust and drag forces are proportional to the square of the rotors speed. \u2022 The center of mass and origin of the coordinate sys- tem related to the quadrotor structure coincide Using the Newton-Euler formulation, the equations of UAV motion are written in the following form: P\u0307 = v, mP\u0308 =  0 0 \u2212mg +R 0 0 T + Fax Fay Faz + dpx dpy dpz  , R\u0307 = R\u2126\u0302, J\u2126\u0307 =\u2212\u2126\u2227 J\u2126+ \u03c4 \u2212Mg +Ma +dr, (1) where m, g and J denote the total mass, the gravitational constant, and the inertial matrix respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000184_05698197208981427-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000184_05698197208981427-Figure2-1.png",
        "caption": "Fig. 2-Grease WL inlet region of rollers",
        "texts": [
            " Such a conclusion does not seem to be warranted in light of the results shown in Fig. 1. Experimental viscometer results for grease presented by Scholten and by Pavlov and Vinogradov (13) approaching shear rates of lo5 to los sec-I support the validity of extrapolating a curve based on Eq. [ I ] to shear rate levels encountered in EHL film thickness calculations for rollers. However, the extrapolated curve would not be expected to cross over the flow curve for the grease base oil. EHL THEORY The two-dimensional flow inlet region of a pair of rollers is shown in Fig. 2. The usual assumptions of negligible side leakage, inertia, gravity, and y and z velocity components are taken. The rollers of radius R1 and R:, are elastically deformed by an applied load per unit roller width. In real rollers it is usual to find the half Hertzian length much larger than the film thickness, but this plot was designed to fit a hypothetical case discussed later. D ow nl oa de d by [ U ni ve rs ity o f A ri zo na ] at 1 5: 11 1 4 D ec em be r 20 12 Elastohydrodynamic Lubrication With Herschel-Bulkley Model Greases 271 As the grease is dragged into the inlet by the moving surfaces of the rollers, a complicated forward-and-reverse flow pattern a t low pressure is depicted a t the far left",
            "2 X lo4 sec-I, except No. 8. ( 0 ) Presheared a t D = 5 X lo4 sec-1. (d) Small preshear history. ( 0 ) ?(grease) falls below base oil) a t max. shear rate. D ow nl oa de d by [ U ni ve rs ity o f A ri zo na ] at 1 5: 11 1 4 D ec em be r 20 12 in practice, and no further analysis of this possibility need be considered. FLOW PATTERN IN THE INLET If (+/rl/) is indc:.xident of pressure, Eq. [12] or [13] can be solved to find the variation of the width of the plug flow region. Results are plotted in Fig. 2 for a Bingham plastic assuming the nontypical value for (+oU/r,,ko) = 10. The plug width narrows to very low values immediately before the parallel section and stays small until the inlet has widened to ten times the minimum width. For larger values of (+OU/~,o/tO) the plug region becomes too narrow to show. Tt follows that in Eq. [IS] X must be very close to 3/2, and that the factor giving the effect of the yield stress on film thickness from Eq. [26] is very close to [I + 2.25(~,ho/ +oU)I. Ultimately the plug widens to fill the inlet. That is, //,,/I/--t 1 ; but the width of the shear zone (h - h,) continues to increase. T o find the velocity of the plug flow region, substitute from Eq. [11] into Eq. [9] and get so th:~t once the variation of It, has been found, the local plug velocity is determined and the complete velocity prolile easily follows. These are shown in Fig. 2. rt is clear that the plug is not a solid, moving as a rigid body. Although it moves through the parallel section with the velocity of the rollers, further out it moves more slowly, and a t large distances it moves backwards out of the inlet. 'I'his, of course, esactly parallels the flow field for oils. An interesting difference is that instead of the backward velocity steadily increasing to U/2 a t greater distances, the plug slows down again and ultimately comes to rest-a more pl:wsible behavior than that of oil",
            " The agree- ment between theory and test for the grease to oil film ratio is good for the Klein-milled grease, but clearly the isothermal theory is incorrect for virgin grease. Shear rate and temperature rise are examined in the next sections as a possible explanation for the experimental results. SHEAR RATE AND PRESSURE DISTRIBUTION An analysis for the shear rate encountered in the entrance region of rollers with the Herschel-Bulkley flow model of Eq. [I], neglecting the yield stress, is carried out following a similar analysis presented by Dyson and Wilson (14) for a Newtonian fluid. I t can be seen from the flow field sketched in Fig. 2 and from Eq. [3] that the maximum shear rate occurs a t the wall of the rollers. Thus, setting y = h/2 and 7, = 0 in Eq. [5] and rearranging gives The pressure distribution in the inlet is plotted in Fig. 7 along with the shear rate a t the wall. The power law esponent has little effect on the pressure distribution, and Fig. 7 shows that the pressure rise is concentrated over a very small distance in the rollers inlet. These curves are D ow nl oa de d by [ U ni ve rs ity o f A ri zo na ] at 1 5: 11 1 4 D ec em be r 20 12 not exact, due to the assumptions leading to Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003888_j.jallcom.2020.156900-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003888_j.jallcom.2020.156900-Figure6-1.png",
        "caption": "Fig. 6. CV diagrams of the NeCuO/Cu2O:NiO sensor with a) various concentrations of glucose at 25 mV/s and b) various scan rates with inset of linear relationship between square root of scan rate and peak current density.",
        "texts": [
            " The improved electrocatalytic ability of the NeCuO/ Cu2O:NiO electrode may be the result of the availability of greater catalytic active sites and a pair of electrons for conjugation, provided by the nitrogen\u2019s p-conjugated rings, introducing electron donor characteristics for the electrode [52]. Furthermore, this improved electroactivity is due to the enhanced electron transfer ability due to increase in electronic conductivity as was confirmed by the Hall effect measurement in earlier section [51,53]. The glucose sensing ability of the NeCuO/Cu2O:NiO electrode were evaluated by increasing glucose concentration from 1 mM to 5 mM (Fig. 6a). It can be clearly seen that the oxidation peak current increases significantly with increasing glucose concentration. At glucose concentration of 5 mM, the response of the sensor to glucose has started to reach saturation. For better investigation of the electrochemical behavior of the NeCuO/Cu2O:NiO sensor cyclic voltammetry studies were performed in a 0.1 M NaOH solution containing 1 mM glucose at various scan rates. The anodic and cathodic peaks current increase with an increase in scan rate applied, as shown in Fig. 6b. In addition, the reduction potential shifts negatively and the oxidation potential shifts positively with the increase of scan rate. The good linear relationship between the square root of the scan rate and the redox peak current would indicate a diffusion driven process which is a relatively fast [14,16,26] and reversible electron transfer reaction [55,56]. This linear relationship can be observed in the inset of Fig. 6b until 100 mV/s. However, at higher scan rates (200 mV/s) the reaction becomes too slow and equilibrium cannot be reached timeously, as the current takes longer to respond to the applied potential creating an irreversible electron transfer reaction [55,56]. To further understand the enhanced electrochemical performance of the NeCuO/Cu2O:NiO electrode Tafel slopes of the different developed electrodes were obtained in 0.1 M NaOH solution containing 1 mM glucose as shown in Fig. 7. The Tafel slopes followed a trend as CuO > NeCuO/Cu2O > CuO:NiO > NeCuO/ Cu2O:NiO. The lowest Tafel slope value of the NeCuO/Cu2O:NiO electrode highlights that the plasma assisted nitrogen doping and presence of NiO enhances the charge transferability of the material [24,57]. Electrochemical impedance spectroscopy was used in this study to investigate the electrochemical characteristic of NeCuO/Cu2O:NiO electrode. The Nyquist plot of the developed sensors obtained is shown in Fig. 8a and the fitted equivalent electrical circuit can be observed in the Data in Brief Fig. 6. The Nyquist plots exhibit two depressed semi-circles and a straight line in the low-frequency region. The semi-circle represented at higher frequencies region can be assigned to the double layered capacitance of the electrodeelectrolyte interaction and the overall charge transfer resistance (Rct) [35,58], the semi-circle at lower frequencies can be assigned to the faradaic reaction [59], and the linear diffusion can be modelled using a Warburg impedance (W). Constant phase elements (CPE) are used instead of a regular capacitor to achieve a more accurate modelling of the EIS data [60]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001980_e2015-50085-y-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001980_e2015-50085-y-Figure9-1.png",
        "caption": "Fig. 9. The south-pointing chariot\u2019s pointer counter-rotates the main body by an angle \u03b2p = \u2212\u03b8, such that it maintains a constant angle with respect to the global coordinates.",
        "texts": [
            " In [11], we observed thatA\u03b8 for the differential-drive car is constant (and therefore conservative) and calculated the change of coordinates that eliminates the \u03b8 row of the local connection. The new body frame we found coincides with the pointer on a south-pointing chariot [38]. This system is a two-wheeled vehicle topped by a horizontally-rotating pointer, synchronized to the wheels by a gear train. When the gear ratios are set correctly, (encoding the change of orientation function \u03b2\u03b8 = \u03b11 \u2212 \u03b12), the pointer exactly counter-rotates the body of the cart, thus maintaining its orientation with respect to the world as shown in Fig. 9. Chinese legend holds that such a device was used as a compass for coordinating military maneuvers prior to the discovery of magnetic needles, though dead-reckoning error would make this impractical and it is more likely that that the historical examples discovered were mechanical or mathematical curiosities [38]. Considering the differential-drive vehicle in the south-pointing chariot frame highlights some interesting properties of the system. First, it emphasizes the existence of a holonomic constraint between the system orientation and the wheel angles: for any given initial combination of \u03b8, \u03b11, and \u03b12, the orientation is a function of the wheel angles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003652_j.ymssp.2019.04.029-Figure22-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003652_j.ymssp.2019.04.029-Figure22-1.png",
        "caption": "Fig. 22. A 3D finite element model built in FEM.",
        "texts": [],
        "surrounding_texts": [
            "The multiple teeth damage on pinion and wheel have been studied in this subsection. Table 1 shows the number of three types of pits including slight pitting, moderate pitting and severe pitting. The distribution of pitting and the method of determining the coordinates of each pit has been given in Section 2.1. The model of a gear is established using CAD software, while these pits can be dug out based on the former determined coordinates. The damaged pinion and wheel can be found in Fig. 19(a) and (b), respectively. It can be found five consecutive teeth have slight pitting, moderate pitting, severe pitting, moderate pitting and slight pitting, respectively, while the other teeth are all health. Fig. 20(a)\u2013(f) shows the six engagement stages between pinion and wheel, representing six different meshing conditions. The mesh stiffness obtained under six meshing conditions have been separately shown in Fig. 21(a)\u2013(f). Under the meshing order shown in Fig. 20(a), the TVMS of 10 pairs of teeth is affected by pitting corrosion. Similarly, under the meshing order shown in Fig. 20(b)\u2013(f), the TVMS of 9, 8, 7, 6, 5 pairs of teeth is affected by pitting corrosion separately. Fig. 21(a) shows the TVMS of these 10 pairs of teeth corresponding to the figure in 20(a). Fig. 21(b)\u2013(f) shows the TVMS of these pairs of teeth separately. In Fig. 21(a)\u2013(e), there are two obvious peaks A and B. Meanwhile, the mesh stiffness of the gear reduces to about 4:4 108 N/m, which means that the mesh stiffness of the gear changes most when one of the pinion and wheel has severe pitting. The mesh stiffness will also be affected by moderate pitting and slight pitting, but it is not significant. Fig. 21(f) shows the TVMS of six pairs of teeth in the meshing order shown in Fig. 20(f). It can be seen that there is only one obvious peak A, which indicates that the severe pitting tooth on the pinion mesh with the severe pitting tooth on the wheel. At this time, the total mesh stiffness is close to zero. For the teeth without severe pitting, the TVMS will be reduced to some extent, but it is not so obvious. According to the meshing order in Fig. 20, it can be concluded that the reduction of mesh stiffness depends mainly on the gear with serious pitting damage. When the pitting degree of a pair of meshing gears is identical, such as Fig. 20(f), two gears will play a decisive role simultaneously. It can be found in Fig. 16 as well as the adjacent regions of A and B in Fig. 21 that similar pitting appears on the pinion and wheel, which has small effect on the overall stiffness. Therefore, the reduction of mesh stiffness is mainly related to the degree of pitting damage. Pitting occurs on both pinion and gear in the model as shown in Fig. 19, while the engagement system of the model is referred to as Fig. 20(f). Then a three-dimensional finite element model shown in Figs. 22 and 23 is established. The health teeth and gear body are mapped using hexahedral elements and the pitting teeth are mapped with tetrahedral elements in the finite element model. The tetrahedral shape is chosen for the pitting teeth as it can simulate the complicated pitting profile. Then, the pitting teeth are mapped further refined. Fig. 24 shows the results of grid stiffness comparison between the proposed method and the FEM. The engagement period of a gear is set to 18.95 . Compared with the results of FEM, in single-tooth engagement, the stiffness at moment P (h1 \u00bc 14:1 ; h2 \u00bc 33:05 ; h3 \u00bc 52 ; h4 \u00bc 70:95 ; h5 \u00bc 89:9 ; h6 \u00bc 108:85 ) and in double-tooth engagement, the stiffness at moment Q (h1 \u00bc 11 ; h2 \u00bc 29:95 ; h3 \u00bc 48:9 ; h4 \u00bc 67:85 ; h5 \u00bc 86:8 ; h6 \u00bc 105:75 ) are chosen to illustrate the comparison results between the analytical method (AM) proposed in this paper and the FEM, listed in Table 7. When the gear pitting occurs, the results between the two methods can be well matched. The calculation amount of the method proposed in this paper is much smaller than that of FEM. In general, the mesh stiffness equation derived in this paper can be used to calculate the TVMS under the condition of multiple pitting tooth in the pinion and wheel."
        ]
    },
    {
        "image_filename": "designv10_5_0002710_9783527803293-Figure35.1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002710_9783527803293-Figure35.1-1.png",
        "caption": "Figure 35.1 Schematic diagram of methodologies used to modify surface of therapeutic cells. (1) Covalent attachment of therapeutic materials to membrane proteins through the interaction of reactive groups such as N-hydroxysuccinamide (\u2013NHS), thiol (\u2013SH), and catechol with amine (\u2013NH2) of cell membrane. (2) Layer-by-layer coating of therapeutic materials by nonspecific",
        "texts": [
            " In general, the aim of this approach is to develop a protective layer on the surface of living cells for certain periods of time using various materials and techniques. Synthetic and natural polymers, nanoparticles, and even living cells have been used to immobilize on the surface of islets or stem cells to enhance therapeutic effect. Covalent binding to functional groups on the surface of cells, insertion of amphiphilic polymers into cell membrane via the hydrophobic interaction with lipid bilayer, and electrostatic interaction based on negatively charged cell surface are general techniques used for surface modification (Figure 35.1) [17]. The various applications of cell surface modification are explained below. 35.3.1.1 Camouflage of Surface Antigens When foreign tissues or cells are delivered into patients, the host immune system recognizes foreign antigens and activates the pathways of immune response, resulting in hyperacute inflammatory reactions and subsequently leading to the destruction of grafted cells. electrostatic adsorption to negatively charged cell membrane. (3) Anchoring amphiphilic therapeutic materials by insertion of hydrophobic part to lipid bilayer membrane"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001310_s00170-012-3922-9-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001310_s00170-012-3922-9-Figure1-1.png",
        "caption": "Fig. 1 SLM system [1]",
        "texts": [
            " Nowadays, SLM technologies are widely used in space, aviation, automotive and other industries. This technology offers a range of advantages compared to conventional manufacturing techniques: shorter time to market, use of inexpensive materials, higher production rate, versatility, high accuracy and ability to produce more functionality in the parts with unique design and intrinsic engineered features [3]. SLM is a non-conventional production process where layers of metal powder are molten with a laser heat source [4] (Fig. 1). The parts are produced on a piston in the building cylinder. To do so, a thin layer of powder is deposited with a coater or roll, starting from one of the feed containers. In a next step, a laser beam source adds heat to melt a cross-section of the final product. A further thin layer of powder is deposited and the process is repeated. By virtue of this \u2018layered manufacturing\u2019, more complex parts can be created [5]. Figure 1 shows a schematic example of an SLM system. Commercial machines differ in the way the powder is deposited (roller or scraper), the atmosphere (Ar or N2) and the type of laser that was used (CO2 laser, lamp or diode-pumped Nd:YAG laser, disk or fibre laser) [1]. In the SLM process, some phenomena such as defects of residual stresses and deformation might occur [6], especially the seriousness of warping deformation restricts melted quality and final application of SLM. To avoid such problems, much work has been done on optimising the processing parameters including scan strategies and laser power et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001187_iros.2015.7354192-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001187_iros.2015.7354192-Figure2-1.png",
        "caption": "Fig. 2: (a) FMCH for double support. (b) Virtual pendulumbased posture control (VPPC) during stance phase.",
        "texts": [
            " In spite of all advantages of (B)SLIP model, since the upper body is represented by a point mass, it cannot address postural control whereas vertical body alignment plays a key role in stabilization of human locomotion [8]. For that purpose, the SLIP must be extended to include a model of the upper body. An extension of the SLIP with a rigid trunk was introduced as TSLIP (for Trunk-SLIP) [9] or ASLIP, for \u201cAsymmetric SLIP\u201d [10]1. The model that we use in this paper is based on BTSLIP (Bipedal TSLIP), shown in Fig. 2. In contrary to most of posture control approaches which are based on control of the trunk orientation with respect to an absolute referential frame [2][4][11], Maus et al. [12] This research was supported in part by the EU project BALANCE under Grant Agreement No. 601003. M. A. Sharbafi and A. Seyfarth are with the Lauflabor Laboratory, Technische Universit\u00e4t Darmstadt, Darmstadt, Germany, {sharbafi, seyfarth}@sport.tu-darmstadt.de 1Here we will use TSLIP because Asymmetric SLIP can also apply to a SLIP model with asymmetric leg properties",
            " With FMCH we (i) achieve stable walking with upright trunk needless to measure absolute leg (or body) angle with respect to ground (ii) present an acceptable explanation of human postural control (mimicking human hip torque pattern (iii) suggest a mechanical representation of postural control method based on template models (iv) introduce a new concept in muscle reflex system which can be used to realize human locomotion. The simulation model which is used in this study is based on BTSLIP model, shown in Fig. 2. In BTSLIP model, legs are modeled by massless springs and a rigid trunk represents the upper body with mass m and moment of inertia J. Walking dynamics (gait cycle) has two phases: single support (SS) and double support (DS). SS starts at takeoff moment of a leg and ends at touchdown of the same leg. Touchdown (TD) is defined as the moment 978-1-4799-9994-1/15/$31.00 \u00a92015 IEEE 5742 that the distal end of the leg hits the ground and takeoff is when the leg leaves the ground. In SS, one leg is in contact with the ground, called stance leg and the swing leg moves virtually (no change in dynamics when the leg is massless) to finish the SS with hitting the ground with desired angle (angle of attack)",
            " This method can mimic human leg adjustment strategies for perturbed hopping [22] and achieve a large range of running velocities by a fixed controller [23]. Here, we use this method for walking. In VBLA, the leg direction is given by vector ~O as a weighted average of the CoM velocity vector ~V and the gravity vector ~G = [0,\u2212g]T (Fig. 1b). ~O = (1\u2212\u00b5)~V +\u00b5~G (6) where weighting constant \u00b5 accepts values between 0 and 1. 2) FMCH for hip torque control: We consider a bidirectional rotational spring between trunk and each leg. With the configuration showed in Fig. 2(a) for double support phase, the hip torques of leg i is determined by \u03c4i = ki(\u03c8i\u2212\u03c8 0 i ) (7) in which ki and \u03c80 i are the hip stiffness and rest angle for leg i, respectively, and \u03c8i is the angle between trunk and leg i as shown in Fig. 2(a). In FMCH control approach we use the leg force for modulating hip stiffness. ki = k0 i F i s Fn s , i = 1,2 (8) where k0 i , F i s ans Fn s are the default values for hip spring stiffness, leg force and normalization value for leg force, respectively. In [24], we showed that for a single leg in contact with ground (with length l), if k0 i is computed by the following equation and \u03c80 i = 0, then a the GRF goes through a point on trunk axis whose distance to hip is equal to r. k0 i = lr (l + r) Fn s (9) Having an intersection point for GRFs during whole gait cycle, placed above CoM, is found in human walking, called VPP (virtual pivot point) [8]. For the TSLIP model shown in Fig. 2(b), the required torque to redirect the GRF toward VPP, is \u03c4V PP = Fs l rh sin\u03c8 + rVPP sin(\u03c8\u2212 \u03b3) l + rh cos\u03c8 + rVPP cos(\u03c8\u2212 \u03b3) (10) in which rVPP and \u03b3 are the VPP distance to CoM and deviation angle from trunk axis, respectively, as shown in Fig. 2(b). In Appendix. A, it is shown that FMCH can approximate VPP out of trunk axis if the hip spring rest angle is computed as follows \u03c80 = rVPP\u03b3 r . (11) Therefore, if the gain for adapting hip stiffness is adaptively adjusted based on leg length (see Eq. 8), leg force feedback can be employed to precisely control VPP. Since the stance leg length changes are minor in walking, l can be replaced by its average value l\u0304. Therefore, from Eqs (7) to (9), based on the following equation, FMCH controller only needs to measure the leg force to adjust hip stiffness \u03c4i = cF i s (\u03c8i\u2212\u03c8 0 i ) (12) and it can also properly approximate VPP if the constant gain (c) is computed as follows c = l\u0304r (l\u0304 + r) (13) We investigated the ability of FMCH in replicating human virtual hip torque in walking",
            " This property besides leg angle and stiffness adjustment can precisely control the motion speed. Finally, with mathematical relation between the hip normalized stiffness and rest length and position of VPP with respect to CoM (the distance and angle from upper body axis), we proposed a method to find VPP based on FMCH model. The main benefit of such calculations appears when the VPP changes during gait e.g., to recover from perturbations or to change the gait speed. In such cases VPP adaptation can be detected from slope changes in r\u03c4 F \u2212\u03c8 curves. APPENDIX From Fig. 2, the distance between VPP and hip (r) is r = \u221a r2 VPP + r2 h +2rhrVPP cos\u03b3 (14) In addition, the angle between line from VPP to hip and trunk axis \u03c8 \u2032 can be found by \u03c8 \u2032 = arctan rVPP sin\u03b3 rh + rVPP cos\u03b3 . (15) If VPP angle \u03b3 < 20\u25e6, (14) and (15) can be approximated by{ r = rVPP + rh \u03c8 \u2032 = rVPP\u03b3 r (16) Eq. (10) gives the required torque \u03c4V PP to have GRF going through VPP. For hip angle range during walking (\u03c8 < 30\u25e6), this equation can be approximated by the following equation with error less than 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002450_j.neucom.2018.11.070-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002450_j.neucom.2018.11.070-Figure1-1.png",
        "caption": "Fig. 1. Schematic of a quadrotor.",
        "texts": [
            " (III) The characteristics such as large control domain, continuous control signals and the good balance between control performance and computational cost could promote the applications of the RPD-SMC + RISE controller in low-cost quadrotors. This paper is organized as follows. The description of the quadrotor dynamic model and the control problem formulation are given in Section 2 . Section 3 details the proposed control strategy. In Section 4 , the numerical simulation results are given to demonstrate the effectiveness of the proposed control strategy. Section 5 gives the conclusions. 2. Model description and problem formulation 2.1. Description of the quadrotor model The schematic of a quadrotor UAV is shown in Fig. 1 . The quadrotor consists of a rigid cross-frame via four propellers. The four propellers mounted at two orthogonal directions: propeller 1 and propeller 3 rotate in the anticlockwise direction; propeller 2 Please cite this article as: Z. Li, X. Ma and Y. Li, Robust tracking control ing, https://doi.org/10.1016/j.neucom.2018.11.070 nd propeller 4 rotate in the clockwise direction. The quadrotor has ix degree-of-freedom (DOF) including translational motions and hree rotational motions with only four independent inputs generted by increasing or decreasing the speeds of the four propellers. .1.1. Kinematics As shown in Fig. 1 , two reference frames are needed to describe he quadrotor kinematics model: the earth frame ( O e \u2212 x e y e z e ) and he body-fixed frame ( O b \u2212 x b y b z b ) . In the ( O b \u2212 x b y b z b ) frame, we ssume that the origin locates at the mass center of the quadroor, x b and y b point toward the rotor 1 and rotor 2 respectively, hile z b points upwards. The position of the quadrotor in the earth rame are represented by \u03be = [ x, y, z ] T . Its attitude is represented y \u03b7 = [ \u03c6, \u03b8, \u03c8 ] T , wher e \u03c6, \u03b8 and \u03c8 ar e the r oll, pitch and yaw ngles respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002233_j.mprp.2015.08.075-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002233_j.mprp.2015.08.075-Figure3-1.png",
        "caption": "FIGURE 3 3D metal printed combustion part for GE\u2019s latest 7HA gas turbine technology.",
        "texts": [
            "075 S P E C IA L F E A T U R E But it is also clear that, despite some limitations, rapid prototyping with SLM does potentially enable a radical shift in the conventional \u2018design, test, validate\u2019 approach. Vortmeyer points to a new manufacturing paradigm \u2018Testing as an integral part of the process\u2019 in which SLM machines are integrated with CAE/CAD/CAM systems to produce an integrated development iteration in a few months. Furthermore, researchers are also exploring a number of avenues in a bid to improve the desirable characteristics of components manufactured using additive technologies and make them every bit as robust as their forged counterparts (Fig. 3). Given that highly complex designs can now be generated in a single process, without the requirement for further assembly, the power sector has already begun adopting additive manufacturing for certain production components. For instance, Martin Scha\u0308fer, at Siemens Corporate Technologies in Berlin, says: \u2018A classic example from our own product development is a new duct system, known as a \u2018\u2018transition duct\u2019\u2019, for gas flows in gas turbines. This curved, thin-walled part has very small channels, and it\u2019s extremely difficult to make it with conventional technologies such as casting and milling"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003687_j.mechmachtheory.2019.103727-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003687_j.mechmachtheory.2019.103727-Figure2-1.png",
        "caption": "Fig. 2. Curved tool profile.",
        "texts": [
            " The modifications are introduced by the variation in machine tool settings and in the tool geometry. The machine tool settings used for pinion tooth finishing are specified in Fig. 1: sliding base setting ( c ), basic radial ( e ), basic machine center to back increment ( f ), basic offset ( g ), tilt angle ( \u03b2), and swivel angle ( \u03b4). The other manufacture parameters are the velocity ratio in the kinematical scheme of the machine tool for the generation of the pinion tooth surface ( i g1 ), the radius of the tool ( r t1 ), and the radii of the tool profile ( r prof 1 , r prof 2 , Fig. 2 ). The tooth surface of the pinion is defined by the following system of equations: r( 1 ) 0 = M p0 \u00b7 M p4 ( i g1 ) \u00b7 M p3 ( c, f, g ) \u00b7 M p2 ( e ) \u00b7 M p1 ( \u03b2, \u03b4) \u00b7 r( T 1 ) T 1 ( r t1 , r prof 1 , r prof 2 ) (1a) v( T 1 , 1 ) 0 \u00b7 e( T 1 ) 0 = 0 (1b) where r ( T 1 ) T 1 is the radius vector of tool surface points, matrices M p0 , M p1 , M p2 , M p3 , and M p4 provide the coordinate transformations from system K T 1 (rigidly connected to the cradle and tool T 1 ) to the stationary coordinate system K 0 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001711_s1560354713060166-Figure11-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001711_s1560354713060166-Figure11-1.png",
        "caption": "Fig. 11. Trajectories of the contact point for I1 = 0.8, I2 = 0.5, I3 = 0.35, D = 1, \u03b5 = 4, M\u03b3 = 0 and a) for various values of \u0394 close to a resonant one; b) for various initial conditions on the resonant torus \u0394 = 0.92445",
        "texts": [
            "3)), we can prove that the average velocity is zero for \u2212\u03b1 < \u0394 < 0 and M\u03b3 = 0. Thus, if a straight line perpendicular to the projection of the angular momentum M is drawn through the initial point of contact on the plane, then by the recurrence theorem (see the Appendix), the ball cannot move away from this straight line all the time: it will continually come arbitrarily close to the line. If, in addition, V\u0303y = 0 at the initial instant of time, then the trace of the contact point will intersect this straight line arbitrarily many times (see Fig. 11a). After the above-mentioned change of time t \u2192 \u03c4 , the function y(\u03c4) = \u03b4y(\u03c4) can be represented as a formal series y(\u03c4) = \u2211 n1,n2 Vn1n2 i(\u03c9un1 + \u03c9vn2) ei(\u03c9un1+\u03c9vn2)\u03c4 , n1, n2 \u2208 Z, (5.8) where Vn1n2 are the coefficients of the Fourier decomposition of velocity Vy(\u03d5u, \u03d5v). This series converges absolutely and uniformly at \u03c4 \u2208 (\u2212\u221e,+\u221e) for almost all rotation numbers r = \u03c9u \u03c9v , and y(\u03c4) is a quasiperiodic function. In this case the Poincare\u0301 map is a family of curves bounded in y, filled everywhere densely with points of the trajectories (see Fig",
            " To visualize this motion, we parameterize the trajectories on the torus by the initial coordinate u0 = u(\u03c4)|\u03c4=0 on the plane of the Poincare\u0301 section v\u0303 = 0 (this can always be done because the flow (5.1) is everywhere transverse to the plane v\u0303 = 0 for 0 < \u0394 < 1) and construct a graph showing the value of the drift for one period of motion on the torus \u0394y = y(t + T )\u2212 y(t) depending on u0. An example of such a graph for Tu Tv = 4 3 is given in Fig. 10. By symmetry V\u0303y(u, v\u0303 + \u03c0) = \u2212V\u0303y(u, v\u0303), each trajectory with a positive mean motion corresponds to a trajectory with the same mean motion in the negative direction, as can be seen well in Fig. 11b. In this case the trajectories of the Poincare\u0301 map with initial conditions lying on the straight line y0 = 0 are n vertical straight lines ( for Tu Tv = n m ) filled with points spaced apart at distances \u0394y(u0) (see Fig. 9b). Depending on the sign of \u0394y, the vertical straight lines are filled in the positive or negative direction along the axis Oy (see Fig. 9b). Remark. We note that the velocity of the mean motion along the axis Oy, even for the most large resonances such as Tu Tv = 4 3 , is two orders less than the velocity of motion along the axis Ox (see Fig. 11). Thus, an experimental detection of this effect by means of immediate measurement is a fairly complicated problem (due to the presence of friction). When it comes to practical observation of the mean motion, it is also appropriate to raise the question of nonzero mean motion on finite (albeit rather large) times. In this case, not only the above-mentioned resonant tori but also their small neighborhoods should be regarded as the region of existence of the mean drift. It can be shown (for example, by averaging methods) that for any sufficiently large t\u2217 < \u221e there exists a neighborhood of a resonant torus in which the trajectories of the contact point do not differ much from resonant tori on times of order t\u2217. Examples of trajectories of the contact point for tori close to a resonant one are given in Fig. 11a. I2 = 0.5, I3 = 0.35, \u03b5 = 4, M\u03b3 = 0, y(t = 0) = 0 and a) \u0394 = 0.92365; b) \u0394 = 0.92445 Tu Tv = 4 3 . 6. THE CASE OF DYNAMICAL SYMMETRY (I1 = I2) If two principal moments of inertia coincide, I1 = I2, for example, in the case of axisymmetric mass distribution, the equations of motion simplify considerably and the reduced system admits two integrals linear in angular momenta. One of them is the area integral (M ,\u03b3), and the other is an integral that is a particular case of the integral found by S.A"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000783_s12206-010-0309-4-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000783_s12206-010-0309-4-Figure5-1.png",
        "caption": "Fig. 5. Gas cavity formation in laser welding with filler wire (the depth of penetration exceed the thickness of test plate).",
        "texts": [
            "The fluctuations of the keyhole are at a maximum value in the critical penetration condition, which explains the increase in the number of gas cavities in the bead. Improvement in the number of gas cavities is also very inconspicuous even when the test plate was fully penetrated with the 3.8 kW laser. A reason for this is that the fluctuations of the keyhole had not been eliminated and the penetration of the bead varied (see No. 4 in Fig. 2) despite the test plate having been completely penetrated. This is an indication that the keyhole did not fully penetrate the molten metal, as exhibited in Fig. 5. As a result, the formation mechanism of gas cavities under these circumstances is similar to those in a nonpenetrating welding process (see No. 1 and No. 2 in Fig. 2), except that the depth of the keyhole is deeper. The bead with few gas cavities was obtained when prefabricated to a gap of 0.4 mm for the butt joint of a 4.0 mm sheet (see Table 3 and Fig. 2). The penetration of the bead was uniform and greater than the thickness of the test panel. All evidence indicates that the gap increased the stability of the keyhole"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002833_tim.2017.2664599-Figure13-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002833_tim.2017.2664599-Figure13-1.png",
        "caption": "Fig. 13. (a) Experiment system. (b) Diagram of the system.",
        "texts": [
            " When a gearbox or a rolling bearing has a localized fault, the measured vibration signal is usually a multicomponent AM-FM signal modulated by the shock impulses generated by a localized fault. Since the DRS-LMD can decompose a complicated AM-FM signal into a series of PFs adaptively, it is especially suitable for gear and rolling bearing fault detection. The experimental data [47] was collected from a gearbox located in the Aircraft Dynamics and Control Lab, Harbin Institute of Technology. The gearbox vibration signal was collected from a one-stage reduction gearbox test rig as shown in Fig. 13(a). This test rig contains an electric motor, a timing belt, a gearbox, a magnetic brake, a speed controller, a brake controller, an accelerometer, and a data acquisition system. The motor rotating speed is controlled by the speed controller, which allows the tested gear to operate under various speeds. The timing belt is applied to connect the ac motor and the shaft. The load is provided by the magnetic brake connected to the output shaft and the torque can be adjusted by the brake controller. As shown in Fig. 13(b), the gearbox is driven by the motor through a timing belt and there are two shafts inside the gearbox, which are mounted to the gearbox housing through rolling bearings. A load of 5 Nm was added in the tests. In this paper, we select Kistler 8704B25 high-sensitivity quartz integrated circuits piezoelectric (ICP) accelerometer. This accelerometer is selected by considering its installation, frequency range and the sensitivity. It was installed on the top of the gearbox housing using a mounted magnetic base"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000043_acc.1988.4790057-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000043_acc.1988.4790057-Figure1-1.png",
        "caption": "Figure 1. Three degree of fredom model of the Manutec r3 robot",
        "texts": [
            " APPLICATIONS Controllers whose designs am based on Lyapunov they have been applied to a variety of engineering control problems including the taking control of rbotic manipulators (2,12,17,33,50,54,92,94,97-99), the suspension control of a magnetically levitated vehicle (10,11), the control of stuctures in the presence of seismic excitations (48,58), and aerospace control problems (100- 102,107); see also (51). Expermnntal results are contained in (54,92,97,99). Applications to economic systems may be found in (37,80-82). Havresting problems are reated in (28,60) and river pollution control problems are considered in (18,61,62,73-75). To illustrate the efficacy of the proposed controllers, (32) presents trackdng controllers for a model of a Manutec r3 robot with 3 degrees of feedom, q1, q2, q3; see Figure 1. Torques are applied to the arms ,y 3 electric motors, one for each arm, and u = [ul,u2, U3] where ui is te control voltage applied to motor iL In this model, eo is the mass of an unain payload locate at P. Figures 2,3 present nnrrical simulation results obtained when the motion to be tracked is t#) E 0.lrad, i =1, 2, 3 and initial conditions are qt-(\u00b0) = 4j(\u00b0) = O, i = 1, 2, 3 . References [1] Ambrosino, G., G. Celentano, and F. Garofalo, Robust Model Tracking Control for a Class of Nonlinear Plants, IEEE Trans"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001130_j.jsv.2011.12.025-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001130_j.jsv.2011.12.025-Figure4-1.png",
        "caption": "Fig. 4. Gear angles for rigidity combination.",
        "texts": [
            " It can easily be demonstrated that standard teeth made with the same material, equal pressure angle and face width, and identical tooth numbers, have equal rigidities regardless of their modules Kf r\u00f0i\u00de\u00f0e,N,F,E\u00de \u00bc FEfCo0\u00feCo1e\u00feCo2N\u00feCo3eN\u00feCo4e2\u00feCo5N2 \u00feCo6e2N\u00feCo7eN2 \u00feCo8e2N2 g (14) In Eq. (14), e\u00bc0 is at the fillet-involute profile junction and e\u00bc1 is at the tip radius. F has (m) units and E (GPa), while Kf r(i) are in (N/m). The components Kf (i) and Kr (i) lead to the rigidity in the direction of the line of action when recombined as dictated by Eq. (15). The important angles are illustrated in Fig. 4 Ki\u00f0e,N,F,E\u00de \u00bc Kf iKri 1 K2 ri cos2\u00f0f0 g\u00de\u00feK2 f i sin2 \u00f0f0 g\u00de ( )1=2 (15) The mesh rigidity is finally obtained with the addition of the contact rigidity (KH). The plain stress radial compression (d [m]) of a cylinder (of radius Req) in contact with a plane is given by Eq. (16) [31]. Therefore, the contact rigidity is obtained from Eq. (17) d\u00bc \u00f0a2=2Req\u00def2ln\u00f04Req=a\u00de 1g (16) KH \u00bc @W @d \u00bc \u00f0pLEn=2\u00def2ln\u00f04Req=a\u00de 1g 1 (17) where a\u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f04W=pL\u00de\u00f0Req=En \u00de q is the semi-contact width (m), L is the cylinder length (m), En\u00bc \u00f0\u00f0\u00f01 n2 1\u00de=E1\u00de\u00fe\u00f0\u00f01 n2 2\u00de=E2\u00de\u00de 1 is the composite modulus (GPa), Ei and ni are the Young modulus and Poisson coefficient, respectively, W is the applied load (N), and Req\u00bc((1/r1)\u00fe(1/r2)) 1 (m) is the equivalent curvature radius"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000648_978-3-642-17531-2-Figure5.38-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000648_978-3-642-17531-2-Figure5.38-1.png",
        "caption": "Fig. 5.38. Double-resonant damper: a) classical passive harmonic damper using a two-mass oscillator, b) mechatronic transducer with resonant circuit (optionally a passive transducer with a shunt)",
        "texts": [
            " A much clearer approach in this respect is offered by the frequency response\u2014particularly in the case of a weakly-damped multibody system\u2014the representation of which in a NICHOLS diagram (gain-phase plot) is discussed in detail in Ch. 10. Mechanical oscillation damping One important task when dealing with multibody systems consists of the artificial damping of mechanical eigenfrequencies. Often size, weight, or other physical restrictions prevent building dissipative elements into the mechanical structure. One recourse is offered by mechanical resonance dampers or harmonic absorbers. Fig. 5.38a demonstrates the principle using an undamped single-mass os30 Attention must naturally be paid to inherent transducer stability problems aris- ing from electrostatic softening and pull-in effects, though these also appear in the case of an elastically-suspended rigid-body load. 5.8 Mechatronic Resonator 371 cillator ( , )m k . The eigenmode of the mass is excited by an external disturbance force. This disturbance is then to be countered by a coupled dissipative single-mass oscillator, or tuned mass damper, ( , , ) T T T m k b ",
            " This principle has been well known for many years (Lehr 1930), (Hartog 1947) and has established itself in a wide range of industries, including harmonic absorbers in buildings and bridges. Mechatronic double resonator Some of the advantages of connecting passive networks to the electrical terminals of a transducer have already been made clear in the two previous sections. In particular, recall the RL resonance circuit for the capacitive transducer of Example 5.1. This concept can be generalized and employed as a mechatronic equivalent\u2014the mechatronic resonator (Fig. 5.38b)\u2014to the passive two-mass damper of Fig. 5.34a. Applying this concept to the case of a capacitive transducer using RL impedance feedback, a (damped) electrical resonator ( , , ) T R L C is con- nected to the mechanical resonator ( , )m k , resulting in a mechatronic double resonator similar to the mechanical double resonator of Fig. 5.38a (Hagood and Flotow 1991), (Preumont 2002), (Moheimani 2003), (Neubauer et al. 2005). 372 5 Functional Realization: The Generic Mechatronic Transducer 5.9 Mechatronic Oscillating Generator 373 The functioning of the mechatronic double resonator\u2014whose theory of operation was discussed in detail in Example 5.1\u2014corresponds precisely to that of the mechanical analog. By suitably tuning the impedance parameters of ( ) FB Z s , maximum damping of both eigenmodes can be achieved. Equivalent configurations The configuration consisting of a voltage-drive capacitive transducer with impedance feedback discussed in Example 5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001961_j.jclepro.2018.10.109-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001961_j.jclepro.2018.10.109-Figure5-1.png",
        "caption": "Fig. 5. Schematic of laser scanning process.",
        "texts": [
            " The electrical energy of the entire SLM process wasmeasured by a portable wattmeter (HOPI HP9800) with a 1-s sampling interval. The power consumed for each set of samples can be distinguished through observations during the SLM processes and using the power-consumption-versus-time profiles. The consumed electrical energy of each set of samples is calculated by the product of the power and the time taken for the corresponding set of samples. It should be noted that the SLM system used is based on a pulsed laser, which melts powders in a point-to-point manner, see Fig. 5. The time that the laser dwells on one spot is defined as the exposure time, which is much shorter than the wattmeter sampling interval. In this case, the power measured by the wattmeter in one sampling interval is assumed to be the average consumed power in the interval. Such an assumption will not greatly influence the results, since each set of samples is the same and is measured using the same method. The density of samples was measured by a 0.1mg electronic balance (Sartorius BSA124S) based on Archimedes' principle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001968_978-94-007-6101-8-Figure4.5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001968_978-94-007-6101-8-Figure4.5-1.png",
        "caption": "Fig. 4.5 Cylindrical robot manipulator",
        "texts": [
            " The correctly written table and the matrices describing the relations between the neighboring coordinate frames are as follows: 64 4 Geometric Robot Model i ai \u03b1i di \u03d1i 1 a1 0 d1 0 2 a2 0 0 \u03d12 3 a3 0 0 \u03d13 0A1 = \u23a1 \u23a2\u23a2\u23a3 1 0 0 a1 0 1 0 0 0 0 1 d1 0 0 0 1 \u23a4 \u23a5\u23a5\u23a6 1A2 = \u23a1 \u23a2\u23a2\u23a3 c2 \u2212s2 0 a2c2 s2 c2 0 a2s2 0 0 1 0 0 0 0 1 \u23a4 \u23a5\u23a5\u23a6 2A3 = \u23a1 \u23a2\u23a2\u23a3 c3 \u2212s3 0 a3c3 s3 c3 0 a3s3 0 0 1 0 0 0 0 1 \u23a4 \u23a5\u23a5\u23a6 The geometric model of SCARA robot mechanism with three degrees of freedom has the following final form: 0A3 = 0A1 1A2 2A3 = \u23a1 \u23a2\u23a2\u23a3 c23 \u2212s23 0 a1 + a2c2+ a3c23 s23 c23 0 a2s2+ a3s23 0 0 1 d1 0 0 0 1 \u23a4 \u23a5\u23a5\u23a6 In the last matrix the following abbreviations sin(\u03d12 + \u03d13) = s23 = s2c3 + c2s3 and cos(\u03d12 + \u03d13) = c23 = c2c3\u2212 s2s3. In another example of developing the DH geometric model we will consider cylindrical robot shown in Fig. 4.5. The displacement of the first rotational joint is described by the angle variable \u03d11. The rotational joint is followed by two translational joints with distance variables d2 and d3. Again we start the DH procedure by drawing the coordinate frames. With three degrees of freedom we are dealing with four coordinate frames. Their axes will be denoted by the indices from 0 to 3. The displacement of the i th coordinate frame with respect to the frame (i \u2212 1) must be determined by only one joint variable"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002004_1.4028532-Figure13-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002004_1.4028532-Figure13-1.png",
        "caption": "Fig. 13 CC Arc-Miura geometry creation. (a) Three point ellipse, (b) projected curved surface, (c) divisor lines and exploded rigid panels, and (d) crease pattern.",
        "texts": [
            "asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use necessary to define two elliptical curves. The first elliptical curve is located along the Arc-Miura mountain crease and so BM and CM are found by substituting mountain crease parameters b1 for b and gMZ for gZ in Equation (6). Mountain ellipse parameters, cM, dM, gM, and hM, can be found with an additional mountain gradient parameter uM and using Eqs. (2)\u2013(6). The first elliptical curve (uM, vM), shown in Fig. 13(a), can then be plotted by substituting these parameters into Eqs. (9) and (10). The second ellipse is found at Arc-Miura valley creases, and it can be plotted once valley gradient parameter uV is obtained. To do this, BV and CV are first defined with Eq. (6) by substituting valley crease parameters b2 for b and gVZ for gZ. Using the projected prismatic base pattern geometry shown in Fig. 13(b), ellipse parameter gV can then be related to the first ellipse with similar triangle geometry gV \u00bc gMCV=CM (38) Substituting this value into Eq. (3) gives tan uV \u00bc 2CV\u00f02\u00fe CV=gV\u00de BV (39) The remaining parameters cV, dV, and hV, can be found by substituting BV, CV, and gV into Eqs. (2), (4), and (5). The second elliptical curve (uV, vV) can then be plotted by using these parameters in Eqs. (9) and (10). 4.3.2 Rigid Subdivision. The projected elliptical surface is subdivided into planar strips to generate the CC-Arc-Miura pattern. Vertices Wk,j are calculated at the intersection of the kth divisor line and the jth zigzag crease (k\u00bc 1, 2,\u2026, s, j\u00bc 1, 2,\u2026, n). In a 3D Cartesian coordinate system with orientation as shown in Fig. 13(c), the coordinate vector (xk,j, yk,j, zk,j) of Wk,j is xk;j \u00bc R1 cos h\u00fe uk;j\u00f0tk\u00de (40) yk;j \u00bc \u00f0k k 1\u00de b2 sin\u00f0gMZ;set=2\u00de S \u00fe vk;j\u00f0tk\u00de (41) zk;j \u00bc R1 sin h\u00fe wk;j\u00f0tk\u00de (42) where R1 is given by Eq. (25) in Ref. [21] as R2 1 \u00bc \u00f0a2 1 \u00fe a2 2 2a1a2 cos gVA\u00de=\u00f02\u00f01 cos n\u00de\u00de and h is given by odd i values in Eq. (28) in Ref. [21] as (j \u2013 1)n/2 for odd j and (j \u2013 2)n/ 2\u00fe n \u2013 na2 for even j. Rotated elliptical coordinates (uk,j, vk,j, wk,j) for odd j lie along the first ellipse, and are obtained by rotating the (uM, vM) ellipse to match the orientation of the corresponding three-node zigzag on the base pattern"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003368_j.mechmachtheory.2020.103890-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003368_j.mechmachtheory.2020.103890-Figure3-1.png",
        "caption": "Fig. 3. The point contact of a rolling ball within the screw-nut joints.",
        "texts": [
            " 1 ; the screw shaft total length is L; F a ( x, x sp ) acts as the complex piecewise nonlinear displacement function. 2.2. Equivalent mechanical model of the kinematic joints 2.2.1. The axial deformation and force of screw-nut joints As shown in Fig. 1 , the screw-nut joints is directly connected to the sliding platform and is subjected to the axial loads. Each ball in the screw-nut joints performs a two-point contact with the groove of screw shaft and nut. The elastic deformations are only generated in the ball, while the screw shaft and nut are viewed as rigid. Fig. 3 shows the two-point contact and spatial location of the ball. In Fig. 3 , F nsn is the normal force of single ball; \u03b1sn is the contact angle between the ball and the raceway; \u03b1h is the helix angle of the screw; \u03b4nn , \u03b4ns and \u03b4nsn are the normal deformation of ball-nut, ball-screw contact point and the ball respectively; \u03b4asn are the axial deformation of the ball; r s and r n are the groove curvature radius of screw and nut respectively. According to the projection relation in Fig. 3 , the normal force and deformation derived from the axial loads and defor- mation of each ball can be obtained by Eq. (2) : \u23a7 \u23a8 \u23a9 F nsn = F a n sn sin \u03b1sn cos \u03b1h \u03b4nsn = \u03b4asn sin \u03b1sn cos \u03b1h \u03b1h = tan \u22121 p sn \u03c0d (2) s 0 where n sn is the number of loaded balls in the screw-nut joints, and it is assumed that each ball is loaded equally; p sn and d s 0 are the pitch and nominal diameter of single helix screw. The relations between normal deformation and force of the ball at two contact points can be established by Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001551_icuas.2015.7152306-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001551_icuas.2015.7152306-Figure5-1.png",
        "caption": "Fig. 5: Quadrotor Formation",
        "texts": [],
        "surrounding_texts": [
            "An experiment was performed using the AscTec Pelican in an attempt to validate the wind effect model. This flight test used an autonomous controller, which controlled the quadcopter\u2019s attitude and height, but was not controlling the vehicle\u2019s lateral position. The uncontrolled lateral position shows the wind effects on the quadrotor without controller interference. While a quadrotor controller in this manner could drift laterally with no wind present, due to sensor inaccuracies, our indoor lab tests showed this effect to be small. Moreover, it was clear from the direction of the drift in the outdoor tests that the drift was indeed primarily due to the wind effects. A similar controller was used in the quadrotor motion simulator to simulate the quadrotor motion. The goal of the experiment was to compare the results from the motion simulator to the actual motion of the quadrotor. The wind was measured in the dominant wind direction and used as the wind input to the motion simulator. The data collected from the GPS is transformed to an x-y-z coordinate system, where x is in the dominant wind direction, y is the cross-wind direction, and -z is the height. The motion of the quadrotor in the dominant wind direction from the experiment is plotted against the simulated motion in Fig. 6. The trends in the simulated motion in the dominant wind direction are as expected, which start off with a large acceleration when the quadcopter is stationary, and as the quadcopter increases speed, the relative wind speed decreases, decreasing the acceleration. This trend is also visible in the experimental results; demonstrating the wind effect model in simulation accurately predicts the quadrotor motion during flight, though this does not necessarily validate the model\u2019s prediction of the detailed forces and moments."
        ]
    },
    {
        "image_filename": "designv10_5_0002810_tmag.2016.2524010-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002810_tmag.2016.2524010-Figure8-1.png",
        "caption": "Fig. 8 The eccentric model.",
        "texts": [
            " Verification of Optimization As shown in TABLE II, the average torque of the optimal motors and initial motors are almost the same, but the optimal motors significantly decrease the torque ripple. The iron losses are calculated by the approach of Bertotti at the rated conditions. Fig.7 shows that the iron losses for both radial and parallel magnetizations are reduced by nearly 27%. It is obvious that the proposed method can effectively decrease iron losses. C. Compared with Parametric Sweep Method The parameter sweep method based on a pole eccentricity is widely employed to decrease the iron losses. Fig.8 shows the eccentric model, where Rd and \u03b81 are the eccentric distance and eccentric angle, respectively. Using FEA, multiple parameters (Rd and \u03b81) are swept to find the optimal PM shape with the minimal iron losses. For the radial magnetization, the eccentric distance and the eccentric angle of the optimal structure are 65.2mm and 42.4 degree, respectively. As shown in Fig.9, the iron loss of the proposed method is smaller than that of the parameter sweep method. Similarly, for the parallel magnetization, the iron loss of the proposed method is almost the same as that of the parameter sweep method when Rd =64"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003001_jsen.2018.2809493-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003001_jsen.2018.2809493-Figure2-1.png",
        "caption": "Fig. 2. Construction method of electrochemical and spectroscopic units of the portable nitrate biosensing device",
        "texts": [
            " Note that even this widerange spectroscopic profile was not individually adequate for nitrate concentration determination because of the effects of unknown compounds in the samples tested by a portable device. In addition to electrochemical and spectroscopic features, operating features including total operating time and mean of storage temperature from the GC/NR electrode preparation to the nitrate determination in the sample and sample\u2019s type and pH were used in nitrate concentration determination. Figure 2 shows the construction method of autonomous electrochemical and spectroscopic units of the portable nitrate biosensing device. After the placement of the 25\u00d730\u00d710 mm fused quartz cuvette (1) containing the sample and mediator in the device, a stepper (6) located the electrodes and argon purge line (7) in the sample for enzyme-based catalytic reduction of nitrate to nitrite. Electrochemical features of the sample during the cyclic voltammetry were measured and recorded for further processing. Afterwards, another stepmotor (3) rotated a circular frame (4) to put the UV-Vis-NIR LEDs (5) with a certain order in front of the cuvette",
            " On the other side of the cuvette, the photodiode (2) was installed to receive the light transmitted through the cuvette. By converting the received light intensity to an electrical current by the photodiode and further operational amplifying and processing of the electrical signal, it was possible to measure the spectral absorption in each studied wavelength by a comparison between emitted and received light intensities. Therefore, spectroscopic data were provided for the sample. After feature extraction, the stepper (6) put the electrodes in 50 mM Bis-Tris buffer (8) when not in use. Figure 2 illustrates the parts followed by a number in parenthesis. It should be noted that for clarity, thermometer, processing part, and temperature adjustment system are not shown in the figure. 1558-1748 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. Figure 3 illustrates the constructed portable device for nitrate concentration determination in a plant extract sample"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002087_j.jsv.2014.01.005-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002087_j.jsv.2014.01.005-Figure1-1.png",
        "caption": "Fig. 1. Schematic of a rotating ring with space-fixed discrete stiffnesses. The fE1 ;E2g basis is fixed in space. The radial u\u00f0\u03b8; t\u00de and tangential v\u00f0\u03b8; t\u00de deformations are measured with respect to the stationary, cylindrical fer ; e\u03b8g basis.",
        "texts": [
            " For vanishing discrete stiffnesses the resulting equations differ from others in the literature and comparisons are made. The governing equations are cast in terms of matrix differential operators, which makes clear the operator adjointness properties and the gyroscopic system structure. Galerkin discretization follows naturally for the equations in matrix differential form. The natural frequencies and vibration modes are determined for a wide-range of rotation speeds for both axisymmetric and non-axisymmetric systems. A schematic of a uniform ring rotating at constant speed \u03a9 is shown in Fig. 1. The ring has radius R, cross-sectional area A, and cross-sectional area moment of inertia I (relative to its neutral surface). The density of the ring is \u03c1 and its elastic modulus is E. The ring is supported by an elastic foundation with stiffness kr in the radial direction and k\u03b8 in the tangential direction. In gears this stiffness represents the gear blank elasticity. The space-fixed discrete springs kmi (i\u00bc 1;2;\u2026;Ns) represent stiffnesses from contacting gear teeth [8,25,26,28,29]. These discrete stiffnesses are tangent to the ring, like for a tooth mesh stiffness that is tangent to a gear0s base circle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001130_j.jsv.2011.12.025-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001130_j.jsv.2011.12.025-Figure5-1.png",
        "caption": "Fig. 5. Oil film.",
        "texts": [
            " Consequently, for a given gear set, the total deformation can be considered to be commensurate with the load. The remaining component (Club) is assumed in this study to be dominated by the oil squeeze contribution. Thus, two conditions are considered: 1\u2014the loaded and 2\u2014the no-load conditions. The elastohydrodynamic lubrication condition exists when the tooth flanks are in contact, and is described by the Reynolds equation, which takes the form of Eq. (18) when neglecting the fluid flow in the axial direction, and assuming an incompressible and iso-viscous fluid. The variables are illustrated in Fig. 5 @ @y h3 @p @y \u00bc 12mu @h @y \u00fe12m @h @t (18) where the first left term is the physical wedge term, while the second is the normal squeeze term, y is the coordinate parallel to the profile tangent, p is the pressure (Pa), h is the film thickness (m), u is the fluid entraining velocity (\u00bc(u1\u00feu2)/2) (m/s), u1 2 are the tooth surface tangential velocities, and m is the dynamic viscosity (Pa s). Since the objective is to establish the squeeze contribution, a Grubin type representation is assumed to be adequate (the contact area is considered as the Hertz area, and an additional surface separation h0 is added for the film thickness)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000492_tie.2011.2168795-Figure16-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000492_tie.2011.2168795-Figure16-1.png",
        "caption": "Fig. 16. Magnitude of the first harmonic of magnetic flux density\u2014motor A.",
        "texts": [
            " The rotational losses were calculated as follows [19], [20], [22]: Prot = [Palt(Bmaj) + Palt(Bmin)] \u03b3(\u03bb,Bmaj) (9) where Palt denotes the measured alternating iron losses. The values of \u03b3 as a function of \u03bb and Bmaj are shown in Fig. 14. Furthermore, the average aspect ratio is about 0.2, and in regions where the ratio is higher, the amplitude of flux density is close to 1.5 T for motor A, for which the correction is quite small. Fig. 15 shows the aspect ratio for the first harmonic for motors A and B. Fig. 16 shows the flux density magnitude for motor A. A rotor cage, even when rotating at synchronous speed, is subjected to magnetic flux density changes due to slotting effects. Therefore, additional losses will occur. These losses are relatively high, up to a significant percentage of total losses. This part of losses was calculated as an average value taken from all time snapshots [23], [24]. To emphasize the need to take into account the motion of the rotor in the calculation of losses, Figs. 17 and 18 show a comparison between losses calculated with and without the rotor movement"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002618_j.addma.2019.100848-Figure10-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002618_j.addma.2019.100848-Figure10-1.png",
        "caption": "Fig. 10. Experimental set-up for the powder flow measurement.",
        "texts": [
            " At a certain plane, the weight of the powders at different positions were measured with cylindrical containers. The experimental test was carried out with the order of small (2 mm) to large (12mm) in the hole size on the containers, then, the different powder mass trapped in different cylinders was obtained. The difference value of two consecutive holes was calculated to verify the proposed model in section 2.1. The cylinder containers were placed under the four-jet nozzles, and the distance between the nozzle and the container was adjustable, as shown in Fig. 10. The powder flow rate (m) was set up as 4 g/min, and gas flow rate (V) was 6 L/min during the model validation. The result of powder flow distribution for different planes is shown in Fig. 11, indicating a relatively good agreement between the modelling and experimental measurements. Because the powder flow at center is unavailable to obtain with the weight measurement method, the measured value was missing at this position for each plane. Corresponded with the simulated result, the powder flow follows Gaussian distribution at the plane of Focal, Focal+1mm, and Focal+2mm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003345_j.ijrmhm.2019.105111-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003345_j.ijrmhm.2019.105111-Figure6-1.png",
        "caption": "Fig. 6. The schematic image shows the formation of remelting parts.",
        "texts": [
            " 5(e)) shows that the elemental contents in the remelted zone (spot 4 in Fig. 5(d)) were close to the nominal composition of the W70 composite, indicating the uniform microstructure in the remelted zone. The remelting effects benefit densification of the composite and produce high relative density of W70 (Fig. 1). When the composite powders were irradiated under high laser power, the laser not only melted the mixed powders, but also caused a remelting zone on the formed parts, as illustrated in Fig. 6. Due to the fast heat dissipation along the formed part, the rapid solidification process occurred and fine dendrites solidified at the solid-liquid interface. As solidification proceeded, the cooling of the remaining liquid slowed due to the latent heat release of the solidification process, thus the supercooling degree in the liquid front was reduced. In this case, the fastest growing direction was perpendicular to the solid-liquid interface and the dendrites grew preferentially along the heat dissipation direction thereby pointing to the center of the molten pool, as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002213_j.mechmachtheory.2014.06.006-Figure16-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002213_j.mechmachtheory.2014.06.006-Figure16-1.png",
        "caption": "Fig. 16. State 12 of the derivative queer-square mechanism (\u03b11 N 0, \u03b12 b 0, \u03b211 = \u03b212, \u03b221 \u2260 \u03b222).",
        "texts": [
            " When the links of the combination limb1p are parallel to each other and at the same time the bars in the combination limb2ap are antiparallel to each other, the angle relations of the derivative queer-square mechanism in category 4 are given as \u03b12 \u00bc \u2212\u03b211 \u03b211 \u00bc \u03b212 \u03b12 \u00fe \u03b82 \u00bc 0 : 8< : \u00f040\u00de The limb1s and limb2s have different relative positions with respect to the base and the platform has different relative positions with respect to the limb1p and limb2ap in the last four sub-states. In state 11, both limb1s and limb2s are higher than the base OA1A2 and the platform E1F1E2F2 is higher than limb1p and limb2ap. Fig. 15 offers the diametric view of the derivative queer-square mechanism in state 11 and its angle relations are given as \u03b11N0;\u03b211b0;\u03b212b0 \u03b12N0;\u03b221N0;\u03b222N0 : \u00f041\u00de When it comes to state 12, the angle \u03b12 changes from positive to negative. The dimetric view of the derivative queer-square mechanism in state 12 is illustrated in Fig. 16. As shown in Fig. 16, the relations between the angles of the revolute joints in the derivative queer-square mechanism in state 12 are provided as \u03b11N0;\u03b211N0;\u03b212N0 \u03b12b0;\u03b221N0;\u03b222N0 : \u00f042\u00de The limb1s and limb2s in state 12 have different relative positions compared to the base. The limb1s and limb1p are higher than the base, and the limb2s and limb2ap are lower than the base. The platform is located in themiddle of the limb1p and limb2ap, in particular it is lower than the limb1p and higher than the limb2ap. The observation of the derivative queer-square mechanism in state 13 is illustrated in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000123_1.4003088-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000123_1.4003088-Figure3-1.png",
        "caption": "Fig. 3 \u201ea\u2026 Subsurface-initiated fatigue spall \u202031\u2021, \u201eb\u2026 outer race fault model, and \u201ec\u2026 cross section of an outer race fault",
        "texts": [
            " The lubricant friction torque, Tlub, is defined by empirical equations 30 as Tlub = 10\u22127fo ofr 2/3dp 3, ofr 2000 16 10\u22126fodp 3, ofr 2000 18 where fr is the rotational speed in rpm, o is the kinematic viscosity of the lubricant in cSt, and coefficient fo, which depends on the bearing type and lubrication, equals unity for deep-groove ball bearings lubricated with oil mist and is given in Ref. 25 for other types of bearings with different lubrications. The rubbing seal friction torque, Tseal, which depends on the geometry and design of the seal, is assumed constant. 2.3 Fault Modeling. Bearings fail by numerous fault modes: corrosion, wear, plastic deformation, fatigue, lubrication failure, electrical damage, fracture, and incorrect design, among others. Most common spalling fatigue leaves pits on races or rollers, as in Fig. 3 a , because of periodic contact stress 31 . Most models for rolling element bearing faults have introduced mathematical impulse functions based on fault frequencies. Here, a kinematicsbased fault modeling is introduced, where the faults are defined in the model based on the surface profile change. For each fault, the width w, depth h, and location of the fault f in the body coordinate system are defined, as shown in Fig. 3 c . Parameters Tf, w, h, rf, and f in the model define the type, size, shape, and location of localized faults, as shown in the block diagram of Fig. 4. Tf defines the type of the fault, w and h represent size, rf determines the shape of the fault, and the location of the fault on each element is determined by f in the model. As a fault passes through the contact, the profile changes induce deflections that result in dynamic interactions between elements, which generate force impulses that induce fault vibrations",
            " ousing stiffness and damping effects are modeled through C and elements with structural stiffness and damping matrices Kv,h nd Rv,h. Each contact model consists of a transformer and a Cc lement. Transformers TF transform the contact coordinate sysems to the global coordinate system, as expressed in Eq. 2 . onlinear elements Cc with the constitutive law of Eq. 14 repesent contact and traction forces. Here, the bond graph model of he bearing with nine balls and two races consists of 11 diamondhape models combined through 18 contact models. Faults are odeled by surface profile changes, as shown in Fig. 3 c . During imulations, the geometry of elements changes based on locations nd growth of faults. Fault impulses and forces are generated via inematics and dynamics. Simulations and Experiment Setup A bond graph model of a deep-groove ball bearing with specications in Table 1 was built and numerically simulated with the oftware 20-SIM 4.0. The Runge\u2013Kutta Dormand Prince integration ethod with variable step size was used in simulations. Initial elocities and accelerations were zero. A radial load was applied o the inner race vertically downward",
            " Here, fault impact signals are modulated with otor frequency fr because the inner race fault, fixed on the inner ace, passes through the load zone at a rate of fr as the inner race otates. Similar behavior with the same frequency is observed in he corresponding experimental signals shown in Fig. 9 d . The agnified portion of vibration signal plotted in Fig. 9 b shows he fundamental fault frequencies of the bearing, which is conrmed by the experiments in Fig. 9 e . As the IRF passes through he contact, two impact responses appear in the vibration signal. he fault model of Fig. 3 suggests that the leading and trailing dges of the surface profile dent would cause impacts with the alls in the load zone. The distance between these two impact ignals contains information on the size faults. Figures 9 c and f present power spectrum of the vibration signals. Depending n the frequency range, harmonics of the fault frequencies indiated by dashed lines might appear in the power spectrum. Figure 10 shows the vibration signals of a bearing with a single F. Fault impact signals spaced by the fault frequency timing 1 / fBF are clearly observed in both simulation and experimental ata"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002997_tie.2018.2807366-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002997_tie.2018.2807366-Figure1-1.png",
        "caption": "Fig. 1. Primary construction of LIM",
        "texts": [
            " LIM are counterparts of rotary induction motors (RIM), and it has found the widest prospects for applications in transportation systems, beginning with electrical traction on small passengers or material supply vehicles (used at airports, exhibitions, electro highways, elevators) and ending with high-speed vehicles, industrial conveyors and military launch systems, etc. In recent decades, many researchers focused on the analysis and control of the LIMs, especially in the 3D finite elements method model and high-performance vector control [1-2]. In Fig. 1, just as a rotary induction motor produces rotary motion, a linear induction motor produces linear motion, or motion in a straight line. The fundamental difference between the two kinds of motors is the finite length of the magnetic and electric circuit of the LIM along the x-direction. The open magnetic circuit leads to an initiation of the so-called L 0278-0046 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002202_1.4894855-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002202_1.4894855-Figure3-1.png",
        "caption": "FIG. 3. (a) Ciliated cylindrical swimmer of radius L = 1 and \u03c6 = \u03c0 /20. (b) Ciliated carpet with double-periodic boundary in x and y directions and \u03c6 = \u03c0 /7. The cilia spacings in the x- and y-directions are given by 0.144L and 0.04L, respectively.",
        "texts": [
            "191 On: Fri, 19 Dec 2014 13:51:09 from the protozoan Opalina,19 see Fig. 1. The rabbit tracheal cilia are used for fluid transport and beat in an antiplectic wave pattern, whereas the Opalina cilia are used to propel the micro-organism and they beat in a symplectic wave pattern. We compare these two beating patterns for a range of symplectic and antiplectic metachronal waves in the context of two model systems: model (I) for swimming of a ciliated circular micro-organism, and model (II) for fluid transport/pumping by a ciliated flat surface, as depicted in Fig. 3. We employ three hydrodynamic measures of ciliary performance, including (i) average swimming speed and average pumping flow-rate, (ii) maximum forces and moments experienced by the cilia, (iii) swimming and pumping efficiencies. If cilia performance were hydrodynamically optimal, one would expect the tracheal cilia to outperform the Opalina cilia in fluid transport, whereas the latter would outperform the former in swimming, in one or all of these measures. This thinking proved to be too simplistic",
            " Our results show that the performance of the Opalina cilia is superior to that of the tracheal cilia in all the hydrodynamicbased performance measures. These findings suggest that the hydrodynamics of a single function may not explain the wide variety of cilia beating patterns observed in biological systems and that other biological parameters and constraints may be at play. We consider two model systems: (I) the swimming of a ciliated cylinder and (II) the fluid pumping by a ciliated carpet, as shown in Fig. 3. The ciliated carpet model is described in details in our previous work.26 Here, we focus on describing the ciliated cylinder model and we briefly highlight the technical differences between the two models. The cylindrical micro-swimmer of radius L is covered by a finite number N of discrete cilia of length . The cilia are distributed uniformly along the cylinder\u2019s surface such that the arc-length between the roots of two neighboring cilia is s = 2\u03c0L/(N + 2). The cilia and their strokes are arranged symmetrically about the x-axis, thus restricting the swimming motion to a pure time-varying translation in the x-direction, see Fig. 3(a). The kinematics of the beating pattern of the individual cilium can be described in a Cartesian frame attached at the base of the cilium by \u03be c(s, t), where s is the arclength along the cilium\u2019s centreline from its base (0 < s < ) and t is time (0 < t < T). Two distinct cilia kinematics are depicted in Fig. 1 based on experimental data: (A) rabbit tracheal cilia and (B) cilia from the protozoan Opalina. In both cases, the kinematics \u03be c(s, t) = (xc, yc) are approximated by Fourier series expansion in t and Taylor series in s with coefficients chosen to match the experimental data",
            " Downloaded to IP: 129.21.35.191 On: Fri, 19 Dec 2014 13:51:09 = 0, no metachronal wave is generated. A negative phase difference amounts to compression of the cilia during the effective stroke phase and results in a symplectic wave that propagates in the same direction as the effective stroke. A positive phase difference amounts to cilia compression during the recovery stroke and results in an antiplectic wave that propagates in the opposite direction to the effective stroke, see Fig. 2. The snapshot depicted in Fig. 3(a) corresponds to ciliary pattern (A) beating in an antiplectic metachronal wave with \u03c6 = \u03c0 /20. In the remainder of this study, we use the radius L of the cylinder to scale length and the inverse of the wave\u2019s angular frequency 1/\u03c9 to scale time. At zero Reynolds number, the fluid motion is governed by the non-dimensional Stokes equations and the incompressibility condition, \u2212\u2207 p + \u03bc\u22072u = 0, \u2207 \u00b7 u = 0, (1) where p is the pressure field, u is the fluid velocity field, \u03bc is the dimensionless fluid viscosity",
            " The relative errors in the average swimming velocity between the numerical solution and Blake\u2019s analytical solution are shown in This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 129.21.35.191 On: Fri, 19 Dec 2014 13:51:09 Fig. 4 as functions of the number of Stokeslets on the cylinder. Clearly, the numerical solution converges to Blake\u2019s solution as the number of Stokeslets increases. For the fluid pumping model shown in Fig. 3(b), the cilia are rooted at the plane z = 0 with doubly periodic boundaries in the x and y directions. The cilia beating motion and metachronal waves take place in the (x, z)-plane such that the overall fluid pumping occurs along the x-axis. In the y-direction, the cilia are more densely packed and beat synchronously. To compute the flow fields generated by such ciliary carpets, we use the regularized Stokeslet method but with three major differences from the case of the self-propelled cylinder"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003984_tec.2020.2980146-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003984_tec.2020.2980146-Figure7-1.png",
        "caption": "Fig. 7. Simulation showing: (a) \u2013 slice at through the 3-D image (on a log scale of absolute values) of a point source at the center of the array in",
        "texts": [
            " There are options in the software to oversample by integer factors, which increases the number of interpolation points on the FFT grid. However, it was found that in most cases this oversampling made little difference to the final results. As the FFT grid is regular it generally has some baselines in the corner regions, which are longer than those from the antenna array. These regions on the FFT grid are identified and the values of the visibilities at these locations are set to zero. An example of this is shown in Fig. 7(b), whereby a 2-D slice from the 3-D visibility function from a simulation is illustrated. There are options in the software to append zeros onto the visibilities on the FFT grid, which although not adding extra information, does result in smoother surface plots and less pixilated images, which aesthetically is more pleasing. When interpolating on to the FFT grid there is found to be little difference between the results of nearest neighbor, linear, and cubic spline interpolation. However, cubic spline did on rare occasions generate wild interpolated values so linear interpolation became the default",
            " To investigate the resolution, the point-spread function of the system was estimated by imaging a point source at the center of the array. Synthetic cross-correlations from this were generated and processed into an image using the algorithm of Section II. This image, representing the point-spread function, has some negative values, as is possible in aperture synthesis systems [28]. The spatial extent of the point-spread function in an \u2013 slice (of the 3-D image) at is shown on a log scale of the absolute values in Fig. 7(a). The first dark ring from the image center represents the first zero crossing of the point spread function and the first bright ring (the first minimum) represents the Rayleigh resolution [29], which by analysis is found to be at a radius of from the center. Sensitivity to the change in point-source position was investigated by examining the phase of the visibility function. Keeping the phase center at the center of the array, the point source was moved a distance of 1 mm in the -direction. A slice in the spatial frequency plane (corresponding to the \u2013 plane) at of the 3-D visibility function for this simulation is shown in Fig. 7(b). The values of the measured visibility function lie on a plane surface tilted in the direction. The gradient of the tilt seen from this plot is 1 mm, the displacement of the point source in the plane. It can be seen in this plot that in the corner regions of the FFT grid the phase of the visibility function has been set to zero, as no data are present in these locations, as discussed in Section II. Fig. 3 and (b) surface plot of a slice at through the visibility phase function when the point source is displaced 1 mm in the -direction from the array center"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001331_tmag.2014.2310179-Figure15-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001331_tmag.2014.2310179-Figure15-1.png",
        "caption": "Fig. 15. Prototypes. (a) Rotor with 10 poles. (b) Rotor with 14 poles. (c) Stator segments with tooth tips. (d) Stator segment without tooth tips. (e) Complete stator and frame with tooth tips. (f) Complete stator and frame without tooth tips.",
        "texts": [
            ", are investigated in Section III. The experimental validation is given in Section IV. 0018-9464 \u00a9 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. The cross sections of the investigated machines are shown in Fig. 1, in which only the stators are shown. In each case, the rotors are surface-mounted permanent magnet (SPM) topologies, having full pole arc magnets (Fig. 15). To obtain a modular structure, flux gaps are inserted into the middle of alternate stator teeth [Fig. 1(a) and (c)]. However, when flux gap width (\u03b20) changes, to limit the magnetic saturation in tooth bodies, the total iron width (2t0) remains unchanged. The tooth tip width (tw) is also constant to keep the slot opening unchanged. Conversely, the UNET machines [Fig. 1(b) and (d)] are obtained by filling the flux gaps of the relevant modular machines with iron. This material is the same as that of the stator iron core",
            " The calculations of average torque versus flux gaps have been carried out for a wide range of modular machines with different slot/pole combinations. By way of example, the results of modular machines with typical slot/pole combinations are shown in Fig. 14. However, the rules established in this paper are general rules, which can also be extended to other slot/pole combinations. To validate the predictions and conclusions obtained by FEA, 12-slot/10-pole and 12-slot/14-pole prototype modular machines both with or without tooth tips have been built (Fig. 15). The parameters of these four machines are given in Table I. The phase back-EMFs of the prototype machines are shown in Fig. 16 and their spectra are shown in Fig. 17. A good match can be observed between the predicted and measured results. The method for measuring the on-load torque is similar to that described in [4] and [25]. The machines are supplied by three-phase currents such as IA = I , IB = \u2212I/2, and IC = \u2212I/2, where I is a dc which can be changed. By fixing the rotor to the maximum average torque position, the static torque against phase RMS current has been calculated (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000857_j.cma.2013.12.017-Figure21-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000857_j.cma.2013.12.017-Figure21-1.png",
        "caption": "Fig. 21. Contact stresses at contact position number 10 of design Example 15 when (a) tip relief is not applied and (b) when optimal tip relief is applied.",
        "texts": [
            " Table 6 shows the optimal parabola coefficients for each case of design. Based on the the obtained results, the following remarks can be made: Fig. 20 shows the evolution of the contact and bending stresses with respect to the parabola coefficient of the tip relief profile for example of design 16. Contact stresses are reduced with the increment of the parabola coefficient until edge contact is avoided. Application of optimal tip relief reduces maximum contact stresses, although maximum bending stresses are slightly increased. Fig. 21(a) shows the maximum contact stresses for example of design 15 at contact position number 10 of the cycle of meshing where edge contact occurs because tip relief was not applied. Fig. 21(b) shows the maximum contact stresses for the same case of design and contact position when optimal tip relief is applied. Without tip relief (Fig. 21(a)), maximum contact stresses reach 3814 MPa, whereas with the optimum tip relief application maximum contact stresses reach 1382 MPa (Fig. 21(b)). Fig. 22 shows the evolution of the contact stresses for version 1 of geometry (Fig. 22(a)) and for version 2 of geometry (Fig. 22(b)) when optimum tip relief is applied. In this case, areas of severe contact stresses are avoided all over the cycle of meshing. Fig. 22(a) shows that contact stresses increase for geometry type 1 and lower cutter mean pitch radius. However, for geometry type 2, almost the same evolution of contact stresses can be achieved, independently of the applied reference cutter pitch radius"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002368_s11071-015-2489-z-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002368_s11071-015-2489-z-Figure1-1.png",
        "caption": "Fig. 1 a The physical model and b a closed loop vector for ith leg of the 6-UPS parallel robot",
        "texts": [
            "Results are next verified with commercial dynamics software. In the second example, the input of the direct dynamics is compared with the output of the inverse dynamics. To do this, another trajectory is first selected and the inverse dynamics is used to obtain the required motor torques. These motor torques are next used as input for the direct dynamics formulation, and a resulting MP trajectory is obtained. This section also covers comparison between Lagrange\u2013Euler formulation and the proposed dynamics method. 2 Inverse position analysis Consider Fig. 1a. Frame {T} and frame {B} are attached to the moving platform, MP, and fixed base, respectively. The rotation matrix, B TR, consists of three Euler angles \u03b8, \u03d5 and \u03bb rotated about x, y and z-axes, respectively and can be defined as B TR = R(x, \u03b8)R(y,\u03d5)R(z, \u03bb) = \u23a1 \u23a3 c\u03bb c\u03d5 \u2212 c\u03d5s\u03bb s\u03d5 c\u03b8 s\u03bb+ c\u03bb s\u03d5 s\u03b8 c\u03bb c\u03b8\u2212 s\u03bb s\u03d5 s\u03b8 \u2212c\u03d5 s\u03b8 s\u03bb s\u03b8\u2212 c\u03bb c\u03b8 s\u03d5 c\u03bb s\u03b8+ c\u03b8 s\u03bb s\u03d5 c\u03d5 c\u03b8 \u23a4 \u23a6 (1) where c and s represent cosine and sine, respectively. Therefore, to express an arbitrary T\u03d1 , defined in {T} to {B}, we have B\u03d1 = B TRT\u03d1 (2) In this paper, a leading superscript represents the coordinate frame in which the vector is referenced. Additionally, bold lower and upper case lettering designate vectors and matrices, respectively. For brevity, the superscript \u201cB\u201d denoting the frame {B} in which vectors are defined is eliminated. Figure 1b represents vectors and coordinate frames used for the kinematic problem of the 6-UPS manipulator. For each kinematic chain, a closed vector-loop equation can be written as follows ai + qac i = B TRTbi + p for i = 1, . . . , 6 (3) where B TR is a rotation matrix to transfer a vector defined in {T} to {B}. Vectors ai , Tbi and p denote position of point Ui relative to frame {B}, position of point Si relative to frame {T} and the translation vector of the tip, point P, respectively. The constraint equations, Eq",
            " 2 a Local coordinates frames for ith passive universal joint, b position vectors and dimensional parameters of ith actuated limb (a) (b) values, qaci , and unit vectors along the actuated prismatic joints, q\u0302ac i , can be obtained using Eq. (3) as follows qaci = \u2225\u2225\u2225BTRTbi + p \u2212 ai \u2225\u2225\u2225 q\u0302ac i = 1 qaci ( B TRTbi + p \u2212 ai ) for i = 1, . . . , 6 (4) As shown in Fig. 2b, the actuated prismatic joints include two cylindrical parts. The center of gravity positions of these parts can be calculated as follows r1i = ai + e1q\u0302ac i and r2i = ai + ( qaci \u2212 e2 ) q\u0302ac i for i = 1, . . . , 6 (5) Furthermore, to calculate the rotation values of U-joint, the following method is utilized. As shown in Fig. 1a, the rotationmatrix, which transfers local moving frame {Fi } to fixed frame {B} for ith passive U-joint, can be obtained as B F iR = R (z, \u03b1i ) R (y, \u03b3i ) R (x, \u03c8i ) = \u23a1 \u23a3 c\u03b1ic\u03b3 i \u2212s\u03b1ic\u03c8 i + c\u03b1i s\u03b3 i s\u03c8 i s\u03b1i s\u03c8 i + c\u03b1i s\u03b3 ic\u03c8 i s\u03b1ic\u03b3 i c\u03b1ic\u03c8 i + s\u03b1i s\u03b3 i s\u03c8 i \u2212c\u03b1i s\u03c8 i + s\u03b1i s\u03b3 ic\u03c8 i \u2212s\u03b3 i c\u03b3 i s\u03c8 i c\u03b3 ic\u03c8 i \u23a4 \u23a6 (6) where \u03b1i is a constant value and is illustrated in Fig. 2a. Using Eq. (6), we have q\u0302ac i = B F iR F i q\u0302ac i = \u23a7\u23a8 \u23a9 s\u03b1i s\u03c8 i + c\u03b1i s\u03b3 ic\u03c8 i \u2212c\u03b1i s\u03c8 i + s\u03b1i s\u03b3 ic\u03c8 i c\u03b3 ic\u03c8 i \u23ab\u23ac \u23ad = \u23a7\u23aa\u23a8 \u23aa\u23a9 q\u0302aci x q\u0302aciy q\u0302aci z \u23ab\u23aa\u23ac \u23aa\u23ad for i = 1, "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000648_978-3-642-17531-2-Figure2.36-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000648_978-3-642-17531-2-Figure2.36-1.png",
        "caption": "Fig. 2.36. Example of topological rules of construction: a) physical configuration of a mechanical system, b) mechanical network, c) analogous electrical network",
        "texts": [
            " Depending 96 2 Elements of Modeling on which physical quantities are assigned to the power variables effort (e) and flow (f), the same system can be described as a transformer or a gyrator. Particular attention should be paid to this fact when such systems are modeled using computer-aided tools and pre-made component libraries. 2.3 Modeling Paradigms for Mechatronic Systems 97 Topological rules of construction Starting with the physical topological structure of network elements, an abstract topological network model can be constructed as an undirected graph including standardized network elements (e.g. Table 2.5) using the following elementary rules (Fig. 2.36): Common potential: Elements with a common potential are connected in parallel in the abstract network graph, Common flow: Elements with a common flow are connected in series in the abstract network graph. Connection rule for inertial masses One pole of the mass symbol (the one with the bar) must always be connected to an inertial system (corresponding to \u201cground\u201d in an electrical network). This is due to the applicability of NEWTON\u2019s second law of motion and thus the inertia mx relative to inertial space"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001740_s00170-015-7974-5-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001740_s00170-015-7974-5-Figure5-1.png",
        "caption": "Fig. 5 Effect of thermocapillary gradients on deposit geometry at the starting position",
        "texts": [
            " Asymmetric downward bulging of deposits on a vertical surface was shown during the laser rapid manufacturing process [31]. It noted that gravity is the key factor causing the downward rounded bulge. Based on prior literature, understanding of interactions between surface tension, gravity, and fluid convection is essential to explain the bulging mechanisms in LAM. The effect of thermocapillary gradient on deposit sidewall geometry can be understood by analysis of the simulation results shown in Fig. 5. Five layer deposits created with melt pools having negative and positive thermocapillary gradient are displayed in Fig. 5a, b, respectively. In both cases, the distinctive bulge of the deposit sidewall is observed at starting position. For simulations with melt pools having mixed thermocapillary gradient with maximum temperatures Tmax of 1818 K and 1914 K in Fig. 5c, d, a decrease in the width of the sidewall bulge is noted for both mixed thermocapillary gradients. The variation of bulge width with thermocapillary gradient types is illustrated by the cross sections in Fig. 6. These results are studied in more detail to better understand the effects of thermocapillary gradient on deposit dimensions in Figs. 7, 8, and 9. The effect of the bulge on deposit sidewall dimension can be expressed in a simple subtraction of minimum width from maximum width. Image processing software (ImageJ, NIH) is used to measure the maximum and minimum values from the simulated results shown in Fig",
            " 6c, d, further reduction in the bulge width is observed for the mixed thermocapillary gradients with two different levels of sulfur. The value is 272 \u03bcm for 6 ppm and 208 \u03bcm for 10 ppm. It is noted that bulge width is decreased by approximately 56 % compared to that for the negative gradient. From these results, it is concluded that nonuniform and inhomogeneous surface finish can be optimized by manipulating thermocapillary gradient. Figure 7 displays the bulge and the fluid flow pattern in the melt pool at fifth layer deposit with a negative thermocapillary gradient. The deposit is cross-sectioned along A\u2013A line shown in Fig. 5b. The bulge is not observed on the sidewall of deposit in Fig. 7a. Mainly outward fluid flow along the melt pool surface exists, and the surface fluid velocity is the fastest in the melt pool. In Fig. 7b, downward flow begins to develop at the melt pool edge, and the velocity decreases to 8.51 cm/s. At this step, the bulge starts to form at the edges but it is not large. In Fig. 7c, d, the bulge becomes more pronounced at the edges with the increase of the width and height of the melt pool and the fluid velocity"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001881_acs.2524-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001881_acs.2524-Figure1-1.png",
        "caption": "Figure 1. Schematic of vehicle longitudinal dynamics.",
        "texts": [
            " However, these signals are typically not measurable. Although several online estimation of vehicle mass and road gradient have been proposed, the employment of additional sensors (e.g., accelerometer [28], GPS [29]) may be susceptible to noises. In particular, the parameters to be estimated are assumed to be constant [22, 27], which is stringent for practical applications. In this example, we will apply the proposed methods to vehicle systems to estimate time-varying road gradient and vehicle mass. For this purpose, Figure 1 depicts the vehicle longitudinal dynamics. We can deduce the vehicle model based on Newton\u2019s Second Law in the longitudinal direction [22, 27] as Pv D 1 m Fengine g.sin.\u0131/C Crr cos.\u0131// Cdrag m v2 D G. Px; g; Fengine/ .t/ (39) where the parameters to be estimated are the mass of the vehicle m and the road gradient \u0131 on which the vehicle traverse. Fengine is the driving force applied on the vehicle, v is the vehicle\u2019s velocity, Crr is the rolling friction coefficient, and Cdrag D CD A=2 denotes the effect of aerodynamic drag effects with CD being the drag coefficient, being the air density and A being the frontal area, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003225_j.mtcomm.2020.100963-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003225_j.mtcomm.2020.100963-Figure9-1.png",
        "caption": "Fig. 9. Schematic representation of the mechanism for glucose oxidation at the electrode surface (activated chemisorption model).",
        "texts": [
            " It can be seen that the scan rates have an effect on both peak currents and as a matter of fact, increasing scan rate leads to a nearly equal increase for anodic and cathodic current peaks. Moreover, peak potential shifted toward more positive values for oxidation process. The regression curves show a linear relationship (R2>0.99) between anodic and cathodic current peaks and the square root of scan rate, demonstrating the diffusion-controlled process of glucose on the surface of decorated GCE. [28,35]. Fig. 9 represents a schematic of the mechanism of glucose oxidation at the electrode surface (activated chemisorption model). Fig. 10 shows the glucose response time from the amperometric curves for bare and decorated GCE (glucose concentration =0.5 mM). As can be seen, the response time of decorated GC for glucose is only about 1.7 s (n = 5, SD = 0.1) whereas the bare GC shows a response time of over 50 s. In order to investigate the effect of some interfering substances on the glucose selectivity of the sensor presented in this work, ascorbic acid (0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001338_iedec.2014.6784685-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001338_iedec.2014.6784685-Figure2-1.png",
        "caption": "Figure 2: (a) RC Servo demonstration board (b) Speed control of a DC motor demonstration board (c) Pneumatic actuator demonstration board (d) Solenoid demonstration board",
        "texts": [
            " The first of these topical areas related to practical aspects of the mechanical/electrical interface in mechatronics systems. The topics covered in this topical area include:  Selection and application of mechanical actuators  Power issues associated with electromechanical devices  Practical design aspects of actuator interface circuits  Dynamic response for systems with moving mechanical parts  Portable power for electromechanical systems with emphasis on different battery technologies and their limitations  Mechanical aspects of RC Servo Actuators (Figure 2(a) shows a pegboard model that was used in the class to demonstrate the control of a typical RC servo by an Arduino controller.)  Important mechanical aspects in the specification of DC Motors (Figure 2(b) shows a pegboard model used to demonstrate the use of pulse width modulation and an Arduino controller to regulate the speed of a DC motor.)  Fluid (pneumatic & hydraulic) systems (Figure 2(c) shows a pneumatic actuator driven by an Arduino controller using a simple power relay.)  Mechanical design considerations in the selection and use of solenoids (The model in Figure 2(d) demonstrates the speed of operation of two types of solenoids when driven by an Arduino controller and a power interface circuit.)  A discussion of small piezoelectric devices and their role as mechanical actuators The second of these topical areas is related to a general understanding of the mechanical devices used in mechatronics systems and the practical aspects associated with their selection and use. The topics covered in this area include:  A comparison of six commercially available mechanical/structural prototyping systems  A comparison of the efficiency and ranges of power capacity for various power transmission devices including gears, chains & belts, bearings, linkages & special mechanisms  Sources of standard power transmission hardware for mechatronics applications Throughout this module, the use of demonstration systems and samples of actual hardware proved to be especially useful to the understanding of how mechanical devices are deployed in mechatronics systems"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000648_978-3-642-17531-2-Figure2.34-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000648_978-3-642-17531-2-Figure2.34-1.png",
        "caption": "Fig. 2.34. Elementary mechatronic gyrator transducer (ideal, lossless): hydraulic transducer",
        "texts": [
            " In the case of a transformer, the transducer constant n determines the relation between pairs of the same power variables 1 2,e e or 1 2,f f of the two ports. In the case of a gyrator, the transducer constant r is used to relate pairs of differing power variables 1 2,e f or 2 1,e f of the two ports. 14 Using so-called multi-ports, the simultaneous interactions between more than two domains can be described in an expanded form. The physical units of the transducer constants n, r are determined by the domain-specific power variables. Fig. 2.33 shows physical examples of transformer type transducers and Fig. 2.34 shows a physical example of a gyrator type transducer. In the matrix form shown, the transfer matrix represents the so-called chain matrix of two-port network theory. Mechanical transducers: variable definitions Recall that, due to the arbitrary assignment of domain-specific power variables, the description of physical transducer implementations is not unique. Particular attention is due in the case of mechanical transducers. Fig. 2.35 shows a lossless DC motor as an example of an ideal electromechanical transducer"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003360_j.procbio.2020.01.025-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003360_j.procbio.2020.01.025-Figure5-1.png",
        "caption": "Fig. 5. Representation of process of Gr/ZnONWAs/GF and electrochemical redox reactions of FA and UA on the surface of Gr/ZnONWAs/GF [59].",
        "texts": [
            " Merits: \u03b1-polyoxometalate\u2013polypyrrole have uniformly arranged well defined molecular complexes and have high electrocatalytic activity. Demerits: Study was not co-related with standard method available for folic acid determination. Fig. 3. Schematic representation of the preparation of the MIP\u2013sol\u2013gel coated PGE [26]. 3.4.3. AuNPs modified Au electrode based Folic acid biosensor The AuNPs decorated Au electrode based FA biosensor has been designed. The surface of the modified gold plate before and after activation was scanned by scanning electron microscopy (SEM) (Supplementary Fig. 5). FA molecules got adsorbed on the surface of AuNPs modified gold electrode & exhibited cyclic voltammogram. The biosensor worked optimally at a scan rate of 100 mV/s with an applied potential of 4.5 V. The biosensor provided a rapid response of about 1 min. Moreover, a good linear response was obtained in the range of 1.0 \u00d7 10\u22128 to 1.0 \u00d7 10\u22126 mol L\u22121 with LOD of 7.50 \u00d7 10\u22129 mol L\u22121. The method evidenced high specificity and selectivity for FA. The biosensor was used in real samples such as FA medicines, flours, and vegetables [29]",
            " BS A -F A to sy lac ti va te d m ag ne ti c be ad 2 \u00d7 10 \u2212 5 \u20131 .3 \u00d7 10 \u2212 4 1. 3 \u00d7 10 \u2212 5 \u2013 \u2013 \u2013 7. 5 0. 99 Bi ol og ic al an d fo od sa m pl es [5 3] 34 . BS A m od ifi ed go ld na no cl us te r 2. 7 \u00d7 10 \u2212 4 \u20130 .0 75 4. 1 \u00d7 10 \u2212 5 0. 2 4 \u2013 7. 4 0. 99 Ph ar m ac eu ti ca ls [5 5] (CVD) using nickel foam as the template. Then, ZnO nanowire arrays (ZnO NWAs) were grown on the GF by hydrothermal synthesis. Finally, graphene (Gr) was deposited on the ZnO NWAs by CVD to obtain the hybrid of Gr/ZnO NWAs/GF (Fig. 5). SEM images of Gr/ZnO NWAs/GF exhibited the 3D macroporous structure of nickel foam with the average pore diameter of \u223c 300 \u03bcm (Supplementary Fig. 22). TEM images revealed the diameter and length of ZnO nanowires as \u223c 50 nm and 2 \u03bcm, respectively. Due to large specific surface area and outstanding electric conductivity, the hybrid can be used for the determination of FA by CV and DPV. The results showed that ZnO NWAs were uniformly and vertically grown on the GF and Gr is deposited on the ZnO NWAs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000516_j.actbio.2012.02.005-Figure10-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000516_j.actbio.2012.02.005-Figure10-1.png",
        "caption": "Fig. 10. Simplified scheme of the fluorescent magnetically drivable nanocatalyst.",
        "texts": [
            " The negative charge of the surface OH groups can be exploited for a simple electrostatic immobilization of the positively charged organic molecules. In this way, RITC as a fluorescent label was attached, resulting in a fluorescent magnetically drivable nanocarrier. This is the first reported example of magnetic fluorescent nanoparticles based on the rhodamine structure allowing the covalent attachment of various biomolecules. Exploiting the chemical properties of the isothiocyanate functionality, glucose oxidase was covalently bound to RITC to develop the first magnetically controllable rhodamine-based nanocatalyst (see Fig. 10). The immobilized enzyme, as a monomolecular layer, retains its catalytic activity towards oxidation of b-D-glucose. The prepared fluorescent magnetically drivable nanocatalyst might be easily used to remove molecular oxygen from aqueous solutions in the case of glucose excess. The presence of the nanocatalyst can be conveniently monitored by its fluorescence. Moreover, the nanocatalyst can be quickly removed by the application of a simple external magnet and re-used several times without a loss of the catalytic efficiency"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003005_tnano.2018.2797325-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003005_tnano.2018.2797325-Figure1-1.png",
        "caption": "Fig. 1. (a) Overview of the magnetic microrobot system. (b) Scanning electron microscope image of the magnetic microrobots (Scale bar is 2 \u00b5m).",
        "texts": [
            " The emergence of microscale robots in recent years has provided new means of noncontact and flexible manipulation of single microobjects [14]\u2013[16] and cells [17], [18], targeted cargo delivery [19] and even fabricating autonomous microvehicles [20]. This study presents the development of a peanut-like swimming microrobot with sub-micrometer feature size. This microrobot can flexibly trap and manipulate single microparticle that is several hundred times the volume of the microrobot. Experimental results demonstrate that the vision-navigated swimming microrobot is capable of tracking a complicated trajectory and automatically transporting microparticles with high positioning accuracy in complex environment. Figure 1(a) shows the configuration of the magnetic microrobot system. A magnetic drive system consisting of five identical coils is used to generate magnetic forces in three orthogonal directions. Two pairs of oppositely mounted coils provide independent magnetic fields along the x- and y-axes while the z-axis magnetic field is produced by the coil underneath. An optical microscope (5times, 20times and 50times) is used for vision-based task plan and motion control. A highspeed DAQ card (NI-PCI-6259) generates a driving signal, which is amplified by the voltage amplifier to drive the coils, producing a magnetic field strength up to 15 mT within a 20 mm \u00d7 20 mm workspace. The system\u2019s drive frequency can reach more than 2 kHz, fully meeting the driving requirements of commonly used swimming microrobots. This microrobotic system can be used for experiments of bio-manipulation and testing in vitro and in vivo. Figure 1(b) shows a scanning electron microscope image of the peanut-like magnetic microrobot used in this work, which has a diameter of about 0.8 \u00b5m and a length of 3 \u00b5m and are synthesized from hematite using hydrothermal process [21]. 1536-125X (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. As shown in Fig. 2(a), when magnetized along its short axis (magnetic moment M), the microrobot is rotated by a magnetic torque (\u03c4 = M\u00d7B) induced by an external rotating magnetic field (B) perpendicular to its long axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000083_j.mechmachtheory.2009.01.010-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000083_j.mechmachtheory.2009.01.010-Figure4-1.png",
        "caption": "Fig. 4. Meshing model for a skew conical gear drive.",
        "texts": [
            " Because conical gears can be regarded as cylindrical gears, with variable profile-shifting along the face width, a change in the contact position also means a change in the meshing characteristics. The relations between the working parameters, the gearing parameters and the detailed design approach can be found in a previous paper [15]. The position of the contact points in a skew conical gear drive with profile-shifted transmission can be determined with the aid of the meshing model shown in Fig. 3 and the frequently adopted working pitch cones model [25] in Fig. 4. The geometrical relation between the working pitch cones of a conical gear drive and the corresponding coordinate systems are illustrated graphically in Fig. 4. The location of the two working pitch cones, with working cone angles hw1 and hw2, is determined based on the assembly parameters: shaft angle R, offset a and working mounting distances Dw1,2. The parameters bC1,2 indicate the distance between the working pitch circle with radius rCw1,2 and the reference pitch circle with radius rC1,2 across the face-width. For position analysis of the contact point, the homogeneous coordinates r1 and r2 of a point on the tooth surface of conical gears 1 and 2, expressed in S1 and S2 coordinates, have to be transferred to Sf coordinates, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002213_j.mechmachtheory.2014.06.006-Figure13-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002213_j.mechmachtheory.2014.06.006-Figure13-1.png",
        "caption": "Fig. 13. State 9 of the derivative queer-square mechanism (\u03b11 b 0, \u03b12 N 0, \u03b211 \u2260 \u03b212, \u03b221 = \u03b222).",
        "texts": [
            " 12 offers an observation of the derivative queer-square mechanism in state 8. The geometrical ranges of the revolute angles of the derivative queer-square mechanism in state 8 are illustrated as \u03b11N0;\u03b211b0;\u03b212b0 \u03b12b0;\u03b221b0;\u03b222b0 : \u00f035\u00de In state 8, limb1s is located in the higher position and limb2s is located in the lower positionwith respect to the baseOA1A2, and the platform E1F1E2F2 is located relatively lower than limb1ap and higher than limb2p. The observation of the derivative queer-square mechanism in state 9 is presented in Fig. 13. Similarly, the ranges of angles \u03b11, \u03b12, \u03b211, \u03b212, \u03b221 and \u03b222 of the derivative queer-square mechanism in state 9 are given as \u03b11b0;\u03b211N0;\u03b212N0 \u03b12N0;\u03b221N0;\u03b222N0 : \u00f036\u00de From Fig. 13 and Eq. (36), we could find that limb1s is located lower than the base OA1A2, limb2s is located higher than the base OA1A2, and the platform E1F1E2F2 is located higher than limb1ap and lower than limb2p in state 9. The observation of the dimetric view of the derivative queer-square mechanism in state 10 is given in Fig. 14. The angle ranges of state 10where angles \u03b211 and \u03b212 have different values and angles \u03b221 and \u03b222 have the same value are \u03b11b0;\u03b211b0;\u03b212b0 \u03b12b0;\u03b221N0;\u03b222N0 : \u00f037\u00de For these four kinds of states where limb1s, limb2s, limb1ap and limb2p have different relative positions, by substituting the particular angle relations in Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002387_9781118773826-Figure13.26-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002387_9781118773826-Figure13.26-1.png",
        "caption": "Figure 13.26 M~H curve of Bi 1-x La x FeO 3 (x=0.4 and X=0.5) measured at RT.",
        "texts": [
            "2, the M~H curve (Figure 13.25a) gives a straight thin loop behavior without saturation with remanence (M r ) value of 0.934 emu/g. With a further increase of concentration from x=0.2 to x=0.3, the area of the M~H loop (Figure 13.25b) is slightly increased. Th is indicates that the canted spin moment increases from antiferro to ferromagnetic ordering. A surprising increase in M r around 2.209 emu/g was observed in this case. Further increase of concentration from x=0.3 to 0.4 indicates that the area of the M~H loop (Figure 13.26a) increased more without saturation. Similar behavior has been observed in the case of x=0.5 (Figure 13.26b) 486 Biosensors Nanotechnology with increased area without saturation. Th e observed values of remnant magnetization were 2.432 emu/g and 2.735 emu/g in the case of x=0.4 and 0.5 respectively. Further, there is increment in coercive fi eld with the increase of La content, which is nearly zero for undoped BiFeO 3 . Th e appearance of ferromagnetism in the La-doped BiFeO 3 ceramics may arise due to the destruction of spin cycloid structure which resulted in limited increase of magnetization. Structural transformation (due to La-ion) destroys the spin cycloid and releases the latent magnetization locked within the cycloid, resulting in enhancement of magnetic properties"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001509_j.apm.2016.07.016-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001509_j.apm.2016.07.016-Figure1-1.png",
        "caption": "Fig. 1. Meshing of a pair of gears: (a) sketch of meshing, (b) scheme of period expanding.",
        "texts": [
            " Many researchers assume that the meshing forces in double teeth meshing zone are distributed uniformly in a pair of teeth, and the friction force is simply defined as the product of the average-distributed meshing force and the friction coefficient. This assumption makes it easy to treat the friction force in meshing tooth pair separately. But in actual gear design, the contact ratio \u025b usually ranges from 1 to 2, that is to say, the number of tooth pairs meshing simultaneously will alternate between 1 and 2, so the friction forces are not uniformly distributed. A pair of gear meshing transmission is shown in Fig. 1 (a), where r b 1 and r b 2 are the radii of addendum circle, r a 1 and r a 2 are the base radii of the pinion and gear, \u03c9 1 and \u03c9 2 are the angular velocity of the pinion and gear, and \u03b1 is the pressure angle on the reference circle. Line N 1 N 2 is the action line while line B 1 B 2 is the working part of the action line, and the gear pair is meshing along the line B 1 B 2 . The details of line B 1 B 2 are shown in Fig. 1 (b), where B 1 and B 2 are separately the starting and ending point of the double tooth meshing, C 1 and C 2 are separately the starting and ending point of the single tooth meshing, and P b is the normal pitch. Time-varying stiffness of gear in a meshing cycle can be represented using the three pairs of teeth. As is shown in Fig. 1 (b), B 1 C 1 and B 2 C 2 are double-tooth meshing regions and C 1 C 1 are single-tooth meshing region. When the tooth pair 2 starts meshing at point B 1 , the tooth pair 1 at front has been in mesh at point C 2 . When the tooth pair 2 moves to point C 1 , the tooth pair 1 is out of mesh at point B 2 , and the tooth pair 3 starts meshing at point B 1 .When the tooth pair 3 moves to point C 1 , the tooth pair 2 is out of mesh at point B 2 . Thus tooth pair 2 goes through a full meshing period T 1 ",
            " He demonstrated that the rectangular-wave representation of time-varying mesh stiffness could achieve most practical purposes. Besides, the rectangular-wave model has been adopted by many researchers and was proved to be suitable for the theoretical study of nonlinear dynamics for the gear system. In this section, we analyze the changes of the time-varying mesh stiffness which is modeled as a rectangular wave. The period expansion method is also used to describe the time-varying mesh stiffness. Take the tooth pair 1, 2, and 3 in Fig. 1 , and the mesh stiffness with period expansion is illustrated in Fig. 2 . In Fig. 2 , k 1 is the stiffness coefficients of single tooth pair in single tooth meshing zone, k 2 is the stiffness coefficients of single tooth pair in double teeth meshing zone, and k max and k min are the maximum and minimum synthetic stiffness coefficients of gear pair, respectively. When tooth pair 2 moves from B 1 ( t = 0) to C 2 ( t = T 0 ), tooth pair 1 keeps in mesh. In this process, the mesh stiffness of the gear pair is the sum of the stiffness of tooth pair 1 and 2, which is equal to k 1 + k 2 ",
            " So the meshing forces, friction forces and friction moments periodically change with the location of contact point. According to dynamic Coulomb\u2019s law, the friction forces are given by: f i = \u03bci \u00b7 \u03bbi \u00b7 F meshi (i = 1 , 2) , (6) where \u03bci is the friction coefficient of the tooth surface, which is periodically changed with relative sliding velocity, and \u03bbi is the direction coefficient of the friction force with expanded period, which can be performed as: \u03bb1 (t) = { 1 (0 < t < t 2 ) \u22121 ( t 2 < t < \u03b5 T 0 ) 0 (\u03b5 T 0 < t < 2 T 0 ) . (7) Friction moments can be derived using the geometric relationship in Fig. 1 (a), which can be expressed as: \u23a7 \u23aa \u23aa \u23aa \u23a8 \u23aa \u23aa \u23aa \u23a9 S 11 (t) = ( r b1 + r b2 ) tan \u03b1 \u2212 \u221a r a 2 2 \u2212 r b2 2 + r b1 \u00b7 w 1 \u00b7 t, S 12 (t) = ( r b1 + r b2 ) tan \u03b1 \u2212 \u221a r a 2 2 \u2212 r b2 2 + r b1 \u00b7 w 1 \u00b7 t + P b , S 21 (t) = \u221a r a 2 2 \u2212 r b2 2 \u2212 r b1 \u00b7 w 1 \u00b7 t = S 11 (t + T 0 ) , S 22 (t) = \u221a r a 2 2 \u2212 r b2 2 \u2212 r b1 \u00b7 w 1 \u00b7 t \u2212 P b = S 12 (t + T 0 ) . (8) where S ( t ) and S (t) (i = 1 , 2) are the friction moments of the i th tooth pair. 1 i 2 i Please cite this article as: L. Xiang et al., Bifurcation and chaos analysis for multi-freedom gear-bearing system with time- varying stiffness, Applied Mathematical Modelling (2016), http://dx"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001565_j.mechmachtheory.2014.12.019-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001565_j.mechmachtheory.2014.12.019-Figure1-1.png",
        "caption": "Fig. 1. Three coordinate systems.",
        "texts": [
            " The Frenet\u2013Serret coordinate system [13], (t, n, b), is fixed at the ball center whose moving trajectory is in line with the t axis direction. The contact coordinate system, (e\u03bb, f\u03bb, g\u03bb), is fixed at the contact points between the ball and raceway and the contact point pointing to the ball center is coincident with the g\u03bb axis direction. Here, \u03bb= A represents the contact point between the ball and nut raceway, and \u03bb= B represents the contact point between the ball and screw raceway. The relationship of contact coordinate system with Frenet\u2013Serret coordinate system and global coordinate system is shown in Fig. 1. As shown in Fig. 1, the angle between b-axis and z-axis is \u03b1, which has the same value of helix angle. The angular velocity of screw and nut are defined as\u03c9 and\u03c9N, respectively. \u03b2B and \u03b2A represent the contact angle of the ball with respect to the screw and nut, respectively. rb is the radius of ball. In order to facilitate the systematic study of the theoretical model, the transformation relationships between the different coordinate systems must be established. The homogeneous coordinate transformations between the two coordinates (t, n, b) and (x, y, z) can be obtained through three transformations",
            " Similarly, the homogeneous coordinate transformations between (e\u03bb, f\u03bb, g\u03bb) and (t, n, b) can be stated as: t n b 1 2 664 3 775 \u00bc 0 1 0 0 \u2212 sin\u03b2B 0 cos\u03b2B rb cos\u03b2B cos\u03b2B 0 sin\u03b2B rb sin\u03b2B 0 0 0 1 2 664 3 775 eB f B gB 1 2 664 3 775 \u00f02a\u00de and t n b 1 2 664 3 775 \u00bc 0 1 0 0 sin\u03b2A 0 cos\u03b2A rb cos\u03b2A cos\u03b2A 0 \u2212 sin\u03b2A \u2212rb sin\u03b2A 0 0 0 1 2 664 3 775 eA f A gA 1 2 664 3 775: \u00f02b\u00de Prior to making a creep analysis of ball screw, it is necessary to solve the spin angular velocity. The model of spinmotion is shown in Fig. 3. The 2-axis is coincident with the spinning axis of the ball. The projection of the 2-axis in the t\u2212 b plane is defined as 1-axis. The angle between 1-axis and 2-axis is \u03b2, and the angle between 1-axis and b-axis is \u03b2\u2032. The spin angular velocity and pitch radius of the ball screw are defined as \u03c9R and rm, respectively. As shown in Fig. 3, \u03c9t, \u03c9n, \u03c9b are given as follows: \u03c9t \u00bc \u03c9R cos\u03b2 sin\u03b20 \u00f03a\u00de \u03c9b \u00bc \u03c9R cos\u03b2 cos\u03b20 \u00f03b\u00de \u03c9n \u00bc \u03c9R sin\u03b2: \u00f03c\u00de As shown in Fig. 1, three axial components of the nut angular velocity (\u03c9N) in the eA- , fA- , and gA-directions can be written as: VNe \u00bc \u2212\u03c9N rm \u00fe rb\u2212\u03b4N\u00f0 \u00de cos\u03b2A\u00bd \u00f04a\u00de VN f \u00bc 0 \u00f04b\u00de \u03c9Ng \u00bc \u2212\u03c9N sin\u03b2A \u00f04c\u00de where \u03b4N is the normal elastic deformation between the ball and nut, which can be calculated based on Hertz contact theory. In the same way, three axial components of the ball's spin angular velocity (\u03c9R) in the eA- , fA- , and gA-directions can be stated as: VbNe \u00bc \u2212 rb\u2212\u03b4N\u00f0 \u00de \u03c9n cos\u03b2A \u00fe\u03c9b sin\u03b2A\u00f0 \u00de \u00f05a\u00de VbN f \u00bc \u03c9t rb\u2212\u03b4N\u00f0 \u00de \u00f05b\u00de \u03c9bNg \u00bc \u03c9b cos\u03b2A\u2212\u03c9n sin\u03b2A: \u00f05c\u00de According to the roll contact theory [12], rolling velocity between the ball and nut is given as: VrAj j \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi VbNe \u00fe VNe\u00f0 \u00de2 \u00fe VbN f \u00fe VN f 2 r =2 \u00f06\u00de There are |VNf| b b |VNe| and |VbNf| b b |VbNe| under the normal working state of ball screw condition",
            " (5a)\u2013(5c), the vertical creep ratio (\u03beeA), horizontal creep ratio (\u03befA) and spin ratio (\u03c6A) are obtained based on the roll contact theory as: \u03beeA \u00bc VbNe\u2212VNe VrA \u00bc 2 \u03c9Nrm\u2212 rb\u2212\u03b4N\u00f0 \u00de \u03c9R cos\u03b2 cos\u03b20 cos\u03b2A \u00fe\u03c9R sin\u03b2 sin\u03b2A\u2212\u03c9N cos\u03b2A \u03c9Nrm \u00fe rb\u2212\u03b4N\u00f0 \u00de \u03c9R cos\u03b2 cos\u03b20 cos\u03b2A \u00fe\u03c9R sin\u03b2 sin\u03b2A \u00fe\u03c9N cos\u03b2A\u00f0 \u00de \u00f08a\u00de \u03be f A \u00bc VbN f\u2212VN f VrA \u00bc 2 rb\u2212\u03b4N\u00f0 \u00de\u03c9R cos\u03b2 sin\u03b20 \u03c9Nrm \u00fe rb\u2212\u03b4N\u00f0 \u00de \u03c9R cos\u03b2 cos\u03b20 cos\u03b2A \u00fe\u03c9R sin\u03b2 sin\u03b2A \u00fe\u03c9N cos\u03b2A\u00f0 \u00de \u00f08b\u00de \u03c6A \u00bc \u03c9bNg\u2212\u03c9Ng VrA \u00bc 2 \u03c9R sin\u03b2 cos\u03b2A\u2212\u03c9R cos\u03b2 cos\u03b20 sin\u03b2A \u00fe\u03c9N sin\u03b2A \u03c9Nrm \u00fe rb\u2212\u03b4N\u00f0 \u00de \u03c9R cos\u03b2 cos\u03b20 cos\u03b2A \u00fe\u03c9R sin\u03b2 sin\u03b2A \u00fe\u03c9N cos\u03b2A\u00f0 \u00de : \u00f08c\u00de Considering the differential slipping caused by surfacewarpage of nut raceway, two components of slipping velocity in the eA- and fA- directions [12] can be expressed as follows: CeA \u00bc \u03beeA\u2212 f A\u03c6A\u2212\u03beh f A\u00f0 \u00de \u00f09a\u00de C fA \u00bc \u03be f A \u00fe eA\u03c6A: \u00f09b\u00de \u03beh(fA) is the slipping item of Heathcote. Based on the roll contact theory, this can be calculated as follows: \u03beh f A\u00f0 \u00de \u00bc 1\u2212 \u03c9N cos\u03b2A \u03c9R cos\u03b2 cos\u03b20 cos\u03b2A \u00fe\u03c9R sin\u03b2 sin\u03b2A f A 2 2rb 2 : \u00f010\u00de As shown in Fig. 1, three axial components of the screw angular velocity (\u03c9) in the eB- , fB- , and gB-directions can be obtained in the following forms: VSe \u00bc \u2212\u03c9 rm\u2212 rb\u2212\u03b4S\u00f0 \u00de cos\u03b2B\u00bd \u00f011a\u00de VSf \u00bc 0 \u00f011b\u00de \u03c9Sg \u00bc \u2212\u03c9 sin\u03b2B \u00f011c\u00de \u03b4S is the normal elastic deformation between the ball and screw, which can be calculated based on Hertz contact theory. Similarly, three axial components of the ball's spin angular velocity (\u03c9R) in the eB- , fB- , and gB-directions can be stated as: VbSe \u00bc \u2212 rb\u2212\u03b4S\u00f0 \u00de \u03c9n cos\u03b2B \u00fe\u03c9b sin\u03b2B\u00f0 \u00de \u00f012a\u00de VbS f \u00bc \u2212\u03c9t rb\u2212\u03b4S\u00f0 \u00de \u00f012b\u00de \u03c9bSg \u00bc \u03c9b sin\u03b2B\u2212\u03c9n cos\u03b2B: \u00f012c\u00de There are |VSf| b b |VSe| and |VbSf| b b |VbSe| under the normal working condition",
            " In order to take full advantage of the linear creep theory [12] and Coulomb friction model, the improved friction expression is stated as: F\u03bb \u00bc f \u03bbQ\u03bb Fr\u03bb f \u03bbQ\u03bb \u22121 3 Fr\u03bb f \u03bbQ\u03bb 2 \u00fe 1 27 Fr\u03bb f \u03bbQ\u03bb 3 Fr\u03bb\u22643 f \u03bbQ\u03bb\u00f0 \u00de f \u03bbQ\u03bb Fr\u03bbN3 f \u03bbQ\u03bb\u00f0 \u00de 8>< >: \u00f024\u00de where \u03bb = A, B and m represent the different contact areas; F\u03bb is the improved friction at contact area; f\u03bb is friction coefficient; Fr\u03bb represents the friction at contact area calculated by linear creep theory with Fr\u03bb \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Fe\u03bb 2 \u00fe F f\u03bb 2 q . In the previous sections, the method to calculate a ball friction is introduced, in this section, a method for calculating ball screw friction will be presented. According to the three coordinate systems shown in Fig. 1, Eqs. (1) and (2b), the total friction of all balls in a circle of ball screw between the ball and nut in the global coordinate system can be given as: FA 0 \u00bc \u2211 n i\u00bc1 \u2212 cos\u03b1 sin\u03b8i \u2212 cos\u03b8i sin\u03b1 sin\u03b8i rm cos\u03b8i cos\u03b1 cos\u03b8i \u2212 sin\u03b8i \u2212 sin\u03b1 cos\u03b8i rm sin\u03b8i sin\u03b1 0 cos\u03b1 \u03b8iL 2\u03c0 0 0 0 1 2 6664 3 7775 0 1 0 0 sin\u03b2A 0 cos\u03b2A rb cos\u03b2A cos\u03b2A 0 \u2212 sin\u03b2A \u2212rb sin\u03b2A 0 0 0 1 2 664 3 775 FeA 0 F fA 0 FgA 0 1 2 664 3 775 \u00f025a\u00de where n is the number of balls in a circle of ball screw; \u03b8i is the position angle of different ball in a circle of ball screw; FeA 0, F fA 0 and FgA 0 represent the projection of the improved friction (FA) in the eA- , fA- , and gA-directions, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002276_tsmc.2017.2744676-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002276_tsmc.2017.2744676-Figure2-1.png",
        "caption": "Fig. 2. Double inverted pendulums connected by a spring.",
        "texts": [
            " The piecewise analysis was shown in [30], and it is omitted for the sake of space limitation. The proof is thus completed. In this section, three simulation examples are presented for the purpose of illustrating the effectiveness of the proposed FTC approach. It should be mentioning that the strict-feedback nonlinear system in Example 1 can be treated as special cases for system (1) while the last example one is with virtual control variables in nonaffine pure-feedback form. A. Example 1 Consider a kind of practical systems, two inverted pendulums connected through a spring shown in Fig. 2, which is described in [15], [19], and references therein in detail. The angular position \u03b8i and the angular rate \u03b8\u0307i of the ith subsystem are denoted as xi,1 and xi,2, respectively, i = 1, 2. The dynamics can be described as follows: \u23a7 \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a9 x\u03071,1 = x1,2 + 1,1 ( y1, y2 ) x\u03071,2 = ( m1grs J1 \u2212 ksr2 s 4J1 ) sin(x1,1) + T 1 u1 + ksrs 2J1 (ls \u2212 bs) + 1,2 ( y1, y2 ) x\u03072,1 = x2,2 + 2,1 ( y1, y2 ) x\u03072,2 = ( m2grs J2 \u2212 ksr2 s 4J2 ) sin(x2,1) + T 2 u2 + ksrs 2J2 (ls \u2212 bs) + 2,2 ( y1, y2 ) y1 = x1,1, y2 = x2,1 where physical parameters of the system are m1 = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003486_j.ijmecsci.2020.105665-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003486_j.ijmecsci.2020.105665-Figure2-1.png",
        "caption": "Fig. 2. Injection molding lunker defects of POM gears through X-ray computerized tomography (CT): (a) Lunker defects in a small module gear; (b) Lunker defects in a medium module gear.",
        "texts": [
            " [27] compared the wear behavior of POM gears manufactured y the machine cutting and the injection molding, and concluded that he wear rates of POM gears are independent of the manufacturing pro- 3 ess. However, injection molding lunker defects may be generated durng the injection molding process. Particularly, to achieve uniform mold lling, polymer gears with medium or large tooth modules commonly se the web type structure. The injection molding lunker could locates here the shape of structure changes sharply, as shown in Fig. 2 . This ight lead to the drastic reduction of fatigue life of polymer gears. Hasl t al. [8] investigated the loading capacity of injection molded POM ears under oil lubrication, and the tooth root breakage failure of POM ears due to cavities is observed. Lack of awareness of the impact of njection molding lunker defects on polymer gear fatigue life severely estricts the large batch production of polymer gears in power transmisions. To address the issue of the injection molding lunker defect, in this ork, a temperature-dependent fatigue life model of polymer gears is stablished, in which the contact and bending fatigue failures are estiated based on separate fatigue criteria, considering their own specific tress-strain histories"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003857_j.addma.2020.101081-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003857_j.addma.2020.101081-Figure3-1.png",
        "caption": "Fig. 3. Geometry of the investigated tensile specimens [34]. Dimensions are given in mm.",
        "texts": [
            " The respective laser parameters were chosen based on the results of previous findings on densification of AISI 316L stainless steel and several tool steels [34\u201336]. It was assumed that the densification behavior of the AISI 316L and the investigated X40MnCrMoN19-18-1 steel were similar, and the chosen parameters were identified as promising. An x/y interlayer stagger strategy was used for the buildup. =E P l eff p t d E (1) For microscopic investigations of the resulting microstructure of the X40MnCrMoN19-18-1 steel, only small cubic samples with an edge length 5mm x 5mm x 2.55mm (length x width x height) were built. Furthermore, tensile specimens (Fig. 3) were produced with the most favorable set of laser parameters in order to characterize the mechanical properties of the L-PBF-built X40MnCrMoN1-18-1 steel compared to the same steel in the HIPed condition. In addition to L-PBF-densified X40MnCrMo19-18-1 steel in the asbuilt condition (L-PBF), L-PBF-built and solution-annealed specimens (L-PBF annealed) were investigated. Solution annealing was performed at a temperature of 1180 \u00b0C for 30min in an inert gas atmosphere. The same powder was used for producing specimens by hot isostatic pressing as a reference state",
            " For this purpose, a Bruker D8-Advanced device was used with a BraggBrentano set-up and CuK\u03b1 radiation (wavelength: 1.5406 \u00c5). The X-ray diffraction pattern was recorded in the range of 30\u201380 \u00b0 2\u03b8 with a step size of 0.01 and an acquisition time of 10 s per step. The obtained diffraction patterns were analyzed using the software DIFFRAC.EVA V3.0. The preparation of the investigated specimens was performed as described in the previous section. Tensile tests were conducted to compare the mechanical properties of the X40MnCrMo19-18-1 steel in the different conditions. The specimen geometry is shown in Fig. 3. Specimens were built with L-PBF or produced from bulk material (HIP) by electrodischarge machining. The specimens produced by L-PBF were oriented with their tensile direction perpendicular to the build direction. The gauge length of the specimens was 10mm at a width of 2mm and a specimen thickness of 2mm. The total length of the specimens was 26mm. Tensile experiments were performed in accordance with DIN EN ISO 6892-1:2016 [37] using a ZWICK-Roell Z100 tensile testing machine. A crosshead speed of 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002930_j.triboint.2016.03.017-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002930_j.triboint.2016.03.017-Figure3-1.png",
        "caption": "Fig. 3. Scheme of the Ball-on-disc Tribometer.",
        "texts": [
            " The temperature profile along any stripe is same as that of an infinitely long band heat source which has a width equal to the stripe length and has the same heat flux profile along the stripe. Hence, the following mesh grids are taken to predict the surface temperature as illustrated in Fig. 2. In the present study, a newly developed ball-on-disc tribometer by Sichuan University is used to measure friction coefficient of mixed lubrication in elliptical contacts with arbitrary velocity vector, as shown in Fig. 3. Both the disc and ball can be independently driven by motorized spindle. The ball-spindle has two degrees of freedom that can move back and forth, and achieve pivot angle at 730\u00b0 around its axis. The disk-spindle always has two degrees of freedom including up-down and left-right. Therefore, an arbitrary velocity vector at the contact zone can be obtained by this experimental setup. The lubricant parameters in this experiment are: kinematic viscosity 45.8 mm2/s (40 \u00b0C); viscosity \u03b70 0.08 Pa s, and pressure-viscosity coefficient 21"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001968_978-94-007-6101-8-Figure5.2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001968_978-94-007-6101-8-Figure5.2-1.png",
        "caption": "Fig. 5.2 Schematic presentation of St\u00e4ubli robot",
        "texts": [
            " Geometric models of robots, such as developed in previous chapter are also called forward models. With the forward geometric model we calculate the pose (position and orientation) of the robot end-segment or robot gripper from known joint variables. When developing an inverse geometric model, we know the position and orientation of the robot end-segment, while it is our task to calculate the joint variables [1]. The schematic presentation of anthropomorphic robot with a spherical wrist is shown in Fig. 5.2. Rotational joints are characteristic for anthropomorphic robot mechanisms. The axis of the first joint runs vertically from the robot base. This is a property of almost all industrial robots, enabling large workspace around the robot base. The axes of the following two joints remind us of human shoulder and elbow. They are parallel and perpendicular to the axis of the first joint. The remaining three rotational joints represent the robot wrist. The axes of all three joints intersect in the same point what will make possible to calculate separately the first three joint variables, which belong to the robot arm, from the last three joint variables, appertaining to the robot wrist. The joint variables are denoted from \u03d11 to \u03d16. T. Bajd et al., Introduction to Robotics, SpringerBriefs in Applied Sciences 73 and Technology, DOI: 10.1007/978-94-007-6101-8_5, \u00a9 The Author(s) 2013 Considering the DH rules, we have drawn all seven coordinate frames in the joints of the St\u00e4ubli robot shown in Fig. 5.2. The z0 axis is placed into the center of the first joint. The x0 axis is made parallel to the x1 axis. The axes of the first and the second joint intersect. The origin of the frame x1, y1, z1 is in the intersection of both axes. The x1 axis is perpendicular to the plane defined by the axes z0 and z1. The axes z1 and z2 are parallel. The origin of the frame is placed in the center of the third joint yielding thus d2 = 0. The x2 axis runs along the common normal in the direction from the lower to higher index",
            " The x4 axis is perpendicular to the plane defined by the axes z3 and z4, while the x5 axis goes perpendicularly to the axes z4 and z5. The robot end-point or robot gripper point is denoted by the letter P. The axes of the corresponding frame are parallel to the axes of the precedent coordinate frame. The fingers of the gripper are rotated in such a way that the unit vectors n, s, and a are placed into the robot end-point. We got acquainted with these vectors already in Fig. 2.5. In order to make Fig. 5.2 more clear, the y axes have been not drawn. From Fig. 5.2 it is not difficult to read the DH parameters, which are inserted into the table. The lengths of the segments d1, a2, d4, and d6 are denoted in Fig. 5.2. i ai \u03b1i di \u03d1i 1 0 \u03c0/2 d1 \u03d11 2 a2 0 0 \u03d12 3 0 \u2212\u03c0/2 0 \u03d13 4 0 \u03c0/2 d4 \u03d14 5 0 \u2212\u03c0/2 0 \u03d15 6 0 0 d6 \u03d16 We write the matrices (4.3) with the DH parameters of each line. The matrices describe the relative poses of the neighboring coordinate frames: 0A1 = \u23a1 \u23a2\u23a2\u23a3 c1 0 s1 0 s1 0 \u2212c1 0 0 1 0 d1 0 0 0 1 \u23a4 \u23a5\u23a5\u23a6 (5.1) 1A2 = \u23a1 \u23a2\u23a2\u23a3 c2 \u2212s2 0 a2c2 s2 c2 0 a2s2 0 0 1 0 0 0 0 1 \u23a4 \u23a5\u23a5\u23a6 (5.2) 2A3 = \u23a1 \u23a2\u23a2\u23a3 c3 0 s3 0 s3 0 \u2212c3 0 0 \u22121 0 0 0 0 0 1 \u23a4 \u23a5\u23a5\u23a6 (5.3) 76 5 Geometric Model of Anthropomorphic Robot with Spherical Wrist 3A4 = \u23a1 \u23a2\u23a2\u23a3 c4 0 s4 0 s4 0 \u2212c4 0 0 1 0 d4 0 0 0 1 \u23a4 \u23a5\u23a5\u23a6 (5",
            "11) nz = s23c4c5c6 \u2212 s23s4s6 + c23s5s6 (5.12) sx = \u2212c6(s1c4 + c1c23s4)+ s6(s1s4c5 + c1(s23s5 \u2212 c23c4c5)) (5.13) sy = c1(c4c6 \u2212 s4c5s6)\u2212 s1(\u2212s23s5s6 + c23(s4c6 + c4c5s6)) (5.14) sz = \u2212s23s4c6 \u2212 s6(s23c4c5 + c23s5) (5.15) ax = s1s4s5 \u2212 c1(s23c5 + c23c4s5) (5.16) ay = \u2212s1s23c5 \u2212 s5(s1c23c4 + c1s4) (5.17) az = \u2212s23c4s5 + c23c5 (5.18) px = d6s1s4s5 \u2212 c1(\u2212a2c2 + s23(d4 + d6c5)+ d6c23c4s5) (5.19) py = a2s1c2 \u2212 s1s23(d4 + d6c5)\u2212 d6s5(s1c23c4 + c1s4) (5.20) pz = c23(d4 + d6c5)+ a2s2 \u2212 d6s23c4s5 + d1 (5.21) The anthropomorphic robot is in Fig. 5.2 displayed in an arbitrary pose. In Fig. 5.3 the same robot mechanism is shown in its initial reference pose, when all joint variables equal zero and the x axes of the neighboring coordinate frames overlap. When developing the inverse geometric model of robot mechanism, we know the position and orientation of robot end-segment, while it is our aim to calculate the joint variables [2, 3]. With another words, we know all nine elements of matrix (5.9) and it is our task to write the expressions for the variables \u03d11 . . . \u03d16. Beside the elements of matrix (5.9) we know also the lengths of all robot segments. From Fig. 5.2 it is not difficult to realize the relation between the points P and Q. When knowing the position of the point P, px , py , pz , we know also the position of the point Q, qx , qy, qz : q = \u23a1 \u23a3 qx qy qz \u23a4 \u23a6 = \u23a1 \u23a3 px py pz \u23a4 \u23a6 \u2212 d6 \u23a1 \u23a3 ax ay az \u23a4 \u23a6 (5.22) 78 5 Geometric Model of Anthropomorphic Robot with Spherical Wrist z6 For the sake of more simple developing of inverse model, we shall lift the base coordinate frame x0, y0, z0 to the level od the second joint. In this way we shall limit our consideration to the second and third segment representing \u201cupper arm\u201d and \u201cforearm\u201d of the anthropomorphic robot"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000467_0954406212470363-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000467_0954406212470363-Figure3-1.png",
        "caption": "Figure 3. Schematic of the deposition pattern.",
        "texts": [
            " Full-fledged FE modelling of a complex 3D geometry (as shown in Figure 1) is impractical and every efforts have been made to choose appropriate and useful assumptions which helps to simulate the laser cladding process close to reality. The following are the specific assumptions considered in the current analysis: 1. Distortion in the DLD processes is a consequence of generated stresses.4 The stress is caused primarily by the thermal gradient20,21,23,24 induced by the laser heating. 2. The laser deposition process is simulated by adding prescribed amount (one segment per time step as shown in Figure 3(b)) of material at specific temperature and time. 3. To limit the overall computational time, each clad layers is discretised into five circular tracks and eight segments, as shown in Figure 3(b). The FEA solution time step size for the deposition of each clad sector is in-line with the experimental deposition rate. 4. The laser beam energy was absorbed predominately by the powder particles25 before they hit the substrate. The substrate was assumed to get heat from the molten deposited clad (melt pool) and not directly from the laser beam. With the above assumptions, the simulation was carried out in two sequential stages. The first stage considered a transient thermal analysis and in the second stage, a structural analysis utilising the thermal history from the previous thermal analysis was used to predict the corresponding distortion",
            " Simplifying the FEMs is a valid assumption and has the potential to give results with the required accuracy and with acceptable computational resources as demonstrated by many previous researchers.26\u201328 The mapped mesh of thermal element (DC3D8), which represents the 3D model used in this analysis, is shown in Figure 4 as a depiction of the elemental form of the geometric physical mapping of the aeroengine component under investigation. The thermal analysis simulates the temperature field arising from the continuous addition of powder with a CO2 laser power of 800W and laser beam diameter of 1.5mm diameter moving continuously at a speed of 1400mm/ min. As schematically illustrated in Figure 3, the clad was deposited as a series of small sectors from bottom to top, forming a layer of continuous ring shape and with a dwell time of 10 s between the deposition of layers. In-line with experimentation, the height of each layer was controlled to be at 1mm. Also, the width of the layers gradually increases (Part I in Figure 3(a)) from the bottom and attains maximum once it reaches the top of the curvature of the base plate (Figure 3(a)) and thereafter it rises steadily. The deposition of clad starts from Track 1 to Track 5 (i.e. inside to outside) and in each track, the small sectors are deposited in the clockwise direction, as shown in Figure 3(b). In total, the deposited clad consists of 954 small sectors. The movement of the laser beam and the deposition of each sector shown in Figure 3 were controlled using ABAQUS python programming, so as to provide the required boundary condition at different positions at different times. Simulation of the temperature required a solution of the general heat conduction equation.20 Powder addition was modelled using the ABAQUS embedded feature of element deactivation/activation, which enables successive discrete addition of new elements to the computational domain. Implementation of the technique in this study was such that the region of the model representing the deposited clad was assigned with a predefined mesh",
            " This required that before the start of the simulation this region was partitioned comprehensively and meshed with the rest of model. At the start of the simulation, the group of elements representing the deposited clad were deactivated to simulate absence of material deposited at that instant. As the simulation progressed, element sets within the group, representing successively deposited powder components were reactivated to simulate material deposition20,29 (one sector per time step as shown in Figure 3); and this was done at a rate corresponding to the beam scanning speed of 1400mm/min. The resulting cooling phase to room temperature served as the final step in the solution of a time-dependent problem that was solved sequentially as a series of constant geometry problems (called steps), which were linked together by introducing the output of problem n as the initial condition for problem n\u00fe 1. Towards the calculation of distortion, the importance of the cooling phase in this time-dependent problem needs to be emphasised",
            " The second stage of the investigation dealt with a parametric study of base plate thickness and deposition patterns, focusing on identifying the combination of these parameters that will give rise to least distortion on the base plate. The FEM consists of 991 time steps (corresponds to a total time of 216min), of which, 27 time steps are used to account for dwell time between layers and the final 10 time steps (corresponds to 300 s) is for the cooling cycle. The clad deposition in the present model is inline with the sequence of the experiment, i.e. tracks deposited from inside to outside and in each track, clads (sector in Figure 3(b)) are deposited in clockwise direction. Figure 5 shows the full sequence of the deposition process and the corresponding temperature distribution during the process. The maximum temperature during the deposition is around 2216 C, which corresponds to the imposed temperature and the minimum temperature is close to 20 C, which is attributed to the water cooling effect simulated at the underside of the base plate. It can be interpreted from the figure that during the start of the deposition, a high thermal gradient is noticed on the sides close to the straight edges of the base plate than the curved edge of the base at University of Ulster Library on April 28, 2015pic",
            "comDownloaded from thickness was considered as 4mm for this analysis. All other parameters are kept constant to the previous models, and an initial pre-stress is imposed in the structural analysis. Figure 12 shows the schematic of the different deposition patterns that were studied using the FEA. The laser deposition pattern influences the shape and magnitude of thermal gradient over the base plate, which ultimately affects the baseplate distortion. Also, in this clad geometry, the layer thickness and length were not uniform (Part I in Figure 3) which eventually makes the deposition pattern as a key processing variable that influences the base plate distortion. The deposition patterns shown in Table 1. Various deposition patterns and sequence used in the analysis. Deposition pattern number Description Deposition pattern \u2013 1 In to out; circular pattern Deposition pattern \u2013 2 Out to in; circular pattern Deposition pattern \u2013 3 In to out; non-circular pattern Deposition pattern \u2013 4 Out to in; non-circular pattern Deposition pattern \u2013 5 In to out; rotate 90 after each deposition in one sector Deposition pattern \u2013 6 In to out; deposit in alternative tracks; circular pattern at University of Ulster Library on April 28, 2015pic"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003811_j.commatsci.2020.109752-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003811_j.commatsci.2020.109752-Figure6-1.png",
        "caption": "Fig. 6. (a) Experimental set-up within the L-PBF chamber, red circle highlights the specimen. (b) Schematic positions of the thermocouples on the substrate (c) Top view of one specimen with thermocouples attached. The (x, y) coordinates (in mm) of these six thermocouples are: CH1 (4.62, 1.09), CH2 (7.38, 1.38), CH3 (10.05, 1.85), CH9 (4.90, 4.25), CH10 (7.42, 3.76), and, CH11 (10.15, 3.32).",
        "texts": [
            " A commercial machine of type SLM280 HL (SLM Solutions Group AG, L\u00fcbeck, Germany) and equipped with a 400 W cw Ytterbium laser and a build platform of size 280 mm \u00d7 280 mm was used for the experiments. The process run in Argon gas atmosphere with oxygen content below 0.1% vol. The commercial 316L stainless steel powder with spherical particle morphology was used as material. The powder had a particle size distribution between 10 and 45 \u00b5m with a mean diameter of 34.69 \u00b5m and the following intercepts of cumulative mass: D10 of 18.22 \u00b5m, D50 of 30.50 \u00b5m, D90 of 55.87 \u00b5m (Ref.: SLM Solutions Group AG, L\u00fcbeck, Germany). Fig. 6(a) provides an overview of the experimental set-up within the L-PBF chamber. The sample builds were made on substrates that were also manufactured by the same powder using AM process on the same machine beforehand. These cuboid substrate structures of dimensions (15 mm \u00d7 5 mm \u00d7 10 mm) contained small grooves on the top surface to fix the thermocouples as shown in Fig. 6(b). Six K-type thermocouples of 0.127 mm diameter were spot welded in the grooves on the top surface of the substrate as shown in Fig. 6(c). The responses from the thermocouple were acquired through a measuring amplifier device MX1609 (HBM GmbH, Darmstadt, Germany) at a sampling rate of 300 Hz. Fig. 6(b) also illustrates the scanning area and the scan pattern, which was used for five different sets of experiments. The laser power and the layer thickness were kept constant at 275 W and 50 \u00b5m, respectively. Likewise, the length of the scan tracks and hatching distance were kept as 10 mm and 0.12 mm, respectively. The neighboring tracks were deposited in alternate mode. Three sets of sample builds, each in a configuration of (5 tracks per layer \u00d7 5 layers), were made at three different scanning velocities (300 mm/s, 700 mm/s, 1100 mm/s)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003720_j.addma.2020.101491-Figure12-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003720_j.addma.2020.101491-Figure12-1.png",
        "caption": "Fig. 12. Twenty-layer DED with unidirectional laser scanning strategy, laser power 1500W, scanning speed 8mm/s, mass feed rate 20 g/min. (a) build profile after the deposition of the 15th layer, (b) build profile after the deposition of the 20th layer, (c) variations of the build height along the build length direction.",
        "texts": [
            " Alternatively, variable hatch spacing could be used to tune the layer height through adjusting the mass distribution via the transport phenomena in the molten pools [35]. A comprehensive understanding of the mechanisms on build height modification via dynamic control of process parameters is important to the successful deposition of large AM components and would be further explored in future work. The measured experimental and computational data of the build height along the build length direction are further shown in Fig. 12. For the 10th layer, the build could be divided into three zones, i.e., the bump beginning zone from 0mm to 12mm, the flat middle zone from 12mm to 27mm, and the declining zone from 27mm to 42mm. One interesting point is that a valley exists between the bumped head zone and the flat middle zone of the layer. Such a variation originates from the liquid metal flow within the molten pool as depicted in Fig. 7. Such a near staircase build profile is undesired for uniform deposition, and may cause serious termination of the printing process"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001803_j.matchar.2017.11.042-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001803_j.matchar.2017.11.042-Figure3-1.png",
        "caption": "Fig. 3. Illustration of a moving melt pool and cellular growth direction as indicated by the solid green arrow. The orientation relationships between the growth direction and the plane (AA\u2032) normal to SD and the micrograph plane (B-B\u2032), respectively, are illustrated. The two coordinates, SD-TD-BD associated with A-A\u2032 and coordinate associated with B-B\u2032, are also illustrated. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)",
        "texts": [
            " Depending on the orientation of the grain (a group of cells), the cells may appear long or short in micrograph meaning large or low aspect ratio, respectively. For grains with a low aspect ratio appearance, cell orientation from EBSD analysis was used so that the crossing line for \u03bb1 measurement is normal to the cell grown direction. Measurements were conducted in locations 5\u201310 \u03bcm away from TB. To aid the illustration of cellular growth direction, a moving melt pool is schematically illustrated in Fig. 3. The melt pool represented by the green outline has moved to one as presented by the red outline along the scan direction (SD) for a distance dv after a time period (t1 to t2). Cross section A-A\u2032 is normal to SD. After SLM, samples were however sectioned along B-B\u2032 which has been explained and indicated in Fig. 1, and thus B-B\u2032 is 20\u00b0 to A-A\u2032. Both A-A\u2032 and B-B\u2032 are parallel to build direction (BD). Transverse direction (TD) is normal to both SD and BD. As B-B\u2032 is the sample metallography plane, unit cell orientations after EBSD analysis have been provided by the software based on this plane and the sample coordinate (xsp-ysp-BD). As an example, cellular solidification starting at a TB location O in Fig. 3 is illustrated. The growth direction is indicated by the green arrow along OP. EBSD analysis has provided direction information \u03d5, between OP and OR where OR is normal to TB in location O in ysp-BD (metallography) plane of the xsp-ysp-BD coordinate. The growth direction with \u03d5 in this xsp-yspBD coordinate needs to be expressed as \u03b8 in the SD-TD-BD (or the equivalent SDo-TDo-BD). This is simply done by using auto-CAD and rotating xsp-ysp-BD to SD-TD-BD by 20\u00b0 about BD carrying the crystal unit cell, followed by measuring \u03b8 directly",
            " It is thus worthwhile that, since \u03bb1 has been extensively measured and R can been estimated, G and T \u0307 are estimated and compared to available data from simulation and from estimation based on the empirical T \u0307-\u03bb1 relationship in literature. As Eq. (1) was developed based on cell growth direction normal to S-L plane, only \u03bb1 with low \u03b8 values applicable. Similar to fusion welding, teardrop ripples on SLM tracks together with fish-scale shape in track cross sectional view can suggest the melt pool shape, as in Fig. 3. Observing track surfaces and cross sectional view of the range of P samples (for considering lack of fusion formation) in Darvish et al.'s study [28], it is reasonable to take an average \u03b7 value in Fig. 2b to be ~10\u00b0, as an approximation. Then, from Fig. 7a, \u03bb1(\u03b8\u2248 10\u00b0)\u2248 0.68 \u03bcm should be taken for applying Eq. (1). Taking \u03b7=10\u00b0, R\u2248 sin10\u00b0\u00b7v= sin10\u00b0 \u00d7 700 mm/s = 121 mm/s. Data of \u0393 listed by Kurz and Fisher [10] for a number of metallic alloys are quite similar at \u0393\u2248 2\u00d7 10\u22127 K m and this is adopted in the present calculation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000218_1.3063817-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000218_1.3063817-Figure9-1.png",
        "caption": "Fig. 9 Pocket velocity vector resolved into radial and tangential components",
        "texts": [
            " 13 nd 14 can be reduced to Euler\u2019s simplified equations of rotaional motion, My c = Iyy c \u0308y c \u2212 Izz c \u2212 Ixx c z c x c 15 Mz c = Izz c \u0308z c \u2212 Ixx c \u2212 Iyy c x c y c 16 ote that in Eqs. 15 and 16 , x c refers to the angular velocity of he cage assembly about the X-axis of the cage reference frame. he average orbital velocity of the pockets approximates the anular velocity of the cage assembly about the X-axis of the cage eference frame and is given by ournal of Tribology om: http://tribology.asmedigitalcollection.asme.org/ on 01/27/2016 Terms x c = i=1 N vPt,i c rCP,i c sgn rCP,i c vPt,i c x N 17 where N is the number of pockets. Figure 9 depicts the vectors referenced in Eq. 17 . The position and velocity of the pocket are defined by the vectors rCP c and vP c , respectively. The velocity vector can be resolved into radial and tangential components. The tangential speed divided by the distance between the pocket and the origin of the cage frame of reference indicates the angular velocity of the pocket\u2019s orbit at each instant in time. In order to apply Euler\u2019s simplified equations of rotational motion, the axes of the cage reference frame must pass through the principal axes of inertia of the cage"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003686_tie.2019.2959504-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003686_tie.2019.2959504-Figure1-1.png",
        "caption": "Fig. 1. Illustration of machine topologies. (a) Conventional FSPM machine. (b) Proposed DF-FSPM machine.",
        "texts": [
            " This paper will show that the proposed DF-FSPM machine exhibits significantly higher torque density than conventional FSPM machine due to the utilization of rotor slot area. Moreover, the DF-FSPM machine also has the potential of high fault-tolerant capability since it employs two sets of armature windings, viz. the stator armature winding and rotor armature winding. The operating principle of the DF-FSPM machine will be unveiled in this paper at the first time. Finally, a prototype machine is tested to validate the finite-element (FE) predictions. II. MACHINE TOPOLOGY Fig. 1 shows typical topologies of conventional FSPM machine and the proposed DF-FSPM machine. In conventional FSPM machine, the armature windings are usually located on the stator side while the rotor slots remain empty for the purpose of brushless operation. The DF-FSPM machine can be derived from the conventional FSPM machine plus an armature winding located in the rotor slots, thus the slot area is expanded for torque density improvement. The two sets of armature windings are separately supplied by two inverters and they can work together or individually, which improves the fault-tolerant capability. In the DF-FSPM machine, either the PM side or non-PM side can be the rotor. Nonetheless, in this paper, the non-PM side is selected to be the rotor since the PM side is relatively fragile compared to the non-PM side due to the modular structure, as shown in Fig. 1(b). The rotor armature winding and its inverter are connected by brushes and slip rings, which may restrict the rotating speed of rotor. Although the brushes and slip rings can decrease the reliability of the rotor machine part, the fault-tolerant capability is improved to some extent. It is because the remaining set of armature winding can still work even if the other set breaks down. Although the reliability can be further improved if the brushes and slip rings can be replaced by wireless energy transfer, it is not the topic of this paper",
            " Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. IV. ELECTROMAGNETIC PERFORMANCE By way of examples, the electromagnetic performance of the proposed DF-FSPM and conventional FSPM machines with 12-stator-pole/10-rotor-tooth is compared in this section. Both are optimized for high torque density. Their main parameters and geometries are shown in Table I, Fig. 7 and Fig. 1. It should be noted that the torque components produced by stator and rotor windings are kept equal during the optimization of DF-FSPM machine for high fault-tolerant capability. Under such condition, about half of the rated torque can still be obtained by keeping current supply of healthy armature winding unchanged when the fault winding is cut off. Both machines have different heat source distributions, and hence they prefer different ways of thermal management. However, to avoid the thermal simulation and simplify the analysis, the comparison is conducted under the fixed copper loss for both machines"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000600_j.mechmachtheory.2013.10.003-Figure17-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000600_j.mechmachtheory.2013.10.003-Figure17-1.png",
        "caption": "Fig. 17. The relationship between the shortest distance and the backlash of the tooth pair.",
        "texts": [
            " The second involves determining where the shortest distance occurred. 7.1. The relationship between the backlash and the shortest distance of the tooth profiles To obtain the initial backlash between profiles of the FS and the CS, the teeth of the deformed FS are considered to be rigid during the action of the WG. The tooth pair with the smallest initial backlash is the first contact pair. The relation between the shortest distance and the backlash of the tooth profile with the DCTP is shown in Fig. 17. The coordinate system is the CS coordinate system. The origin O is located on the rotational center of the CS, and axis x is the symmetric line of the CS tooth space. The movement trail of any point on the CS profile is an arc. Therefore, the backlash can be expressed as follows: jmin \u00bc dmin= cos \u03b11 \u00fe \u03b12\u00f0 \u00de: \u00f022\u00de Here, \u03b11 \u00bc arctan kdmin ; \u03b12 \u00bc arctan xA1=yA1\u00f0 \u00de, where kdmin is the slope of the line along shortest distance. 7.2. The shortest distance calculation of the tooth profile with the DCTP in different positions As mentioned above, the DCTP comprised two arcs connected with a common tangent"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000050_nme.2959-Figure22-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000050_nme.2959-Figure22-1.png",
        "caption": "Figure 22. Final residual longitudinal stress distribution.",
        "texts": [],
        "surrounding_texts": [
            "In this section, the simulation of the construction of a titanium wall by SMD is presented. The same geometry, material properties and process parameters than in the previous example were Copyright 2010 John Wiley & Sons, Ltd. Int. J. Numer. Meth. Engng 2011; 85:84\u2013106 DOI: 10.1002/nme used, which were validated by comparison to experiments. The only difference is the number of layers that are deposited to form the wall. The image sequences given in Figures 25 and 26 show the addition of filler material for each layer in four time instants with temperature plots. Figure 27 shows the residual longitudinal stresses that were developed 500 s after the beginning of the process."
        ]
    },
    {
        "image_filename": "designv10_5_0000807_j.mechmachtheory.2013.06.013-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000807_j.mechmachtheory.2013.06.013-Figure6-1.png",
        "caption": "Fig. 6. The contact line families on surface \u22112.",
        "texts": [
            " The following is an overview of the computational steps that are to be used for the calculation of the contact line families, and the program is developed by the application of the code of MATLAB: (1) Use vector function r2(ur,\u03b8r(ur,\u03c8s),\u03c8s) (see Eq. (10)) and take \u03c8s = const. (2) Assign ur and compute x2, y2, z2 from r2(ur,\u03b8r(ur,\u03c8s),\u03c8s) = R2(ur,\u03c8s), and then we obtain a contact line on surface \u22112. (3) Choose another value of \u03c8s and repeat the above steps, then we obtain the contact line families on surface \u22112. The design parameters of face-gear drive considered for this example are represented in Table 1. The results represented in Fig. 6 are obtained considering ur2 \u2264 ur \u2264 ur1 and Eq. (11). Fig. 6(a) and (b) shows that the contact line is a symmetric distribution in the tooth surfaces of the face-gear. As shown in Fig. 6(a), the meshing angle \u03c8s of the shaper is in the range of \u2212 17.6\u2218 to 18.8\u2218. The maximum value of \u03c8s occurs when the contact line reaches point A (see Fig. 7) and the minimum value of \u03c8s occurs when the contact line reaches point B (see Fig. 7) where point B is located at the bottom of the working tooth surface of the face-gear (Figs. 6(a) and 7). Using Eqs. (4) and (10), assume Rs ur ; \u03b8r\u00f0 \u00de \u00bc xs; ys; zs;1\u00f0 \u00de \u00f012\u00de R2 ur ;\u03c8s\u00f0 \u00de \u00bc x2; y2; z2;1\u00f0 \u00de: \u00f013\u00de Using Eqs. (12) and (13), and the values of \u03c8s(max) and \u03c8s(min) are determined by following functions f ur;\u03c8s max\u00f0 \u00de \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x22 \u00fe y22 q \u2212R2 \u00bc 0 z2 ur;\u03c8s max\u00f0 \u00de \u00fe rsm \u00bc 0 8< : \u00f014\u00de f ur ;\u03c8s min\u00f0 \u00de \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x22 \u00fe y22 q \u2212R1 \u00bc 0 ur \u00bc ur1 ( \u00f015\u00de R1, R2 are the inner radius and the outer radius of the face-gear, respectively. where Since the contact line is a symmetric distribution in the tooth surfaces of the face-gear, it is easy for us to obtain the value of \u03c8\u2032 s max\u00f0 \u00de \u00bc \u2212\u03c8s min\u00f0 \u00de and \u03c8\u2032 s min\u00f0 \u00de \u00bc \u2212\u03c8s max\u00f0 \u00de (see Fig. 6(b)). TCA is designated for the simulation of meshing and contact of surfaces \u22111 and \u22112 of pinion and face-gear respectively, which provides a way to investigate the influence of errors of alignment on transmission errors and shift of bearing contact. The TCA procedure is based on the application of coordinate systems shown in Fig. 8. S1, S2 and Sf are fixed to pinion, face-gear and the frame of machine respectively. Sq, Se and Sd are auxiliary coordinate systems as in Fig. 8. Parameters, \u0394E, B and B cot \u03b3 simulate the location of Sq with respect to Sf"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003030_j.triboint.2018.10.029-Figure10-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003030_j.triboint.2018.10.029-Figure10-1.png",
        "caption": "Fig. 10. Different simulated wear states shown on a single tooth in comparison with test gear photographs.",
        "texts": [
            " It is remarkably that the simulation shows that the pitting is not initiated at the point of the tooth flank with the highest tooth flank pressure, but there where the pressure and also the crack density according to micropitting is high. The worst combination of these two parameters exists usually at the transition from micropitting to the non-micropitting area. Consequently, this transition is the point where the initiation of a macroscopic pitting is most probable. This point is of course moving with the transition in the direction to the pith point during the simulated operation. The shown simulation results have a conformity to the real application of gears and the simulation has been validated by several bench tests. Fig. 10 shows the comparison of simulation and test rig results and demonstrates the high conformity. Five pictures of the same tooth flank are juxtaposed after different increasing load cycle (=LW) numbers. The typical sequence and dependency of the three mechanisms wear, micropitting and pitting is illustrated by this tooth flank after various times of testing in a test rig trial. The red curve on the pictures represents the simulated profile form deviation according to the previously described models and equations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001137_j.robot.2014.10.009-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001137_j.robot.2014.10.009-Figure2-1.png",
        "caption": "Fig. 2. A pick-and-place manipulator mounted on a ship with uncertain dynamics.",
        "texts": [
            " The objectives of a practical implementation based on the described control design are to choose the parameter values \u03bb, Am, Asp, \u0393 , and k in order to achieve desirable performance bounds on the prediction error r\u0303 , as well as to drive r sufficiently close to zero so that qa approaches the desired value qad within some desired bound. The adaptation gain \u0393 and the loop-shaping gain Asp decide the rate of adaptation. The matrix Am characterizes proportional\u2013derivative feedback terms for fine-tuning the performance. We restrict attention in this section to a typical pick-and-place manipulator operating on a ship in a high sea state, a scenario also investigated in [14,38\u201340]. The system is sketched in Fig. 2, in which w := (w1,w2,w3) is an inertial reference triad (with gravity along the negative w3-axis) and b := (b1, b2, b3) is a triad rigidly attached to the ship. We restrict attention to motions of the ship described by (\u03c6b, xb, zb), where \u03c6b represents the rolling angle of the ship (i.e., the rotation of w about w3 that yields b), and xb and zb represent the displacement of the ship\u2019s center of mass Cship relative to the inertial reference frame alongw1 andw3, respectively. These motions are caused by the unknown influence of surfacewinds,waves, and ocean currents"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001880_j.applthermaleng.2014.02.008-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001880_j.applthermaleng.2014.02.008-Figure4-1.png",
        "caption": "Fig. 4. The structure of the equivalent stator slots.",
        "texts": [
            " (2) Insulating paint of copper wire distributes homogeneously. (3) The slot equivalent insulating layer and the stator core are closed tightly. (4) The temperature difference of each wire in slot is neglected. Under the above assumptions, the copper wire in slot can be dealt with a heat conductor equivalently (not including varnish film). Impregnating varnish, slot insulation, varnish film of the copper wire can also be dealt with another heat conductor. The structure of the equivalent stator slots is shown in Fig. 4. The conductivity factors of all the insulating material are calculated as follows [18]. Keq \u00bc Pn i\u00bc1 di Pn i\u00bc1 di Ki (1) where, Keq is effective thermal conductivity, di (i\u00bc 1,2,3..n) is the thickness of each heat conductor, Ki is average thermal conductivity of each heat conductor. At steady state, the 3D thermal field can be obtained by the following equation [18]. v vx lx vT vx \u00fe v vy ly vT vy \u00fe v vz lz vT vz \u00bc q (2) where, T is the temperature, lx, ly, lz are the thermal conductivity in x, y, z direction respectively, q is the heat generation per unit volume"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003394_j.compstruct.2020.112698-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003394_j.compstruct.2020.112698-Figure9-1.png",
        "caption": "Fig. 9. Equivalent Von Misses stress in the case of a metal roll cage: a) entire structure and b) detail. Red areas represent zones where the stress level is close or higher than the Ti-alloy yield strength (930 MPa).",
        "texts": [
            " The numerical simulation was performed in line with similar studies performed by the authors for metal roll cages [67] using the load/constraint conditions described above. Shell 181 elements were also employed in this case, with 3431 nodes and 34,269 elements with dimension between 5 and 27 mm. Fig. 8 exhibits the total and directional deformations for the metal roll cage. With a maximum displacement of 20.6 mm in the vertical (Z) direction, 27.2 mm longitudinally (Y) and 7.5 mm transversally (Y), the cage was deformed by 28.3 mm toward the passengers. As shown in Fig. 9, several zones enter the plastic regime (>930 MPa) or exceed the failure stress (>1070 MPa), with local Von Mises equivalent stresses exceeding 1500 MPa in some regions. Risk to the occupants in the case of a rollover is clear, providing the opportunity to adopt improvements in the design. Manufacturing of the composite safety cage began with preparation of molds for the various subparts. The molds were manufactured by layup on models produced by CNC machining based on three\u2010 dimensional CAD representations of the various parts [48]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001179_1350650113513572-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001179_1350650113513572-Figure2-1.png",
        "caption": "Figure 2. Asperity model inspired by the micro-EHL analysis as considered by Lee and Cheng.18",
        "texts": [
            " Two-sided roughness was studied by Rhow and Elrod14 and Berthe and Godet;17 in this later paper, however, a stationary Reynolds equation was used. Elrod in his roughness review16 summarises practical questions and answers in relation to roughness and its function in lubrication. Here they are transcribed in Table 1, which at that time (1977) summarised the knowledge about roughness effects in lubrication. Recent developments \u2013 elastohydrodynamic lubrication (EHL) Lee and Cheng18 were among the early ones to consider the elastic deformation in the micro-geometry. They analysed the passage of an asperity through an EHL contact (see Figure 2), allowing elastic deformation. They observed that indeed the asperity experienced substantial elastic deformation, throwing doubts on models of \u2018partial\u2019 elastohydrodynamic lubrication in which the initial roughness is retained. Later progress in computational techniques, specially the introduction of multigrid techniques by Lubrecht, allowed researchers to study the behaviour of longitudinal and transverse ridges or dents, or sinusoidal ripples, e.g. Kweh et al.,19 Lubrecht et al.20 and including non-Newtonian and transient effects, Chang et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001601_1.4754521-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001601_1.4754521-Figure2-1.png",
        "caption": "FIG. 2. Free body diagram of a spherical micro-object in contact with the substrate in the induced rotational flows when viewed along the radial axis, ignoring radial and vertical fluidic drag forces. The microscopic roughness on the object and the substrate is enlarged.",
        "texts": [
            "38 If such lift-off occurs, then the object would tend to move with the surrounding flow without surface contact; if lift-off does not occur, then to initiate microobject movement, the propelling viscous drag force expe- rienced by the object must overcome the surface friction. \u2022 Orbiting criterion: To hold the object in a circular orbit rather than being ejected radially from the micromanipulator, the required centripetal force must be supplied by the total contribution from radial hydrodynamic forces and surface friction if the object is in contact with the substrate. As shown in Fig. 2, the radial shear-induced force points towards the rotation center where the tangential flow velocity is higher39 and thus would be the major hydrodynamic force to provide the centripetal force. A more detailed analysis is given in the following section. It should be noticed that the motion criterion is a neces- sary but not sufficient prerequisite to the orbiting criterion. The major forces acting on a micro-object in the induced rotational flow field are shown in the free body diagram of Fig. 2. While the object shape studied in this section is a sphere, the results can apply roughly to other shapes as well through similar analysis. The following terms are predefined: qobj and qf l are the density of the object and the [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 131.181.251.130 On: Sat, 22 Nov 2014 08:12:12 surrounding fluid, respectively. a is the radius of the microobject, is the kinematic viscosity of the fluid, uc is the flow velocity at the position of object\u2019s center, vobj is the velocity of the object, cr is the shear rate along the radial direction of the flow field, and cz is the shear rate along the vertical direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003593_tcyb.2020.2985221-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003593_tcyb.2020.2985221-Figure1-1.png",
        "caption": "Fig. 1. Unknown nonasymmetric dead zone.",
        "texts": [
            " , un]T is the control input vector, and d is the disturbance which is assumed to be bounded, with d = [d1, d2]T . Remark 1: The design of this algorithm is inspired by the existing wheeled mobile robot system in the laboratory. Due to the influence of complex working conditions, the requirements of the wheeled mobile robot system for torque input basically satisfy the form similar to the dead zone. Therefore, this chapter combines the qualification conditions that the torque input needs to meet into an asymmetric dead zone, and on this basis, the control algorithm design is completed. According to Fig. 1, the actuator dead-zone input can be defined as ui(t) = Di(\u03c4i) = \u23a7 \u23a8 \u23a9 mr,i ( \u03c4i(t) \u2212 br,i ) , if \u03c4i(t) \u2265 br,i 0, if \u2212 bl,i < \u03c4i(t) < br,i ml,i ( \u03c4i(t) + bl,i ) , if \u03c4i(t) \u2264 \u2212bl,i (2) Authorized licensed use limited to: University of Durham. Downloaded on May 16,2020 at 00:29:06 UTC from IEEE Xplore. Restrictions apply. where mr and ml are the right and left slope of the dead zone, respectively; br and bl are the breakpoints; and mr, ml, br, and bl are positive constants. Then, the dead zone can be rewritten as ui(t) = mi\u03c4i(t) + bi (3) where mi(t) = { mr,i if \u03c4i(t) > 0 ml,i if \u03c4i(t) \u2264 0 (4) bi(t) = \u23a7 \u23a8 \u23a9 \u2212mr,ibr,i if \u03c4i(t) \u2265 br,i \u2212mi(t)\u03c4i(t) if \u2212 bl,i < \u03c4i(t) < br,i ml,ibl,i if \u03c4i(t) \u2264 \u2212bl,i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002213_j.mechmachtheory.2014.06.006-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002213_j.mechmachtheory.2014.06.006-Figure9-1.png",
        "caption": "Fig. 9. State 5 of the derivative queer-square mechanism (\u03b11 b 0, \u03b12 N 0, \u03b211 = \u03b212, \u03b221 = \u03b222).",
        "texts": [
            " 8, the derivativemechanism changes to state 4 whose angle ranges satisfy \u03b11N0;\u03b211 \u00bc \u03b212b0 \u03b12b0;\u03b221 \u00bc \u03b222N0 : \u00f029\u00de It can be observed from Fig. 8 that limb1s has a relatively higher position, limb2s has a relatively lower position compared to the base OA1A2 and the platform E1F1E2F2 is lower than limb1p and higher than limb2p in state 4. Through rotating a negative angle \u03b11 and positive angle \u03b12 from the singular position, the derivative queer-square mechanism achieves state 5. The schematic diagram of state 5 is shown in Fig. 9. The angle ranges of state 5, which also satisfies the angle relation in Eq. (27), are illustrated as \u03b11b0;\u03b211 \u00bc \u03b212N0 \u03b12N0;\u03b221 \u00bc \u03b222b0 : \u00f030\u00de In state 5, limb1s is lower than the base OA1A2, limb2s is higher than the base and the platform E1F1E2F2 locates in the position higher than limb1p but lower than limb2p. Through rotating the negative values for angles \u03b11 and \u03b12 from the singular position, limb1s and limb2s have a relatively lower position compared to the base where state 6 is. The angle ranges in state 6 are given as \u03b11b0;\u03b211 \u00bc \u03b212b0 \u03b12b0;\u03b221 \u00bc \u03b222b0 : \u00f031\u00de In state 6, the limb1s, limb2s, limb1p and limb2p are lower than the base, and the platform E1F1E2F2 is lower than the limb1s, limb2s, limb1p and limb2p, as illustrated in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001150_j.mechmachtheory.2011.10.001-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001150_j.mechmachtheory.2011.10.001-Figure9-1.png",
        "caption": "Fig. 9. 3D model.",
        "texts": [
            " The output mechanism is floating plate mechanism, which is composed by the quadrate hole in the floating plates, the rollers and the protrudent parts on the cycloid gear and double supporting plates. Compared to the conventional pin-hole output mechanism, the floating plate mechanism has the following advantages: higher efficiency, larger load capacity, continuous motion; simple structure, easy to be manufactured and assembled; the output torque is moment of couple and no force on the eccentric bearing, which can extend the lifetime of the bearing. The 3D model of double-enveloping cycloid drive is as Fig. 9, and the physical prototype is as Fig. 10. The success of trial production of the physical prototype shows that double-enveloping theory can be applied for cycloid drives. Fig. 11 is the experimental test rig for the transmission error test. The test method is using static testing under no load operation condition. The polyhedron prism is connected to the output shaft of the gear reducer, and the output rotation angle can be tested by autocollimator. The rotation angle of the input shaft can be obtained from the stepper motor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003800_s40430-020-2208-7-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003800_s40430-020-2208-7-Figure5-1.png",
        "caption": "Fig. 5 Contact analysis model with manufacturing errors",
        "texts": [
            " The rotating speed of pin gear depends entirely on the rotating speed of the original rotating arm. Therefore, in this mechanism, the pin gear is considered as the input end and the cycloidal gear is the output end. After then, the tooth contact analysis can be completed. According to the meshing principle of cycloidal-pin gear, a contact analysis model of cycloidal-pin gear planetary (5)\u0394 k = Fpk rk Journal of the Brazilian Society of Mechanical Sciences and Engineering (2020) 42:133 1 3 133 Page 6 of 14 transmission with manufacturing errors is established, as shown in Fig.\u00a05. In order to facilitate the meshing analysis of gear teeth, the number of pin teeth from 1 to n (n is the number of teeth) is generally numbered in advance, so that the specific number of multiple teeth meshing at the same time can be clearly pointed out in the meshing analysis process. As shown in Fig.\u00a05, a pair of teeth in meshing state of pin gear and cycloidal gear is numbered as No. 0 teeth, and based on this, coordinate systems Sp0(xp0, yp0) and Sc0(xc0, yc0) which are fixed with No. 0 pin teeth and cycloidal teeth are established, respectively. Thus, the pin teeth and cycloidal teeth numbered i (0 \u2264 i \u2264 n) correspond to coordinate systems S(i) p (x(i) p , y(i) p ) and S(i) c (x(i) c , y(i) c ) , respec- tively. Point K is the meshing contact point, and 1 and 2 are the rotation angles of the pin gear and cycloidal gear relative to the yf axis, respectively",
            " 14 Transmission errors with pitch error and without pitch error T ra ns m is si on e rr or ( ar cs ec ) Pin wheel angle (deg)Pin wheel angle (deg) T ra ns m is si on e rr or ( ar cs ec ) (399.746,15.646) (234.053,-12.282) (a) Transmission error without pitch error (b) Transmission error with pitch error Journal of the Brazilian Society of Mechanical Sciences and Engineering (2020) 42:133 1 3 133 Page 12 of 14 influence of pitch error, TCA calculation is needed for multiple teeth. The example chooses No. 0 tooth in Fig.\u00a05 as the datum. Firstly, the initial meshing reference point of No. 0 tooth (transmission error value is 0) is determined, and the pin gear rotation angle (0) 1 and cycloid gear rotation angle (0) 2 of the meshing reference point are solved. Then, TCA is used to solve all gear pairs in turn. Figure\u00a014 shows the results of two transmission errors with pitch error and without pitch error. As can be seen from Fig.\u00a014a, the transmission error curve fluctuates smoothly without considering the influence of pitch error, and the maximum transmission error value is 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001006_s10846-014-0143-5-Figure15-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001006_s10846-014-0143-5-Figure15-1.png",
        "caption": "Fig. 15 Blade spring model [155]",
        "texts": [
            " The infinitesimal lift and drag of the blade element dr are given as: dL = 1/2\u03c1aU 2cbCl\u03b1\u03b1bdr (33) dD = 1/2\u03c1aU 2cbCddr (34) The forces perpendicular and parallel to the hub plane can be expressed in terms of the lifting and drag forces as follows: dF\u2016 = dL sin \u03c6b + dD cos \u03c6b (35) dF\u22a5 = dL cos \u03c6b \u2212 dD sin \u03c6b (36) Following the procedures from [13, 155], the total force on the blades parallel (F\u2016) and perpendicular (F\u22a5) to the hub plane can be expressed in terms of the air stream velocity components as: dF\u2016 \u2248 1 2 \u03c1cbCl\u03b1 ( \u03b6UT UP \u2212 U2 P ) dr + 1 2 \u03c1cbCDU2 T dr (37) dF\u22a5 \u2248 1 2 \u03c1cbCl\u03b1(\u03b6U2 T \u2212 UT UP )dr (38) The total pitch of the blade is given as \u03b6 = \u03b60 \u2212 \u03b61 cos \u03c8b\u2212\u03b62 sin \u03c8b, where \u03b60 is the collective pitch to control the thrust of the rotor and \u03b61 = Alon\u03b4lon, \u03b62 = Blat \u03b4lat are the linear functions of the pilot\u2019s lateral and longitudinal cyclic control stick inputs (\u03b4lat , \u03b4lon) and lateral and longitudinal control derivatives (Alon, Blat ). As seen in Fig. 15, the blade is modeled as a rigid thin plate rotating about the shaft at an angular rate of . The angular position of the blade in the hub plane is denoted as \u03c8b measured from the tail axis. The blade flapping hinge is modeled as a torsional spring with stiffness K\u03b2 . The moments acting on the blade are due to the lifting force described in Section 3.5, weight of the blade, the inertial forces acting on the blade, and the restoring force of the spring. Equating all the moments acting on the blade results in: \u03b2\u0308 \u00b7 ( 2 \u00b7 K\u03b2 Ib \u00b7 1 2Ib mbgR2 b)\u03b2 = 1 2Ib \u03c1cbCl\u03b1 \u222b RB 0 r(\u03b6U2 T \u2212 UT UP )dr (39) where the blade\u2019s inertia is given by Ib =\u222b Rb 0 mbr 2dr "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001838_j.bios.2015.05.071-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001838_j.bios.2015.05.071-Figure9-1.png",
        "caption": "Fig. 9. TensorTip Combo Glucometer component summary (Cnoga Medical Ltd., 2013).",
        "texts": [
            " Each individual ear clip requires monthly re-calibrations against invasive basal and postprandial fingertip measurements which may take 90\u2013120 min; this can be done at home however is recommended at the clinic. The ear clip must be replaced every 6 months and USB is used to download data and recharge the battery (HarmanBoehm et al., 2010). It also has verbal instructions for individuals with eyesight impairment. This is a dual non-invasive and invasive glucose monitor where the finger is inserted into the device. It comes with an invasive add-on which uses fresh capillary whole blood for personal calibration (Cnoga Medical Ltd., 2013). The components of the device can be summarised by Fig. 9. 3.3.1.1. Dexcom G5 and G6 CGM. The Gen-5 sensor is to be released in late 2015; designed to port directly to a smart phone using lowenergy Bluetooth (Gregg, 2013a). This connection is protected by Patent US 2014/0012118 A1. The Gen-6 is being developed for 2015\u20132017 and will be highly resistant to 24 drugs commonly used in hospitals; including Tylenol and Acetaminophen up to 1000 mg. As a result it will be very accurate with said single digit MARD. It will also be factory calibrated and wearable for 10 days without having to calibrate with finger stick measurements"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003199_j.mechmachtheory.2019.103576-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003199_j.mechmachtheory.2019.103576-Figure9-1.png",
        "caption": "Fig. 9. Face-gear line of singularities representing undercut. Face-gear tooth is cut outside this line.",
        "texts": [
            " (35) to (37) are needed to calculate the singular points. So we may obtain the relation F 2 s (u s , \u03b8s , \u03c6s ) = 2 1 + 2 2 = 0 (39) Solving both Eqs. (19) and (39) enables the calculation of the position of singular points on the flank surface. The quadratures in Eq. (39) lead to an unsteady function; hence, it makes it difficult to solve it quickly by stable numerical approaches. From this, it is advantageous to solve one of the Eqs. (35) and (36) first and to check if the resulting parameters fulfil the other equation afterwards. Fig. 9 shows the line of singularities representing the undercut of a face-gear. In most cases, and especially for face-gear drives with a high gear ratio, it is sufficient to calculate the singularity for the lowest flank line and to cut the face-gear tooth outside this point. If the cut is to be made further inside, for example, to increase the usable flank or to increase the tooth stiffness, the exact geometry at the interior of the tooth must be calculated. A method for calculating the tooth shape in this area is presented in the next chapter"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001880_j.applthermaleng.2014.02.008-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001880_j.applthermaleng.2014.02.008-Figure5-1.png",
        "caption": "Fig. 5. The magnetic flux distribution of the healthy and faulty motor.",
        "texts": [
            " In magnetic field model, the saturation and harmonics are taken into account, so the losses can be evaluated correctly. The solution run time is 9 s, 12 s and 13 s and the iteration number is 13, 16 and18 respectively in themagnetic field simulationwith healthy rotor, one broken bar and two broken bars. The magnetic flux of the motor under rated load for the cases of symmetrical (with healthy rotor) and asymmetrical (with a one-broken-bar and a continuous twobroken-bar) rotor condition are shown in Fig. 5. From it, we can know that thedistribution ofmagneticfield for the case of nobroken bars is symmetrical, while the symmetry of magnetic field distribution is distorted in the case of broken bars and a higher degree of magnetic saturation can be observed around the broken bars. In the rotor bar, complex vector magnetic potential _Az should satisfy [21]. v2 _Az vx2 \u00fe v2 _Az vy2 \u00bc jum0s _Az m0 _Jsz (12) where, s is the conductivity of the bars, m0 is the permeability, _Az is magnetic vector potential, _Jsz \u00bc _Im=Sb, _Im is the current passing through bar, and Sb is the cross-sectional area of bar, and the current density distribution, including the healthy rotor and faulty rotor is showed in the following Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000492_tie.2011.2168795-Figure10-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000492_tie.2011.2168795-Figure10-1.png",
        "caption": "Fig. 10. Magnitude of the first harmonic of magnetic flux density for motor A.",
        "texts": [],
        "surrounding_texts": [
            "For that purpose, the Opera-2d/RM was chosen with the transient eddy-current solver extended to include the effects of rigid body (rotating) motion and connection of external circuits. The mesh was refined to minimize the solution errors and achieve reasonable compromise between accuracy and calculation times. The final mesh consists of 41 872 elements and is shown in Fig. 7. The application of the field-circuit method to the modeling of the magnetic field distribution in an induction motor, taking into account the movement of the rotor, requires the introduction of a special element into the model, which suitably connects the stationary and moving parts. In the rotating machine module of Opera-2d, this element takes the form of a gap element. The gap region (Fig. 8) is divided quite uniformly into 528 elements along the circumference of the gap. This yields the time of displacement of one element that is equal to about 7.5 \u00d7 10\u22125 s at synchronous speed, comparable with the average time step of computation. The gap region subdivision is essential to avoid erroneous oscillations in the field solution due to meshing. The machine was operated at synchronous speed and fed by a sinusoidal voltage. The computation accounts for the conductance of the rotor bars. The start of the modeling period is related to the instant of switching on the voltage while the rotor rotates with synchronous speed. Despite the fact that the voltage in the first two cycles increases linearly, there is an initial transient; hence, computation continues up to 0.2 s when the transient has disappeared (this is monitored by watching the phase currents and electromagnetic torque). Several snapshots were taken over the voltage cycle that followed. Fig. 9 shows the magnetic field distribution after the 0.2-s time. A number of sample points were chosen to allow for the subsequent DFT analysis. Eighty points were in fact used, and it was found important that the subdivision angle of the air gap and the angle between sample points were not the same or multiples of each other. Using the values of x and y components of magnetic flux density in each element calculated at sample points, the DFT analysis was performed in order to assess the contribution of higher harmonics Bpk = N\u22121\u2211 n=0 Bp(n)e \u2212i2\u03c0kn N , p=x and y; k=0, 1,. . ., N 2 (6) where k is the harmonic order and N is the number of sample points. The components of the flux density were calculated in the stationary frame of reference. The DFT applied to elements of the rotor moving with the rotor necessitates a simple transformation in terms of the rotor position angle Bx(rf) =Bx(sf) cos(\u03b1) + By(sf) sin(\u03b1) By(rf) = \u2212Bx(sf) sin(\u03b1) + By(sf) cos(\u03b1) (7) where \u03b1 describes the position of the rotor in a given time instant. The number of calculated harmonics was selected according to the Nyquist\u2013Shannon sampling theorem as half of the number of sample points. The core losses in each element were evaluated using the specific core loss expression, in which the parameters\u2014dependent on frequency\u2014and flux were derived from a test conducted on a sample laminated ring core. To highlight the importance of motion of the rotor, calculations were done with and without including the rotor movement. Detailed results may be found at the end of the section. Figs. 10\u201313 show the distribution of calculated magnitudes of the flux density harmonics for motors A and B. More results can be found in Appendix A. Core losses were calculated as a sum of losses due to individual harmonics and are based on specific losses measured on a ring sample at a given frequency. The superposition of losses constitutes the main simplifying approximation of the method. In reality, the higher harmonic losses are related to the resultant saturation of the magnetic circuit as influenced primarily by the first harmonic and the phase displacement of the first and higher harmonics [17]. Notwithstanding this simplification, the approach used gives quite realistic results because of the dominating influence of eddy-current losses at higher frequencies, which are less sensitive to the changes in the saturation level due to the fundamental harmonic. The DFT analysis was conducted for each element of the mesh separately using the time samples. As a result, we can construct as many tables as the computed harmonics are, each containing the results of the DFT analysis for each element in the form of sine and cosine components of the flux density. This allows color zone maps to be produced, employing the built-in procedures of a standard software package but using the relevant table as a source. This makes it also possible, for each element, to calculate the lengths of the major and minor axes of the elliptic hodograph of vector B in time and define its axis ratio (the degree of roundness of the ellipse). Loci of magnetic flux density for motor B can be found in Appendix C. Another problem that we often encounter when calculating core losses is related to rotational losses. At low and medium flux density values, the rotational losses may be several times higher than the alternating flux density losses. There are two possible approaches to resolve the difficulties. The first, presented in [18], introduces correction coefficients for hysteresis and excess losses, while the second applies correction to the total loss computed for a purely alternating flux [19], [20]. The second approach, which is more convenient in our case, was used to correct the calculated losses. The correction was made only for the first harmonic. The model of loss increase derived in [19] and [20] only applies to 50 Hz and cannot be directly used at higher frequencies. Moreover, the correction is mainly applied to the hysteresis losses as their contribution to the total losses decreases significantly as frequency increases. For the machine examined, this problem is not critical because only a small volume of the core is subjected to the rotational flux (less than 12% for the first harmonic). For high-power machines, on the other hand, about 60%\u201370% of the stator core volume is subjected to an alternating flux and about 30\u201340% to a rotational flux [21]. The degree of rotation is expressed in terms of the axis ratio, which is defined as the ratio of the minor and major axes \u03bb = Bmin Bmaj (8) where Bmaj and Bmin are the peak flux density values along the major and minor axes of the field loop. The rotational losses were calculated as follows [19], [20], [22]: Prot = [Palt(Bmaj) + Palt(Bmin)] \u03b3(\u03bb,Bmaj) (9) where Palt denotes the measured alternating iron losses. The values of \u03b3 as a function of \u03bb and Bmaj are shown in Fig. 14. Furthermore, the average aspect ratio is about 0.2, and in regions where the ratio is higher, the amplitude of flux density is close to 1.5 T for motor A, for which the correction is quite small. Fig. 15 shows the aspect ratio for the first harmonic for motors A and B. Fig. 16 shows the flux density magnitude for motor A. A rotor cage, even when rotating at synchronous speed, is subjected to magnetic flux density changes due to slotting effects. Therefore, additional losses will occur. These losses are relatively high, up to a significant percentage of total losses. This part of losses was calculated as an average value taken from all time snapshots [23], [24]. To emphasize the need to take into account the motion of the rotor in the calculation of losses, Figs. 17 and 18 show a comparison between losses calculated with and without the rotor movement. More results can be found in Appendix B. From these results, it is clear that including motion of the rotor is crucial for accurate loss calculation. Figs. 19 and 20 show the iron loss components, from the fundamental to the 40th harmonic, according to the harmonic order. One can notice significant contribution of slotting harmonics to the total losses. Fundamental losses amount to only about a half of the total losses. Thus, the losses in the rotor are dominated by the losses in the tooth tips. Despite the similarities between the constructions of both motors, the distributions of harmonics for motors A and B differ due to a significant difference in the magnetic circuit saturation level [25]. The no-load core losses calculated using the field-circuit method for motors A and B are presented in Table I."
        ]
    },
    {
        "image_filename": "designv10_5_0003313_j.mechmachtheory.2019.03.012-Figure21-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003313_j.mechmachtheory.2019.03.012-Figure21-1.png",
        "caption": "Fig. 21. Detailed comparison of the no contact region for the phase diagram of Fig. 15 . Model A to the left, model B to the right.",
        "texts": [],
        "surrounding_texts": [
            "Non-linear analysis is conducted by simulating the transmission\u2019s response for a variety of scenarios, using in house developed MATLAB & Simulink code. The equations of motion (9) are reformulated for implementation in Simulink, using function blocks with MATLAB functions for the non-linear operations, such as solving (3) or computing the active tooth pairs according to (8) . An ode45 solver is used for integration. In particular, 100 different scenarios are examined, comprising 10 values for input rotation speed, linearly distributed between 600 and 6000 rpm and 10 values for output load, logarithmically distributed between 1 and 100 Nm. All scenarios are examined in two simulation variants, one in which the complete set of non-linear equations of motion (9) is utilized (model A) and one in which the model is simplified by reducing the number of DOFs (model B). In the latter model, tooth inertia is ignored and the values of tooth angles are derived from a static equilibrium condition, based on the values of \u03d51 and \u03d52 . As a result, tooth angles become dependent variables instead of DOFs. This simplified approach is used for determining the influence of tooth inertia modeling on the simulated response."
        ]
    },
    {
        "image_filename": "designv10_5_0003301_j.mechmachtheory.2019.01.014-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003301_j.mechmachtheory.2019.01.014-Figure5-1.png",
        "caption": "Fig. 5. Schematic of a single-nut ball screw under load.",
        "texts": [
            " In some particular cases, the rolling balls will lose contact with the grooves, and the contact force Q ij is 0. The dynamic model of vertical stiffness is piecewise function of vertical displacement as reported in Ref. [3,18] and these papers only analyze the effects of vertical load on dynamic response. With the increase of displacement, the stiffness of linear guide first decreases and then increases. In this analysis, the dynamic model is constructed by considering the coupling of three dimensional forces and two moments on the vibration of the feed system. Fig. 5 shows a single-nut ball screw under load; this is applied preload by a variable lead. The displacement of screw-nut along the X axis is caused by the elastic deformation of balls between screw-shaft and screw-nut. The deformation of ball is shown in Fig. 6 , and the contact force can be calculated using the Hertz contact theory F n = ( \u03b5 n \u22121 \u03b4n ) 3 2 (16) where \u03b5n is the Hertzian contact constant between balls and ball screw. To obtain the contact force, the relationship between contact deformation and contact load can be derived as shown in Fig",
            " Then, the new contact angels of right and left rolling balls can be obtained as follows: tan \u03b11 = A 0 s sin \u03b10 A cos \u03b1 + x (20) 0 s 0 ns tan \u03b11 \u2032 = A 0 s sin \u03b10 A 0 s cos \u03b10 \u2212 x ns (21) The total elastic deformations \u03b4n and \u03b4n \u2032 of rolling balls can be given by 2 \u03b4n = A 1 \u2212 A 0 n (22) 2 \u03b4n \u2032 = A 1 \u2032 \u2212 A 0 n (23) The contact forces of rolling balls in the left and right sections along the X axis can calculated as follows: F n = ( \u03b5 n \u22121 \u03b4n ) 3 2 cos \u03b11 = ( \u03b5 n \u22121 \u03b4n ) 3 2 ( A 0 n cos \u03b10 + x ns ) \u221a ( A 0 n sin \u03b10 ) 2 + ( A 0 n cos \u03b10 + x ns ) 2 (24) F n \u2032 = ( \u03b5 n \u22121 \u03b4n \u2032 ) 3 2 cos \u03b11 \u2032 = ( \u03b5 n \u22121 \u03b4n \u2032 ) 3 2 ( A 0 s cos \u03b10 \u2212 x ns ) \u221a ( A 0 s sin \u03b10 ) 2 + ( A 0 s cos \u03b10 \u2212 x ns ) 2 (25) The interface force acting on the worktable is the sum of contact force of the balls in the right and left grooves, which is a piecewise function about the relative displacements. With the increase of load F x , the contact force F n of balls in the left grooves increases, and the contact force F n \u2019 of balls in the right grooves decreases to 0. As shown in Fig. 5 , the interface force also acts on the screw-shaft and causes the deformation of screw-shaft. The axial motion of screw-shaft is allowed at the rear end, and only the right section of screw-shaft is subjected to both tension and torsion. The tensile and torsional stiffness depend on the position of the screw-nut, which can be expressed by [5] K s ( X l ) = 1 / ( 1 / 4 GE \u03c03 d 4 1 16 G \u03c02 d 2 1 ( X L \u2212 X l ) + 32 P 2 E( X L \u2212 X l ) + 1 / \u03c0d 2 1 4( X L \u2212 X l ) ) (26) where X l is the distance between screw-nut and rear bearing unit, and X L is the screw length of screw-shaft"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003691_j.jallcom.2020.153840-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003691_j.jallcom.2020.153840-Figure2-1.png",
        "caption": "Fig. 2. Deposition efficiency dependence on the scanning velocity v and the powder feed rate m for different laser spot diameter values: a) 1.63\u00b10.03 mm, b) 1.76\u00b1 0.04 mm, and c) 1.85\u00b10.05 mm.",
        "texts": [
            " The unique methodology gave a strong clue for easy parameters selection enabling obtaining high quality clads, however no information about cladding effciency was provided. The easiest parameters to change and manipulate from a practical perspective are the spot diameter, scanning velocity, and mass powder feed rate; thus, these parameters were chosen as variables. Using the highest available laser power was justified by the potential industrial use and goal to obtain the most effective process possible. The influence of the abovementioned parameters is presented for each sample series (A, B and C) in the 3D graphs (Fig. 2). As shown in the graphs, the best results for efficiency were obtained with a small scanning velocity v, which was expected. To some extent, a decrease in the mass powder flow rate increased the efficiency as well. However, in the investigated range, it did not appear to exert a very significant effect, since a local maximum in the efficiency was observed at approximately 4 g/min of powder fed into the molten metal pool for samples produced using the smallest spot diameter (series A). For all series of deposited samples, the actual powder efficiencywas found to be between 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000560_j.jsv.2009.03.013-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000560_j.jsv.2009.03.013-Figure3-1.png",
        "caption": "Fig. 3. Loads acting on a roller.",
        "texts": [
            " This solution, valid at any point of the ring, takes into account the flexural and the extensional deformations: uY \u00f0y\u00de \u00bc Fc N ro 2pE Ao \u00fe F c N r3o pE Io X1 q\u00bc1 1 \u00f0\u00f0qN\u00de2 1\u00de2 cos\u00f0qNy\u00de (6) For the complete loading of the outer ring, this yields u\u00f0y\u00de \u00bc XN j\u00bc1 \u00f0Qoj F c\u00de X2 n\u00bc0 Kn cos\u00f0n\u00f0fj y\u00de\u00de \u00fe uY \u00f0y\u00de (7) The roller bearing behavior is described by solving a set of dynamic, equilibrium and geometric nonlinear equations, including both cage and lubricant effects. The problem is planar, so only pure radial loading is considered, assuming perfect geometry for the rolling elements and no ring misalignment. Fig. 3 shows a roller loaded at the roller/race contact (Q), at the front or rear roller/cage pocket contact (QC1 and QC2, respectively), and submitted to a centrifugal force (Fc). Dry or lubricated traction forces at the roller/race and roller/pocket (F, FC1 and FC2, respectively) are of primary importance in roller equilibrium. A resisting torque (CP) due to an asymmetric hydrodynamic pressure field and the oleodynamic drag force (FOL) are considered. Due to small internal clearances needed for high-speed operation, friction effects at the roller end/cage pocket (friction torque CC) and roller end/guiding flange (traction force FE and friction torque CE) are also considered"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000035_tie.2010.2095392-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000035_tie.2010.2095392-Figure2-1.png",
        "caption": "Fig. 2. Overview of PAROYS-II.",
        "texts": [
            " Section II provides the hardware features of PAROYS-II, including the diameter-change adaptive mechanism and driving modules. In Sections III-A and B, normal-force control and posture control are described. An inclination estimation method of the pipes and an optimal normal-force control scheme are described in Sections III-C and D, respectively. Section IV discusses experimental results, and conclusions of the research are provided in Section V. PAROYS-II is composed of three parts, as shown in Fig. 2: a center module, a track module, and an active pantograph mechanism. The pantograph mechanism and the track module are located symmetrically on the center module, 120\u25e6 apart. The center module expands or contracts the pantograph to adapt to changes in pipe diameter. The track module rotates freely about the pantograph mechanism to maintain contact with uneven surfaces. The control unit composed of ATMEGA128 and an inertial measurement unit (IMU) is attached to the center module of the robot. PAROYS-II has a maximum speed of 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001461_icra.2013.6631355-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001461_icra.2013.6631355-Figure2-1.png",
        "caption": "Fig. 2. UPAT\u2013TTR hardware setup",
        "texts": [
            " Additionally, the UPAT-TTR is developed so as to be equipped with those sensorial and control subsystems, that guarantee its operational autonomy. The article is structured as follows: In Section II the specifics of the UPAT-TTR platform are presented. In Section III the system model, and in Section IV the state estimation subsystem are presented. In Section V the control scheme and in Section VI experimental results of the system\u2019s controlled hovering operation are presented. The article is concluded in Section VII. The complete setup of the UPAT-TTR is depicted in Figure 2. Detailed hardware and software specifics for this experimental prototype are found in [1]. The key characteristics of the current platform design, implemented in order to obtain a UAV capable of performing autonomous hovering operation in small-scale areas, are presented: The Main Control Unit (MCU) is based on an Intel Atom Z530 1.6 GHz CPU-based Kontron pITx Single Board Computer, running a common Ubuntu Linux desktop distribution. The handling of low-level communication and control signals is achieved via full-speed USB interfacing of the MCU to an ARM Cortex M3-based microcontroller"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000497_978-90-481-9262-5_57-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000497_978-90-481-9262-5_57-Figure1-1.png",
        "caption": "Fig. 1 (a) CAD draft of the spatial cable-driven parallel robot IPAnema with eight cables and six degrees-of-freedom. (b) Geometry and kinematics of a general cable robot.",
        "texts": [
            "ey words: Cable-driven parallel robot, forward kinematics, controller, real-time. In the last decade, a lot of research has been carried out to study both, theory (see e.g. [1\u20133]) and implementation [4] of cable-driven parallel robots. For a mobile platform with n degrees-of-freedom, in general, at least m = n + 1 cables are required to fully control the motion [5]. Therefore, many cable robots are under-determined with respect to distribution of forces in the cables and overdetermined with respect to forward kinematics (Fig. 1a). As a consequence of the latter, it is challenging to calculate the forward kinematics of the cable robot in realtime. Thus, one has to estimate the pose of the mobile platform from given length of the cables. In the literature, different approaches for that problem were suggested. In general, the forward kinematics of parallel robots can have up to 40 solutions and the algorithm by Husty [6] gives deep insight into the number of solutions and their mathematical structure. Unfortunately it seems inadequate for real-time implementation",
            " A closed-form kinematic code for the so-called 3-2-1 configuration is well suitable for 529 Machine, DOI 10.1007/978-90-481-9262-5_57, \u00a9 Springer Science+Business Media B.V. 2010 J. Lenar\u010di\u010d and M.M. Stani\u0161i\u0107 (eds.), Advances in Robot Kinematics: Motion in Man and A. Pott real-time application [11, 12] but relies on a special non-generic geometry. Bruckmann [13] presented a method to cope with winches using pulley mechanisms to guide the cables. For better reference, the kinematic foundation of cable robots are briefly reviewed. Figure 1b shows the kinematic structure of a spatial cable robot, where the vectors ai denote the proximal anchor points on the robot base, the vectors bi are the relative positions of the distal anchor points on the movable platform, and li denote the vector of the cables. The length of the cables is abbreviated by li = ||li||2. Applying a vector loop, the closure-constraint reads ai \u2212 r\u2212Rbi \u2212 li = 0 for i = 1, . . . ,m , (1) where the vector r is the Cartesian position of the platform and the rotation matrix R represents the orientation of the platform"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000317_1.2890112-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000317_1.2890112-Figure2-1.png",
        "caption": "Fig. 2 Coordinate systems for the univ",
        "texts": [
            "org/ on 01/28/201 rt u = rt 0,rc, h, 0,r0, i;u 1 where 0 is the profile angle, rc is the curvature radius of the spherical blade, h is the hook angle, 0 is the offset angle, r0 is the cutter radius, and i is the initial setting angle of the cutter head. In the face-milling cutter head, the inner and outer blade groups are evenly arranged on two respective concentric circles; therefore, in the above equation, only the profile angle and the curvature and cutter radii need be taken into account. 3 Mathematical Model of a Universal Face-Hobbing Hypoid Gear Generator A mathematical model of a universal face-hobbing hypoid gear generator for spiral bevel and hypoid gears was established in Ref. 9 . As shown as Fig. 2, this machine is a virtual cradle-type machine having tilt, a cradle, work-gear support mechanisms, and so on, so that it can simulate existing face-milling and facehobbing cutting systems with or without AFM motions. The coordinate systems St xt ,yt ,zt and S1 x1 ,y1 ,z1 are rigidly connected to the cutter head and the work gear, respectively. The transformation matrices St to S1 yield the following surface locus for the cutting tool in coordinate system S1: r1 U u, , c, 1 = M1f U 1 \u00b7 M fa U i, j, c,SR,Em, A, B, m; c \u00b7 Mat U \u00b7 rt u 2 where and 1 are the rotation angles of the cutter and work gear, respectively, and u is the variable of the blade edge"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003601_j.ast.2020.105995-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003601_j.ast.2020.105995-Figure2-1.png",
        "caption": "Fig. 2. Two quadrotors slung load system with flexible beam ADAMS.",
        "texts": [
            " The two quadrotors in the system receive force and torque as inputs, and the system outputs the translational and angular velocities of the 5 bodies in the system. Using these respective angular velocities, the respective transformation matrices to the inertial frame are propagated. From the transformation matrices for each body, the respective Euler angles are derived. Thus a full dynamical model for the slung load system is obtained. The developed control algorithms are then tested on this model. Fig. 2. On the designated leader quadrotor, a hierarchical two loop control system is implemented. The outer loop of this control system features a linear quadratic tracking (LQT) velocity controller that tracks reference velocity commands sent out by the operator and generates the control force command (thrust vector) that the leader quadrotor must track to achieve the desired velocity commands. This generated control force command is then sent to the inner loop of the control system. Through the pitching and rolling motion of the quadrotor, the inner loop orients the total force acting on the quadrotor to match the control force command coming from the outer loop"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000035_tie.2010.2095392-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000035_tie.2010.2095392-Figure6-1.png",
        "caption": "Fig. 6. Free-body diagram of the pantograph mechanism.",
        "texts": [
            " The robot also estimates the inclination of the pipe and controls the normal force according to the inclination. Maintaining a normal force between the driving mechanism of an in-pipe robot and the inner wall of a pipe is very important to maintaining proper traction. PAROYS-II estimates the normal force without using force sensors by observing the relationship between the forces acting on the pantograph mechanism. The restored force exerted by the springs and the normal force applied to the pantograph are both shown in Fig. 6. The following equation is the relationship between the normal force and the restoring forces by static analysis: N = 2Kd tan \u03b8 cos \u03c6 (1) where K is the stiffness, d is the displacement of the suspension spring, \u03b8 is the half included angle of the pantograph mechanism, and \u03c6 is the rotation angle of the track module from the condition of the inner wall. Two angular sensors are located at both closing ends of the pantograph to detect the angle \u03b81 and \u03b82. The angles \u03b8 and \u03c6 are computed using \u03b8 = \u03c0 \u2212 (\u03b81 + \u03b82) 2 (2) \u03c6 = \u03b82 \u2212 \u03b81"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000648_978-3-642-17531-2-Figure4.25-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000648_978-3-642-17531-2-Figure4.25-1.png",
        "caption": "Fig. 4.25. Generalized free two-mass oscillator",
        "texts": [
            " Pair of real zeros: non-minimum phase behavior As a sort of continuous perpetuation of the variation in behavior induced by the presence of imaginary infinite zeros, pairs of zeros can migrate in from infinity along the real axis (Fig. 4.24a, dashed arc). This results in a symmetric pair of real zeros at s b . Due to the existence of a zero in the right half-plan, this results in so-called non-minimum phase behavior with challenging properties for control (Ogata 2010), (Horowitz 1963). Generalized free two-mass oscillator In order to gain some engineering intuition for the various zero configurations, consider the generalized unsuspended two-mass oscillator shown in Fig. 4.25. This example is sufficiently simple to permit the use of analytical relations, while demonstrating all important configurations. Equations of motion Let the two-mass oscillator under consideration be characterized by two bodies, a massless elastic connection and generalized force application to Bodies 1 and 2. Using the generalized coordinates 1 2 ,y y the resulting equations of motion are 11 12 1 1 1 12 22 2 2 2 m m y k k y F m m y k k y F . (4.75) Note the fully dense mass matrix34, which also describes linked bodies",
            " A new configuration is present for a fully dense mass matrix ( 12 0m ): in this case, a nonminimal phase pair of real zeros appears. Generalized measurement variable Deeper insight into the migration pattern of the zeros is achieved by considering a linear combination of the generalized coordinates of the two bodies as a generalized measurement variable: 1 1 2 2 z y y . (4.78) With a suitable choice of 1 2 , , a variety of measurement principles can be modeled: variable measurement location: 1 2 (1 )z L y y , 0 1 , 1 1 , 2 , see Fig. 4.25, relative measurement: 1 2 z y y , 1 2 1, 1 . Implementation example of variable measurement location By varying the parameter , the measurement location can be continuously varied between Body 1 and Body 2. Physically, such a case is present in linearly elastic longitudinally vibrating rods (Fig. 4.26a), torsion rods (Fig. 4.26b) or elastic gearboxes (Fig. 4.26c). Over the length of the rods, there is a linearly increasing deformation of the form 1 2 1 1 2 (1 ) y y z y L y y L , which can be measured with a position sensor attached at the location y L (Miu 1993)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001835_j.robot.2015.05.006-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001835_j.robot.2015.05.006-Figure1-1.png",
        "caption": "Fig. 1. Quadrotor and related frames. In black, the inertial frame \u03a3i . In red, the body frame \u03a3b . In blue, the propellers speed and the label of each motor. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)",
        "texts": [
            " Themost popular configurations of VToL UAVs employed in the above defined scenarios are the quadrotor and the hexarotor, which are platforms equipped with four and six propellers, respectively, aligned in the same direction. Hence, these aerial vehicles are underactuatedmechanical systems having six degrees of freedombut only four independent control inputs.Without loss of generality, in the remainder of this paper, the chosen VToL UAV is a quadrotor. Define a world-fixed inertia reference frame \u03a3i and a bodyfixed reference frame \u03a3b placed at the UAV\u2019s center of mass (see Fig. 1). The absolute position of the UAV with respect to \u03a3i is denoted by pb =  x y z T. Using the roll\u2013pitch\u2013yaw Euler angles, \u03b7b =  \u03c6 \u03b8 \u03c8 T, the attitude of the UAV is defined by the rotation matrix Rb(\u03b7b) \u2208 SO(3), expressing the rotation of \u03a3b with respect to\u03a3i, given by [42] Rb(\u03b7b) = c\u03b8 c\u03c8 s\u03c6s\u03b8 c\u03c8 \u2212 c\u03c6s\u03c8 c\u03c6s\u03b8 c\u03c8 + s\u03c6s\u03c8 c\u03b8 s\u03c8 s\u03c6s\u03b8 s\u03c8 + c\u03c6c\u03c8 c\u03c6s\u03b8 s\u03c8 \u2212 s\u03c6c\u03c8 \u2212s\u03b8 s\u03c6c\u03b8 c\u03c6c\u03b8  , where s\u00d7 and c\u00d7 are abbreviations for sine and cosine, respectively. Let p\u0307b and \u03c9b denote the absolute translational and angular velocities of the UAV, respectively, while p\u0307b b and \u03c9b b describe the absolute translational and angular velocities of the aerial vehicle expressed in\u03a3b, respectively",
            " \u2013 and whose dependencies on (p\u0307b, p\u0308b,\u03c9 b b, \u03c9\u0307 b b,R(\u03b7b), t), where t denotes the time variable, have been omitted for brevity. The detailed expressions of both the input forces f bb and torques \u03c4b b depend on the configuration of the considered aerial vehicle. Most of the VToL UAVs are underactuated systemswith six degrees of freedom and fourmain control inputs. Hence,many UAVs can be characterized by three input control torques \u03c4b b =  \u03c4\u03c6 \u03c4\u03b8 \u03c4\u03c8 T and one input control force f bb =  0 0 u T, where u denotes the thrust perpendicular to the propellers rotation plane. In the quadrotor case of Fig. 1, the relationship between the thrust, the control torques, and the squared propellers speed w2 i , with i = 1, . . . , 4, is [22] u = \u03c1u(w 2 1 + w2 2 + w2 3 + w2 4), (3a) \u03c4\u03c6 = l\u03c1u(w2 2 \u2212 w2 4), (3b) \u03c4\u03b8 = l\u03c1u(w2 3 \u2212 w2 1), (3c) \u03c4\u03c8 = cw2 1 \u2212 cw2 2 + cw2 3 \u2212 cw2 4, (3d) where l is the distance between each propeller and the center of mass of the quadrotor, \u03c1u > 0 and c > 0 are the thrust and drag factors, respectively. It is worth noticing that many aerodynamics effects are neglected through this representation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000960_s1560354711050030-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000960_s1560354711050030-Figure7-1.png",
        "caption": "Fig. 7.",
        "texts": [],
        "surrounding_texts": [
            "If the question is posed globally, that is, an attempt is made to carry out Hamiltonization of a dynamical system as a whole on the manifold M4, then it is easy to see that there exist obstructions. We present a simple example showing of what type these can be. Example 6. As M4 we consider the four-dimensional sphere S4 = {x2 1 + \u00b7 \u00b7 \u00b7 + x2 5 = 1} \u2282 R 5. We consider the vector field \u03be = (\u03bbx2,\u2212\u03bbx1, \u03bcx4,\u2212\u03bcx3, 0). It is easy to see that this vector field has an invariant measure induced on the sphere by the standard volume form dx1 \u2227 \u00b7 \u00b7 \u00b7 \u2227 dx5, and two first integrals x5 and x2 1 + x2 2. Locally, this vector field can be easily Hamiltonized (even without change of time), but no suitable global symplectic structure exists on S4 simply because the four-dimensional sphere S4 is not a symplectic manifold [29]. One can give an example showing that obstructions to Hamiltonization exist even in a neighborhood of a two-dimensional \u2018integral manifold\u2019 X = {H = h0, f = f0}, but in the case where X has singularities. The idea of such an example uses one not quite obvious property of an integrable Hamiltonian system. A typical singular integral manifold is the Cartesian product of some graph K (see Fig. 6) by a circle (see, for example, [30]). The vertices of the graph correspond to the periodic trajectories of the system, and the (open) edges to the separatrix manifolds. The behavior of a Hamiltonian vector field on a separatrix manifold, which is an annulus from the topological viewpoint, can be of three different types. Either all the trajectories are closed, or they are asymptotic to the boundary circles of the annulus, which, in turn, can be oriented in the same or opposite direction (see Fig. 3). We consider the last situation (Fig. 3c). It can be easily realized on a singular leaf of the type X K \u00d7 S1, where K is the graph with two vertices and four edges depicted in Fig. 6 (in the book [30] it is called C2). Here, the singular trajectories corresponding to the vertices of the graph are oriented in the opposite fashion. It is known (see [30], Proposition 3.10) that if a singular integral surface of this type occurs in an integrable system, then this surface is unstable, that is, it decomposes into two simpler integral surfaces for an arbitrarily small change of the energy level of the system. However, if a priori there is not any symplectic structure, then nothing prevents us from constructing the vector field as follows. REGULAR AND CHAOTIC DYNAMICS Vol. 16 No. 5 2011 Example 7. First we consider an actual integrable Hamiltonian system with a singular integral surface X K \u00d7 S1 with the Hamiltonian vector field described above (that is, as in Fig. 3c). An example of construction of an integrable system with this dynamics on a singular leaf can be found in [30]. We fix the corresponding level of the Hamiltonian Q3 = {H = h0} and restrict our vector field v to Q3. We forget altogether about the behavior of this vector field outside Q3. We now consider the new manifold M4 = Q3 \u00d7 (\u2212\u03b5, \u03b5). Let t \u2208 (\u2212\u03b5, \u03b5) be an additional coordinate. We extend naturally the additional integral f and the function H to M4 by setting f(x, t) = f(x) and H(x, t) = t, where x \u2208 Q3 and t \u2208 (\u2212\u03b5, \u03b5). The vector field v can be trivially extended from Q3 to M4 = Q3 \u00d7 (\u2212\u03b5, \u03b5) in such a way that for every t it becomes tangent to Q3 t = Q3 \u00d7 {t} and simply coincides with the original vector field under the natural identification of Q3 t with Q3. In other words, the behavior of v on all levels {H = h0} is absolutely identical (for the original Hamiltonian vector field this was not the case, since the singular surface X had to decompose into two simpler ones!). The vector field thus constructed has the two integrals f and H and, furthermore, preserves the natural measure \u03bc \u2227 dt on M4, where \u03bc is the measure on Q3 that was preserved by the original vector field. This vector field cannot be Hamiltonized, since for every t \u2208 (\u2212\u03b5, \u03b5) the singular leaf by construction contains a separatrix manifold with dynamics shown in Fig. 3c and does not decompose as H changes, which is impossible in the case of Hamiltonian systems (see [30], Proposition 3.10). Example 8 (Monodromy as an obstruction to Hamiltonization). The topological structure of the fibration of the phase space into integral manifolds in the neighborhood of a singular fiber can also be viewed as an obstruction to Hamiltonization. One of such obstructions has been found by R. Cushman and J.Duistermaat [31]. We briefly describe this construction. Consider a dynamical system on M4 with an invariant measure and two first integrals H and F . In many integrable (both hamiltonian and non-holonomic) systems there appear equilibrium points of focus type. The singular integral surface Xsing = Xs0 passing through such a point is a torus with one or several pinched points (Figs. 8a and 8b). This singular surface is isolated in the sense that REGULAR AND CHAOTIC DYNAMICS Vol. 16 No. 5 2011 all neighboring integral surfaces Xs are regular and diffeomorphic to a two-dimensional torus (while approaching the singular surface X\u222b\u3009\\} some \u201cdistinguished\u201d cycles on these tori shrink and finally become the singular points). In terms of the integral map \u03a6 : M4 \u2192 R 2(H,F ) and its bifurcation diagram \u03a3 \u2282 R 2(H,F ), this means that the image \u03a6(Xsing), as a point s0 \u2208 \u03a3, is isolated so that all the other points s \u2208 U\u03b5(s0) \\ {s0} are regular. On each torus Xc, we can consider a rotation number \u03c1(s) which is well defined and is invariant under the time scaling (as soon as we fixed a pair of basis cycles on Xc). It is clear that locally \u03c1(s) is a smooth function of s (or, equivalently, of H and F ) which may have a singularity at s0 and usually does. Moreover, in many examples of this kind s0 is a branch point of logarithmic type. From the topological view point this means that the fibration into 2-dimensional tori over the punctured neighborhood of the singular point s0 \u2208 \u03a3 is not trivial (although it is locally trivial): a torus Xs moving around s0 comes back to the initial position with some non-trivial transformation of basis cycles. This topological phenomenon, called the monodromy, is, in particular, an obstruction to the existence of single-valued action-angle variables over U\u03b5(s0) \\ {s0}, see [32]. It is well known (see [33, 34]) that for focus types singularities of integrable Hamiltonian systems the behavior of \u03c1 depends on the number k of singular points on Xs0. Namely, if the basis cycles on Xs are properly chosen then each turn around s0 leads to the increment of \u03c1 by k \u2208 Z. Roughly speaking, each focus point gives a contribution of 1 to the increment of \u03c1. In [31] it was shown that the situation in the non-Hamiltonian case is somewhat similar but the principal difference is that each separate focus point gives a contribution of \u00b11, where the sign \u00b1 may vary from one point to another (this sign is related to the choice of orientation which in the Hamiltonian case is uniquely determined by the symplectic structure and, therefore, this sign can consistently be chosen the same for all the focus points). For example, for a doubly pinched torus (Fig. 8b) it may happen that the monodromy is trivial, i.e., \u0394\u03c1 = 1 + (\u22121) = 0. Such a situation would be an obstruction to Hamiltonization in a neighborhood of Xsing, as in the Hamiltonian case we necessarily have \u0394\u03c1 = 1 + 1 = 2. In [31] the authors suggested an example of a non-holonomic system where such a scenario is likely to be realized. This is the dynamical system describing the rolling of a homogeneous ellipsoid on a plane (the non-holonomic constrain is that the velocity of the point of contact is zero). Unfortunately, in this paper there are no convincing enough arguments for this conjecture. In this system there is indeed a singular fiber Xsing with two focus points (i.e., doubly pinched torus shown in Fig. 8b) but our preliminary considerations have led us to the opposite conclusion: the monodromy for this system will be the same as in the Hamiltonian case: \u03c1 \u2192 \u03c1 + \u0394\u03c1 = \u03c1 + 2. We think that this question is worth being studied and we hope to do it in the nearest future. In any case, finding a concrete example of a non-holonomic mechnical system in which the above described obstruction is realized remains an open and very interesting problem."
        ]
    },
    {
        "image_filename": "designv10_5_0003301_j.mechmachtheory.2019.01.014-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003301_j.mechmachtheory.2019.01.014-Figure4-1.png",
        "caption": "Fig. 4. Load-displacement relationship between balls and grooves.",
        "texts": [
            " The deformation between ball and grooves determines the contact force on the basis of Hertzian theory, which can be expressed as follows: Q i = ( \u03b5 l \u22121 \u03b4i )3 / 2 (1) where \u03b5l is the Hertzian contact constant, which is determined from the contact geometry and material properties of linear guide. The calculation method of the Hertzian contact constant \u03b5l is provided in Refs. [ 3 , 18 ]. Considering the displacements ( y, z ) and deflection angles ( \u03b2 , \u03d5) of worktable \u2160 , the relationship between load and deformation is shown in Fig. 4 . To obtain the deformation between ball and groove, the distance s 1 j between groove curvature centers of carriage and rail can be introduced as follows: s 11 = \u221a ( s 0 sin \u03b80 + z \u2212 \u03b2 2 ( l + W ) + \u03d5L 2 )2 + ( s 0 cos \u03b80 + y ) 2 (2) s 12 = \u221a ( s 0 sin \u03b80 + z \u2212 \u03b2 2 ( l \u2212 W ) + \u03d5L 2 )2 + ( s 0 cos \u03b80 \u2212 y ) 2 (3) s 13 = \u221a ( s 0 sin \u03b80 \u2212 z + \u03b2 2 ( l \u2212 W ) \u2212 \u03d5L 2 )2 + ( s 0 cos \u03b80 \u2212 y ) 2 (4) s 14 = \u221a ( s 0 sin \u03b80 \u2212 z + \u03b2 2 ( l + W ) \u2212 \u03d5L 2 )2 + ( s 0 cos \u03b80 + y ) 2 (5) where s 0 is the initial distance between curvature centers of grooves, which can be written as s 0 = r c + r r \u2212 d + 2 \u03b40 (6) where r c and r r are the groove radius of carriage and rail, respectively, and d is the nominal ball diameter",
            " The system exhibits hardening type nonlinearity and super harmonic resonances in each direction and the vibration of DOF z shows softening type nonlinearity near the super harmonic resonance region \u2208 (0.23,0.34). Moreover, the resonance frequencies of DOF y, z , and \u03b2 are different from each other. It can be observed that the vibration amplitudes near the primary resonances exhibit two jumping phenomena, resulting from the mutual coupling between the resonance peaks of vibrations. In order to better understand the dynamic characteristics of the feed system, the excitation force and gravity are treated as control parameters to analyze the mutual coupling influences. As shown in Fig. 4 , linear guides support the worktable through balls in upper and lower grooves. With the increase of excitation force, the contact force trend of upper balls is opposite to that of lower balls. In Ref. [3,19] , the contact stiffness of linear guide system is analyzed and the rolling balls lose contact with the grooves of rail under some conditions. Then, a time varying and piecewise function about displacements is formulated to characterize the contact forces. The excitation forces along different directions affect the contact state of linear guides and the stiffness caused by linear guides"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003848_j.jmatprotec.2020.117032-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003848_j.jmatprotec.2020.117032-Figure2-1.png",
        "caption": "Fig. 2. Process chain for manufacturing hybrid parts with discrete tooth geometry.",
        "texts": [
            ", 2017) and 316L (Papke and Merklein, 2020) sheet metal with additively manufactured elements. In this work, the process chain is enhanced by a sheet bulk metal forming operation. In pre-investigations on 316L hybrid parts (Papke and Merklein, 2020) parameters for realizing cylindrical additively manufactured elements on a sheet metal are identified. The achieved relative density is higher than 99.9 % and a bonding strength of 563 \u00b1 28 MPa under shear load is reached (Papke and Merklein, 2020). The process chain used in this work is shown schematically in Fig. 2. It exemplarily illustrates manufacturing of parts with tooth geometries on a sheet metal. The first process step is additive manufacturing by PBF-LB, which is a powder bed based additive manufacturing process. The process consists of the iterative process steps: recoating the build plate with powder, selective melting of powder with a laser beam and lowering the build platform. The additively manufactured elements are built directly on the sheet metal without any support structures. Subsequently of additive manufacturing, the outer geometry of the sheet metal with additively manufactured structure is realized by laser cutting",
            " 4c show tooth alignment radii of R40 and R35.2. A radius of R35.2 mm needs a much higher form filling. In this work, the layout R35.2 is used to receive a higher effective tooth length, which is beneficial for the use case as a functional gear component. The combination of sheet bulk metal forming operations, orbital forming, deep drawing and upsetting results in a process chain of subsequent forming operations to realize a gear component. The process chain is shown in Fig. 5. By comparing the process chain of PBF-LB and forming (Fig. 2) with the process chain of subsequent sheet bulk metal forming operations (Fig. 5) it can be seen that, the main difference is the process step for manufacturing the tooth geometry on the sheet metal. In case of the hybrid approach, the tooth geometries are manufactured by PBF-LB on a flat sheet metal, whereas the teeth also can be manufactured by orbital forming. The process chain is not extended, but the fundamental process step of manufacturing the functional elements of the component is replaced by additive manufacturing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001256_1.4006646-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001256_1.4006646-Figure2-1.png",
        "caption": "Fig. 2 Structured vibration modes of high-speed planetary gears at Xc \u00bc 0:3. The real and imaginary parts of the mode shape are shown by a solid (blue) line and a dashed (red) line, respectively. The dotted black line is the gear body nominal position.",
        "texts": [
            " In investigating the results, special attention is paid to the multiplicity of each eigenvalue, the motion of the central elements (carrier, ring, and sun), the relationships between the individual planet motions, and the phase relationships due to gyroscopic motion. Lin and Parker [6] presented unique properties of the vibration modes of stationary planetary gears. The naming convention used in Ref. [6] is retained here. Table 2 gives the natural frequencies (Im(k)) and their multiplicities for 3, 4, and 5 equally-spaced planets at the nondimensional carrier speed Xc \u00bc 0:3. Stationary system natural frequencies are shown for comparison. Figure 2 shows representative modes shapes for the four-planet system. The following paragraphs summarize the modal properties of stationary planetary gears from Ref. [6] and the observations from the high-speed planetary gear numerical results. Planet Modes. For stationary systems, planet modes occur in systems with four or more planets. In these modes, the central members have no motion. The motion of each planet is a constant multiple of any other planet\u2019s motion. When they occur, there are exactly three planet modes, and they have multiplicity N 3 (for N 4)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003907_asjc.2478-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003907_asjc.2478-Figure1-1.png",
        "caption": "FIGURE 1 Schematic diagram of quadrotor structure [Color figure can be viewed at wileyonlinelibrary.com]",
        "texts": [
            " The design of the terminal sliding-mode controller can make the error of the system converge to zero in a finite time and effectively reduce the influence of the disturbance. The Lyapunov function is used to prove the stability of the system with the bounded disturbance, and the system can converge to zero in a finite time. In Section 4, the stability and rapidity of the method are verified by simulations. In addition, an experiment of quadrotor is built, and it verify the robustness of the developed terminal sliding-mode controller in terms of neural network. Coordinate system and motion diagram of the quadrotor are considered as shown in Figure 1. It is performed via earth-fixed frame SE(OXYZ) and body-fixed frame SB(OXYZ). Rotation angle \u03d5 around the X axis of quadrotor body coordinate system is called roll angle. When angle \u03d5 right flip, \u03d5 is called positive angle. Similarly, the pitch angle \u03b8 is up or down on Y axis, and the pitch-up angle formed through the upward head of the airframe is denoted as a positive value. And the yaw angle \u03c8 is left or right on Z axis, and the rightward yaw angle of the airframe is defined to be positive. Four motors are the power source of the quadrotor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000492_tie.2011.2168795-Figure26-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000492_tie.2011.2168795-Figure26-1.png",
        "caption": "Fig. 26. Magnitude of the eighth harmonic of magnetic flux density for motor A.",
        "texts": [],
        "surrounding_texts": [
            "This paper has presented a no-load core loss analysis of three-phase energy-saving small-size induction motors fed by sinusoidal voltage, using a combination of the timestepping FEM and an analytical approach, which offers rapid computation. In this field-circuit approach, the distribution and changes in magnetic flux densities of the motor are computed using a time-stepping FEM. A DFT is then used to analyze the magnetic flux density waveforms in each element of the model obtained from several snapshots taken over a voltage cycle of the time-stepping solution. Rotational aspects of the field are accounted for by introducing a correction to the first harmonic of the alternating losses. The core losses in each element are evaluated using the specific core loss expression, in which the frequency-dependent parameters and flux are derived from a test conducted on a sample laminated ring core. The results are compared with measurements, and good agreement is observed for both methods. However, the field-circuit timestepping method is quite time consuming, so for optimization, the rapid analytical method is to be recommended. APPENDIX A FLUX DENSITY HARMONICS See Figs. 25\u201327. APPENDIX B CORE LOSS SPECTRUM See Figs. 28 and 29."
        ]
    },
    {
        "image_filename": "designv10_5_0003907_asjc.2478-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003907_asjc.2478-Figure7-1.png",
        "caption": "FIGURE 7 Structure of quadrotor helicopter",
        "texts": [
            " Besides, we give the hovering flight comparison between the SMC method and the RTSMC method, where the height is 3 m, and the perturbations are added at time of 10 s. The hovering height and the attitude curves are shown in Figures 5 and 6, respectively. Compared with the SMC method, we can find that the RTSMC method makes the flight attitude more stable, the response faster, and the control accuracy significantly improved. In addition, it has stronger anti-disturbance ability when perturbations are inserted in the system. The quadrotor used in the experiment is shown in Figure 7. The length of diagonal axis of the quadrotor is 15 cm, and it becomes 20 cm when propellers are installed. The whole weight of the machine is less than 1 kg. The attitude controller is STM32F103rbt with the sampling time 1ms. The sensor for attitude measurement is accelerometer and gyroscope, which are respectively used to measure the above three angles and their correspond angular velocity. The attitude and position control are performed per 5 ms. We use ultrasonic sensors to detect the height of the quadrotor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001195_978-90-481-9707-1_71-Figure16.2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001195_978-90-481-9707-1_71-Figure16.2-1.png",
        "caption": "Fig. 16.2 The body-fixed frame and the inertial reference frame. A pair of motors (1 and 3) spins counterclockwise, while the other pair spins clockwise (2 and 4). The pitches on the corresponding propellers are reversed so that the thrust is always pointing in the b3 direction for all propellers. However, while the reaction moments on the frame of the robot are also in the vertical direction, the signs are such that they oppose the direction of the angular velocity of the propeller",
        "texts": [
            " Two intermediate frames E and F are produced by first rotating through an angle about the a3 axis and then rotating about an angle about the e1 axis. Finally, the body frame B of the quadrotor is defined by rotating about an angle about the f2 axis. The origin of the body frame is attached to the center of mass of the quadrotor with b3 perpendicular to the plane of the rotors pointing vertically up (aligned with a3) during perfect hover. The basis vectors of the body frame are parallel to the principal axes of inertia of the quadrotor. The center of mass is denoted as C (Fig. 16.2). Since bi are principal axes, the inertia matrix referenced to the center of mass along the bi reference triad, I , is a diagonal matrix. In practice, the three moments of inertia can be estimated by weighting individual components of the quadrotor and building a physically accurate model in SolidWorks or approximated using known inertia tensors of simple shapes (e.g., cylinders for the motors). The key parameters for the rigid body dynamics of the quadrotors used for simulation and experiments in this text are as follows: (a) Total mass of the quadrotorm (b) The distance from the center of mass to the axis of a motor: L (c) The components of the inertia dyadic using bi as the basis vectors: \u0152IC bi D 2 4 Ixx 0 0 0 Iyy 0 0 0 Izz 3 5 : The inertial properties of each of the quadrotor platforms are detailed in Table 16"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003187_j.addma.2019.03.017-Figure11-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003187_j.addma.2019.03.017-Figure11-1.png",
        "caption": "Fig. 11. horseshoe component fabricated in DED process.",
        "texts": [
            " Notably, this distance remains approximately constant throughout the DED process. As a result, the cladding height estimation error can be compensated by applying a constant calibration distance to the inspection results. 5.1. Powder bed modeling and finite element heat transfer The validity of the proposed measurement method was evaluated by depositing a horseshoe component with dimensions of 60mm x 30mm and a radius of r=15mm on a stainless steel 316 substrate measuring 100mm x 100mm x 10mm, as shown in Fig. 11. Note that a horseshoe component was deliberately chosen since it comprises straight lines, curves and a right angle, and thus allows various types of scanning path to be tested. Table 1 shows the processing parameters employed in the DED process. Note that the horse component consists of four layers, which means that the total deposition thickness is about 3.2mm. As shown in Fig. 12, three digital cameras were evenly spaced around the periphery of an imaginary circle with a diameter of 60 cm having the DED substrate located at its center"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000648_978-3-642-17531-2-Figure7.18-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000648_978-3-642-17531-2-Figure7.18-1.png",
        "caption": "Fig. 7.18. Elliptical rotation: a) schematic arrangement with two orthogonal longitudinal resonant actuators and elastic linkages, b) trajectory of the actuator head (a LISSAJOUS figure); the arc 1 2",
        "texts": [
            "40) with spatial and temporal phase offsets of 90\u00b0: ( , ) cos cos cos /2 cos /2 t p x t A kx t A kx t . (7.41) As standing waves can be quite easily realized with stationary actuators, Eq. (7.41) represents the key to generating mechanical traveling waves using stationary transducer elements in the smallest of volumes. Elliptical trajectories Kinematically speaking, for a limited volume, Eq. (7.41) is interpreted as the elliptical motion trajectory of a selected actuator point (usually the actuator tip or head), as is elucidated below. Fig. 7.18a shows the schematic arrangement of a spatially orthogonal actuator configuration, in which temporally orthogonal driving inputs ( 90 ) precisely fulfill Eq. (7.41). In this case, an elliptical orbit results\u2014also termed an elliptical rotation (Fig. 7.18b). Formally, when excited using the same frequency , this trajectory can be described in a coordinate system ( , )x y with a LISSAJOUS figure defined by (for variable definitions, see Fig. 7.18) 2 2 2 2 2 2 cos sin x yx y x y xy A AA A . For 90 , the axisymmetric ellipse illustrated in Fig. 7.18b results. PP represents the range of stiction in the contact between actuator tip and slider 7.5 Mechanical Resonators 487 One fundamental kinematic obstacle which must be overcome in any implementation can already be recognized in Fig. 7.18a. With a fixed actuator stator, the linkages (also termed horns in the literature) must be elastically deformable to permit an elliptical orbit (see also Fig. 7.17). Resonant elliptical rotation The elliptical orbit shown in Fig. 7.18 can be stimulated at the transducer eigenfrequency , taking advantage of the resulting large motion amplitudes. For practical implementations, however, two principal difficulties arise in the process. Spatial and temporal orthogonality can only be maintained with difficultly due to relatively loose transducer tolerances (Hemsel et al. 2006), (Bauer 2001). One further critical aspect is the elasticity of the linkages. Elasticity is thoroughly desired, and indeed absolutely necessary for operation",
            " This contact is absolutely necessary, as ultimately, the normal force N F generates a stiction force S S N F F at the contact point between the actuator tip and rotor/slider surface, with a static coefficient of friction S . The details of the contact mechanics are quite complicated\u2014see e.g. (Wallaschek 1998). To provide a basic understanding of the functioning of an ultrasonic transducer, the most significant effects are sketched out below. The motion consists of two basic phases: advancing the rotor/slider in a stiction phase (arc 1 2 PP in Fig. 7.18b) and retracting the actuator head in a sliding friction phase (arc 2 1 P P in Fig. 7.18b). During the stiction phase, 488 7 Functional Realization: Piezoelectric Transducer the deformation K x increases the normal force\u2014and thus the stiction force S F \u2014as a function of the stiffness of the L/T coupler and rotor/slider. By bending the coupler (the desired direction of bending must be ensured using appropriate measures), further longitudinal extension of the actuator applies a pushing force L F on the slider and thus starts an advancing motion. With a contraction of the actuators, the inertia of the slider prevents it from following the backward motion of the actuator head, so that in the sliding phase, the latter can move back along the slider to point 1 P without loss of displacement in the motor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003624_j.aej.2020.09.059-Figure11-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003624_j.aej.2020.09.059-Figure11-1.png",
        "caption": "Fig. 11 Trajectory tracking results of MRM generated by the OZNN (54) with noise interference. (a) Whole tracking trajectories. (b) Top graph of tracking trajectories. (c) Desired path and actual trajectory. (d) Tracking errors at the joint velocity level.",
        "texts": [],
        "surrounding_texts": [
            "A novel ITFCZNN with a new AF for solving dynamic matrix inversion (DMI) problems is presented and investigated in this paper. The theoretical analysis and numerical simulation results are conducted to verify its effectiveness and robustness for solving DMI, and the theoretical analysis agrees well with numerical simulation results. Comparing with the OZNN models activated by other commonly used AFs, the proposed ITFCZNN model has remarkable improvements in robustness and convergence performance, which will satisfy the scientific and engineering applications demanding on accurate and fast online real-time computation. The future research directions may focus on the research of the proposed ITFCZNN model in the situation of noises without explicit mathematical expressions and the complex cases with various mixed noises, the robustness and effectiveness of the discrete-time ITFCZNN model and the applications of the ITFCZNN model in practical engineering robotic manipulator control. ence zeroing neural network for dynamic matrix inversion and its application to 16/j.aej.2020.09.059 Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper."
        ]
    },
    {
        "image_filename": "designv10_5_0002270_tmag.2017.2706764-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002270_tmag.2017.2706764-Figure3-1.png",
        "caption": "Fig. 3 Open-circuit field distributions.",
        "texts": [
            " As a result, if a high negative magneto-motive force (MMF) has been applied to push the working point of VPM below the knee point, it will recover along the recoil line and reach a new resultant remanent flux density (Brk) that is lower than the original maximum one (Br), after the MMF is released. A magnetization ratio factor km can be introduced to illustrate the resultant state of VPM: = / (1). P 0018-9464 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. Therefore, the VPM magnetization state is flexibly regulated, resulting in variable flux in the proposed VFM machine. Fig. 3 shows the open-circuit field distributions in the two typical states, i.e. fully forward VPM (km=100%) in Fig. 3(a) and non-magnetic VPM (km=0%) in Fig. 3(b). Although the strong CPMs guarantee the polarity of air-gap field, the magnetic field is obviously weaker in the state with nonmagnetic VPM. Furthermore, the phase back-EMFs in the two states are compared in Fig. 4, where the amplitude with the fully forward VPM is significantly higher than that with the nonmagnetic VPM, indicating the variable flux is obtained. Moreover, it should be noted that the back-EMFs are always symmetrical thanks to the winding configurations. Although the proposed VFM machine features variable PM flux, the two kinds of PMs will make distinct contributions to the accumulative field, which may result in a distinctive issueunbalanced rotor poles and thus unipolar end leakage flux"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003881_j.mechmachtheory.2020.104047-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003881_j.mechmachtheory.2020.104047-Figure5-1.png",
        "caption": "Fig. 5. Displacement relation between cage and ball.",
        "texts": [
            " According to the geometric relationship, the contact angles \u03b1ik and \u03b1ok between ball and raceways can be respectively written as { \u03b1ik = arctan ( d ib sin \u03b10 + z ib \u2212h k sin ( \u03b10 ) \u2212z b d ib cos \u03b10 + y ib \u2212h k cos ( \u03b10 ) \u2212y b ) \u03b1ok = arctan ( d ob sin \u03b10 + z b d ob cos \u03b10 + y b ) (7) Then the distances D ib and D ob between the rolling element and the raceway groove curvature centers are obtained as:{ D ib = ( d ib sin \u03b1o + z ib \u2212 h k sin ( \u03b10 ) \u2212 z b ) / sin \u03b1ik D ob = ( d ob sin \u03b1o + z b ) / sin \u03b1ok (8) Using Hertz theory, we are able to calculate the contact deformations and contact forces between ball and raceways as: { \u03b4ik = D ib \u2212 d ib \u2212 c i \u03b4ok = D ob \u2212 d ob \u2212 c o (9){ Q ik = \u03beik K ik \u03b4 3 / 2 ik Q ok = \u03beok K ok \u03b4 3 / 2 ok (10) where K ik and K ok are the load-deformation coefficients, and they can be simplified according to Refs. [27, 28] . \u03be ik and \u03be ok are respectively defined as \u03beik = { 1 , \u03b4ik > 0 0 , \u03b4ik \u2264 0 (11) \u03beok = { 1 , \u03b4ok > 0 0 , \u03b4ok \u2264 0 (12) To investigate the motion of the cage, the cage coordinate system shown in Fig. 4 is established, and the interaction displacement relation between cage and ball is illustrated in Fig. 5 . The motion of the cage can be described by the displacement of the cage center in y-direction and z-direction and its rotational degree of freedom about x -axis, which are denoted as ( y c , z c , \u03b8 c ). When a bearing runs at high speed under combined axial and radial load, there would occur overloading area and light-loading area within the bearing. The rolling element drives cage forward in the over-loading area because of the speed difference between ball and cage; on the contrary, the cage pushes rolling elements to rotate in the light-loading area",
            " \u03b4 ck (13) f ck = \u03bcc F ck (14) where c is the equivalent damping, and it can be regarded as a constant [29] ; \u03bcc is the friction coefficient. In this study, c and \u03bcc are respectively set to 200 N/(m/s) and 0.05. And \u03b4ck is the relative displace between the k th ball and cage, which can be expressed as: \u03b4ck = { z ck | z ck | > 0 0 else (15) z ck = ( \u03b8c \u2212 \u03b8k ) d m 2 + z c sin \u03c6k + y c cos \u03c6k \u2212 x b sin 2 \u03c6k \u2212 x i cos \u03c6k \u2212 y i sin \u03c6k (16) where z ck is the relative position between the k th ball and cage. From Fig. 5 and Eqs. (13)\u2013(16) , the dynamic equations of the cage are derived as: \u23a7 \u23aa \u23aa \u23aa \u23aa \u23aa \u23a8 \u23aa \u23aa \u23aa \u23aa \u23aa \u23a9 m c .. y c \u2212c . y c \u2212 N b \u2211 k =1 (\u2212F ck cos \u03b8k \u2212 f ck sin \u03b8k ) = 0 m c .. z c \u2212c . z c \u2212 N b \u2211 k =1 (\u2212F ck sin \u03b8k + f ck cos \u03b8k ) = 0 I c . \u03c9 c = N b \u2211 k =1 F ck d m 2 \u2212 f ck D 2 (17) where m c and I c are the mass and moment of inertia of cage respectively; d m is the pitch diameter; \u03c9 rk = . \u03b8k and \u03c6k = \u03b8k + 2 \u03c0(k \u2212 1) / Z b , \u03c9 rk is the orbital speed of the k th rolling element around the z -axis; Z b is the number of the ball"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002838_978-3-319-54169-3-Figure2.18-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002838_978-3-319-54169-3-Figure2.18-1.png",
        "caption": "Fig. 2.18 Properties of the system: a elastic force distribution, b motor-torque characteristics",
        "texts": [
            " For the generalized coordinates: the displacement of the oscillator x and the rotation angle of the motor \u03d5, the motion of the system is described with a system of two coupled non-linear differential equations (m1 + m2) x\u0308 + cx\u0307 + Fk = m2d ( \u03d5\u0308 sin\u03d5 + \u03d5\u03072 cos\u03d5 ) ,( J + m2d 2 ) \u03d5\u0308 = m2dx\u0308 sin\u03d5 + M (\u03d5\u0307) , (2.76) where Fk is the elastic force in the spring. The weight of the elements is neglected as the motion of the system is in horizontal plane. For the clearance vk , the spring has not an influence on the motion of the system as the elastic force Fk is zero (Fig. 2.18a). For the case of spring extension it is assumed that the elastic force is the linear displacement function Fk (x) = kx + fk = kx + \u23a7\u23a8 \u23a9 \u2212k vk 2 if x > vk 2\u2212kx if \u2212 vk 2 \u2264 x \u2264 vk 2 k vk 2 if x < \u2212 vk 2 . (2.77) 32 2 Linear Oscillator and a Non-ideal Energy Source where kx is the linear part of the force and fk is different in the interval in front of and beyond clearance and also in the clearance. By introducing the dimensionless displacement y = x d , (2.78) and dimensionless time \u03c4 = \u03c9t, (2.79) and also (2",
            "80) where \u03c9 = \u221a k m1+m2 is the eigenfrequency of the system, (\u2032) \u2261 d/d\u03c4 and \u03b6 = c\u221a k (m1 + m2) , \u03ba = 1 dk , \u03bc = m2 (m1 + m2) , \u03b7 = m2d2( J + m2d2 ) , \u03be = 1 \u03c92 ( J + m2d2 ) . (2.81) 2.3 Oscillator with Clearance Coupled with a Non-ideal Source 33 The dimensionless elastic force is \u03ba fk (y) = \u23a7\u23a8 \u23a9 \u2212 Vk 2 if y > Vk 2\u2212y if \u2212 Vk 2 \u2264 y \u2264 Vk 2 Vk 2 if y < \u2212 Vk 2 , (2.82) where Vk = vk d is the dimensionless clearance. In dimensionless coordinates the torque is the function of the dimensionless angular velocity \u03d5\u2032 M ( \u03d5\u2032) = M0 ( 1 \u2212 \u03d5\u2032 \u03bd0 ) (2.83) where \u03bd0 = 0 \u03c9 . The parameter M0 has a significant influence on the gradient of the curve (see Fig. 2.18b): for higher values of parameter the gradient is higher and tends to vertical position when the power is unlimited and the system is ideal. The motion of the system, with small nonlinearity and energy supply close to ideal, is considered. Due to real properties of the system it can be concluded that the parameters \u03b1, \u03bc, \u03ba, \u03b7 and \u03be in (2.80) are small. The parameters are described as \u03b6 = \u03b5\u03b61, \u03bc = \u03b5\u03bc1, \u03b7 = \u03b5\u03b71, \u03be = \u03b5\u03be1, (2.84) where \u03b5 << 1 is a small parameter. For (2.84) the differential equations of motion (2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002072_j.colsurfa.2018.12.035-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002072_j.colsurfa.2018.12.035-Figure4-1.png",
        "caption": "Fig. 4. XRD (A), HRTEM images (B and C) and SAED pattern (D) for the ultra-long nanowires of nickel phosphate.",
        "texts": [
            "7 eV in P 2p spectrum correspond to the binding energies for PO4 3\u2212, HPO4 2\u2212 and H2PO4 \u2212, respectively. Therefore the P 2p peaks at 132.8 eV and 133.6 eV in Fig. 3C indicate that phosphorous species were present as PO4 3- and HPO4 2- in the ultra-long nanowires of nickel phosphate. In Fig.3D, the peaks of 531.2 eV and 532.4 eV can be attributed to the 1 s orbital electron transition of the oxygen atom in the form of Ni-O-P and P = O [26]. To further confirm the crystalline phase structure of the ultra-long nanowires of nickel phosphate, their XRD data are characterized in Fig. 4A [27]. The sharp peaks demonstrate that the crystalline phase materials are obtained [28]. The diffraction peaks at 15.10, 26.09, 39.66, 40.23 correspond to the (100), (111), (112) and (-212) plane of the Ni3(PO4)2 component (PDF card No. 70-1796), respectively. The diffraction peaks at 11.48, 28.58, 30.18, 35.78 correspond to the (020), (142), (114) and (214) plane of the NiHPO4\u22193H2O component (PDF card No. 39-0706), respectively. Therefore, the yielded ultra-long nanowires of nickel phosphate are composed of Ni3(PO4)2 and NiHPO4\u22193H2O. The lattice parameters for the ultra-long nanowires of nickel phosphate are identified by high resolution transmission electron microscopy (HRTEM) in Fig. 4B and C. A crystal lattice spacing of ca. 0.580 nm is consistent with the (100) plane of Ni3(PO4)2 and that of ca. 0.780 nm is consistent with the (020) plane of NiHPO4\u22193H2O. It further reveals the presence of Ni3(PO4)2 and NiHPO4\u22193H2O. In Fig. 4D, SAED pattern shows clear diffraction cycles, indicating the polycrystalline structure of the ultra-long nanowires of nickel phosphate where the superstructure is organized by the nanocrystalline subunits [29]. The hydrolysis product of phosphoric acid is related to the pH value of the solution in Fig. 5A as follows [30]: = \u00d7+K H H PO H PO[ ][ ]/[ ] 7.5 10a 2 4 3 4 3 1 = \u00d7+K H HPO H PO[ ][ ]/[ ] 6.2 10a 4 2 2 4 8 2 = \u00d7+K H PO HPO[ ][ ]/[ ] 2.14 10a 4 3 4 2 13 3 Since the pH of reaction solution for preparing the ultra-long nanowires of nickel phosphate is 14.0, the speciation distribution from phosphate hydrolysis is calculated as follows: \u00d7H PO H PO[ ]/[ ] 7.5 102 4 3 4 11 \u00d7HPO H PO[ ]/[ ] 6.2 104 2 2 4 6 PO HPO[ ]/[ ] 21.44 3 4 2 It shows only H2PO4 \u2015 and PO4 3\u2015 are present in significant amounts in the reaction solution. This explanation is consistent with the conclusions of XRD, HRTEM and SAED analysis in Fig. 4. A possible growth mechanism for the ultra-long nanowires of nickel phosphate in hydrothermal reaction is tentatively illustrated in Fig. 5B. Here urea plays a role in the formation of the ultra-long nanowires of nickel phosphate [26]. On the one hand, the urea dissociates under high temperature and high pressure to release NH4 + and OH\u2015 in solution [31,32]. (NH2)2CO+H2O\u21922NH3+CO2 (1) NH3+H2O\u2192NH4 ++OH\u2015 (2) Both urea and its hydrolysis product NH4 + exhibit high coordination ability with Ni2+, resulting in the slow and constant release of Ni2+ to react with H2PO4 \u2015 and PO4 3\u2015"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002219_tcyb.2015.2388691-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002219_tcyb.2015.2388691-Figure1-1.png",
        "caption": "Fig. 1. Schematic of ball and beam system.",
        "texts": [
            " The adaptive parameters q1, q2, \u03b51, and \u03b52 will affect the adaptation convergence rate, and \u03b51 and \u03b52 are also related to the ultimate bound of the closed-loop control system. Therefore, \u03b51 and \u03b52 should be selected small. To guarantee the fast convergence, q1 and q2 should be chosen large. Parameter \u03b5 should be chosen as small as possible to achieve better steady state performance, however, smaller \u03b5 will result in worse chattering. An illustration example of the selection of those parameters can be founded in the simulation example presented below. Example 1: In this section, we apply the proposed control schemes to stabilize a ball and beam system as shown in Fig. 1. The beam is made to rotate in a vertical plane by applying a torque at the center of rotation, and the ball is placed on the beam, where it is free to roll (with 1 degree of freedom (DOF)) along the beam. We will assume that the ball remains in contact with the beam and the rolling occurs without slipping, which imposes a constraint on the rotational acceleration of the beam. The parameters used in this system are shown in Table I. By choosing the beam angle \u03b8 and the ball position \u03b3 as generalized position coordinates for the system, the Lagrangian equations of motion are given by [39] 0 = ( Jb R2 + M ) \u03b3\u0308 + Mg sin \u03b8 \u2212 M\u03b3 \u03b8\u03072 \u03c4 = (M\u03b3 2 + J + Jb)\u03b8\u0308 + 2M\u03b3 \u03b3\u0307 \u03b8\u0307 + Mg\u03b3 cos \u03b8 where \u03c4 is the torque applied to the beam"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000648_978-3-642-17531-2-Figure4.2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000648_978-3-642-17531-2-Figure4.2-1.png",
        "caption": "Fig. 4.2. Schematic model of a rigid-body system: Bi rigid bodies (mass, inertia), J joint/gearbox (massless), C connecting rod (massless), E elastic connecting element (spring, massless), D damping element (dashpot, massless), Z friction, R rolling wheel, A force/torque actuator (massless), Fext external force, {I} inertial frame, {i} body-fixed coordinate system",
        "texts": [
            " For the mathematical description of the dynamics of the former, the concepts of rigid-body mechanics ( systems of differential equations, DAE systems) are used; for the latter, the concepts of continuum mechanics ( systems of partial differential equations) (Schwertassek and Wallrap 1999). Model type: rigid-body system For the systems design tasks considered in this book, a sufficiently detailed yet manageable abstraction proves to be the rigid-body system. This term refers to a multibody system with rigid component bodies and lumped connecting elements (Fig. 4.2). In a rigid-body system, only the bodies possess mass properties (mass, moments of inertia). All other elements are considered massless and serve to model geometric constraints and internal forces. In the context of modeling, then, concrete physical components may need to be separated into functional and mass properties, i.e. the mass of a specific component should be suitably allocated to a rigid body. Kinematic links Geometric relationships between bodies are modeled using kinematic linking elements. Concrete examples include connecting rods C, joints and gearboxes J, and rolling wheels R, all with potential inherent motion profiles ( )t (Fig. 4.2). The internal forces required to maintain these geometric constraints are called constraint forces. 214 4 Functional Realization: Multibody Dynamics Force elements The generation of motion-dependent internal forces is modeled using elastic connections (spring elements) E, velocity-dependent damping elements D, and motion-dependent friction forces Z. Assuming small motions, elastic and damping elements can often be described with sufficient accuracy by linear relations. General friction forces (static and kinetic friction), however, always result in nonlinear relations. In mechatronic systems, active force sources in the form of force and torque actuators A are also found (Fig. 4.2). External forces Internal exciting forces are complemented by external forces ext F , which are applied to the rigid bodies. These are understood to be forces, which\u2014in contrast to the internal forces\u2014lead to an increase in the total system momentum in the inertial frame, e.g. potential forces, and reaction forces (only if neglecting the loss of propellant mass). Coordinate systems The motions of rigid bodies are described by the relative positions and orientations of reference frames with corresponding 4",
            " The base reference frame is a suitably chosen inertial frame {I} ; each body i is assigned a body-fixed coordinate system {i} . Moving reference frame The mechanical structure of a mechatronic system can often perform large motions relative the chosen inertial frame, possibly following nonlinear laws of motion (e.g. vehicles, manipulators, telescoping arms). Often, however, it is only the motion of a few system bodies relative to a moving reference frame that is of interest (e.g. body B3 relative to body B0 in Fig. 4.2 or the suspension of a wheel relative to a moving vehicle frame). This also means that often the relative motions under consideration remain small and thus permit the use of linear models (springs, dampers). In such a case, the moving frame serves as the reference, e.g. coordinate system {0} in Fig. 4.2 with translation and rotation 0 ( )r t and 0 ( )t , respectively. However, care should be taken in deriving the equations of motion in such cases1. Open and closed kinematic chains One important property of multibody systems is their topology. This is understood to be the spatial and actionflow arrangement of the individual MBS elements. From a systems engineering point of view, what is important in this respect is the distinction between open and closed kinematic chains (Schwertassek and Wallrap 1999). Open kinematic chain, tree structure: in this case, the MBS divides into two separate components if all kinematic connecting elements between any single arbitrary pair of rigid bodies are removed; e.g. the chain 0 1 2 3 B B B B in Fig. 4.2. Closed kinematic chain, kinematic loop: the condition for a tree structure is not satisfied; e.g. the chain 0 1 4 5 B B B B in Fig. 4.2. When setting up equations of motion for kinematic loops, the compatibility of the motions of component bodies in the loop must be correctly guaranteed (closure condition). 1 Note: NEWTON\u2019s second law of motion holds only in an inertial space, see also Floating Frame of Reference Formulation in Schwertassek, R. and O. Wallrap (1999). Dynamik flexibler Mehrk\u00f6rpersysteme. Vieweg. 216 4 Functional Realization: Multibody Dynamics The relevant physical foundations for rigid-body systems can be found in many good mechanics text books\u2014e",
            " Dynamics The study of dynamics (also named kinetics) describes the changes in translational and rotational motion quantities under the influence of forces and torques in space. For the motion of a point mass in an inertial space, Fig. 4.3 illustrates the terms kinematics and dynamics (in a coordinate-free representation). Relative kinematics A foundation for describing motion in a moving reference frame is provided by the relative kinematic relations between different coordinate systems. For example, consider the two bodies B0 and B1 in Fig. 4.2. Let body B0 experience an imposed translational motion 0 ( )r t and rotational motion 0 ( )t . Bodies B0 and B1 are kinematically connected by a joint. Let the relative positions of the two body-fixed coordinate systems be 01 r . 4.3 Physical Fundamentals 217 The absolute velocity of the origin of {1} is then2 [ I] [I] [0] 1 1 0 0 01 01 v r r r r imposed relative velocity velocity (4.1) and the absolute acceleration (also in an coordinate-free representation) [ ] [I ] [I ] [0] [0] 1 1 0 0 01 0 0 01 0 01 01 + 2 Ia r r r r r r imposed Coriolis relative acceleration acceleration (4",
            " 8 In general, for a vector x , the relation [ I ] [ i ]x x x holds, where is the angular velocity of the body-fixed reference frame {i} relative to an inertial frame {I} , and [ i ]x is the time derivative with respect to the body-fixed frame {i} . 4.3 Physical Fundamentals 221 This is always the case when only the motion of the center of mass is considered (e.g. the orbit of a satellite) or when the rotational degrees of freedom are artificially constrained (e.g. with guide rails). Example 4.1 Moving frame of reference, virtual inertial frame. To illustrate modeling with a moving reference frame, consider the configuration shown in Fig. 4.4 (cf. bodies B0 and B1 in Fig. 4.2, though connected here via force elements). The two rigid bodies 0 (mass 0 m ) and 1 (mass 1 m ), elastically connected with a linear spring k, and excited by force actuator A (actuation force FA) and external force 1 F applied to Body 1, are to undergo purely horizontal motion in an inertial space {I} . Let the spring be relaxed when 1 0 01 x x l . Model creation Considering free-body equations for the bodies and applying the center of mass theorem Eq. (4.8), this two-body system gives the equations of motion in inertial coordinates9: 0 0 0 1 01 1 1 1 0 01 1 , "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001536_ffe.12755-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001536_ffe.12755-Figure4-1.png",
        "caption": "FIGURE 4 Compact tension (CT) sample with dimension labels",
        "texts": [
            " This treatment was performed with the same purpose as for the annealing\u2010furnace cooling treatment not only to alter the microstructure but also to see the effect of the water\u2010quenching treatment. Water quenching has been reported to give rise to compressive residual stresses in the quenched part.26 The effect of this treatment on the crack growth behaviour has not been analysed on 316L SLM material before. The samples were made with dimensions according to the ASTM dimensional requirements for CT specimens (ASTM E647/ASTM F279227; see Figure 4 and Table 3). The ASTM E64728 standard requires that the crack sizes measured on the front and back surfaces do not differ by more than 0.25 B for the corresponding data to be valid. This implies a maximum difference of approximately 1.1 mm for the samples in this study. To ensure that the samples are predominantly loaded in the elastic range under the applied cyclic loading (with sufficiently small plastic zone at the crack tip) so that LEFM is applicable, the ASTM E647 requires that the relation W\u2212a \u2265 4=\u03c0\u00f0 \u00de Kmax \u03c3YS 2 (1) is satisfied for all crack lengths"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001998_s1061934815040152-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001998_s1061934815040152-Figure3-1.png",
        "caption": "Fig. 3. A scheme of molecular imprinting using SAM method. Adapted from [76].",
        "texts": [
            " SAMs are the rigid nanostructures organized around the template molecule formed at the electrode surface. The technique can be considered as a two di mensional imprinting. In the preparation of this sys tem, simultaneous adsorption of template and mer captan molecules take place at the metallic electrode surface, usually an Au electrode. The recognition of template is possible if the specific interactions are de veloped between the template and alkylthiol chain to form a stable complex. This technique is illustrated in Fig. 3. The advantages of this technique are easy prep aration and the possibility of the introduction of dif ferent chemical functionalities. However, the main disadvantage is very low stability of the non crosslinked film, due to which the recognition sites are collapsed by lateral diffusion of molecules, especially when template molecules have been removed [19, 76]. P.Y. Chen et al. [77] developed an amperometric sensor for the determination of DA. The modified screen printed gold electrode was fabricated using thioglycolic acid (TGA), allyl mercaptan (AM), medi ator, quercetin (Q) and MIP using SAM technique"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003187_j.addma.2019.03.017-Figure13-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003187_j.addma.2019.03.017-Figure13-1.png",
        "caption": "Fig. 13. Distribution of measurement points along side of horseshoe.",
        "texts": [
            " However, due to the reference point measurement algorithm proposed in this study, small experimental setup errors have only a minor effect on the measurement outcome, and can thus be effectively ignored. Following the DED manufacturing process, the horseshoe component was scanned lengthwise by an optical 3-D scanner (GOM ATOS- Compact Scan) to provide a benchmark against which to compare the cladding height estimates obtained from the proposed inspection system. The scanning process was performed along the green line shown in Fig. 13. The height data were extracted from the scanned image and analyzed using GOM-Inspect software. The precision of the scanning results was determined to be around 0.001mm. The scanned profile is shown by the green line in Fig. 14. Meanwhile, the circles in Fig. 14 show the estimated height profile obtained using the proposed reference point inspection method. As shown in Fig. 13, the cladding layer height was extracted from the scanned profile at 12 separate positions along the length of the horseshoe. However, due to experimental noise in the camera images, it was impossible to obtain accurate estimates of the cladding height from the two end points (#1 and #12) using the proposed inspection system. Thus, inspection results were available for only 10 measurement points (#2\u02dc#11). The measurement results obtained from the 3-D scanned profile and proposed vision-based system are listed, respectively, at the specified sampling points"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003199_j.mechmachtheory.2019.103576-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003199_j.mechmachtheory.2019.103576-Figure6-1.png",
        "caption": "Fig. 6. Helical shaper and face-gear with axle offset and shaft angle of 70 \u25e6 .",
        "texts": [
            " For a shaft angle of \u03b3s = 90 \u25e6, the envelope surface is described by a plane. Its normal vector is the face-gear rotation axis and it is located at z 2 = \u2212r as , where r as is the shaper addendum radius. At a shaft angle of \u03b3 s = 90 \u25e6, but without axle offset, the surface is described by a cone. Only in the case of an applied axle offset and a shaft angle of \u03b3 s = 90 \u25e6, the envelope surface must be calculated. Fig. 5 shows the surfaces of the involute shaper used to generate the face-gear geometry and the corresponding surfaces of the face-gear teeth. In Fig. 6 , a face-gear drive for a helical shaper with axle offset and shaft angle of 70 \u25e6 is shown as an example. The facegear geometry is generated by the meshing of the shaper as explained above. The corresponding main parameters are listed in Table 1 . 2.5. Solving the equation of meshing 2.5.1. Spur involute shaper In case of teeth without helix angle, the parameter u s used to determine a position vector on the usable flank can be calculated directly after simplification of the equation of meshing (19) by setting \u03b2 to zero"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002039_978-3-319-54927-9_4-Figure12-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002039_978-3-319-54927-9_4-Figure12-1.png",
        "caption": "Fig. 12 Example of grasping a tube connector from a transport box (a): after detecting the box and approaching the observation pose (b), the part is successfully grasped (c)",
        "texts": [
            " In case of pallets, we first detect and locate the horizontal support surface of the pallet and then segment and approach the objects on top of the pallet for further object recognition, localization and grasping [3]. For boxes, we first locate the top rectangular edges of the box and then approach an observation pose above the box center to take a closer look inside and to localize and grasp the objects in the box [27]. In the following, we will provide further details about these two variants of the picking pipeline and how the involved components are implemented as a set of primitives in the SkiROS framework. An example of this three-step procedure fors grasping a part from a transport box is shown in Fig. 12. The Placing Skill is responsible for reliable and accurate kitting of industrial parts in confined compartments [28]. It consists of twomain modules the armmotion and the kit locate. The first is responsible for reliable planning and execution of collision-free trajectories subject to task-depended constrains, while the kit locate is responsible for the derivation of the kitting-box pose. The high precision and reliability of both is crucial for a successful manipulation of the objects in the confined compartments of the kitting box"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000086_ac00260a031-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000086_ac00260a031-Figure1-1.png",
        "caption": "Figure 1. Enzyme thermistor with aluminum constant temperature jacket: (1) polyurethane Insuilation; (2) Plexiglas tube with bayonet lock for column insertion; (3) thermostated aluminum cyllnder; (4) heat exchangers; (5) enzyme column; (6) thermistor attached to a gold capillary; (7) column outlet (in this thermostated metal block the temperature Is controlled to withln f0.002 \" C on 'equilibratlon).",
        "texts": [
            " Swirl and let stand 1 h with periodic swirling. Filter on a glass filter and wash the activated beads with 500 mL of doubly distilled water. To 1 mL of beads add 3 mL of 0.1 M phosphate buffer containing 50 units of the dialyzed enzyme with 100 rL of catalase solutioii. Mix well and put on a shaker in a cold room overnight. Wash the beads with 200 mL of 0.1 M phosphate buffer, pH 7.5, faillowed by 200 mL of 0.5 M NaC1. This preparation is loaded in a small plastic column (1 mL volume) which is then mounted inta a Plexiglas holder (Figure 1) that can be inserted in the enzyme thermistor unit. Similarly, a second enzyme column is prepwed exactly as above but without the catalase solution. Apparatus. Enzyme Electrode. The electrode probe, prepared as described above, can be plugged into a Universal Sensors adaptor, which is a small tubular device designed both to apply the constant potential required by the O2 probe and to convert the output current resulting into a voltage that can be read directly on any pH-voltmeter. In this case an Orion Research pH/millivolt meter 811 was used. Thermistor Probe. The column of immobilized enzyme is mounted into the enzyme thermistor device (10) as shown in Figure 1. A thermostated (30 \"C) aluminum cylinder contains A T (m'C1 6 4 2 0 0.6 n I 0 .4 10 min - I il i I I I I Time Flgure 2. Recorder tracing In the enzyme thermlstor probe determination of ethanol with an alcohol oxidase/catalase column. the heat exchanger capillary tubes and provides a constant temperature (h2 x \"C) environment to the enzyme column (0.2-1 mL). There are two parallel fluid lines, which could be used either independently or with one of them as a reference system. The sample/buffer is pumped through the enzyme thermistor unit with a peristaltic pump at a flow rate of 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000492_tie.2011.2168795-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000492_tie.2011.2168795-Figure9-1.png",
        "caption": "Fig. 9. Equipotential lines of the vector potential corresponding to 0.2-s time. (Left) One flux tube contains a flux per unit length of 0.001 Wb/m. (Right) Magnitude of magnetic flux density at 0.2-s time for motor B.",
        "texts": [
            " The computation accounts for the conductance of the rotor bars. The start of the modeling period is related to the instant of switching on the voltage while the rotor rotates with synchronous speed. Despite the fact that the voltage in the first two cycles increases linearly, there is an initial transient; hence, computation continues up to 0.2 s when the transient has disappeared (this is monitored by watching the phase currents and electromagnetic torque). Several snapshots were taken over the voltage cycle that followed. Fig. 9 shows the magnetic field distribution after the 0.2-s time. A number of sample points were chosen to allow for the subsequent DFT analysis. Eighty points were in fact used, and it was found important that the subdivision angle of the air gap and the angle between sample points were not the same or multiples of each other. Using the values of x and y components of magnetic flux density in each element calculated at sample points, the DFT analysis was performed in order to assess the contribution of higher harmonics Bpk = N\u22121\u2211 n=0 Bp(n)e \u2212i2\u03c0kn N , p=x and y; k=0, 1,"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003227_s11517-020-02143-7-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003227_s11517-020-02143-7-Figure4-1.png",
        "caption": "Fig. 4 The rotational angle measurement model",
        "texts": [
            " Based on the pinhole imaging principle, the coordinates of corner point i in OC \u2212 XCYCZC are defined as Pj i X j i ; Y j i ; Z j i . It can be calculated by: Z j i x ji y ji 1 0 @ 1 A \u00bc M X j i Y j i Z j i 0 @ 1 A \u00f04\u00de where M \u00bc f 0 0 0 f 0 0 0 1 0 @ 1 A, Z j i \u00bc h\u00fe R\u2212 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2\u2212 Y j i 2q , and h is the distance from the camera to the top point of the catheter. Then, the axial moving distance of corner point i between frame j and frame j + 1 can be calculated by: \u0394X j \u00bc \u2211 n i\u00bc1 X j\u00fe1 i \u2212X j i \u00f05\u00de where n(0 < i \u2264 n) is the total features number. As shown in Fig. 4, the rotational angle can be calculated by: \u25b3\u03b8 j \u00bc \u2211 n i\u00bc1 arcsin Y j\u00fe1 i R \u2212arcsin Y j i R ! \u00f06\u00de where arcsin Y j\u00fe1 i R \u2208 \u2212 \u03c0 2 ; \u03c0 2 . In order to allow the sensing rod sliding freely through the guiding hole, there is a gap between the sensing rod and the guiding element. A deviation angle between the sensing rod and the guiding hole could be caused by assembling error, as shown in Fig. 5. It leads to motion coupling of feature point in axial direction and rotational direction. In other word, catheter\u2019s axial motion causes both feature point displacements along x-axis and y-axis owing to the angle deviation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000807_j.mechmachtheory.2013.06.013-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000807_j.mechmachtheory.2013.06.013-Figure4-1.png",
        "caption": "Fig. 4. Generation of pinion by rack-cutters: (a) installment of pinion rack-cutter, (b) generation of the pinion.",
        "texts": [
            " (4), and assume rs ur; \u03b8r\u00f0 \u00de \u00bc xs; ys; zs;1\u00f0 \u00de: \u00f06\u00de The values of ur1 and ur2 are represented as: ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x2s ur1\u00f0 \u00de \u00fe y2s ur1\u00f0 \u00de q \u2212rsa \u00bc 0ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x2s ur2\u00f0 \u00de \u00fe y2s ur2\u00f0 \u00de q \u2212rsm \u00bc 0 8< : \u00f07\u00de rsa and rsm are the radius of addendum circle and the root circle radius of the standard gear cutter with involute teeth where respectively. The pinion surface \u22111 is calculated as the envelope to the family of the rack cutter surface A1, as shown in Fig. 4. Movable coordinate systems Se and S1 are rigidly connected to the rack-cutter and the pinion respectively (Fig. 4(a) and (b)); Sn\u2217 is the fixed coordinate system. The installment angle \u0394\u03b2 (Fig. 4(a)) is provided for the improvement of bearing contact between the pinion and the face gear [13]. The position vectors r1 of the pinion surface are expressed in Eq. (8) in the coordinate system S1 as, where r1 uc; \u03b8c;\u03c8e\u00f0 \u00de \u00bc M1e \u03c8e\u00f0 \u00dere uc; \u03b8c\u00f0 \u00de Ne ue\u00f0 \u00de\u22c5v 1e\u00f0 \u00de e \u00bc f 1e uc;\u03c8e\u00f0 \u00de \u00bc 0 \u00f08\u00de the matrix M1e describes coordinate transformation from Se to S1; ve1e is the relative (sliding) velocity. 2.3. Generation of tooth surface of profile modified spur face-gear The profile modified spur face-gear surface \u22112 is calculated as the envelope to the family of the shaper surface \u2211s, as Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000807_j.mechmachtheory.2013.06.013-Figure11-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000807_j.mechmachtheory.2013.06.013-Figure11-1.png",
        "caption": "Fig. 11. Generation surface of disk wheel.",
        "texts": [
            " In the grinding process, the disk wheel rotates around its own axis zw, and also swings around the axis zs. The face-gear rotates around its own axis z2. In addition, in order to cut the tooth surface of the face-gear completely, the disk wheel also needs to traverse in each generating roll position along the entire face width (see Fig. 10(a)). The disk wheel is the tool applied to crown the profile modified spur face-gear. The surface of the disk wheel is a surface of revolution around the axis zw in Fig. 11(b), and its generating line is the transversal section of the shaper for zs = 0, in other words \u03b8r = 0 in Eq. (4). Coordinate systems Ss and Sw are rigidly connected to the shaper and the disk wheel respectively, and Sw0 is a fixed coordinate system. Ews is the distance between the axis zw and xs; \u03b8w is the surface parameter of the disk wheel. The position and normal vectors of the disk wheel surface in the coordinate system S2 are determined as: rw ur ; \u03b8w\u00f0 \u00de \u00bc \u2212Mws \u03b8w\u00f0 \u00ders ur ;0\u00f0 \u00de Nw ur ;\u03c8s\u00f0 \u00de \u00bc \u2212Lws \u03c8s\u00f0 \u00deNs ur\u00f0 \u00de \u00f016\u00de matrix Mws describes coordinate transformation from Ss to Sw. The matrix Lws is the 3 \u00d7 3 order sub matrix of matrix Mws where where \u22121 is multiplied because the surface as shown in Fig. 11(a) has around the axis of zs rotated 180\u00b0 relative to the surface determined by Eq. (4). We remind that the shaper surface \u2211s is in line contact with the disk wheel surface \u2211w and with the face-gear tooth surface \u22112. However lines Lsw and Ls2 show that they do not coincide with each other but are intersected at any position of meshing. We designate by Lsw the line of tangency between\u2211s and\u2211w and by Ls2 the line of tangency between\u2211s and\u22112. Fig. 12 shows that lines Ls2 and Lsw intersect with each other at a position of meshing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002387_9781118773826-Figure13.24-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002387_9781118773826-Figure13.24-1.png",
        "caption": "Figure 13.24 M~H curve of Bi 1-x La x FeO 3 (x=0.0 and x=0.1) measured at RT.",
        "texts": [
            " [109] Th is means that the spontaneous magnetization of bulk single crystal BiFeO 3 should be zero even though its symmetry permits weak ferromagnetism. Th e DC magnetization M~H and M~T measurements were carried out at room temperature (RT) and at low temperature (~10\u2013325 K) under fi eld cooled (FC) and zero fi eld cooled (ZFC) conditions using Vibrating sample magnetometer (VSM) model PPMS-6000. 13.5.6 Some of the Important Results on Pure and Substituted BiFeO 3 Th e magnetization curves (M~H) of all the samples were measured at room temperature (300 K). Figure 13.24(a) shows the M~H response for pure BiFeO 3 ceramics in which the sample exhibited straight line behavior in the M~H curve up to the measured fi eld of 14 T. It gives a clear cut indication of the antiferromagnetic nature consistent with our report [110] and other literature reports [111\u2013113]. Figure 13.24(b) shows the magnetization curve (M~H) for 10% La-substituted bismuth ferrite Bi 1-x La x FeO 3 (x=0.1) sample. It is evident from Figure 13.24 that pure BiFeO 3 compound behaves like an antiferromagnet, whereas the 10% La-substituted compound shows very small remanence (M r ) of 0.588 emu/g. Structural, Electrical and Magnetic Properties 485 With a further increase of La concentration from x=0.1 to x=0.2, the M~H curve (Figure 13.25a) gives a straight thin loop behavior without saturation with remanence (M r ) value of 0.934 emu/g. With a further increase of concentration from x=0.2 to x=0.3, the area of the M~H loop (Figure 13.25b) is slightly increased"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001658_j.jsv.2017.08.014-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001658_j.jsv.2017.08.014-Figure2-1.png",
        "caption": "Fig. 2. Dynamic model of gear-rotor-bearing system.",
        "texts": [
            " kw\u00f0t\u00de \u00bc kw1\u00f0t\u00de kw2\u00f0t\u00de=\u00f0kw1\u00f0t\u00de \u00fe kw2\u00f0t\u00de\u00de (27) Complete gear transmission system consists of gear pair(s), supporting shafts, bearings and other auxiliary components. A gear-rotor-bearing system formulated by abstracting the motor and other auxiliary components mounted in the input and output shafts as a rotor. Considering the effect of bearing clearance, its nonlinear load is closer to the engineering practice. It is a multiple clearance, multi-parameter coupled and multi-degree-of freedom system. The simplified theoretical model of a single-stage spur involute cylindrical gearbox is illustrated in Fig. 2. The gearmeshing part can be simplified as two rotators coupledwith viscous dampers and nonlinear springs. Three important nonlinear factors such as time-varying stiffness including temperature stiffness, backlash and comprehensive transmission error are considered. There are some assumptions so that the parametric and nonlinear effects in the meshing are accentuated. Gears are inflexible. The meshing of the gears is simplified as viscous dampers and nonlinear springs. The influences of prime mover and load are not considered",
            " They are inner ring, outer ring and rolling elements. Clearance exists between the inner ring and rolling elements or rolling elements and the outer ring. And it is one of the main nonlinear factors in the system, too. The bearing clearance function can be written as follows when dimensionless bearing clearance Dbi \u00bc dbi=\u00f02b\u00de\u00f0i \u00bc 1;2\u00de. fb1\u00f0x7\u00de \u00bc 8< : x7 Db1; x7 >Db1 0; Db1 x7 Db1 x7 \u00fe Db1; x7 < Db1 (39) 8< x9 Db2; x9 >Db2 fb2\u00f0x9\u00de \u00bc : 0; Db2 x9 Db2 x9 \u00fe Db2; x9 < Db2 (40) A gearbox of a metro train is selected as the research object as shown in Fig. 2. The material of the gear is 40Cr. The related parameters of the gearbox are given in Table 1. The lengths of two shafts are 450 mm. The elastic modulus of the shafts is 2 1011 Pa, the Poisson ratio is 0.3. Every shaft is supported by two bearings, 7306. The preload load of bearing is 200 N. The torque is 150 N,m. The related parameters of bearings are given in Table 2. The dimensionless parameters can be calculated according to Tables 1 and 2, are given in Table 3. Other dimensionless coefficients of the time-varying stiffness can be calculated by the computer programs according to the meshing parameters real-timely"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001923_icra.2017.7989452-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001923_icra.2017.7989452-Figure1-1.png",
        "caption": "Fig. 1. The quadrotor tail-sitter (Coordinate systems are defined in section III) Video available at: https://youtu.be/K-Z8JsAQQMM",
        "texts": [
            " [5] developed a quadrotor tailsitter named Quadshot with two extra elevons for level flight control. Atsushi Oosedo et al. [6] removed all the elevons and used only four motors for both hovering and level flight control. These work mainly focused on the flight controller design, without explicitly addressing the wind disturbance. This paper presents the design, development, and control of a quadrotor tail-sitter UAV that is suitable for outdoor fully autonomous operation. The developed quadrotor tailsitter UAV is shown in Fig. 1. When compared to a dualrotor tail-sitter UAV, a quadrotor configuration has mitigated aerodynamic interference between the wing and propellers. The attitude control is independent in all three directions: pitch, roll, and yaw, enabling an easier attitude control when the wind is present. We will discuss the design of our prototype from the aspects of addressing wind disturbance, vibration, and inwind landing. Experimental results show that the developed UAV has negligible vibration level, and can achieve stable hovering and reliable landing even when the cross wind is present",
            " The remainder of this paper is organized as follows: the aircraft design and development will be presented in section II. In section III, we will introduce the aircraft dynamic and aerodynamic model, based on which a flight controller will be designed and verified by simulation results. Experimental results will be supplied in section IV to verify the aircraft design and flight controllers capability. In section V, conclusions will be drawn and recommendation of future works will be discussed. As shown in Fig. 1, the quadrotor tail-sitter UAV consists of a off the shelf airframe called X5 flying wing and four motors that are symmetrically located around the airframe. Similar to the prototype developed in [6], the developed aircraft uses only the four rotors for full attitude and altitude control for both hovering and level flight. In addition, the developed aircraft incorporates several key designs that enable it to operate in an outdoor environment where the wind is present. These designs are described as follows. As shown in Fig. 1, the large wing area can introduce a significant level of damping effect during level flight and wind disturbance during hovering. Achieving satisfactory roll control performance in level flight and wind disturbance rejection in hovering, therefore, requires a large moment that usually exceeds the rotor reactional torque. In order to augment the control action (i.e. body-axis rolling moment), the four motors are inclined in a way shown in Fig. 2. The motor was inclined along the motor diagonal axis (shown by the dotted blue line) by \u03b4",
            " The resulting landing will remain stable if the tilt angle \u03b8 is within \u03b3, elsewhere unstable. In our design, \u03b3 = 35\u25e6. Simulation results shown in section III imply that a tilting angle of 35\u25e6 corresponds to wind speed of 6.5 m/s. Therefore, the developed UAV can successfully land within at least 6.5 m/s cross wind, theoretically. In the real indoor test, around 5 m/s cross wind is presented and the vehicle does land successfully. Pixhawk Autopilot [9] is used for controller implementation. A pitot tube is used to measure airspeed along body x-axis (as shown in Fig. 1). A 4 cell battery with 4480 mAh capacity is used for power supplement. DJI E305 propulsion system with 2312E motors and 9450 propellers is used to provide thrust and moment. The weight of our vehicle is 1.4 kg, wingspan is 1.01 m, and mean aerodynamic chord is 0.24 m. The body coordinate frame used in this paper follows the same conventions of fixed wing as shown in Fig. 1. The local north-east-down (NED) coordinate is chosen as the inertial frame. Rotation along xi, yi and zi are defined as roll, pitch, and yaw, respectively. The rotation between body frame and inertial frame is denoted as R, which lies on SO(3) [10]. As the UAV will tilt its pitch angle by almost 90\u25e6 during the transition, conventionally used ZYX Euler angles of parameterization fail due to its singularity at pitch angle 90\u25e6. As a consequence, z-x-y Tait-Bryan angles are used to display the UAV attitude in simulation and flight log"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003375_j.actaastro.2020.04.016-Figure16-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003375_j.actaastro.2020.04.016-Figure16-1.png",
        "caption": "Fig. 16. Satellite structure overview.",
        "texts": [
            " Besides, two pieces of PC permalloy works as magnetic dampers to attenuate angular velocity, whose locations are shown in Fig. 15a. Fig. 15b shows an image of the satellite following the earth's magnetic field. This passive attitude stabilization is possible only when the membrane is not deployed. After the deployment of the membrane, the satellite will tumble. The authors simulated the attitude of the satellite on orbit before and after the membrane deployment, constructing an in-house simulator on Matlab. The main structure consists of four main panels made of aluminum (Fig. 16a). In the mission, the satellite will separate to 1U and 2U. To achieve this separation and to satisfy the precision requirements, jigs are designed for assembly. Four corners that touch the launch pod are covered with hard anodized coatings to reduce the coefficient of friction (Fig. 16b). The Tokyo Tech ground station is utilized for communicating with the satellite. The station has Yagi antennas for UHF/VHF bands and a parabola antenna for 5.8 GHz communication (Fig. 17). The development of the payload and that of the bus are held at different places following different timelines (Fig. 18). The whole development process took almost four years. Professors, research assistants at Tokyo Tech, and the Sakase Adtech Co., Ltd. developed the membrane deployment unit, whereas the WEL Research Co"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001750_tnb.2015.2475338-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001750_tnb.2015.2475338-Figure3-1.png",
        "caption": "Fig. 3. Two types of FET-based GBB: (a) back gate FET and (b) liquid gate FET (reproduced by permission of The Royal Society of Chemistry [58]).",
        "texts": [
            " However, for EIS-based GBBs, little research related to the influence of graphene\u2019s electrical properties has been conducted to date. Enhancements introduced previously for impedimetric- and EC-based GBBs can be used to promote the performance of FET-based GBBs. Using a suspended graphene FET structure also shows an enhancement [94] owing to the charge traps at the interface. These traps act as external scattering centers that result in the degradation of transport properties, but electrical 1/f noise is consequently suppressed [95]. As shown in Fig. 3, there are two general types of FET-based GBBs: namely, back gate FETs [31], [96] and liquid gate FETs [11], [97]. The \u201cback gate\u201d refers to changes in the conductivity of the graphene substrate due to the presence of biomolecules. Thus, \u201cback\u201d refers to a second gate voltage due to changes in the threshold voltage arising from changes in the source-drain voltage. The liquid gate can be distilled water, an electrolyte, or a buffer solution. The response of graphene to a surface charge or a change in ion density shows its potential application in liquid-gate FET-based biosensors [98]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001443_ls.1271-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001443_ls.1271-Figure2-1.png",
        "caption": "Figure 2. Hertz pressure distribution in line and point contacts.",
        "texts": [
            " The beneficial effect on EHL film thickness of having both elastic deformation and enhancement of lubricant viscosity with pressure is evident Accurate determination of EHD fluid film pressure and contact size requires full numerical solution of the pressure, viscosity and deformation equations. However, for many purposes, an acceptable approximation is to assume that the contact has the pressure distribution and size given by the Hertz equations.5 These predict a parabolic pressure distribution for a line contact and an ellipsoidal one for a point contact as shown in Figure 2. The maximum Hertz pressure and also the contact dimensions for a line contact and circular point contact can be calculated from the equations in Table II. In this table, WL is the applied load per unit length (line contact), W is total applied load (point contact), po is the maximum Hertz pressure and a is the predicted half-width (line contact) or contact radius (point contact). E\u2019 and R are the reduced elastic modulus and the reduced radius, respectively. These combine the individual elastic moduli and radii of the two surfaces (1,2) according to equations (8) and (9), respectively, where E is the elastic modulus and \u03bd is the Poisson\u2019s ratio of the surfaces: Copyright \u00a9 2014 John Wiley & Sons, Ltd",
            " In EHL contacts, po is usually in the range 0.5 to 4GPa while 2a is typically 100 to 600\u03bcm. The mean pressure can, of course, be calculated from the applied load divided by the contact area but is also given by \u03c0/4po for line and 2/3po for circular contact. For EHD contacts, the previous equations are only approximate, especially for pressure. Numerical solution of the EHD problem yields pressure distributions of the form shown in Figure 3, as compared with the parabola predicted by Hertz for a static, dry contact and shown in Figure 2. There is a build-up Copyright \u00a9 2014 John Wiley & Sons, Ltd. Lubrication Science 2015; 27:45\u201367 DOI: 10.1002/ls Copyright \u00a9 2014 John Wiley & Sons, Ltd. Lubrication Science 2015; 27:45\u20136 DOI: 10.1002/l of pressure in the contact inlet upstream of the central flat region (which is crucial in generating a fluid film) and a pressure maximum (known as a pressure spike), followed by a very rapid collapse of pressure at the contact exit. A key feature of almost all practical EHD contacts (as opposed to many bench tests such as the fourball and block on ring test) is that the contacting surfaces roll together"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002120_j.mechmachtheory.2015.09.010-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002120_j.mechmachtheory.2015.09.010-Figure4-1.png",
        "caption": "Fig. 4. The cutter retracting method of shaping a non-circular gear.",
        "texts": [
            " When processing cylindrical gears, as the normal direction of the gear pitch curve is consistent with the center line, cutter interference can be effectively avoided with this method. However, as far as non-circular gears are concerned, this method would be infeasible due to the normal direction of the gear's pitch curve being different from that of the center line. A practical method to avoid cutter interference while processing non-circular gears is to make the cutter center move in the direction of the gear pitch curve through the compound motion of the relieving mechanism and machine axes when the cutter approaches the bottom dead center. Fig. 4 shows the positional relationships of the machine axes during the compound relieving motion. Supposing that the relieving distance of the relieving mechanism is \u0394E and the center distance between the gear and cutter is E ' ', then the position of the cutter center O2 ' ' is: x00o2 \u03c600 ; ho \u00bc x0o2 \u03c6;ho\u00f0 \u00de \u00fe \u0394E cos \u03b30 y00o2 \u03c600 ;ho \u00bc y0o2 \u03c6; h00o \u00fe \u0394E sin \u03b30 ( : \u00f041\u00de Supposing that the position of the gear following the relieving motion is at P ' ' and its polar angle is \u03c6 ' ', then the coordinate value of P ' ' is: x00p \u03c600 \u00bc r \u03c600 cos \u03c600 y00p \u03c600 \u00bc r \u03c600 sin \u03c600 ( : \u00f042\u00de And the vector is: O2 0 0P0 0 \u00bc x00p \u03c600 \u2212x00o2 \u03c6; ho\u00f0 \u00de y00p \u03c600 \u2212y00o2 \u03c6; ho\u00f0 \u00de h iT : \u00f043\u00de In terms of Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003386_j.ast.2020.105974-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003386_j.ast.2020.105974-Figure3-1.png",
        "caption": "Fig. 3. Possible configurations with different quadrotor attitudes subject to disturbance.",
        "texts": [
            " 2(a)\u2013(c) can be considered as the projection of the resultant force of two adjacent practical cables in yb zb plane. (a) When the roll angle is zero, the payload will stay right under the quadrotor in the stable configuration. The tensions in these two cables are F1 = F2 = mg 2 cos\u03b21 (7) where \u03b21 = \u03c0 2 \u2212 \u03b1 with \u03b1 = arccos l y L . Note that L is the equiv- alent cable length L = \u221a l2 \u2212 l2x . To analyze the robustness of the configuration in Fig. 2(a), suppose there exists a small disturbance d acting on the payload along the horizontal direction as shown in Fig. 3(a). In this case, the tensions in the cables satisfy the following equations F1 sin\u03b21 + d = F2 sin\u03b21 (8) F1 cos\u03b21 + F2 cos\u03b21 = mg (9) The solutions to Eqs. (8) and (9) are F1 = mg 2 cos\u03b21 \u2212 d 2 sin\u03b21 , F2 = mg 2 cos\u03b21 + d 2 sin\u03b21 (10) From Eq. (10), it can be found that F1 = 0 holds if d equals to mg tan\u03b21 and d = \u2212mg tan \u03b21 implies F2 = 0. That is, the system cannot remain in the configuration in Fig. 3(a) with a disturbance larger than mg tan\u03b21. In other words, the configuration in Fig. 3(a) can withstand the disturbance with magnitude less than mg tan \u03b21. (b) If the roll angle \u03c6 satisfies \u03c6r \u2265 \u03c6 > 0 with \u03c6r = \u03c0 2 \u2212 \u03b1, as shown in Fig. 3(b), the stable configuration contains two tensioned cables. With a horizontal disturbance, the tensions in the cables satisfy the following equations F1 sin\u03b22 + d = F2 sin\u03b23 (11) F1 cos\u03b22 + F2 cos\u03b23 = mg (12) where \u03b22 = \u03c0 2 \u2212 \u03c6 \u2212 \u03b1 and \u03b23 = \u03c0 2 + \u03c6 \u2212 \u03b1. Note that \u03b1 has the same value as that in case (a). From Eqs. (11) and (12), one has F1 = mg sin\u03b23 \u2212 d cos\u03b23 sin(\u03b22 + \u03b23) , F2 = mg sin\u03b22 + d cos\u03b22 sin(\u03b22 + \u03b23) (13) From the above equation, d = mg tan \u03b23 and d = \u2212mg tan \u03b22 imply F1 = 0 and F2 = 0, respectively. That is, the payload is stable with \u2212mg tan \u03b22 \u2264 d \u2264 mg tan \u03b23. It should be noted that if the roll angle equals to \u03c6r , \u03b22 = 0 holds, which implies that only the positive disturbance d \u2264 mg tan \u03b23 is tolerable. (c) If the roll angle is larger than \u03c6r , the tension only exists in one cable and the stable position of the payload is right under the left attached point. As shown in Fig. 3(c), the system can be considered as a simple pendulum with a complicated constraint. That is, the system is a simple pendulum when its swing angle less than \u03b1 \u2212 \u03b1\u2217 . However, if the payload has a swing angle larger than \u03b1 \u2212 \u03b1\u2217 , the constraint from the right cable will take effect. Similar to the traditional quadrotor transportation system with cable-suspended payload, even with a small disturbance, the payload will oscillate slightly. That is, the configuration in Fig. 3(c) cannot tolerate any disturbance. Another interesting issue is what will happen if the unperturbed system in Fig. 3(c) starts from a position left to the leftdotted line in Fig. 3(c), such as the initial position in Fig. 4. That is, the initial oscillation angle is larger than \u03b1\u2212\u03b1\u2217 , where \u03b1\u2217 = \u03c0 2 \u2212\u03c6. In the case that the dissipation of the mechanical energy is ignored, the payload will move along the solid curve in Fig. 4. However, when the payload moves through the nonsmooth point, the slack cable will be tightened instantaneously, i.e., an impact force will exist in the cable. Since the cable of concern has a huge modulus of elasticity for tension, the impact damping is also huge, which means that the system energy will decrease rapidly at this point",
            " 4, it will quickly converge to a simple harmonic motion along the red solid curve in Fig. 4. Different from the systems with one cable, there exists coupling between the quadrotor attitude and the payload motions in the developed aerial transportation system. Next, the influence of the torques acting on the quadrotor from the payload in the stable configurations shown in Fig. 2 will be discussed. It is clear that F1 is equal to F2 and no additional torque exists in the unperturbed Case (a). For Case (a) with disturbance shown in Fig. 3(a), the torque acting on the quadrotor from the payload is \u03c4a = \u2212F1l y sin\u03b1 + F2l y sin\u03b1 = dly sin\u03b1 sin\u03b21 (14) In the perturbed case with a small roll angle, the disturbance torque can be expressed as \u03c4b = mg sin\u03b22 + d cos\u03b22 \u2212 mg sin\u03b23 + d cos\u03b23 sin(\u03b22 + \u03b23) l y sin\u03b1 = \u2212mgly sin\u03c6 tan\u03b1 + dly cos\u03c6 tan\u03b1 (15) In the case with a large roll angle, the resulting torque on the quadrotor with an unperturbed payload is \u03c4c = \u2212F1l y sin\u03b1\u2217 = \u2212mgly cos\u03c6 (16) Therefore, the following conclusions can be drawn. (i) The disturbance acting on the payload has an effect on the attitude motion of the quadrotor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003759_j.ymssp.2019.02.044-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003759_j.ymssp.2019.02.044-Figure3-1.png",
        "caption": "Fig. 3. Sun planet link and line of action.",
        "texts": [
            " 2, global displacements of the sun gear and planet gear can be expressed as functions of local displacement Usg \u00bc Us cos hc Vs sin hc Vsg \u00bc Us sin hc \u00fe Vs cos hc rbr Wsg \u00bc Ws 8>< >: \u00f01\u00de Ung \u00bc Un cos hc Vn sin hc \u00fe rc cos hc Vng \u00bc Un sin hc \u00fe Vn cos hc rbr rc sin hc\u00f0 \u00de Wng \u00bc Wn 8>< >: \u00f02\u00de with hc is the instantaneous angular position of the carrier. Hence, local displacements from Eqs. (1) and (2) can be expressed as: Us \u00bc Usg cos hc \u00fe Vsg sin hc \u00fe rbr sin hc Vs \u00bc Usg sin hc \u00fe Vsg cos hc \u00fe rbr cos hc Ws \u00bc Wsg 8>< >: \u00f03\u00de Un \u00bc Ung cos hc \u00fe Vng sin hc \u00fe rc \u00fe rbr sin hc Vn \u00bc Ung sin hc \u00fe Vng cos hc \u00fe rbr cos hc Wn \u00bc Wng 8>< >: \u00f04\u00de The displacement along the line of meshing force (Fig. 3), with respect to the carrier, is expressed by Saada et al. [1] as: dsn \u00bc Vs cosusn Us sinusn Un sinas Vn cosas \u00feWs \u00feWn \u00f05\u00de So, with respect to the new frame, Eq. (5) can be expressed as: d g sn \u00bc Usg sin usn \u00fe hc\u00f0 \u00de \u00fe Vsg cos usn \u00fe hc\u00f0 \u00de Ung sin as hc\u00f0 \u00de Vng cos as hc\u00f0 \u00de \u00feWsg \u00feWng \u00fe rr cos usn\u00fe hc\u00f0 \u00de cos as hc\u00f0 \u00de\u00f0 \u00de \u00fe rc sinas \u00f06\u00de The position of the sun is given by Rs !\u00bc Usg i !\u00fe Vsg j ! \u00f07\u00de The velocity of the sun is given by _Rs ! \u00bc _Usg i !\u00fe _Vsg j ! \u00f08\u00de The strain energy of the sun is Eps \u00bc 1 2 ks U2 sg \u00fe V2 sg \u00fe 1 2 kswW 2 sg \u00fe 1 2 XN 1 ksn t\u00f0 \u00ded g sn 2 \u00f09\u00de The kinetic energy of the sun is Ecs \u00bc 1 2 ms _U2 sg \u00fe _V2 sg \u00fe 1 2 Is r2bs _W2 sg \u00f010\u00de By applying LAGRANGE formulation given by Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000821_j.triboint.2010.02.002-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000821_j.triboint.2010.02.002-Figure1-1.png",
        "caption": "Fig. 1. Experimental apparatus for RCF measurements and test specimen (roller).",
        "texts": [
            " It was found that lubricant emitted from micro-dents could effectively lift off the real roughness features that provided an increase in average but also the local minimum film thicknesses. In the current study this approach is further observed by considering the effect of surface texturing on RCF within non-conformal rolling/sliding contacts operated under mixed lubrication conditions to find out whether this possible beneficial effect on film thickness is not accompanied by the reduction in RCF life. Experimental apparatus (Fig. 1) consisting of two discs loaded and running against cylindrical test specimen (roller) was used to consider the effect of surface texturing on RCF. Discs had 145 mm diameter and radius in the plain oriented perpendicular to the direction of motion was 4.5 mm, and the roller had 9.6 mm diameter. Both discs and roller were made from AISI 52100 bearing steel and Rockwell hardness was 60 after quenching and grinding. RMS surface roughness measured by stylus technique was about 0.1 and 0.2mm for roller and discs, respectively",
            " For these conditions the lubrication parameter L, defined as the ratio of minimum film thickness within the smooth contact to reduced surface roughness, is between 0.4 and 0.6. All experiments were carried out at 33 1C. The level of the vibration of the roller was monitored and apparatus was automatically shut off once the vibration level corresponding to the surface damage was reached. One test specimen (roller) can be used up to 12 measurements (one measurement corresponds to one track, see Fig. 1). The roller surface is indented mechanically using a Rockwell indenter (Fig. 2) to obtain micro-dents with well-defined shapes. The indenter had an angle of a cone 1201 and radius of a diamond tip 0.2 mm. The indentation process was fully controlled by a PC with appropriate software. A vertical movement of the indenter was controlled by a step motor whereas the desired load was checked using a strain guage. Rotation of the roller was also controlled by step motor through a clutch. Such a configuration Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001757_j.jsv.2016.02.040-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001757_j.jsv.2016.02.040-Figure1-1.png",
        "caption": "Fig. 1. The conceptual relationship between road excitation, airgap eccentricity and SRM vertical force.",
        "texts": [
            " To suppress SRM vibration, some structures and controllers [15\u201317] have been investigated by eliminating SRM torque ripple and radial force. These studies contribute to suppress SRM vibration, however the SRM effect on vehicle vibration characteristic has not been considered enough. For the electric vehicle vibration system, the vertical component of SRM residual unbalanced radial force, namely SRM vertical force, is one of the major concerns. The SRM vertical force, airgap eccentricity and road excitation may be highly coupled as shown in Fig. 1, where the road excitation induces SRM stator and rotor vibration, which will cause airgap deformation, i.e. airgap eccentricity. The airgap eccentricity yields SRM vertical force. Meanwhile, SRM vertical force has negative effect on stator and rotor vibration which will eventually aggravate airgap eccentricity. So the airgap eccentricity and SRM vertical force is coupled with each other along with the road excitation. Unlike the traditional vehicle propulsion systems with a torque vibration damper, the SRM applies the SRM vertical force excitation directly on wheel, which will induce great negative effect on IWM-EV vibration performance"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000901_j.bioelechem.2012.10.001-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000901_j.bioelechem.2012.10.001-Figure1-1.png",
        "caption": "Fig. 1. (a) Scheme of microelectrodes with gold interdigitated transducers, (b) Spirulina immobilized on the reference electrode, and (d) SEM image of Spirulina cells population pe",
        "texts": [
            " Cells were fixed with covalent links using glutaraldehyde solution (3%, v/v) purchased from Sigma-Aldrich, specially purified for use as an electron cells immobilized on the working electrode, (c) Spirulina cells, with inhibited APA rformed between gold fingers of interdigitated transducers. microscopy fixative. Spirulina-based biosensors were immerged in this solution for 45 min. After, a series of dehydration in successive absolute ethanol solutions were applied for 10 min using increased concentrations (20%, 40%, 60%, 80%, and 100% ethanol). The conductometric transducers (Fig. 1.a) were fabricated at the V.Ye. Lashkaryov Institute of Semiconductor Physics (Kyiv, Ukraine). Each of them consisted of two identical pairs of interdigitated thin film electrodes (150 nm thick), fabricated by gold vapor deposition onto a non-conducting pyroceramic substrate (5\u00d730 mm). The technique of sensor manufacturing has been reported previously [26,27]. A 50 nm thick intermediate Cr layer was used to improve the adhesion of Au to the substrate. Both the digit width and interdigital distance were 10 \u03bcm, and their length was ~1.5 mm. As a result, the sensitive area of each pair of electrodes was ~2.9 mm2 (Fig. 1.a). A biosensor analyzer consisted of a sensor block and an electronic measuring block (portable four-channel biosensor analyzer) was developed in collaboration with Institute of Electrodynamics of National Academy of Sciences of Ukraine and it was reported by Dzyadevych et al. [27]. The sensor block consisted of a stand with a fixed block of holders; eachholderwas connected to the fingers of an appropriate conductometric biosensor. An electronic measuring block consisted of the following modules: a secondary transducer and a basic measurementcontrol module",
            " All EIS measurements were taken at a frequency range of 100 mHz to 100 kHz at room temperature. The same glass cell (4 mL) was filled with HEPES (5 mM) under vigorous magnetic stirring. IDT electrodes were cleaned by sonication for 10 minutes, followed by chemical treatment in Piranha solution (H2SO4/H2O2, 3:1 v/v) for 5 minutes. The electrodes were then rinsed with absolute ethanol and finally dried under a flow of nitrogen. Finally, cyanobacteria solution (0.7 \u03bcL)was deposited directly onto the sensitive area of the first pair of IDTs representing the work electrode (Fig. 1.b). The cells were adsorbed preferentially to the ceramic substrate as observed through SEM (Fig. 1.d). Throughout the study, the cyanobacteria concentration was 0.3 g/L and it was chosen after optimization. The variation of Spirulina concentration in the initial solution did not affect the shape of the curve, while at the saturation concentration of the substrate the curve varied slightly (data not shown). On the second pair of IDTs representing the reference electrode (Fig. 1.c), Spirulina cells where the APA had already been inhibited f Spirulina cells. by mercury solution (10\u22126 M) were immobilized using the same volume (0.7 \u03bcL). These cyanobacteria cells were inhibited in mercury solution; this was made 24 h before immobilization. This configuration allowed differential mode measurements. EIS is a valuable tool to characterize phenomena at the interface. For this, electrochemical admittance spectra were recorded for a bare microelectrode and after immobilization of Spirulina cells"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000316_j.bios.2006.11.016-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000316_j.bios.2006.11.016-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram of",
        "texts": [],
        "surrounding_texts": [
            "ioelec\no H o s i p e c a a\nm 2 o d o t a d e t t b i c a\nr i s w c a d a s n t p\ne a a c a w T c T c a t m\nc 1\nO\nH\ni e m c o T a\n2\n2\np ( s S P 3 C u m (\n2\np l T fl w p t p f e\nY. Xie et al. / Biosensors and B\nr coating approaches (Lee et al., 2004; Tian et al., 2003). owever, it is still unlikely to assemble these powdery nantubes to form well-aligned array on substrates in a large cale. To date, multiporous semiconductor films supported on ndium\u2013tin oxide (ITO) conductive glass, glassy carbon or metal latinum disk are widely used as the matrix of the working lectrode, which can be fabricated by a sol dip-coating proess. Such sorts of superficially coated oxide film electrodes re then modified by different enzymes to form the functionlized modules, which are finally applied to construct various\nicro-devices (Topoglidis et al., 2001; Yang et al., 004).Traditional biosensors usually use these porous xide film electrodes as the interactive matrix for compound etection and quantitative determination. The microstructure f these oxide layers mostly affects the interfacial adsorpion of protein probes (Kenausis et al., 2000; Reimhult et l., 2002). Unfortunately, the randomly aligned oxide film ecreases its interaction surface area. The surface-adsorbed nzymes are also likely to desquamate from the coating film o lessen its bioactivity after continuous utilization. Addiionally, a high electrical resistance due to the weak bond etween semiconductor film and its substrate also inhibits nterfacial electron transfer process during electrochemial interaction. These defects evidently restrain it sensing pplication.\nThis study presents a new three-dimensional electrode mateial of highly ordered and self-organized TiO2/Ti nanotube array nstead of particulate TiO2/ITO single-sided film to act as a upporting matrix. Each tube channel with independent singleall structure can provide individual nano-spaced reaction hamber. Both TiO2 and Ti are good biocompatible materils, which exhibits a superior bioaffinity to accumulate the issolved molecules on TiO2 surface (Oh et al., 2005). As sensing matrix, TiO2/Ti nanotube array has a much higher urface area-to-volume ratio, stronger micromechanical conection strength and a better electron transfer channel than he ordinary TiO2/ITO electrode formed by surface coating rocess.\nThe oxidase enzyme-based biosensor is developed by mploying TiO2/Ti nanotube array electrode. A bioelectrocatlytic redox system is established for amperometeric detection nd concentration measurement. The glucose oxidase (GOD) an catalyze glucose to conduct an enzymatic specialty reaction long with concomitant release of hydrogen peroxide (H2O2), hich enables an electrochemical redox on TiO2/Ti electrode. he responsive current intensity mostly reflects the interfaial electron transfer amount on the enzyme-functionalized iO2/Ti nanotube array electrode. The quantitative relationship an be associated between amperometric current and molecule mount in a certain range, which provides a fundamental heory principle for this biosensing application. The ampero-\netric detection mechanism of GOD-modified TiO2 biosensor\nc f o n\ntronics 22 (2007) 2812\u20132818 2813\nan be schematically shown below (Wilkins and Atanasov, 996):\nGlucose + GOD\u2013flavinadeninedinucleotide(FAD)\n\u2192 Gluconolactone + GOD\u2013reducedstatesofFAD(FADH2)\n2 + GOD\u2013FADH2 \u2192 H2O2 + GOD\u2013FAD\n2O2 + 2e\u2212(TiO2) \u2192 2OH\u2212\nIt is therefore very feasible to develop such a functionalzed biosensor using enzymes-modified TiO2/Ti nanotubular lectrode. Furthermore, as a universal biological measureent method, a serial of similar biosensors can also be onstructed on the principle of biomolecules pair interaction f antigen\u2013antibody interaction or supramolecular recognition. he novel configuration could donate a high performance in the rea of molecule detection and concentration determination.\n. Experimental\n.1. Materials\nTitanium foil (Ti, purity > 99.6%, thickness 0.14 mm) was urchased from Goodfellow Cambridge Ltd. Glucose oxidase GOD, EC 1.1.3.4., from Aspergillus niger, 2000\u201310,000 units/g olid, without added oxygen) and d-(+) glucose (Glu, anhydrous, igma No. G-5250) were purchased from Sigma\u2013Aldrich Co. yrrole monomer (Py, purity > 99%), hydrogen peroxide (H2O2, 0 wt.%) and other chemical reagents purchased from Fluka hemical Corp. are analytical grade. Doubly distilled water was sed throughout. All electrochemical experiments and measureents were carried out in a 0.1 M phosphate buffer solution PBS) of pH 6.8.\n.2. Preparation of TiO2 nanotube array biosensor\nGOD\u2013TiO2/Ti nanotube array electrode was fabricated by the rocesses of electrochemical anodization and coupling encapsuation. Firstly, the TiO2 nanotube array was directly formed on i substrate by a potentiostatic anodization at 20 V in acidic uoride electrolyte. A post-calcination process (450 \u25e6C, 2 h) as then followed to crystallize TiO2 nanotubes from amorhous to anatase phase. Under a nitrogen-purging condition, his TiO2/Ti electrode was immersed in 50 g L\u22121 GOD, 0.1 M hosphate buffer solution for 12 h at 4 \u25e6C. To improve interacial connection strength between enzymes and titania, the lectropolymerization process for surface immobilization was onducted in 2.0 mM conductive monomer of pyrrole at 0.8 V or 20 min. As a result, the functionalizing process of TiO2 nantube array was achieved by coupling deposition of GOD inside anotubular channels to form a compacted enzyme layer with",
            "2814 Y. Xie et al. / Biosensors and Bioelectronics 22 (2007) 2812\u20132818\nbioele\nb l o c\n2\nJ m g v e e q\n2\nb a q C c a t e u d c p a\nr e I w P e F\n3\n3\nb i o d t l o T a 6 i d a c n\niocatalytic reactivity. Sufficiently rinsing treatment was folowed to keep an ultra thin adsorption layer on the inner surface f TiO2 tubules so that more functional groups of GOD enzymes ould contact with glucose for bioelectrocatalysis.\n.3. Characterization and analytical methods\nBoth field emission scanning electron microscopy (FESEM, EOL JSM-6335F) and high resolution transmission electron icroscopy (HRTEM, JEOL-2010F) were used to investiate surface morphology and microstructure. Linear sweep oltammetry and impedance analysis were applied to evaluate lectrochemical behaviors of pure TiO2/Ti and GOD\u2013TiO2/Ti lectrodes. A time-based amperometeric response was used for uantitative determination.\n.4. Experimental setup and procedures\nBioelectrocatalytic application of TiO2 nanotube array-based iosensors was investigated for amperometric detection of H2O2 nd glucose. Measurement system was setup in a cylindrical uartz cell by using an electrochemical workstation (CHI 660C, H Instruments Co., Ltd., USA) with a standard three-electrode onfiguration. Both pure TiO2/Ti and GOD\u2013TiO2/Ti nanotube rray were used as the working electrodes with an effective reacion area of 2.0 cm2. A standard Hg/Hg2Cl2 saturated calomel lectrode (SCE) was used as a reference electrode and Pt foil was sed as a counter electrode. Standard calibration curve of H2O2 etermination (responsive current intensity versus compound oncentration) was initially conducted in PBS under a constant otential. Quantitative determination of glucose was achieved by mperometric measurement of H2O2 based on electrochemical\nt s f w\nctrocatalytic detection setup.\neduction reaction, which was preferentially generated by inhernt ligase chain reaction of enzyme\u2013substrate of GOD\u2013glucose. n order to keep its original bioactivity of GOD enzymes, the hole electrochemical process was carried out in 50 mL, 0.1 M BS electrolyte aerated with 25 mL min\u22121 oxygen gas. The lectrochemical experimental system is schematically shown in ig. 1.\n. Results and discussion\n.1. Microstructural characterization\nThe morphology and structure of TiO2/Ti electrode had een examined by FESEM and HRTEM observation and their mages are shown in Fig. 2. FESEM image reveals that highly rdered and vertically aligned TiO2 nanotube array could irectly grow on both sides of titanium foils. These uniform ubes had a unique open-mouth structure on the top of titania ayer while they are closed on the bottom due to the presence f oxide barrier layer with a thickness of tens of nanometer. he average tubule height and wall thickness reached to 540 nd 15 nm, respectively. The inner diameter was estimated to 0 nm, which might benefit the enzymatic encapsulation modfication of glucose oxidase holoenzyme with an approximate imension of 70 A\u030a \u00d7 55 A\u030a \u00d7 80 A\u030a (Hecht et al., 1993). The spect-ratio of each nanotube was tailored below 10, which ould favor interfacial adsorption and electron transfer in these ano-spaced channels. Furthermore, nanocrystal structure of itana nanotube wall had been investigated by HRTEM meaurement along its axial direction. The series of interference ringes were clearly exposed on the surface of crystals, which ere corresponding to the characteristic {1 0 1} crystal lattice",
            "Y. Xie et al. / Biosensors and Bioelectronics 22 (2007) 2812\u20132818 2815\nF n\np T n c\nF \u2212\n3\nt c t e t w a T t b i g s T e h m g i s t e\ne n r r w m r i t b t ig. 2. (A) Top-view FESEM and (B) cross-sectional FESEM images of TiO2 anotube array and (C) HRTEM image of TiO2 nanotube wall. lanes with the interplanar spacing of d{1 0 1} = 0.36 \u00b1 0.01 nm. his fact indicates that the well-defined anatase titania anotube array with a fine crystallinity had been formed ompletely. T o r a\nig. 3. Impedance curves of TiO2 film/ITO and TiO2 nanotube array/Ti at 0.40 V vs. SCE over a frequency of 0.01 Hz\u2013100 KHz.\n.2. Electrochemical properties\nThe conductivity of the functional electrodes could influence he amperometric signal intensity in the bioelectrocatalytic proess. Electrochemical impedance spectroscopy had been applied o explore the total conductivity of the titania/titanium composite lectrode over the frequency range of 0.01\u2013100 kHz. Along with he moderate increase of frequencies, the electrode\u2019s impedance as dramatically decreased at a low frequency stage below 1 Hz nd then gradually achieved to a steady value above 10 Hz. he impedances at 1 kHz are particularly important because hey generally correspond to the characteristic frequency of iointeraction potential (Abidian et al., 2006). Significantly, the mpedance of TiO2/Ti nanotube array electrode at 1 kHz was reatly decreased by about two orders of magnitude in comparion with that of traditional TiO2/ITO film electrode (see Fig. 3). he impedance value mostly reflects the efficiency of interfacial lectron transfer in a certain degree. Lower impedance means igher conductivity for the working electrodes. Therefore, the ore effective heterogeneous bonding was achieved by directly rowing titania nanotubes on titanium substrate rather than castng titania sol\u2013gel film on ITO substrate. Such an integrative tructure between TiO2 and Ti ultimately might prompt the elecron transfer efficiency as well as the responsive sensitivity of lectrochemical reaction.\nLinear sweep voltammetry (LSV) was applied to examine lectrochemical behaviors of pure TiO2/Ti and GOD\u2013TiO2/Ti anotube array electrode in PBS electrolyte. Experimental esults are shown in Fig. 4. In the absence of H2O2, direct eduction peak began to appear when the negative potential as below \u22120.43 V for pure TiO2/Ti electrode, which was ostly due to hydrogen generation by water decomposition eaction (2H2O + 2e\u2212 \u2192 H2 + 2OH\u2212) (see curve a). However, n the presence of H2O2, the rapid generation of a strong reducion peak was observed when the negative potential was only elow \u22120.20 V, which was mainly due to electrochemical reducion of H2O2 on TiO2 (H2O2 + 2e\u2212 \u2192 2OH\u2212) (see curve b).\nhe intensity of such a reduction current mostly depended n H2O2 concentration as well as the applied potential. This eduction peak could be intensively enhanced when a more negtive potential was applied on TiO2/Ti electrode. It means that"
        ]
    },
    {
        "image_filename": "designv10_5_0000911_tmech.2014.2311382-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000911_tmech.2014.2311382-Figure9-1.png",
        "caption": "Fig. 9. Experimental setup. (a) Schematic diagram and (b) Picture of the experimental test apparatus.",
        "texts": [
            " 2(b), the stiffness of the wave generator at zero output torque can be estimated using the following relation: Kw0 = 2Tf s N\u03a8 (33) where \u03a8 denotes the hysteresis loss and Tf s is the harmonic drive\u2019s starting torque. From (27), the maximum torsion of the wave generator at one direction is 1/(Cw NKw0). It is also evident from Fig. 2 that the total deformation due to the wave generator compliance at one direction is half of the hysteresis loss \u03a8. Therefore, one can write 0.5\u03a8 = 1 Cw NKw0 . (34) Solving (34), one can obtain Cw = 2 NKw0\u03a8 . (35) To investigate the behavior of harmonic drive systems, a test station is set up as shown in Fig. 9. In this experimental setup, the harmonic drive is driven by a brushed DC motor from Maxon, model 218014. Its weight is 480 g, with maximum rated torque of 188 mNm, and torque constant of 0.321 Nm/amp. A linear power amplifier and the Q8 data acquisition board from Quanser, Inc., are used to drive the motor and collect experimental data. The harmonic drive in the setup is SHD-17-100-2SH with gear ratio of 100:1, and rated torque of 16 Nm from Harmonic Drive AG. The link-side position is measured using Netzer absolute position electric encoder with 19-bit resolution and the link-side torque is measured using ATI six-axis force/torque sensor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001443_ls.1271-Figure10-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001443_ls.1271-Figure10-1.png",
        "caption": "Figure 10. Transformed rotational speeds of the elements in the rolling bearing.",
        "texts": [
            "5mm (negative since it is concave). This gives Rx=7.2mm and Ry=300mm. For rolling bearings, calculation of the entrainment speed U is often the most complicated stage since the ball moves around the bearing as it rotates, so the contacts between the ball and the raceways move in space. This is most easily dealt with by assuming that the ball rotates around the bearing with a (unknown) circumferential angular speed \u03c9c. This rotational speed is then subtracted from the inner and outer raceway angular speeds as shown in Figure 10, to effectively create a frame of reference in which the ball is stationary. Now, we assume that there is pure rolling at both the inner and outer raceway/ball contacts so At inner raceway contact; r\u03c9r \u00bc R \u03c9i \u03c9c\u00f0 \u00de (40) Copyright \u00a9 2014 John Wiley & Sons, Ltd. Lubrication Science 2015; 27:45\u201367 DOI: 10.1002/ls Simultaneous solution of these two equations eliminates the unknown \u03c9c and gives \u03c9r \u00bc R 2r R\u00fe 2r R\u00fe r \u03c9i (42) so, U \u00bc r\u03c9r \u00fe r\u03c9r 2 \u00bc R\u03c9i 2 R\u00fe 2r R\u00fe r (43) For the bearing contact previously, this gives U = 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000845_j.scient.2012.01.004-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000845_j.scient.2012.01.004-Figure1-1.png",
        "caption": "Figure 1: Bearing geometry and degrees of freedom.",
        "texts": [
            " Finally, the developed finite element model is used to simulate the behavior of some typical spindlebearing systems and its validity is examined against available experimental data. In the mechanical modeling of the bearing, five degrees of freedom are considered for the relative displacement of the inner ring with respect to the outer ring. Without loss of generality, the outer ring is assumed to be fixed, because any displacement of outer rings can be included by attributing them to the inner ring with a minus sign. The bearing degrees of freedom are shown in Figure 1. These consist of three linear displacements (\u03b4x, \u03b4y, \u03b4z) and two rotations (\u03b3y, \u03b3z). \u03b8 is the nominal contact angle of the bearing ball. In order to analyze the bearing kinematics, the internal configuration of rolling elements and their load equilibrium should be considered. General forces acting on a rolling element are shown in Figure 2. The instantaneous contact angles of the inner and outer rings are denoted by \u03b1i and \u03b1o, respectively. These angles differ from the nominal contact angle, \u03b8 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001548_rcs.1427-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001548_rcs.1427-Figure1-1.png",
        "caption": "Figure 1. Principles of tool/flange and robot/world calibration: A marker M is attached to the robot\u2019s end effector E and measured by the tracking system or an ultrasound station T. Tool/flange and robot/world calibration is used to determine the unknown transforms RTT, the transform from the robot\u2019s base to the tracking system, and ETM, the transform from the end effector\u2019s local system to the marker\u2019s local system",
        "texts": [
            " \u2022 In the case of deficient tracking data, a partial solution is presented, that is, when the localisation device only provides translational data or does not provide full rotational data. First, the novel non-orthogonal calibration method is presented for tracking data providing full six DOF. Later, an adaptation of the method for tracking data with only partial tracking information having less than six DOF is described. The last variation deals with preconditioning of the equation system. A na\u00efve approach to tool/flange and robot/world calibration is to look at the general relation RTE ETM\u00bcRTT TTM; (1) which is illustrated in Figure 1. Here, the matrices ETM, the transform from the robot\u2019s end effector to the marker, and RTT , the transform from the robot\u2019s base to the tracking system are unknown. To compute these matrices, n measurements for different robot poses are taken, resulting in n equations RTE i E TM\u00bcRTT TTM i; i \u00bc 1; . . . ; n: (2) Typically, the robot\u2019s end effector is moved to random points selected from inside a sphere with radius r. Additionally, a random rotation of up to d degrees in yaw, pitch and roll is added to the pose"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001443_ls.1271-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001443_ls.1271-Figure3-1.png",
        "caption": "Figure 3. Typical elastohydrodynamic pressure profile.",
        "texts": [
            "5 Use of the previous tables enables the maximum contact pressure, po, and the contact dimensions to be calculated. In EHL contacts, po is usually in the range 0.5 to 4GPa while 2a is typically 100 to 600\u03bcm. The mean pressure can, of course, be calculated from the applied load divided by the contact area but is also given by \u03c0/4po for line and 2/3po for circular contact. For EHD contacts, the previous equations are only approximate, especially for pressure. Numerical solution of the EHD problem yields pressure distributions of the form shown in Figure 3, as compared with the parabola predicted by Hertz for a static, dry contact and shown in Figure 2. There is a build-up Copyright \u00a9 2014 John Wiley & Sons, Ltd. Lubrication Science 2015; 27:45\u201367 DOI: 10.1002/ls Copyright \u00a9 2014 John Wiley & Sons, Ltd. Lubrication Science 2015; 27:45\u20136 DOI: 10.1002/l of pressure in the contact inlet upstream of the central flat region (which is crucial in generating a fluid film) and a pressure maximum (known as a pressure spike), followed by a very rapid collapse of pressure at the contact exit",
            " If the two surfaces move in opposite directions with respect to the contact, then it is possible for SRR to be much greater than 2, with very low entrainment speeds but high sliding speeds. This occurs in some cam\u2013follower contacts. Typical film shapes are shown for a circular point EHD contact (ball on flat) and a line EHD contact (roller on flat) in the experimental optical interference images in Figure 4. In both images, the inlet is on the left. There is quite constant film thickness across most of the contact with a reduced film thickness or \u2018constriction\u2019 at the rear and sides. This is also shown in Figure 3. The film thickness at this constriction is approximately 70% of the central film thickness and tends to be thinner at the sides than at the rear of the contact. The lubricant film cavitates as it emerges from the rear of the contact, as can be seen on the right hand side of both images. One of the most important features of EHL is that unlike conventional hydrodynamic lubrication, there is no direct relationship between the EHD film thickness and the EHD friction. The reason for this comes from the shape of the EHD film"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001601_1.4754521-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001601_1.4754521-Figure3-1.png",
        "caption": "FIG. 3. Photograph of the electromagnetic-coil setup which contains six coils. A: camera for top-view vision feedback, B: microscope lens, C: top \u00fez coil, D: \u00fex coil (one of four horizontal coils), E: x coil, F: experiment workspace, G: bottom z coil. The y coil is removed to allow viewing of the workspace, and the \u00fey is behind the workspace seen from the view.",
        "texts": [
            " If the total effect of the hydrodynamic forces fails to overcome Ff , the motion criterion is not met and the object will remain stationary. The magnetic micro-manipulators used in this study are fabricated from a mixture of neodymium-iron-boron (NdFeB) particles (MQP-15-7, Magnequench) and polyurethane base (TC-892, BJB Enterprises), via a typical soft-lithography-based micro-molding process.31 The substrate with embedded magnetic micro-docks is a spin-on-glasscoated (21F, Filmtronics) SU-8 substrate (SU-8 2050, MicroChem) with molded NdFeB docks. An electromagnetic-coil system (see Fig. 3), consisting of three orthogonal pairs of [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 131.181.251.130 On: Sat, 22 Nov 2014 08:12:12 electromagnetic coils, is used to generate uniform magnetic fields to actuate and control the magnetic micromanipulators.31 All experiments are carried out in a 30 mm 30 mm 1 mm open-top container filled with silicone oil with a kinematic viscosity of 50 cSt to create a low Re environment. The magnetic field used to actuate the magnetic micromanipulators has a field strength up to 5 mT supplied by the electromagnetic-coil system as shown in Fig. 3. The capabilities of rotational micro-manipulator locomotion and non-contact micro-object manipulation are shown in Fig. 4(a), where a 360 lm-diameter magnetic spherical micro-manipulator transports a 200 lm-diameter polystyrene bead with a density of 1.05 g/cm on a glass substrate. An external magnetic field with strength of 3.5 mT rotating at a frequency of jXj \u00bc 30 Hz was applied to induce the synchronous rotation of the magnetic manipulator. In this experiment, the rotation tilt angle was kept small (<10 ), resulting in a translational manipulator speed of approximately 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003341_ffe.13123-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003341_ffe.13123-Figure3-1.png",
        "caption": "FIGURE 3 Geometry of the tested Gaussian specimens",
        "texts": [
            " Therefore, for investigating the effect of these types of defect on the fatigue response, HCF tests with conventional testing machines are more appropriate. The machining of the specimens to the final shape is more appropriate to investigate the role of internal defects,19 but since it removes a larger layer of material, it does not permit a proper assessment of the influence of surface and subsurface defects, which originate during the manufacturing process. The geometry of the tested Gaussian specimens is shown in Figure 3. Fully reversed constant stress amplitude tension\u2010 compression tests at a loading frequency of 20 kHz were carried out up to failure or up to 109 cycles (run\u2010out number of cycles) by using the ultrasonic testing equipment available at Dynlab in Politecnico di Torino.18 The applied stress amplitude at the specimen center, scenter, was kept constant during the tests through a feedback control based on the stress amplitude, shorn, obtained from the strain measured with a strain gage (control gage) bonded to the horn"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003661_j.neucom.2019.04.087-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003661_j.neucom.2019.04.087-Figure1-1.png",
        "caption": "Fig. 1. n-link rigid robotic manipulator model.",
        "texts": [
            "2 Mathematical model description Consider an n-link robotic manipulators expressed by ( ) ( , ) ( ) ( ) ( )t t   M q q C q q q G q \u03c4 d , (10) where q=[q1,,qn] T R n is the angular position vector of the joints, and q R n and q R n are the velocity and acceleration vectors; R n is torque vector of the joints, and dR n is the disturbance vector; MR n\u00d7n , CR n\u00d7n and GR n are respectively the symmetric positive definite inertia matrix, the Coriolis and centrifugal matrix, and the gravitational torque matrix. The model of the n-link robotic manipulator is shown in Figure 1. Due to the parametric uncertainties, the three matrixes become unknown with uncertainties, and the system (10) can be rewritten as follows ACCEPTED M ANUSCRIP      0 0 0 , ( ) ( ) ( , ) ( , ) ( ) ( ) ( ) ( )t t        M q M q q C q q C q q q G q G q \u03c4 d (11) where M0, C0, G0 represent the known normal terms and M, C, and G the uncertain ones, which can be assumed upper-bounded. In most existing works, the upper-bounds are generally needed to be assumed known and used in the controller design, such as [39,40]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002049_s11661-017-4330-4-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002049_s11661-017-4330-4-Figure1-1.png",
        "caption": "Fig. 1\u2014Build geometries and coordinate systems for bars built with (a) parallel scan (P) and (b) crosshatch scan (X) strategies as well as the (c) wrought sample.",
        "texts": [
            "[15] Powder was delivered using a Powder Feed Dynamics Mark XV Precision Powder Feeder to a custom-designed four-nozzle powder delivery system. Powder used for AM builds was Micro-melt 304L from Carpenter Powder Products with powder dimension specified as a range from 44 to 105 lm. The chemical composition of the powder is shown in Table I. Two processes were used to deposit bars having dimensions of 2.5 9 2.5 9 10 cm. A laser power of 3.8 kW was utilized in the first process with powder flow rates of 23 g/min. This process implemented a parallel scan geometry, shown schematically in Figure 1(a), with table speed set at ~63.5 cm/minute, and the hatch spacing of adjacent scan lines within a given layer set at 1.925 mm. The laser scan direction was the X-direction. The resultant build rate was 1.27 mm/layer. The second process used a power of 2.0 kW and a crosshatch scan approach (Figure 1(b)), which involved 90 deg rotated scan directions in alternating layers. Powder flow rates were 18 g/min, table speed was fixed at ~50.8 cm/min, and the hatch spacing of adjacent scan lines was set at 1.925 mm. The latter process was characterized by a build rate of ~0.89 mm/layer. The growth direction for both processes was labeled the Z-direction. In both processes, deposition generally involved placing a substrate at a location that was approximately 10 mm from the nozzle exits. This corresponds to the focus point of the powder flow",
            " However, at this location, the laser beam is in a defocused position and has a measured beam diameter (1/e2) of 4 mm. Previous characterization of the beam at this location using a PRIMES Focus Monitor confirmed a Gaussian energy distribution and the aforementioned diameter. For base lining, traditionally wrought 304L stainless steel samples were prepared. The wrought stainless steel samples were extracted from the center of a 10.2-cm diameter, cold finished, cylindrical bar with the sample straining axis parallel to the bar axis (Z-direction) as depicted in Figure 1(c). The center of the wrought bar likely experienced little or no cold work judging from the low yield stress, broad elastic\u2013plastic transition, and lack of crystallographic texture, to be shown later, and thus can probably be considered close to an annealed state. The composition of wrought and both forms of produced AM stainless steel were nearly identical, except the nitrogen level of the AM material was 0.08 wt pct, compared to 0.04 wt pct in the wrought material. Further details of the compositions of the AM and wrought samples are included in Table I",
            " Beyond, ~300 MPa, the slope of the curves in both tension and compression begins to increase slightly. In particular, at large tensile strains, the phase strain begins to curve upward slightly, increasing in slope to 313 GPa over the final 4 points and unloads with a slope of 223 GPa (not shown for clarity). The increase of modulus during unload is likely due to the evolution of the (111) texture at high tensile strains,[11,39,40] while the larger increase during loading above 600 MPa suggests that stress is being shed from the portion of the material being probed by diffraction Fig. 1 is out of the page. METALLURGICAL AND MATERIALS TRANSACTIONS A to some other portion of material (e.g., grain or sub-grain boundaries or possibly ferrite that is not observed in the diffraction pattern). Figures 10(b) through (d) show the phase rt vs ephi plots for both phases (austenite and ferrite) for the crosshatch and parallel scan AM material. Figure 10(b) and (c) depict the tensile behavior, while Figure 10(d) depicts the compressive behavior. In the case of the compression test, the axis has been reversed such that the longitudinal stress/lattice strain always goes up and to the right"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001273_icpe.2011.5944562-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001273_icpe.2011.5944562-Figure1-1.png",
        "caption": "Fig. 1. Double-output AC machine drive",
        "texts": [
            " This work further discusses the two-phase operation mode in which one faulted phase is isolated from the remaining portion of the circuit. Simulink simulation results are presented. Index Terms Double-output, fault tolerance, open-winding machine, open circuit fault, short circuit fault I. INTRODUCTION HE double-output AC machine drive has attractive features in applications where high power and/or high power quality is desired from an open-winding machine while the DC link voltage is limited, e.g. the electric and hybrid vehicle power conversion system [1]. The typical drive topology for an open winding machine is shown in Fig. 1 [2]. The two grounds in Fig. 1 may or may not be tied together. This provides the flexibility of using either single common DC source feeding both of the inverters, or two isolated DC sources feeding two inverters independently. The major difference between these two configurations is the presence of a zero-sequence path in the former case; therefore they should be In this inverter configuration, since the voltage is directly applied across one phase winding instead of two windings as in a standard drive, the available phase voltage is increased by a factor of 3 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000754_j.mechmachtheory.2013.10.006-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000754_j.mechmachtheory.2013.10.006-Figure4-1.png",
        "caption": "Fig. 4. The gearbox and its assembly.",
        "texts": [
            " Experiments were performed on a Machinery Fault Simulator\u2122 (MFS) and a schematic diagram of it is shown in Fig. 3. This machine could be used for the simulation of a range of machine faults like in the gearbox, shaft misalignments, rolling element bearing damages, resonances, reciprocating mechanism effects, motor faults, and pump faults. In the MFS experimental setup, 3-phase induction motor was mounted to the rotor that was connected to the gear box through a pulley and belt mechanism. The gear box and its assembly are illustrated in Fig. 4. In the study of faults in gears, three different types of faulty pinion gears namely the chipped tooth (CT), missing tooth (MT) and worn tooth (WT) along with normal gear (or no defect, i.e. ND) gear were used (see Fig. 5). The real time data in frequency domain were measured using a tri-axial accelerometer (sensitivity: x-axis: 100.3 mV/g, y-axis: 100.7 mV/g, z-axis: 101.4 mV/g) mounted on the top of the gearbox (see Fig. 6) and the data acquisition hardware. Measurements were taken for the rotational speed of 10 Hz to 30 Hz at the interval of 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002003_we.1721-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002003_we.1721-Figure2-1.png",
        "caption": "Figure 2. Sample of an EM, out of the work by Holierhoek et al.52",
        "texts": [
            " However, since the choice of the EM implicitly determines the MM and CM, it can, in practice, be the case that the EM is chosen on the basis of the capabilities of available software. In previous years, the gearbox and the DTS are modeled as one single torsional spring with a fixed gear ratio. But there is a trend to increase the number of degrees of freedom (DOFs) to better understand the dynamic behavior of gearboxes. Most of the authors dealing with WT drive train dynamics emphasize the need for more comprehensive models to cover as many relevant phenomena as possible.50 An example of an EM is shown in the succeeding text (Figure 2). The following listing is based on the indirect drive concept: For basic investigations, the model of a DTS can consist of the two big inertias, the rotor and the generator, connected by a torsional flexibility and damping, allowed only to rotate. This type of model gives a first impression about drive train dynamics and can be used for a simplified representation of a DTS for analysis with focus on other parts of the turbine, e.g., tower or rotor design analysis. In these models, the complexity is strongly depended on the formulation of the input parameters for the drive train, the stochastic excitation from the wind and the generator load"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003759_j.ymssp.2019.02.044-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003759_j.ymssp.2019.02.044-Figure5-1.png",
        "caption": "Fig. 5. Planet-ring link and line of action.",
        "texts": [],
        "surrounding_texts": [
            "The developed expressions of Mr ; \u20acXrg ; Tr1;Kr ;Xrg ; Tr2;Xng ; Fr and Fr ind can be found in B.\n3.3. Equation of motion of the carrier\nUc;Vc and Wc are the local displacements of the carrier measured with respect to a frame tied to the carrier. Ucg ;Vcg and Wcg are the global displacements of the carrier measured with respect to a frame tied to the stationary ring\ngear. Fig. 6 displays both local and global displacements. As shown in Fig. 6, global displacements of the carrier can be expressed as functions of local displacements.\nUcg \u00bc Uc cos hc Vc sin hc Vcg \u00bc Uc sin hc \u00fe Vc cos hc rc Wcg \u00bc Wc 8>< >: \u00f023\u00de\nHence, local displacements of the carrier from Eq. (23) can be expressed as:",
            "Uc \u00bc Ucg cos hc \u00fe Vcg sin hc \u00fe rc sin hc Vc \u00bc Ucg sin hc \u00fe Vcg cos hc \u00fe rc cos hc Wc \u00bc Wcg 8>< >: \u00f024\u00de\nThe radial and tangential deflections of the planet bearings (Fig. 7) are expressed by Saada et al. [1] as:\ndnrd \u00bc Vc sinun \u00fe Uc cosun Un \u00f025\u00de\ndntg \u00bc Vc cosun Uc sinun \u00feWn \u00f026\u00de\nSo, with respect to the new frame and taking into account Eqs. (4), (24), (25) and (26), the radial and tangential deflections\nof the planet bearings can be expressed as:\nd g nrd \u00bc Ucg cos un \u00fe hc\u00f0 \u00de \u00fe Vcg sin un \u00fe hc\u00f0 \u00de Ung cos hc Vng sin hc \u00fe rbr sin un \u00fe hc\u00f0 \u00de sin hc\u00f0 \u00de \u00fe rc \u00f027\u00de\nd g ntg \u00bc Ucg cos un \u00fe hc\u00f0 \u00de \u00fe Vcg sin un \u00fe hc\u00f0 \u00de Ung cos hc Vng sin hc \u00fe rbr sin un \u00fe hc\u00f0 \u00de sin hc\u00f0 \u00de \u00f028\u00de\nThe position of the carrier is given by\nRc !\u00bc Ucg i !\u00fe Vcg j ! \u00f029\u00de\nThe velocity of the carrier is given by\n_Rc ! \u00bc _Ucg i !\u00fe _Vcg j ! \u00f030\u00de\nThe potential energy of the carrier is\nEpc \u00bc 1 2 kc U2 cg \u00fe V2 cg \u00fe 1 2 kcwW 2 cg \u00fe 1 2 XN 1 kpn d g nrg 2 \u00fe d g ntg 2\n\u00f031\u00de\nThe kinetic energy of the carrier is\nEcc \u00bc 1 2 mc _U2 cg \u00fe _V2 cg \u00fe 1 2 Ic r2c _W2 cg \u00f032\u00de\nBy applying LAGRANGE formulation given by Eqs. (33), (34) is concluded\n@Epc @Ucg \u00fe d dt @Ecc @ _Ucg\n! @Ecc\n@Ucg \u00bc 0\n@Epc @Vcg \u00fe d dt @Ecc @ _Vcg\n! @Ecc\n@Vcg \u00bc 0\n@Epc @Wcg \u00fe d dt @Ecc @ _Wcg\n! @Ecc\n@Wcg \u00bc @Tc @Wcg\n8>>>>>>< >>>>>:\n\u00f033\u00de\nMc \u20acXcg \u00fe XN 1 kpnTc1 \u00fe Kc\n! Xcg \u00fe\nXN 1 kpnTc2Xng \u00bc Fc \u00fe Fc ind \u00f034\u00de\nThe developed expressions of Mc; \u20acXcg ; Tc1;Kc;Xcg ; Tc2;Xng ; Fc and Fc ind can be found in C.\n3.4. Equation of motion of one planet\nIt was shown previously that local displacements (Ui 8i 2 sun; planet; carrier; ring) are expressed as global displacements (Uig) with respect to the fixed frame tied to the carrier in Eqs. (3), (4), (14) and (24). The displacements along different lines of action (d g\nsn; d g nr) and the radial and tangential deflections of planet bearing (d g nrd; d g ntg) are also developed as global displace-\nments in Eqs. (6), (16), (27) and (28) (Fig. 8). The position of the planet is given by\nRn ! \u00bc Ung i !\u00fe Vng j ! \u00f035\u00de\nThe velocity of the planet is given by\n_Rn ! \u00bc _Ung i !\u00fe _Vng j ! \u00f036\u00de\nThe potential energy of the planet is"
        ]
    },
    {
        "image_filename": "designv10_5_0000600_j.mechmachtheory.2013.10.003-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000600_j.mechmachtheory.2013.10.003-Figure1-1.png",
        "caption": "Fig. 1. Basic parameters of the DCTP.",
        "texts": [
            " To ensure the uniqueness, geometry invariability, and continuity of the expression for the tooth profile, an exact representation for the DCTP is imperative for solving the CTP. In this section, a representation of the DCTP is presented based on the arc length coordinate. Here, the tooth profile is assumed to be composed of the common tangent and a double-circular-arc to achieve a larger engaged region and cause more teeth to mesh with one another. 3.1. Local coordinate system and the definition of basic parameters of the DCTP The 2D section of the DCTP of the FS is shown in Fig. 1 and is composed of three parts: arc HG, FE, and straight line GF. To describe the parameters conveniently, a local coordinate system Sf(Of; xf, yf) is defined as follows: xf is the symmetric line of the tooth, whereas yf is the tangent of the FS pitch circle. According to the symmetry of the profile, the DCTP on one side can be defined by the eight parameters listed in Table 1, which involve four parameters (d, s\u204e, \u03b6, and hl\u204e) for straight line GF, two arc parameters (\u03c1a\u204e and ha\u204e) for the tooth face, and two arc parameters (\u03c1f\u204e and hf\u204e) for the tooth flank"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001394_tec.2016.2597059-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001394_tec.2016.2597059-Figure4-1.png",
        "caption": "Fig. 4. a) Schematic view of the proposed Litz wire structure with a direct liquid cooling channel and b) dimensions of the conventional Litz wire with the same copper space factor assuming that the current density is half of that in the proposed winding.",
        "texts": [
            " The windings were produced manually for the proof-ofconcept machine. Common piping tools are utilized e.g. for cutting the pipes and end connection are done by cutting ring tube couplings. During the assembling it was notified that sharp bends are not acceptable in the case of Litz wires with tubes because the insulations on the surface area will shift when the wires are bent. Therefore, this new winding procedure should be automated for large scale manufacturing. A schematic view of the applied wire with direct liquid cooling channel is shown in Fig. 4 (a) and Litz wire parameters are presented in table V. The wire dimensions lead to the copper space factor kCu 0.77 of the Litz wire. TABLE V WIRE PARAMETERS Parameter Value Litz wire height, wh 8 mm Litz wire width, ww 7.6 mm Litz wire parallel strands 188 Litz strand diameter, dw 0.5 mm Cooling tube inner diameter, di 3 mm Cooling tube outer diameter, do 4 mm The area of a wire wh\u00d7ww 60.8 mm The area of wire (without cooling channel) wh\u00d7ww- \u03c0\u00d7 (do/2)2 48.2 mm The area of 200 Litz strands 200\u00d7\u03c0\u00d7 (dw/2)2 36",
            "77 Despite the fact that a certain area of the wire is occupied by the cooling channel (which leads to a smaller space for the copper in the winding), the use of a direct liquid cooling channel inside of the wire still allows to significantly reduce the total wire area compared with more conventional cooling management systems. If we assume that the proposed cooling management is capable of providing 200\u2013300 % of the current density of traditional cooling approaches, it would lead to a situation that in order to supply the nominal current of the proposed winding, the area of traditional winding should be 48.2 mm2\u00d7(2~3) = 100~150 mm2, Fig. 4 (b). However, the total area of the proposed winding with the cooling channel is only 60.8 mm2. Each winding pair on each of the double stators share a phase with the nearest opposing pair of the second stator. All coolant inlets and outlets are connected to the primary cooling loop in parallel. Fig. 5 illustrates the winding connections. The electrical parameters of the machine were calculated by 2D and 3D finite element analysis. The 2D model of the axialflux PMSM included one computational plane with its average radius [19]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003800_s40430-020-2208-7-Figure10-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003800_s40430-020-2208-7-Figure10-1.png",
        "caption": "Fig. 10 Comprehensive transmission error curve",
        "texts": [
            " The rotation angle of the cycloidal gear and pin gear is substituted in Eq.\u00a0(25), and a series of transmission error values are obtained. 4. According to the transmission error data, the transmission error curve can be drawn with the pin gear rotation angle 1 as the abscissa axis and the transmission error ( 1) as the longitudinal axis. For the theoretical design profile, there is no pitch error, so the first transmission error curve can be translated by a pitch angle q = 2 \u2215zp to obtain a comprehensive transmission error curve, as shown in Fig.\u00a010. In Fig.\u00a010, intersection points A and B represent meshing start point and meshing end point, respectively. The transmission error between points A and B reflects the actual meshing interval of cycloidal-pin gear. The actual meshing area of the cycloidal gear can be obtained by substituting the rotation angle of the cycloidal gear corresponding to the transmission error curve in Eq.\u00a0(6). In order to verify the correctness of the theory and method in this paper, according to the manufacturing error of cycloidal gear measured, the tooth profile expression of cycloidal gear including manufacturing error is reconstructed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000648_978-3-642-17531-2-Figure8.8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000648_978-3-642-17531-2-Figure8.8-1.png",
        "caption": "Fig. 8.8. LORENTZ force (electrodynamic force) ed F on a moving charge in a magnetic field",
        "texts": [
            " This also gives rise to the alternate term for electromagnetic (EM) transducers: reluctance transducers. Electrodynamic force law: the LORENTZ force In addition to the natural laws expressed by MAXWELL\u2019s equations, the LORENTZ force law (or electrodynamic force law) for a moving charge in a magnetic field is of great importance to electromagnetically-acting transducers (Thomas et al. 2009), (Hughes 2006). Using the LORENTZ force law5 L F q v B , (8.22) it follows that the differential force on a current element (see Fig. 8.8) is ed dq v i ds dF dq v B i ds B . 5 The second component of the LORENTZ force\u2014the force F qE applied by an electric field on an electric charge\u2014is not important here, and is thus not further considered. 8.3 Generic EM Transducer: Variable Reluctance 507 The total force on a current-carrying one-dimensional conductor of length l (with arbitrary curvature and spatially varying B ) then obeys the general electrodynamic force law ed l F i ds B . (8.23) For the special case of a rectilinear conductor of length l in a homogeneous magnetic field, ed F l i B , (8"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001564_j.triboint.2013.06.017-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001564_j.triboint.2013.06.017-Figure3-1.png",
        "caption": "Fig. 3. Loads acting on a ball.",
        "texts": [
            " The first load P1 is due to the interference between the inner ring and the shaft. The centrifugal-induced displacement on the inner ring decreases P1 when the spindle speed is increased. The second load P2 is due to the axial preload. The third load P3 is due to the centrifugal forces of the rotating ball, which continuously increases with the bearing speed. The summed bearing load during operation is the summation of P1, P2 and P3 if the thermal effect is excluded. Fig. 2(b) shows the equilibrium of the bearing rings preload. Fig. 3 shows the entire system of forces and moments acting on a ball. The centrifugal force P3 is decomposed into two components: FN in the normal direction and FP in the direction tangential to the points of contact with the raceways. This makes it possible to unequivocally describe the influence of the centrifugal forces. In this way, a simple relationship between the pressures Qo and Qi has been obtained, counterbalancing the centrifugal force acting in directions defined by radii OA and OB. Qi \u00bc P3 sin \u03b1o sin \u00f0\u03b1i \u03b1o\u00de \u00f01\u00de Qo \u00bc P3 sin \u03b1i sin \u00f0\u03b1i \u03b1o\u00de \u00f02\u00de To determine the internal load distribution in ball bearings, consider Fig",
            " 5 that cos \u03b1oj \u00bc X2j \u00f0f o 0:5\u00deD\u00fe\u03b4oj sin \u03b1oj \u00bc X1j \u00f0f o 0:5\u00deD\u00fe\u03b4oj cos \u03b1ij \u00bc A2j X2j \u00f0f i 0:5\u00deD\u00fe\u03b4ij sin \u03b1ij \u00bc A1j X1j \u00f0f i 0:5\u00deD\u00fe\u03b4ij 8>>>>< >>>>: \u00f05\u00de and X2 1j \u00fe X2 2j \u00bc \u00bd\u00f0f o 0:5\u00deD\u00fe \u03b4oj 2 \u00f06\u00de \u00f0A1j X1j\u00de2 \u00fe \u00f0A2j X2j\u00de2 \u00bc \u00bd\u00f0f i 0:5\u00deD\u00fe \u03b4ij 2 \u00f07\u00de Consider a plane passing through the bearing axis with the centre of a ball located at any azimuth. If \u201couter raceway control\u201d is approximated at a given ball location, the ball gyroscopic moment is resisted entirely by friction force at the ball-outer raceway contacts and, in Fig. 3, Tij \u00bc 0 andToj \u00bc 2Mgj=D. The normal ball loads in accordance with normal contact deformations are as follows: Qo\u00f0i\u00de \u00bc Ko\u00f0i\u00de\u03b4 1:5 o\u00f0i\u00de \u00f08\u00de For steel balls in this paper, the centrifugal force acting on a ball is calculated as follows [22]: P3\u00bc 2:26 10 11D3n2 mdm \u00f09\u00de j 1 0 j j md 1 (a) angular position of the rolling element (radial) (b). Based on Fig. 3, considering the equilibrium of forces in the horizontal and vertical directions Toj cos \u03b1oj \u00fe Qoj sin \u03b1oj Tij cos \u03b1ij Qij sin \u03b1ij \u00bc 0 \u00f010\u00de P3\u00fe Toj sin \u03b1oj \u00fe Qij cos \u03b1ij Qoj cos \u03b1oj Tij sin \u03b1ij \u00bc 0 \u00f011\u00de The gyroscopic moment at each ball is defined as follows [22]: Mgj \u00bc J\u00f0wR=w\u00dej\u00f0wm=w\u00dejw2 sin \u03b2 \u00f012\u00de where \u03c9m is the orbital speed of the ball, \u03c9R is the rotational speed of the bearing element and J is the mass moment of inertia. wR=w; wm=w and \u03b2 are given as follows [22,24]: tan \u03b2\u00bc sin \u03b1o\u00f0 cos \u03b1o \u00fe D=dm\u00de \u00f013\u00de \u03c9R \u03c9 \u00bc 1=\u00f0D=dm\u00de cos \u03b2 \u00f0 cos \u03b1o \u00fe tan \u03b2 sin \u03b1o=1\u00fe \u00f0D=dm\u00de cos\u03b1o\u00de \u00fe \u00f0 cos \u03b1i \u00fe tan \u03b2 sin \u03b1i=1 \u00f0D=dm\u00de cos \u03b1i\u00de \u00f014\u00de \u03c9m=\u03c9\u00bc \u00bd1 \u00f0D=dm\u00de cos \u03b1i =\u00bd1\u00fe cos \u00f0\u03b1i \u03b1o\u00de \u00f015\u00de To find the values of da, the only remaining requirement is to establish the condition of equilibrium applying to the entire bearing P2\u00bc \u2211 Z j \u00bc 1 \u00f0Toj cos \u03b1oj \u00fe Qoj sin \u03b1oj\u00de \u00f016\u00de where P2 and Z represent the axial external load and ball number, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001940_j.jsv.2018.02.033-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001940_j.jsv.2018.02.033-Figure4-1.png",
        "caption": "Fig. 4. Structural diagram of the electromechanical system.",
        "texts": [
            " The nonlinearity permeability of the steel, mFe, is obtained using a function of the magnetic field intensity H in accordance with the equations as follows [17]. mFe\u00f0H\u00de \u00bc 8>< >: K2 ln\u00f0K1jHj \u00fe 1\u00de jHj Hs0 K1K2 H \u00bc 0 (7) where, H \u00bc DM=l and DM is the magnetic potential across the iron section and l is the length of the iron section. In this motor-gear system, the external load is applied on the carrier of the planetary gear system, and the power is transmitted from the motor to the sun gear of the planetary gear system through the shaft as shown in Fig. 4. The shaft is treated as a particle without mass and only torsional stiffness of the shaft is considered. Meanwhile, the bearings of the shaft or motor rotor are not considered in this study. All the gears are spur gear without error and the planet gears are evenly distributed around the sun gear, and there is no shaft misalignment between the sun gear and the shaft or the motor rotor. Since the rotational speed of the electric motor is varying due to the internal and external excitations of the entire system, the transient rotational speed of the gear system has to be considered in this electromechanical dynamic simulation of themotor- gear system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001286_tec.2017.2651034-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001286_tec.2017.2651034-Figure9-1.png",
        "caption": "Fig. 9. Stator structure and acoustic field point.",
        "texts": [
            " Vibration Prediction and Validation An accurate structure model is required to predict the vibration and thus the equivalent modeling of stator core and winding should be considered, which is available by considering the anisotropy of material parameters. The detailed modeling process of stator assembly is shown in [20] and the relative errors between calculated modal frequencies and those from test are all below 5%. It is noted that the motor studied in this paper has a relatively short end winding. Hence, in the equivalent stator model, the end winding is neglected, as shown in Fig. 9. This simplication, however, is probably not appropriate for distributed winding machines which have a long end winding. Therefore, the equivalent model of end winding in distributed winding machines should be considered. Fig. 6 shows the modal shapes and frequencies when the motor is mounted in the test bed. The winding is hided to show the shapes more clearly. After the force is transferred from electromagnetic mesh to structural mesh, MSM is employed to calculate the vibration. The principle of MSM is described in [21]",
            " Thus, the sound pressure of a certain acoustic field point is expressed as        T ns( )p f f v f ATV (3) Here, ATV(f) is the acoustic transfer vector which reflects the linear relationship between surface vibration and noise, vns(f) is the normal velocity of stator surface. In addition, the frequency response function (FRF) between nodal force and vibration can be obtained by modal information. Thus, noise transfer function (NTF) between nodal force and sound pressure at a certain field point is acquired by combining FRF and ATV(f). Fig. 10 shows the average of NTFs between all of excitation points and acoustic field point shown Fig. 9. The modal analysis is conducted in ANSYS and ATV(f) is obtained via BEM in LMS Virtual.lab. The dominating peaks of NTF can be explained by the stator modes which are listed in Fig. 6. It is found the peak frequencies coincide with stator modal frequencies. But the amplitude of the peaks are also relevant with sound radiation efficiency, which depends on geometry of the vibrating surfaces, acoustic treatment of the surfaces, field point location, frequency and physical properties of the acoustic medium"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001497_sia.5981-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001497_sia.5981-Figure1-1.png",
        "caption": "Figure 1. Schematic representation of samples building.",
        "texts": [
            " The beam intensity was adjusted to ensure that the new powder layer was melted and lightly penetrated the previous one, to accomplish a good connection between layers (wetting the underneath layer) at the same time.[18] The parts manufactured with DMLS process have high residual thermal stresses. In order to avoid the bending, stress relieving for 2 h at 300 \u00b0C was carried out before removing the specimens from the building platform. The specimens built with the circular face parallel to the building platform are named XY; the others \u2013 with the circular face perpendicular to the xy-plane \u2013 are called XZ (Fig. 1). The tests were carried out on both as-processed surface and after polishing with emery paper and 0.1\u03bcm alumina powder. Before tests, all the specimens were ultrasonically degreased in acetone. The polished specimens were passivated in air for 24 h before electrochemical tests. Figure 2 shows metallographic sections of XY and XZ specimens. The macrostructure reveals the tracks of laser scans during the specimens manufacturing. Microstructures achieve unique, directional growth features far from equilibrium, because the melting occurs in layer of alloyed metal powders forming small melt pools, which rapidly solidify"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003195_j.ijleo.2019.163068-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003195_j.ijleo.2019.163068-Figure1-1.png",
        "caption": "Fig. 1. Schematic models with 4 layers for (a) solid-powder geometry and (b) solid-support geometry.",
        "texts": [
            " In this study, a 3D transient heat model was developed to investigate the heat flow on three different underlying surfaces. The model solves the equations of conservation of mass, momentum and energy to measure the temperature fields, melt pool geometrical features, thermal variables and to evaluate melt pool shape change with laser position. The model also incorporates the temperature dependent mechanical and physical properties of powder bed, support structure and solid substrate. The moving heat source in SLM process was simulated on two different models using ANSYS package as shown in Fig. 1. A simplified cubical geometry (1.5\u00d70.3\u00d7 0.35 mm3) was chosen with a symmetry boundary on the right to reduce computational time. The Gaussian nature of the heat source used in SLM varies exponentially in a space from the center of the applied source and it is described as [11]. = + q P R S exp x x y y Vt R exp z z S 2 2(( ( ) ) | | 2 0 2 0 2 2 0 (1) Where, x, y and z are the space coordinates with scanning direction along positive y-axis and building direction along negative zaxis. V is the scanning speed with the onset at = = =x y \u00b5m z0, 150 , and 00 0 0 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002751_j.jmapro.2019.02.022-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002751_j.jmapro.2019.02.022-Figure5-1.png",
        "caption": "Fig. 5. Transient melt hydrodynamics during laser heating, Temperature field (K) (colour contour plot), velocity field (arrow plots). P= 70W, tp= 0.1ms (Laser stopped at 0.1 ms).",
        "texts": [
            " It is important to note that the maximum velocity occurs near the top edge of the melt pool owing to dominating thermo-capillary flow. Paul et al. [27], also reported the melt velocity in the range of m/s, in the case of macro melt pool convection under thermo-capillary stresses. Further, such high velocities (U0.01 ms= 7.62m/s, U0.02 ms= 10m/s) may arise due to shallow melt pools under the influence of high shear stress owing to large thermal gradients. However, with Lcharcterstic\u02dc20 \u03bcm, Reynolds number in these cases does not exceed the threshold of the laminar regime. Fig. 5, shows the melt hydrodynamics for the period of 0.03ms to 0.1 ms of laser heating. It can be observed that with the progression of laser heating, recoil pressure becomes prominent resulting in melt deformation up to 14 \u03bcm at the center. Further, under the influence of recoil pressure, the melted material gets displaced from the center towards the edge of the melt pool. It is important to note that melt displacement due to recoil pressure leads to the formation of a rim like structure near the edge of the melt pool"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003379_j.commatsci.2020.109788-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003379_j.commatsci.2020.109788-Figure5-1.png",
        "caption": "Fig. 5. (a) Schematic of the DED-AM process; (b) finite element model of the DED sample.",
        "texts": [
            " Here, Tinitial = Ta, the heat convection boundary condition = \u2212 \u2212\u2202 \u2202k T h T T( ) ( )T n a , and h = 100 W/(m2\u00b7K) is the heat transfer coefficient [29]. The influence of thermal radiation is neglected in this model. Powder particles from one nozzle are selected to study the laser\u2013particle interaction, as depicted in Fig. 4. The angle between the powder tube and the vertical direction is 32\u00b0, D = 21 mm is the distance between two non-adjacent powder tubes, and d = 3 mm is the diameter of a single powder tube according to the experimental machine. To obtain the temperature distribution, the FEM for thermal transfer is established. Fig. 5(a) shows the schematic of the DED-AM process. The laser scanning direction is along the X-axis. Fig. 5(b) illustrates the FEM of the DED sample, which consists of two regions: the substrate and the deposition layers. Here, 25,992 nodes and 21,420 elements are used to mesh the substrate and the dimensions are 80 \u00d7 15 \u00d7 20 mm while 72,611 nodes and 64,000 elements are used to mesh the deposition region. The dimensions of the deposition region are 50 \u00d7 3 \u00d7 6 mm with 20 layers. The element type used is a linear fullintegration eight-node brick element for both the substrate and the deposition layers"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003691_j.jallcom.2020.153840-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003691_j.jallcom.2020.153840-Figure1-1.png",
        "caption": "Fig. 1. Exemplary samples after deposition with the cutting pattern in order to obtain cross-sections of clads for metallographic observations and hardness measurements (a), a calibration curve of powder feeder (b), schematic representation of microhardness measurement strategy (c).",
        "texts": [
            " To define the powder mass flow value, the calibration of the device was performed with the use of a specially designed laboratory-scale balance-based instrument that provides high-precision \u201conline\u201d calibration of a powder feeder. The instrument estimated the amount of the powder fed (in grams) for 1 min at a specified wheel rotation speed. The mass powder flow dependence (g/min) on the rotational speed of the feeder wheel (rev/min) was very reproducible (in most cases, approximately 0.01e0.02 g/min precision was obtained) and approximately linear over the investigated range. The calibration curve with error bars is presented in Fig. 1b. The uncertainty of the calibration was estimated based on the standard deviation of repeated measurements for each calibration point, as well as the estimated error of the laboratory balance used for calibration. Each substrate plate before and after cladding was separately weighed (3 times) on a laboratory balance with a precision of 0.0001 g. The obtained values were averaged, and themass of the materials deposited on the sample was calculated by subtracting the initial mass of the plate from the final mass of the plate coated with the deposited material",
            " The deposition efficiency was calculated by dividing the mass of the powder deposited on the substrate by the mass of the powder that was blown from the nozzles for the time in which the laser was on during the deposition process. The uncertainty of the efficiency was calculated as sum of the relative uncertainties of the mass measurement and mass of the powder delivered. The samples used for metallographic observations were cut from the as-deposited plates using a liquid-cooled precision cutting machine (Struers) to form small wedge-shaped plates (see Fig. 1a) without overheating them to prevent changes in the microstructure and properties. The optical microscopy analysis was performed using a Nikon ECLYPSE NA200 microscope with the NIS-Elements software. The geometric properties of the clads were measured using a Galileo AV200 microscopewith the QC300 indicator unit. The geometric analysis was conducted by measuring the dimensions of the metallographic sample cross-sections (according to the scheme shown in Fig. 1c. Four clads were measured for every condition, and the obtained values were averaged for every parameter set. The microhardness analysis (10 measurements per sample) was performed on the top surface of the clads. Each indentation was made approximately 50 mm below the surface of the clad. This strategy is shown in Fig. 1c and was used to ensure that the data were as reliable and as comparable as possible, since the hardness may differ over the clad volume due to different heat dissipation conditions and different cooling rates. The laser spot sizes were measured by \u201cshooting\u201d the laser beam onto black photographic paper, and the reported values were the average based on 10 measurements. The effective diameter of the remelted metal was not the same and was highly dependent on the parameters, such as the scanning speed and the powder feed rate"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002139_b978-0-08-100433-3.00004-x-Figure4.14-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002139_b978-0-08-100433-3.00004-x-Figure4.14-1.png",
        "caption": "Figure 4.14 Average surface roughness, Ra_ave, and facet Ra at min (Ra_ave) for functional housing: all surfaces (upper), relevant surfaces only (lower). Da \u00bc 2 degree.",
        "texts": [
            " However, it is technically necessary that the surface finish of the mating features and mounting holes be minimised to ensure robust technical function. For this scenario, the average surface roughness, Ra_ave, is not an appropriate surface roughness objective because the surface roughness of features other than the mating features is inconsequential to component function. For example, minimising average surface roughness of the entire component results in a minima of Ra_ave at a1 \u00bc a2 \u00bc 0 degrees (Fig. 4.14). This minima repeats with a period of 180 degrees and results in low Ra facets on the large planar surfaces and mounting holes (however with large Ra facets on cylindrical mounting holes). However, when only relevant surfaces are considered, the global minima for Ra_r occurs at a1 \u00bc 90 degrees and a2 \u00bc 0 degree (ie, the minima orientation for Ra_ave does not exist), and low Ra facets occur on the cylindrical mating features (Fig. 4.12, lower). Note that for the orientation that is optimal for minimising average surface roughness over the entire component (a1 \u00bc a2 \u00bc 0 degree; Fig. 4.14, top), the Ra_ave of relevant facets only is not optimal (Fig. 4.11, bottom). This case study demonstrates that the use of Ra_ave as the surface roughness objective can result in erroneous design guidance when the component consists of surfaces that are irrelevant to component function. To provide greater insight into the optimal component orientation for AM, this work contributes various outcomes to the available literature: \u2022 To ensure robust design data, the surface roughness versus build inclination of SLMmanufactured Ti64 was assessed experimentally and reported in detail, including measured roughness data and high-resolution macroscopy for upper and lower surfaces"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000231_j.mechmachtheory.2010.01.003-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000231_j.mechmachtheory.2010.01.003-Figure4-1.png",
        "caption": "Fig. 4. Examples of wear distributions on tooth flanks for spur and helical unmodified gears after 2 million cycles on the pinion. (a) Spur gear. (b) Helical gear.",
        "texts": [
            " The equivalent normal deviations with respect to perfect involute flanks are modified accordingly and the solution process is repeated over the next n cycle sequence. The estimate of a realistic n is crucial and it must verified that, for a given total number of load cycles N, the final wear pattern is independent of n as illustrated in Fig. 3. High-precision wide-faced spur and helical gears (face width larger than 10 modules roughly) are considered and the corresponding data are listed in Tables 3 and 4 (the wear coefficient K0 has been taken from [4], Figs. 24 and 26). Focusing on the first sequence of n = 2106 load cycles on the pinion, Fig. 4 shows the wear distribution obtained on the pinion and the gear flanks. In any transversal section, the usual wear distribution on the profile is observed; wear is maximal on the pinion especially at engagement whereas the areas near the pitch point are less affected. These results agree well with the experimental evidence of [4,20\u201322] as long as mild abrasive wear is prevalent. Different evolutions and wear patterns have been reported by Onishchenko and co-worker [7,12] but for larger wear cycle numbers possibly corresponding to severe wear associated with possible surface failures such as pitting and plastic deformations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003887_j.etran.2020.100080-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003887_j.etran.2020.100080-Figure7-1.png",
        "caption": "Fig. 7. Asymmetrical rotor configura",
        "texts": [
            " But in the laboratory experiments, the prototype machine was only tested to about 130 Nm. As a variant of reluctance machines, PMASynRMs inherit the drawback of large torque ripple. N. Bianchi optimized the pitch and angle of flux barriers to reduce the torque ripplewhile keeping the same average torque [62], and H. Cai et al. minimized torque ripple by 35% by adjusting the width of flux barrier opening [61]. Asymmetrical rotor configurations were proposed in Refs. [62e64] to further reduce the torque ripple and augment overall torque, as shown in Fig. 7. However, the harmonic content was dramatically increased for both the flux distribution and back EMF, which would have negative effects on the machine loss. Ferrite PM has higher temperature stability than rare-earth and can operate at around 250 C. However, the residual flux density is much lower compared with rare-earth, which makes ferrite PMs quite vulnerable to demagnetization when facing directly to the armature reactive field. Some recent papers have put in evidence that the electric loading must be limited, and the flux barriers must be shaped properly to avoid demagnetization"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003170_msec2018-6477-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003170_msec2018-6477-Figure1-1.png",
        "caption": "Figure 1: The schematic diagram of the laser-based powder bed fusion (LPBF) process.",
        "texts": [
            " Subsequently, these features were linked to the process parameters using machine learning approaches. Through these image-based features, process conditions under which the parts were built was identified with the statistical fidelity over 80% (F-score). Keywords: Laser Powder Bed Fusion, Porosity, In-process Monitoring, Image Analysis, Spectral Graph Theory, Multifractal Analysis. Powder bed fusion (PBF) refers to a family of Additive Manufacturing (AM) processes in which thermal energy selectively fuses regions of a powder bed [1]. Figure 1 shows the schematic of the PBF process that embodies a laser power source for melting the material, accordingly, the convention is to refer to the process as Laser Powder Bed Fusion (LPBF). A galvanic mirror scans the laser across the powder bed. The laser is focused on the bed with a spot size on the order of 50 \u00b5m \u2012 100 \u00b5m in diameter, the laser power is typically maintained in the range of 200 W to 400 W, and the linear scan speed of the laser is varied in the 200 mm/s to 2000 mm/s range [2]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002136_s12206-016-0611-x-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002136_s12206-016-0611-x-Figure6-1.png",
        "caption": "Fig. 6. Contact stiffness ck and oil film stiffness ok .",
        "texts": [
            " 5 also shows the initial condition of 0H only affects the vibration in the first several time periods and the response of the system gradually reaches the same steady state value ( )0 0H t H\u00ae\u00a5 = = 0.4923 . In this study, the initial perturbation of relative real mutual approach was fixed as 78.7326 10 m-\u00b4 i.e. ( )0 0 8.7326hD = \u00b4 710 m- . To evaluate the contribution of the oil film stiffness on the total stiffness, the Yang-Sun contact stiffness [22], which is calculated by \u201clinearizing\u201d the Hertzian contact theory, is also calculated. The contact stiffness is caused by the deformation of the elastic bodies. Fig. 6 clearly illustrates the definition of contact stiffness and oil film stiffness. The Yang-Sun linearized Hertzian contact stiffness is expressed as ( )24 1ck E B vp \u00a2= - , (21) where E\u00a2 is the equivalent elasticity modulus, v is Poisson\u2019s ratio, B is the width of the tooth. In terms of the contact stiffness and the oil film stiffness, the total stiffness during contact can be expressed as 1.0 1.01.0total o c k k k \u00e6 \u00f6 = +\u00e7 \u00f7 \u00e8 \u00f8 . (22) Fig. 7 shows the mutual approach at the steady state within the load region, 5 5 0 5 10 ,90 10 ) /f N m\u00ce \u00b4 \u00b4\uff08 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002371_humanoids.2015.7363442-Figure10-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002371_humanoids.2015.7363442-Figure10-1.png",
        "caption": "Fig. 10: Transforms and coordinate frames involved in computing the distance d\u0394. The current end-effector frame is C1 and the hand pose for grasping handle is C\u2032 1.",
        "texts": [
            " These quadratic cost terms represent penalizations of the weighted sum on the joint displacements between the waypoints, posture deviation from a nominal posture in joint space and posture error in Cartesian space. The first term can limit the movement of the robot and smooth the trajectory. The second term is used to satisfy desired joint variables when all the constraints have been met. Similarly, the third term is used to push links to specific positions and orientations. The posture error in Cartesian space can be obtained by calculating the distance d\u0394 from a given configuration to a task space region introduced in [24]. For example, in Fig. 10, the end-effector frame C1 defined in our Atlas model is on the left wrist. We generate an end-effector frame C2 for representing the pose of the object held by the hand by setting an offset transform T 1 2 . The desired grasp location C3 is near the door handle. We expect to generate a trajectory that can lead the robot end-effector to reach the desired grasping location. Thus, the distance d\u0394 means the displacement between C2 and C3, which can be computed by converting the transform T 3 2 (5) into a 6\u00d71 displacement vector from the origin of the coordinate of C3 by (5)",
            " For a push door, two trajectories need to be planned, which are approaching the door handle and turning the door handle. For a pull door, the robot also has to pull the door back and block the door from closing with the other hand. The following list describes the specific constraints for each step required to open the door. 1) Approaching Handle: A Cartesian posture constraint is added on the final step of the trajectory for approaching the door handle. The parameters of the constraint are the desired position and orientation for the robot end effector to grasp the handle (see Fig. 10), which are computed based on the handle configuration detected by the robot vision system. 2) Turning Handle: During the handle turning motion, the handle hinge does not translate. There is only the rotation movement of the hinge. Two Cartesian posture constraints are applied to the trajectory. First is the final step constraint. The offset transform T 1 2 is from grasper frame C1 to the current handle hinge frame C2, while the target frame C3 is the current handle hinge frame rotating around 80o"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002521_tec.2016.2590988-Figure13-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002521_tec.2016.2590988-Figure13-1.png",
        "caption": "Fig. 13. Cross-sections of 6/10-pole E- and C-core PS-SFPM machines.",
        "texts": [
            " A1- C1- B1- A2- C2- B2- A3- C3- B3- A4- C4- B4 anti-clockwise. Consequently, pea in the 12/10-pole alternate poles wound PS-SFPM machine is half of that in the 12/14- pole SFPM machine with all poles wound, i.e. 4 and 8 respectively. With consideration of pPM=6 and nr=10, it is found that (11) can also be matched in the 12/10-pole PSSFPM machine with alternate poles wound. Figs. 13(a) and (b) illustrate the cross-sections of 6/10-pole E-core and C-core PS-SFPM machines, respectively. The 6/10-pole E-core PS-SFPM machine, Fig. 13(a), also has 6 alternate pole wound coils in the outer stator, similar to 12/10- pole alternate pole wound PS-SFPM machine Fig. 12, albeit with different winding layouts. However, the PM number in the E-core machine is half, i.e. 6. In 6/10-pole E-core and C- 0885-8969 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. core PS-SFPM machines, the outer air-gap armature reaction MMF is given in Fig. 14, which can be expanded to Fourier series as, { \ud835\udc39\ud835\udc34\ud835\udc35\ud835\udc36(\ud835\udf03, \ud835\udc61) = \u2211[ 3\ud835\udc49\ud835\udc34\ud835\udc35\ud835\udc36 2 \ud835\udc40\ud835\udc34\ud835\udc35\ud835\udc36\ud835\udc5e sin(\ud835\udf09)] \u221e \ud835\udc5e=1 \ud835\udc49\ud835\udc34\ud835\udc35\ud835\udc36 = 4\u221a2\ud835\udc41\ud835\udc50\ud835\udc3c\ud835\udc5f\ud835\udc5a\ud835\udc60 \ud835\udf0b \ud835\udf09 = { \u2212\ud835\udc5e\ud835\udf03 + \ud835\udc5b\ud835\udc5f\ud835\udefa\ud835\udc5f\ud835\udc61, \ud835\udc5e = 6\ud835\udc5f \u2212 5 \ud835\udc5e\ud835\udf03 + \ud835\udc5b\ud835\udc5f\ud835\udefa\ud835\udc5f\ud835\udc61, \ud835\udc5e = 6\ud835\udc5f \u2212 1 0, \ud835\udc5e = \ud835\udc52\ud835\udc59\ud835\udc60\ud835\udc52 (15) where MABCq for the E-core PS-SFPM machine is \ud835\udc40\ud835\udc34\ud835\udc35\ud835\udc36\ud835\udc5e = (1/\ud835\udc5e) [1 + 2 cos ( \ud835\udc5e\ud835\udf0b 6 )] sin(\ud835\udc5e\ud835\udf033) (16) and MABCq for the C-core PS-SFPM machine is It can be concluded from (12) with j=-1 and (15)-(17) that the 6/10-pole E- and C-core PS-SFPM machines shown in Fig. 13 have the same armature reaction MMF harmonic orders as the 12/13-pole PS-SFPM machine, Fig. 1(c), albeit with different magnitudes. Therefore, pea is the same in these three machines, i.e. 7. Again, (11) can be matched in the 6/10-pole E- and C-core PS-SFPM machines. The magnetic gearing characteristics of the 12/10-pole alternate poles wound, 6/10-pole E- and C-core PS-SFPM machines are synthesised in Table V, compared with the 12/10-pole all poles wound one. Due to the same nr=10 and pea=4 between 12/10-pole all and alternate poles wound PS- SFPM machines, magnetic gearing ratio Gr are the same as 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001711_s1560354713060166-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001711_s1560354713060166-Figure2-1.png",
        "caption": "Fig. 2. The bifurcation diagram and the bifurcation complex of the reduced system in the Chaplygin ball problem. Grey indicates the region of possible values of the integrals.",
        "texts": [
            " Therefore, for a classification of motions, we shall use a bifurcation diagram or a bifurcation complex [5] of the reduced system and, if necessary, point to differences between the foliations of the complete system and those of the reduced system. A more detailed description of foliation of the phase space of the complete system and its relation with the foliation of the reduced system can be found in [6]. A bifurcation diagram and a bifurcation complex for the reduced system on the plane of values of the first integrals 2DE (M,M) = DE C = h, (M,\u03b3)\u221a (M,M) = M\u03b3\u221a C = g (2.3) are presented in Fig. 2 [6]. We recall how a bifurcation complex is built: a given number of various leaves which is equal to the number of invariant manifolds (tori) corresponding to the same values of the first integrals in these regions is assigned to all regions on the bifurcation diagram which are bounded by bifurcation curves; then these leaves are glued together along the bifurcation curves corresponding to rearrangements of these manifolds (see [4] for details). As a rule, it is convenient to depict the complex in three-dimensional space (see Fig. 2), where one of the axes is auxiliary. The advantages of the bifurcation complex over the bifurcation diagram are that, firstly, it is easy to judge by the complex how many invariant tori and periodic solutions correspond to various values of the first integrals and, secondly, all stable periodic solutions lie only on those bifurcation curves which are on the edges of the complex. (There is some inconvenience in plotting appropriate three-dimensional figures.) REGULAR AND CHAOTIC DYNAMICS Vol. 18 No. 6 2013 The corresponding bifurcation curves are defined by \u03c3i : h = bi + b2 i 1 \u2212 bi g2, bi = DAi = D Ii + D , i = 1, 2, 3, \u03c34 : g = 1, \u03c35 : g = \u22121. As is well known, there are three cases depending on the values of the first integrals h and g. I. The generic position case \u03c9 \u2226 ei, M \u2226 \u03b3. For this there are possible values of integrals which do not lie on bifurcation curves, see Fig. 2a. In the phase space T SO(3) the trajectory is the orbit of one of the pair of two-dimensional invariant tori corresponding to these values of the first integrals. The evolution of the vectors M ,\u03b3 is defined by the reduced system M\u0307 = M \u00d7 \u03c9, \u03b3\u0307 = \u03b3 \u00d7 \u03c9. (2.4) The vectors \u03b1 and \u03b2 (using the arbitrariness in the choice of fixed axes) can be chosen in the form \u03b1 = M \u00d7 \u03b3\u221a C \u2212 M2 \u03b3 , \u03b2 = M \u2212 M\u03b3\u03b3\u221a C \u2212 M2 \u03b3 , (2.5) where F1 = M\u03b3 and F4 = C are the values of the corresponding first integrals (2.2). According to (1",
            "1) the following inequalities hold in this case: 0 < a1 < a2 < a3 < 1, 0 < \u03b1 < \u03ba < \u03bc, 1 < \u03bc. We parameterize the common level set of these integrals by two parameters E , \u0394 as follows: 2E = E , F4 = DE \u03bc + \u0394 \u03ba + \u0394 , \u2212\u03b1 < \u0394 < 1, then the equations of motion for the variables u, v can be written as u\u03072 = D\u22121E (\u03ba + \u0394)(\u03b1 cos2 u + cos2 v)2 (\u03ba + cos2 v)2(1 + \u03b1 cos2 u) \u03bc + cos2 v (\u03b1 cos2 u + \u0394), v\u03072 = D\u22121E (\u03ba + \u0394)(\u03b1 cos2 u + cos2 v)2 (\u03ba \u2212 \u03b1 cos2 u)2(\u03b1 + cos2 v) \u03bc \u2212 \u03b1 cos2 u (cos2 v \u2212 \u0394). (3.3) In the bifurcation diagram of Fig. 2a, the case at hand corresponds to a segment of the straight line g = 0, h = DE C \u2208 [b1, b2], and \u0394 \u2208 [\u2212\u03b1, 1]. As seen in the bifurcation complex (Fig. 2b), each value \u0394 = 0 corresponds to a pair of isolated invariant manifolds of the system. The values \u0394 \u2208 {\u2212\u03b1, 0, 1} correspond to critical periodic solutions of the system (\u0394 = \u2212\u03b1 corresponds to the rotation about the largest axis, \u0394 = 0 to that about the medium axis and \u0394 = 1 to that about the smallest axis). The remaining values of \u0394 can be divided into two intervals. 1) \u0394 \u2208 (\u2212\u03b1,0): in this case, v\u0307 is sign-definite (on one of two invariant tori v\u0307 > 0, on the other torus v\u0307 < 0), so it is convenient to choose the domain of definition of the spheroconical coordinates as (u, v) \u2208 ( \u2212\u03c0 2 , \u03c0 2 ) \u00d7 (\u2212\u03c0, \u03c0)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001885_j.matpr.2015.10.028-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001885_j.matpr.2015.10.028-Figure5-1.png",
        "caption": "Fig. 5. Geometry of the die for visioplastic analysis of the material flow, a) 3D-model, b) drawing, longitudinal cut, c) real manufactured die (according to [8])",
        "texts": [
            " The question is, whether the rough surfaces in the die inlet influence the material flow and if these areas can stay as manufactured or if they have to be mechanically refinished. In order to prove this, a visioplastic analysis was carried out. The idea was, to compare the material flow along two different die surfaces which are conventionally and additively manufactured. In order to have equal process boundary conditions, both trials were carried out in one and the same die. For this, a die with different surfaces was developed (Fig. 5 a)). To enable the ejecting of the discard out of the die, a die for the manufacturing of a full section profile with a diameter of \u00d8 20 mm (instead of a bridge die) was manufactured with an enlarged prechamber (Fig. 5 b)). The die was manufactured with an allowance of 0.3 mm of the hot working steel 1.2709, except for one half of the prechamber. Before ageing, all fitting surfaces and the die bearings were refinished by machining. Finally, the prechamber consists one half each of a machined and of a rough (as laser melted) surface. The macroscopic geometry is fully symmetric. Hence, possible local changes in the material flow can be attributed only to local differences in the surface roughness [8]. In order to facilitate the ejection of the aluminum, the prechamber in the die is tapered by 3\u00b0 in extrusion direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000127_nme.1620100603-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000127_nme.1620100603-Figure1-1.png",
        "caption": "Figure 1. Harmonically vibrating undamped uniform beam member 12 of length L, bending stiffness E l and mass per unit length m. Member displacement components n,, t , , m,, n,, t,, m2 and member force components N , , T,, M I , N , , T,, M,. These components are amplitudes which are to be multiplied by the common time factor sin ot or exp iot",
        "texts": [
            " Howson and Williams,22 Szidaro~szky\u2019~ and Djodjo2\u201c studied the combined effect on beam vibration of rotatory inertia, shear deformation and static axial load as did KolouSek Great care must here be exercised to find a consistent small-deflexion theory. It has been shown by Djodjo\u2019\u201c that the combined theories put forward in 7,23 are inconsistent. The combined (and consistent) theory reviewed and reformulated inz9 and applied inZ7v2\u2019 leads to the same results as those A different derivation is offered, see29 and below. BERNOULLI-EULER MEMBER The relationship N = Fn between the member displacement n and the member force N of a harmonically vibrating uniform beam member 12 (Figure 1) can be written, in the local coordinate system 1 x\u2019z\u2018, E l L3 - _ The dimensionless KolouSek functions Ki in (1) depend on the dimensionless frequency parameter /Iz5 of the member, The reference angular frequency wo is the lowest angular eigen-frequency the beam would have in transverse bending vibration if its ends 1 and 2 had been simply supported. For instance, Possible hinged or guided connections of the member ends 1 and 2 to the joints of the frame are specified as member releases in PFVIBAT. They are accounted for in the program by condensation of the 6 x 6 member stiffness matrix F in (1) before its being transformed (using the angle a in Figure 1) to the global co-ordinate system Oxz and assembled into the structure stiffness matrix E in (8). In all, KolouSek6 defined 17 functions K i for transverse beam vibration, see also References 7 and 8. To facilitate manual computations, they have been graphically represented and numerically tabulated versus P in Reference 25. In addition to the translatory inertia m and the bending flexibility 1/EZ included in the BernoulliEuler theory, rotatory inertia mr2, shear flexibility l/kGA and static axial load H (causing second-order bending moments and shear forces in the beam member 12 in Figure 1) can optionally be considered in PFVIBAT. New elements Fij in the 6 x 6 member stiffness matrix F in (1) are derived from the following theory : The transverse translation w = w(x\u2019), clockwise rotation u = u(x\u2019), shear deformation y = y(x\u2019), bending deformation IC = ~(x\u2019), shear force T = T(x\u2019) and bending moment M = M(x\u2019) of a generic beam lamina dx\u2019 (Figure 2) are collected in three column matrices (Figure 3). The external transverse and moment loads are W and I/. The external static axial load is H and is counted positive when compressive",
            " The kinematic compatibility operator G, the constitutive operator Sd and the dynamic compatibility operator G\u201d of the differential beam element (Figure 2) are (Figure 3) The two matrix differential operators G and G\" in (4a,c) are seen to be each other's adjoints (as was anticipated by the superscript a). They contain the same geometric information (which they should do in a consistent linear theory). The general matrix differential equation governing w and u of a non-uniform beam is easily found by the three-step transformation chain G\"SdG (Figure 3) as 1 W - mw - Hw\" GaSdG[r] = [ V - mr2v ( 5 ) where primes and dots denote differentiation with respect to the local length co-ordinate x' (Figure 1) and the time t , respectively. New elements K , to K , in the member stiffness matrix F in (1) are found by taking kGA and E l as constants, putting W = 0 and I/ = 0, assuming w = X(x') sin cot and u = Y(x')sin cot PFVIBAT-A PROGRAM FOR PLANE FRAME VIBRATION ANALYSIS 1225 and solving for the mode functions X and Y by use of (5) and the boundary conditions (Figure 1) X ( 0 ) = t , Y(0) = - m , X ( L ) = t , Y ( L ) = - m 2 (6a-d) For instance, the function K , in (3) is replaced by r 2 where X and Y in (7a) shall belong to the case t , = t , = 0 = rn, and m, = 1 and where Y in (7b) shall belong to the case t , = 0 = rn, = m, and t , = 1 (the alternative (7b) was found to be the numerically most favourable one and was programmed in PFVIBAT). The functions K , , and K , , in (1) pertaining to the longitudinal vibration of the member 12 (Figure 1) do not change. Required condensation of F is performed as before. STRUCTURE-FORCED VIBRATION The global translational and rotational amplitudes of the joints of a harmonically vibrating frame (Figure 4) are collected in a column matrix p termed the structure displacement. The amplitudes of the vectorially associated external loads upon the joints are collected in a column matrix P termed the structure load. The condensed and transformed local stiffness matrices F = F(o) of all members (Figure 1) are assembled to form the global stiffness matrix E = E(w) of the frame structure. The governing matrix equation is Ep = P (8) Rigid, hinged and rolling (in the x- and/or z-direction) supports of the frame are considered in PFVIBAT by special procedures in handling (8). It should be noted that the analysis and the program are here restricted to concentrated loads on the chosen joints of the frame structure. The structure may be non-anchored (implying one, two or three zero eigenfrequencies). For any given angular frequency o of a forced vibration case, unknown components of p (free displacements) and unknown components of P (support reactions and loads imposing prescribed non-zero displacements) can be found by (8). When all components of p are known, all displacements n and forces N at the member ends (Figure 1) and all (longitudinal, rotational, transversal) displacements u(x\u2019), u(x\u2019), w(x\u2019) and sectional forces N(x\u2019), T(x\u2019), M(x\u2019) along the members can be calculated. PFVIBAT prints p, P, n, N and plots [u2(x\u2019)+w2(x\u2019)]* and M(x\u2019). Joints must be placed in positions where rigid bodies (Figure 5a) are connected to a frame. In PFVIBAT, the actual connection can be modelled in two ways (Figs. 5b and 5c). The exact contribution to the structure stiffness matrix E in (8) from a rigid body attached to the joint J (Figure 5b) is given by Here, M , is the total mass of the body, i, its radius of gyration with respect to a y-axis through the mass centre MC, a and c the x- and z-distances (with sign) between J and MC, p J x , pJz and p,, the translational and rotational displacements of joint J , and AP,,, APJZ and AP,, those parts of the total external force and moment loads P J x , P,, and P,, on the rigid body at J which are required to make the body perform the displacement described",
            " 202, was omitted in Reference 22). Angular antiresonance frequencies 3 are calculable as angular eigenfrequencies of a modified frame submitted to the additional prescription p j = 0. Normalized eigenmodes p\" (sum of squares of components of p\" made equal to unity) and pertinent modal masses m,, are also obtainable by PFVIBAT. From the information contained in p\", the program calculates the local displacements ~ \" ( x ' ) , ~ \" ( x ' ) , w\"(x') along each beam member. The contribution Am,, to m,, from one member 12 (Figure 1) is determined by Am,, = m [ { U ~ ( X ' ) } ~ + { W \" ( X ' ) } ~ + ~ ~ ( ~ \" ( X ' ) } ~ ] dx' (10) I Numerical integration is employed in PFVIBAT to evaluate (10). The contribution Am,, to m,, from one rigid body (Figure 5 ) with global mass centre translations uLc and wLc and rotation u i B is determined by Am,, = M , [ { uLc) + { wLc} + i f { u\",} 2] (1 1) TRANSIENT VIBRATION The undamped angular eigenfrequencies a,, the normalized eigenmodes (represented by p\") and the pertinent modal masses m,, of a frame can be calculated by PFVIBAT as mentioned above",
            "213 3.202 10.49 11.08 15.93 21.50 ( 144 Example 2. Forced harmonic vibration First, solely the horizontal load Q sin ot (with Q = 1.OOO kN and o = 0-500 rad/s) on joint 2 in Figure 6 will be considered. The maximum stress in the undamped frame is required. The PFVIBAT bending moment plot (analogous to Figure 7b) shows that the beam section just above support 3 is likely to be the most stressed. The sectional forces (for sin ot = + 1) on end 2 of beam* @ are read from the printed output as (cf. Figure 1) @ = 0.263 kN @ = 1.301 kN M P = 9.45 kNm (1 5a,b,c) Second, solely the horizontal displacements q sin ot (with q = 1@00 mm and o = 0.500 rad/s) of the support joints 3 and 6 will be considered. This loading case is equivalent to a rigid body vibration of the ground having the maximum acceleration 0 2 q = 0.250 mm/s2. The maximum linear acceleration lalmax of the joints of the undamped frame is required. The PFVIBAT displacement plot (analogous to Figure 7a) shows that joint 1 has the numerically largest total translation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000545_05698196608972134-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000545_05698196608972134-Figure1-1.png",
        "caption": "FIG. 1. Disk geomet ry of Amsler ma chine.",
        "texts": [
            " In this paper the au thors present experimental results, together with published data, which allow a new correlation to be obtained for the coefficient of frict ion in terms of \"external\" param eters, load , speed, viscosity radius, and surface finish. A study is made of the oil film thickness as measured by voltage discharge and the reason for the very large drop in thi ckness with load is shown to be due to sur face temperature changes. Disk machine Two disk machines were used, the one an Amsler which consists of two steel disks (Fig. 1) moun ted on shafts of 2.08 inches center distance. One shaft rotated 10% slower than the other. The smaller disk varied in diameter from 17i to 2 inches and the relative surface velocities of the two, VdVl varied from 7-3 to % (see Appendix 1). On one disk there was a raised t rack 7S inch wide, the other was mounted on a bush of hard resin to insulate it from the head stock of the Amsler and so permi t voltage discharge measurements of the film thickness to be obtained. Th e surface temperature of the upp er disk was measured by a surface thermo couple placed at one side of the track and embedded in the surface by copper amalgam , thus ensur ing good thermal conduct ivity between the junction and the t rack"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000234_02678290903062994-Figure19-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000234_02678290903062994-Figure19-1.png",
        "caption": "Figure 19. A photo-cantilever, with the director along the z-axis, illuminated with light travelling along the x-axis; adapted from (37).",
        "texts": [
            " For thicker elastomer films, the attenuation of light caused by the trans ! cis isomerisation becomes important. Illumination and the subsequent changes in the order parameter change the natural length of the sample, a gradient in illumination then creates a gradient in natural length and the cantilever responds by bending. Warner and Mahadevan (37) investigated the mechanical response of illuminated films of photo-active elastomers in the limit of small strain elasticity. They analysed the situation shown in Figure 19 where the director n is aligned along the z-axis, and the illuminating light travels along the x-axis. The effect of illumination and thus of the subsequent changes in the order parameter are modelled by a change in the natural length of the sample along the z-axis. This is a photo-strain photo zz . Mostly it is a contraction along the director and hence photo zz < 0. The simplest assumption is that it is proportional to the intensity I\u00f0x\u00de of light at this depth x. Thus we take the photo-strain relative to the new natural length to be cI\u00f0x\u00de, with c a constant"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003262_s00170-018-1799-y-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003262_s00170-018-1799-y-Figure2-1.png",
        "caption": "Fig. 2 Schematic of test molds. a Design of the test molds. b Design of the cooling channels. c SLM-fabricated test molds with the connector. d Locations of temperature measurement points",
        "texts": [
            " In addition, the inlet temperature and outlet temperature of coolant was also measured. The heat transfer coefficient was calculated using a theoretical model. It was found that both the flow rate and heat transfer coefficient of SLM-fabricated channels were poorer than drilled channels. The achieved findings in this study verified the importance of improving the dimensional accuracy and surface quality of SLM-fabricated cooling channels in order to obtain better cooling performance. The designed test molds are shown in Fig. 2. The test molds had dimensions of 100 mm\u00d7 100 mm\u00d7 20 mm. Inside the mold, the shape and dimensions of cooling channels are presented in Fig. 2b. The cooling channels had a total length of 546 mm. For the CNC-fabricated cooling channels, except for the inlet and outlet, all the other holes were blocked to obtain an enclosed cooling passage. Three types of molds with different cooling channel diameters, specifically \u03c62 mm, \u03c63 mm, and \u03c64 mm, were fabricated via SLM and CNC, respectively. The inlet and outlet of the fabricated test molds were then linked to connectors, as presented in Fig. 2c. In the center of the test mold, a circular hole with a diameter of\u03c675 mmwas designed to place a heating unit to heat the mold. Along the diagonal direction, three temperature measurement points were placed to measure the temperature variation. The locations of the temperaturemeasurement points are shown in Fig. 2d. A spiral heating ring was placed in the central hole of the test mold and the temperature of the heating ring was set to 250 \u00b0C. A K-type thermocouple was integrated within the heating ring, and a temperature controller with solid state relay (SSR) output was used to keep the heating ring at 250 \u00b0C. The temperature variations at the temperature measurement points were obtained to evaluate the cooling performance of the cooling channels. The schematic of the testing system is presented in Fig. 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003834_j.jmapro.2020.10.024-Figure11-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003834_j.jmapro.2020.10.024-Figure11-1.png",
        "caption": "Fig. 11. The theoretical scheme formation structure during DED (a) and UDED (b) processes.",
        "texts": [
            " Gorunov Journal of Manufacturing Processes 59 (2020) 545\u2013556 and X-ray tomography, the authors showed that the first effects associated with cavitation in water, ethanol, glycerin, and molten aluminum are detected after 0.5 s of ultrasonic treatment [35]. Cooling rate have great influence on the formation structure during DED specimens [10]. It is known, that during DED process, the heating and cooling rates in point contact laser and part are more than 106 \u030aC/s. This time probably is not enough for cavitation beginning. Each material needs its own frequency and power parameters of ultrasonic vibrations. Probably, cavitation can also arise in a solid-liquid region. Thus, based on analysis, Fig. 11 shows a scheme that describes the theory of the formation of UDED samples proposed in the present studies. The amplitude of ultrasonic vibrations varies sinusoidally to direction of build up of the sample (along the height of the sample from substrate) [32]. Analyzing the experimental results, it was found that small equiaxed grains are formed only in specific places of the sample and these regions are individual for each frequency and power of ultrasonic vibrations (Figs. 6 and 7). It can be assumed that the formation of regions with small equiaxed grains occurs in regions where the amplitude has a maximum"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000416_s0033583500002742-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000416_s0033583500002742-Figure1-1.png",
        "caption": "Fig. 1. Simulation of the experiments of Okuno & Hiramoto (1979). The two types of experiments done by Okuno and Hiramoto are shown schematically in the upper left and upper right. The micropipette holding the sperm head is shown at s = \u2014a for experiments of type I, and at s = o for experiments of type II. Simulations were performed according to text equation (4.2), for Eb = iooopN/tm, E, = o, and for the four cases discussed in Appendix I with the parameters indicated. Z?j, and Es are the elastic bending resistance and the elastic shear resistance, respectively.",
        "texts": [
            " Indeed, Baba (1972) recognized that the absence of any drastic change in rigidity between actively beating and immobilized cilia or during the beat cycle suggested that transverse connexions remained intact throughout the whole course of ciliary motion. The question then arises as to whether one can deduce the contribution of the shear-resistant links from a more detailed analysis of the data of Okuno & Hiramoto (1979). In their experiments, Okuno & Hiramoto fixed the flagellum at either end, applied a force, F, in the middle, and measured the deflexion d (Fig. 1). Force balance requires that F = Fx + F2, and moment balance requires that Fxa = F2b, where a and b are the distances from the point of application of the force to the proximal and distal ends of the flagellum, respectively. If the force is applied at the centre, a = b = L/z. In Fig. 1 this case is depicted in the left panel. The relation between elastic bend resistance, deflexion, and force is given by FN = Eb\u2014^, (4.1) where Eb is the elastic bending resistance. Integration of (4.1) gives {-a < s < 0), a = { 1 (4.2) The external moment in the two segments is given by \u2014 Eb da/ds: Cj) ( \u2014 a < s < o), M = I (4.3) The moments vanish at s = \u2014 a and s = b, so c\u00b1 = a and c[ = \u2014 b. Since the moment is continuous at a: = o, so is d; continuity of a requires that bc2 = ac'2. For small deflexions, f\u00b0 f\u00b0 d = a ds, and similarly, d ~\\ ads",
            "1) is replaced by where y(s) is the effective sliding displacement between filaments at any point s along the flagellum and S is the internal shear force, given by S = \u2014Esy if the shear resistant links are linearly elastic and uniformly distributed along the length of the flagellum. Appendix I presents the solutions to this equation for the two kinds of experiments performed by Okuno & Hiramoto, i.e. a flagellum supported at each end and deformed by a force, F, applied at the centre (type I) or a flagellum fixed at the proximal end and deformed by a force applied at some distance, L, from the immobilized end (type II) (Fig. 1). Different solutions are obtained for each case, depending on whether one assumes that the tubules are tied together at the proximal end or are free to slide everywhere. For flagella in situ, it is usually assumed that little or no sliding occurs at the basal region (for example, Hiramoto & Baba, 1978). Okuno & Hiramoto (1979) computed their results for type I experiments on the assumption that Es = o, and obtained a value of icT21 N m2 ( = io3 pN /tm2) for Eb. If we take 0 = 1 5 /im and d = 5 /tm as representative values for their experiments, the force applied to the flagellum [evaluated from equation (4.4)] was ~8-9pN. This allows computation of Eg from the equations derived in Appendix I if one assumes a value for Eb. Fig. 1 shows the results of a computation comparing cases I a and Ib with Eb = 30 pN fim2, Es = 12 pN with the value obtained [from equation (4.2)] for Eb = iooopN/im2, Es = 0 (the value of Eb computed by Okuno & Hiramoto on the assumption that there were no interconnexions between the tubules). It can be seen that there is Biophysics of flagellar motility 135 scarcely any difference in shape whether the tubules are tied together at the proximal end or are free to slide everywhere. Furthermore, there is little difference in shape between Eb = iooopN/im2, Es = o and \u2022E& = 3opN/*m2, Es \u2014 12 pN; the deflexions, d, from the horizontal are 4-1 /on for the former and 5-1 fim for the latter",
            " This neglects any nonlinearity in the shear-resistant links (Hines & Blum, 1978) but this will have little effect on the analysis. The basic equations describing this system at equilibrium are: ^ (A 1) f \u00b0 J - Biophysics of flagellar motility 163 Sds= o, (A 2) M(s)= -Eb^-j'Jds', (A3) where FN, M, and 5 are the external shear force, the external bending moment, and the internal shear force, respectively, and y is the effective sliding displacement between filaments. We consider four cases, corresponding to the two types of experiments performed by Okuno & Hiramoto (Fig. 1). Case la. The filaments are free to slide and the moments at each end are zero, and M=(o5F(a + s) -a<s<o, \\-o-sF(a-s), o < s < a. v ^ The general solution to equation (A 1) is (Acosh(i)(s+a) +Bsinho)(s+a)-Fl2Es, . . y W ~ U ' cosho)(s-a) + B' sinh(o(s-a) + F/2E { 5) where w = E3/Eb. For cases la and Ib we restrict ourselves with little loss of generality but considerable savings in algebraic labour and clarity of presentation to the situation when the force, F, is applied to the centre of the flagellum. Because of symmetry we may consider only the half-flagellum from s = o to s = a for case la. At s = a, the moment is zero, i.e. da./ds\\Sc,a = o. Use of this boundary condition in equation (A 5) leads to y(s) = A' cosh a>(s-a)+ F/zEs (0 < s < a). (A 6) Symmetry also requires that 7(0) = o, so that A = \u2014F/2ES cosh a. Thus 1 \\ F T coshc<;(s-aY| y(s) = \u2014 1 v ; \\,o < s <a. (A 7) zEs L cosh wa J J To calculate the displacement, d (see Fig. 1), we evaluate d = \u2014I sin a ds. Jo fa For small displacements, d ~ \u2014 a ds. Incompressibility of the Jo filaments implies that dy/ds = da./8s. Since symmetry requires that a(o) = o as well as 7(0) = 0, a = y. For small displacements, then, , fa , Fa [\"tanh coa ] . 0 . d ~ - \\ a ds = -g-\\ 1 . (A 8) Jo 2ES[ <oa J For small w, ~ 1 \u2014(wa)2/3- Thus for Es <^ Eb, d approaches the value given in text equation (4.4), i.e. d = \u2014 Fas/6Eb. Case Ib. The same as case la except that the filaments are tied together at the proximal end of the flagellum, i",
            " (A 12)x 2(oa 2EQ cosh 2<ua Biophysics of flagellar motility 165 Knowledge of a( \u2014 a) permits evaluation of d if sodesired, since ~ a(s) ds. J -a Case IIa. In the second kind of experiment performed by Okuno & Hiramoto (1979) the flagellum is fixed at the proximal end by insertion into the sperm head and the sperm head is held immobilized by gentle suction from a micropipette. A force is applied at a distance, L, from the point of insertion of the flagellum into the sperm head and the shape and deflexion of the flagellum are measured (Fig. 1). For case Ha we assume that the filaments are not tied together at the proximal end, but are free to slide everywhere. Use of the boundary condition M(L) = \u2014Eb dy/ds\\s=,L = o in the general solution to equation (A 1) yields y(s) = A cosho)(s-L)-F/Es. Use of equation (A 2), which may be written as 7 ds = o, allows Jo evaluation of A = Fo)L/Es sinh OJL. Thus ,./.\\ _ F\\o>L cosh co(s-L). , _ - 1 . (A 13) sinhwL J v J / By hypothesis, a(o) = o, so a(s) can be evaluated from y(s)-a(s) = 7(0)-a(o): a(s) = \u2022=\u2014r-j-\u2014j [cosh d){s \u2014 L) \u2014 cosh wL]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002023_s11012-016-0502-3-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002023_s11012-016-0502-3-Figure4-1.png",
        "caption": "Fig. 4 Schematic of the meshing tooth pairs with tip-fillet",
        "texts": [
            " Ma State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi\u2019an Jiaotong University, Xi\u2019an 710049, Shanxi, People\u2019s Republic of China Ei f j i \u00bc a; b\u00f0 \u00de The tooth profile error of the ith tooth pair at meshing point j with tip-fillet Egear r The loaded transmission error of the gear Ei r j i \u00bc a; b\u00f0 \u00de The static transmission error of the ith tooth pair at meshing point j Ea s j The spacing error of the tooth pair a at meshing point j f The friction force on tooth surface fh, fv The vertical and the horizontal components of the friction force F The total meshing force Fh, Fv The vertical and the horizontal components of the meshing force Fi (i = 1, 2) The meshing force of the ith tooth pair Fi j i \u00bc a; b\u00f0 \u00de The meshing force of the ith tooth pair at meshing point j Fr, Ft The gear meshing force in radial and tangential directions G Shear modulus Iy1, Iy2 The cross section moment of inertia j The meshing point k The total mesh stiffness of the gear pair kan,i (n = 1, 2) (i = 1, 2) The axial compressive stiffness of the ith tooth pair, subscript n denotes the driving and driven gear ka_f The axial compressive stiffness considering friction kbn,i (n = 1, 2) (i = 1, 2) The bending stiffness of the ith tooth pair, subscript n denotes the driving and driven gear kb_f The bending stiffness considering friction kfn (n = 1, 2) The stiffness of fillet-foundation, subscript n denotes the driving gear and driven gear kf11, kf21 The fillet-foundation stiffness of the driving gear and driven gear during single-tooth engagement khi (i = 1, 2) The Hertzian contact stiffness of the ith meshing tooth pair ksn,i (n = 1, 2) (i = 1, 2) The shear stiffness of the ith tooth pair, subscript n denotes the driving gear and driven gear ks_f The shear stiffness considering friction ktn,i (n = 1, 2) (i = 1, 2) The stiffness of tooth of the ith tooth pair, subscript n denotes the driving gear and driven gear ktooth The total mesh stiffness of meshing tooth pairs kitooth i \u00bc 1; 2\u00f0 \u00de The mesh stiffness of the ith tooth pair L The tooth face width m Module of the gear pair N The number of meshing tooth pairs O1 The center of the driving gear Oc The center of the gear tip-fillet Qi j i \u00bc a; b\u00f0 \u00de The teeth deformation of the ith tooth pair under unit force at contact point j rai (i = 1, 2) The radius of the addendum circle of the driving gear and driven gear rbi (i = 1, 2) The radius of the base circle of the driving gear and driven gear rc The radius of the gear tip-fillet rint Hub radius of the gear pair Sa, Sr The separation distances of tooth pairs c and a along the line of action tP The time between the beginning point of the single-tooth engagement and the pitch point T The torque applied to the driving gear xDE, yDE The coordinates of the point on the involute curve DE in x and y directions xOc, yOc The coordinates of the point Oc in x and y directions xb The distance between the contact point and the central line of the tooth yb The distance between the contact point and original point in the horizontal direction y1, y2 The horizontal coordinates of arbitrary point at transition curve and involutes curve z The number of teeth X1 The rotating angular velocity of the driving gear a The pressure angle of the pitch circle a1 The pressure angle corresponding to point A (see Fig. 3) a2 The pressure angle corresponding to point D (see Fig. 3) ac The angle corresponding to the point Oc (see Fig. 4) ap The pressure angle corresponding to point E (see Fig. 4) b The operating pressure angle b2 The angle corresponding to the point D (see Fig. 4) bc The angle corresponding to the point Oc (see Fig. 4) c The angular displacement of arbitrary point at the transition curve h1 The rotational angle of driving gear hb The half tooth angle on the base circle of the gear hB The rotational angle at the beginning point of the single-tooth engagement hP The rotational angle of the pitch point k1N, k2N (N = 1, 2) The correction coefficient of the fillet-foundation stiffness of the driving gear and driven gear, N denotes the number of meshing tooth pairs l The friction coefficient s The angular displacement of arbitrary point at the involute curve sc The meshing angle at the position of the involute starting point Time-varying mesh stiffness (TVMS) has a larger influence on the vibration of gear systems, and how to calculate the TVMS has gained a lot of attention from many scholars",
            " xb denotes the distance between the contact point and the central line of the tooth, yb denotes the distance between the contact point and original point in the horizontal direction, y1 and y2 are the horizontal coordinates of arbitrary point at transition curve and involutes curve, the calculation of dy1=dc and dy2=ds can be found in Ref. [22]. h1 denotes the rotational angle of driving gear, hP denotes the rotational angle of the pitch point, both of them can be found in Fig. 3. 2.3 Effect of gear tip-fillet on TVMS A schematic of the meshing tooth pairs with gear tipfillet is displayed in Fig. 4. In Fig. 4a, Oc is the center of the tip-fillet, and rc is the radius of the tip-fillet. Based on the previous analytical model [6], an IAM suitable for the spur gear pair with gear tip-fillet is established. In Fig. 4a, there is a following geometric relationship. Dx \u00bc ra sin b2 Dy \u00bc ra cos b2 ; \u00f013\u00de whereDx andDy are the coordinates of pointD in x and y directions, respectively. ra is the radius of the addendum circle;b2 \u00bc hb inv\u00f0arccos rb ra \u00de, hb is the half tooth angle on the base circle of the gear, and rb is the radius of the base circle. The pressure angle of point E can be calculated by: 1 kb f \u00bc Z a p 2 \u00bd\u00f0cos b l sin b\u00de\u00f0yb y1\u00de xb\u00f0sin b\u00fe l cos b\u00de 2 EIy1 dy1 dc dc \u00fe Z b sC \u00f0cos b l sin b\u00de\u00f0yb y2\u00de xb\u00f0sin b\u00fe l cos b\u00de EIy2 dy2 ds ds; \u00f0h1\\hP\u00de Z a p 2 \u00bd\u00f0cos b\u00fe l sin b\u00de\u00f0yb y1\u00de xb\u00f0sin b l cos b\u00de 2 EIy1 dy1 dc dc \u00fe Z b sC \u00f0cos b\u00fe l sin b\u00de\u00f0yb y2\u00de xb\u00f0sin b l cos b\u00de EIy2 dy2 ds ds; \u00f0h1 [ hP\u00de 8 >>>>>>>>< >>>>>>>>: ; \u00f010\u00de 1 ks f \u00bc Z a p 2 1:2\u00f0cos b l sin b\u00de2 GAy1 dy1 dc dc\u00fe Z b sC 1:2\u00f0cos b l sin b\u00de2 GAy2 dy2 ds ds; \u00f0h1\\hP\u00de Z a p 2 1:2\u00f0cos b\u00fe l sin b\u00de2 GAy1 dy1 dc dc\u00fe Z b sC 1:2\u00f0cos b\u00fe l sin b\u00de2 GAy2 dy2 ds ds; \u00f0h1 [ hP\u00de 8 >>< >>: ; \u00f011\u00de 1 ka f \u00bc Z a p 2 \u00f0sin b\u00fe l cos b\u00de2 EAy1 dy1 dc dc\u00fe Z b sC \u00f0sin b\u00fe l cos b\u00de2 EAy2 dy2 ds ds; \u00f0h1\\hP\u00de Z a p 2 \u00f0sin b l cos b\u00de2 EAy1 dy1 dc dc\u00fe Z b sC \u00f0sin b l cos b\u00de2 EAy2 dy2 ds ds; \u00f0h1 [ hP\u00de 8 >>< >>>: ; \u00f012\u00de r2b \u00f0ra rc\u00de2 \u00fe \u00f0rb tan ap rc\u00de2 \u00bc 0; \u00f014\u00de where rc is the radius of gear tip-fillet circle and ap is the pressure angle of point E",
            " In the curve section ofME, the original tooth profile involute becomes a circular arc, the amount of modification of the circular arc along the line of action Ef can be calculated by: Ef \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0yDE yOc \u00de2 \u00fe \u00f0xDE xOc \u00de2 q rc; \u00f015\u00de where yDE and xDE are the coordinates of the point on the involute curve DE in x and y directions, which can be calculated according to the involute curve (the detailed expressions for yDE and xDE can be found in Ref. [22]); yOc \u00bc OOc cos bc; xOc \u00bc OOc sin bc; OOc \u00bc rb cos ac ; bc \u00bc hb tan ap \u00fe ac; ac \u00bc arccos rb ra rc : In Fig. 4b, the solid lines and dashed lines represent the actual gear profiles with gear tip-fillet and the theoretical gear profiles, respectively. The gear tooth errors can lead to the difference between actual profiles and theoretical profiles, such as the tooth profile modification and the manufacturing errors. Symbols a, b and c represent three sequential tooth pairs; AB and CD denote the theoretical double-tooth engagement zones; BC denotes the theoretical single-tooth engagement zone; EM denotes the tip-fillet and P is the pitch point"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001394_tec.2016.2597059-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001394_tec.2016.2597059-Figure9-1.png",
        "caption": "Fig. 9. Temperature distribution (in \u00baC) within the indirect cooled machine at 75 kW power and speed of 1500 min-1.",
        "texts": [
            "8 Thermal conductivity of Aluminium (radial direction), W/K\u00b7m 237 Thermal conductivity of Magnets (radial direction), W/K\u00b7m 9 Thermal conductivity of Stator Winding Insulation (radial direction), W/K\u00b7m of 0.26 Thermal conductivity of Glass Fibre (radial direction), W/K\u00b7m 0.43 0885-8969 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. The temperature distribution (CFD model simulation) of the indirect cooled machine at 75 kW power and speed of 1500 min-1 is presented in Fig 9 and the direct cooled machine in Fig. 10. The difference of these cooling methods can be clearly seen on the stator winding areas and stator yoke areas of depicted temperatures in Fig. 9 and 10. According to the simulations one may expect also rotor yoke temperatures be lower while utilizing direct cooling methods inside the coils. However these simulations gave similar heat amounts for magnet areas in rotor side. PAO has boiling point at 419 \u00b0C and flash point at 238 \u00b0C which means that the cooling fluid temperature is not limiting the machine cooling but the insulation class. The CFD thermal simulations of the earlier developed prototype utilizing indirect water cooling are explained in [18] and from those simulations the results on 377 Nm load at 1500 min-1 are depicted in Table VII"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002838_978-3-319-54169-3-Figure3.1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002838_978-3-319-54169-3-Figure3.1-1.png",
        "caption": "Fig. 3.1 Torque curves for various values of control parameter Vm and constant parameter n: a linear property (n = 1), b cubic property (n = 3)",
        "texts": [
            " The DC series wound motor develops a large torque and can be operated at low speed. It is a motor that is well suited for starting heavy loads. Because of that it is often used for industrial cranes and winches, where very heavy loads must be moved slowly and lighter loads moved very rapidly. Introducing the dimensionless time parameter \u03c4 , the relation (3.4) transforms into ( ) = (Vm \u2212 Cm )n, (3.5) where ( ) is the dimensionless driving torque with dimensionless parameters Vm and Cm and angular velocity . In Fig. 3.1 the torque curves for various values of control parameter Vm and constant parameter n are plotted: (a) linear property (n = 1), (b) cubic property (n = 3). It can be concluded that for increasing of the control parameter Vm the curves move to right in the ( ) \u2212 plane. For the arbitrary value of the motor frequency, the higher the control parameter Vm , the higher the value of the torque ( ). In Fig. 3.2, the torque curves for constant value of parameter Vm and various values of the order of nonlinearity is plotted"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000035_tie.2010.2095392-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000035_tie.2010.2095392-Figure1-1.png",
        "caption": "Fig. 1. Variations of (a) diameter, (b) curvature, and (c) inclination, (d) branched pipe, and (e) uneven inner surface.",
        "texts": [
            " The development of in-pipe robots that are able to navigate the narrow, dark, and curved inner surfaces of pipes is therefore an important field of research. In-pipe robots have been in research and development for many years but have yet to be fully developed for effective use. The inner space of a pipe has geometric constraints to which an in-pipe robot must adapt. The constraining variables include the diameter, curvature, and inclinations of the pipes, all of which may vary. In-pipe robots also require the ability to adapt to branched pipes and to uneven inner surface conditions caused by obstacles or rust. Fig. 1 shows some of these geometric variations. To successfully maneuver inside various pipelines, a robot should be able to adapt to these variations. Manuscript received September 30, 2009; revised April 15, 2010, July 3, 2010, and August 6, 2010; accepted September 16, 2010. Date of publication November 29, 2010; date of current version September 20, 2011. J. Park, W.-H. Cho, and H.-S. Yang are with the School of Mechanical Engineering, Yonsei University, Seoul 120-749, Korea (e-mail: avarta99@ yonsei"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000803_s1000-9361(11)60430-5-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000803_s1000-9361(11)60430-5-Figure3-1.png",
        "caption": "Fig. 3 Sketch of angular contact ball bearing.",
        "texts": [
            " However, the poly-harmonics i in in =2 3,\u00b7\u00b7\u00b7, may interact with the forward whirling mode and cause dynamic amplification at their intersections. In addition, the backward whirling mode may also be excited by the lubrication and friction of the bearing and other random broadband noises. 2.3.2. Bearing irregularity Angular contact ball bearings are widely used in MWA. In general, two of them are assembled in couple to provide support in the radial and axial of the flywheel. A typical angular contact ball bearing consists of an internal ring, an external ring, numbers of ball bearings, and a cage, as shown in Fig. 3. In the figure, D is the average bearing diameter, d the diameter of the ball, the contact angle. The irregularity of them will introduce disturbances during rotating [16-21]. And the angular frequencies of each disturbance can be obtained by analyzing the relative motion of each part [22]. Assume the internal ring is fixed, while the external ring is rotating with an angular velocity of . The angular velocity of the cage relative to the internal ring is as follows: ci 1 1 cos 2 d D (5) The angular velocity of the cage relative to the external ring is as follows: ce 1 1 cos 2 d D (6) The angular velocity of the ball is as follows: 2 b 1 cos 2 D d d D (7) The angular velocities of the ball passing the internal and external ring are as follows: bi ci 1z n (8) be ce 1z n (9) where z is the number of the balls in the bearing, 1,2, ,n N , N is the number of bearings in the MWA"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000156_s00170-009-2024-9-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000156_s00170-009-2024-9-Figure7-1.png",
        "caption": "Fig. 7 Computed melt pool profile along the fourth layer at a location 7 mm from the left end of the substrate: a isometric view, b top view, c front view. Corresponding process parameters are: laser power\u2014 500 W, scanning velocity\u2014 10 mm/s, and powder mass flow rate\u20144 g/min",
        "texts": [
            " Figure 6b depicts that the width of the melt pool is sufficient to form the complete track width, and Fig. 6c shows that the depth of the melt pool is extended up to one layer of bottom elements only. Noting the fact that two layers of elements (height ~0.125 mm) represent one layer of deposition (height ~0.250 mm), it is clear that the current combination of laser power and scanning velocity is insufficient to create a melt pool depth extending up to the previously deposited layer. An improper interlayer bonding is thus expected. Similar plots are shown in Fig. 7a\u2013c, however, at a higher laser power of 500 W keeping all other parameters constant. Figure 7c clearly shows that the melt pool depth extends through not only the top two layers of elements, which represent the presently depositing layer, but also to the third layer of elements from the top surface that corresponds to part of the previously deposited layer. Figure 7b also shows that the width of the melt pool conforms to the same of layer track continuously. A comparison of Figs. 6 and 7 clearly manifests the need to select the right combination of laser power and scanning velocity for a given powder mass flow rate to ensure proper interlayer material bonding. Figures 3, 4, 5, 6, and 7 depict that the temperature history and the melt pool dimensions during the deposition process using LENSTM technique depend on several process parameters for a given substrate size and build layer dimensions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001022_1.4005336-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001022_1.4005336-Figure4-1.png",
        "caption": "Fig. 4 A limb singularity, condition (a.2)",
        "texts": [
            " Since z and mi are two independent directions, this matrix is rank deficient whenever its last three columns (corresponding to infinite-pitch twists) become linearly dependent. On the other hand, in any robot configuration one has: Ai, Bi, and Ci are three distinct points, AiBi\\z and mi k= fi. Thus, the ith limb of the 4-RUU PM may exhibit a limb singularity whenever (a.1) \u00f0rCi rAi \u00de zk , AiCik z. In that case, Fi\u00bc (fi;rCi fi) crosses Ai at point Ci. As a result, Fi acts as a constraint force and the 4-RUU PM loses the translational DOF along fi. Figure 3 illustrates such a configuration; (a.2) \u00f0rCi rBi \u00de zk , f ik z as shown in Fig. 4. In that case, Fi crosses Ai at infinity, i.e., at point j\u00bc (z;0). Consequently, the 4-RUU PM loses the translational DOF along z. If several limb singularities occur simultaneously, then the robot may lose several DOF. Besides, if some limb singularities and a constraint singularity occur simultaneously, then the lowermobility PM may lose some allowed motions and gain some other limited motions at the same time. As a consequence, this may lead to unwanted changes on the motion pattern of the PM"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002436_j.ymssp.2018.06.034-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002436_j.ymssp.2018.06.034-Figure3-1.png",
        "caption": "Fig. 3. Calculated imbalance forces acting on the cage for various mass imbalance conditions and inner race rotation speeds.",
        "texts": [],
        "surrounding_texts": [
            "Fig. 7 shows the cage whirling motion for mass imbalance conditions of 0.49, 11.58, and 23.18 g cm and inner race rotational speeds of 5000 and 11,000 rpm. The green dotted lines represent the outer guidance clearance of the cage measured at room temperature. In addition, the guidance clearance in the cryogenic environment was analytically calculated to predict the modified maximum range of the cage under actual operating conditions by using commercial 3D modeling software. Thus, the blue dotted lines indicate the maximum movable range of the cage at cryogenic temperatures. Although the cage is assembled with metal rings and bolts, owing to the large coefficient of thermal expansion, the cage guidance clearance is reduced by 26% at cryogenic temperatures. The red trajectory traces the cage rotation for 1 s at medium time (30 s) in each operating range. The cage whirling orbit was the largest for a mass imbalance of 23.18 g cm at an inner race speed of 5000 rpm. Moreover, a comparatively circular orbit was observed at this condition. Furthermore, the cage whirling motion increased for all speed conditions as the mass imbalance increased owing to the increasing imbalance force on the cage. However, the whirling orbit of the cage did not exceed the maximum possible range owing to the operating clearance between the cage and outer race land. Theoretically, the imbalance force of the cage increases as a function of the square of the rotation speed of the cage. Thus, the effect of the mass imbalance is more apparent at 11,000 rpm than at 5000 rpm. On the other hand, the cage whirling orbit decreased in size as the speed increased for all mass imbalance conditions owing to the increasing fluid force on the cage. Fig. 8(a) and (b) present waterfall plots of the relative cage motion measured at the bearing housing in the Y direction for cage mass imbalance conditions of (a) 0.49 g cm and (b) 23.18 g cm. The measurement results of the cage whirling amplitude are shown for relative time ranging from 10 s to 60 s for a constant inner race speed of 11,000 rpm. Generally, a rotor supported by a ball bearing contains has a super-asynchronous component as the number of balls (Z \u00b1 1). Therefore, the actual measured signal of the cage includes not only the synchronous motion of the cage but also the influence on the whirling motion of the inner race. Fig. 8(a) shows dominant synchronous (1X) and super-synchronous (2X) cage responses with small peak amplitudes. On the other hand, Fig. 8(b) shows large synchronous and super-synchronous motion of the cage generated by the large mass imbalance of the cage. Furthermore, the figure shows that the amplitude and frequency of synchronous (1X) motion fluctuate with increasing time. Fig. 9 shows the average amplitude of the cage whirling as a function of the rotation speed of the inner race during speedup tests for various mass imbalance conditions. The average amplitude of the cage whirling increases significantly as the mass imbalance increases for all speed conditions owing to the increasing mass imbalance on the cage, except for the case with a speed of 2000 rpm. In addition, the influence of mass imbalance increased as the speed increased to 11,000 rpm. On the other hand, the average cage whirling amplitude decreased with an increase in the inner race speed, with the smallest value observed at 11,000 rpm. The measured results indicate that the whirling frequency of the cage is approximately 42% of the inner race rotation frequency. Thus, the maximum tangential velocity is approximately 52 m/s at the outer surface of the cage. Thus, the cage whirling amplitude was affected by the hydraulic force of LN2 resulting from the small outer guidance clearance between the cage and the race land, as well as the relative motion between the balls. The hydraulic force caused by LN2, which flowed between the outer guide land of the cage and the outer race land, acted on the cage as a restoring force to move the center of the bearing. Therefore, the cage whirling amplitude is reduced at high speeds [25]. Fig. 10 shows the PDF, which is a function that describes the distribution of a probability variable, calculated from the measured whirling frequency of the cage for various mass imbalance conditions and rotating speeds of the inner race. The red line is the fitting curve of the PDF, the range of the horizontal axis was kept at 30 Hz to allow for a quantitative comparison of the PDFs for the different cases, and the column width of the PDF was 0.5 Hz. The detailed expression is shown in Part 1 (Eq. (1)) of this paper. In general, abnormal collisions between the ball bearing elements and the cage result in a non-uniform whirling velocity of the cage. The PDF distribution is expected to be wide, since the whirling speed of the cage depends on the behavior of the cage. The standard deviation of the PDF increased in all the cases with the increase in the mass imbalance of the cage. On the other hand, the PDF widened with the increase in the rotating speed of the inner race. These results suggest that the number of intermittent collisions between the cage and the ball bearing elements resulting from the cage imbalance force increased as the speed of the inner race increased. Accordingly, fluctuations in the whirling frequency of the cage increased markedly with increasing mass imbalance at 11,000 rpm. On the other hand, the effect of such fluctuations on the mass imbalance of the cage was small at 5000 rpm at the average frequency of cage whirling. However, the effect of the fluctuations on the mass imbalance of the cage increased rapidly as the rotation speed increased to 11,000 rpm at the average frequency of cage whirling. This could be attributed to the fact that intermittent collisions between the outer surface of the cage and the outer race land increased owing to the radial force of the cage generated by the mass imbalance. Fig. 11 shows the standard deviation of the PDF as a function of the inner race speed for various mass imbalance conditions. A value of zero implies that the whirling frequency of the cage was the same at every speed. On the other hand, a nonzero value is indicative of the width of the distribution of whirling frequency of the cage. For the entire range of mass imbalance conditions, the variation in the whirling frequency of the cage increased gradually with the increase in the rotation speed of the inner race up to 11,000 rpm. The effects of the mass imbalance were more pronounced at 11,000 rpm compared to lower speeds. For a mass imbalance of 0.49 g cm, the standard deviation was 3.08 at 11,000 rpm, which is 31% smaller than that for the largest mass imbalance. These results indicated that an increase in the mass imbalance increased the standard deviation at high speed rapidly. In addition, these results also highlighted the effects of changes in the mass imbalance and rotor speed on cage behavior. Fig. 12 shows the relationship between the standard deviation of the whirling frequency of the cage and the whirling ratio of the cage and inner race as a function of the mass imbalance conditions for a rotating speed of the inner race of 11,000 rpm. The whirling frequency of the cage was determined as a function of the rotating frequency of the inner race. The detailed equation is shown in Part 1 (Eq. (2)) of this paper. The actual measured whirling ratio is generally greater than the calculated value owing to the increase in the contact angle by static load on the ball bearing. The measured whirling ratio of the cage was larger than the predicted value 0.414, except for the case with a mass imbalance of 23.18 g cm. The whirling ratio of the cage decreased as the mass imbalance increased, and the difference in the value was 4.7% between the smallest and the largest mass imbalance. In addition, the whirling ratio of the cage did not change significantly, except for the cases with mass imbalance conditions of 0.49 and 23.18 g cm. The intermittent collisions between the cage and the ball bearing elements interfered with the constant whirling of the cage because of the contact force and the friction coefficient. Thus, the intermittent collisions not only disturbed the constant whirling ratio of the cage but also reduced it. Consequently, the relative stability of the cage increased as the whirling ratio of the cage increased within the scope of this experiment. Generally, the torque value of the ball bearing is dominant in the relationship between the race and the ball. However, the abnormal motion of the cage can reduce the lubrication performance in the ball bearing tested in this study, since the cage functions as a solid lubricant in the ball bearing. In addition, abnormal particles of the cage material generated by inappropriate wear can instantaneously increase the torque value in the ball bearing between the race and the ball. Fig. 13 shows the measurement results of the ball bearing torque for various mass imbalance conditions and inner race speeds depend on the traction force of the outer race. The torque values indicate the last value for each rated speed, since the initial torque after an increase in speed fluctuates significantly because of the effects of running in as well as because of the wear of the soft metallic coating. When the rotation speed of the inner race was 2000\u20138000 rpm, the ball bearing torque increased with increase in the cage mass imbalance, except for the case with a mass imbalance of 23.18 g cm. In addition, the bearing torque increased significantly with increase in the mass imbalance for a rotating speed of the inner race of 11,000 rpm because the imbalance force of the cage increases as a function of the square of the rotation speed of the cage. These results show that the negative stiffness in the radial direction is caused by the mass imbalance due to the collision between the cage and the outer race, which increases the torque of the bearing."
        ]
    },
    {
        "image_filename": "designv10_5_0001676_j.jmapro.2018.04.002-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001676_j.jmapro.2018.04.002-Figure2-1.png",
        "caption": "Fig. 2. CAD model for build samples.",
        "texts": [
            " The experiment was designed to have better understanding of build height effect and the speed effect on the melt pool sizes. The samples were built under the same laser power of 180W and beam diameter, but each with a different laser scanning speed: 400mm/s, 600mm/s and 800mm/s. The specimens are designed to have given dimension so as to include all three scanning speed samples in the same field of view. Each part has a cross-section of 60mm length by 5mm width (in X and Y), and has a height of 25mm (in Z). The parts were placed with 1mm distance from each other. Fig. 2 shows 3D CAD model with the actual arrangement of the parts during the build. There are two notches on the part with a horizontal distance of 30mm, which were used for thermal image spatial resolution calculation purpose. The camera field of view is set to cover the region between the notches for all three samples. Cross sectional scanning strategy was adopted instead of default chessboard scanning for the temperature profile collection purpose e.g., easy to extract temperature profile along horizontal or vertical direction from thermal image"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000428_0005-2795(75)90348-7-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000428_0005-2795(75)90348-7-Figure5-1.png",
        "caption": "Fig. 5. a.c. polarograms of metmyoglobin. 0.1 M KC1, 25 \u00b0C, tm= 3 s. Metmyoglobin concentrations in/zM: 1, 0; 2, 0.6; 3, 1.2; 4, 1.5; 5, 1.9; 6, 2.2; 7, 2.7; 8, 3.2; 9, 6.0.",
        "texts": [
            " polarographic steps (Fig. 3). The peak height increases linearly with the protein concentration (Figs 3a and 4) and the pulse amplitude (Figs 3b and 4). The increase in concentration results in the shift of the summit potential to more negative values as well as in the increase of the half-width of the peak. a.c. polarography As generally observed with proteins [37], adsorption of metmyoglobin causes a sharp decrease of the electrode differential capacitance in the vicinity of the zero charge potential (Fig. 5). Although the d.c. polarographic steps are found in the adsorption area, corresponding peaks for the reduction of the prosthetic groups do not occur in the a.c. polarograms. In accordance with the shift of El~ 2 with the protein concentration, and the slope of the d.c. polarographic steps this behaviour shows the irreversibility of electrode process. Evaluation of the concentration and drop-time dependence of the a.c. polarograms in the adsorption region shows that the relative decrease of capacitance A ~'/~'0 depends linearly both on concentration and tm ~/2 (Fig",
            " The latter of these two processes may lead to the pH dependence of the limiting current, to the too low D values according to the Ilkovic equation, and to variation of the half-step potential with the protein concentration. The linear dependence of the height of the pulse polarographic peak on the pulse amplitude (Fig. 4) is in agreement with that observed with simple inorganic depolarizers [43] as well as with peaks yielded by proteins in Brdicka's cobalt solution [2] and differs from that of nucleic acids [4446]. This difference is not surprising if we take into consideration the potential range in which methemoglobin is adsorbed at the electrode (Fig. 5) and its reduction potential (Figs 1 and 3); the desorption potent ia l o f the pro te in differs too much f rom the reduct ion potent ia l to cause the non- l inear i ty of the dependence observed with nucleic acids. A n essential condi t ion for b iochemical u t i l iza t ion of the ca thodic reduct ion of pro te ins is the generat ion of nat ive reduct ion products . Betso et al. [20], performing a ca thodic reduct ion o f fe r r icy tochrome c, ob ta ined a p roduc t the spec t rum of which indicates changes of the te r t ia ry s t ructure; however, it exhibi ted approxi - mate ly the same enzymat ic act ivi ty as the mater ia l reduced with di thionite "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003486_j.ijmecsci.2020.105665-Figure19-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003486_j.ijmecsci.2020.105665-Figure19-1.png",
        "caption": "Fig. 19. Test gear sample and the test rig: (a) An injection molding POM gears; (b) The power open type gear test rig with oil-jet lubrication.",
        "texts": [
            " Under light loading conditions, POM gears ould fail as tooth flank failure, while tooth root damage becomes the ominating failure mode under a considerable large torque, 100 Nm for nstance. The final failure mode is more sensitive to the loading condiion, but the presence of lunker defects rises the possibility of tooth root reakage, particularly under moderate or heavy-duty conditions. . Experimental verification To verify the proposed numerical model, some durability tests of OM against steel gear pairs are performed under oil lubrication. The OM gears are manufactured by injection molding with accuracy grade f 11 (according to DIN 3962), as shown in Fig. 19 (a), while the steel inion is manufactured by machine cutting with accuracy grade of 7 according to DIN 3962). In this experiment, the gear durability test rig consists of two spinle boxes, two driving motors, guideway, frame, and the measurement ystem, representing a power open experimental system. Spindle box 1 lides along the guideway to adjust the center distance with the preision of 0.001 mm. During operating, the pinion is set with the fixed peed of 1500 r/min, and the output torque is selected as 40, 60, 80, r 100 Nm, corresponding to the simulation conditions. Oil jet lubriation is provided for the study and the lubrication oil is classified as SO-VG100, as shown in Fig. 19 (b). The oil flow rate is about 1 L/min, nd the oil temperature during the test is 30 \u00b1 2 \u00b0C. Fig. 20 shows the comparison of gear fatigue life span between exeriments and simulations under different loading conditions. The blue olid line represents the tooth flank fatigue life curve without defects, nd the blue, dash line means the tooth root fatigue life curve with the on-defect and the maximum injection molding lunker defect in this ork respectively. The injection molded POM gears fail as flank fatigue ailure under the torque of 40 Nm, and root fracture occurs as the outut torque exceeds 60 Nm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003887_j.etran.2020.100080-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003887_j.etran.2020.100080-Figure9-1.png",
        "caption": "Fig. 9. Rotor configuration of a typical spoke-type machine [71].",
        "texts": [
            " To conclude, PMASynRM machines mainly rely on the reluctance torque component and usually have a lower operating power factor and efficiency. Higher number of flux barriers can increase the rotor saliency, but it also complicates the rotor structure. To obtain high performance ferrite PM motors with similar tions for PMASynRM [62e64]. torque density as rare-earth machines, many researchers investigate the \u2018spoke-type\u2019 structures, also known as \u2018flux squeeze\u2019 configuration, which concentrates the fluxes from the PM to achieve approximately the same air-gap flux density as the rare-earth machine, as shown in Fig. 9. A. Isfanuti et al. in Refs. [69] compared surface NdFeB and spoketype ferrite machines for low power applications, and found that the same torque can be achieved with high efficiency but higher torque ripple for low cost ferrite machines. Eriksson and Bernhoff in Ref. [70] evaluated the spoke-type wind generators of the same power range with ferrite and NdFeB PMs, and revealed that ferrite generators would be 50% heavier with only 30% of PM cost. E. Spooner et al. proposed a modular design of ferrite spoke-type wind generators for easy assembly and low manufacturing costs [71]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002687_tmag.2017.2665580-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002687_tmag.2017.2665580-Figure1-1.png",
        "caption": "Fig. 1. Machine topology comparison. (a) Existing model. (b) Proposed consequent pole structure.",
        "texts": [
            " Besides, in vehicle application which requires wide constant power speed range, the hybrid excitation PM machines (HE-PMMs) have been gaining attention. However, the existing HE-PMMs often require a special field winding fed with DC current, which brings a space conflict between the stator PM and armature winding, Moreover, it will increase the machine cost. In order to achieve the function of hybrid excitation without field winding, the so-called DC-biased sinusoidal current or current superimposition stator-PM machines was developed [4], [5]. The machine structure is shown in Fig. 1 (a), the innovation is that the DC current is fed into the armature winding, and the PMs are inserted into the center of stator teeth. However, it is found that the flux produced by DC current must flow through the iron near the PM, then flows into the air gap, thus, the stator tooth iron near the PM core parts are saturated easily, and the machine torque density is limited. As an improvement work of Ref. [4], this paper presents a stator-PM, consequent-pole vernier machine with DC-biased sinusoidal current. As shown in Fig.1 (b), the proposed machine exhibits the advantages of FSCWs and stator-PM. In addition, the greatest feature is that the magnets are inserted in only half of the stator teeth, thus saving the cost of magnet materials. In this paper, with theoretical analysis and finite element analysis (FEA), the operation principle, no-load exciting field, back-EMF, torque capacity are analyzed, and the electromagnetic performance are compared with the existing machine having the same geometrical parameters, the same coil turns, and the same phase current. It is found that the proposed DC-biased current can improve the torque density compared with the regular sinusoidal current under the premise of same copper loss. Besides, the comparison results show that proposed machine exhibits higher back-EMF, higher output torque both in pure AC current configuration and DCbiased current configuration. The winding arrangement and the direction of DC current are shown in Fig. 1. The number of stator/rotor slots are 12/10, and the armature winding pole pair is 4. The corresponding drive circuit can be referenced in [5]. As shown in Fig. 1, salient rotor structure are adopted which similar in FSPMs. For the stator part, the significant difference from existing models is that the PMs are only inserted in one half of stator teeth consequently. Moreover, the stator teeth embed with PM are special designed, while the stator teeth without PM are rectangle. The current expressions for phase A are\uff1a - 2 sin( ) 2 sin( ) A ac e dc A ac e dc i I w t I i I w t I          (1) where we electrical angular velocity, Idc and Iac are the DC and AC current root mean square (RMS) values, respectively, and \u03b1 is the current angle",
            " 9 reveals the average torque variation with current based on the maximal torque control strategy. As shown, with pure sinusoidal current, the torque increase ratio decreases gradually, while with the hybrid excitation, the torque can maintain a high increase as the emerging torque component is proportional to the square of the current, that is to say, the emerging torque component produced by DC and AC current grows faster than PM torque. Therefore, the proposed current configuration can improve the machine over load capacity. The electromagnetic performance of machines in Fig.1 are compared while keeping the same geometrical parameters, the same coil turns, and the same phase current. The results in Table III show that the proposed machine exhibits higher back-EMF, higher output torque both in pure AC current configuration and DC-biased current configuration. The reason is that in the proposed consequent pole structure, only half of stator tooth iron shoes suffer from the saturation. Besides, the consequent pole can reduce the equivalent air gap length. Therefore, the performance of the consequent pole structure is better than that of the existing machine"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003831_tia.2020.3029997-Figure12-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003831_tia.2020.3029997-Figure12-1.png",
        "caption": "Fig. 12. Numerical verification of 2-D analytical end-winding thermal model.",
        "texts": [
            " \ud835\udc47\ud835\udc52\ud835\udc64(\ud835\udc65, \ud835\udc66)|\ud835\udc66=\ud835\udc3f = \ud835\udc474,\ud835\udc52\ud835\udc64 (28) The partial differential equation (24) can be solved by using the separation of variables. Applying the boundary conditions (25)-(28), the analytical solution \ud835\udc47\ud835\udc52\ud835\udc64(\ud835\udc65, \ud835\udc66) is expressed as: \ud835\udc47\ud835\udc52\ud835\udc64(\ud835\udc65, \ud835\udc66) = \u2211 [\ud835\udc39\ud835\udc57(\ud835\udc65) sin(\ud835\udf06\ud835\udc57\ud835\udc66) + \ud835\udc3a\ud835\udc58(\ud835\udc66) sin(\ud835\udf06\ud835\udc58\ud835\udc65)] \u221e \ud835\udc57,\ud835\udc58=1 (29) \ud835\udc39\ud835\udc57(\ud835\udc65)=\ud835\udc37\ud835\udc57,1sinh (\ud835\udf06\ud835\udc57\ud835\udc65) +\ud835\udc37\ud835\udc57,2cosh (\ud835\udf06\ud835\udc57\ud835\udc65) (30) \ud835\udc3a\ud835\udc58(\ud835\udc66)=\ud835\udc37\ud835\udc58,3sinh (\ud835\udf06\ud835\udc58\ud835\udc66) +\ud835\udc37\ud835\udc58,4 cosh(\ud835\udf06\ud835\udc58\ud835\udc66) + \ud835\udc38\ud835\udc58 (31) with \ud835\udf06\ud835\udc57 = \ud835\udc57\ud835\udf0b \ud835\udc3f , \ud835\udf06\ud835\udc58 = \ud835\udc58\ud835\udf0b \ud835\udc3b (32) \ud835\udc38\ud835\udc58 = 2?\u0307?\ud835\udc52\ud835\udc64\ud835\udc3b 2 \ud835\udf06\ud835\udc52\ud835\udc64(\ud835\udc58\ud835\udf0b) 3 (1 \u2212 cos (\ud835\udc58\ud835\udf0b)) (33) where the coefficients \ud835\udc37\ud835\udc57,1, \ud835\udc37\ud835\udc57,2, \ud835\udc37\ud835\udc58,3 and \ud835\udc37\ud835\udc58,4 are calculated by using the Sturm-Liouville theory. \ud835\udc3f and \ud835\udc3b are the length and the width of the end-winding, respectively. Fig. 12 shows a good agreement between the analytical end-winding model and the FEA results, where the boundary conditions \ud835\udc471\u22124,\ud835\udc52\ud835\udc64 are 118.4\u00b0C, 102.8\u00b0C, 128.9\u00b0C and 117.0\u00b0C; the thermal conductivity as well as generated heat loss are 0.58 W/(m\u22c5K) and 1.0 W, respectively. The number of summations (\ud835\udc57 and \ud835\udc58) of the analytical model in (29) equals 20. The maximum error occurs in the vertices of the two sides and keeps within 2.0%. The predicted average temperatures by the FEA, the analytical method and the 2-D \u201cT-type\u201d network in the x-y domain are 128",
            " Applying the method of separation of the variables, the mathematical solution can be expressed in (A3.1)-(A3.2) \ud835\udc47\ud835\udc52\ud835\udc64(\ud835\udc5f, \ud835\udc67) = \u2211 \ud835\udc39\ud835\udc5a(\ud835\udc5f) sin(\ud835\udf061\ud835\udc5a\ud835\udc67) + \ud835\udc3a\ud835\udc5a(\ud835\udc5f) sinh(\ud835\udf062\ud835\udc5a\ud835\udc65) \u221e \ud835\udc5a=1 + \ud835\udc473,\ud835\udc52\ud835\udc64 (A3.1) \ud835\udc39\ud835\udc5a(\ud835\udc5f) = \ud835\udc371\ud835\udc5a\ud835\udc3c0(\ud835\udf061\ud835\udc5a\ud835\udc5f) + \ud835\udc372\ud835\udc5a\ud835\udc3e0(\ud835\udf061\ud835\udc5a\ud835\udc5f) +\ud835\udc4a\ud835\udc5a (A3.2) \ud835\udc3a\ud835\udc5a(\ud835\udc5f) = \ud835\udc373\ud835\udc5a\ud835\udc3d0(\ud835\udf062\ud835\udc5a\ud835\udc5f) \u2212 \ud835\udc374\ud835\udc5a\ud835\udc4c0(\ud835\udf062\ud835\udc5a\ud835\udc5f) where \ud835\udc3d0 and \ud835\udc4c0 are the zero order Bessel function of the first and the second kinds; \ud835\udc3c0 and \ud835\udc3e0 are the zero order modified Bessel function of the first and the second kinds; \ud835\udc371\u22124\ud835\udc5b are coefficients; \ud835\udf061\ud835\udc5b and \ud835\udf062\ud835\udc5b are eigenvalues. \ud835\udc4a\ud835\udc5a is the particular solution. Details can be found in [23]. By introducing the conditions in Fig. 12, the temperature distributions of end-winding derived in the Cartesian and cylindrical coordinates are shown in Fig. 22. Since the selected cross-section is rectangular, the results are almost the same. [1] Z.Q. Zhu and D. Howe, \u201cElectrical machines and drives for electric, hybrid, and fuel cell vehicles,\u201d Proc. of IEEE, vol. 95, no. 4, pp. 746- 765, 2007. [2] J. Ou, Y. Liu, R. Qu and M. Doppelbauer, \u201cExperimental and theoretical research on cogging torque of PM synchronous motors considering manufacturing tolerances,\u201d IEEE Trans"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003277_tmag.2018.2839740-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003277_tmag.2018.2839740-Figure1-1.png",
        "caption": "Fig. 1. Diagram of the analyzed machines. (a) 27-slot/30-pole doublelayer SPM machine. (b) 27-slot/30-pole double-layer CP SPM machine. (c) 27-slot/30-pole four-layer CP SPM machine.",
        "texts": [
            " Then, the electromagnetic characteristics which include the air-gap flux density, back EMFs, cogging torque, and torque ripple are compared with finite-element (FE) analysis and verified by experiments. Finally, it is the conclusion. In order to compare the electromagnetic performance of the CP machines with the double-layer and four-layer windings, the 27-slot/30-pole machine is employed. The traditional 27-slot/30-pole SPM machine and CP SPM machines with the double-layer and four-layer windings are optimized. The stator and rotor together with the winding connections of the machines are shown in Fig. 1(a)\u2013(c), respectively. The parameters of the analyzed machines and PM material are listed in Table I. The capital symbols I, II, and III represent the traditional 27-slot/30-pole SPM machine and the traditional 27-slot/30-pole double-layer and four-layer CP SPM machines, respectively. 0018-9464 \u00a9 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. HARMONICS IN BACK EMFS BY FOUR-LAYER WINDING The CP PMSM is a machine in which a set of PMs with the same polarity are replaced with iron core"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003988_tmech.2020.2982436-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003988_tmech.2020.2982436-Figure1-1.png",
        "caption": "Fig. 1. Multirotor UAV with fault.",
        "texts": [
            " The dynamics and kinematics of a multirotor UAV with actuator faults and the fault estimation for each actuator are presented in section 2. Section 3 presents the control reconfiguration for the multirotor UAV subjected to failures of motors. The FTC methods are described step-by-step considering various issues resulting from actuator faults, motor constraints, and rapid yaw rates. Finally, numerical simulations and experiments are conducted to validate the effectiveness of the FTC. The multirotor UAV shown in Fig. 1 is an under-actuated system notwithstanding the number of input thrusts. The maximum rank of the input matrix is four while the number of degrees of freedom is six: three positions and three orientations. Multirotor UAVs are typically designed as symmetric rigid bodies, including the input thrusts, so that the orientation, roll, pitch, and yaw, are controlled stably for balance. Each thrust input plays an essential role in controlling the attitude of the UAV in operation. If any fault involving an actuator or propeller occurs and affects the thrust, control becomes difficult and the UAV could fall to the ground"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003900_tro.2020.3031236-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003900_tro.2020.3031236-Figure2-1.png",
        "caption": "Fig. 2. Schematic of the autonomous suturing setup. Blue arrows represent frames, the pink object represents tissue, the yellow part represents wound, and the four red dots surrounding the wound represent desired entry/exit points. The other five red dots are used to find the tissue angle.",
        "texts": [
            " We represent rigid motions and rotations by the special Euclidean group SE(n) and the special orthogonal group SO(n) in dimension n. The needle shape is the arc length of the needle divided by (\u03c0\u00d7needle diameter). We denote an identity matrix \u2208 Rn\u00d7n as In, and zero and one matrices \u2208 Rm\u00d7n as 0m\u00d7n and 1m\u00d7n, respectively. We use \u2212\u2192 A , \u2212\u2192 Ax, and \u2212\u2192 A y to refer to vector A and its x and y components, respectively. We use \u2297 for Kronecker matrix product operator. There are a total of seven frames defined to address the autonomous suturing (see Fig. 2): camera (C), robot base (B), Authorized licensed use limited to: Western Sydney University. Downloaded on June 15,2021 at 01:31:14 UTC from IEEE Xplore. Restrictions apply. robot end-effector (E), grasper (Gr), needle center (NC), and stitch (S) frames. One of the main pillars of an automated suturing framework is stitching planning, which deals with optimal motion of the needle inside the tissue based on clinical criteria. Examples of such criteria [28] are: entering the tissue perpendicularly; reaching specific suture depth; and minimizing tissue trauma"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003684_tcst.2019.2952826-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003684_tcst.2019.2952826-Figure2-1.png",
        "caption": "Fig. 2. Testbed for the quadrotor UAV aerial transportation system.",
        "texts": [
            " (66) Based on (64) and (66), it can be concluded that V\u0307 (t) \u2264 \u2212 2\u03b2 \u03b6max V (t). (67) The upper bound for V (t) can be obtained as V (t) \u2264 V (0) exp \u2212 2\u03b2 \u03b6max t . (68) Now, the upper bound for p(t) can be obtained as follows: p(t) \u2264 \u03b6max \u03b6min p(0) exp \u2212 2\u03b2 \u03b6max t . (69) Thus, for po(0) \u2208 D(po), the closed-loop system in (20) and (43) is locally exponentially stable. To implement the control laws presented in Section IV and verify the control performance, a motion tracking-based indoor flight testbed is employed. The testbed is shown in Fig. 2. The feedback of quadrotor\u2019s position and the payload\u2019s swing angle are obtained via the motion capture system. Via the Ethernet, these signals are sent to the ground station. Through a wireless module, the signals are transmitted to the onboard control unit. The attitudes of the UAV is measured by an onboard inertial measurement unit (IMU). Based on the above signals, the proposed control algorithm runs in an onboard Pixhawk flight control unit. The parameters of the quadrotor UAV with a suspended payload are listed as follows: mQ = 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001853_j.msea.2014.06.016-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001853_j.msea.2014.06.016-Figure2-1.png",
        "caption": "Fig. 2. Geometry of room-temperature tensile specimen in mm.",
        "texts": [
            " 3# group was prepared for the room temperature tensile test of GSM in transverse direction, recorded as GSM-T. 4# group was prepared for the room temperature tensile test of Ti\u20136Al\u20134V in transverse direction, recorded as TC4\u2013T. The tests of the latter three groups aim to compare the strength of GSM with that of Ti6\u2013Al\u20134V and Ti\u20136.5Al\u20133.5Mo\u20131.5Zr\u20130.3Si in transverse direction. There are three specimens in each group to get the average values. Geometrical shape and size of the specimen are shown in Fig. 2. Fig. 3 shows the macro-morphology of GSM in the longitudinal section. In the lower part, i.e., Ti\u20136Al\u20134V, large columnar grains grow epitaxially in the opposite direction of the heat flux and penetrate multiple deposited layers. The orientation of columnar grains is almost in line with the deposition direction. However, in the upper part, i.e., Ti\u20136.5Al\u20133.5Mo\u20131.5Zr\u20130.3Si, the direction of columnar grains is not parallel to the deposition direction but tilted to the right. The grain morphology in the gradient zone (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000648_978-3-642-17531-2-Figure12.5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000648_978-3-642-17531-2-Figure12.5-1.png",
        "caption": "Fig. 12.5. Planar manipulator with two degrees of freedom",
        "texts": [
            " The computed Cartesian TCP uncertainties retain the same \u201c 3 \u201d metric as the underlying base quantity , i.e. the computed positioning accuracy approximates the maximum possible Cartesian positioning deviations with respect to a given nominal value (with an approximate statistical certainty of 99.7%S ). Example 12.2 Planar manipulator with two degrees of freedom. 2 Note that the sensitivity coefficients have the physical dimension [cm/rad], so that the angular uncertainty must be converted to [rad]. 778 12 Design Evaluation: System Budgets Problem statement Fig. 12.5 shows a planar manipulator modified from that of Example 12.1 with an additional controlled sliding joint with degree of freedom l . For a certain class of command signals, a controller ensures a control accuracy of 0.9 (3 ) and 2 mm (3 )l . The system parameters are: 0 40 cml , [0, 40 cm]l , max 45 . Find the positioning accuracy of the tool center point (TCP) in Cartesian coordinates. Statistical performance model The Cartesian coordinates of the tool center point are determined by the two controlled manipulator axes and l via the following nonlinear geometric relation, shown here for the x-coordinate: 0 ( ) cos T x l l "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001126_s12555-011-9214-6-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001126_s12555-011-9214-6-Figure5-1.png",
        "caption": "Fig. 5. Experimental setup: DOB is applied to reject the external disturbances and the friction in the gear box.",
        "texts": [
            " A possible structure of GD(z) is 1 1 0 1 1 0 ... ( ) , ... n n n n D m m m b z b z b G z z a z a \u2212 \u2212 \u2212 \u2212 + + + = + + + (18) where m and n are the numbers of poles and zeros of Gn \u2013 1(z), respectively. a0, ..., am\u20131 and b0, ..., bn are the parameters to be optimized. They are initialized to the parameter values of Gn \u20131(z). 4.1. Conventional DOB design In this section, challenges in the implementation of DOB are discussed through a case study. The plant is Rotary Series Elastic Actuator [4], which is a simple DC motor system shown in Fig. 5. The DOB is applied to reject disturbances from the load side as well as the friction in a gear reducer. Since the DOB makes the system follow the nominal model by rejecting the disturbances and the model uncertainties, it is possible for the system to show the desired performance in a theoretical sense. For more detailed information on the system in Fig. 5, see [4]. For the design of DOB, a nominal model, Gn(s), and the corresponding uncertainty bound, W(s), are required. For this purpose, the frequency responses were obtained by experiments as shown in Fig. 6. The amplitude of the sinusoidal excitation was varied from 0.1V to 5V. Note that the frequency response depends on the input amplitude, which implies that the system is not linear. The nonlinear effects are to be treated as external disturbances and rejected by the DOB. The nominal model, Gn(s), can be obtained either 1) by averaging the data sets, or 2) based on a frequency response obtained by an appropriate input magnitude"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003793_j.mechmachtheory.2019.103764-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003793_j.mechmachtheory.2019.103764-Figure3-1.png",
        "caption": "Fig. 3. Diagram of GTF gearbox structure.",
        "texts": [
            " The sun gear is a floating part, which is splined with the input shaft and meshes with five circumferentially evenly distributed star gears. The star gears are designed with gear-bearing integration [24] . The star gears are internally supported by bearing and meshed with the ring gear, which is a semi-floating component and taken as the output end of the gear train, connected to the output shaft by bolts; the gravity of the entire gear box and the torque generated by the gear meshing is carried through planet carrier supported by elastic base. 3. Dynamic model of GTF transmission system Fig. 3 shows the structure diagram of GTF gearbox transmission system with elastic support base of planet carrier. Based on the elastic support model of the planet carrier in the GTF gearbox, the degree of freedom of the planet carrier is included in the system dynamics model. Fig. 4 shows the dynamic model of the GTF gearbox transmission system, a pure torsional nonlinear dynamic model of the input and output shaft and spline pairs is established by the lumped mass method. Since the gears of the star gearing system are fixed-axis rotation, an absolute coordinate system OXYZ is established for central floating components (sun gear, ring gear, planet carrier), and coordinate systems o i x i y i z i are built for each star gear, in which the coordinate center is the rotational center of each star gear, the direction of X \u2212 axis is along the radial direction of the floating member, and the Y \u2212 axis is tangential along the center floating member"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001130_j.jsv.2011.12.025-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001130_j.jsv.2011.12.025-Figure8-1.png",
        "caption": "Fig. 8. Normal approach of the flank.",
        "texts": [
            " The transition between the value sets is determined by a critical Reynolds number (Rec). Recr6000 refers to the low speed formulation, whereas RecZ9000 requires a high speed representation. The authors of the reference suggested a linear interpolation for Rec between the limits. Rec\u00bc _yRF u (40) The model solution initially assumes that the active tooth flanks are in contact. Consequently, the contact condition and mesh rigidity are controlled by the normal approach of the flanks (Ap (mm)) Eq. (41). Fig. 8 illustrates this variable. Considering the coordinate systems shown in Fig. 2, a positive value of Ap corresponds to a positive load between the active flanks (Wdyn40). Conversely, a negative normal approach with amplitude exceeding the backlash (2B cos f) causes a back flank contact (Wdyno0). Any other negative value of Ap corresponds to a no-contact situation. The relative position of the teeth then fixes the side (active or back) bearing the lubricant influence; the lubricant is assumed to be trapped on the thinnest gap side"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000738_tpas.1967.291749-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000738_tpas.1967.291749-Figure5-1.png",
        "caption": "Fig. 5. Nyquist diagrams-plot of F(jfr), fR = 0.1.",
        "texts": [
            " The per unit parameters of the machine are given in Table 1. The dashed line shown in Fig. 4 indicates the pull-out or maximum steady-state torque at the various operating speeds. Negative torque output denotes generator action. The continuous curve (contour) shown in Fig. 4 forms the boundary between stable and unstable regions of operation. More specifically, the contour connects all initial operating points for which the locus of F(jv) passes through the (-1,0) point. The Nyquist diagrams shown in Fig. 5 help to explain further the significance of this contour. The four plots of F(jv) shown in Fig. 5 correspond to the initial operating points indicated in Fig. 4 as (a), (b), (c), and (d). These operating points occur at a machine speed of O.1we electrical radians per second; in this case, the stator applied voltages would vary at 6 Hz. Also, when TO = 0.3 p.u., o0 = -0.199 rad; Te0- 0.24 p.u., 60 = -0.074 rad; Teo 0.18, 6o = 0.013 rad; Teo = 0, 50 = 0.21 rad. With Teo = 0.24 p.u., point (b), the locus of F(jv) shown in Fig. 5, passes through the (-1, 0) point as v varies from - to + co. Therefore, point (b) locates a point on the contour shown in Fig. 4. At the initial operating conditions wherein TeO = 0, point (d), and Teo = 0.18 p.u., point (c), the plot of F(jv) encircles the (-1, 0) point. The system is unstable at these operating conditions. However, with Teo = 0.3 p.u., point (a), the plot of F(jv) fails to encircle or pass through the (-1, 0) point; the system is stable. It is clear that in order to establish a complete contour it is necessary to determine the condition of loading, at each operating speed, which will cause the locus of F(jv) to pass through the (-1, 0) point"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002401_s11661-017-4164-0-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002401_s11661-017-4164-0-Figure3-1.png",
        "caption": "Fig. 3\u2014Schematic diagram showing locations where tensile and metallographic specimens were extracted from each Inconel 625 and Ti-6Al-4V build.",
        "texts": [
            " Additional details of the laser-based DED deposition process parameters and equipment used in the deposition process are described elsewhere.[19] After deposition of each layer, subsequent layer deposition either initiated immediately (0-second dwell time) or subsequent deposition did not initiate until after an additional dwell time of either 20 or 40 seconds. These interlayer dwell times were added to mimic the additional dwell times that would be required for the fabrication of larger components. Samples were extracted from a location 1 cm from the end of each Ti-6Al-4V and Inconel 625 build, as shown in Figure 3, and metallographically prepared for microstructural characterization. For the Inconel 625 builds, a 10 pct oxalic acid electrolytic etch (6 V, 20 seconds) was used to prepare samples for microstructural characterization. Ti-6Al-4V samples were etched using Kroll\u2019s reagent (92 mL DI water, 6 mL nitric acid, 2 mL hydrofluoric acid). Locations at the substrate-build interface, 5 mm from the substrate, 10 mm from the substrate, 20 mm from the substrate, 30 mm from the substrate, and 35 mm from the substrate were analyzed in order to provide location-specific microstructural information",
            " Hardness measurements were taken along the height of the build starting 5 mm below the substrate-build interface and extending to the top of each build in 5-mm increments. An applied load of 1000 g was used for both the Ti-6Al-4V and Inconel 625 builds. The microhardness measurements reported here were averaged from six measurements made at each height above the substrate analyzed. In each of the Ti-6Al-4V and Inconel 625 builds, flat tensile specimens that meet ASTM E8 standards[33] with gage dimensions of 1.7 mm 9 3 mm 9 6.58 mm were extracted from selected locations and orientations, as shown in Figure 3, using wire EDM machining. Within the builds, tensile specimens were extracted from two orientations. The \u2018\u2018longitudinal\u2019\u2019 oriented specimens were extracted with the long axis parallel to the deposition direction (x direction in Figure 3), and the \u2018\u2018transverse\u2019\u2019 oriented specimens were removed from the wall structure with the long axis parallel to the build direction (z direction in Figure 3). Tensile testing of each specimen was performed using an Instron model 4202 test frame with a 10-kN load cell (Instron model 2512-147). The specimens were tested at a constant loading rate and the strain rate averaged 0.002 and 0.001 s 1 for the Inconel 625 and Ti-6Al-4V specimens, respectively. During mechanical testing, digital image correlation (DIC) was used to analyze the localized strain. DIC is a non-contact method for measuring deformation fields. A uniform speckle pattern of white and black paint was applied to the gage region of each tensile specimen"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002828_aa543e-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002828_aa543e-Figure9-1.png",
        "caption": "Figure 9. The four types of sun gear under consideration. (a) Healthy sun gear, (b) distributed wear, (c) tooth root crack and (d) tooth missing.",
        "texts": [
            " An accelerometer (with a sensitivity of 100 mV g\u22121 and a frequency range of 0\u201310 kHz) and a shaft encoder (produced by Encoder Products Co. with 1 pulse per revolution) are used to capture the vibration and tacho signals simultaneously. The data are captured under speeded up conditions from 0 RPM to 3000 RPM within 8 s. The sampling frequency is set to be 7680 Hz to accommodate all the interesting frequency contents for this test rig. The whole setup arrangement is shown in figure\u00a08 [23]. In the experimental process, four types of sun gear are considered (three faulty), as shown in figure\u00a09. The vibrations in the time domain for all four types of sun gear are shown in figure\u00a010. In the following, for demonstration purposes, the vibration data from the tooth-missing fault (figure 9(d)) are used to establish the effectiveness of the proposed signal selection scheme. The physical parameters for the planetary gearbox are listed in table\u00a0 6, in which the gear teeth, number of planet gears and transmission ratio are given and calculated. The shaft of the sun gear is the input, while the shaft of the planet carrier is the output. In the experimental setup, the ring gear of the planetary gearbox is stationary and the sun gear is the input of the planetary gearbox system. Another very important calculation for the planetary gearbox is its characteristic orders"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000648_978-3-642-17531-2-Figure3.7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000648_978-3-642-17531-2-Figure3.7-1.png",
        "caption": "Fig. 3.7. Undamped eigenmodes under an explicit single-step method (only top half-plane shown)",
        "texts": [
            " For such cases, simulation using the state transition matrix\u2014allowable due to the generally linear description of MBSs (e.g. via the finite element method)\u2014 offers an ideal solution alternative (see Sec. 3.5). Eigenmodes of multibody systems One oft-overlooked difficulty appears in the course of simulating weakly-damped (or in the extreme case, undamped) oscillatory systems (harmonic oscillators). In particular, for multibody systems, high-frequency eigenmodes with vanishingly small damping are examined during sensitivity and robustness investigations to verify robust stability. Harmonic oscillator Fig. 3.7 shows two typical cases for a harmonic oscillator (undamped oscillations). In this example, the concept of absolute stability suggests that for the conjugate complex eigenvalues 2 2j , the step size h should be reduced until 2 2jh lies within the region of absolute stability. As this is already the case for the conjugate complex eigenvalues 1 1j , the question presents itself: does a simulation with 1 1jh deliver the correct result? The answer is: no! The true solution for this harmonic oscillator is 1 0( ) 0 sin( )y t y t , i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001006_s10846-014-0143-5-Figure14-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001006_s10846-014-0143-5-Figure14-1.png",
        "caption": "Fig. 14 Helicopter blade cross-section [155]",
        "texts": [
            " The next component, UT , is parallel to the hub plane and tangential to the blade in the direction of the blade rotational motion as seen in Fig. 13a and d. The last component, UR , lies on the hub plane and points radially pointing outward in the direction of and parallel to the blade, as seen in Fig. 13a and c. The total air velocity seen by the blade is given as U = \u221a U2 T + U2 P . At any time during flight, the blade experiences a pitch angle, \u03b6 = \u03b1b +\u03c6b, related to the angle of attack \u03b1b of the blade with respect to the airstream U , which approaches the blade at an inflow angle \u03c6b, as seen in Fig. 14. The lift and drag on the blade are determined through blade element analysis. By considering the blade as a two-dimensional airfoil, the lift and drag vectors at each blade element may be determined. The infinitesimal lift and drag of the blade element dr are given as: dL = 1/2\u03c1aU 2cbCl\u03b1\u03b1bdr (33) dD = 1/2\u03c1aU 2cbCddr (34) The forces perpendicular and parallel to the hub plane can be expressed in terms of the lifting and drag forces as follows: dF\u2016 = dL sin \u03c6b + dD cos \u03c6b (35) dF\u22a5 = dL cos \u03c6b \u2212 dD sin \u03c6b (36) Following the procedures from [13, 155], the total force on the blades parallel (F\u2016) and perpendicular (F\u22a5) to the hub plane can be expressed in terms of the air stream velocity components as: dF\u2016 \u2248 1 2 \u03c1cbCl\u03b1 ( \u03b6UT UP \u2212 U2 P ) dr + 1 2 \u03c1cbCDU2 T dr (37) dF\u22a5 \u2248 1 2 \u03c1cbCl\u03b1(\u03b6U2 T \u2212 UT UP )dr (38) The total pitch of the blade is given as \u03b6 = \u03b60 \u2212 \u03b61 cos \u03c8b\u2212\u03b62 sin \u03c8b, where \u03b60 is the collective pitch to control the thrust of the rotor and \u03b61 = Alon\u03b4lon, \u03b62 = Blat \u03b4lat are the linear functions of the pilot\u2019s lateral and longitudinal cyclic control stick inputs (\u03b4lat , \u03b4lon) and lateral and longitudinal control derivatives (Alon, Blat )"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000782_j.mechmachtheory.2012.11.006-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000782_j.mechmachtheory.2012.11.006-Figure3-1.png",
        "caption": "Fig. 3. Rotational (a) and translational (b) components of TE.",
        "texts": [
            " The two gears can be numbered arbitrarily and the reference frame overlapswith that of gear 1. This reference frame is fixed to the gear carrier, which can be fixed to the ground (conventional gear stage) or rotating (epicyclic gear stage). All the coordinate frames are chosen having no gear misalignment in the initial conditions. Dynamic TE is calculated at each timestep in the reference transverse plane at the pitch circles, therefore it is expressed as a relative displacement in the tangent direction. This relative displacement accounts for the following two contributions (Fig. 3): where and D DTE \u00bc DTEr \u00fe DTEt \u00f01\u00de DTEr is due to relative rotation of the gears and is given by: DTEr \u00bc \u03b81rpo1 \u00fe e\u03b82rpo2 \u00f02\u00de rpi \u00bc zi ez1 \u00fe z2 CD xrj j \u00f03\u00de TEr is due to relative translation in the tangential direction and is given by: DTEt \u00bc \u2212eCD\u00fe yr: \u00f04\u00de Angles \u03b8i in Eq. (2) are calculated between the actual x axes of the gear frames and the reference x axis, positive in the direction of the reference z axis, in the reference transverse plane (xryr) as shown in Fig. 4. The variable e in Eq. (2) is used to account for internal or external gears"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000888_j.oceaneng.2011.07.006-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000888_j.oceaneng.2011.07.006-Figure2-1.png",
        "caption": "Fig. 2. Schematic diagram of a simplified 3DOF ship moving in a horizontal plane.",
        "texts": [
            " The definition of the six degree-of-freedom motion of a marine vessel is shown in Fig. 1. However, the influence of roll and pitch motions on the dynamics of the ship is often neglected in the horizontal plane. Furthermore, since gravity and buoyancy is vertical to the horizontal plane, which have little influence on the motion of the horizontal plane, heave motion can also be neglected. Hence a simplified 3-DOF ship moving in the horizontal plane is discussed, whose schematic diagram is shown in Fig. 2. In the horizontal plane, a 3-DOF ship is modeled as follows in Fossen (2002): _Z \u00bc J\u00f0Z\u00deu M _u\u00feC\u00f0u\u00deu\u00feD\u00f0u\u00deu\u00fetd \u00bc t Y \u00bc Z 8>< >: \u00f01\u00de where u\u00bc \u00bdu,v,r T denotes the linear velocities in surge, sway and angular velocity in yaw. The vector Z\u00bc \u00bdx,y,c T denotes the position and orientation of the ship in earth-fixed coordinates. M\u00bcMB\u00feMA is a matrix of inertia including added mass effects, where MB is the body mass matrix and MA are the added mass matrix of the ship. C\u00f0u\u00de is the Coriolis and centripetal matrix with the following form: C\u00f0u\u00de \u00bc 0 0 m22v 0 0 m11u m22v m11u 0 2 64 3 75 Matrix J represents the kinematic transformation from bodyfixed coordinates to earth-fixed coordinates J\u00f0Z\u00de \u00bc cosc sinc 0 sinc cosc 0 0 0 1 2 64 3 75 t\u00bc \u00bdtutvtr T is a vector of control inputs and td denotes the external disturbances from ocean waves and currents"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002146_j.surfcoat.2017.01.116-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002146_j.surfcoat.2017.01.116-Figure3-1.png",
        "caption": "Fig. 3. Boundary conditions of the numerical model.",
        "texts": [
            "13 mm at the surface domain. The solution is performed with the direct PARDISO = 0 T, MN = 0), (b) with only a steady magnetic field (B = 0.8 T, MN= 0), (c) with an nd field (B = 0.8 T, MN = \u22121). solver associated with generalized-\u03b1 temporal solver (the time step is selected by the solver automatically). The computation time is about 16 h for a LMI layer of 25 mm long. The parameters for the nozzle and carrier gas are given in Table 2. The other required boundary conditions are illustrated together in Fig. 3. The physical properties of the molten pool and reinforcement particles are summarized in Table 3 [40,44\u201346]. The temperature-dependent properties of the AISI 316L steel are illustrated in Fig. 4 [47\u201349]. The velocity distribution in the longitudinal section of the molten pool is shown in Fig. 5.MN represents the direction of thedirectional Lorentz force. When MN = 1, the direction of Lorentz force is opposite to the gravity force. When MN = \u22121, the direction of Lorentz force coincides with the gravity force"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001550_rnc.3215-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001550_rnc.3215-Figure1-1.png",
        "caption": "Figure 1. Planar endgame geometry.",
        "texts": [
            " The kinetic and potential energies of the system are calculated and used to derive the equations of motion. Then, the generalized forces are derived using flight loads to construct the dynamic aeroelastic model. Full nonlinear equations of the air vehicle and target motions that is entitled as engagement kinematics is described in this section. As described earlier, the IGC system only improves the performance of the endgame phase while it does not noticeably affect the midcourse phase [9]. The IGC design for the endgame phase is considered in this paper. The planar endgame geometry is shown in Figure 1. The Cartesian inertial reference frame is depicted as XI \u2013OI \u2013ZI axes. The subscripts FV and AT are used to denote the flight vehicle and the aerial target, respectively. The range between FV and AT is r ; the line of sight (LOS) angle with respect to inertial reference is denoted by ; the flight path angle, speed, and normal acceleration of the flight vehicle are denoted by F V ; VF V , and aF V , respectively. The flight path angle, speed, and normal acceleration of the aerial target are denoted by AT , VAT , and aAT , respectively",
            " Note that Vr must be negative in the endgame scenario and when it crosses zero, the endgame should be terminated. It is assumed that the aerial target is flying at constant speed and carries out only lateral maneuvers. The target lateral maneuvers are bounded and considered as the first-order linear dynamic, with time constant AT . To obtain the state space equations for the nonlinear kinematics, one can differentiate (2) with respect to time, which leads to R D 1 r aF V C VF V P cos. F V / C aAT C VAT P cos. AT C / Pr r P : (5) As it is shown in Figure 1, F V D \u02db, where and \u02db are the flight vehicle\u2019s pitch angle and the angle of attack, respectively. Substituting (1) into (5), the LOS rate dynamics can be reformulated as follows:\u00b4 R D 1 r aF V C 2VF V P cos. \u02db / C aAT C 2VAT P cos. AT C / P D q (6) where q is the angular velocity of the flight vehicle. The dynamic model of the elastic flight vehicle can be obtained based on the governing equations of motion. Based on the Lagrangian approach, the kinetic and potential energy of the system and the Rayleigh dissipation damping function are calculated and used to derive the equations of motion. Then, the generalized forces are derived using flight loads to construct the dynamic aeroelastic model [11]. Copyright \u00a9 2014 John Wiley & Sons, Ltd. Int. J. Robust Nonlinear Control (2014) DOI: 10.1002/rnc Using the coordinate systems depicted in Figure 1, the flight vehicle planar dynamics are expressed. The flight vehicle equations of motion are derived in the rotating body-fixed coordinate frame Xb F V Zb , where the Xb axis is aligned with the flight vehicle\u2019s longitudinal axis. In this research, only the first aeroelastic mode is considered in the design and analysis. In order to analyze the stability of a flexible body at supersonic flow, the first vibration mode can be considered [14]. Higher elastic modes have high natural frequencies and very low amplitudes and have no remarkable effect on control design and stability analysis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002120_j.mechmachtheory.2015.09.010-Figure19-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002120_j.mechmachtheory.2015.09.010-Figure19-1.png",
        "caption": "Fig. 19. Finished gears.",
        "texts": [
            " There are two machine tool control methods; one is the velocity control based on the NC platform of ARM & DSP & FPGA [31] with the linkage model of Eq. (40). The other control method is the position control based on the CNC system with the linkage model of Eq. (38). Here, the second method was taken: the cutting processes were implemented with the help of a numerical control gear shaping machine based on the SINUMERIK 840D system. Fig. 18 shows the processing of the drive gear (a) and the driven gear (b). Fig. 19 shows the finished drive gear (a) and driven gear (b), where the tooth profile of each finished gear is the same as the corresponding tooth profile shown in Fig. 17. The surface roughness of the finished gears seems fine in Fig. 19, while the manufacturing precision still needs further investigation. Fig. 20 shows that the two gears are in a good contact state and they could roughly meet the design requirement. However, further research of an effective test method is needed. In combination with the principles of shaping non-circular gears, kinematic relation of the machine, and the manufacturing processes, this paper presented a 3-linkage model with an equal arc-length cutting method involving feed. Additionally, the feeding parameter settings, stock design method, retracting interpolation, and cutter datum presetting relating to the process were discussed in this paper"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001183_1077546311403791-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001183_1077546311403791-Figure1-1.png",
        "caption": "Figure 1. Model of the test rig; (a) Front view; (b) Side view of including gear meshing stiffness and damping.",
        "texts": [
            " To meet the objectives in the present study, a nine DOF model is developed with the following features: . Representation of the drive and load inertias . Representation of the gear inertias . Drive and load shaft flexibilities and damping . The effect of the transmission path between the gear shaft and the accelerometer . Representation for the tooth root crack effect . Representation for the gear TE The considered model consists of two gears on two shafts which are connected to a load and driver, as illustrated in Figure 1. The model includes four inertias; I1 and I2 represent the gears, and Il and Id represent the load and the driver. Torsional and transverse stiffnesses and dampings of the shafts are included in this model. Five masses are included in the model; m1 and m2 represent the gears,m3 andm4 represent the foundation and bearings, and mp represents the plate where the accelerometer is mounted. Due to the symmetry in the gearbox, each shaft transverse stiffness is modeled as one spring attached to the bearing, k1 and k2 in Figure 1. Similarly the shaft transverse dampings are modeling as viscous dampers as c1 and c2. The two bearing foundations are connected to each other by spring k34 and damper c34. Mass m3 is supported on the main base by a spring k3 and damper c3. Mass m4 is supported on the main base by a spring k4 and damper c4. The plate mass mp is supported on mass m3.The two couplings connections between the shafts, and the load and the drive are modeled as torsional stiffnesses, kt1 and kt2, and torsional dampings, ct1 and ct2, The model assumes that the transverse vibration of the gears and all masses are taken along the gear line of action. From Figure 1, the following equations are derived Id \u20ac d \u00fe ct1\u00f0 _ d _ l \u00de \u00fe kt1 \u00f0 d l \u00de \u00bc Td \u00f01\u00de I1 \u20ac 1 \u00fe ct1 \u00f0 _ 1 _ d \u00de \u00fe kt1\u00f0 1 d \u00de \u00bc WR1 \u00f02\u00de I2 \u20ac 2 \u00fe ct2 \u00f0 _ 2 _ l \u00de \u00fe kt2\u00f0 2 l \u00de \u00bcWR2 \u00f03\u00de Il \u20ac l \u00fe ct2\u00f0 _ l _ 2\u00de \u00fe kt2 \u00f0 l 2\u00de \u00bc Tl \u00f04\u00de at LAURENTIAN UNIV LIBRARY on March 3, 2013jvc.sagepub.comDownloaded from m1 \u20acy1 \u00fe c1\u00f0 _y1 _y3\u00de \u00fe k1\u00f0 y1 y3\u00de \u00bcW \u00f05\u00de m2 \u20acy2 \u00fe c2\u00f0 _y2 _y4\u00de \u00fe k2\u00f0 y2 y4\u00de \u00bc W \u00f06\u00de m3 \u20acy3 \u00fe c34\u00f0 _y3 _y4\u00de \u00fe k34\u00f0 y3 y4\u00de \u00fe c1\u00f0 _y3 _y1\u00de \u00fe k1\u00f0 y3 y1\u00de \u00fe cp\u00f0 _y3 _yp\u00de \u00fe kp\u00f0 y3 yp\u00de \u00fe c3 _y3 \u00fe k3y3 \u00bc 0 \u00f07\u00de m4 \u20acy4 \u00fe c2\u00f0 _y4 _y2\u00de \u00fe k4\u00f0 y4 y2\u00de \u00fe c34\u00f0 _y4 _y3\u00de \u00fe k34\u00f0 y4 y3\u00de \u00fe c4 _y4 \u00fe k4y4 \u00bc 0 \u00f08\u00de mp \u20acyp \u00fe cp\u00f0 _yp _y3\u00de \u00fe kp\u00f0 yp y3\u00de \u00bc 0 \u00f09\u00de where W is the dynamic meshing force given by W \u00bc km\u00f0 1R1 2R2 \u00fe y2 y1\u00de \u00fe cm\u00f0 _ 1R1 _ 2R2 \u00fe _y2 _y1\u00de \u00fe kmxE \u00fe cm _xE \u00f010\u00de where xE and _xE are the displacement and velocity excitations of the TE (Lee et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000050_nme.2959-Figure24-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000050_nme.2959-Figure24-1.png",
        "caption": "Figure 24. Computational out-of-plane displacement.",
        "texts": [
            " These stress maps show that a compressive stress is formed in front of the fusion zone, Copyright 2010 John Wiley & Sons, Ltd. Int. J. Numer. Meth. Engng 2011; 85:84\u2013106 DOI: 10.1002/nme whereas a tensile stress is developed at the back of the fusion zone, and is mainly determined by the thermal expansion effects. The residual y-displacement observed in the plate after the experiment is shown in Figure 23, where flatness measures at the top face are given. This measure can be compared with results from computations given in Figure 24. The value of 0.7 mm observed experimentally can be compared with the value of 0.5 mm calculated by simulation. Very good agreement between the FEM Copyright 2010 John Wiley & Sons, Ltd. Int. J. Numer. Meth. Engng 2011; 85:84\u2013106 DOI: 10.1002/nme results and experimental measurements was observed, which gives confidence in the proposed FE model. In this section, the simulation of the construction of a titanium wall by SMD is presented. The same geometry, material properties and process parameters than in the previous example were Copyright 2010 John Wiley & Sons, Ltd"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000123_1.4003088-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000123_1.4003088-Figure7-1.png",
        "caption": "Fig. 7 Test bed fo",
        "texts": [
            "64 Fault Level III 6.30\u00d71.26 2.82\u00d71.41 1.41\u00d71.41 0.45\u00d70.90 le roller: \u201ea\u2026 bearing with housing, \u201eb\u2026 s, \u201ec\u2026 free body diagram, and \u201ed\u2026 bond ts ing int JANUARY 2011, Vol. 133 / 011102-5 of Use: http://www.asme.org/about-asme/terms-of-use a t d w O r r s t e b t b v L b t s s A s p 5 fi z b r r r r be 0 Downloaded Fr ffect the response since faults are not stationary with respect to he load zone. Here, the model is simulated with ORF located own at the load zone Experiments were conducted on the test rig shown in Fig. 7 ith three types of rolling element bearing faults IRF, BF, and RF. The test rig consists of a rotating shaft supported by two olling element bearings Table 1 . A three-phase induction motor otates the shaft through a beam coupling. Bearing loaders apply tatic radial loads to bearings, and a magnetic loader applies rotaional loads to the shaft through a gearbox and belts. Acceleromters measure the vertical and horizontal vibrations of the outoard bearing housing. Eddy current proximity probes measure he vertical and horizontal displacements of the shaft close to the earing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003301_j.mechmachtheory.2019.01.014-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003301_j.mechmachtheory.2019.01.014-Figure1-1.png",
        "caption": "Fig. 1. Model of machine tool table system.",
        "texts": [
            " Moreover, the computational and experimental results are compared to validate the proposed model. Based on the analysis of piecewise smooth interface forces, dynamic equations are established to investigate the nonlinear vibration behaviors and deformation characteristics of the feed system. The coupling effects of excitation amplitude and variation of screw-nut position on dynamic behaviors and stability are investigated from amplitude-frequency curve, 3-D frequency spectrum, largest Lyapunov exponent, waveform, phase diagram, and Poincare section. As shown in Fig. 1 , a typical feed system of CNC machine tool is mainly composed of a worktable, linear guides, ball bearing units, ball screw, and motor. The cutting force is the vector sum of three perpendicular components: feed force, normal force, and passive force [34] . To analyze the dynamic behaviors of the multi-degree-of-freedom system, the cutting force F sin \u03c9t is resolved into three forces F x sin \u03c9 t, F y sin \u03c9 t , and F z sin \u03c9 t , and two moments M x = ( h + 0.5 b ) F y sin \u03c9t and M y = ( h + 0.5 b ) F z sin \u03c9t , which act on the mass center of worktable"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002004_1.4028532-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002004_1.4028532-Figure3-1.png",
        "caption": "Fig. 3 Ellipse creation on a prismatic Miura-base pattern. (a) Ellipse through three points, (b) longitudinal axes projection, (c) base and ellipse parameters, and (d) lower and upper bounds of u .",
        "texts": [
            " This forms a PQ mesh and allows simple simulation of pattern folded motion. Reducing the CC geometry to an assembly of planar rigid origami plates also removes the need to consider local curvature of the projected elliptical surface. These two stages, deemed the ellipse creation and rigid subdivision stages, respectively, are used to create parametrizations for rigid-foldable CC geometry. 3.1 Ellipse Creation. An elliptical curve is defined through three sequential zigzag points in a prismatic Miura-base pattern, shown in Fig. 3(a). Equivalent ellipses can be defined through zigzag creases to either side of the initial ellipse, and a curved surface projected between them. This projection is along the longitudinal folded axes of the base pattern, shown in Fig. 3(b). This process successfully creates a developable, CC surface for two reasons: any specified elliptical curve will form the intersection of some cutting plane and a cylindrical or conical developable surface, and the folded axes of a prismatic origami pattern form a reflection in the plane in which the zigzag nodes lie. The surface developed in this way is deemed a CC Miura pattern. The process for determining the ellipse in a CC-Miura pattern is as follows. The uj \u2013 vj plane is defined as coplanar with three jth zigzag nodes",
            " The three known zigzag points do not provide enough information to find the four ellipse coefficients and a unique ellipse, rather 121404-2 / Vol. 136, DECEMBER 2014 Transactions of the ASME Downloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use they specify a family of possible elliptical curves. One additional parameter must be specified to determine a unique ellipse. This is defined as the gradient parameter u, which is the initial gradient of the elliptical curve in the u0 \u2013 v0 plane, shown in Fig. 3(c). By defining u in addition to the base pattern geometry, a unique ellipse can be found from the following equations: h \u00bc B=2 (2) g \u00bc 2C2 \u00bd4C B tan u (3) c \u00bc C g (4) d \u00bc B=2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1=\u00f01 g2 c2 \u00de r (5) where B \u00bc 2b sin\u00f0gZ=2\u00de and C \u00bc b cos\u00f0gZ=2\u00de (6) Gradient parameter u is limited to minimum and maximum bounds, umin and umax. The lower and upper limits of u correspond to minimum and maximum values of coefficient g, at g\u00bc 1 and g\u00bc 0, respectively, shown in Fig. 3(d). Substituting these values of g into Eq. (3) allows the bounds to be determined as a function of the prismatic base pattern geometry as follows: umin \u00bc 4C=B;when g! 1 (7) and umax \u00bc p=2; when g \u00bc 0 (8) Note that an ellipse with gradient u \u00bc umin at g! 1 is equivalent to a parabola through the three original zigzag points. For geometry creation purposes, it is often more convenient to express Eq. (1) as a parametric function of t, where ( tlim t tlim) u0 \u00bc g\u00fe c cos t (9) v0 \u00bc h\u00fe d sin t (10) tlim \u00bc arctan cB 2dg (11) It is possible to unroll the elliptical curve of the initial projected curved surface in order to obtain a crease pattern"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003346_j.mechmachtheory.2019.103671-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003346_j.mechmachtheory.2019.103671-Figure1-1.png",
        "caption": "Fig. 1. Arrangement of the planer four-bar linkage for path generation.",
        "texts": [
            " The organization of the remainder of this paper is as follows: In Section 2, the use of Fourier coefficients for representing a planar curve is reviewed. In Section 3, the formulation of the proposed synthesis equations is presented. Thereafter, the preprocessing method to build the relationship between the points of the prescribed path and the input angle is presented in Section 4. The synthesis procedure and error analysis of the proposed method are presented in Section 5. In Section 6, the efficiency and applicability of the proposed method is demonstrated by solving five examples. Finally, conclusions are drawn in Section 7. Fig. 1 shows a path generating four-bar linkage ABCD with the various design parameters that are relevant to the path generation task. Here, P is the coupler point, \u03b2 is the angle made by the frame with the x-axis, \u03d5 and \u03d50 are the respective the input angle and initial angle of the input link, d, a, b, and c are the lengths of the frame, input, coupler, and output links, respectively, and f and \u03b1 define the position of the point on the coupler plane that generates the path. \u03b8 is the angle made by the coupler BC with the frame AD in a given configuration of the mechanism"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000236_j.mechmachtheory.2010.06.004-Figure16-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000236_j.mechmachtheory.2010.06.004-Figure16-1.png",
        "caption": "Fig. 16. New standard asymmetric elliptic cuter AE1.",
        "texts": [],
        "surrounding_texts": [
            "For the discussions and suggestions I wish to thank Prof. Pauli Pedersen."
        ]
    },
    {
        "image_filename": "designv10_5_0000755_s00170-013-5102-y-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000755_s00170-013-5102-y-Figure3-1.png",
        "caption": "Fig. 3 Model and mesh generation",
        "texts": [
            " The temperature at a selected point (located in the midline, 8 mm away from current top face) was chosen as reference temperature. After the deposition of a layer, the component was cooled in air until the reference temperature dropped to the threshold value, and then the deposition of the next layer started. Besides, the reverse deposition pattern was applied in the study. Adjacent layers were deposited along reverse directions. 3 Modeling and simulation procedure 3.1 Geometric model The geometric model and finite element meshes are shown in Fig. 3. The x direction is the welding direction, namely, the longitudinal direction; the y direction is the throughthickness direction; and the z direction is the depositing direction, namely, the transversal direction. Both the deposited component and base plate are fully meshed with hexahedral elements for the five-layer trial calculation in the calibration. The element birth and death (activation and deactivation) technique is used to simulate material deposition. To realize the actual temperature history, the simulation strictly follows the time sequence of experimental deposition"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000024_0278364909104296-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000024_0278364909104296-Figure2-1.png",
        "caption": "Fig. 2. The sagittal (left) and frontal (right) planes of a hipped three-dimensional bipedal robot. Note that leg splay angle is a constant modeling parameter.",
        "texts": [
            " Although we cannot analytically calculate this map to determine its stability about x , we can numerically approximate it through simulation, allowing us to analyze orbit stability by the map\u2019s linearization, Pk . Based on discrete linear system theory, we then know that a k-periodic hybrid orbit is locally exponentially stable if and only if the eigenvalue magnitudes of Pk are strictly within the unit circle. For the numerical details we refer the interested reader to Goswami et al. (1996). We now construct the model of a four-DOF bipedal robot with a hip and splayed legs (Figure 2). Although this is a three-dimensional extension of the two-dimensional compassgait biped seen in the sagittal plane of Figure 2, it is important to note that the three-dimensional model does not at TEXAS SOUTHERN UNIVERSITY on October 15, 2014ijr.sagepub.comDownloaded from have stable passive walking gaits down slopes. We, therefore, use reduction-based control on this serial-chain robot to construct pseudo-passive three-dimensional walking gaits from the sagittal plane. This model\u2019s hybrid control system is 4D : x f4D x g4D x u x D4D G4D x 4D x x G4D The configuration space for the 4-DOF biped can be represented by Q4D SO 3 1 (Spong and Bullo 2005)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002243_j.matpr.2016.03.021-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002243_j.matpr.2016.03.021-Figure1-1.png",
        "caption": "Fig. 1 Schematic of fatigue specimen\u2019s orientations",
        "texts": [
            " Table1. Chemical composition of the EOS Titanium Ti64 ELI powder % Al V Fe O C N H Ti Norm value 5.50 \u00f7 6.50 3.50 \u00f7 4.50 <0.25 <0.10 <0.08 <0.06 <0.012 Balance Actual value 6.08 3.90 0.25 0.085 0.007 0.006 0.002 Balance The miniature specimens for fatigue testing (5.2 mm x 5.2 mm in cross-section and 18 mm in length) were produced according to three different orientations of their long axis with respect to build direction z to evaluate the potential effect of material anisotropy on fatigue, see Fig. 1. A multi-directional scan strategy was used, i.e. the laser scan direction was rotated by 67\u00b0 in the X-Y plane every layer in order to reduce the content of residual stresses. All DMLS fatigue specimens were stress relieved by a heat treatment in air (at 380 \u00b0C for 8 hours). Metallographic specimens were cut from fractured fatigue test specimens with three orientations according to X, Y and Z-axis. The microstructure was observed by light microscope Zeiss Axio Observer Z1M on 10% HF etched metallographic surfaces",
            " The average porosity of DMLS parts was 0.24 %. The size distribution was characterized by 52 % of pores with a diameter in the range from 0 to 5 \u03bcm and the largest local pores reached the size of 120 \u03bcm. The results of the fatigue testing are shown in Fig. 3, in terms of the S-N plot of stress amplitude vs. log number of cycles to failure. The target fatigue lifetime was set at 2 x 106 cycles. Fatigue test results showed that the specimens subject to stress directed parallel to the layers (X-Y and Y-Z of Fig. 1) exhibited basically identical fatigue behavior. The fatigue lifetime of specimens oriented in the vertical direction (Z-X in Fig. 1) is significantly lower. This result is in agreement with the finding published in [5, 7] where the strong effect of interlayer defects on the initiation of fatigue cracks was pointed out is assumed. A fine \u03b1\u02b9-martensitic microstructure could retard the propagation of the small cracks, and thus offer great resistance to fatigue loading but subsurface porosity and surface roughness decrease the fatigue life of the DMLS titanium alloy [7]. Fatigue crack initiation occurred always at the surface due to the applied bending loading and due the surface roughness"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001286_tec.2017.2651034-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001286_tec.2017.2651034-Figure6-1.png",
        "caption": "Fig. 6. Modal shapes and frequencies. (a) Mode 1: 1267 Hz. (b) Mode 2: 2460 Hz. (c) Mode 3: 3259 Hz. (d) Mode 4: 5056 Hz.",
        "texts": [
            " The detailed modeling process of stator assembly is shown in [20] and the relative errors between calculated modal frequencies and those from test are all below 5%. It is noted that the motor studied in this paper has a relatively short end winding. Hence, in the equivalent stator model, the end winding is neglected, as shown in Fig. 9. This simplication, however, is probably not appropriate for distributed winding machines which have a long end winding. Therefore, the equivalent model of end winding in distributed winding machines should be considered. Fig. 6 shows the modal shapes and frequencies when the motor is mounted in the test bed. The winding is hided to show the shapes more clearly. After the force is transferred from electromagnetic mesh to structural mesh, MSM is employed to calculate the vibration. The principle of MSM is described in [21]. Considerable calculation quantity is required for vibration calculation during run-up, especially when the vibration in high-frequency band is concerned. For this reason, MSM is recommended for vibration prediction when the stator structure is linear",
            " 1500 2000 2500 3000 3500 4000 4500 5000 R o ta ti o n al s p ee d ( rp m ) 100002000 4000 6000 80000 Frequency (Hz) R ad ia l fo rc e d en si ty ( ) 1500 2000 2500 3000 3500 4000 4500 5000 R o ta ti o n al s p ee d ( rp m ) R ad ia l fo rc e d en si ty ( ) Frequency (Hz) 0885-8969 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. Fig. 7 shows the calculated and tested vibration during runup. Both results show that main vibration orders include the 6kth orders and those around fc, which can almost find their corresponding force orders in Fig. 4(a). In particular, when the force is close to Mode 2 and Mode 3 shown in Fig. 6, resonance occurs with significant vibration observed. Fig. 8 compares the calculated 24th and 42nd order vibration with the tested results. These two order vibrations show large amplitude in low and medium frequency band. The variation trend in simulation and test is almost the same. It is found that the amplitude of the 24th order vibration increases with the speed because the corresponding 24th order force gets closer to Mode 2 when the speed increases. However, the 42nd order vibration rises sharply around 3500 rpm and 4600 rpm when the corresponding 42nd order force respectively passes through Mode 2 and Mode 3, as shown in Fig",
            " In addition, the frequency response function (FRF) between nodal force and vibration can be obtained by modal information. Thus, noise transfer function (NTF) between nodal force and sound pressure at a certain field point is acquired by combining FRF and ATV(f). Fig. 10 shows the average of NTFs between all of excitation points and acoustic field point shown Fig. 9. The modal analysis is conducted in ANSYS and ATV(f) is obtained via BEM in LMS Virtual.lab. The dominating peaks of NTF can be explained by the stator modes which are listed in Fig. 6. It is found the peak frequencies coincide with stator modal frequencies. But the amplitude of the peaks are also relevant with sound radiation efficiency, which depends on geometry of the vibrating surfaces, acoustic treatment of the surfaces, field point location, frequency and physical properties of the acoustic medium. 0885-8969 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001006_s10846-014-0143-5-Figure12-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001006_s10846-014-0143-5-Figure12-1.png",
        "caption": "Fig. 12 Helicopter blade pitching motion",
        "texts": [],
        "surrounding_texts": [
            "where \u03c9\u0302B is the skew-symmetric matrix representation of the angular rate vector. The orientation dynamics are derived using Eq. 10 [70, 138, 155, 177] as: \u0307 = \u23a1 \u23a3 \u03c6\u0307 \u03b8\u0307 \u03c8\u0307 \u23a4 \u23a6 = ( )\u03c9B (11) where ( ) is given as: ( ) = \u23a1 \u23a3 1 sin \u03c6 tan \u03b8 cos \u03c6 tan \u03b8 0 cos \u03c6 \u2212 sin \u03c6 0 sin \u03c6/ cos \u03b8 cos \u03c6/ cos \u03b8 \u23a4 \u23a6 (12) 3.3 Complete Helicopter Dynamics The position and velocity dynamics together with the orientation dynamics form the complete helicopter equations of motion in terms of the helicopter\u2019s bodyfixed frame forces and moments, and are given as: p\u0307I = vI v\u0307I = 1 m Rf B R\u0307 = R\u03c9\u0302B I \u03c9\u0307B = \u2212\u03c9B \u00d7 (I\u03c9B) + \u03c4B (13) with pI and vI denoting the position and linear velocity of the helicopter center of gravity (CG) with respect to an earth-fixed reference frame. In addition to the forces acting on the body, the effect of gravity on the body frame is considered by transforming the gravity vector from the inertial frame, gI = [0 0 g]T , to body-frame, gB = RT (t)gI . Expanding the Newton-Euler equations of motion in Eq. 7 and adding the force of gravity, the translational velocity and angular rate equations of motion with respect to the body-fixed frame are given as: u\u0307 = rv \u2212 qw + R31g + X/m (14) v\u0307 = pw \u2212 ru + R32g + Y/m (15) w\u0307 = qu \u2212 pv + R33g + Z/m (16) p\u0307 = qr(Jyy \u2212 Jzz)/Jxx + L/Jxx (17) q\u0307 = pr(Jzz \u2212 Jxx)/Jyy + M/Jyy (18) r\u0307 = qp(Jxx \u2212 Jyy)/Jzz + N/Jzz (19) The position and orientation trajectory dynamics may be obtained by integrating the rigid body dynamics in Eqs. 14 \u2013 19 through the kinematic equations in Eq. 13. The inertial position can be found given the body velocities through p\u0307I = vI = RvB . The Euler rates can be found through the relationship \u0307 = ( )\u03c9b in Eq. 11. The final position and orientation dynamics are given as: x\u0307I = c\u03b8 c\u03c8u + (s\u03b8 s\u03c6c\u03c8 \u2212 c\u03c6s\u03c8 )v + (s\u03b8 c\u03c6c\u03c8 + s\u03c6s\u03c8 )w (20) y\u0307I = c\u03b8 c\u03c8u + (c\u03c6c\u03c8 + s\u03c6s\u03c8s\u03b8 )v + (c\u03b8 s\u03c8s\u03b8 \u2212 c\u03c8s\u03c6)w (21) z\u0307I = \u2212s\u03b8u + c\u03b8 s\u03c6v + c\u03c6c\u03b8 x (22) \u03c6\u0307 = p + s\u03c6t\u03b8 q + c\u03c6t\u03b8 r (23) \u03b8\u0307 = c\u03c6q \u2212 s\u03c6r (24) \u03c8\u0307 = s\u03c6 c\u03b8 q + c\u03c6 c\u03b8 r (25) 3.4 Forces and Torques A result of the main and tail rotor rotation is the generation of thrust and torques acting on the helicopter body. Gravity is also acting on the helicopter body, and must be taken into account while determining the total body forces on the helicopter. The forces and torques acting on the helicopter are functions of the main rotor thrust, TMR , tail rotor thrust, TT R , and the main rotor cyclic angles, a1 and b1 [70]. The torques acting on the helicopter body are a result of the forces being offset from the center of gravity. The relation below defines the relationship between the force (F ), distance (d) and the resultant torque: \u03c4 = Fd (26) The thrust generated by the main rotor results in a translational force on the helicopter. This thrust is perpendicular to the Tip-Path-Plane (TPP) which is the plane formed by the blade tips. This force vector can be decomposed into components along the bodyframe x, y, and z axis. The magnitude of the thrust vector is represented as TMR . The components of the main rotor forces as a result of the blade flapping and thrust are given by: FB MR = \u23a1 \u23a3 XMR YMR ZMR \u23a4 \u23a6 = \u23a1 \u23a3 \u2212TMR sin a1 \u2212TMR sin b1 \u2212TMR cos a1 cos b1 \u23a4 \u23a6 (27) Unlike the main rotor, the tail rotor generates a force perpendicular to the rotor hub. The pilot has no control of the flapping angles. As a result, the resulting force component is in the y-direction only. The components of the tail rotor thrust are given by: FB T R = \u23a1 \u23a3 XT R YT R ZT R \u23a4 \u23a6 = \u23a1 \u23a3 0 TT R 0 \u23a4 \u23a6 (28) The gravitational force on the helicopter is represented in the inertial Earth-fixed frame in the downward direction given as FI g = [0 0 mg]T . This force may be expressed as components with respect to the body-fixed frame, given as follows [13, 70, 106]: FB g = \u23a1 \u23a3 Xg Yg Zg \u23a4 \u23a6 = R( )F I g = \u23a1 \u23a3 \u2212 sin \u03b8mg sin \u03c6 cos \u03b8mg cos \u03c6 cos \u03b8mg \u23a4 \u23a6 (29) For the main rotor torque, the main rotor offset distance from the helicopter center of gravity is defined as [lm, ym, hm]T [154]. The resulting torque contributed by the main rotor is given as: \u23a1 \u23a3 LMR MMR NMR \u23a4 \u23a6 = \u23a1 \u23a3 YMRhm \u2212 ZMRym \u2212XMRhm \u2212 ZMRlm XMRym + YMRlm \u23a4 \u23a6 (30) For the tail rotor torque, the distance offset of the tail rotor from the helicopter center of gravity is defined as [lt , 0, ht ]T . The resulting torque contributed by the main rotor is given by: \u23a1 \u23a3 LT R MT R NT R \u23a4 \u23a6 = \u23a1 \u23a3 YT Rht 0 \u2212YT Rlt \u23a4 \u23a6 (31) The main rotor generates an aerodynamic drag as it rotates. This drag results in a torque, QMR [70, 100], which is perpendicular to the TPP and can be decomposed into components along the body frame by projecting the torque vector on to the hub plane. The resultant components are given as: \u23a1 \u23a3 LD MD ND \u23a4 \u23a6 = \u23a1 \u23a3 QMR sin a1 \u2212QMR sin b1 QMR cos a1 cos b1 \u23a4 \u23a6 (32) 3.5 Main and Tail Rotor The helicopter receives most of its propulsive force from the main and tail rotors. The aerodynamics of the rotors, especially that of the main rotor, are highly nonlinear and complex. In order to reduce the complexity and simplify the dynamics for modeling and control design purposes, a number of assumptions are considered [13, 32, 33, 154, 155] as follows: rotor blades are rigid in both bending and torsion, small flapping angles, uniform inflow across rotor blade, no inflow dynamics used, effects of coning, due to flapping angles, is constant, forward velocity effect omitted, coupling ratio for pitch-flap is disregarded, and constant rotor speed. The dynamics of the main and tail rotors are controlled by input control commands. However, they are also affected by the motion of the helicopter. These control commands are represented by uc = [\u03b4lon \u03b4lat \u03b4ped \u03b4col]T . The thrust magnitudes of the main and tail rotors are controlled by the collective commands \u03b4col and \u03b4ped , respectively. The main rotor blade flapping dynamics is controlled by the cyclic inputs \u03b4lon and \u03b4lat , which control the tilt of the TPP. Control of the propulsive forces is achieved by controlling the direction and inclination of the TPP. Thrust produced by the rotor blades is perpendicular to the TPP. The orientation of the TPP is dependent on main rotor blade flapping dynamics. During rotation, the blades exhibit a flapping motion, a lead-lagging motion, and a pitching motion of the blade, as shown in Figs. 10, 11, and 12 respectively. These motions make-up the rotor blade DOF and are denoted by \u03b2, \u03be , and \u03b6 , respectively. The aerodynamic forces on the rotor blade depend on the orientation of the blade at any time. The blade\u2019s pitch angle, \u03b6 , affects the lift and drag of the blade elements. The flapping angle of the blade affects the inertial forces on the blade along the direction of the main rotor thrust vector. Determining the lift and drag generated by the main rotor requires consideration of the blade\u2019s flapping motion, \u03b6 , helicopter forward velocity with respect to the air, also known as free stream velocity denoted by V\u221e, rotation of the blade about the shaft in the form of angular velocity, , and also the inflow velocity of air through the rotor [155]. This total air velocity on the blade, U , can be decomposed into three components. These components are defined in relation to the plane perpendicular to the rotor shaft, known as the hub plane. The plane hub frame is defined as Fh = {Oh, ih, jh, kh} where ih points backwards towards the tail, jh points to the right of the helicopter, and kh points up. Two components are in the hub plane while the third is out of the plane. All three components are normal to the hub plane. The out of plane component is perpendicular to the hub plane pointing downward and is denoted by UP , as seen in Fig. 13c. The next component, UT , is parallel to the hub plane and tangential to the blade in the direction of the blade rotational motion as seen in Fig. 13a and d. The last component, UR , lies on the hub plane and points radially pointing outward in the direction of and parallel to the blade, as seen in Fig. 13a and c. The total air velocity seen by the blade is given as U = \u221a U2 T + U2 P . At any time during flight, the blade experiences a pitch angle, \u03b6 = \u03b1b +\u03c6b, related to the angle of attack \u03b1b of the blade with respect to the airstream U , which approaches the blade at an inflow angle \u03c6b, as seen in Fig. 14. The lift and drag on the blade are determined through blade element analysis. By considering the blade as a two-dimensional airfoil, the lift and drag vectors at each blade element may be determined. The infinitesimal lift and drag of the blade element dr are given as: dL = 1/2\u03c1aU 2cbCl\u03b1\u03b1bdr (33) dD = 1/2\u03c1aU 2cbCddr (34) The forces perpendicular and parallel to the hub plane can be expressed in terms of the lifting and drag forces as follows: dF\u2016 = dL sin \u03c6b + dD cos \u03c6b (35) dF\u22a5 = dL cos \u03c6b \u2212 dD sin \u03c6b (36) Following the procedures from [13, 155], the total force on the blades parallel (F\u2016) and perpendicular (F\u22a5) to the hub plane can be expressed in terms of the air stream velocity components as: dF\u2016 \u2248 1 2 \u03c1cbCl\u03b1 ( \u03b6UT UP \u2212 U2 P ) dr + 1 2 \u03c1cbCDU2 T dr (37) dF\u22a5 \u2248 1 2 \u03c1cbCl\u03b1(\u03b6U2 T \u2212 UT UP )dr (38) The total pitch of the blade is given as \u03b6 = \u03b60 \u2212 \u03b61 cos \u03c8b\u2212\u03b62 sin \u03c8b, where \u03b60 is the collective pitch to control the thrust of the rotor and \u03b61 = Alon\u03b4lon, \u03b62 = Blat \u03b4lat are the linear functions of the pilot\u2019s lateral and longitudinal cyclic control stick inputs (\u03b4lat , \u03b4lon) and lateral and longitudinal control derivatives (Alon, Blat ). As seen in Fig. 15, the blade is modeled as a rigid thin plate rotating about the shaft at an angular rate of . The angular position of the blade in the hub plane is denoted as \u03c8b measured from the tail axis. The blade flapping hinge is modeled as a torsional spring with stiffness K\u03b2 . The moments acting on the blade are due to the lifting force described in Section 3.5, weight of the blade, the inertial forces acting on the blade, and the restoring force of the spring. Equating all the moments acting on the blade results in: \u03b2\u0308 \u00b7 ( 2 \u00b7 K\u03b2 Ib \u00b7 1 2Ib mbgR2 b)\u03b2 = 1 2Ib \u03c1cbCl\u03b1 \u222b RB 0 r(\u03b6U2 T \u2212 UT UP )dr (39) where the blade\u2019s inertia is given by Ib =\u222b Rb 0 mbr 2dr . The flapping dynamics, \u03b2(t) in Eq. 39, can be expressed as a Fourier series neglecting the higher order terms, only keeping the first order harmonics, as: \u03b2(t) = a0 \u2212 a1 cos \u03c8b \u2212 b1 sin \u03c8b (40) Differentiating Eq. 40 and substituting \u03b2, \u03b2\u0307, and \u03b2\u0308 into Eq. 39, the flapping dynamics can then be written as a system of the form x\u0308 + Dx\u0307 + Kx = F . Here, the state vector x = [a0 a1 b1]T , a0 is the coning, a1 is the longitudinal tilt, and b1 is the lateral title angle of the TPP. The state space representation, where x1 = x and x2 = x\u0307, is given as: [ x\u03071 x\u03072 ] = [ 0 I \u2212K \u2212D ] [ x1 x2 ] (41) The TPP dynamics are simplified [13, 155] by assuming a constant coning angle, disregarding the hinge offset, assuming a zero pitch-flap coupling ratio, and disregarding the effects of forward velocity. The simplified dynamics are given in Eq. 42 for the longitudinal dynamics and Eq. 43 for the lateral dynamics as follows: \u03c4f a\u0307 = \u2212a \u2212 \u03c4f q + Abb + Alon\u03b4lon (42) \u03c4f b\u0307 = \u2212b \u2212 \u03c4f p + Bba + Blat \u03b4lat (43) Here, the time rotor constant, \u03c4f = 16 \u03b3 , is a function of the angular velocity, , and the Lock number, \u03b3 = 16 \u03b3 . Additionally, Ab = \u2212Ba = 8 \u03b3 (\u03bb2 b \u2212 1), are the rotor cross coupling terms, and \u03bb\u03b2 = K\u03b2 2Ib + 1 is the flapping frequency ratio. The total thrust and counter-torque produced by the main rotor is a function of the forces acting on the blades perpendicular and parallel to the hub plane. The expressions are given as: Tmr = Nmb 2\u03c0 \u222b 2\u03c0 0 \u222b Rt 0 dF\u22a5,t cos \u03b2d\u03c8m (44) Qmr = Nmb 2\u03c0 \u222b 2\u03c0 0 \u222b Rt 0 ldF\u2016,t d\u03c8m (45) Unlike the main rotor, the tail rotor only has a collective pitch, \u03b6t . The tail rotor blade experiences induced air velocity and has flow components similarly to the main rotor. The perpendicular and parallel force components resemble Eqs. 37 and 38 of the main rotor. The tail rotor thrust and counter-torque can be found using Eqs. 46 and 47 [13] and are given as: Ttr = Ntb 2\u03c0 \u222b 2\u03c0 0 \u222b Rt 0 dF\u22a5,t d\u03c8t (46) Qtr = Ntb 2\u03c0 \u222b 2\u03c0 0 \u222b Rt 0 rdF\u2016,t d\u03c8t (47) 3.6 Complete Set of Helicopter Equations of Motion The key equations that describe the helicopter motion and are necessary for flight controller design are summarized in Table 1."
        ]
    },
    {
        "image_filename": "designv10_5_0000960_s1560354711050030-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000960_s1560354711050030-Figure5-1.png",
        "caption": "Fig. 5. Schematic depiction of a four-dimensional neighborhood of the periodic trajectory \u03b3 and illustration of the three-dimensional Poincare\u0301 map described in the proof (the boundary of the neighborhood depicted in the form of a torus is not invariant under the flow in the general case).",
        "texts": [
            " Obviously, the flow on this neighborhood can be modeled as follows. First consider the cylinder D3 \u00d7 R with coordinates (p, q, h) on the disc D3 (where h is the value of the first integral H) and with coordinate t on the line R. Then we identify on it the points with coordinates (p, q, h, t) and (\u03a6(p, q, h), t + f(p, q, h)), (15) where \u03a6: D3 \u2192 D3 is the three-dimensional Poincare\u0301 map and f(p, q, h) is the return time of the trajectory that started from a point (p, q, h) located on the three-dimensional Poincare\u0301 section {t = 0} (see Fig. 5). In the local coordinates under consideration, the vector field is written in the form v = \u2202 \u2202t . Thus, we have introduced the coordinates (p, q, h, t) in the neighborhood. Of course, they satisfy some periodicity condition. It is the identification rule (15) that expresses this condition. The fact that the system has the first integral H implies that the three-dimensional Poincare\u0301 map is written in the form p\u0303 = p\u0303(p, q, h), q\u0303 = q\u0303(p, q, h), h\u0303 = h, where (p\u0303, q\u0303, h\u0303) = \u03a6(p, q, h) are the coordinates of the image of a point under the Poincare\u0301 map"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003596_tmech.2020.2995138-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003596_tmech.2020.2995138-Figure3-1.png",
        "caption": "Fig. 3. Force error due to under-actuation: \u00b5i is the desired force and fi is the actual force along the thrust direction; \u03b4i is the error.",
        "texts": [
            " It is also assumed that limt\u2192\u221e q\u0308d(t) = 0, which is quite reasonable as the drones are expected to come to rest at the end of their flight. If the quad-copters were fully-actuated, then a control force \u00b5i \u2208 R3 of the following form could be employed for their position control, \u00b5i , \u2212kpi(qi \u2212 qdi)\u2212 kdi(q\u0307i \u2212 q\u0307d) +miq\u0308d (10) where kpi , kdi \u2208 R3\u00d73 are positive definite matrix gains. However, under-actuation prevents generating control forces with an arbitrary direction, unless they are aligned with the drones thrust directions. Figure 3 shows the resulting force error \u03b4i(\u03b7i, \u03b7di , fi) \u2208 R3 due to the under-actuation, where \u03b4i(\u03b7i, \u03b7di , fi) = fiR(\u03b7i)z \u2212 \u00b5i , fi ( R(\u03b7i)\u2212R(\u03b7di) ) z (11) Authorized licensed use limited to: Auckland University of Technology. Downloaded on June 02,2020 at 21:12:59 UTC from IEEE Xplore. Restrictions apply. 1083-4435 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003820_tie.2020.3003596-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003820_tie.2020.3003596-Figure1-1.png",
        "caption": "Fig. 1. Structure of the three-phase 12/8-pole DSEM.",
        "texts": [
            " Then the influence of the commutation angle parameters on the operation performance of the proposed DITC method is analyzed by simulations in Section IV. In Section V, the steadystate experimental results of the proposed DITC and the CCC method are given to verify the analysis and simulation results. Finally, the simulation and experiment under the step reference torque condition are carried out to verify the dynamic performance of the proposed DITC method. II. DIRECT INSTANTANEOUS TORQUE CONTROL OF DSEM Fig. 1 shows the structure of the three-phase 12/8-pole DSEM. The DSEM has the field and phase windings installed in the stator slot and there are no coils or magnet on the rotor. Authorized licensed use limited to: University of Exeter. Downloaded on July 16,2020 at 02:40:04 UTC from IEEE Xplore. Restrictions apply. 0278-0046 (c) 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001267_tmag.2011.2178100-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001267_tmag.2011.2178100-Figure9-1.png",
        "caption": "Fig. 9. Calculated mode shapes of the PMDC motor at (a) Mode 1,",
        "texts": [
            " The structural finite-element model is constructed according to the geometric dimensions and the material properties of the motor. The materials of the stator, the rotor, the permanent magnet, the glue, the right end-shield, and the commutator are low-carbon steel, cold-rolled silicon steel, ferrite magnet, epoxide-resin, hard plastic, and copper, respectively, of which the mechanical properties are given in Table I. In the structural finite-element model, the connection conditions between the shaft and the end-shields are modeled with the multipoint-constrain elements MPC184. Fig. 9 shows the calculated mode shapes and related natural frequencies of the present motor. These mode shapes are considered to be mainly responsible for the radiation of the acoustic noise [17]. The calculated natural frequencies with respect to the modes 1 to 6 are 3270 Hz, 4664 Hz, 5453 Hz, 6085 Hz, 9029 Hz, and 11 044 Hz, respectively. In order to validate the structural finite-element model, the calculated natural frequencies in Fig. 9 are compared with those from measurements. Unfortunately, the frequency ranges of the measuring instruments are limited from 20 Hz to 6400 Hz; thus, only the modes 1 to 4, of which the natural frequencies are within the measuring-ranges of the instruments, are validated. The measured results of modes 1 to 4 are 3110 Hz, 4700 Hz, 5296 Hz, and 5929 Hz, respectively. The relative errors between the calculation and the measurement are therefore 5.1%, 0.77%, 2.9%, and 2.6%, respectively. More details about measuring the modal parameters of the motor can be found in [3]. Hz; (b) Mode 2, Hz; (c) Mode 3, Hz; (d) Mode 4, Hz; (e) Mode 5, Hz; (f) Mode 6, Hz. By analyzing two PMDC commutator motors of the same type, we conclude that thicker glue considerably reduces the natural frequencies of some modes in Fig. 9. Table II compares the measured natural frequencies of the modes 1 to 4 between the two PMDC motors of the same type. Although the two motors have the identical geometric dimensions and material parameters, the natural frequencies of Motor 2 are unexpectedly lower than those of Motor 1. The discrepancy of the natural frequencies is thought to be caused by the glue because the thicknesses of the manually glued epoxide-resins can hardly keep uniform in the two motors. Thus, the thicker glue can act as a \u201cmore soft\u201d spring, which can decrease the stiffness of the motor and lead to the lower natural frequencies"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001940_j.jsv.2018.02.033-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001940_j.jsv.2018.02.033-Figure5-1.png",
        "caption": "Fig. 5. Lateral-torsional dynamic model of the spur planetary gear system.",
        "texts": [
            " Since the rotational speed of the electric motor is varying due to the internal and external excitations of the entire system, the transient rotational speed of the gear system has to be considered in this electromechanical dynamic simulation of themotor- gear system. Therefore, the rotational and translational displacements for each gear and the carrier are chosen as the generalized coordinates in the dynamic model of the planetary gear system. In this section, a lateral-torsional dynamic model of the spur planetary gear system of variable speed process is developed. The structure of the planetary gear system is shown in Fig. 5. The angle displacements of the sun and ring gear qi (i\u00bc s, r) are relative values which is measured in the moving coordinate system oixiyi. The coordinate system oixiyi is fixed on the carrier and rotates with the carrier. The carrier angle displacement qc is absolute value which is measured in the static coordinate system ocxcyc. The planetary gear angle displacement qpi (i\u00bc 1, 2, 3) is also a relative value which are measured in the moving coordinate system onxnhn. The coordinate system onxnhn is fixed on the carrier andmoves with the carrier"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003200_j.apsusc.2019.143649-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003200_j.apsusc.2019.143649-Figure9-1.png",
        "caption": "Fig. 9. Velocity and morphology evolution on the cross-section at different times. The white contour donates the melting temperature.",
        "texts": [
            " It was known that the molten pools under two cases were subjected to the same kind of interfacial forces, which would induce a backward flow behind the laser beam. However, the morphologies of the melt track were distinctly different. Thus, it was reasonable to deduce that recoil pressure and Marangoni convection were not the sufficient conditions for the fish scale patterns and this surface structure was mainly attributed to the regular morphology change of the molten pool induced by pulsed laser. Fig. 9 shows the cross sections of the molten pool from 224.30 \u03bcs to 341.32 \u03bcs. The molten pool was obviously depressed at 224.30 \u03bcs due to the recoil pressure. After the laser beam moved away, the temperature was reduced accompanied by an exponential decrease in recoil pressure, and the surface tension subsequently dominated the movement of the surface. It was apparent that the velocity was highest in the center of the molten pool, indicating a fast flow in the center region. Simultaneously, the fluid has a tendency to move from the sides to the center, giving rise to the sustained depressed surface on both sides"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000035_tie.2010.2095392-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000035_tie.2010.2095392-Figure5-1.png",
        "caption": "Fig. 5. (a) Active and (b) passive compliances of a joint when the robot passes over an uneven surface.",
        "texts": [
            " In addition, the gear train transfers the power of a dc motor to the three lead screws so that they can rotate synchronously. Each track module is composed of two parts: frontal and rear tracks. A compliance active joint connects the tracks. The compliance active joint is composed of a radio-controlled (RC) servomotor and a torsion spring as shown in Fig. 4. The RC servomotor is attached to the rear tracks, and the torsion spring is connected to the motor and the frontal track. The compliance active joint allows the robot to be adaptive to uneven surfaces. Fig. 5 shows the performance of an active compliance joint when the robot travels over an uneven surface. When the robot passes over a protrusion, the RC servomotor adjusts the rotating angle to maintain contact between the frontal track and the pipe, as shown in Fig. 5(a). In contrast, the joint causes the track module to fold, so that it remains in contact with the surface, as shown in Fig. 5(b). The track module is connected to the pantograph by an unconstrained revolute joint, allowing it to rotate freely. Even when the inner wall of a pipe is not parallel to the robot, the track remains passively connected to the wall. These two features of the track module contribute to a larger contact area between the robot and the pipe wall, strengthening the robot\u2019s ability to overcome obstacles. PAROYS-II is able to traverse horizontal, vertical, and curved pipes, utilizing two simple control methods: normalforce control and posture control"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003793_j.mechmachtheory.2019.103764-Figure11-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003793_j.mechmachtheory.2019.103764-Figure11-1.png",
        "caption": "Fig. 11. Arrangement of bearings on input and output shaft.",
        "texts": [
            " (3) , the distance between the bearing and gear plane of star gearing system could results in the difference of vibration characteristics and the floating amounts of those components in the system. Therefore, the location of bearings on the rotors can be rearranged to control the vibration amplitude in order to achieve better load sharing performance and reduce the floating amount of those components. The range of length that bearings can placed in the rotors are shown in Fig. 10 , it can be easily seen that the bearings can only be placed in certain range of length among the whole rotors. The arrangement and permutations of bearings are shown in Fig. 11 , in which b i represent the position of bearings, the number of i becomes bigger as the distance between bearing and the gear plane of star gearing system closer. In general, the valid length of input shaft is nine times the thickness of bearings that match the input shaft, while the valid length of output shaft is six times the thickness of bearings that match the output shaft. The permutations of bearings\u2019 position is shown in Fig. 12 , the effective length of input shaft is divided into nine equal parts, while the length of each part is equal to the thickness of bearing that selected for the input shaft, the effective length of output shaft is divided into six equal parts for the same principle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002053_s40194-018-0567-9-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002053_s40194-018-0567-9-Figure1-1.png",
        "caption": "Fig. 1 Diagram of direct energy deposition",
        "texts": [
            "eywords Laser ultrasonics . Additive manufacturing . Online process . Direct metal deposition . Direct energy deposition This paper addresses themain metallic additivemanufacturing (AM) processes: direct energy deposition (DED) and powder bed fusion. Direct energy deposition consists in focusing the energy delivered by a laser to heat powder, melting it and simultaneously melting material that is being deposited into the substrate\u2019s melt pool (cf. Fig. 1). Powder bed fusion consists in selectively melting a powder bed layer using a laser. AM is attracting considerable interest due to all the possibilities that it offers in comparison to forging process. AM has now applications in the leading-edge sectors such as aerospace and healthcare [1]. Despite AM generating considerable interest, this is not a time-tested technology, and some limits hinder the widespread of AM. Dimensional precision, reliability, and repeatability of the process remain questions [2\u20134]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002031_tec.2016.2637311-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002031_tec.2016.2637311-Figure1-1.png",
        "caption": "Fig. 1. Cross section and winding configurations of 6/7 VFRM with separated AC and DC windings (The rotor pole is aligned with phase A, i.e., \u03b8e = 0\u030a).",
        "texts": [
            " In the integrated current control, the zero sequence current is utilized as the field current, while the dq-axis currents generate the rotating field. For zero sequence current generation, the zero vector redistribution technique is employed, which utilizes the voltage difference between the two inverters. In order to utilize the vector control, the voltage equation of the 6/7 VFRM is derived in the synchronous dq-axis frame. Simulation and test results show the effectiveness of the proposed scheme. Fig. 1 shows the cross section and stator windings of the VFRM, whose number of stator teeth is 6 and rotor poles is 7, i.e., 6/7 VFRM. The initial position (\u03b8e = 0\u00b0) is defined to be where the center of the rotor pole is aligned with one tooth of phase A wound with coil A1. Hence, if a constant current is excited in the A1 winding, the rotor will be aligned with the stator tooth wound by the A1 winding. For the VFRM drives, the separated field current control method can be applied [7]. Fig. 2 shows the conventional field excitation current control block diagram with the external field current source and three-phase inverter",
            " Hence, the torque ripple caused by the even and third order harmonics can be much lower compared with the 6/4 and 6/8 VFRMs. In order to control the field and dq-axis currents, conventional PI current controllers are implemented based on a space vector control strategy. The field and armature windings can be connected to form a single coil in parallel as an integrated winding in Fig. 3 since the field and armature windings are identically wound on each stator tooth. The polarities of the field and armature windings are indicated in Fig. 1, in which the polarities between field and armature windings are the same in A1, B1, and C1. However, due to the coil back-emf, A2, B2, and C2 have a different 0885-8969 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. polarity between the field and armature windings [4]. Therefore, in order to utilize the integrated windings, they should be divided into two winding sets due to the opposite polarity between the armature winding sets, while the polarities of the dc component are the same"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003199_j.mechmachtheory.2019.103576-Figure16-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003199_j.mechmachtheory.2019.103576-Figure16-1.png",
        "caption": "Fig. 16. Relationship between distance to face-gear rotation axis l 2 and face-gear radius R 2 .",
        "texts": [
            " a d = r s \u2212 r 1 = (N s \u2212 N 1 ) m n 2 cos \u03b2 (51) According to the standard DIN 3960 [22] the centre distance a for a given working transverse pressure angle \u03b1w is calculated by a = a d cos \u03b1s cos \u03b1w (52) The resulting shift is calculated by a (c) = a \u2212 a d = m n (N s \u2212 N 1 )( cos \u03b1s \u2212 cos \u03b1w ) 2 cos \u03b2 cos \u03b1w (53) The corresponding shaper profile shift coefficient for the crowned geometry is given by x (c) s = x s + (N s \u2212 N 1 )(in v \u03b1w \u2212 in v \u03b1s ) 2 tan \u03b1n (54) According to Ripphausen [25] , the relationship between working transverse pressure angle \u03b1w and the face-gear radius R 2 for a drive with a shaft angle of \u03b3 = 90 \u25e6 and no axle offset is given by cos \u03b1w = N 2 m n cos \u03b1s 2 R 2 cos \u03b2 (55) In case of axle offset, the helix angle \u03b2 must be replaced by the modified helix angle \u03b2\u2217 \u03b2\u2217 = \u03b2 \u2212 asin ( E R 2 ) (56) From this, the working transverse pressure angle can be estimated for the general case by cos \u03b1w = N 2 m n cos \u03b1\u2217 s 2 R 2 cos \u03b2\u2217 with \u03b1\u2217 s = atan ( tan \u03b1n cos\u03b2\u2217 ) (57) where the representative face-gear radius R 2 for an arbitrary shaft angle can be approximated by R 2 = l 2 sin \u03b3 \u2212 r s cos \u03b3 (58) The relationship between R and l is illustrated in Fig. 16 . 2 2 The influence of a different number of teeth between pinion and shaper, the shift a ( c ) and modification of profile shift is illustrated in Fig. 17 . The design parameters are listed in Table 3 . The diagram of Fig. 18 shows the resulting crowning distribution. In the given examples, the difference of the number of teeth between pinion and shaper has been set to two (N s \u2212 N 1 = 2) . Variation of a ( c ) shifts the position of minimum backlash while the profile shift coefficient needs to be adapted to keep the overall clearance of the pinion tooth between the face-gear teeth constant"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003005_tnano.2018.2797325-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003005_tnano.2018.2797325-Figure2-1.png",
        "caption": "Fig. 2. Diagrams of microrobot in rolling mode (a) without and (b) with the boundary and in kayaking mode (c) without and (d) with the boundary.",
        "texts": [
            " This microrobotic system can be used for experiments of bio-manipulation and testing in vitro and in vivo. Figure 1(b) shows a scanning electron microscope image of the peanut-like magnetic microrobot used in this work, which has a diameter of about 0.8 \u00b5m and a length of 3 \u00b5m and are synthesized from hematite using hydrothermal process [21]. 1536-125X (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. As shown in Fig. 2(a), when magnetized along its short axis (magnetic moment M), the microrobot is rotated by a magnetic torque (\u03c4 = M\u00d7B) induced by an external rotating magnetic field (B) perpendicular to its long axis. This reciprocal motion can not create a net translation in a low Reynolds (Re) number environment [22]. However, once there is a non-slip boundary within a certain distance below the microrobot (Fig. 2(b)), resistance balance is broken and the microrobot rolls along the boundary with translational velocity v. In addition, if a constant magnetic field is added perpendicular to the rotating magnetic field, the resulting conical magnetic field (half-cone angle \u03b1) will drive the microrobot in kayaking mode (Fig. 2(c)). In this case, the ends of the microrobot alternately approach and withdraw from the solid-liquid boundary (Fig. 2(d)), resulting in unequal interactive forces at both ends. The end of the microrobot close to the boundary produces more propulsive force, as in a kayaker\u2019s paddle. To understand the mechanism of the particle transportation using the rolling microrobot, the Rotating Machinery Module of COMSOL Multiphysics was used to study the rotationinduced fluid flow and pressure distribution on a microparticle. The microrobot is modeled as a micropeanut with a length of 3 \u00b5m and a diameter of 0.8 \u00b5m on both sides; the microparticle is modeled as a sphere with a diameter of 10 \u00b5m"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001758_jrproc.1956.275102-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001758_jrproc.1956.275102-Figure8-1.png",
        "caption": "Fig. 8-Zones of setting and primability in the transfluxor.",
        "texts": [
            " Each curve exhibits a sharp threshold followed by an approximately linearly rising curve. 5 ~~~~~~SYMMETRICAL /\\\\ 0 ALTERNA~~~~STINDRIV TOOE fOC- MEE UN The setting characteristics for symmetrical energization with equal drive and prime pulses, shown on Fig. 7, may be explained by considering first the idealized situation for a normal setting in which two zones are created in leg 2; one near the larger aperture where the flux is reversed and one near the smaller aperture where it remains unaffected (see Fig. 8). When the prime pulse on leg 3 is insufficient to produce a magnetizing force greater than the coercive force at the location of the boundary between the two zones, no flux will be transferred to leg 3. There will be a definite value of prime for a given setting, for which transfer will start to occur. The amount of transferred flux will be proportional to that portion of the cross section of leg 2 which is included between the boundary separating the set and nonset zones around the larger aperture and the boundary between the primable and non-primable zones around the small aperture, as shown in Fig. 8. This flux increases with setting, for a given prime, at a rate which is independent of the priming value. When the priming pulse becomes large enough to produce 3251956 PROCEEDINGS OF THE IRE interchange of flux betweeni legs 3 anid 1, it will effectively produce a setting of leg 1 even when no previous setting on leg 1 was applied. This is the spurious \"unblocking\" due to symmetrical drive and prime mentioned earlier. The characteristics of Fig. 7 have approximately the shape to be expected from these considerations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003227_s11517-020-02143-7-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003227_s11517-020-02143-7-Figure7-1.png",
        "caption": "Fig. 7 Experimental setup for calibration and detection accuracy evaluation a without catheter and b with a medical catheter as the operating handle",
        "texts": [
            " Second, the detection accuracy of the developed sensor is evaluated under standard condition. Finally, an EIS robot system is developed by integrating a prototype of the master controller and a developed slave robot. Basing on the EIS robot system, tests of a basic catheter insertion task are conducted in an EVE to evaluate the performance of the developed master controller. Firstly, in order to avoid the effects of the catheter deformation, evaluation experiments without the catheter are conducted using the experimental setup shown in Fig. 7a. The developed master controller is fixed on the test bed. The linear module is used to drive the sensing pipe along axial direction. The axial moving distance is set to be 550 mm. And, the electric actuator is used to drive the sensing pipe along circumferential direction. The rotational moving angle is set to be 1100\u00b0. The sensing pipe of the developed sensor is directly fixed with the shaft of the electric actuator. The axial distance and rotational angle of the sensing pipe detected respectively by encoder A and encoder B (HK50, made by Shenzhen HZJ Co",
            " The maximum rotational motion detection errors vary from 7.44\u00b0 to 13.72\u00b0, and the relative maximum errors are from 0.68 to 1.25%. The maximum standard deviation of rotational motion detection error is 7.35\u00b0. The axial and rotational moving distances during one representative test are shown in Fig. 8. It can be seen that the curve of the axial and rotational moving distances detected by the proposed master controller fits well with those of the standard value recorded by encoder A and encoder B. Secondly, using the experimental setup shown in Fig. 7b, experiments are conducted with the whole master controller to evaluate its detection performance combining the effects of the catheter deformation. A clinical catheter (with size of 5f) of the developed master controller is fixed to the shaft of the electric actuator. Two groups of experiments are designed. The length of the catheter between the fixing point with the electric actuator and the fixing point with the rigid rod inside the master controller is respectively set to be 100 mm and 400 mm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003767_j.conengprac.2019.03.012-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003767_j.conengprac.2019.03.012-Figure1-1.png",
        "caption": "Fig. 1. Variable-pitch quadrotor.",
        "texts": [
            " This was done previously in Gupta et al. (2016) but had a few shortcomings. Whilst there are similarities between the two models, significant differences can be observed when it comes to control design. These distinctions become discernible in the subsequent sections on control design and control allocation. Translational and rotational dynamics of the quadrotor are derived in this section using linear and angular momentum conservation laws. First, inertial and body-fixed frames of reference are defined as shown in Fig. 1. The subscripts I and b indicate inertial and body-fixed frames, respectively. Combined thrust produced by the four rotors and the force of gravity are considered to be the dominant forces acting on the quadrotor. Aerodynamic forces on the airframe are not examined since their effect on the overall flight dynamics is not significant. The translational dynamics in inertial frame can be written as \u239b \u239c \u239c \u239d ?\u0308? ?\u0308? ?\u0308? \u239e \u239f \u239f \u23a0 = \u239b \u239c \u239c \u239d \ud835\udc50\ud835\udf03\ud835\udc50\ud835\udf13 \ud835\udc60\ud835\udf19\ud835\udc60\ud835\udf03\ud835\udc50\ud835\udf13 \u2212 \ud835\udc50\ud835\udf19\ud835\udc60\ud835\udf13 \ud835\udc50\ud835\udf19\ud835\udc60\ud835\udf03\ud835\udc50\ud835\udf13 + \ud835\udc60\ud835\udf19\ud835\udc60\ud835\udf13 \ud835\udc50\ud835\udf03\ud835\udc60\ud835\udf13 \ud835\udc60\ud835\udf19\ud835\udc60\ud835\udf03\ud835\udc60\ud835\udf13 + \ud835\udc50\ud835\udf19\ud835\udc50\ud835\udf13 \ud835\udc50\ud835\udf19\ud835\udc60\ud835\udf03\ud835\udc60\ud835\udf13 \u2212 \ud835\udc60\ud835\udf19\ud835\udc50\ud835\udf13 \u2212\ud835\udc60\ud835\udf03 \ud835\udc60\ud835\udf19\ud835\udc50\ud835\udf03 \ud835\udc50\ud835\udf19\ud835\udc50\ud835\udf03 \u239e \u239f \u239f \u23a0 \u239b \u239c \u239c \u239c \u239d 0 0 \u2212\ud835\udc481 \ud835\udc5a \u239e \u239f \u239f \u239f \u23a0 + \u239b \u239c \u239c \u239d 0 0 \ud835\udc54 \u239e \u239f \u239f \u23a0 (1) The rotation matrix relating the body frame to the inertial frame of reference is formed by Euler angles (\ud835\udf19 - roll, \ud835\udf03 - pitch, and \ud835\udf13 - yaw, in that sequence)",
            " A decision variable \ud835\udefe is introduced to command the vehicle to flip and utilize its reverse thrust capabilities. This is defined as \ud835\udefe = { 1, for normal mode \u22121, for inverted mode (11) When the quadrotor is required to flip, \ud835\udefe is set to \u22121. This is also used to alter the commanded roll and pitch angles during inverted flight which shall be discussed in the control design section. The control inputs \ud835\udc482, \ud835\udc483, and \ud835\udc484 are derived next in terms of the thrust coefficients. Similar to fixed-pitch quadrotors, positive roll of a variable-pitch quadrotor in H-configuration (see Fig. 1) can be achieved by providing higher thrust to rotors 3 and 4, and correspondingly lower thrust to rotors 1 and 2. Positive pitch of the vehicle can be achieved by providing higher thrust to rotors 1 and 4, and correspondingly lower thrust to rotors 2 and 3. As a result of the drag force acting on each rotor, torques produced by rotors 2 and 4 are along the positive zb-axis and torques produced by rotors 1 and 3 are along the opposite direction. A non-zero net torque along the zb-axis causes yawing motion",
            " Theorem 2 shows that the time interval for which altitude control is lost can be calculated by decoupling the roll dynamics and computing its settling time for a step change. Theorem 1. Assuming that sin \ud835\udf03 \u2248 \ud835\udf03 holds throughout the flip maneuver, for a given input saturation of 2\ud835\udc5a\ud835\udc54 for the total thrust \ud835\udc481, the region of the flight envelope where altitude control is lost during flipping is given by \ud835\udf19 \u2208 [ \u2212 2\ud835\udf0b 3 ,\u2212 \ud835\udf0b 3 ] \u222a [ \ud835\udf0b 3 , 2\ud835\udf0b 3 ] . Proof. The subsystem \ud835\udc46\ud835\udc34 with \ud835\udc481 = \u00b12\ud835\udc5a\ud835\udc54 and cos \ud835\udf03 \u2248 1 can be expressed as ?\u0307?3 = \ud835\udc654 ?\u0307?4 = \ud835\udc54 \u2213 2\ud835\udc54 cos\ud835\udf19 (55) From (55), it is observed that zero acceleration or a net downward acceleration (along positive zI-axis, see Fig. 1) if \ud835\udc54\u22132\ud835\udc54 cos\ud835\udf19 \u2265 0. The set of roll angles for which this inequality holds can be derived as follows. At cos\ud835\udf19 = \u00b1 1 2 , ?\u0307?4 = 0 which implies the desired altitude cannot be tracked and the quadrotor either remains in a state of hover or drifts at a constant velocity along zI-axis. For all values of \ud835\udf19 in the interval ( \u2212 2\ud835\udf0b 3 ,\u2212 \ud835\udf0b 3 ) \u222a ( \ud835\udf0b 3 , 2\ud835\udf0b 3 ) , the inequality | cos\ud835\udf19| < 1 2 \u27f9 \ud835\udc54 \u2213 2\ud835\udc54 cos\ud835\udf19 > 0 holds true. From this, the range of values of \ud835\udf19 for which altitude control is lost is given by \ud835\udf19 \u2208 [ \u2212 2\ud835\udf0b 3 ,\u2212 \ud835\udf0b 3 ] \u222a [ \ud835\udf0b 3 , 2\ud835\udf0b 3 ] "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002828_aa543e-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002828_aa543e-Figure8-1.png",
        "caption": "Figure 8. Experimental test rig.",
        "texts": [
            " A magnetic brake with a torque range of 1\u201365 lb ft\u22121 is used to apply the load. An accelerometer (with a sensitivity of 100 mV g\u22121 and a frequency range of 0\u201310 kHz) and a shaft encoder (produced by Encoder Products Co. with 1 pulse per revolution) are used to capture the vibration and tacho signals simultaneously. The data are captured under speeded up conditions from 0 RPM to 3000 RPM within 8 s. The sampling frequency is set to be 7680 Hz to accommodate all the interesting frequency contents for this test rig. The whole setup arrangement is shown in figure\u00a08 [23]. In the experimental process, four types of sun gear are considered (three faulty), as shown in figure\u00a09. The vibrations in the time domain for all four types of sun gear are shown in figure\u00a010. In the following, for demonstration purposes, the vibration data from the tooth-missing fault (figure 9(d)) are used to establish the effectiveness of the proposed signal selection scheme. The physical parameters for the planetary gearbox are listed in table\u00a0 6, in which the gear teeth, number of planet gears and transmission ratio are given and calculated"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000807_j.mechmachtheory.2013.06.013-Figure10-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000807_j.mechmachtheory.2013.06.013-Figure10-1.png",
        "caption": "Fig. 10. Illustration of simultaneous meshing of shaper, disk wheel and face-gear.",
        "texts": [
            " The principle of profile modified face-gear grinding based on disk wheel This part will present a new method of grinding modified spur face-gear. The method can use simple wheel and existing gear grinding machine tool to realize the profile modified spur face-gear grinding. The presented method of grinding the face gear is based on the application of a disk wheel. The process of grinding is based on the simulation of meshing of the face gear with one single tooth of the shaper. The principle of grinding is shown in Fig. 10 below. In the grinding process, the disk wheel rotates around its own axis zw, and also swings around the axis zs. The face-gear rotates around its own axis z2. In addition, in order to cut the tooth surface of the face-gear completely, the disk wheel also needs to traverse in each generating roll position along the entire face width (see Fig. 10(a)). The disk wheel is the tool applied to crown the profile modified spur face-gear. The surface of the disk wheel is a surface of revolution around the axis zw in Fig. 11(b), and its generating line is the transversal section of the shaper for zs = 0, in other words \u03b8r = 0 in Eq. (4). Coordinate systems Ss and Sw are rigidly connected to the shaper and the disk wheel respectively, and Sw0 is a fixed coordinate system. Ews is the distance between the axis zw and xs; \u03b8w is the surface parameter of the disk wheel"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003394_j.compstruct.2020.112698-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003394_j.compstruct.2020.112698-Figure8-1.png",
        "caption": "Fig. 8. Total (a) and directional deformations in the case of a metal roll cage for: b) vertical (z axis) and c) longitudinal directions (y axis). Red arrows show the largest displacements (>20 mm) due to the rollover loads.",
        "texts": [
            " Made of Ti\u2010alloy with a density of 4620 kg/m3, it consisted of a 13.6 m tube with 30 mm diameter and 1.2 mm thickness split into 16 segments of different lengths and welded, with an overall weight of 6.82 kg. Details are reported in Table 2. The numerical simulation was performed in line with similar studies performed by the authors for metal roll cages [67] using the load/constraint conditions described above. Shell 181 elements were also employed in this case, with 3431 nodes and 34,269 elements with dimension between 5 and 27 mm. Fig. 8 exhibits the total and directional deformations for the metal roll cage. With a maximum displacement of 20.6 mm in the vertical (Z) direction, 27.2 mm longitudinally (Y) and 7.5 mm transversally (Y), the cage was deformed by 28.3 mm toward the passengers. As shown in Fig. 9, several zones enter the plastic regime (>930 MPa) or exceed the failure stress (>1070 MPa), with local Von Mises equivalent stresses exceeding 1500 MPa in some regions. Risk to the occupants in the case of a rollover is clear, providing the opportunity to adopt improvements in the design"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003451_j.measurement.2019.107043-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003451_j.measurement.2019.107043-Figure5-1.png",
        "caption": "Fig. 5. The mesh structure and converge test results of finite element model.",
        "texts": [
            " The CAD models of the gear samples with different pressure angles were designed by using MATLAB and CATIA software. The fully rounded rack cutter was used for the models to get higher pressure angles as 20 \u201335 . The CAD models of the test samples for the FEA were given in Fig. 4. CSPA of all test samples was constant 20 , and the drive side was selected from 20 to 35 with 5 increments. The generated CADmodels were exported to ANSYSWorkbench for generating finite element models. As the first step of this stage was the meshing operation. Hexahedral elements were preferred for the mesh structure (Fig. 5.). Mesh converge tests were conducted for all cases in this study to improve the reliability of the FE analysis. As an example of the mesh converge tests performed, the results of the variation of elastic deformations were investigated for different element numbers for the 20 \u201320 pressure angle and 1500 N static loading condition. As can be seen in Fig. 5, the elastic deformation increased with the increase in the element number. However, after the 280,000 elements, the variation of the elastic deformation became stable. Thus, 280,000 elements were defined as the converged mesh number for this study. In order to define the Hertzian part of the deflection at the loading point, the size of the mesh structure near the point of loading was used as suggested by Coy [27]. The size of the grid near the point of loading was chosen with the following equation: e bh \u00bc 0:2 c e \u00fe 1:2 for 0:9 c e 3 \u00f02\u00de where c and e are the length and width of the element respectively, and bh is the Hertzian contact width as follows: Table 1 The mechanical properties of AISI 4140 steel"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001069_j.phpro.2014.08.095-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001069_j.phpro.2014.08.095-Figure2-1.png",
        "caption": "Fig. 2. Experimental stand principal scheme: 1 - optical part including 3-ytterbium fiber laser, 4 - optical collimator, 5 \u2013 pi-Shaper, 6 - scanning head, 7 - F-theta focusing lens, 8 - laser beam optical path, 9 - high-speed camera Photron SA5 10 - macro lens NAVITAR 6000, 11 - optical mirror BCube, 12 - optical attenuator 13 - CCD camera LaserCam-HRTM; and 2 - mechanical part including 14 - stainless steel substrate with Co-Cr powder layer, 15 - movable piston, 16 working platform, 17-micrometer, 18 - PC.",
        "texts": [],
        "surrounding_texts": [
            "of SLM related to the laser source, the base platform, the atmosphere, and the powder. All the parameters were graded as the input and output controlled technological parameters (Fig. 1).\nThe following tasks have been formulated: to develop an experimental stand for selective laser melting of the powders including a system of laser beam modulation and a system of video monitoring; to establish on the system stable the Gaussian, the flat-top and the inverse-Gaussian laser beam mode; to investigate the working parameters of the system for each laser beam mode (for Co-Cr powder) with the purpose to obtain stable single tracks; to adapt a video monitoring system for studying the single track formation while processing for the negative effects as granules escape; to study the output parameters for the single tracks produced at different laser modes as the geometrical parameters and the homogeneity and the free-of-powder consolidation zone (heat-affected); to estimate the single track penetration depth and its metallurgical homogeneity in the cross-section.\nThe experimental stand (Figs. 2, 3) has been developed. The laser source is the ytterbium fiber laser LK-200-V with the wavelength =1.07 \u03bcm. The collimated laser beam has the effective diameter of 5 mm after optical collimator 4. The laser beam goes through f-piShaper 5 and next through scanner 6, where afterwards achieves the working base platform and the powder by the movable optical mirrors and focus lens 7.",
            "The profile of the laser beam is monitored by CCD-camera 13. Optical mirror BCube 11 and an optical attenuator have been used for reduction of the laser beam power on the objective of the camera. High-speed camera 9 (frame rate 775000 s-1, maximum resolution 1,024 x 1,000 pixels) has been used to visualize the melting process.\nThe mechanical part of the stand consists of the base platform 14 made of low-carbon stainless steel which is used as a basis for deposing the powder (diameter 45 mm and height 8 mm). The discrete step of the engine can be varied. The platform base is placed on working piston 15 of platform 16. The movement of piston is controlled by micrometer 17. The geometrical tolerance for the working surfaces was \u00b1 0.02 mm.\nCo-Cr powder was used in experiments (Co (60-65)%, Cr (26-30)%; Mo (5-7)%; Si and Mn less 1%, Fe less 0,75%, less 0,16%, Ni less 0,10%). Protecting atmosphere was not used because there was no possibility to put all monitoring and optical equipment on the stand. According to the literature data, Co-Cr powder has a low reactivity with air in comparison with other powders (Ti6Al4V alloy, maraging steel etc.).",
            "The powder layer thickness was measured by optical microscope Olympus BX51M. The cross-sections of single tracks were prepared by conventional methods using the technological complex ATM (consists of the cutting machine, the hydraulic press, and the polishing machine).\nThe structure of single tracks was studied by scanning electronic microscope VEGA 3 LMH (TESCAN) with the maximum magnification about 1M. The microscope is equipped with the secondary and backscattered electron detectors and EDX analysis of Oxford Instruments.\n3.2. Experimental methods and techniques\nIn the experiments, a layer of powder is deposited on the working platform. The thickness of the each layer was monitored by the optical microscope. A micrometric screw was revolved on the table to control the thickness and the focus distance from the working base to the upper surface of the powder layer. The thickness was measured in three different points. The average thickness for the powder was 80 \u03bcm (\u00b15 \u03bcm).\nIn accordance with the focus distance of F-theta lens of 420 mm, the working surface was placed at this distance to attain the maximum energy concentration on the powder surface. The placement of the working platform was fixed as the initial placement of the working surface. The laser beam mode and the effective diameter were detected by the CCD-camera (Fig. 4).\nIn accordance with the special features of the experimental stand and for reduction of the error influence for the rotate ring on the optical tool as piShaper an optical system was fixed. Hence the changes of the power distribution were produced by distance changes from working surface to focus lens. The effective diameter of the laser beam (86.5%) was defined as 0.111 mm, the effective area was 0.261 mm2.\nFor calculation of the distance between different distributions the next formula has been used:\n2 2'8 D f R (1)\n- laser wave length, 'f - focus distance F-theta lens, D - laser beam diameter after collimator."
        ]
    },
    {
        "image_filename": "designv10_5_0002440_s40964-018-0064-0-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002440_s40964-018-0064-0-Figure1-1.png",
        "caption": "Fig. 1 a Arrangement of stainless steel samples on the substrate, b, c geometry of the sample designed for measuring the effective powder layer thickness",
        "texts": [
            " A nominal build layer thickness of 20\u00a0\u00b5m was used for printing all LPBF parts. Parameter values for laser speed, laser power, and hatching distance were set to be 1108\u00a0mm/s, 227\u00a0W and 90\u00a0\u00b5m, respectively. A Retsch Camsizer X2 (Retsch Technology GmbH, Haan, Germany) was used to measure the powder size distribution and a Keyence VK-X250 (Keyence Corporation, Osaka, Japan) confocal microscope was used to measure the surface topology and dimensions of the LPBF samples. To achieve a representative data set, nine parts with a cross section of 4\u00a0mm\u00a0\u00d7\u00a06\u00a0mm (Fig.\u00a01b) and 4\u00a0mm height were printed at various locations on the substrate (Fig.\u00a01a). The substrate was divided into nine regions with parts printed at the center of each region as shown in Fig.\u00a01a. Parts were made with thin walls (Fig.\u00a01b) parallel to the recoater moving direction. Each part had three slots with depths of 20\u00a0\u00b5m, 40\u00a0\u00b5m and 60\u00a0\u00b5m as shown in Fig.\u00a01c. These slots were made to validate the surface depth data measured by the confocal microscope. The height difference between adjacent slots (20\u00a0\u00b5m) was designed to confirm if the build layer thickness had reached a steady-state regime. Procedure to measure the ELT is shown in Fig.\u00a02. To print the thin walls (Fig.\u00a01b), a new layer of powder was laid on top of the previously solidified part (Step 1). Next, the laser scanned the powder to print the thin walls. At this point, the printing is complete. Then, the recoater was moved towards the right to its original position as shown in Step 2 and then moved to left across the build compartment while the build plate was kept at the same height as the last recoating step so that it could scratch some areas on the printed walls (Step 3). The scratched areas resulted in flattened peaks that were used as reference points to measure the ELT. In addition, as the flatted peaks correspond to the height of the previous layer, the height difference between the peaks and the surface of the sample would be equal to the effective layer thickness of powder on top of the build surface (Step 3). The 20-\u00b5m, 40-\u00b5m and 60-\u00b5m steps on the samples (Fig.\u00a01c) along with the reference height from scratched walls were used to measure the ELT during LPBF. Finite element (FE) simulations were performed to study the effect of ELT on the temperature change during the LPBF process. FE simulations using COMSOL Multiphysics\u00ae were performed to model temperature distribution and melt pool dimensions with layer thickness of 20 and 150\u00a0\u00b5m. Laser exposure parameters such as speed and power were based on experimental values (laser speed, laser power, and hatching distance were set to be 1108\u00a0mm/s, 227\u00a0W and 90\u00a0\u00b5m, respectively)",
            " Heat transfer due to atmospheric convection was applied to all boundaries and radiative heat transfer was considered on the top surface. 1 3 Micrograph of a sample with a layer of the powder particles is shown in Fig.\u00a04. This sample was made by gluing the powder particles on top of the printed part with droplets of Super Glue (a low-viscose liquid cyanoacrylate adhesive) and then cutting and polishing the section normal to the surface to measure ELT. The method described in the previous section was applied to the nine samples printed on various areas of the substrate (Fig.\u00a01a). Figure\u00a05 demonstrates the measurement of ELT from the laser confocal microscopy results. Areas, where recoater made contact with the supporting walls on the sample surface, are highlighted in Fig.\u00a05a. Flat regions represent the contact points with the recoater and hence the elevation of the powder for the last printed layer. Figure\u00a05b, c shows the magnified 2D and 3D views of the highlighted region in Fig.\u00a05a, respectively, and shows the flat surface produced by the recoater scratch on the supporting walls",
            " In contrast to studies and simulations on powder compaction and ELT in LPBF, findings of this research show that ELT (153\u00a0\u00b5m) is about an order of magnitude larger than the build layer thickness (20\u00a0\u00b5m) for 17-4 PH stainless steel for the input process parameters used in this paper. As ELT is much larger than the nominal layer thickness, simulated results show a pronounced effect on the temperature distribution (up to 120\u00a0\u00b0C under prediction) and melt pool dimensions (up to ten times overprediction) during LPBF. Table 2 Measurements and statistical data of areas shown in Fig.\u00a0 6 with respect to the reference plane for SS 17-4 PH samples shown in Fig.\u00a01 Sample Average depth (\u00b5m) Relative height difference (\u00b5m) Area 1 Area 2 Area 3 Area 1\u2013Area 2 Area 2\u2013Area 3 Average 153 176 195 22 19 SD 16.4 16.2 15.3 4.4 4.1 1 3 Acknowledgements This work was supported by funding from the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Federal Economic Development Agency for Southern Ontario (FedDev Ontario). The authors would also like to acknowledge the help from Jerry Ratthapakdee and Karl Rautenberg for helping with design and printing the LPBF parts"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001155_j.measurement.2014.02.029-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001155_j.measurement.2014.02.029-Figure4-1.png",
        "caption": "Fig. 4. (a) Drive train diagnostic simulator test set up and (b) arrangement in single stage spur gear box.",
        "texts": [
            " Following this, the first \u2018n\u2019 consecutive part signals which have already been resampled to a time \u2018T\u2019, should be added in series and merged to form the re-scaled signal corresponding to one revolution. The same process is to be repeated for the next \u2018n\u2019 consecutive part signals to obtain the re-scaled signal for second revolution and so on. Thus, the signals for every revolution, almost synchronous with each other can be obtained. Classical TSA can now be performed on this signal. Experiments were performed on drivetrain dynamics simulator (DDS). The test setup shown in Fig. 4a, consists of single stage gear box with a pinion and gear of 14.5 degree pressure angle, each made of steel supported by 100 diameter, steel shaft. The axes of shafts are supported by 6 deep groove ball bearings. The gearing system is lubricated by splash lubrication provided at the bottom of gear housing as shown in Fig. 4b. The main specifications of gear box are as follows: 1. Single stage gear box with 1 driver pinion gear of 32 teeth on input shaft and 1 driven gears of 80 teeth on output shaft respectively. 2. The input shaft of the gear box is powered by a three phase, 3 HP, 0\u20135000 rpm variable speed motor. 3. The output shaft is connected with 4\u2013220 lb.in capacity magnetic particle brake. It can be seen from the schematic of gearbox test rig Fig. 5 that, more than one test gears can be mounted on shaft 1 at a time to save time in changing the gears"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003327_acsami.9b08159-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003327_acsami.9b08159-Figure1-1.png",
        "caption": "Figure 1. Mechanism of the motile micropump based on ZnO/PS Janus micromotors. (a) Schematic of the motion mechanism: ZnO/PS Janus micromotor is powered by ion gradient generated through the chemical reaction at the ZnO surface. As a result, the Janus motor moves towards the ZnO side. (b) Schematic of the pumping mechanism: an outward electric field (the red arrows) generated in response to the different diffusion speed of Zn2+ and OH\u2212 released from the reaction between the ZnO/PS Janus micromotor and water. An electroosmotic flow (the blue arrows) is created at the same direction with the electric field because of the double electric layer of the glass slide. The negatively charged silica particles (the green microspheres) are pumped away from the ZnO/PS micromotor because the electroosmotic force overbears the electric field force. (c) Theoretical simulation of ion concentration distribution released by the ZnO/PS Janus micromotor at 3 and 15 s. (d) Optical microscopy images of the motile micropump based on the water-driven ZnO/PS Janus micromotor in suspension of 1.21 \u03bcm silica particles. Scale bar, 25 \u03bcm.",
        "texts": [
            " Particularly, after showing messages, micropatterns can disappear naturally, followed by rewriting different messages by fabricating another micropattern on the same area. Such a versatile motile micropump system offers a simple, costeffective micropatterning process, paving the way for new opportunities for novel functional surface science and potential applications, such as producing secret messages, dynamically changeable microchannels, and adaptive optics or microfluidics. 2.1. Mechanism of the Motile Micropump. As shown in Figure 1a, the self-propelled Janus micromotor is fabricated by coating PS microspheres with a zinc oxide (ZnO) layer. The ZnO side of the Janus micromotor reacts with water spontaneously at room temperature to release zinc ions and hydroxide ions. Consequently, a high local ion concentration of Zn2+ and OH\u2212 is formed around the ZnO surface, leading to an ion gradient across the ZnO/PS Janus micromotor. Unlike the concentration gradient of molecules, the electrolyte gradient causes a chemophoretic flow in the direction opposite to the osmophoresis.50,51,59,61\u221263 The induced chemophoretic flow propels the micromotor toward the ZnO side. The schematic diagram in Figure 1b illustrates the pumping mechanism of the ZnO/PS Janus micromotor in water mixed with passive silica particles. A diffusion-induced electric field, resulting from the large difference in diffusion coefficients between the cation \u201cZn2+\u201d (D(Zn2+) = 0.703 \u00d7 10\u22125 cm2/s64) and the anion \u201cOH\u2212\u201d (D (OH\u2212) = 5.273 \u00d7 10\u22125 cm2/s64), is established pointing outward the ZnO/PS Janus micromotor. The existence of the electric double layer on the negatively charged sodium borosilicate glass slide sets up an electroosmotic flow around the ZnO/PS micromotor",
            " This means that the electroosmotic force overbears the electric field force based on the above equation.13,17,65 Consequently, the surrounding negatively charged silica particles can be pumped away from the ZnO/PS Janus micromotor in the direction of the electroosmotic flow force. Meanwhile, the distribution of silica particles pumped by the ZnO/PS Janus micromotor depends on the local ion distribution.13 To further understand the distribution of passive silica particles in the motile micropump system, we performed the simulation of local ion distribution using COMSOL Multiphysics. Figure 1c displays the simulation results of local ion distribution changing with time around the ZnO/PS Janus micromotor. A higher local ion distribution appears along with the track line of the ZnO/PS Janus micromotor at 15 s, while ions just distribute around the micromotor initially. Note that the passive silica particles among the higher local ion distribution area can be pumped away from the ZnO/PS Janus micromotor, resulting in a clear exclusion region along with the movement of the ZnO/PS Janus micromotor, while the silica particles in other areas where the ion concentration is very low cannot move and just stay where they are. The optical microscopy image of Figure 1d (captured from Video S1) shows the experimental result of the motile micropump. The micropattern fabricated by the static micromotor is similar to the pattern created by the traditional micropump, as indicated in Figure S2a. Based on the cooperation between the property of the traditional micropump and the self-powered ZnO/PS Janus micromotor in water, the micromotor (the larger black particle in Figure 1d) can travel through the negatively charged silica particles (the dense smaller particles in Figure 1d) and produce a micropattern in a silica particle suspension. 2.2. Micropatterning Resolution of the Motile Micropump. Similar to the traditional micropatterning method, resolution is an important factor of the micropatterning process for motile micropump systems. Therefore, the influence of the diameters of the Janus micromotor on the resolution of the micropatterning process has been investigated experimentally and theoretically. Here, the ZnO/PS Janus micromotors with diameters of 2, 5, and 10 \u03bcm are used for micropatterning, as displayed in Figure 2a\u2212c, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000843_j.sysconle.2012.01.009-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000843_j.sysconle.2012.01.009-Figure2-1.png",
        "caption": "Fig. 2. Left wing damaged generic transport model.",
        "texts": [
            " (57), the optimal control modification can also be expressed as \u0398\u0307 (t) = \u2212\u0393 \u03a6 (x (t))  e\u22a4 (t) PB + \u03a6\u22a4 (x (t)) \u0398 (t)G2 (58) whereG2 > 0 is a diagonalmatrix ofmodification parameterswith the following special cases: \u2022 G2 = \u03bdK\u22122 i for first-order reference models with proportional\u2013integral\u2013derivative control. \u2022 G2 = \u03bdK\u22122 p for first-order reference models with proportional control or second-order reference models with proportional\u2013derivative control. A flight simulation was conducted using a generic transport model (GTM) [17] with a 28% loss of the left wing as shown in Fig. 2. Since the damage is asymmetric, all the three axes are fully coupled together throughout flight. A level flight condition ofMach 0.6 at 15,000 ft is selected. Upon damage, the aircraft is re-trimmed with T = 13,951 lb, \u03b1\u0304 = 5.86\u00b0, \u03c6\u0304 = \u22123.16\u00b0, \u03b4\u0304a = 27.32\u00b0, \u03b4\u0304e = \u22120.53\u00b0, \u03b4\u0304r = \u22121.26\u00b0. The remaining right aileron is the only roll control effector available. The reference model is specified by \u03c9p = 2.0 rad/s, \u03c9q = 1.5 rad/s, \u03c9r = 1.0 rad/s, and \u03b6p = \u03b6q = \u03b6r = 1/ \u221a 2. The actuator dynamics are modeled with \u03bba = \u03bbe = \u03bbr = 50/s and position limits of \u00b135\u00b0 for the aileron and elevator and \u00b110\u00b0 for the rudder"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000812_j.jfranklin.2011.09.006-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000812_j.jfranklin.2011.09.006-Figure2-1.png",
        "caption": "Fig. 2. Schematic diagram of the 3-DOF helicopter.",
        "texts": [
            " y angular position of the pitch axis, rad f angular position of the roll axis, rad c angular position of the yaw axis, rad Jy moment of inertia of the system around the pitch axis, kg m2 Jf moment of inertia of the helicopter body about the roll axis, kg m2 Jc moment of inertia of the helicopter body about the yaw axis, kg m2 Vl voltage applied to the left motor, V Vr voltage applied to the right motor, V Kf force constant of the motor combination, N la distance between the base and the helicopter body, m lh distance from the pitch axis to either motor, m Tg effective gravitational torque, N m Kp constant of proportionality of the gravitational force, N In this work, a 3-DOF helicopter manufactured by Quanser was employed for the experimental tests (see Fig. 1). The 3-DOF helicopter system is composed of the helicopter body, which is a small arm with one propeller at each end, and the helicopter arm, which connects the body to a fixed base. The system cannot exhibit translational motion, but it can rotate freely about three axes (see Fig. 2). The helicopter position is characterized by the roll, yaw and pitch movements. The roll movement corresponds to the rotation of the helicopter body about the helicopter arm, the yaw movement corresponds to the rotation of the helicopter arm about the vertical axis and the pitch movement corresponds to the rotation of the helicopter arm about the horizontal axis. The control variables are the input voltages to the power amplifiers that drive each one of the two DC motors connected to the helicopter propellers. The following equations (see Fig. 2), describe the 3-DOF helicopter dynamics: \u20acc \u00bc Kpla Jc sin\u00f0f\u00de \u00f01\u00de \u20acy \u00bc Tg Jy \u00fe Kf la Jy \u00f0Vl \u00fe Vr \u00fe xy\u00de \u00f02\u00de \u20acf \u00bc Kf lh Jf \u00f0Vl Vr \u00fe xf\u00de \u00f03\u00de y\u00bc \u00bdc y f T \u00f04\u00de where the uncertainties/perturbations are represented by xy and xf. On the other hand, y 2 R3 is the output of the system. Now, defining us \u00bcVl \u00fe Vr and ud \u00bcVl Vr, for the sake of simplicity, the model (1)\u2013(3) can be rewritten as _x1 \u00bc x2 _x2 \u00bc F \u00f0x1,x2\u00de \u00fe B\u00f0u\u00fe x\u00f0x1,x2\u00de\u00de y\u00bc x1 \u00f05\u00de where x1 \u00bc \u00bdc y f T represents the angular positions, while the angular velocities are represented by x2 \u00bc \u00bd _c _y _f T , the input vector u\u00bc \u00bdus ud T , the nominal part of the system is represented by the nonlinear functions vector F \u00f0x1,x2\u00de \u00bc Kpla Jc sin\u00f0x13\u00de Tg Jy 0 T The input matrix is defined as B\u00bc 0 0 Kf la Jy 0 0 Kf lh Jf 2 666664 3 777775 The following conditions are assumed to be fulfilled henceforth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002004_1.4028532-Figure11-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002004_1.4028532-Figure11-1.png",
        "caption": "Fig. 11 CC Arc geometry creation. (a) Three point ellipse, (b) projected curved surface, (c) divisor lines and exploded rigid panels, and (d) crease pattern.",
        "texts": [
            " (2)\u2013(5) and the elliptical curve to be plotted with Eqs. (9) and (10). As all ellipses are identical, the superscript j is again replaced with 0. Permissible bounds for u remain unchanged from that used for the CC-Miura. 4.2.2 Rigid Subdivision. The projected cylindrical surface is subdivided into planar strips to generate the CC-Arc pattern. Vertices Wk,j are calculated at the kth divisor lines and the jth zigzag crease (k\u00bc 1, 2,\u2026, s, j\u00bc 1, 2,\u2026, n). In a 3D Cartesian coordinate system with orientation as shown in Fig. 11(c), the coordinate vector (xk,j, yk,j, zk,j) of Wk,j is xk;j \u00bc R cos h\u00fe uk;j\u00f0tk\u00de (33) yk;j \u00bc \u00f0k k 1\u00de b sin\u00f0gZ;set=2\u00de S \u00fe vk;j\u00f0tk\u00de (34) zk;j \u00bc R sin h\u00fe wk;j\u00f0tk\u00de (35) where R is given by Eq. (14) in Ref. [21] as R \u00bc a2=\u00f02 sin\u00f0n2=2\u00de\u00de and h is given by odd i values in Eq. (16) in Ref. [21] as (j \u2013 1)(n1\u00fe n2)/2 for odd j and (j \u2013 1)(n1\u00fe n2)/2\u00fe (n2 \u2013 n1)/2 for even j. Rotated elliptical coordinates (uk,j, vk,j, wk,j) are obtained by rotating the \u00f0u0; v0\u00de ellipse to match the orientation of the corresponding three-node zigzag on the base pattern uk;j\u00f0tk\u00de vk;j\u00f0tk\u00de wk;j\u00f0tk\u00de 2 4 3 5 \u00bc cos\u00f0h\u00fe hj\u00de 0 0 1 sin\u00f0h\u00fe hj\u00de 0 2 4 3 5 u0\u00f0tk\u00de v0\u00f0tk\u00de (36) where hj is the rotation of the corresponding three-node zigzag, given by hj \u00bc \u00f0p\u00fe n1 \u00fe n2\u00de=2 for odd j \u00f0p\u00fe n1 \u00fe n2\u00de=2 for even j (37) Again, a 3D Cartesian system was used, rather than a cylindrical coordinate system, as it is simpler to incorporate the rotated uk,j, vk,j, and wk,j terms"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003867_j.matdes.2020.108691-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003867_j.matdes.2020.108691-Figure6-1.png",
        "caption": "Fig. 6. Schematic of the milling process.",
        "texts": [
            " The cutting forces were recorded and analysed by the Kistler Dynoware software. The surface finish of the workpiece after each cut was observed by a Keyence VHX-1000 (Osaka, Japan) digital microscope. The surface roughness (Ra) of the workpiece was measured by a Form Talysurf-120 profilometer, and the tool wear was examined by a Keyence VHX-1000 (Osaka, Japan) digital microscope. The procedures of the milling process are described below. After the workpiece was clamped in position, install a new cutter and cut the supports with a depth of cut of 0.2 mm, as shown in Fig. 6 from the top to the first black dotted line. After Cut 1was completed, replace with a new cutter and cut 8 times continuously, each time with a depth of cut of 0.2mm. Therefore, a total of 1.6mmheightwas cut, leaving a 0.2 mm height of the support structures, as shown in Fig. 6 from the first black dotted line to the first solid yellow line. Replace with a new cutter and cut with a depth of cut of 0.2 mm, which is equivalent to removing the support structures from the surface of theworkpiece, as shown in Fig. 6 from thefirst solid yellow line to the second black dotted line. This position is defined as the reference line, which is the edge of the support structures. Unacceptable stubble can be observed on the surface of the workpiece after Cut 2. Therefore, replacewith a new cutter and cut theworkpiece with a depth of cut of 0.2 mm, as shown in Fig. 6 from the second black dotted line to the third black dotted line. As a result, theworkpiece has been cut 0.2 mm. As stubble was observed on the surface of the workpiece after Cut 3, the cutting process continued. Replace with a new cutter and cut 0.2 mm further, as shown in Fig. 6 from the third black dotted line to the fourth black dotted line. At this point, the workpiece has been cut 0.4 mm. All the support structures have been removed after Cut 4. Therefore, the removal of support structures by milling is considered to be completed. From the results of the previously measured hardness distribution (the results are explained in Section 3.1), the Cut 2, Cut 3 and Cut 4 are in the hardness decreasing zone. Cut 5 is selected 3.6 mm away from the edge of the support structures, it is in the hardness stable zone. Cut 5 is not meant to remove the support structures; it aims to evaluate the previous hardness distribution results. After Cut 4, replace with a new cutter and cut 15 times continuously, the depth of cut was maintained at 0.2 mm for each cut, as shown in Fig. 6 from the fourth black dotted line to the second solid yellow line. Replace with a new cutter and cut with a depth of cut of 0.2 mm, as shown in Fig. 6 from the second solid yellow line to the last black dotted line. The samemilling processwasmade for both cone and block support structures. Cut 1 to Cut 5 are single cut runs and the cutting depth was maintained at 0.2 mm for every single run. After each cut, a new cutter was replaced to ensure that the tool wear does not affect the data. The detailed descriptions are as illustrated in Fig. 6. 2.6. Modelling and simulation with finite element method To investigate the influence of support structures on the cutting performance in the milling process, a 3D finite element method (FEM) model was conducted in ABAQUS/Explicit software. Cone and block support structures were built as 3D deformable solids, and the dimension parameters were corresponded to the measured results (see Fig. 2). Two support arrays were extruded with section shapes on a cuboid base, as shown in Fig. 7. The base representing the finally obtained workpiece was meshed with 23,922 C3D8R elements, and the cone and block support structures were meshed with 194,769 C3D8R and 757,450 C3D10M elements, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001880_j.applthermaleng.2014.02.008-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001880_j.applthermaleng.2014.02.008-Figure8-1.png",
        "caption": "Fig. 8. The temperature distribution of the motor (unit: C).",
        "texts": [
            " The solution run time is about 20 s in the process of thermal field simulation under the healthy and faulty conditions. The system of simultaneous linear equations generated by the thermal finite element procedure is solved by a direct elimination process (Gaussian elimination approach), so the iteration number is 1 in every case. It is necessary to state that it took a long time to complete the temperature-rise experiments, so the ambient temperatures changed, and the ambient of the above three states are 20.5 C, 16.5 C, 17 C respectively. Fig. 8(a), (b) and (c) are the steady thermal fields of the motors with healthy cage, one broken bar and two adjacent broken bars respectively. The temperature distribution tendencies of the motor are similar in various situations, that is, the rotor temperature is highest and stator winding temperature is higher than stator core temperature. The motor frame temperature is the lowest in the solution region. Therefore the broken-bar fault has an unobvious effect on the overall temperature distribution of the motor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001982_j.triboint.2015.09.004-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001982_j.triboint.2015.09.004-Figure1-1.png",
        "caption": "Fig. 1. Diagram of SRB motion and load analysis.",
        "texts": [
            " Effects of some parameters on SRB's temperature rise are numerically analysed with a calculating example. In order to simplify the theoretical analysis, the following assumptions are proposed: (1) roller-raceway contact is in the range of elastic deformation; (2) the geometrical errors and roughness of bearing's components are ignored; (3) effects of gravities of roller, cage and inner ring are ignored; (4) the roller's centrifugal effect is ignored due to the fact that SRBs usually work in low speed condition. For an SRB subjected to a radial load shown in Fig. 1, the inner ring rotates at an angular velocity of \u03c9i, driving the rollers and cages revolving at \u03c9c around the OZ axis. All the rollers are revolving on their own axes at \u03c9r. SRBs usually work in low speed and heavily-loaded applications, where the skid between rollers and raceways is negligible, so the motion relationship of the rollerraceway can be regarded as pure rolling [18]. Thus, the average linear velocities of roller-inner raceway contact and roller-outer raceway contact can be expressed as [18], Uij \u00bc 0:5dm 1 \u03b3 \u03c9i \u03c9c\u00f0 \u00de\u00fe D=dm \u03c9r \u00f01\u00de Uoj \u00bc 0:5dm 1\u00fe\u03b3 \u03c9c\u00fe D=dm \u03c9r \u00f02\u00de The roller-raceway contact in an SRB is illustrated in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000471_1.3529236-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000471_1.3529236-Figure7-1.png",
        "caption": "FIG. 7. Schematic illustration of the modeled nematode body shape for force and power calculation. The nematode body is assumed to be an extruded volume of thickness d bounded by the shape contour C. The shaded area segment dS represents a infinitesimal rectangular element on the lateral side of the body of length ds. n is the unit normal vector of the area segment pointing away into the fluid. The local fluid stress on dS is given by n \u00b7 . The local drag acting upon dS by the fluid follows as fdrag=n \u00b7 dS.",
        "texts": [
            " The fluid shear-stress is then calculated using the known values of the fluid viscosity see Fig. 1 b and Table I . The drag force on the nematode body is calculated by integrating the shear-stress over the nematode body surface. In the limit of low Re, the total force on the swimming nematode is zero and the nematode propulsive force is balanced by the fluid drag force, such that Fprop t +Fdrag t =0. The hydrodynamic drag force Fdrag on the swimming nematode is calculated on a body of thickness d that is bounded by a shape contour C Fig. 7 . The body\u2019s thickness is 80 m, corresponding to the nematode diameter, and the shape contour is experimentally obtained using image analysis. The drag force on each area segment dS Fig. 7 is given by fdrag=n \u00b7 dS=n \u00b7 ds \u00b7d , where n is the unit normal vector and is the fluid stress defined as = \u0307= V + V T . Here, \u0307 is the shear-rate. Hence, the local fluid stress and the local drag force on each segment can be obtained. The total drag force is computed by integrating over the entire body surface, such that Fdrag t = Cfdrag= Cds \u00b7n \u00b7 \u00b7d. Using the overall force balance, the propulsive force is then Fprop t =\u2212Fdrag=\u2212 Cds \u00b7n \u00b7 \u00b7d. The corresponding mechanical power is P t =\u2212 Cfdrag \u00b7V . Thus, the total propulsive force and mechanical power can be obtained at each instant over a swimming cycle. Here, the power dissipated in viscous shear P represents a lower limit on the total power that the nematode uses to swim.45 In addition, one should note that estimates of Fprop and P include only the contributions of fluid stresses on the sides of the model body shape Fig. 7 but neglect the additional contributions from top and bottom surfaces, where velocimetry data are unavailable. Hence, our approximation should be interpreted as an underestimate of the total propulsive force and power delivered in reality by nematodes. The magnitude of the propulsive force Fprop and the mechanical power P averaged over one swimming cycle is shown in Fig. 8. The error bars are the standard deviations of the averages. The calculated experimental values for the force and power are 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002595_rpj-10-2017-0196-Figure18-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002595_rpj-10-2017-0196-Figure18-1.png",
        "caption": "Figure 18 (a) Illustration of the method, (b) overhang length and overhang angle for a single layer and (c) slicing result demonstration",
        "texts": [
            " The key task is to calculate these two parameters. Two steps are conducted as follows. First is the initial trial segmentation for the latter overhang segmentation. In this step, the initial ith segment plane is determined by offsetting the i-1th segment plane. The offset is the initial segment height given by the user. For the case of i = 1, the 0th segment plane is defined as the base plane. Next is the overhang segmentation. This step optimizes the build direction and segment thickness. As described in Figure 18, the initial ith segment plane intersects with the model, generating a segment contour denoted asLt,. The segment contour resulting from intersecting of the i 1th segment is denoted as Lb. LetCb andCt denote the projections of these two segment contours onto the i 1th segment plane. According to the relationship between Cb and Ct, there are three cases. Ct [ Cbmeans no overhang, Ct 62 Cb and Ct \\ Cb = 1 means a large overhang structure and Ct 62 Cb and Ct \\ Cb = 1 means a small overhang structure"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000648_978-3-642-17531-2-Figure2.35-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000648_978-3-642-17531-2-Figure2.35-1.png",
        "caption": "Fig. 2.35. Lossless DC motor as an ideal electromechanical transducer: a) mechanical power variables :effort , :flow gyrator, b) mechanical power variables :effort , :flow transformer, MK designates the motor constant",
        "texts": [
            "33 shows physical examples of transformer type transducers and Fig. 2.34 shows a physical example of a gyrator type transducer. In the matrix form shown, the transfer matrix represents the so-called chain matrix of two-port network theory. Mechanical transducers: variable definitions Recall that, due to the arbitrary assignment of domain-specific power variables, the description of physical transducer implementations is not unique. Particular attention is due in the case of mechanical transducers. Fig. 2.35 shows a lossless DC motor as an example of an ideal electromechanical transducer. Depending 96 2 Elements of Modeling on which physical quantities are assigned to the power variables effort (e) and flow (f), the same system can be described as a transformer or a gyrator. Particular attention should be paid to this fact when such systems are modeled using computer-aided tools and pre-made component libraries. 2.3 Modeling Paradigms for Mechatronic Systems 97 Topological rules of construction Starting with the physical topological structure of network elements, an abstract topological network model can be constructed as an undirected graph including standardized network elements (e"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002084_j.ijplas.2015.09.007-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002084_j.ijplas.2015.09.007-Figure8-1.png",
        "caption": "Figure 8. Finite element meshes used for (a) central hole tension, (b) notched tension, and (c) shear loading.",
        "texts": [
            " If failure is detected, the element deletion flag is set, leading to removal of the corresponding integration point in the subsequent time step (Abaqus, 2012). M ANUSCRIP T ACCEPTE D A combined analytical and numerical approach is taken to identify the model parameters. The finite element models are therefore presented first before detailing the calibration procedures and comparing the simulation predictions with the experiments. Finite element simulations are performed for the notched tension, central hole tension and shear experiments using the software Abaqus/explicit. For each specimen, the corresponding finite element model (Fig. 8) comprised only the gage section and a small portion of the specimen shoulders which was located between the global extensometer measurement points shown as blue solid dots in Figs. 4b, 4c and 4d. In all models, we assumed symmetry of the mechanical fields with respect to the specimen mid-plane (x-yplane), i.e. only half the thickness was modeled with eight first-order elements along the (half-) thickness direction for the NT, the CH and the SH specimens. Furthermore, we imposed symmetry boundary conditions along the longitudinal plane (y-z-plane) for all specimens"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000777_j.jmbbm.2013.08.011-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000777_j.jmbbm.2013.08.011-Figure3-1.png",
        "caption": "Fig. 3 \u2013 Representation of the X and Y-oriented specimens and associated finite element meshes.",
        "texts": [
            " In the second case, near the strut external surfaces of this central part, the size of elements was reduced to about 40 mm and progressively increased to reach 150 mm in their core. The maximal principal stresses obtained using both meshes were similar with the mean relative differences not exceeding 3%. However, more significant differences were obtained concerning the determination of stress gradients \u03c7 (about 10%). The results presented in this paper were provided by the finest meshes. They were composed of 694,985 elements and 733,093 nodes for the X-oriented sample and 398,280 elements and 456,243 nodes for the Y-oriented one. They are depicted in Fig. 3. An elastic, linear and isotropic constitutive law was supposed for pure titanium. The corresponding Young\u2032s modulus E\u00bc 100; 000 MPa and Poisson\u2032s ratio \u03bd\u00bc 0:30 of the SLM made components were taken from Barbas et al (2012). Symmetry boundary conditions were applied on the appropriate faces of both meshes. Simple tension and compression loads were simulated by applying a uniform tension t\u00bc712:73 MPa on the cross-section corresponding to the threaded parts of the samples. This tension is equivalent to a tension/compression force of F\u00bc71000 N and apparent axial stresses in the gauge part of the porous structures of \u03a3X \u00bc79:0 MPa and \u03a3Y \u00bc79:6 MPa respectively in X and Y samples"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000236_j.mechmachtheory.2010.06.004-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000236_j.mechmachtheory.2010.06.004-Figure5-1.png",
        "caption": "Fig. 5. The tooth top parameterization that cuts the drive side tooth root, here shown for a positive value of \u03bc. a) The parameterization of including a super ellipse is shown to be also outside the design domain. b) The super elliptical shape is forced back into the design domain by a distortion.",
        "texts": [
            " This also means that the involute on the costs and m sidemight not be as long as it would have been using the ISO cutting tooth, but this is ignored because of the unidirectional loading assumption. he design domain for the optimization shown as the hatched part. The coast side pressure angle and drive side pressure angle are shown together with the dius on the cutting tool coast side. Final part to be parameterized is the drive top, this is done by a modified super elliptic shape. The design domain is shown as the hatched part in Fig. 4 and enlarged in Fig. 5. As seen in Fig. 4 the design domain size is variable and controlled through the parameter \u03bc, with the restrictions from the boundaries this parameter must fulfill. where \u03bcmin = \u2212\u03c0 4 + 5 4 tan\u00f0\u03b1c\u00de\u2266 \u03bc \u2266\u03c0 4 \u22125 4 tan\u00f0\u03b1d\u00de = \u03bcmax \u00f010\u00de From the optimization presented in Ref. [1] it was found that in order to minimize the stress concentration it is important that the parameterization includes a straight part before entering the elliptical shape, but in that paper the tooth were symmetric. The idea used in the present paper is instead that the design domain can change size through the design parameter \u03bc . The remaining top part is as indicated in Fig. 5a parameterized by a super elliptical shape, only the first quarter of the super ellipse is used. Parametric form of the super ellipse is x = a0 + a1cos\u00f0t\u00de\u00f02=\u03b7\u00de M; t\u2208\u00bd0 : 90\u2218 \u00f011\u00de y = b0 + b1sin\u00f0t\u00de\u00f02=\u03b7\u00de M; t\u2208\u00bd0 : 90\u2218 \u00f012\u00de the constants are given by a0 = \u03bc ; a1 = \u03c0 4 \u2212tan\u00f0\u03b1d\u00de\u2212\u03bc ; b0 = 1; b1 = 1 4 As indicated in Fig. 5a the super ellipse might potentially come outside the design domain, which is not wanted since this has an influence on the length of the involute of the cut tooth. To move the super ellipse back a distortion is added to the x position parameterization. The distortion is indicated in Fig. 5b by rotating the dashed line. The quarter distorted super ellipse parameterization is given by x = a0 + a1cos\u00f0t\u00de\u00f02=\u03b7\u00de 1\u2212 b1 a1 tan\u00f0\u03b1d\u00desin\u00f0t\u00de\u00f02=\u03b7\u00de M; t\u2208\u00bd0 : 90\u2218 \u00f013\u00de y = b0 + b1sin\u00f0t\u00de \u00f02=\u03b7\u00de M; t\u2208\u00bd0 : 90\u2218 \u00f014\u00de Using the parameterization given by Eqs. (13) and (14) it is possible both to achieve the design space upper limit by letting \u03b7\u2192\u221e or the lower boundary by letting \u03b7\u21920. The given parameterization fulfills that the gradient/slope is continuous, i.e., no jumps in the slope if \u03b7\u22671. The presented total cutting tool tooth parameterization is in principle controlled by four parameters; the two pressure angles \u03b1d and \u03b1c, the length parameter \u03bc and the super elliptic power \u03b7"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000645_icra.2013.6631280-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000645_icra.2013.6631280-Figure2-1.png",
        "caption": "Fig. 2: Reference Frames for Manipulator Arms",
        "texts": [
            " MANIPULATOR MODEL Forward kinematics for the two serial chain manipulators are derived using Denavit-Hartenberg (DH) parameters as 978-1-4673-5643-5/13/$31.00 \u00a92013 IEEE 4922 shown in Table I. Parameters e, d, a, and a are in standard DH convention and q;, qr, qr, and q{ are joint variables of each manipulator arm i = [A, B]. Both arms are symmetrical and offset equally from the vehicle's geometric center. Since the general kinematic structure is identical for the right and left arms, the coordinate frames are the same for each arm, only the link B-O is different. Reference frames are shown in Fig. 2 which relate the inertial or world frame, W, to the vehicle or body frame, B, to the tool or end-effector frame, E. To make the DH parameters consistent, an additional frame T is set in the origin of frame L4 (Fig. 2). The direct kinematics function relating the quadrotor body to the end-effector frame is obtained by chain-multiplying the transformation matrices together: (1) To account for quadrotor position and orientation with re spect to the world frame W, an additional matrix multipli cation has to be made with a 6-DOF Euler transformation matrix T{f,. Using the recursive Newton-Euler approach, each arm is modeled as a serial chain RRRR manipulator. The quadrotor body frame is first modeled as a static revolute joint with a constant angular offset for each MM-UAV arm (Link B0)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001968_978-94-007-6101-8-Figure2.7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001968_978-94-007-6101-8-Figure2.7-1.png",
        "caption": "Fig. 2.7 RPY angles for the case of robot gripper",
        "texts": [
            " The orientation is often described by the following sequence of rotations: R : roll\u2014about z axis P : pitch\u2014about y axis Y : yaw\u2014about x axis This description is mostly used with orientation of a ship or airplane. Let us imagine that the airplane flies along z axis and that the coordinate frame is positioned into the center of the airplane. Then, R represents the rotation \u03d5 about z axis, P belongs to the rotation \u03d1 about y axis and Y to the rotation\u03c8 about x axis, as shown in Fig. 2.6. All rotations are performed with respect to a fixed reference frame. 22 2 Rotation and Orientation The meaning of RPY angles for the case of robot gripper is shown in Fig. 2.7. As it can be realized from Figs. 2.6 and 2.7, the RPY orientation is defined with respect to a fixed coordinate frame. In Sect. 2.1 we learned, that consecutive rotations about different axes of the same coordinate frame can be described by the premultiplication of the rotation matrices, or with another words the rotations are performed in the reverse order. We start with the rotation \u03d5 about z axis, continue with rotation\u03d1 about y axis and finish with the rotation \u03c8 about x axis. The reverse order of rotations is evident also from the name of RPY angles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001130_j.jsv.2011.12.025-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001130_j.jsv.2011.12.025-Figure3-1.png",
        "caption": "Fig. 3. Gear variables.",
        "texts": [
            " [15,16] is also employed; the vibration excitation inherent to the tooth meshing is generated as the gears roll and the instant stiffness changes. Moreover, to reduce the calculation times, a new tooth stiffness function is proposed. Furthermore, because of the literature survey and additional verifications not included in this paper, the model is based on the assumption that during the tooth separation periods, the iso-viscous hydrodynamic lubrication contribution to the mesh damping is negligible, as compared to the oil squeeze effects. Fig. 2 and Eqs. (4)\u2013(7) describe the model, while Fig. 3 illustrates some of the variables J1 \u20acy1\u00feR1 cosf 1\u00fe 1 Nc XNc i \u00bc 1 wiSiA1i ! Wdyn\u00feC1 _y1 \u00bc T1 (4a) J2 \u20acy2\u00feR1 cosf mg\u00fe 1 Nc XNc i \u00bc 1 wiSiA2i ! Wdyn\u00feC2 _y2 \u00bc T2 (4b) Wdyn \u00bc Km y1R1 cosf\u00fey2R2 cosf \u00feCm _y1R1 cosf\u00fe _y2R2 cosf h i C2 1 mgR1 cosf _y2 (5) A1\u00f01\u00de \u00bc \u00f0x\u00feDxmc\u00de (6a) A1\u00f02\u00de \u00bc x (6b) A1\u00f03\u00de \u00bc \u00f0x Dxmc\u00de (6c) A2\u00f0i\u00de \u00bc f\u00f01\u00femg\u00detanf A1ig (6d) S\u00bc 1 if xioA1\u00f0i\u00deotanf 0 if A1\u00f0i\u00de \u00bc tanf 1 if tanfoA1\u00f0i\u00deoxo 8>< >: (6e) Dxmc \u00bc 2p N1 (7a) xi \u00bc t1m R1 cosf (7b) xo \u00bc t1n R1 cosf (7c) where x, xi,xo are the roll angle, the roll angle at mesh beginning, the roll angle at mesh end (rad), Dxmc is the angular pitch (rad), yj, _yj, \u20acyj are the angular position (rad), velocity (rad s 1) and acceleration (rad s 2) of wheel j, f is the operating pressure angle (deg"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000921_ic50066a058-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000921_ic50066a058-Figure2-1.png",
        "caption": "Figure 2.-The idealized dodecahedral configuration (left) and the corresponding square antiprism (right) showing the orthogonal relationship of the two principal axes of the polyhedra and the usualZ angle- and edge-labeling scheme.",
        "texts": [
            " ,4 demonstration of this point is set forth in Figure 1 , where stereoviews of the idealized CP and a structure which is halfway between the two are presented, From the drawings the reader can appreciate the necessity for the reference axes and the lines identifying the polyhedron edges. These can only be provided after the choice of CP has been made. t Figure l.-(a) the idealized D z d triangular dodecahedron; (b) the idealized D4d square antiprism; (c) the idealized intermediate configuration. The views constitute stereoscopic pairs and can be viewed with a small hand stereoscope. Previously,\u2019 attention has been focused on the polyhedron-shape parameters, 2-4 as defined originally by Hoard and Silverton? (see Figure 2). Although these parameters are without question the most useful set for describing the two CP, they are not necessarily the most convenient for distinguishing between CP. T o illustrate, let us consider the angular-shape parameter, 8 , which refers to the angle between a metal-ligand bond axis and the principal axis of the CP. There are some immediate difficulties since two such parameters (0, and Bb) are generally defined for the dodecahedron as opposed to one for the antiprism2 and since the principal axis, 8, of the square antiprism is orthogonal to the principal axis, 3, of the corresponding dodecahedron. By \u201ccorresponding dodecahedron,\u201d we mean the one (1) For references see S. J. Lippard, P Y O ~ Y . Inorg. C h e w . , 8, 109 (1967). (2) J. L. Hoard and J. V. Silverton, Inovg. Chem., 9, 235 (1963). (3) D. L. Kepert, J . Chcm. Soc., 4736 (1966). (4) R. V. Parish, Cooud. Chem. Rev., 1, 439 (1966). Vob. 7, No. 8, August 1968 CORRESPONDENCE 1GS7 formed by a suitable distortion5 of the square antiprism, as shown in Figure 2 . Clearly, a comparison of angular-shape parameters will offer little basis for choice between the two CP. It is of course possible to define new angular-shape parameters for the dodecahedron which would be directly comparable to the B parameter of the corresponding antiprism, but this is generally not the most convenient course nor does i t provide a definitive basis for choosing a CP (vide infra). Problems can also arise when the various other shape parameters (edge lengths and angles within the polyhedron faces) are considered",
            " These parameters are usually normalized by the metal-ligand bond distance2 which, although it is a single value for the idealized antiprism, can have two values for the corresponding dodecahedron. Additional ambiguities occur in mixedligand and unsymmetrical chelate complexes, where variations in metal-ligand bond lengths and nonbonded ligand-ligand distances might be expected. Furthermore, whereas only two edge lengths are required to describe the idealized square antiprism, four are needed for the corresponding dodecahedron (Figure 2 ) , a situation which can also cause problems. For example, let us suppose that a complex is dodecahedral but that the investigator has chosen to describe it as the related square antiprism (Figure 2 ) . In order to calculate the length of the s edges, he averages the values for edge lengths 1-2, 2-3, 3-4, 4-1, 5-6, 6-7, 7-8, and 8-5. This process naturally obscures the nonequivalence of the m and g edge lengths of the corresponding dodecahedron and is therefore of questionable value. As a possible approach which appears to avoid most of the above limitations and complications, we suggest that use can be made of the original suggestion of Hoard and Silverton2 that the dodecahedron may be considered as consisting of two mutually perpendicular trapezoids, whose line of intersection contains the central metal atom and coincides with the 2 axis. Accordingly, for any given molecule which is thought to be dodecahedral, the best planes through the atoms comprising the two trapezoids may be calculated, and, from the direction cosines, the angle between these planes may be computed and compared to the ideal (6) J. C. Bailar in \u201cHelvetica Chemica Acta Fasciculus Extraordinarius Alfred Werner,\u201d Basel, 1967, p 90. value of 90\u2019. In Figure 2, the appropriate planes for the dodecahedron contain the metal atom and either (1) the set of ligand atoms 2 , 1, 6, 5 or (2) the set of ligand atoms 4, 3, 8, 7 for the orthogonal plane. For comparison, we have computeds the angle between the corresponding best planes for the idealized square antiprism (Figure 2) which has a value of 77.4\u2019. In the idealized antiprism, these planes are of course not planes a t all, but it is still possible to compute the \u201cbest plane\u201d through the appropriate atoms. This angle thus appears to be both a useful and valid criterion for choosing an eight-coordinate CP. To summarize, we suggest that a given eight-coordinate complex can best be identified with one of the idealized CP in the following manner: (1) compute the trapezoidal best planes for a supposed dodecahedron ; ( 2 ) calculate the value for the angle of intersection between these assumed planes ; (3) compare the angle so obtained with the values of 90\u2019 for the idealized dodecahedron and 77",
            " Of interest is the authors' commentlo that the deviations from their idealized choice of geometry (square antiprism) were such that the molecule tended toward dodecahedral symmetry. It appears to be generally true that the observed distortions of either polyhedron are toward the other. In the case of Y(acac)s(HzO)z, the angle of 86.1' clearly points to the dodecahedron as the most suitable CP, whereas no distinction seems possible on the basis of d T and d~ values. Using the dodecahedral model, the three chelating ligands are found to span m edges with two water molecules occupying the remaining A and B sites (see ref 2 and Figure 2 for nomenclature adopted here). This ligand-wrapping pattern is quite reasonable, since bidentate chelates have been found to span dodecahedral m edges in a variety of other comp1exes.l The original authors, on the other hand, discuss their results using the square antiprism as the idealized CP.12 I n particular, they compare the observed average polyhedron-shape parameters with those calculated by Hoard and Silverton2 for minimization of ligand repulsive energy and imply good agreement. We have made an analogous comparison for the dodecahedral model, the results of which are shown in Table I1 along with the treatment of the original authors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000123_1.4003088-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000123_1.4003088-Figure5-1.png",
        "caption": "Fig. 5 Dynamics of a rigid body u with a diamond-shape vector bond gr",
        "texts": [
            " 5 and 10 , state equations are extracted from ond graphs. Bond graphs have many advantages. Multiphysics ynamic systems, such as electrical, mechanical, magnetic, fluid, hemical, and thermodynamic systems, can be modeled and inked together. Also, finite element model FEM can be embeded in model 11 . Furthermore, the modularity characteristic of ond graphs permits system growth. 3.1 Multibody Dynamics With Bond Graphs. The dynamcs of a 6DOF rigid body system with the global coordinate XYZ nd the body coordinate xyz, as shown in Fig. 5 a , can be repreented with Newton\u2013Euler\u2019s equations, Mx\u0308 = 1 n Fi 19 J\u0304\u0308\u0304 = \u0304 + 1 n r\u0304i F\u0304i \u2212 \u0307\u0304 J\u0304\u0307\u0304 20 xpressed in the global and the body coordinate systems, espectively. The body is subjected to external forces Fi and moment \u0304, also xpressed in the global and the body coordinates, respectively. he second term on the right side of Euler\u2019s equation 20 repreents moments due to external forces. The last term is the Eulerian Tf=1 IRF 2 BF 3 ORF w\u00d7h [mm2] rf = w/h 0 < \u03b2f <2\u03c0 [rad] Fault PositionFault ShapeFault SizeFault Type ig",
            " 5 b and 5 c , Newton\u2019s and Euler\u2019s equations can be represented as 1 junctions that embed conservation of linear momentum and conservation of angular momentum. Transformers TF with modulus of Ai transform coordinates between Euler\u2019s and Newton\u2019s equations and also convert external forces to moments acting on the center of mass. External moments \u0304i are represented by sources of efforts Se. The gyroscopic term \u0307\u0304 J\u0304\u0307\u0304 is incorporated as a modulated RE element. The overall bond graph structure of the system in Fig. 5 a with dynamic equations 24 is the diamond-shaped bond graph structure of Figs. 5 b and 5 c . A multibody system consisting of n rigid bodies can be modeled by connecting n diamond-shape bond graph structures together through constraint models. 3.2 Bond Graph Model of Rolling Element Bearings. A deep-groove ball bearing consisting of nine balls, inner race, and er external loads are represented nd aph model Transactions of the ASME of Use: http://www.asme.org/about-asme/terms-of-use o g n i E g e f F w p r i b s a f r H R a e t N r t s m s a k 4 fi s m v t n tac J Downloaded Fr uter race is modeled as a multibody system using vector bond raphs. The outer race is fixed in a housing characterized by stiffess and damping in the vertical and horizontal directions. The nner race moves and rotates under external forces and torques Fig. 6 a . Weights are applied as external loads on each body. ach element is modeled using the diamond-shaped vector bond raph structure of Fig. 5. Contacts are modeled as nonlinear C lements representing nonlinear stiffness, damping, and traction orces inherent in Eq. 14 . The bond graph model of a bearing with races and one ball, in ig. 6 d , has three of the diamond-shape bond graph structures ith two contact models in between. Each diamond structure aplies Newton\u2013Euler\u2019s equations 24 to inner race, balls, and outer ace via the 1 junction. Each has rotational inertia J, translational nertia M, transformer TF with modulus matrix A transforming ody coordinate system to the global coordinate system Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000282_1.38785-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000282_1.38785-Figure1-1.png",
        "caption": "Fig. 1 Aircraft reference frames.",
        "texts": [
            " The reference frames used in this paper are the Earth-fixed reference frame FE, used as the inertial frame; the vehicle-carried local Earth reference frame FO, with its origin fixed in the center of gravity of the aircraft, which is assumed to have the same orientation as FE; the wind-axes reference frame FW , obtained from FO by three successive rotations of , , and ; the stability-axes reference frameFS, obtained fromFW by a rotation of ; and the body-fixed reference frameFB, obtained fromFS by a rotation of , as is also indicated in Fig. 1. The body-fixed reference frame FB can also be obtained directly from FO by three successive rotations of yaw angle , pitch angle , and roll angle . More details and transformation matrices are given in, for example, [34,35]. Assuming that the aircraft has a rigid body, which is symmetric around the X\u2013Z body-fixed plane, the relevant nonlinear coupled equations of motion can described by [34] _X 0 V cos cos V sin cos V sin 2 4 3 5 (1) _X 1 1 m D T cos cos g sin 1 mV cos L sin Y cos T sin sin cos sin cos 1 mV L cos Y sin T cos sin sin sin cos g V cos 2 4 3 5 (2) D ow nl oa de d by B IB L IO T H E K D E R T U M U E N C H E N o n N ov em be r 11 , 2 01 4 | h ttp :// ar c"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001565_j.mechmachtheory.2014.12.019-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001565_j.mechmachtheory.2014.12.019-Figure3-1.png",
        "caption": "Fig. 3. The position of third coordinate system.",
        "texts": [
            " Similarly, the homogeneous coordinate transformations between (e\u03bb, f\u03bb, g\u03bb) and (t, n, b) can be stated as: t n b 1 2 664 3 775 \u00bc 0 1 0 0 \u2212 sin\u03b2B 0 cos\u03b2B rb cos\u03b2B cos\u03b2B 0 sin\u03b2B rb sin\u03b2B 0 0 0 1 2 664 3 775 eB f B gB 1 2 664 3 775 \u00f02a\u00de and t n b 1 2 664 3 775 \u00bc 0 1 0 0 sin\u03b2A 0 cos\u03b2A rb cos\u03b2A cos\u03b2A 0 \u2212 sin\u03b2A \u2212rb sin\u03b2A 0 0 0 1 2 664 3 775 eA f A gA 1 2 664 3 775: \u00f02b\u00de Prior to making a creep analysis of ball screw, it is necessary to solve the spin angular velocity. The model of spinmotion is shown in Fig. 3. The 2-axis is coincident with the spinning axis of the ball. The projection of the 2-axis in the t\u2212 b plane is defined as 1-axis. The angle between 1-axis and 2-axis is \u03b2, and the angle between 1-axis and b-axis is \u03b2\u2032. The spin angular velocity and pitch radius of the ball screw are defined as \u03c9R and rm, respectively. As shown in Fig. 3, \u03c9t, \u03c9n, \u03c9b are given as follows: \u03c9t \u00bc \u03c9R cos\u03b2 sin\u03b20 \u00f03a\u00de \u03c9b \u00bc \u03c9R cos\u03b2 cos\u03b20 \u00f03b\u00de \u03c9n \u00bc \u03c9R sin\u03b2: \u00f03c\u00de As shown in Fig. 1, three axial components of the nut angular velocity (\u03c9N) in the eA- , fA- , and gA-directions can be written as: VNe \u00bc \u2212\u03c9N rm \u00fe rb\u2212\u03b4N\u00f0 \u00de cos\u03b2A\u00bd \u00f04a\u00de VN f \u00bc 0 \u00f04b\u00de \u03c9Ng \u00bc \u2212\u03c9N sin\u03b2A \u00f04c\u00de where \u03b4N is the normal elastic deformation between the ball and nut, which can be calculated based on Hertz contact theory. In the same way, three axial components of the ball's spin angular velocity (\u03c9R) in the eA- , fA- , and gA-directions can be stated as: VbNe \u00bc \u2212 rb\u2212\u03b4N\u00f0 \u00de \u03c9n cos\u03b2A \u00fe\u03c9b sin\u03b2A\u00f0 \u00de \u00f05a\u00de VbN f \u00bc \u03c9t rb\u2212\u03b4N\u00f0 \u00de \u00f05b\u00de \u03c9bNg \u00bc \u03c9b cos\u03b2A\u2212\u03c9n sin\u03b2A: \u00f05c\u00de According to the roll contact theory [12], rolling velocity between the ball and nut is given as: VrAj j \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi VbNe \u00fe VNe\u00f0 \u00de2 \u00fe VbN f \u00fe VN f 2 r =2 \u00f06\u00de There are |VNf| b b |VNe| and |VbNf| b b |VbNe| under the normal working state of ball screw condition",
            " 4, the three axial components of the spin angular velocity of the ball 1 (\u03c9R1) in the em- , fm- , and gm-directions can be stated as: Vme1 \u00bc rb\u2212\u03b4m\u00f0 \u00de \u03c9n1 cos\u03b1 \u00fe\u03c9b1 sin\u03b1\u00f0 \u00de \u00f017a\u00de Vmf1 \u00bc \u03c9t1 rb\u2212\u03b4m\u00f0 \u00de \u00f017b\u00de \u03c9mg1 \u00bc \u03c9b1 cos\u03b1\u2212\u03c9n1 sin\u03b1: \u00f017c\u00de \u03b4m is the normal elastic deformation between the balls, which can be calculated based on Hertz contact theory. In the sameway, three axial components of the ball's spin angular velocity (\u03c9R) in the em- , fm- , and gm-directions can be expressed as: Vme2 \u00bc \u2212 rb\u2212\u03b4m\u00f0 \u00de \u03c9n2 cos\u03b1 \u00fe\u03c9b2 sin\u03b1\u00f0 \u00de \u00f018a\u00de Vmf2 \u00bc \u2212\u03c9t2 rb\u2212\u03b4m\u00f0 \u00de \u00f018b\u00de \u03c9mg2 \u00bc \u03c9n2 sin\u03b1\u2212\u03c9b2 cos\u03b1 \u00f018c\u00de where \u03c9R1 and \u03c9R2 can be obtained based on \u03c9R using homogeneous coordinate transformations (Eq.(1)). The relationship between \u03c9t1, \u03c9n1 and \u03c9b1 (or \u03c9t2, \u03c9n2 and \u03c9b2) and \u03c9R1 (or \u03c9R2) is shown in Fig. 3 and Eqs.(3a)\u2013(3c). There are |Vmf1| b b |Vme1| and |Vmf2| b b |Vme2| under normal working conditions for a ball screw. According to the roll contact theory and Eq. (6), rolling velocity between the balls can be simplified as: Vrm \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Vme2 \u00fe Vme1\u00f0 \u00de2 \u00fe Vmf2 \u00fe Vmf1 r =2\u2248\u2212 Vme1 \u00fe Vme2\u00f0 \u00de=2 \u00bc rb\u2212\u03b4m\u00f0 \u00de \u03c9n2 cos\u03b1 \u00fe\u03c9b2 sin\u03b1\u00f0 \u00de\u2212 rb\u2212\u03b4m\u00f0 \u00de \u03c9n1 cos\u03b1 \u00fe\u03c9b1 sin\u03b1\u00f0 \u00de\u00bd =2: \u00f019\u00de The vertical creep ratio (\u03beem), horizontal creep ratio (\u03befm) and spin ratio (\u03c6m) can be written as: \u03beem Vme1\u2212Vme2 Vrm \u00bc 2 rb\u2212\u03b4m\u00f0 \u00de \u03c9n1 cos\u03b1 \u00fe\u03c9b1 sin\u03b1\u00f0 \u00de \u00fe rb\u2212\u03b4m\u00f0 \u00de \u03c9n2 cos\u03b1 \u00fe\u03c9b2 sin\u03b1\u00f0 \u00de rb\u2212\u03b4m\u00f0 \u00de \u03c9n2 cos\u03b1 \u00fe\u03c9b2 sin\u03b1\u00f0 \u00de\u2212 rb\u2212\u03b4m\u00f0 \u00de \u03c9n1 cos\u03b1 \u00fe\u03c9b1 sin\u03b1\u00f0 \u00de \u00f020a\u00de \u03befm \u00bc Vmf1\u2212Vmf2 Vrm \u00bc 2 \u03c9t1 \u00fe\u03c9t2\u00f0 \u00de rb\u2212\u03b4m\u00f0 \u00de rb\u2212\u03b4m\u00f0 \u00de \u03c9n2 cos\u03b1 \u00fe\u03c9b2 sin\u03b1\u00f0 \u00de\u2212 rb\u2212\u03b4m\u00f0 \u00de \u03c9n1 cos\u03b1 \u00fe\u03c9b1 sin\u03b1\u00f0 \u00de \u00f020b\u00de \u03c6m \u00bc \u03c9mg1\u2212\u03c9mg2 Vrm \u00bc 2 cos\u03b1 \u03c9b1 \u00fe\u03c9b2\u00f0 \u00de\u2212 sin\u03b1 \u03c9n1 \u00fe\u03c9n2\u00f0 \u00de rb\u2212\u03b4m\u00f0 \u00de \u03c9n2 cos\u03b1 \u00fe\u03c9b2 sin\u03b1\u00f0 \u00de\u2212 rb\u2212\u03b4m\u00f0 \u00de \u03c9n1 cos\u03b1 \u00fe\u03c9b1 sin\u03b1\u00f0 \u00de : \u00f020c\u00de Considering the differential slipping caused by ball surface warpage, two components of slipping velocity in the em- and fmdirections [12] are given as: Cem \u00bc \u03beem\u2212 f m\u03c6m\u2212\u03beh f m\u00f0 \u00de \u00f021a\u00de Cfm \u00bc \u03befm \u00fe em\u03c6m: \u00f021b\u00de \u03beh(fm) is the slipping item of Heathcote, which is expressed based on the roll contact theory and can be obtained as: \u03beh f m\u00f0 \u00de \u00bc 1\u00fe\u03c9n2 sin\u03b1\u2212\u03c9b2 cos\u03b1 \u03c9b1 cos\u03b1\u2212\u03c9n1 sin\u03b1 f m 2 2rb 2 \u00f022\u00de Based on Kalker's [11] theory of linear creep, vertical friction (Fe\u03bb) and horizontal friction (Ff\u03bb) at the contact area can be defined as: Fe\u03bb \u00bc \u2212Gc0 2C1 \u03bee\u03bb\u2212\u03beh\u03bb\u00f0 \u00de \u00f023a\u00de F f\u03bb \u00bc \u2212Gc0 2 C2\u03be f\u03bb \u00fe C3c0\u03c6\u03bb \u00f023b\u00de where \u03bb = A, B and m represent different contact areas; G is the shear modulus; c0 \u00bc ffiffiffiffiffi ab p ; a and b are semi-major axis and minor semi-axis of contact ellipse, respectively, which can be calculated based on Hertz contact theory; C1, C2 and C3 are the creep coefficients [11], which can be calculated using the empirical formula as C1 = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003076_tmag.2019.2955884-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003076_tmag.2019.2955884-Figure1-1.png",
        "caption": "Fig. 1. Structure of the proposed exterior-rotor multiple teeth PM-SRM.",
        "texts": [
            " This efficacious structure leads to a dramatic increase in the output torque and power. The motor topology and its working principle are clarified based on the simplified magnetic equivalent circuit (MEC). The static and dynamic performances of the proposed motor are illustrated and the results are compared with those of its PMless counterpart and a classical 12/10 SRM. Finally, a prototype of the proposed motor is manufactured, and the test results are presented followed by a brief conclusion. Fig. 1 depicts the configuration of the proposed exteriorrotor PM-SRM with multiple teeth structures. The motor is composed of three phases, each of which has four concentrated windings. Each stator pole consists of four small teeth and the rotor comprises 50 teeth, so the motor has a 48/50-tooth configuration. Six PMs are embedded inside the gap between the end teeth of the neighboring stator poles, all of which have the same magnetization direction. Table I lists the main dimensions and parameters of the proposed PM-SRM, PMless SRM, and a classical external rotor 12/10-pole SRM"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002546_rcs.1824-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002546_rcs.1824-Figure4-1.png",
        "caption": "FIGURE 4 Tendon transmission schematic of the PSM1",
        "texts": [
            " M \u03b8\u00f0 \u00de\u20ac\u03b8 \u00fe C \u03b8; _\u03b8 _\u03b8\u00feN \u03b8\u00f0 \u00de \u00bc \u03c4 (1) where \u03b8 \u2208 R6 \u00d7 1 is the vector of joint variables, \u03c4 \u2208 R6 \u00d7 1 is the vector of joint torques, M(\u03b8) \u2208R6 \u00d7 6 is the symmetric positive definite inertia matrix,C \u03b8; _\u03b8 \u2208 R6\u00d76 is the Coriolis and centrifugal force matrix, and N(\u03b8) \u2208R6 \u00d7 1 is the vector of gravitational forces. To implement external force estimation and motion decoupling, the mapping relationship between joint space and motor driving space is needed. The first and second joints are driven by twin motors in a parallel configuration. To facilitate analysis, these two twin motors are equivalent to one motor. The tendon transmission schematic of the PSM1 is shown in Figure 4. The mapping relationship between tendon displacements and joint angular displacements can be expressed as the following equation: s\u00bc A\u03b8 (2) FIGURE 3 The link structure and the zero configuration of the open\u2013loop where s = [s1 \u22ef s12] T is a 12 \u00d7 1 dimensional tendon displacement vector, \u03b8 \u00bc \u03b81 \u22ef \u03b86\u00bd \u03a4 is a 6 \u00d7 1 dimensional joint angle vector, and A \u00bc r1 \u2212r1 0 0 0 0 0 0 0 0 0 0 0 0 r2 \u2212r2 0 0 0 0 0 0 0 0 0 0 0 0 r3 \u2212r3 0 0 0 0 0 0 0 0 0 0 0 0 r4 \u2212r4 0 0 0 0 0 0 0 0 0 0 0 0 r5 \u2212r5 0 0 0 0 0 0 0 0 0 0 r7 \u2212r6 r8 \u2212r8 2 6666666664 3 7777777775 \u03a4 is a 12 \u00d7 6 dimensional matrix about the radii of pulleys coupled relative joint axes, and r5 = r6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000648_978-3-642-17531-2-Figure8.2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000648_978-3-642-17531-2-Figure8.2-1.png",
        "caption": "Fig. 8.2. Electromagnetically-acting transducers: transducer classes",
        "texts": [
            " Unfortunately, it has become common in many places to employ \u201celectromagnetic transducer\u201d as a generic term for transducers based on either principle. The ensuing confusion of terms is unmistakable. It is true that both transducer principles employ the physical phenomenon of electromagnetic transduction, as described by the MAXWELL\u2019s equations and the LORENTZ force. To establish a clear and unambiguous terminology, this book thus employs the superordinate term \u201celectromagnetically-acting transducer\u201d and designates the subordinate transducer types as electromagnetic (EM) transducers and electrodynamic (ED) transducers (Fig. 8.2). In fact, it would be more consistent and unambiguous to use terms such as reluctance transducer or LORENTZ transducer, directly describing the fundamental physical principle being exploited1. Systems engineering significance From a systems engineering point of view, the functions \u201cgenerate forces/torques\u201d and \u201cmeasure mechanical states\u201d realizable with electromagnetic phenomena represent the actuators and sensors of a mechatronic system (see Fig. 8.1). For both tasks, it is the transfer characteristics in the causal directions shown in Fig",
            " In turn, time variation of the magnetic field induces a spatiallyvarying electric field ( , )E r t in the neighborhood of the electric conductor. The spatially-varying electric and magnetic fields are thus coupled and can be exploited for engineering purposes in a variety of ways with suitable spatial arrangement of the exciting line currents. MAXWELL\u2019s equations for quasi-stationary fields The fundamental physical relationships of these phenomena are defined by MAXWELL\u2019s equations for quasi-stationary fields2 (Jackson 1999). The equations applying to the magnetic field3 are, in integral form4, (see Fig. 8.2) AMP\u00c8RE\u2019s law: H Hs A H ds G dA , (8.1) FARADAY-MAXWELL equation: s A d E ds B dA dt , (8.2) Continuity equation: 0B dA , (8.3) Material equation: B H , (8.4) 2 Meaning slowly-varying fields. Given such, the free current density G will be significantly greater than the displacement current density /D t , so that the latter can be neglected in the formulation given in Eq. (8.1). 3 The FARADAY-MAXWELL equation in Eq. (8.2) is not explicitly required to derive the elementary transducer equations. The corresponding induction relation results automatically from the LAGRANGE equations",
            "2 Physical Foundations 499 Line currents AMP\u00c8RE\u2019s law (8.1) describes how a magnetic field with a spatially-distributed field intensity ( )H r arises from the flow of an electric current. In this book, it is currents carried in essentially one-dimensional conductors\u2014so-called line currents\u2014 L C A i G dA which are of interest. Magnetomotive force (MMF) From AMP\u00c8RE\u2019s law (8.1), it further follows that the path integral over a closed magnetic field line of length H s equals the sum of line currents encircled by the field line (see Fig. 8.2), i.e. : H H j js A H ds G dA i F . (8.6) The quantity F [A] or [AT, ampere-turns] is termed the magnetomotive force (MMF) Magnetic flux Using the magnetic flux density B , the material equation (8.4) describes the action of a magnetic field in a medium (e.g. air or iron). The total flux density penetrating an area A is termed the magnetic flux [V s Weber Wb] (see Fig. 8.2), where : A B dA . (8.7) Homogeneous magnetic field AMP\u00c8RE\u2019s law (8.1) describes the relationship between the exciting current and the contour integral of the magnetic field intensity, not the field intensity itself. However, Eq. (8.1) still forms the basis magnetic field calculations (Jackson 1999), (Hughes 2006). For simple, symmetric configurations, it can be straightforwardly employed to derive predictive design models. One often easily met assumption is that of a homogeneous magnetic field, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002213_j.mechmachtheory.2014.06.006-Figure14-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002213_j.mechmachtheory.2014.06.006-Figure14-1.png",
        "caption": "Fig. 14. State 10 of the derivative queer-square mechanism (\u03b11 b 0, \u03b12 b 0, \u03b211 \u2260 \u03b212, \u03b221 = \u03b222).",
        "texts": [
            " Similarly, the ranges of angles \u03b11, \u03b12, \u03b211, \u03b212, \u03b221 and \u03b222 of the derivative queer-square mechanism in state 9 are given as \u03b11b0;\u03b211N0;\u03b212N0 \u03b12N0;\u03b221N0;\u03b222N0 : \u00f036\u00de From Fig. 13 and Eq. (36), we could find that limb1s is located lower than the base OA1A2, limb2s is located higher than the base OA1A2, and the platform E1F1E2F2 is located higher than limb1ap and lower than limb2p in state 9. The observation of the dimetric view of the derivative queer-square mechanism in state 10 is given in Fig. 14. The angle ranges of state 10where angles \u03b211 and \u03b212 have different values and angles \u03b221 and \u03b222 have the same value are \u03b11b0;\u03b211b0;\u03b212b0 \u03b12b0;\u03b221N0;\u03b222N0 : \u00f037\u00de For these four kinds of states where limb1s, limb2s, limb1ap and limb2p have different relative positions, by substituting the particular angle relations in Eq. (33) into the platform constraint\u2013screw system and obtaining the reciprocal screw, the result of platform motion\u2013screw system is shown as S f n o \u00bc S f1 \u00bc 1 0 0 h i j\u00bd T n o ; \u00f038\u00de where, h \u00bc s\u03b11 2l1s\u03b211c\u03b212s\u03b12\u2212l2s\u03b12s\u03b211c\u03b212\u2212l2s\u03b12c\u03b211s\u03b212 \u00fe 2l2c\u03b12s\u03b211s\u03b212 \u22122l1c\u03b211s\u03b212s\u03b12 \u00fe 2l3c\u03b12s\u03b212s\u03b11c\u03b211\u22122l3c\u03b12s\u03b211s\u03b11c\u03b212 2c\u03b11 c\u03b211s\u03b212\u2212c\u03b212s\u03b211\u00f0 \u00de s\u03b12\u2212s \u03b12 \u00fe \u03b82\u00f0 \u00dec\u03b12 \u00fe c \u03b12 \u00fe \u03b82\u00f0 \u00des\u03b12\u00bd ; i \u00bc l3s\u03b212s\u03b11c\u03b211\u2212l3s\u03b211s\u03b11c\u03b212 \u00fe l2s\u03b211s\u03b212 c\u03b211s\u03b212\u2212c\u03b212s\u03b211 ; andj \u00bc c \u03b12\u00fe\u03b82\u00f0 \u00de l2s\u03b12s\u03b212c\u03b211 \u00fe 2l1s \u03b12 \u00fe \u03b82\u00f0 \u00dec\u03b12s\u03b211c\u03b212\u22122l1c \u03b12 \u00fe \u03b82\u00f0 \u00des\u03b12s\u03b211c\u03b212 \u00fe2l2s\u03b211s\u03b212c\u03b12 \u00fe 2l3c\u03b12s\u03b212s\u03b11c\u03b211\u22122l3c\u03b12s\u03b211s\u03b11c\u03b212 \u22122l1s \u03b12 \u00fe \u03b82\u00f0 \u00dec\u03b12s\u03b212c\u03b211\u2212l2s\u03b12s\u03b211c\u03b212 \u00fe 2l1c \u03b12 \u00fe \u03b82\u00f0 \u00des\u03b12s\u03b212c\u03b211 \u00fe2l2c \u03b12 \u00fe \u03b82\u00f0 \u00des\u03b12s\u03b212c\u03b212\u22122l2s \u03b12 \u00fe \u03b82\u00f0 \u00dec\u03b12s\u03b212c\u03b211 0 BB@ 1 CCA 2 \u2212s \u03b12\u00fe\u03b82\u00f0 \u00dec\u03b12\u00fec \u03b12\u00fe\u03b82\u00f0 \u00des\u03b12\u00fes\u03b12\u00bd c\u03b212s\u03b211\u2212c\u03b211s\u03b212\u00f0 \u00de : The platformmotion\u2013screw system shows that the platform of the derivative queer-squaremechanismhasmobility onewhen the bars in the combination limb1ap are antiparallel to each other and thebars in the combination limb2p are parallel to each other"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001488_piee.1965.0386-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001488_piee.1965.0386-Figure9-1.png",
        "caption": "Fig. 9 Penetration of a rotating flux wave into a lamination",
        "texts": [
            "3 The reduction of leakage reactance The eddy currents that are induced on the rotor surface not only cause losses in the surface itself, but, by damping the differential harmonic leakage flux, cause more harmonic currents to flow in the squirrel-cage bars, and hence also increase the bar I2R losses. To account for this effect, the differential harmonic leakage has to be multiplied by a reduction factor kdh, as shown in eqn. 6. This factor will now be calculated. ( vrry -y- + a to travel on the two sides of a lamination of thickness ft, PROC. IEE, Vol. 112, No. 12, DECEMBER 1965 as shown in Fig. 9. The phasor flux density inside the lamination satisfies the equation The solution for Byv therefore has the form B^ = Cxe kx + C2e~kx (33) where Cx and C2 are constants. Using the condition that the flux density at the surface of the lamination (x = \u00b1 h/2) is JBOV = fi^o/fOv, where HQy is the surface m.m.f., one finally obtains \u2014 B{Ov cosh kx cosh \u2014 The total flux carried by the lamination per unit length in the z direction is <D = +A/2 \\ByJy J-hl2 = JBOV T tanh \u2014 kh ~2 If no eddy currents were present, the lamination would carry a flux O0v = B0Ji"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003237_j.matdes.2020.108824-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003237_j.matdes.2020.108824-Figure6-1.png",
        "caption": "Fig. 6. Residual stress distribution in all directions: (a) transverse stress, (b) radial stress and (c) longitudinal stress.",
        "texts": [
            " From the stable value of the final residual stress, SSPT can significantly reduce the longitudinal residual stress and the transverse residual stress. In the case with SSPT, the transverse stress and the longitudinal stress at the coating center are closer to the measured transverse stress (-21MPa) and longitudinal stress value (152MPa). Jo ur na l P re -p ro of Fig. 5. Temperature and stress evolution at midpoint o: (a) midpoint o, (b) temperature evolution, (c) transverse stress and (d) longitudinal stress. Fig. 6 (a), (b) and (c) show the transverse (along the X-axis direction), radial (along the Y-axis direction) and longitudinal (along the Z-axis direction) residual stress distribution under two conditions (with SSPT and without SSPT) respectively. It can be seen from Fig. 6 that SSPT has certain influence on the distribution of residual stress in all directions. For the transverse residual stress (along the X-axis direction), SSPT can significantly reduce the residual stresses at various locations on the model surface. The maximum tensile stress and the maximum compressive stress are 262 MPa and -172 MPa in the case without SSPT, while the maximum tensile stress and the maximum compressive stress are reduced to 229 MPa and -140 MPa in the case with SSPT. The transverse compressive stress in the middle of the substrate was caused by the shrinkage of the substrate pulled by the shrinkage of the coating solidification"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003090_j.mechatronics.2020.102388-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003090_j.mechatronics.2020.102388-Figure1-1.png",
        "caption": "Fig. 1. BIT-NAZA.",
        "texts": [
            " The existence of force-tracking errors on the unknown terain is demonstrated in Section 3 . Section 4 introduces the adaptive mpedance control with variable stiffness, and the theoretical analysis n the stability of the proposed control method is also clarified. This ontrol algorithm is verified by a series of simulations and experiments n Section 5 . Finally, conclusions are made to summarize the main work f this paper in Section 6. . Wheel-legged robot and system model of robot and nvironment .1. BIT-NAZA The wheel-legged robot used in this study, called BIT-NAZA (as hown in Fig. 1 ), is an electric parallel wheel-legged robot, which conists of four 6-DOF (six-degree-of-freedom) parallel platforms that are sed as legs of the robot, and four actuated wheels that are mounted n the above top of the platform as end-effectors. The presence of both heel and leg enables the robot more flexible and diverse movements. he main parameters of BIT-NAZA are listed in Table 1 . The goal of BIT-NAZA is to execute a transportation task with comliant interaction and maintain a level posture through the expansion of It is mainly composed of an inverted parallel 6-DOF platform and a heel"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001652_s00170-017-0760-9-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001652_s00170-017-0760-9-Figure8-1.png",
        "caption": "Fig. 8 Geometry of cladded specimen models. a Single-track showing the 3D view and the cross section taken at the center of the specimen. bMultitrack specimen showing the cladding direction for all beads",
        "texts": [
            " The study shows that the maximum residual stress variation is negligible by increasing the number of elements to more than 9964 for the single-bead specimen (Fig. 7). The geometry with 6, 8, and 10 elements throughout the thickness of the substrate sheet section was tested, and it was found that eight elements through the thickness of the 10 mm substrate were appropriate for the accuracy andmodel running time. The geometry dimensions and FE mesh used in the experiment and the models are shown in Fig. 8a, b. The size of the uniform element of the substrate was 0.5 \u00d7 0.5 \u00d7 2 mm, and the smallest element size of the bead was approximately 0.4 \u00d7 0.4 \u00d7 2 mm. The quality of the mesh was evaluated using the Jacobi algorithm, and the minimum value of 0.75 and maximum value of 1.0 were found. This high resolution is especially necessary for the adequate simulation of the moving heat source. The mesh elements of the bead are initially inactive and are activated with the temperature change. Constraints are needed to prevent rigid body motion, so one corner was fixed, and two corners were clamped in the y direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001711_s1560354713060166-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001711_s1560354713060166-Figure1-1.png",
        "caption": "Fig. 1.",
        "texts": [
            "1) The configuration space of the system under consideration is the manifold SO(3) \u00d7 R2, where the first factor corresponds to the orientation of the ball and the second defines the position of the contact point. We parameterize it by the pair (Q, r), where the orthogonal matrix is Q = \u239b \u239c\u239c\u239c\u239d \u03b11 \u03b21 \u03b31 \u03b12 \u03b22 \u03b32 \u03b13 \u03b23 \u03b33 \u239e \u239f\u239f\u239f\u23a0 \u2282 SO(3). REGULAR AND CHAOTIC DYNAMICS Vol. 18 No. 6 2013 The columns of the matrix correspond to the coordinates of fixed unit vectors given in the moving axes (e1,e2,e3), and the vector \u03b3 = (\u03b31, \u03b32, \u03b33) coincides with the normal to the plane (see Fig. 1), \u03b1,\u03b2 are parallel to the plane, and the vector r = (x, y) defines the coordinates of the contact point in the fixed axes. (In what follows, unless otherwise stated, all vectors except for r are assumed to be given in the fixed axes.) The angular momentum of the ball relative to the contact point P is M = I\u03c9 + D\u03b3 \u00d7 (\u03c9 \u00d7 \u03b3), D = mb2, (1.2) where \u03c9 is the angular velocity of the ball. As is well known [15, 18, 21], after eliminating the constraints, the system of equations governing the evolution of the orientation Q and the position (x, y) of the ball can be represented using this vector as M\u0307 = M \u00d7 \u03c9, \u03b3\u0307 = \u03b3 \u00d7 \u03c9, \u03b1\u0307 = \u03b1 \u00d7 \u03c9, \u03b2\u0307 = \u03b2 \u00d7 \u03c9, (1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002004_1.4028532-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002004_1.4028532-Figure8-1.png",
        "caption": "Fig. 8 Two tessellations of the CC-Miura pattern unit geometry. (a) Tessellation 1 and (b) tessellation 2.",
        "texts": [
            " As a final comment on the creation of the CC-Miura pattern, it should be noted that many different curves can be defined through three nodes on a prismatic base pattern, beyond the simple elliptical curve discussed above. More complex conic curves can be derived by fitting partial elliptical curves through half-units of the base prismatic geometry, and can still be completely defined with the single gradient parameter u. Different curves defined with the same gradient on the same prismatic base are termed tessellations. Tessellation 1 is defined as the geometry obtained by fitting the basic ellipse through sequential zigzags in the manner described above, shown in Fig. 8(a). Tessellation 2 is defined as the geometry obtained by fitting an ellipse and a reversed ellipse through sequential zigzags and so is similar to commonly seen sinusoidal CC patterns, shown in Fig. 8(b). Note that the shown tessellation 2 pattern has a doubled number of divisor lines, S\u00bc 8, to better express the continuous curve. These alternate tessellations can be realized by pointing the u0\u00f0tk\u00de and v0\u00f0tk\u00de terms in Eqs. (16) and (17) to a different parametric curve. For example, tessellation 2 is generated with new expressions u0\u00f0tk\u00de \u00bc \u00f0g\u00fe c cos\u00f02tk \u00fe tlim\u00de\u00de=2 for 0 k < S\u00fe 1 \u00f0g\u00fe c cos\u00f02tk tlim\u00de\u00de=2 for S\u00fe 1 k < 2S (24) v0\u00f0tk\u00de \u00bc \u00f0h\u00fe d sin\u00f02tk \u00fe tlim\u00de\u00de=2 for 0 k < S\u00fe 1 \u00f0h\u00fe d sin\u00f02tk tlim\u00de\u00de=2 for S\u00fe 1 k < 2S (25) Many other tessellations can be formed in this manner"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003719_j.ymssp.2020.107133-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003719_j.ymssp.2020.107133-Figure1-1.png",
        "caption": "Fig. 1. Experimental platforms: (a) experimental apparatus, and (b) schematic diagram.",
        "texts": [
            " In this section, an experimental platform is designed to present the pressure/displacement characteristics of the PAM under different working conditions, including operating frequencies and loads. Then, the effects of input frequencies and mechanical loads on hysteresis behaviors are disclosed quantitatively based on the experimental data. Hysteresis in the PAM can be examined between pressure and displacement or between force and displacement [35\u201339]. This paper focuses on the pressure/displacement-based hysteresis because pressure usually acts as the direct input in most applications. The experimental apparatus is shown in Fig. 1(a). The PAM tested in this experiment system is an in-house built prototype McKibben PAM [40] with an initial length of 130 mm and an initial diameter of 8 mm. Besides, the main experimental devices consist a dSPACE, a computer, a pressure sensor (Honeywell 40PC150G2A), a pneumatic cylinder (SC32 50- S), pneumatic triplets, a displacement sensor (WXY31), a proportional valve (SMC, ITV2050-212L), and an air compressor. One end of the PAM is fixed to a fixed base and the other end is linked to the cylinder. The required external load is exerted to the PAM by the cylinder. During the experiment, inflation pressure is supplied to the actuator via a proportional pressure regulator driven by 0\u201310 V analog inputs, and displacements and inflation pressure of the PAM are measured by a displacement sensor and a pressure sensor, respectively. Fig. 1(b) displays the schematic diagram of the experimental setup, where the desired excitation signals generated in the dSPACE is utilized to regulate the pressure of the PAM to required value. The measured data from the displacement sensor and pressure sensor is received in the dSPACE and recorded on the computer for further analyses. The hysteresis properties of the PAM are firstly characterized by major loop tests under a range of mechanical loads and excitation frequencies. In the initial state, the PAM with no pressure inside is applied to a mechanical load",
            " 9 shows the identification parameters of the hysteresis submodel. Based on the selection of Nr , a quadratic polynomial P u\u00bd t\u00f0 \u00de \u00bc 1:5556u t\u00f0 \u00de - 0:7691u t\u00f0 \u00de2 is applied to fit the memoryless function in Eq. (3). Thus the identified results of the hysteresis submodel have been shown in Fig. 10. In order to identify the load-dependent dynamic submodel in Fig. 6, training data is required to reflect the actuator responses with variable-frequency signals under different loading conditions. Taking advantage of the experimental system shown in Fig. 1, the PAM is actuated by a chirp signal with frequency ranging from 0 to 1 Hz in a period of 100 s. To highlight the influence of loads on the output behavior of the PAM, a lower input pressure amplitude of 1.6 bar is selected. All Experimental outputs are collected under mechanical loads varying from 0 kg to 12 kg with an increasement of 1 kg. The load of 12 kg is the maximum safe load capacity for the experimental PAM corresponding to the pressure amplitude of 1.6 bar. As an illustration, Fig. 11 displays the input-output experimental data of the PAM under a load of 1 kg"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001606_jestpe.2013.2284096-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001606_jestpe.2013.2284096-Figure6-1.png",
        "caption": "Fig. 6. (a) Parallel gear stage, (b) dynamic model representation, and (c) model representation in Simscape/SimDriveline.",
        "texts": [
            " This phenomenon contributes to the definition of gear meshing stiffness [33]\u2013[37], which plays an important part in the dynamics of the meshing gears. In this paper, a purely torsional model of the gearbox with constant meshing stiffness is built in the Simscape/SimDriveline environment. The model development and analysis of both planetary and parallel gear stages are briefly discussed in the following sections. The development and simulations of this drivetrain model are discussed in detail in [31]. Fig. 6(a) shows a parallel gear set, which is a torque reducer, commonly employed in wind turbine drivetrains. Fig. 6(b) represents its flexible equivalent, in which the constant meshing stiffness acts along the line of action of the meshing gears. This stiffness kmesh, with respect to the driving (i.e., input) gear, can be represented as [6] kmesh = kgear(rb1 cos \u03b2)2 (2) where the gear tooth stiffness kgear can be determined according to international standards [38], [39]. Fig. 7 shows a planetary gear set with three planet gears, which is the configuration installed in the GRC drivetrain. The rotational input enters from the carrier of the planetary gear stage, which provides rotational motion through the planet gears, and finally to the sun gear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003995_j.ijmecsci.2020.105782-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003995_j.ijmecsci.2020.105782-Figure1-1.png",
        "caption": "Fig. 1. Definition of coordinate systems of ball bearing in the dynamic model: inertial coordinate system [O; X,Y,Z ], coordinate system [O bj ; x bj ,y bj ,z bj ] for the j th ball, coordinate system [O c ; x c ,y c ,z c ] for the cage, coordinate system [O pj ; x pj ,y pj ,z pj ] for the j th pocket, coordinate system [ O \u030b; x \u030b, y \u030b, z \u030b] for the local contact between ball and raceway.",
        "texts": [],
        "surrounding_texts": [
            "r [ [\ni T r t l v t b r e i s e o r r\ne a t t t i s s c a u v [ i o b\ns o c e i i i t b t t p b w o s\n2\nb p w i w\n2\nn F x F t d [ T t t t r c c c\n2\nc\nNomenclature\nQ i/o contact force between ball and raceways F i/o traction force between ball and raceways M i/o traction moment between ball and raceways F c j centrifugal force of j th ball F ci y , F ci z centrifugal force of cage F D viscous drag force F co y , F co z interaction force between outer ring and cage M co x friction moment between outer ring and cage G b , G c The gravity load of ball and cage, respectively \ud835\udc39 \ud835\udc57\n\ud835\udc50\ud835\udc4f\ud835\udc5b impact force between ball and cage pocket\n\ud835\udc39 \ud835\udc57\n\ud835\udc50\ud835\udc4f\ud835\udc53 frictional force between ball and cage pocket\nm b mass of the ball I b rotational inertia of ball I i inertia moment of ball around Z axis m c mass of cage I c rotational inertia of cage R radius of the guiding surface of cage L width of the cage C p clearance of cage pocket C g guiding clearance of cage \ud835\udf00 relative eccentricity of cage. m i mass of shaft assembly d ball diameter d m bearing pitch diameter \ud835\udf11 b j position angle of j th ball \ud835\udf11 c position angle of cage \u2206x b , \u2206z b displacement of ball in x b , z b axis \u2206y c , \u2206z c displacement of cage in y c , z c axis \u2206x i , \u2206y i , \u2206z i displacement of inner ring in x i , y i , z i axis \ud835\udf14 o orbital revolution speed of ball \ud835\udf14 x , \ud835\udf14 y , \ud835\udf14 z rotating angular velocity of ball around x b , y b , z b axis \u2206V i/o sliding speed between ball and raceways \ud835\udf14 i shaft rotation speed \ud835\udf14 c cage rotation speed \ud835\udefci/j contact angle u entrainment speed between cage and outer ring \ud835\udc5f \ud835\udc5d\n\ud835\udc4f\ud835\udc4f\ud835\udc57 motion of ball in pocket coordinate system\nK l lubricant stiffness K c dry contact stiffness \ud835\udf07bc friction coefficient between ball and cage pocket\nesearches on the effects of ball diameter tolerance, arrangement of balls 41] and thermal-related fit clearance between outer ring and pedestal 42] on the loading condition and vibration intensity of bearing.\nIt is found that the cage is one of the most problematic components n a rolling bearing from the point of view of bearing dynamics [19] .\nakabi et al. [43] analyzed the cage slip ratio and cage wear rate in a adial loaded cylindrical roller bearing. Their simulation results showed hat wear rate is larger when the bearing is operating under lower radial oad and higher rotation speed. Niu et al. [44] investigated the roles of arious forces acting on the cage in the stable cage whirl motions on he basis of Gupta\u2019s model and found that the contact force between\nall-cage pocket plays an important role in the increase of cage whirl adius and in the maintenance of the constant whirl speed. Ghaisas t al. [19] employed a dynamic bearing model (DBM) to investigate the nfluence of internal clearance and the clearance ratio on the cage intability. Later, Ashtekar et al. [45] investigated the dynamics of rolling lement bearings with surface irregularities and localized defects based n the DBM model. Their simulation results showed that the surface iregularities and localized defects alter the contact force magnitude and esult in dynamic instability in the motion of bearing components. Nogi\nt al. [46] developed a simple theory for cage instability, and proposed\ncritical cage friction coefficient formula. Takabi et al. [47] estimated he traction curves of lubricants based on the experiment results, and hen explored the unstable motion of cage under different operating emperatures. Sathyan et al. [48] experimentally investigated the cage nstability failures in spacecraft bearings. The results of this study howed that the operating temperature has significant influence on the tability of cage, and the dynamic characteristics are different for the age with different pocket geometries under extreme operating tempertures. Abele et al. [49] experimentally investigated the cage motion\nsing an image-based approach, and the suitability of this method is erified by experiments on a bearing test rig. Kingsbury and Walker 50] conducted an experimental investigation of the cage motion in an nstrument ball bearing during stable and unstable operation, and their bservations agree well with predictions from a squeal model based on\nall-cage frictional coupling.\nIt can be found that some bearing dynamic models have been uccessfully established, and the effects of various factors including perating conditions, bearing structure parameters and lubrication ondition have been explored. However, the space bearings indeed ncounter the problems such as abnormal torque fluctuation and cage nstability. As the space bearings experience significantly different gravty environments, the microgravity effects on the bearing performance s still unclear, which is of importance in bearing design, ground based ests and space service. In this paper, the nonlinear dynamic behavior of\nearing under microgravity and gravity were investigated. To this end, he bearing dynamic model was established in the Section 2 considering he gravity effects. And then the proposed model was verified by comaring with published experimental results in Section 2.2 . The skidding ehavior, impact and stability of cage under microgravity and gravity\nere discussed in Section 2.3 and Section 2.3 . The instability mechanism f cage was explored in detail, and the criterion for the cage to maintain table under extreme operation conditions was further proposed.\n. Theoretical model\nA bearing dynamic model, considering the interactions between earing components and lubricant with temperature effect, has been roposed by authors in recent work [6] , however, the effect of gravity as not emphasized. In this section, the model is comprehensively\nmproved to consider the effect of gravity. The model is introduced\nith emphasis on the consideration of gravity as follows.\n.1. Coordinate systems of bearing\nIn order to describe the force and motion of each bearing compoent, the following five coordinate systems are introduced as shown in ig. 1: inertial coordinate system [O; X,Y,Z ], coordinate system [O bj ; bj ,y bj ,z bj ] for the j th ball, coordinate system [O i ; x i ,y i ,z i ] (shown in ig.1 in Ref. [6] ) for the inner ring, coordinate system [O c ; x c ,y c ,z c ] for he cage and coordinate system [O pj ; x pj ,y pj ,z pj ] for the j th pocket. Their efinitions can be referred to ref. [6] . Additionally, coordinate system O \u030b; x \u030b, y \u030b, z \u030b] is defined for the local contact between ball and raceway.\nhe proposed model considers six degrees of freedom of the ball, three\nranslations of inner ring along their own axes, the orbital rotation of he cage around x c axis and the translational motion of cage center in he y c z c plane. The outer ring is fixed in the housing and the inner ring otates with revolution speed \ud835\udf14 i . Initially, it is assumed that the cage enter is located at the outer ring center, and the ball is located at the enter of cage pocket. The reference points for displacements of ball, age and inner ring are their initial positions.\n.2. Dynamic differential equations of j th ball\nDue to the clearance between ball and pocket, some balls are in ontact with the cage pockets while others are not. The contact state",
            "b a f i d f r a a t\n\ud835\udc5a\n\ud835\udc5a\n\ud835\udc3c\n\ud835\udc3c\n\ud835\udc3c\n\ud835\udc3c\nW e c r i I\nQ t c t\n\ud835\udc05\n\ud835\udc0c\n2\nf i o f\n\ud835\udc5a\n\ud835\udc5a\n\ud835\udc3c\nw b c s s\netween ball and cage pocket is determined based on the motion nalysis [6] . Each ball is subjected to the following forces: contact orces from inner ring, outer ring and cage pocket; traction forces from nner ring and outer ring; friction force from pocket; centrifugal force\nue to orbital revolution and drag force from lubricant. Under these orces, the motions of the ball can be classified into following motions: otary motions around its own axes, translational motions along its own xes in the coordinate [ O bj ; x bj ,y bj ,z bj ]; orbital motion around bearing xis in the coordinate [ O; X,Y,Z ]. The differential equations governing he motion of the j th ball under gravity are as follows:\n\ud835\udc4f \u0394?\u0308? \ud835\udc4f = \ud835\udc44 \ud835\udc5c\ud835\udc57 \ud835\udc60 in \ud835\udefc\ud835\udc5c\ud835\udc57 \u2212 \ud835\udc44 \ud835\udc56\ud835\udc57 \ud835\udc60\ud835\udc56\ud835\udc5b \ud835\udefc\ud835\udc56\ud835\udc57 + \ud835\udc39 \ud835\udc66 \u2032\u2032 \ud835\udc56 cos \ud835\udefc\ud835\udc56\ud835\udc57 \u2212 \ud835\udc39 \ud835\udc66 \u2032\u2032 \ud835\udc5c cos \ud835\udefc\ud835\udc5c\ud835\udc57 (1)\n\ud835\udc4f \u0394?\u0308? \ud835\udc4f = \ud835\udc44 \ud835\udc56\ud835\udc57 cos \ud835\udefc\ud835\udc56\ud835\udc57 + \ud835\udc39 \ud835\udc50\ud835\udc57 \u2212 \ud835\udc44 \ud835\udc5c\ud835\udc57 cos \ud835\udefc\ud835\udc5c\ud835\udc57 + \ud835\udc39 \ud835\udc66 \u2032\u2032 \ud835\udc56 sin \ud835\udefc\ud835\udc56\ud835\udc57 \u2212 \ud835\udc39 \ud835\udc66 \u2032\u2032 \ud835\udc5c sin \ud835\udefc\ud835\udc5c\ud835\udc57 \u2212 \ud835\udc39 \ud835\udc57 \ud835\udc4f\ud835\udc50\ud835\udc53 \u2212 \ud835\udc58 \ud835\udc3a \ud835\udc4f cos \ud835\udf11 \ud835\udc4f\ud835\udc57\n(2)\n\ud835\udc4f ?\u0307? \ud835\udc57\ud835\udc65 \u2032 =\n\ud835\udc51 2 ( \ud835\udc39 \ud835\udc65 \u2032\u2032\ud835\udc5c cos \ud835\udefc\ud835\udc5c\ud835\udc57 \u2212 \ud835\udc39 \ud835\udc65 \u2032\u2032 \ud835\udc56 \ud835\udc50\ud835\udc5c\ud835\udc60 \ud835\udefc\ud835\udc56\ud835\udc57 + \ud835\udc39 \ud835\udc57 \ud835\udc50\ud835\udc4f\ud835\udc53 ) \u2212 \ud835\udc40 \ud835\udc56 \ud835\udc60\ud835\udc56\ud835\udc5b \ud835\udefc\ud835\udc56\ud835\udc57 \u2212 \ud835\udc40 \ud835\udc5c \ud835\udc60\ud835\udc56\ud835\udc5b \ud835\udefc\ud835\udc5c\ud835\udc57 (3)\n\ud835\udc4f ( \ud835\udf14 \ud835\udc57\ud835\udc66 \u2032 \u2212 \ud835\udf14 \ud835\udc57\ud835\udc50 \ud835\udf14 \ud835\udc57\ud835\udc67 \u2032 ) =\n\ud835\udc51 2 ( \ud835\udc39 \ud835\udc66 \u2032\u2032\ud835\udc5c \u2212 \ud835\udc39 \ud835\udc66 \u2032\u2032 \ud835\udc56 ) (4)\n\ud835\udc4f ( ?\u0307? \ud835\udc57\ud835\udc67 \u2032+ \ud835\udf14 \ud835\udc57\ud835\udc50 \ud835\udf14 \ud835\udc57\ud835\udc66 \u2032 ) = \ud835\udc51\n2 ( \ud835\udc39 \ud835\udc65 \u2032\u2032\ud835\udc5c \ud835\udc60\ud835\udc56\ud835\udc5b \ud835\udefc\ud835\udc5c\ud835\udc57 \u2212 \ud835\udc39 \ud835\udc65 \u2032\u2032 \ud835\udc56 \ud835\udc60\ud835\udc56\ud835\udc5b \ud835\udefc\ud835\udc56\ud835\udc57 ) + \ud835\udc40 \ud835\udc56 cos \ud835\udefc\ud835\udc56\ud835\udc57 + \ud835\udc40 \ud835\udc5c cos \ud835\udefc\ud835\udc5c\ud835\udc57 (5)\n\ud835\udc56 ?\u0307? \ud835\udc57\ud835\udc5c = \ud835\udc39 \ud835\udc65 \u2032\u2032 \ud835\udc56 \ud835\udc45 \ud835\udc56 \u2212 \ud835\udc39 \ud835\udc65 \u2032\u2032 \ud835\udc5c \ud835\udc45 \ud835\udc5c + \ud835\udc39 \ud835\udc57 \ud835\udc50\ud835\udc4f\ud835\udc5b \ud835\udc51 \ud835\udc5a\n2 \u2212 \ud835\udc39\n\ud835\udc57 \ud835\udc37\n\ud835\udc51 \ud835\udc5a\n2 + \ud835\udc58 \ud835\udc3a \ud835\udc4f sin \ud835\udf11 \ud835\udc4f\ud835\udc57\n\ud835\udc51 \ud835\udc5a\n2 (6)\nhere k is switching coefficient, k = 0 or 1. When the bearing is oprated under the microgravity condition, the gravity of ball has no ontribution to the force and moment, and thus is removed from the ight side of Eqs. (2) and (6) , namely, k = 0. Other variables are defined n Nomenclature. nteraction force between ball and inner/outer raceway\nThe contact forces between the j th ball and inner/outer raceways i j and Q o j are calculated based on Hertz contact theory [30] . The\nraction force ( F i x \u201d/y \u201d, F o x \u201d/y \u201d) and traction moment ( M i , M o ) are alculated based on EHD lubrication model, which can be expressed as he following integration equations [30] :\n\ud835\udc56 \u2215 \ud835\udc5c = \u2212 1 \u210e \ud835\udc56 \u2215 \ud835\udc5c\n\ud835\udc4e\n\u222b \u2212 \ud835\udc4e\n\ud835\udc4f\n\u222b \u2212 \ud835\udc4f\n\ud835\udf02\ud835\udc56 \u2215 \ud835\udc5c ( \ud835\udc65 \u2032\u2032, \ud835\udc66 \u2032\u2032)\u0394\ud835\udc49 \ud835\udc56 \u2215 \ud835\udc5c ( \ud835\udc65 \u2032\u2032, \ud835\udc66 \u2032\u2032) \ud835\udc51\ud835\udc65 \u2032\u2032\ud835\udc51\ud835\udc66 \u2032\u2032 (7)\n\ud835\udc56 \u2215 \ud835\udc5c = \u2212 1 \u210e \ud835\udc56 \u2215 \ud835\udc5c\n\ud835\udc4e \u222b \ud835\udc4f \u222b \ud835\udf02\ud835\udc56 \u2215 \ud835\udc5c ( \ud835\udc65 \u2032\u2032, \ud835\udc66 \u2032\u2032)( \ud835\udc65 \u2032\u2032 ?\u20d7? + \ud835\udc66 \u2032\u2032\ud835\udc57 )\u0394\ud835\udc49 \ud835\udc56 \u2215 \ud835\udc5c ( \ud835\udc65 \u2032\u2032, \ud835\udc66 \u2032\u2032) \ud835\udc51\ud835\udc65 \u2032\u2032\ud835\udc51\ud835\udc66 \u2032\u2032 (8) \u2212 \ud835\udc4e \u2212 \ud835\udc4f\n.3. Differential equations of motion for the cage\nAs shown in Fig. 2 , the cage is subjected to the impact and friction orces from balls and hydrodynamic force at cage-guiding surface nterface from outer ring. Here the cage is assumed to be guided by the uter ring. The motion of cage center under gravity is described by the ollowing equations:\n\ud835\udc50 \u0394?\u0308? \ud835\udc50 = \ud835\udc39 cb \ud835\udc66 + \ud835\udc39 co \ud835\udc66 + \ud835\udc39 \ud835\udc50\ud835\udc56\ud835\udc66 (9)\n\ud835\udc50 \u0394?\u0308? \ud835\udc50 = \ud835\udc39 cb \ud835\udc67 + \ud835\udc39 co \ud835\udc67 + \ud835\udc39 \ud835\udc50\ud835\udc56\ud835\udc67 \u2212 \ud835\udc58 \ud835\udc3a \ud835\udc50 (10)\n\ud835\udc50 ?\u0307? \ud835\udc50 = \ud835\udc40 cb \ud835\udc65 + \ud835\udc40 co \ud835\udc65 (11)\nhere F co y , F co z and M co x are interaction forces and frictional moment etween cage and guiding surface of outer ring represented in inertia oordinate system [O; X,Y,Z ], which are tranformed from the correponding variables F\u2019 coy , F\u2019 coz and M\u2019 cox defined in the cage coordinate ystem [O c ; x c ,y c ,z c ] [6] . G c is the weight of cage, and k is the same",
            "s n b\n\ud835\udc39\n\ud835\udc39\n\ud835\udc40\nI\ne h a c\n\ud835\udc39\n\ud835\udc39\n\ud835\udc40\no r\n\ud835\udc39\nI\ne\n\ud835\udeff\n\ud835\udc39\nl b w a\nt f\n\ud835\udc39\nw t s\n2\nu\n\ud835\udc5a\n\ud835\udc5a\n\ud835\udc5a\nw F c a\nt b m\n3\nl w l\nf c w F f k r t r\nd e a i o t c e\nm s g o 1 t o a r b\nwitching coefficient as in Section 2.2 , if k = 0, the gravity of cage is eglected. F cb y , F cb z and M cb x are resultant forces and moment acted y all balls on cage as shown by Eq. (12) ~Eq. (14) .\n\ud835\udc50\ud835\udc4f\ud835\udc66 = \ud835\udc41 \u2211 \ud835\udc57=1 (\u2212 \ud835\udc39 \ud835\udc57 \ud835\udc4f\ud835\udc50\ud835\udc5b \ud835\udc60\ud835\udc56\ud835\udc5b \ud835\udf11 \ud835\udc4f\ud835\udc57 + \ud835\udc39 \ud835\udc57 \ud835\udc4f\ud835\udc50\ud835\udc53 \ud835\udc50\ud835\udc5c\ud835\udc60 \ud835\udf11 \ud835\udc4f\ud835\udc57 ) (12)\n\ud835\udc50\ud835\udc4f\ud835\udc67 = \ud835\udc41 \u2211 \ud835\udc57=1 (\u2212 \ud835\udc39 \ud835\udc57 \ud835\udc4f\ud835\udc50\ud835\udc5b \ud835\udc60\ud835\udc56\ud835\udc5b \ud835\udf11 \ud835\udc4f\ud835\udc57 + \ud835\udc39 \ud835\udc57 \ud835\udc4f\ud835\udc50\ud835\udc53 \ud835\udc50\ud835\udc5c\ud835\udc60 \ud835\udf11 \ud835\udc4f\ud835\udc57 ) (13)\n\ud835\udc50\ud835\udc4f\ud835\udc65 =\n\ud835\udc51 \ud835\udc5a\n2 \ud835\udc41 \u2211 \ud835\udc57=1 \ud835\udc39 \ud835\udc57 \ud835\udc4f\ud835\udc50\ud835\udc5b (14)\nnteraction force between cage and outer raceway\nWhen the bearing is operated under stable condition, the relative ccentricity of cage center \ud835\udf00 is smaller than unity and there exists ydrodynamic action between the cage and outer raceway. The cage is cted by the guiding forces F\u2019 coy , F\u2019 coz and the moment M\u2019 cox , which is alculated based on infinitely short bearing theory as follows [51] :\nco \ud835\udc66 \u2032 =\n\u2212 \ud835\udf020 \ud835\udc62 \ud835\udc3f\n3 \ud835\udf00 2\n\ud835\udc36 2 \ud835\udc54 (1 \u2212 \ud835\udf00 2 ) 2\n(15)\nco \ud835\udc67 \u2032 =\n\ud835\udf0b\ud835\udf020 \ud835\udc62 \ud835\udc3f\n3 \ud835\udf00\n4 \ud835\udc36 2 \ud835\udc54 (1 \u2212 \ud835\udf00 2 ) 3\u22152\n(16)\nco \ud835\udc65 \u2032 =\n2 \ud835\udf0b\ud835\udf020 \u0394\ud835\udc49 \ud835\udc5c \ud835\udc45\n2 \ud835\udc3f\n\ud835\udc36 \ud835\udc54\n\u221a 1 \u2212 \ud835\udf00 2\n(17)\nWhen the cage motion become unstable and the relative eccentricity f cage center \ud835\udf00 is larger than unity, the dry contact force at cage-outer ing interface is calculated by the Palmgren formula as follows [21] :\n\ud835\udc50\ud835\udc5c\ud835\udc67 \u2032 =\n\ud835\udc38 \u2032\ud835\udc59 8\u22159\n4\n( \ud835\udeff\n0 . 39\n)10\u22159 (18)\nnteraction force between ball and cage pocket\nThe normal contact force \ud835\udc39 \ud835\udc57\n\ud835\udc50\ud835\udc4f\ud835\udc5b between j th ball and pocket can be\nxpressed as follows:\n\ud835\udc4f\ud835\udc5d\ud835\udc57 = \u221a |||\ud835\udc5f \ud835\udc5d \ud835\udc4f\ud835\udc5d\ud835\udc57\ud835\udc65 |||2 + |||\ud835\udc5f \ud835\udc5d \ud835\udc4f\ud835\udc5d\ud835\udc57\ud835\udc67 |||2 \u2212 \ud835\udc36 \ud835\udc5d (19)\n\ud835\udc57 \ud835\udc50\ud835\udc4f\ud835\udc5b = \u23a7 \u23aa \u23a8 \u23aa \u23a9 \ud835\udc3e \ud835\udc59 \u221a |||\ud835\udc5f \ud835\udc5d \ud835\udc4f\ud835\udc5d\ud835\udc57\ud835\udc65 |||2 + |||\ud835\udc5f \ud835\udc5d \ud835\udc4f\ud835\udc5d\ud835\udc57\ud835\udc67 |||2 \ud835\udeff\ud835\udc4f\ud835\udc5d\ud835\udc57 \u2265 0 \ud835\udc3e \ud835\udc50 |||\ud835\udeff\ud835\udc4f\ud835\udc5d\ud835\udc57 ||| + \ud835\udc3e \ud835\udc59 \ud835\udc36 \ud835\udc5d \ud835\udeff\ud835\udc4f\ud835\udc5d\ud835\udc57 < 0\n(20)\nThe expressions of contact force-deformation coefficient K c and\nubricant stiffness K l can refer to [52,53] . Positive \ud835\udc39 \ud835\udc57 \ud835\udc50\ud835\udc4f\ud835\udc5b means that the\nall contacts the front side of the pocket and push the cage to move, hile negative \ud835\udc39 \ud835\udc57\n\ud835\udc50\ud835\udc4f\ud835\udc5b means the ball contacts the backside of the pocket\nnd the cage has to push the ball to move as shown in Fig. 2 .\nThe ball-cage pocket contact is assumed to be in boundary lubricaion regime, and Coulomb friction law is used to calculate the frictional orce between the j th ball and pocket:\n\ud835\udc57 \ud835\udc50\ud835\udc4f\ud835\udc53 = \ud835\udf07\ud835\udc4f\ud835\udc50 \ud835\udc39 \ud835\udc57 \ud835\udc50\ud835\udc4f\ud835\udc5b (21)\nhere \ud835\udf07bc is the friction coefficient between ball and cage pocket. In he present paper, referring to [53] , it is set as 0.08 due to the purely liding and the limited oil supply.\n.4. Differential equations of motion for the inner ring\nThe differential equations of transitional motion for the inner ring\nnder gravity can be expressed as follows:\n\ud835\udc56 \u0394?\u0308? \ud835\udc56 = \ud835\udc39 a \u2212 \ud835\udc50\u0394?\u0307? \ud835\udc56 \u2212 \ud835\udc44 \ud835\udc65 (22)\n\ud835\udc56 \u0394?\u0308? \ud835\udc56 = \u2212 \ud835\udc50\u0394?\u0307? \ud835\udc56 \u2212 \ud835\udc44 \ud835\udc66 (23)\n\ud835\udc56 \u0394?\u0308? \ud835\udc56 = \ud835\udc39 r \u2212 \ud835\udc50\u0394?\u0307? \ud835\udc56 \u2212 \ud835\udc44 \ud835\udc67 \u2212 \ud835\udc58 \ud835\udc3a \ud835\udc56 (24)\nhere m i is shaft assembly mass, F a is the externally applied axial load,\nr is the externally applied radial load, and Q x , Q y , Q z are the resultant ontact forces from all the balls; G i is the weight of the shaft assembly, nd k is also the switching coefficient.\nEqs. (1) ~(6) , (9) ~(11) and (22) ~(24) formulate dynamic differenial equations of the motions for each element in angular contact ball earing, and these equations are solved by the fourth-order Runge-Kutta\nethod with adaptive stepsize control.\n. Model verification\nFirstly, the dynamic model was verified by comparing with pubished experimental results. The angular contact ball bearing 7013AC\nas chosen as tested bearing, and its geometrical parameters were\nisted in Table 1 as given in Ref. [54] .\nThe frequency spectrum of the radial displacement (along the Z axis) rom proposed model and experimental data taken from Ref. [54] were ompared. The rotating speed of bearing was 4800rpm, and the bearing\nas subjected to 1000N axial force and 1000N radial force. As shown in ig. 3 , the inner ring rotation frequency f i , the cage rotation frequency c and combination frequencies coming from inner ring and cage ( f i \u00b1 f c ) can be observed in the spectrum from simulation. The simulated esults were compared with experimental results, and it can be found hat the frequency and amplitude of cage motion from simulation esults were generally in good agreement with the experimental data.\nThe displacement amplitudes at cage rotation frequency f c under ifferent axial load and radial load obtained by present model and xperimental results from Ref. [54] were compared as shown in Fig. 4 nd Fig. 5 . It is shown that the amplitudes at f c increased with the ncrease of rotating speed and axial load of bearing, while the increase f radial load resulted in the decrease of amplitudes at f c . The ampliudes at f c predicted by the present dynamic model under different onditions showed the same trend with the experiment, as a result, the ffectiveness of the proposed model was validated.\nMoreover, the comparisons of cage mass center trajectory under icrogravity obtained from present model and Niu\u2019s model [44] were hown as Fig. 6 . The geometrical parameters were listed in Table 1 as iven in Ref. [44] , the gravity of cage was neglected and the bearing was perated under solid lubrication condition. When the bearing rotates at 0,000rpm, it can be seen from Fig. 6 (a) and (b) that the whirl orbit and he whirl radius calculated by present model were consistent with that f Niu\u2019s model. As shown in Fig. 6 (c) and (d), both the present model nd Niu\u2019s model show that the cage motion became unstable at larger otation speed ( n i = 30,000rpm). With the increase of rotation speed, oth the trajectories of the cage mass center gradually varied from"
        ]
    },
    {
        "image_filename": "designv10_5_0000807_j.mechmachtheory.2013.06.013-Figure13-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000807_j.mechmachtheory.2013.06.013-Figure13-1.png",
        "caption": "Fig. 13. Coordinate systems of generation \u22112 by \u2211w.",
        "texts": [
            " Therefore, generation of \u22112 by the disk wheel has to be based on a two-parameter enveloping process wherein two independent sets of parameters are provided as: (1) a set of angles of rotation (\u03c8w,\u03c82) of the disk wheel and the face gear, and (2) a translational motion lw of the disk wheel. Parameters \u03c8w and \u03c82 are the angles of rotation of the disk wheel and the face gear related by the equation: \u03c82 \u00bc Ns\u03c8w=N2 \u00f017\u00de N2 and Ns are the number of teeth of the face gear and that of the shaper respectively. Parameter lw of the translational where motion is provided as collinear to the axis of the shaper. The profile modified spur face-gear surface \u22112 is calculated as the envelope to the family of the disk wheel surface \u2211w, as Fig. 13 shows. Coordinate systems Ss, Sw and S2 are rigidly connected to the shaper, the disk wheel and the face-gear respectively, and Sw0 and S20 are fixed coordinate systems. Ews is the distance between the axis zw and xs. The position vector of the face-gear surface is determined as: r2 ur ; \u03b8w;\u03c8w; lw\u00f0 \u00de \u00bc M2w \u03c8w; lw\u00f0 \u00derw ur ; \u03b8w\u00f0 \u00de Nw ur; \u03b8w\u00f0 \u00de\u22c5v w2;lw\u00f0 \u00de w \u00bc f 1\u00f0 \u00de w2 ur; \u03b8w;\u03c8w; lw\u00f0 \u00de \u00bc 0 Nw ur; \u03b8w\u00f0 \u00de\u22c5v w2;\u03c8w\u00f0 \u00de w \u00bc f 2\u00f0 \u00de w2 ur; \u03b8w;\u03c8w; lw\u00f0 \u00de \u00bc 0 8>< >: \u00f018\u00de Matrix M2w describes coordinate transformation from Sw to S2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002124_j.triboint.2015.12.046-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002124_j.triboint.2015.12.046-Figure2-1.png",
        "caption": "Fig. 2. Coordinate transformation.",
        "texts": [
            " (1) and (2) in the Cartesian coordinate system of the lubricating gap leads with the angle between the contact line and the flank line \u03b2B \u00bc arctan tan \u03b2 sin \u03b1n\u00f0 \u00de to the velocity portions u and v, which are effective in x and y direction: u1 y\u00f0 \u00de \u00bc ut1 cos \u03b2B u2 y\u00f0 \u00de \u00bc ut2 cos \u03b2B \u00f03\u00de v1 y\u00f0 \u00de \u00bc ut1 sin \u03b2B v2 y\u00f0 \u00de \u00bc ut2 sin \u03b2B \u00f04\u00de The geometry of the lubricating gap in the calculation domain is derived directly from the involutes of the tooth flanks at any point of the line of action. This requires describing precisely any point on the tooth flanks Yinv within the calculation domain in the local coordinate system of the lubricating gap (x, y, z). The tooth flank profile of a helical gear can be shown at any transverse cut by a two-dimensional involute (cf. Fig. 2). The curve of this involute is described in a fixed plane coordinate system (xt\u2033, zt\u2033) with the origin in the center of the gear wheel. The position of point Yinv on the involute is defined in the plane coordinate system (xt\u2033, zt\u2033) dependent on the roll angle \u03c8ytinv as follows: x\u2033tinv \u00bc rb sin \u03c8 ytinv _\u03c8 ytinv cos \u03c8 ytinv \u00f05\u00de z\u2033tinv \u00bc rb cos \u03c8 ytinv \u00fe_\u03c8 ytinv sin \u03c8 ytinv \u00f06\u00de Starting from the position of point Yinv in the coordinate system (xt\u2033, zt\u2033), it is transferred into a fixed coordinate system (xt0, zt0), which is also plane and which describes the involute in the transverse cut of point Y0: x0tinv \u00bc x\u2033tinv cos \u03c6btinv \u00fez\u2033tinv sin \u03c6btinv \u00f07\u00de z0tinv \u00bc x\u2033tinv sin \u03c6btinv \u00fez\u2033tinv cos \u03c6btinv \u00f08\u00de The angle \u03c6btinv introduced in the Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000593_1.4023300-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000593_1.4023300-Figure1-1.png",
        "caption": "Fig. 1 One-stage planetary gear dynamic model",
        "texts": [
            " The dimensions of gear tooth root cracks applied in this paper are defined in Sec. 3. The effect of the gear tooth crack with different sizes and inclination angles on the dynamic responses of the planetary gear system are investigated in Sec. 4 which is followed by conclusions in Sec. 5. 2.1 Dynamic Model of Planetary Gear System. The dynamic model stressed in this paper is a one-stage planetary gear train, which consists of one sun (s), carrier (c), ring (r), and N planets (p) with the rotational motion of the ring gear constrained, as displayed in Fig. 1. Each element has three degrees of freedom with one rotation and two translations. Thus, the total number of degrees of freedom is 3(N\u00fe 3). The rotation wn \u00bc hnrn(n\u00bc r, c, s, 1,\u2026N) where hn is the angular displacement and rn is the base radius. The positive direction for rotation is defined as along anticlockwise. The translational motions of these so called central elements (namely the sun, carrier, and ring gear) xn, yn (n\u00bc r, c, s) and that of the planets un (radial), vn (tangential), (n\u00bc 1,\u2026N) are defined in a rotating carrier reference frame which is fixed to the carrier with origin O",
            " cspn, crpn represent, respectively, the mesh phase lags of the nth sun\u2013planet and the nth ring\u2013planet gear pairs in mesh relative to the first sun\u2013planet mesh, where crpn \u00bc cspn \u00fe csr and csr is the phase lag between the nth sun\u2013planet and nth ring\u2013planet gear meshes. More detailed information about the mesh phasing of gear pairs in mesh of a planetary gear set can be found in Refs. [17\u201319]. Zs, Zp denote the number of sun and planet gear teeth. hs, hc, and hn are the angular displacements of the sun, the carrier, and the nth planet gear defined in Fig. 1. The subscript n is the planet number ranging from 1 to N where N is the number of planets. Then the incorporation of the crack model into the dynamic model of the planetary gear set can be implemented by substitution of the sun\u2013planet and ring\u2013planet gear mesh stiffness in Eqs. (20)\u2013(21) into the mesh stiffness matrix Ke(t) in Eq. (3). In order for the investigation on the effect of tooth root crack on the planetary gear system, a crack is seeded intentionally in one tooth of the sun and the planet gear, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000508_1.4001012-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000508_1.4001012-Figure2-1.png",
        "caption": "Fig. 2 Mechanism of surface initiated pitting \u202011\u2021",
        "texts": [
            " This mechanism is the dominant mode of failure in rolling element bearings that have smooth surfaces and operate under elastohydrodynamic lubrication EHL conditions 1,9 . Surface originated pitting, on the other hand, occurs in cases where surface irregularities in the form of dents or scratches are present. Here, cracks initiate at the surface stress risers, and thereafter, propagate at a shallow angle 15\u201330 deg to the surface 10 . When they reach a critical length or depth, the cracks branch up toward the free surface, removing a piece of surface material and form a pit, as shown in Fig. 2 11 . This mechanism of failure is common in gears where substantial sliding occurs between the contacting surfaces. Fatigue mechanism in general consists of three stages as follows: i crack initiation, ii crack propagation, and iii final catastrophic failure. In rolling contacts, initial fatigue cracks occur at the microscale; therefore, in order to study their behavior accurately, the microstructure of materials needs to be taken into account. Miller 12 showed that the scatter in fatigue lives needs to be studied by considering the effect of the material microstructure on early crack growth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000236_j.mechmachtheory.2010.06.004-Figure15-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000236_j.mechmachtheory.2010.06.004-Figure15-1.png",
        "caption": "Fig. 15. a) Close-up of the stress concentration zone for the optimized gear with 68 teeth, the design parameters shown are \u03b1c=20\u00b0, \u03b1d=36\u00b0, \u03b7=1.94 and \u03bc=\u03bcmin. The stress is reduced with 44.3% as compared to the ISO profile. b) Close-up of the stress concentration zone for the optimized gear with 68 teeth, the design parameters shown are \u03b1c=35\u00b0, \u03b1d=20\u00b0, \u03b7=1.81 and \u03bc=0.1. The stress is reduced with 19.4% as compared to the ISO profile.",
        "texts": [
            " [14] the reported improvement in the bending stress is 17% which can be compared directly with the 20.1% found here. Close agreement is found although the results in [14] were found without using shape optimization. It is also noticed that in contradiction to the results from optimizing only the root shape of the standard tooth the results are better for a gearwithmore teethwhen \u03b1dN\u03b1c. However, the improvement in the bending stress is of the same order as with z=17. To verify this we finally optimize a gear with z=68. Optimization results are presented in Fig. 15. Results are of the same order for this gear. Improvements in the bending stress found are 44.3% and 19.4%, respectively. From the performed parameter studies it is found that the reduction in the bending stress is not very sensitive to small changes in the design parameters. This leads to the idea of a standard or two standard cutting racks, these are presented in the next section. From the optimized designs presented in the previous section, specifically the design parameter values, it seems that it is possible to make two standard rack cutters, one where the drive side pressure angle is fixed at \u03b1d=20\u00b0 and another where the coast side pressure angle is fixed at \u03b1c=20\u00b0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001274_j.triboint.2015.11.005-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001274_j.triboint.2015.11.005-Figure1-1.png",
        "caption": "Fig. 1. Loads and displacements of TRBs in (a) a global coordinate system (x, y, z), (b) a local coordinate system (r, \u03d5, z), and (c) roller contact forces and displacements.",
        "texts": [
            " The obtained results are rigorously discussed. In order to estimate TRB torque, the contact forces between the roller and races should be determined in advance. Calculation of these forces is based on solving the bearing dynamic equations relevant to the equilibrium of the rollers and inner ring. For an aligned TRB under pure axial force Fz, the contact forces can be approximated as described by Aihara [16]. However, such a situation is very rare in actual bearing applications. For a general loading condition, as shown in Fig. 1(a), the inner ring of the TRB is assumed to be loaded by an external load vector Ff gT \u00bc Fx; Fy; Fz;Mx;My ; \u00f01\u00de and the corresponding inner ring displacement vector is \u03b4 T \u00bc \u03b4x; \u03b4y; \u03b4z; \u03b3x; \u03b4y : \u00f02\u00de Considering the TRB cross-section at a particular roller of location angle \u03d5, as indicated in Fig. 1(b), because the roller is displaced from its initial position by {v}T\u00bc{vr,vz,\u03c8}, the roller contact forces Qi, Qe, and Qf are generated, as illustrated in Fig. 1(c). Here, the subscripts i, e, and f denote the inner raceway, outer raceway, and flange, respectively. Qi and Qe can be calculated using the well-known slicing method [19,21\u201323]. In this method, the roller\u2013raceway contact region is divided into ns slices, and the total contact force is calculated by the summation of the contact forces in the individual slices qk. It should be noted that the slice contact force is not uniformly distributed, but depends on the roller and raceway profiles. Thus, when forces Qi and Qe are moved to the middle of the nominal contact length, as illustrated in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000754_j.mechmachtheory.2013.10.006-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000754_j.mechmachtheory.2013.10.006-Figure3-1.png",
        "caption": "Fig. 3. A schematic diagram of the machinery-fault simulator.",
        "texts": [
            " After getting the optimized SVM classifier, the final testing data set is used for finding the final classification. The fitness function used is the accuracy as discussed in performance measure of Section 2. Bounds for design parameters are selected so that computational time is minimized. Table 2 shows the fitness function and design parameters with bounds for the optimization technique for the two SVM techniques with the RBF kernel. Experiments were performed on a Machinery Fault Simulator\u2122 (MFS) and a schematic diagram of it is shown in Fig. 3. This machine could be used for the simulation of a range of machine faults like in the gearbox, shaft misalignments, rolling element bearing damages, resonances, reciprocating mechanism effects, motor faults, and pump faults. In the MFS experimental setup, 3-phase induction motor was mounted to the rotor that was connected to the gear box through a pulley and belt mechanism. The gear box and its assembly are illustrated in Fig. 4. In the study of faults in gears, three different types of faulty pinion gears namely the chipped tooth (CT), missing tooth (MT) and worn tooth (WT) along with normal gear (or no defect, i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002624_j.addma.2019.100940-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002624_j.addma.2019.100940-Figure2-1.png",
        "caption": "FIGURE 2. A conceptual set up of the detection system",
        "texts": [
            " A phase-shifting algorithm and an optimum three-fringe number selection method[23] are employed to accurately calculate wrapped and absolute unwrapped phase maps, respectively. Finally, the proposed in-situ inspection system is constructed on a prototype powder delivery system and finally on an industrial/commercial EBM machine. Examples of real measurements of the powder bed are demonstrated, which give feedback during a typical AM build process. A conceptual illustration of the in-situ measurement system applied to an EBM machine is shown in Figure 2. The final implementation will be within a new prototype EBM machine comprising an electron beam melting source, powder delivery system, a powder bed transfer stage and the fringe projection re -p ro of inspection system. The machine itself is a newly launched commercial machine, unfortunately at present there are commercial restrictions regarding the detailed specification of the machine. However, the machine exhibits the same in-process out-of-plane defects that are common across all AM machines in this category: rake damage, delamination, swelling, porosity, lack of powder"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000218_1.3063817-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000218_1.3063817-Figure6-1.png",
        "caption": "Fig. 6 Degrees of freedom for a cage pocket or block",
        "texts": [
            " The forces on these blocks act through the beams to apply an equivalent force and couple to the pockets. When a ball bearing is subjected to only radial loading and/or interference preloading, the motion of the cage occurs entirely on the bearing\u2019s plane of symmetry. Planar motion of a rigid body, such as the pockets and blocks comprising the cage, can be described using just three coordinates. Two coordinates describe the translation, and one defines the orientation of the body, as illustrated in Fig. 6. However, a continuous deformable body requires infinite DOF to describe its motion in the plane. The cage model in this analysis is neither a rigid body nor a continuous deformable body; rather, it is a discretized model comprised of several hundreds of rigid bodies. 3DOFs describe the planar motion of each of these constituent bodies, and the overall motion of the cage is determined by continuity. Subjecting the inner race of a bearing to axial or combined axial and radial loads results in cage motion that is nonplanar or 3D"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000648_978-3-642-17531-2-Figure1.10-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000648_978-3-642-17531-2-Figure1.10-1.png",
        "caption": "Fig. 1.10. Schematic configuration of a telescope with adaptive optics",
        "texts": [
            " The process of composition is always a fascinating, deeply creative process, and in systems design, requires skillful play upon the keyboard of engineering science. It is the aim of this book to communicate fundamental elements of such \u201cvirtuosity\u201d. Problem statement In high-resolution telescopes, the spatial phase distribution of impinging light wavefronts plays a determining role in the achievable resolution. Due to atmospheric turbulence, adjacent light rays experience differing phase delays, resulting in an uneven wavefront at the entry to the telescope (see Fig. 1.10 in the upper section of the light path). If the telescope mirror is constructed as a matrix of movable (controllable) mirrors, the spatial phase delays can be corrected so that an approximately parallel wavefront is formed in the focal plane of the telescope (see Fig. 1.10 in the lower-right section of the light path). To calculate the correction for a wavefront, its phase distribution must be measured with a wavefront sensor, allowing a control loop to calculate corrective signals for the mirror displacements. This principle of optical correction is termed adaptive optics (Roddier 2004), (Hardy 1998), (Fedrigo et al. 2005). 18 1 Introduction Adaptive vs. active optics Adaptive optics should not be confused with the principle of active optics. In the latter, mirror elements are also actively displaced, though primarily with the object of compensating geometric deformations due to manufacturing tolerances, environmental factors, and dynamic effects during slewing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000803_s1000-9361(11)60430-5-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000803_s1000-9361(11)60430-5-Figure4-1.png",
        "caption": "Fig. 4 \u201cOdd\u201d and \u201cEven\u201d presses.",
        "texts": [
            " (11) where Q is the contact force, n! the contact displacement, and nK the contact stiffness coefficient. Equation (11) shows that the contact force increases with an exponent of 3 / 2 of the displacement. In general, angular contact ball bearings in the MWA are preloaded by axial force to increase the stiffness and remove the clearance. The stiffness of the angular contact ball bearing is not only \u201cnonlinear\u201d, but also \u201ctime-variant\u201d, i.e., the stiffness of the ball bearing varies with time when the system is rotating [25]. Figure 4 shows the two extreme conditions of the radial stiffness. rF is radial applied force on the bearing, Qri is the corresponding contact force of each ball. The stiffness of the condition of \u201codd\u201d press and \u201ceven\u201d press are different, thus, the stiffness of the MWA is slightly changing with rotating of the MWA, with a frequency of z . 2.4.2. Coupling of the stiffness In reality, both of the radial and axial stiffnesses of the MWA change slightly with the load and they are coupled with each other. According to Hertizan theory, the stiffness of the ball bearing can be expressed by the contact stiffness of the ball with the internal and external rings [25], as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000428_0005-2795(75)90348-7-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000428_0005-2795(75)90348-7-Figure1-1.png",
        "caption": "Fig. 1. d.c. polarograms of hemoproteins. 25 \u00b0C, 0.l M phosphate buffer, concentration 0.l mval/l. 1, ferricytochrome c, pH 6; 2, methemoglobin, pH 6; 3, deuterohemin, pH 11.5; 4, metmyoglobin, pH 6.0.",
        "texts": [
            " The oxygen partial pressure at 50~ saturation and the sigmoid coefficient were calculated on a computer R 300 (VEB Kombinat Robotron Dresden) by means of an ALGOL program. The absorption spectra of solutions were measured by means of a Unicam SP 700 spectrophotometer. The kinetics of azide binding to partially reduced methemoglobin was performed by means of a DURRUM stopped flow device. d.c. and pulse polarography Cytochrome c, methemoglobin and metmyoglobin produce well-defined reduction steps (Fig. 1). The half-step potentials E1/2 for these hemoproteins are considerably more negative than the redox standard potentials, and are shifted in the cathodic direction with rising concentrations. The limiting current lu,, in equinormal solutions with respect to hemin (val/1) differs substantially for the three proteins. ~[.A] o.os o 0:5 i c.10~ [ v ~ ] Pig. 2. Concentration dependence of the polarograpbi\u00a2 limiting cu~ye~ts, l , deuterobemi~; 2, metbemoglobin; 3, metmyoglobin; 4, ferficytochrome c. Same conditions as in Pig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000782_j.mechmachtheory.2012.11.006-Figure13-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000782_j.mechmachtheory.2012.11.006-Figure13-1.png",
        "caption": "Fig. 13. Contact point axial positioning with shuttling.",
        "texts": [
            " Shuttling happens intrinsically for helical gears, due to the traveling contact lines from one corner of the tooth surface to the opposite, or can be due to shifts in contact stress distribution caused by gear misalignment. Shuttling is included in the proposed gear element considering the contact pressure distribution calculations in LDP. For each operating condition, LDP is able to decompose the contact force resultant according to static equivalence. In particular, taking a pivot point on one edge of the active facewidth, LDP returns a force value calculated at the opposite edgewhich causes the same moment of the resultant contact force (Fig. 13). This force value can be used to calculate the axial position of the contact force resultant normalized on the active face width according to: sp \u00bc Ftn1 Ftn : \u00f025\u00de This parameter is stored in a second look-up table, calculated for the same discrete range of operating conditions used for the mesh stiffness, and interpolated during the multibody simulation. Eq. (12) is therefore modified as follows to account for shuttling: Oz \u00bc 0 0 min FW1; FW2\u00f0 \u00de\u22c5sp DTE; PMC;CD;M\u00f0 \u00de 8< : 9= ;: \u00f026\u00de Simulations for a reference helical gear pair (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001228_j.robot.2011.11.014-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001228_j.robot.2011.11.014-Figure1-1.png",
        "caption": "Fig. 1. Prototype of a planar 2RRR/RR RA-PKM.",
        "texts": [
            " Parameterization-singularities refer to configurations where a selected set of independent coordinates becomes invalid. An obvious choice for minimal coordinates is to use a subset q2 consisting of \u03b4 actuator coordinates, that is, q2 is a subset of qa. This is equivalent to consider the PKM as non-redundantly actuated and to express its motion in terms of \u03b4 actuator coordinates. Consequently, parameterization-singularities are exactly the input-singularities of the non-redundantly actuated PKM. The planar 2RRR/RR PKM in Fig. 1 has DOF \u03b4 = 2, and is redundantly actuated by the m = 3 actuators at the base joints. The PKM is naturally parameterized in terms of two of these three actuator coordinates, and parameterization-singularities can be observed if the joint angles of two of these actuators are used as independent coordinates. As example consider a motion of the PKM where its EE follows a circle. Fig. 2(a) shows the two configurations where the coordinates q1 and q2 are not valid independent parameters for the PKM model",
            " If only \u03b4 independent actuator coordinates are used, the feedback term does not account for the overall error in configurations where the motion is not uniquely determined by these \u03b4 actuator motions, i.e. in parameterization-/input-singularities of the nonredundantly actuated PKM (Section 2.2). On the other hand the redundant feedback causes counteraction of the m actuators since only \u03b4 actuator coordinates are independent but the m feedback commands are not. Thanks to the non-linear feed forward this is not as significant as for pure linear decentralized control as reported in [30]. The developed model was implemented in a CTC control scheme of the planar 2 DOF 2RRR/RR PKM prototype in Fig. 1. For comparison experimental results are also reported for the standardminimal coordinate method with and without switching. The mechanism is manufactured with high precision. The PKM is controlled by means of DC motors (Maxon Re30) at the three base joints. Thusm = 3, and the PKM is redundantly actuated. The base joints are mounted at the vertices of an equilateral triangle with 400mm lateral lengths. Each arm segment has a length of 200mm. The weight of one arm is 134 g. For the purpose of analyzing the robustness with respect to measurement errors encoders with a rather low resolution of 500 increments per turn are used"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000351_09544062jmes1844-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000351_09544062jmes1844-Figure3-1.png",
        "caption": "Fig. 3 Gear set assembly",
        "texts": [
            " The resulting geometry is then subdivided into quadrilateral regions, paying particular attention to their form, avoiding shapes that could lead the software to generate unacceptably distorted quadrilateral elements (Figs 2(a) and (b)). Furthermore, in order to reduce the computational requirements, only five pair of teeth are modelled, assuming that the effects on the meshing of the other pairs are negligible. The teeth and the gear bodies are then meshed, refining the contact zones and the zones where a high stress gradient is expected (Fig. 2(c)). After defining the material properties, the gear and the pinion are assembled (Fig. 3) and the contact surfaces are defined. The contact between the teeth flanks is handled by ABAQUS using a general purpose contact algorithm: the actual contact areas and stresses are then determined, without introducing any simplification based on some particularity of gear geometry. The constraints are defined so that it will be possible to automatically run a sequence of static analyses. The procedure can then be summarized as the following key points. 1. Creation of two reference points at the gear and pinion centres"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002915_s11665-019-04435-y-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002915_s11665-019-04435-y-Figure1-1.png",
        "caption": "Fig. 1 Schematic plot of the general phenomena in the L-PBF additive manufacturing process",
        "texts": [
            ", lack of fusion-induced pores and keyhole-induced pores. Lack of fusion-induced pores is likely to be formed if a low energy beam irradiates the top powder layer since the powder particles may not be fully melted and pores between particles remain unfilled by molten metal fluid. On the contrary, keyholeinduced pores may be generated if excessive energy is applied on the powder bed, where the melt pool as well as keyhole dynamics can contribute to the formation of pores beneath the powder bed. Figure 1 shows the schematic plot of the general phenomena in the L-PBF, which is also called selective laser melting (SLM). The effect of process parameters on porosity evolution in AlSi10 Mg samples was experimentally investigated by Aboulkhair et al. (Ref 2). Fabricated samples were crosssectioned and polished to study the presence of pores using optical microscopy, and the process window for high density (low porosity) parts was presented. In addition, Gong et al. (Ref 3) performed indirect measurements of melt pool cross sections after solidification"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001880_j.applthermaleng.2014.02.008-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001880_j.applthermaleng.2014.02.008-Figure2-1.png",
        "caption": "Fig. 2. The solving model of the temperature field.",
        "texts": [
            " In order to evaluate the thermal behavior of the induction motor, a complete thermal evaluation of the prototype motor fitted with thermistor was carried out in the laboratory, and the temperaturerise of the motor in all the spots of interest can be obtained. The temperature on the frame of the machine was tested by infrared thermoprobe, and the wind speed on the shell surface was measured by anemometer EY3-2A. 3. Thermal field modeling and boundaries of the solving region 3.1. The thermal field modeling The 3-D model of the motor is employed in this paper, and the FEM solution was achieved by the software \u201cANSYS\u201d. Thermal models in Fig. 2 have been developed for the prototype motor, which allows us to estimate the stator and rotor temperature. The proposed model is intended to compute the motor temperature in steady-state condition. In Fig. 3, S1eS7 are the boundaries of the solving region. The region S1 is the face of the motor frame, S2 is the internal surface of the connecting box, S3 is the contact surface of motor frame and stator, S4 is the end face of the stator, S5 is the internal surface of the stator and the outer surface of the rotor, S6 is the end face of the rotor, S7 is the end face of the end-ring"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002383_j.matdes.2016.03.151-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002383_j.matdes.2016.03.151-Figure1-1.png",
        "caption": "Fig. 1. (a) Schematic diagram and (b) self-designed equipment of the laser cladding process.",
        "texts": [
            " The significance of this work can be summarized in several folds. Firstly, this study explores the capabilities of laser cladding technique to fabricate the anti-corrosion claddings. Secondly, this study will address the microstructural characterizations of laser clad components, and make a comparison to the conventional bulk forming techniques. Lastly, the modeled material constitutive description is expected for further studies on post-treatments of the claddings. The principle of laser cladding is shown in Fig. 1(a). There are two types of nozzles, through which powder particles are injected onto the substrate. A coaxial nozzle provides spherical powder fromwhole radial directions and performs independent from the direction of motion. A lateral nozzle, by contrast, feeds powder along an axis at a fixed angle to that of the substrate and laser beam. In the laser cladding procedure, treated area is heated by absorption of energy delivered by the laser beam. Powders totally melt and then quickly re-solidify for creating a track, which can be characterized by high density and metallurgical bonding to the substrate. The heated regions are self-quenched after passing of the laser beam by diffusion of heat to the cold bulk. In this research, Cr-Ni-based stainless steel was fabricated on the surface of scrapped parts by a self-designed semi-conductor laser cladding equipment, as shown in Fig. 1(b). Substrates used for clad deposition were AISI 1045 steel axles with dimension of\u03a6120 \u00d7 300 mm. The substrates were preferably de-scaled by sanding, degreased with gasoline and dried in air prior to laser cladding operations. By this way, dust, oxide, grease can be removed efficiently and low secondary waste was generated. Moreover, thermal oxide filmwas thoroughly avoided, thereby easily ensuring a higher purity of the cladding. Then, the substrates were mounted on three-jaw chuck rotating around a horizontal axis in front of a lateral synchronous powder feeding device which, in turn, could be traversed horizontally"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003102_j.apor.2020.102378-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003102_j.apor.2020.102378-Figure1-1.png",
        "caption": "Fig. 1. Definition of the earth-fixed OX0Y0 and the body-fixed AXY coordinate frames.",
        "texts": [
            " (2018)): If R\u2026x x x{ , , , } ,n1 2 p > 0, then + + + + + +x x x n x x x( ) max( , 1)( )n p p p p n p 1 2 1 1 2 . If =p m n/ 1, and m, n are odd integers, then x x x x2p p p p 1 2 1 1 2 . Lemma 3. (Zhang et al. (2018b)): A scalar dynamic system is expressed as = =y l sig y l sig y y y( ) ( ), (0)m m 1 2 01 2 (3) where l1 > 0, l2 > 0, m1 > 1, 0 < m2 < 1. Consequently, the origin for system (3) is said to be fixed-time stable and the settling time T is determined as < = +T T l m l m 1 ( 1) 1 (1 ) .max 1 1 2 2 (4) Two reference coordinate systems are commonly presented in Fig. 1. Due to the motions in heave, pitch and roll being open-loop stable, these motions can be neglected. Therefore, the 3-DOF kinematics and dynamics of an MSV can be established as Yang et al. (2013) = + + = + R v Mv C v v D v v b ( ) ( ) ( ) (5) where the vectors R= x y[ , , ]T 3 and R=v u r[ , , ]T 3 are system states. [x, y]T \u2208 \u211c2 are positions of an MSV in the earth-fixed frame. \u03c8 \u2208 \u211c is a heading angle. u \u2208 \u211c is the forward velocity in the surge. R is the transverse velocity in the sway. r \u2208 \u211c is the angular velocity in the yaw axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003486_j.ijmecsci.2020.105665-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003486_j.ijmecsci.2020.105665-Figure9-1.png",
        "caption": "Fig. 9. Simulation model with a lunker defect.",
        "texts": [
            " It clearly reveals that the lunker defect prone to aggreate directly below the tooth root area. After the collection of inforation of a total number of 205 lunker defects, the average value of efect diameters is determined as 0.94 mm, and the average distance etween the rotation center and injection molding lunkers is 50.45 mm. he maximum value of defect diameters is 5.5 mm, and the maxium distance between the rotation center and injection molding lunkers s 51.89 mm. The simulation model of the POM gear with a predefined injection olding lunker defect is shown in Fig. 9 . The shape of defects is selected s ellipses with the fixed aspect ratio of 2:1, and the major axis is seected as 1, 2, 3, 4, 5, or 6 mm to investigate the effect of lunker size. he distance between the defect center and the rotation center is set as 1.5 mm, directly underneath the teeth. The schematic diagram of this fatigue life prediction methodology, mphasizing the impact of temperature, is shown in Fig. 10 . The diagram ummarizes the tooth flank and tooth root fatigue simulation of polymer ear with an injection molding lunker defect"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003759_j.ymssp.2019.02.044-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003759_j.ymssp.2019.02.044-Figure7-1.png",
        "caption": "Fig. 7. Deflections of planet bearings.",
        "texts": [
            " Ucg ;Vcg and Wcg are the global displacements of the carrier measured with respect to a frame tied to the stationary ring gear. Fig. 6 displays both local and global displacements. As shown in Fig. 6, global displacements of the carrier can be expressed as functions of local displacements. Ucg \u00bc Uc cos hc Vc sin hc Vcg \u00bc Uc sin hc \u00fe Vc cos hc rc Wcg \u00bc Wc 8>< >: \u00f023\u00de Hence, local displacements of the carrier from Eq. (23) can be expressed as: Uc \u00bc Ucg cos hc \u00fe Vcg sin hc \u00fe rc sin hc Vc \u00bc Ucg sin hc \u00fe Vcg cos hc \u00fe rc cos hc Wc \u00bc Wcg 8>< >: \u00f024\u00de The radial and tangential deflections of the planet bearings (Fig. 7) are expressed by Saada et al. [1] as: dnrd \u00bc Vc sinun \u00fe Uc cosun Un \u00f025\u00de dntg \u00bc Vc cosun Uc sinun \u00feWn \u00f026\u00de So, with respect to the new frame and taking into account Eqs. (4), (24), (25) and (26), the radial and tangential deflections of the planet bearings can be expressed as: d g nrd \u00bc Ucg cos un \u00fe hc\u00f0 \u00de \u00fe Vcg sin un \u00fe hc\u00f0 \u00de Ung cos hc Vng sin hc \u00fe rbr sin un \u00fe hc\u00f0 \u00de sin hc\u00f0 \u00de \u00fe rc \u00f027\u00de d g ntg \u00bc Ucg cos un \u00fe hc\u00f0 \u00de \u00fe Vcg sin un \u00fe hc\u00f0 \u00de Ung cos hc Vng sin hc \u00fe rbr sin un \u00fe hc\u00f0 \u00de sin hc\u00f0 \u00de \u00f028\u00de The position of the carrier is given by Rc "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002154_1.4037570-Figure13-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002154_1.4037570-Figure13-1.png",
        "caption": "Fig. 13 Optimum build orientation part 1",
        "texts": [],
        "surrounding_texts": [
            "Figures 13 and 14 and Tables 7 and 8 show the optimization results generated by the developed model for different parts built with Ti\u20136Al\u20134V with the estimated values for the different mechanical properties (in terms of % relative to wrought reference), surface roughness, and build time and cost."
        ]
    },
    {
        "image_filename": "designv10_5_0002645_j.mechmachtheory.2015.02.006-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002645_j.mechmachtheory.2015.02.006-Figure2-1.png",
        "caption": "Fig. 2. Coordinate system applied for the tooth of pinion generated by the planar tooth of a rack cutter.",
        "texts": [
            " (2)\u2013(8) can be rewritten in the following matrix form: AX \u00bc B \u00f09\u00de where A \u00bc 1 T1 T2 1 T3 1 T4 1 T5 1 T6 1 1 Tm\u2212\u03bb1T\u00f0 \u00de Tm\u2212\u03bb1T\u00f0 \u00de2 Tm\u2212\u03bb1T\u00f0 \u00de3 Tm\u2212\u03bb1T\u00f0 \u00de4 Tm\u2212\u03bb1T\u00f0 \u00de5 Tm\u2212\u03bb1T\u00f0 \u00de6 0 1 2 Tm\u2212\u03bb1T\u00f0 \u00de 3 Tm\u2212\u03bb1T\u00f0 \u00de2 4 Tm\u2212\u03bb1T\u00f0 \u00de3 5 Tm\u2212\u03bb1T\u00f0 \u00de4 6 Tm\u2212\u03bb1T\u00f0 \u00de5 1 Tm T2 m T3 m T4 m T5 m T6 m 1 Tm \u00fe \u03bb2T\u00f0 \u00de Tm \u00fe \u03bb2T\u00f0 \u00de2 Tm \u00fe \u03bb2T\u00f0 \u00de3 Tm \u00fe \u03bb2T\u00f0 \u00de4 Tm \u00fe \u03bb2T\u00f0 \u00de5 Tm \u00fe \u03bb2T\u00f0 \u00de6 0 1 2 Tm\u2212\u03bb2T\u00f0 \u00de 3 Tm\u2212\u03bb2T\u00f0 \u00de2 4 Tm\u2212\u03bb2T\u00f0 \u00de3 5 Tm\u2212\u03bb2T\u00f0 \u00de4 6 Tm\u2212\u03bb2T\u00f0 \u00de5 1 T2 T2 2 T3 2 T4 2 T5 2 T6 2 2 66666666664 3 77777777775 B \u00bc \u03b51 0 0 \u03b52 \u03b53 0 \u03b54\u00bd 8>>>>>>< >>>>>>: : Based on the theory of linear algebra, the coefficient vector X can be solved as follows: X \u00bc A\u22121B: \u00f010\u00de Substituting Eq. (10) into Eq. (1) yields: \u03b4\u03c62 \u03b51; \u03b52; \u03b53; \u03b54;\u03bb1;\u03bb2\u00f0 \u00de \u00bc A\u22121BYT : \u00f011\u00de We designate by \u2211c surfaces of rack-cutter (Fig. 2(a,b)) for generation of the pinion. The rack-cutter performs translational motion, wherein the pinion performs related rotation. The pinion is a modified tooth surface whose deviation from standard involute tooth surface is controlled by the H-TE. Based on the theory of gearing, as depicted in Fig. 2(c), the generating rack cutter translates horizontally when the generated pinion rotates about a fixed axis. The reference circle of the gear rolls without sliding with respect to the pitch line of the rack cutter. Coordinate systems Sc (xc, yc, zc) and S1 (x1, y1, z1) are applied to connect rigidly to the rack cutter and the pinion, respectively. The generating surface of the pinion can be expressed as: r1 u; l1;\u25b3\u03b81; \u03b81\u00f0 \u00de \u00bc M1crc u1; l1\u00f0 \u00de n1 \u00bc L1cnc f 1 u1; l1;\u25b3\u03b81; \u03b81\u00f0 \u00de \u00bc n1v c1 \u00bc 0: 8< : \u00f012\u00de Here,M1c is the 4 \u00d7 4matrix that describes the coordinate transformation from Sc to S1, and L1c is the 3 \u00d7 3 submatrix ofM1c"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003346_j.mechmachtheory.2019.103671-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003346_j.mechmachtheory.2019.103671-Figure3-1.png",
        "caption": "Fig. 3. Path-generation mechanism shown in Fig. 1 is positioned into the relocation coordinate system.",
        "texts": [
            " After the values of s, u, v, and l are obtained, the values for w can be directly calculated from Eq. (15\u20133). Once s, l, u, v, and w are determined, r, a, f, \u03bc, and \u03d50 can be obtained as follows: r = \u00b1 \u221a ls, a = \u00b1\u221a uv, f = w, \u03bc = \u2212i ln s , \u03d5 = \u2212i ln u . r 0 a To find the unknowns, b, c, d, \u03b2 , and \u03b1, a loop closure equation can be derived by summing the vectors around the loop containing a, b, c, and d. For simplicity, the origin O of the coordinate system is relocated at joint A, and the x-axis is aligned with the frame AD, as shown in Fig. 3. The loop-closure equation of the four-bar linkage is given as follows: a + b = d + c. (19) Using complex exponential notation, Eq. (19) can be written as follows: aei(\u03d5+\u03d50\u2212\u03b2) + bei\u03b8 \u2212 d = cei\u03c8 . (20) The conjugate of Eq. (20) can be written as follows: ae\u2212i(\u03d5+\u03d50\u2212\u03b2) + be\u2212i\u03b8 \u2212 d = ce\u2212i\u03c8 . (21) By eliminating the output angle \u03c8 by multiplying Eq. (20) by Eq. (21), we obtain: h\u22123e\u2212i\u03b8 + h\u22122e\u2212i\u03b8 ei\u03d5 + h\u22121e\u2212i\u03d5 + h0 + h1ei\u03d5 + h2ei\u03b8 e\u2212i\u03d5 + h3ei\u03b8 = 0, (22) where h\u22123 = \u2212bd, h\u22122 = baei(\u03d50\u2212\u03b2), h\u22121 = \u2212dae\u2212i(\u03d50\u2212\u03b2), h0 = a2 + b2 + d2 \u2212 c2,h1 = \u2212daei(\u03d50\u2212\u03b2), h2 = bae\u2212i(\u03d50\u2212\u03b2), and h3 = \u2212bd"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003009_ffe.12830-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003009_ffe.12830-Figure2-1.png",
        "caption": "FIGURE 2 Geometry of the Gaussian specimen used for the experimental tests",
        "texts": [
            " Gaussian specimens were recently proposed by the research group of the Politecnico di Torino to increase the tested risk\u2010volume in ultrasonic fatigue tests, with respect to that attainable with traditional hourglass and dog\u2010bone specimens.31 According to the well\u2010known dependency between defect size and risk\u2010volume (size\u2010effect), tests on large risk\u2010volumes allow for a more proper assessment of the defect size distribution and a reliable estimation of the VHCF response. Gaussian specimens were tested in the as\u2010built condition, which represents the worst condition with respect to fatigue loads. Therefore, tests on as\u2010built specimens permit to assess a lower and conservative limit for the VHCF response. Figure 2 shows the geometry of the Gaussian specimen used for the experimental tests. Before the experimental tests, specimens were finely polished by using sandpapers with increasing grit (from 240# to 1200#) in order to remove macroscopic surface defects and residual parts of the support structures. The surface roughness Ra of the tested specimens, equal to 1.41 \u00b1 0, 26 \u03bcm, was measured on 5 specimens by using a Mitutoyo Surftest SV\u2010500 instrument. Figure 3 shows a Gaussian specimen before (Figure 3A) and after the polishing process (Figure 3B)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001474_j.engappai.2013.08.017-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001474_j.engappai.2013.08.017-Figure6-1.png",
        "caption": "Fig. 6. Thruster distribution.",
        "texts": [
            " Based on the proof presented, the overall stability is guaranteed. Therefore, a stable tracking control can be achieved by using the proposed control strategy. The simulation study is based on a simplified model of underwater vehicles (Seaeye Falcon UUV from Laboratory of Underwater Vehicles and Intelligent Systems, Shanghai Maritime University). The UUV has five thrusters, four thrusters are in the horizontal plane and the other one is in vertical plane (Fig. 5). A brief sketch of the vehicle's horizontal thruster distribution is shown in Fig. 6. UUV hydrodynamic parameters are shown in Table 1 from (Jonathan, 2006). The proposed controller was simulated for the horizontal motion of UUV i.e. the coupled motion in surge, sway and yaw (q\u00bc \u00bdu v r and \u03b7\u00bc \u00bdx y \u03c8 ). The total vector of propulsion forces and moments in the horizontal plane (Omerdic and Roberts, 2004): \u03c4X \u03c4Y \u03c4N 2 64 3 75\u00bc cos \u03b1 cos \u03b1 cos \u03b1 cos \u03b1 sin \u03b1 sin \u03b1 sin \u03b1 sin \u03b1 A\u2032 A\u2032 A\u2032 A\u2032 2 64 3 75 T1 T2 T3 T4 2 6664 3 7775 \u00f028\u00de where \u00bd \u03c4X \u03c4Y \u03c4N T is the total forces/moments acting on the UUV center of mass, \u00bd T1 T2 T3 T4 T is the forces of the four thrusters individually, A\u2032\u00bc \u00f0a=2\u00de cos \u03b1\u00fe\u00f0b=2\u00de sin \u03b1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001304_chicc.2015.7260521-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001304_chicc.2015.7260521-Figure1-1.png",
        "caption": "Fig. 1: Quadrotor used in this paper",
        "texts": [
            " It is a foundation for landing an aircraft on a ship which demands strict landing time and good tracking performance. The rest of the paper is organized as follows: Section 2 describes the quadrotor system and its dynamical model. An improved ground effect model for quadrotor is presented in Section 3.The robust altitude controller is designed in Section 4 and experimental results on the quadrotor are given in Section 5. Finally, Section 6 concludes the paper and points out our future work. The experimental quadrotor developed by our UAV laboratory, is depicted in Fig. 1. It is based on the mechanical frame of the Flycker MH750, and the diagonal wheelbase of rotors is shorten to 600mm because of the modified arms. Four MH-4115 rotors and four 1505 propellers combine to give the quadrotor a maximum take-off weight of 5.5 Kg. The control system of the quadrotor contains an onboard flight control processor, a downward facing camera with a 2-axis gimbal mounted on the bottom of the vehicle, an onboard minicomputer and a sensor system. The sensor system consists of an inertial measurement unit (IMU) module (which includes a 3-axis digital accelerometer, three gyroscopes and a compass), an ultrasonic sensor, and a Novatel GPS module"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000739_elan.201200456-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000739_elan.201200456-Figure1-1.png",
        "caption": "Fig. 1. Three-dimensional schematic view of the microfluidic devices showing the relative positions of the working microband electrode (WE), Ag/AgCl reference electrode (REF) and platinum counter electrode (CE) inside the microfluidic channel. The WE is a bare Pt or Pt/Pt-black microband electrode.",
        "texts": [
            " These two channel components were then assembled irreversibly through oxygen plasma (Harrick), so that the microchannels were perpendicular to the parallel microband electrodes. The effective electrode lengths were limited by microchannel width (L=200 mm) and the volume of solution above the microbands was restricted by the microchannel height (h= 20 mm). During each experiment, only one WE was connected and only one channel was filled with solution, the others remaining empty. The scheme of the device is described in Figure 1. The thickness of the Pt/Pt-black electrodes was assessed by a DektakXT stylus profiler (Bruker) before integration of the microchip. Images of the surface morphology of the deposited Pt-black films were also obtained by SEM (S-800; Hitachi). All electrochemical experiments, were performed versus the Ag/AgCl reference electrode (REF) at room temperature by use of Autolab PGSTAT 30 (Eco Chemie) S P E C IA L IS S U E 896 www.electroanalysis.wiley-vch.de 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim Electroanalysis 2013, 25, No"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000034_ip-d:19820002-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000034_ip-d:19820002-Figure1-1.png",
        "caption": "Fig. 1 State paths of 2nd-order system",
        "texts": [
            "2 Scalar illustrative example To illustrate some of the basic concepts of VSS design, consider the scalar system x2(t) = -al{t)xx(t)-a2(t)x2{t) (altaitb>0)_ (14) x = (xi, x2) T is the state vector and Cj, a2 and b are constant or time-varying parameters whose precise values may be unknown. Consider the discontinuous control u = x2 > 0 x2 < 0 05) where c > 0 and u* =\u00a3u . The switching function is s = ex i + x2, and the line s = 0 is the surface on which the control has a discontinuity. It can be readily shown that the state x reaches the switching line s = 0 in a finite time T, as depicted in Fig. 1 for suitable choice of u*, u~. The state x crosses the switching line and enters the region s < 0, resulting in the value of u being altered from u+ to u~. Depending on the values of the system parameters, the state trajectory may continue in the region of s < 0, yielding bangbang control. Alternatively, the state trajectory may immediately recross the switching line and enter the region s > 0. This yields sliding (or chatter) motion. Assuming that the switching logic works infinitely fast, the state x is constrained to remain on the switching line s = 0 by the control which oscillates between the values u+ and u~"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000648_978-3-642-17531-2-Figure5.2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000648_978-3-642-17531-2-Figure5.2-1.png",
        "caption": "Fig. 5.2. Schematic of a loaded generic mechatronic transducer T with one mechanical degree of freedom, electrically connected to a voltage or current source, mechanically loaded with an elastically-suspended rigid body and an external force excitation (inertial or relative to a reference point)",
        "texts": [
            " Thus, the generic transducer creates a methodological and modeling framework for the detailed representations of physical transducer principles to be discussed in later chapters. In order to avoid redundancy in the presentation, this chapter forgoes any explanatory physically-oriented examples; these can be found in subsequent chapters. The center of attention here is a unified formal description and notation, forming the reference point for subsequent chapters. 280 5 Functional Realization: The Generic Mechatronic Transducer For systems design, it is the dynamic interaction between the excitation and system variables of a transducer which is important. Fig. 5.2 shows the generalized system configuration for a loaded generic mechatronic transducer with one mechanical degree of freedom, which can model both actuator and sensor functionality. Mechanically, the generic transducer consists of a stationary element\u2014 the stator\u2014and a mobile element\u2014the armature\u2014moving parallel to the transducer force direction. The stator is rigidly attached to a base structure supplying the reaction force. The armature is connected to a mobile structure having mass\u2014the load. In Fig. 5.2, a rigid body with mass m is depicted as the load; for more complex arrangements, a multibody system (MBS) as described in Ch. 4 can be imagined in its place. To generate the transducer force T F , electrical auxiliary energy in the form of a controlled voltage source S u or current source S i is required. Often, due to the particular physics of an implementation, only unidirectional force generation is possible, so that the armature must be provided with a restoring force. In Fig. 5.2, this is achieved with an elastic suspension with stiffness k ; for a free mass, 0k . 5.2 General Generic Transducer Model 281 The mechanical excitation is provided by a generalized external force excitation ( ) ext F t . An imposed (back-effect-free) displacement excita- tion ( )w t can be modeled elastically with ( ) ext w F k w x or rigidly with ( ) ( )x t w t corresponding to w k . System-oriented causal structures The configuration in Fig. 5.2 can be used to derive the system-oriented causal structure of the generic mechatronic transducer shown in Fig. 5.3. Excitations are the independent variable ( ) S u t or ( ) S i t of the auxiliary energy source, and the mechanical force ( ) ext F t . Affected variables can include the armature displacement ( )x t and electrical power variables dependent on the varying transducer geometry, i.e. the transducer current ( ) T i t or voltage ( ) T u t . Transducer as an actuator If the transducer is driven as a force actuator, then either ( ) S u t or ( ) S i t is the time-varying control input. The connected mechanical structure to be moved is modeled\u2014with back-effect\u2014as a rigid body m or, potentially, a multibody system (see Ch. 4). The external excitation force describes disturbances applied to the structure. The affected variables include the motion variable ( )x t of the mechanical load and the dependent (uncontrolled) variable of the electrical auxiliary energy source. Transducer as a sensor As a sensor, the transducer in Fig. 5.2 is capable of representing forces ( ) ext F t or displacements ( )x t affecting the transducer geometry. This can occur directly as a measurement of voltage ( ) T u t or current ( ) T i t , or indirectly as a displacement measurement ( )x t . In this latter operating mode, the transducer is operated at a steady-state electrical set point 0 . S u U const or 0 . S i I const . The only transducer mass m which need be considered is then the armature mass (e.g. the electrode for capacitive transducers). The excitation variables ( ) ext F t can often be mod- eled using a back-effect-free connection as in Fig. 5.2. 282 5 Functional Realization: The Generic Mechatronic Transducer Controlled auxiliary energy sources On the electrical side, transducers generally require an auxiliary energy source. For operation as an actuator, this provides the necessary (low to very high) power for mechanical motion. For operation as a sensor, the transducer is driven to a steady-state operating point with, as a rule, low to very low power use. Table 5.1 presents the symbol, two-port circuit, and an example realization for a controlled voltage source and a controlled current source",
            " From a methodological point of view, a general modeling framework which can be used to discuss diverse physical transducer principles in a unified form is also desirable. Model hierarchy The discussions in later chapters of various energy conversion principles using particular physical phenomena will refer to the model hierarchy shown in Fig. 5.4. The present chapter discusses the generalizable relationships therein, forming a unified methodological scaffold via the generic mechatronic transducer of Fig. 5.2. Reference configuration Fundamental investigations are carried out using a lossless transducer configuration with a simple, elastically-suspended rigid-body load. This model forms a conservative system, encompasses all significant multi-domain properties, and enables clear understanding with well-defined analytical relationships for the system dynamics. Model extensions which lead towards realization of the abstract model\u2014in particular concerning dissipative phenomena and multibody loads\u2014are presented at the end of this chapter",
            " Finally, considering concrete external electrical and mechanical loads on the transducer and using the constitutive two-port parameters, signalbased linear time- and frequency-domain models are derived, offering an optimal compromise between model clarity and ease-of-use for the controller design and dynamic analysis approaches preferred in this book. Model Branch A: the unloaded generic transducer Fundamental transducer functionalities are discussed using an unloaded (unconnected) transducer model (Model Branch A in Fig. 5.4, left). Constitutive ELM basic equations: A1 The starting point is the constitutive electromechanical (ELM) basic equations (A1) relating energy and power variables of the physical domains under consideration (both electrical and mechanical, see Fig. 5.2). It can be shown that there exists a domain-independent general approach for setting up these equations, so that all further considerations can largely proceed generically. ELM energy functions: A2 Formal integration of the constitutive ELM basic equations (A1) gives the ELM energy functions (A2) in the form of energies and co-energies, which are then combined in the LAGRANGian. 1 From a methodological point of view, a \u201ccontinuous\u201d workflow within a single modeling paradigm may by all means reach the highest level of modeling aesthetics",
            " Model Branch B: the loaded generic transducer The actual transducer functionality of interest for a mechatronic product\u2014 namely the interaction between moving mechanical structures and electrical interfaces to information processing functions\u2014is discussed using a loaded (i.e. connected to electrical and mechanical loads) transducer model (Model Branch B, Fig. 5.4, right). The procedure mirrors the methodology of Model Branch A. Reference configuration For pragmatic, didactic reasons, the chosen reference configuration is limited to the external loading indicated in Fig. 5.2 with lossless auxiliary energy sources (voltage or current) and a non-dissipative elastic connection to a rigid-body load. Constitutive equations: B1 The physical constitutive relations (B1) must also be defined for the external loading. For the reference loads (lossless electrical source, elastically-suspended rigid body), this is trivial. For external components deviating from these assumptions, corresponding relations must be defined. Energy functions: B2 Formal integration of the constitutive equations (B1) again gives energy functions (B2) in the form of energy and co- 5",
            "3, the constitutive ELM transducer equations for both representations (Q-coordinates and PSI-coordinates) are once again contrasted. Table 5.3 also presents the derived equations for linear electrical transducer dynamics (cf. Eq. (5.3)). 9 Note that in Eq. (5.20), the first equation describes the balance of forces 0 i T gen F F F or T gen F F , i.e. the left-hand side of Eq. (5.20) is equal to T F , which accounts for the sign placement in Eq. (5.21). It can be easily seen that as a result\u2014in accordance with the coordinate definition in Fig. 5.2\u2014the positive transducer force also works in the positive x-direction. The second equation describes the transducer voltage T , in other words, the time-differential of the underlying constitutive equation. In the case of coupling via the magnetic field (inductive dynamics), this implies ( , ) T T d x q dt . 302 5 Functional Realization: The Generic Mechatronic Transducer Implications From Table 5.3, it is possible to recognize the following important general property of the unloaded generic transducer: , , ( , 0, 0) ( , 0, 0) 0 T Q T F x F x , (5",
            " At the mechanical level, 12 12 ( ), ( )H s Y s describe the ELM force generation mecha- nisms, while at the electrical level, 21 21 ( ), ( )H s Y s describe the electrical quantities induced by motion (polarization currents, induced voltages). 11 In the literature, mechanical impedance does not refer uniquely to either the re- lationship between force and displacement or that between force and velocity. The differential stiffness is the linear approximation (tangent) to the forcedisplacement curve of the transducer at the current operating point R x . 5.4 The Loaded Generic Transducer 311 Mechanical energy Building upon the unloaded transducer in Fig. 5.4, the elastically-suspended, rigid-body load shown in Fig. 5.2 introduces a kinetic energy storage element (mass m ) and a potential energy storage element (spring k ). These have the linear constitutive relations, independent of the electrical subsystem (see Table 2.2), , F kx p mx . Integrating these relations is unproblematic, and, following the method of Fig. 5.7a, results in the well-known energy functions 21 ( ) 2mech V x kx , 21 ( ) 2mech T x mx . (5.36) LAGRANGian For the complete, loaded transducer system, the LAGRANGian of the unloaded transducer in Eqs",
            "37) or (5.38) in place of o Q L or o L . Some additional thought must, however, be given to the excitation functions. Causal structure: voltage/current source In contrast to the unloaded transducer, the definition of external excitation variables (right-hand side 312 5 Functional Realization: The Generic Mechatronic Transducer of the EULER-LAGRANGE equations) requires establishing a causal structure. On the mechanical side, this is rather simple: the external force ( ) ext F t acts as the excitation (Fig. 5.2) and represents the generalized force gen F . However, on the electrical side, as shown in Fig. 5.2, there is a choice of two possible excitations: a controlled voltage source ( ) S u t or a controlled current source ( ) S i t . Fig. 5.11 shows a two-port representation equivalent to Fig. 5.2. This results in a total of four model families, as each excitation type ( ) S u t or ( ) S i t can be represented in either Q- or PSI-co- ordinates. These four variants are sketched out in Table 5.6, and will now be discussed further. Voltage source With a controlled voltage source, the voltage ( ) S u t \u2014and thus the flux linkage ( ) S t and its time derivatives ( ), ( ) S S t t \u2014can be forced independently of the loading at the terminals. The ensuing flow of charge is represented by ( ) T q t , ( ) ( ) T T q t i t , and ( ) T q t , and is dependent on the loading at the terminals",
            " The PSI-representation is, however, representationally clearer, as the electrical excitation only acts over a forward path, and the electromechanical feedback acts only within the mechanical system. For this reason, when considering voltage-drive transducers, the discussion here prefers the PSI-coordinate representation. Fig. 5.12a sketches the gen- 314 5 Functional Realization: The Generic Mechatronic Transducer eral causal structure for a voltage-drive transducer along with the applicable model variables. Current source When using the controlled current source option ( ) S i t , as shown in Fig. 5.2 and Fig. 5.11, the dual considerations to those for voltage drive can be directly applied. In PSI-coordinate representation, there are two generalized coordinates , T x , and thus a coupled system of differential equations (Table 5.6, second row, left column). In this case, the Q-coordinate representation leads to the simpler variant, as the dependent transducer voltage T u can be directly computed from an algebraic relation in the source charge and its time derivatives, and the armature position and its time derivative (Table 5",
            " Current source: Q-representation Due to its superior representational clarity, when considering current-drive transducers, the discussion here prefers the Q-coordinate representation. Fig. 5.12b sketches the general causal structure of a current-drive transducer along with the applicable model variables. 5.4 The Loaded Generic Transducer 315 316 5 Functional Realization: The Generic Mechatronic Transducer Linear electrical dynamics For the special case of linear electrical transducer dynamics assumed here (cf. Eq. (5.3)), the nonlinear equations of motion given external loading as in Fig. 5.2 and Fig. 5.11 are listed in Table 5.7. The preferred model variants (because of their simpler structure) are shaded gray. Determining equations for equilibrium positions When implementing the general transducer models in Tables 5.4 and 5.7, steady-state operating points for steady-state excitations are of interest. Limiting further consideration to the preferred representation forms in Tables 5.4 and 5.7, only the mechanical equation of motion is relevant in determining possible equilibrium positions for operation",
            " Instead, the LAPLACE transform of the linear transducer model is examined, and the ELM two-port parameterization using the hybrid formulation ( )sH of Eq. (5.29) and the admittance formulation ( )sY of Eq. (5.35) are introduced. A comparison with the preferred coordinate representations for the electrical drive immediately demonstrates an advantageous assignment of ELM two-port parameters in the loaded linear transducer model: voltage drive admittance formulation Y , current drive hybrid formulation H . Voltage-drive transducer: signal-based model Considering the system configuration in Fig. 5.2, the linearized transducer equations, and the constitutive transducer equations (5.35) results in the following model for a loaded generic transducer with voltage drive (lossless, ideal electrical subsystem): Mechanical load: 2 , ( ) ( ) ( ) ( ) T u ext ms X s k X s F s F s , Electromechanical coupling: , ( ) ( ) ( ) ( ) ( ) T u T S F s X s s I s U s Y . (5.48) 13 The time-domain representation can be derived directly from Eqs. (5.24), (5.31), and (5.45). 322 5 Functional Realization: The Generic Mechatronic Transducer The corresponding signal flow diagram is shown in Fig",
            " 2003), (Preumont 2006)\u2014for which representations are mostly tailored to the parameters and notation of the particular transducer type. The following section demonstrates that the general transducer description chosen in this book and based on the ELM two-port parameters enables a generalized representation of electromechanical coupling factors, which is completely independent of the particular transducer type. 352 5 Functional Realization: The Generic Mechatronic Transducer Calculation The goal of this section is to calculate the ELM coupling factor for a mechanically loaded transducer with an elastic rigid-body load (see Fig. 5.2). This calculations can proceed by examining energy balances over an electrical (Fig. 5.31a) or mechanical (Fig. 5.31b) charge/discharge cycle. For a reciprocal transducer, both operations result in the same ELM coupling factors. In both cases, however, the calculation is non-trivial as the lack of mechanical damping prevents steady-state electrical and mechanical values from being established. To avoid this circumstance, this section considers a dissipative electrical drive\u2014concretely, an ideal voltage source with serial resistance22 (Fig",
            " As such processes do not require specialized sources of energy, but rather take advantage of sources of energy available in the everyday environment, they are often termed energy harvesting or energy scavenging. This energy generation principle has particular significance for the self-sufficiency of mobile electronic devices such as mobile telephones, sensors, and medical implants (Priya 2007). Technical layout The working principles of a mechatronic oscillating generator are depicted in Fig. 5.39. A seismic mass is elastically suspended in a housing via a mechatronic transducer. The housing is made to move by an external excitation ( )w t , applying a displacement excitation to the mass (see Fig. 5.2). The energy mech W stored in the mass-spring system is converted into electrical energy el W in the mechatronic transducer, and can be used at a load impedance ( ) L Z s , or\u2014following transformation in a rec- tifier\u2014can be stored electrically (e.g. in a battery) for later use (Mateu and Moll 2007). By using a seismic mass, no provision need be made to input forces; an oscillating generator can be easily placed onto any moving mechanical structure, e.g. automobiles, bicycles, shoes, prostheses, etc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001982_j.triboint.2015.09.004-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001982_j.triboint.2015.09.004-Figure5-1.png",
        "caption": "Fig. 5. Thermal network diagram of an SRB-shaft-bearing housing system.",
        "texts": [
            " [18], \u03c1 is the mass density of the mixture of lubricant and air in the housing, and le is the effective length of the roller. The total heat generation rate of Z rollers' churning can be written as, Hd \u00bc 0:5ZFddm\u03c9c \u00f025\u00de An SRB without sealing components generally consists of two rows of rollers, two cages, an inner ring and an outer ring. Therefore, the total heat generation rate of the SRB can be expressed as, Htot \u00bc 2 HRRC\u00feHd\u00feHCL\u00feHP\u00f0 \u00de \u00f026\u00de In order to facilitate theoretical analysis, some assumptions are proposed to the grease-lubricated SRB-shaft-bearing housing system depicted in Fig. 5. (1) The temperature of node A is the ambient temperature, while the temperature values of other 10 nodes are known. (2) The temperature of every node at any moment is represented by one temperature value, i.e., ignoring the inner heat conduct effect at each node. (3) The heat transfer between the bearing's outer ring and the housing hole's inner wall is contact heat exchange. (4) The heat exchange types between housing, two ends of the shaft and the air include: natural heat convection and heat radiation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001938_j.conbuildmat.2018.02.201-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001938_j.conbuildmat.2018.02.201-Figure4-1.png",
        "caption": "Fig. 4. Numerical models with boundary conditions for (a) HSB and (b) BHSB.",
        "texts": [
            " The density, Young\u2019s modulus, and Poisson\u2019s ratio of the impactor were 8050 kg/m3, 210 GPa, and 0.3, respectively. The sandwich beam specimens were fully fixed except for the axial translation and rotation about the out-ofplane axis at both ends. For each level of energy, three samples were tested to obtain a consistent set of results, the testing procedure of which was in accordance with the ASTM D7136 [20]. Also, the specimens were impacted at the center of the beam mid-span. ABAQUS 6.13-1/Explicit [21] was used to model the lowvelocity impact behavior of sandwich beams. As shown in Fig. 4, two models were developed: one each for BHSB and HSB. The 4- node shell elements with reduced integration (S4R) were used to discretize the top skin, bottom skin, and aluminum honeycomb while the 8-node linear brick elements with reduced integration (C3D8R) were used to discretize the rubber. The impactor was discretized using 4-node linear tetrahedron elements (C3D4). The simulated beams dimensions were the same as those of experimental specimens. CFRP was modeled as an elastic material defined with the \u2044ELASTIC lamina option while the rubber core was modeled as a hyperelastic isotropic material using the \u2044HYPERELASTIC ISOTROPIC option",
            " A high-density element mesh was located in the impacted and the supported zones while the region away prescribed with a gradual decrease in the mesh number to optimize the computational cost and accuracy. The numbers of element were 17217 and 18797 for HSB and BHSB, respectively. The adhesive bonding between main layers was assumed perfect by employing the surface-based tie constraint. The interactions between the beam layers were defined with the general contact description. For the impact loading, a predefined velocity for each energy level was applied. The velocities for 7.28 J, 9.74 J, and 12.63 J were 2.204 m/ s, 2.548 m/s, and 2.9 m/s, respectively. Fig. 4 shows the boundary conditions of the two beams and impactor where ux;uyanduz are the translations in the X-, Y-, and Z-directions, respectively, whereas hx; hyandhz are the rotations about the X-, Y-, and Z-axes, respectively. The impactor was fixed \u00f0ux;uz; hx; hy and hz \u00bc 0\u00deexcept for uy and the beams both ends were also fixed \u00f0uy; uz; hx; and hy \u00bc 0\u00de except for ux and hz. A friction factor of 0.5 was assigned [22]. For the first impact load case, a velocity was assigned to the impactor via the predefined field in the initial state description in ABAQUS"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000992_j.epsr.2012.08.002-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000992_j.epsr.2012.08.002-Figure5-1.png",
        "caption": "Fig. 5. 3D dynami",
        "texts": [
            " r } (nph+ndr)\u00d71 (12) In order to couple the electromagnetic behavior of the induction machine with the mechanical system equations, the electromagnetic torque is expressed as [13] Tem = 1 2 nds\u2211 i ndr\u2211 j dPij d \u03b52 ij with \u03b5ij = ij Pij (15) where is the relative angular position of the rotor, \u03b5ij , ij and Pij are, respectively, the magnetic potential difference, the flux and the permeance in the air gap branch between nodes i and j. 2.2. Mechanical model: 3D dynamic gear model The mechanical system is simulated by the 3D dynamic model of single stage spur or helical gear shown in Fig. 5. Gears are assimilated to rigid-cylinders which are linked by a series of time-varying, non-linear springs representing mesh stiffness time variations and non-linearity [14]. The input and output shafts are modeled by two-node Timoshenko beam elements with circular cross sections whereas bearings are introduced by additional lumped stiffness elements [14,17]. In order to take into account the gear environment, the electromagnetic torque in (15) is applied at node 1 on the pinion shaft (Fig. 5a). On the other end, a load machine assimilated to a torsional stiffness element and an equivalent inertia is introduced at node 6 on the gear shaft (Fig. 5a). The mechanical system dynamic behavior is therefore accounted for by six nodes with six degrees-of-freedom (DOF) per node, namely: torsion ( k), bending (vk, wk, k and k) and axial displacement (uk) where subscript k refers to the node number. It is to be noticed that these DOFs represent the infinitesimal elastic generalized displacements superimposed on rigid-body rotations considered as the state of reference [15]. As illustrated in Fig. 5b, the gears are assimilated to rigid cylinders with all six DOFs characterized by infinitesimal displacement screws (3 translations and 3 rotations) expressed in the reference frame R ( S, T, Z ) attached to the pinion\u2013gear pair as ( k) { uR k (Ok) = vk S + wk T + uk Z \u03c9R = k S + k T + k Z (16) k where k = 2 for the pinion, k = 5 for the gear, Ok is the center of gear k; vk, wk and uk are the translational DOFs; k, k and k are the rotational DOFs. 32 N. Feki et al. / Electric Power Syste fl a w p t fl e ( t a p V w p o c i i t m a t t e Mi j ) j ) \u00b7 { w i v i v{ The deflection at any potential point of contact Mi j on the tooth anks is determined based on the shifting property of screws ( k) nd can be expressed as( Mi j ) = { V ( Mi j )}T {q} \u2212 \u0131e ( Mi j ) (17) here {q} = {v2, w2, u2, 2, 2, 2, v5, w5, u5, 5, 5, 5}T is the inion\u2013gear pair DOF vector",
            " { V ( Mi j )} is the pinion\u2013gear structural vector associted with point Mi j which embodies the pinion\u2013gear geometrical roprieties at Mi j and reads( Mi j ) = { n \u2212\u2212\u2212\u2212\u2192 O2Mi j \u2227 n \u2212 n \u2212\u2212\u2212\u2212\u2212\u2192 O5Mi j \u2227 n }T (18) here n is the outward unit normal vector with respect to the inion flanks. Following [14] and [16], mesh elasticity is modeled by a series f independent stiffness elements distributed along the theoretical ontact lines in the base plane (Wrinckler foundation) as illustrated n Fig. 6. The base plane is one of the tangent planes to both the pinon and gear base cylinders (Fig. 5b) where all the contacts between he teeth take place for involute tooth profiles. Each stiffness ele- ent corresponding to any potential point of contact Mi j is time nd position dependent as the relative positions of the meshing eeth vary during the gear rotation. Centrifugal and gyroscopic effects being neglected, the equaions of motion point to the following non-linear parametrically xcited differential system [14]: [M] { Y\u0308 } + [C] { Y\u0307 } + \u23a1 \u23a3[Kc] + Nl\u2211 i Ns\u2211 j ( k ( Mi j ) \u00b7 H ( ( Mi j )) \u00b7 { V ( = { F0 (t) } + { Fe2 (t) } + \u23a7\u23a8 \u23a9 Nl\u2211 i Ns\u2211 j ( k ( Mi j ) \u00b7 H ( ( Mi j )) \u00b7 \u0131e ( Mi here { Y } = {v1, w1, u1, 1, 1, 1, v2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000755_s00170-013-5102-y-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000755_s00170-013-5102-y-Figure2-1.png",
        "caption": "Fig. 2 Experimental setup",
        "texts": [
            " The comparison between the simulated and experimental results shows that the prediction error of temperature history is <30 \u00b0C in the simulated case. The weld-based additive manufacturing system used in the study is a combination of gas metal arc welding (GMAW) and numerical control (NC) machine. The location, orientation, and movement of the welding torch as well as process parameters are controlled by the NC machine. AWS ER70S6 steel wire of 1.6 mm diameter was employed as the welding consumables. The shielding gas composition was pure argon. As shown in Fig. 2, a single-pass multilayer structure was deposited on the side edge of base plates so that the temperature on the large face of the base plate could be recorded by IR camera. The evolution of the temperature field was recorded using an IR camera FLIRThermaCAMA320, which captured dynamical IR images of 320\u00d7240 resolution. The temperature data were treated using the software ThermaCAM Researcher. Interlayer temperature control was carried out in experiments. The temperature at a selected point (located in the midline, 8 mm away from current top face) was chosen as reference temperature"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000782_j.mechmachtheory.2012.11.006-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000782_j.mechmachtheory.2012.11.006-Figure6-1.png",
        "caption": "Fig. 6. Contact point location.",
        "texts": [
            " In the reference transverse plane this point is always located as the operating pitch point, while its axial coordinate is calculated differently whether shuttling effects are enabled or disabled. When disabled, the contact point is located in themiddle of the active face width.When enabled, the axial coordinate accounts for contact pressure distribution as explained in Section 5. The three components of the contact pointwhen shuttling is disabled are given, with respect to the reference frame (Fig. 6), by: where distan refere C \u00bc q1 \u00fe s\u00bd CD\u00feOz \u00f010\u00de s\u00bd \u00bc z1 ez1\u00fez2 0 0 0 z1 ez1\u00fez2 0 0 0 1 2 4 3 5 \u00f011\u00de Oz \u00bc 0 0 1=2min FW1; FW2\u00f0 \u00de 8< : 9= ; \u00f012\u00de q1 is the displacement vector of the origin of gear 1, [s] in Eq. (11) is matrix scaling the x and y components of the center ce vector to find the operating pitch point in the transverse plane, and Oz in Eq. (12) is a vector applying an offset along the nce z axis equal to the minimum between the two face widths FWi. The static effects of operating conditions are considered in the mesh stiffness when generating the look-up tables through LDP"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000568_j.surfcoat.2012.10.053-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000568_j.surfcoat.2012.10.053-Figure1-1.png",
        "caption": "Fig. 1. Experimental setup for optical diagnostics of laser cladding process.",
        "texts": [
            " Deposition of multi-material coatings on a complex form surface and Direct Manufacturing of 3D FGM objects by DMD is the promising techniques capable of meeting industrial challenges in advancedmaterials processing [6,23,24]. Development of on-line monitoring and process control, and its integration with DMD machines is a priority task [25\u201328]. The objective of the present study is to demonstrate the advantages of comprehensive optical monitoring of DMD technology applying diverse and complementary optical diagnostic tools. The originally developed multi-wavelengths pyrometer was applied for temperature measuring in the center of the laser spot during laser cladding (Fig. 1) [29]. The device measures the brightness temperature from 900 \u00b0C up to 3000 \u00b0C at 12 wavelengths in the 1.001\u20131.573 \u03bcm spectral range with 50 \u03bcs acquisition time in a single spot with 800 \u03bcm diameter. The particular feature is the utilization of narrow spectral bandwidth of 50 nm. The device consists of a separated receiving optical unit and an InGaAs photodetector connected by optical fiber [30]. The 2D pyrometer catches a signal by Si photodiodes from a rectangular matrix (10\u00d710) and measures a brightness temperature at a single wavelength \u03bb=0",
            " The CCD-camera based diagnostic tool is useful for a particle-in-flight visualization, for a control of particle jet stability, and for a real-timemeasurement of particle-in-flight velocity. The optical monitoring can be used to optimize the conditions of powder injection in particular when powders of different natures (size, density, etc.) are injected simultaneously to produce a multifunctional multimaterial coating. The optical heads of the pyrometers and infrared camera were fixed directly onto the laser cladding head (Fig. 1). Schema of brightness temperature measurement by pyrometers and infrared camera in laser cladding is presented in Fig. 2. The present study was performed on TRUMPF 505 DMD commercial industrial-scale laser cladding installation. The machine is equipped by a 5 kW CO2 laser source. A computer-controlled powder injection set-up consists of: two powder feeding system being able to mix different powders in-situ the process at the same time; coaxial cladding nozzle mounted CNC five-axis gantry assuring a precise movement with a controlled scanning speed in complex trajectories"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003626_s11837-020-04428-6-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003626_s11837-020-04428-6-Figure3-1.png",
        "caption": "Fig. 3. (a) Three-dimensional rendering of hemispherical porosity defects imprinted in AM specimens. (b, c) Design pattern of hemispherical defects of different diameters and depths relative to the plate surface (all dimensions are in mm). Red wireframe boxes indicate (b) a larger defect pattern and (c) smaller defect pattern (Color figure online).",
        "texts": [
            " Fabrication of SS316L plate was based on 20-lm powder layers. The dimensions of the plate are length 9 width 9 thickness: 6 in 9 3 in 9 0.4 in (152 mm 9 76 mm 9 10 mm). A pattern of calibrated defects consisting of hemispherical porosity regions containing un-sintered metallic powder was imprinted into the SS316L plates. The defects were imprinted into the plates during fabrication using an STL (sterelithography) file with a drawing of the pattern of hemispherical inclusions. A computer rendering of the pattern of defects is shown in Fig. 3a. Drawings with labels showing diameters and depths of the imprinted defects are shown in Fig. 3b and c. The depth of a defect is defined as the distance from the surface of the plate to the top of the curved face of the hemispherical inclusion. Note that there are two patterns of defects in the plate: one with diameters / = 5 mm, 6 mm and 8 mm and depths d = 2 mm, 3 mm, 4 mm and 5 mm, and another one with diameters / = 1 mm, 2 mm, 3 mm and 4 mm and depths d = 1 mm, 2 mm, 3 mm, 4 mm and 5 mm. The two patterns are indicated by red wireframe boxes in Fig. 3b and c, respectively. The diameters of defects decrease along the lines parallel to the longer side of the plate, while the depth along these lines is held constant. Along the lines parallel to the shorter side of the plate, the depth increases, while the diameter is fixed along these lines. For hemispherical-shape defects, the ratio of characteristic lateral and transverse dimensions is unity. As discussed in \u2018\u2018Thermal Tomography Imaging of SS316L\u2019\u2019 section, diffusion of heat around defect boundaries is expected to have a negative impact on the visibility of defects in TT reconstructions",
            " The Gaussian-filtered image with AWGN removed from the TT reconstruction is displayed in Fig. 4b. Compared to the TT reconstruction in Fig. 4a, the Gaussian-filtered image in Fig. 4b has less noise at the expense of image blurring. The dictionary matrix used in the SC/KSVD algorithm is displayed in Fig. 4c. The image in Fig. 4d shows the TT reconstruction with AWGN removed using the SC/K-SVD method. Compared to Fig. 4a and b, the image in Fig. 4d has decreased noise and sharper features. Grayscale images of reconstruction of the smaller pattern of defects, as shown in Fig. 3b, are displayed in Fig. 5. TT reconstruction at depth z = 1 mm is shown in Fig. 5a. Note that defects (d1, /4), (d1, /3) and possibly (d1, /2) are visible. The Gaussianfiltered image with AWGN removed from TT reconstruction is displayed in Fig. 5b. Compared to the TT reconstruction in Fig. 5a, the Gaussian-filtered image in Fig. 5b has less noise at the expense of image blurring. The dictionary matrix used in the SC algorithm is displayed in Fig. 5c. The image in Fig. 5d shows the TT reconstruction with AWGN Zhang, Saniie, and Heifetz Detection of Defects in Additively Manufactured Stainless Steel 316L with Compact Infrared Camera and Machine Learning Algorithms removed using the SC/K-SVD method"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000648_978-3-642-17531-2-Figure2.23-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000648_978-3-642-17531-2-Figure2.23-1.png",
        "caption": "Fig. 2.23. Generalized energy variables: Definitional Relationships II",
        "texts": [
            " For the modeling of mechatronic systems, the following generalized energy variables are defined: Generalized potential, effort e Generalized velocity, flow f Generalized momentum 0 0 ( ) : ( ) ( ) t t p t e d p t or dp e dt , e p Generalized coordinate, displacement 0 0 ( ) : ( ) ( ) t t q t f d q t or dq f dt , f q Generalized power ( ) ( ) : : ( ) ( ) dE t dq dp P t f t e t dt dt dt Generalized energy ( ) ( ) ( ) ( ) dq dp dE t P t dt f t e t dt e dt e dq f dt f dp dt dt 0 ( ) ( ) ( ) t t E t f e d 2.3 Modeling Paradigms for Mechatronic Systems 75 Generalized potential energy 0 ( ) ( ) q q V q e q dq (2.1) Generalized potential co-energy 0 ( ) ( ) e e V e q e de Generalized kinetic energy 0 ( ) ( ) p p T p f p dp Generalized kinetic co-energy 0 ( ) ( ) f f T f p f df (2.2) A summary representation of the relationships created by these definitions is presented in Fig. 2.22 and Fig. 2.23. 76 2 Elements of Modeling Conjugate variables The tuples ( , )p q and ( , )e f are respectively termed conjugate energy variables and conjugate power variables. Constitutive equations Among the equations involving the generalized energy variables, the so-called constitutive equations ( )e e q and its inverse relation ( )q q e , as well as ( )q q p and ( )p p q , represent the domain-specific physical laws, which relate energy variables to one another. For the majority of applications, the generalized displacement coordinates q and q along with the constitutive equations ( )e e q and ( )p p q offer a convenient starting point for model creation. Energy and co-energy The energy and co-energy variables are only equal in the case where there is a linear relationship between the energy and power variables (Fig. 2.23), i.e. e q or 1 f q p . The energy and co-energy are generally linked via a so-called LEGENDRE transformation ( ) ( ), ( ) ( ) . V e e q V q T f f p T p NEWTONian mechanics In the context of NEWTONian mechanics with lumped parameters, there exists a linear relationship between momentum and velocity, i.e. momentum ( )p M x v , and angular momentum ( )h I . Thus the kinetic energy T and co-energy T are equal. It is only with relativistic effects that kinetic energy T and co-energy T begin to differ (Fig",
            "22) Effort accumulator d e t f t dt or 0 0 1 t t f t f t e d . (2.23) The proportionality constants , , used in relations (2.21) through (2.23) represent the parameters of the corresponding lumped network elements. In the form presented, these parameters are specified as constant, so that linear time-invariant relations between the power variables e and f result. In the general case, however, time varying and nonlinear relationships are also possible (see also the constitutive equations in Sec. 2.3.1 and Fig. 2.23). 2.3 Modeling Paradigms for Mechatronic Systems 93 Analogous relations In any particular domain, the parameters , , are typically assigned individual names and symbols (Tables 2.2, 2.3). To the great chagrin of the engineer, however, this assignment is rather inconsistent, particularly the assignments for mechanical systems. In the field of network theory (Thomas et al. 2009), (Reinschke and Schwarz 1976), (Lenk et al. 2011), the assignment of effort and flow shown in Table 2.3 has become the norm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002417_02670836.2017.1398513-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002417_02670836.2017.1398513-Figure6-1.png",
        "caption": "Figure 6. The model of the SLM parts.",
        "texts": [
            " To verify the application of the AlSi10Mg alloys, fabricated by selective laser melting, this paper studies the structure of an aeronautical part using an ambient vibration test. The ambient vibration test is an importantmethod to assess and evaluate a part\u2019s product vibration environmental adaptability. In the process of test implementation, determination and induction of vibration test conditions, fixture design and the layout of sensors or other conditions was found to directly affect the authenticity, reliability and validity of the product\u2019s vibration resistance ability evaluation. As shown in Figure 6, the aeronautical component has a size of 236\u00d7 224\u00d7 52.7mm, and the thickness is 2mm. In assembly, ameasurement unit (1100 g) is fixed on the plate by a four M4 threaded hole. In the conventional manufacturing process, the aeronautical component is manufactured using the technology of sheet metal formed (SMF) with material 2A12 alloy. In this study, the structural performance of conditional SMF parts D ow nl oa de d by [ U N IV E R SI T Y O F A D E L A ID E L IB R A R IE S] a t 2 3: 27 1 8 N ov em be r 20 17 is compared with the SLM parts using AlSi10Mg alloys"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000857_j.cma.2013.12.017-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000857_j.cma.2013.12.017-Figure2-1.png",
        "caption": "Fig. 2. Schematic representation of fixed-setting cutters: (a) outer cutting blade for generation of concave side, and (b) inner cutting blade for generation of convex side.",
        "texts": [
            " Therefore, two independent fixed-setting face-milling cutters are used for the curvilinear gear generation: (a) the cutter for generation of the concave side of the gear tooth surfaces that will be provided with outside cutting blades; (b) the cutter for generation of the convex side of the gear tooth surfaces that will be provided with inside cutting blades. In this case, the generation processes of concave and convex gear tooth surfaces become independent, the radii of the cutters can be optimized according of the sought-for type of contact, and in this way, generated curvilinear gears might be in line or localized point contact. The main drawback for this type of generation is that manufacturing time will be increased. Fig. 2 shows a scheme of the cross section of a fixed-setting cutter provided with outer cutting blades for generation of the concave side of the gear tooth surfaces (Fig. 2(a)) fixed-setting cutter provided with inner cutting blades for generation of the convex side of the gear tooth surfaces (Fig. 2(b)). Fig. 3 shows the generating process for curvilinear gears no matter whether fixed-setting or spread-blade face-milling cutters are considered. During the generation process, the face-milling cutter is translated with lineal velocity vc perpendicular to the rotation axis of the gear blank whereas the gear blank is rotated with angular velocity xgb. The face-milling cutter pitch plane remains tangent to gear pitch cylinder. Finally, the gear tooth surfaces are generated as the envelope to the family of positions of the face-milling cutter blades in his rolling without sliding relative movement over the gear pitch cylinder"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003313_j.mechmachtheory.2019.03.012-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003313_j.mechmachtheory.2019.03.012-Figure1-1.png",
        "caption": "Fig. 1. Lumped element model for a single gear stage.",
        "texts": [
            " Index i receives the value of 1 when referring to the pinion or driving gear and 2 when referring to the driven gear. I i and I ti are coupled via a torsional spring ( k ti ), which corresponds to each tooth\u2019s bending, shear, compressive and root compliance. This spring is accompanied by a torsional damping element ( c ti ) which represents the intrinsic material damping associated with the aforementioned compliance. Contacting pairs of teeth are also coupled to each other via a non-linear contact force, represented in Fig. 1 in the form of a spring ( k ). h In total, the model comprises a pair of degrees of freedom for the gear hubs ( \u03d5 1 and \u03d5 2 ) and an additional pair of DOFs for each tooth pair considered ( \u03d5 t 1 and \u03d5 t 2 ). \u03d5 i corresponds to the rotation of each gear hub around its axis, whereas \u03d5ti corresponds to the equivalent rotation of each gear tooth around its root. A number of geometric factors involved in the proposed model, such as the leverages ( L i and L ti ), are variable and depend on the meshing position"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003146_6.2018-1116-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003146_6.2018-1116-Figure3-1.png",
        "caption": "Figure 3. ICE control effectors suite.",
        "texts": [
            " Unlike conventional spoilers, SSDs open a slot between the lower and upper wing skins when deflected, allowing the redirection of the air flow at high AoA to recover control effectiveness of the trailing-edge actuators. SSDs provide improved lateral-directional control effectiveness at high AoA and transonic flight with respect to conventional spoilers. The SSDs are placed upstream of most trailing-edge control surfaces, and therefore have a strong influence on their control effectiveness at low AoA. The configuration of the ICE control effectors is shown in Figure 3. The dynamics of the control effectors are modeled as second-order transfer functions. A low-bandwidth and a high-bandwidth transfer functions are used depending on the effectors: 7 of 25 American Institute of Aeronautics and Astronautics D ow nl oa de d by U N IV E R SI T Y O F A D E L A ID E - IN T E R N E T o n Ja nu ar y 17 , 2 01 8 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /6 .2 01 8- 11 16 Hl(s) = (18)(100) (s+ 18)(s+ 100) (22) Hh(s) = (40)(100) (s+ 40)(s+ 100) (23) The position limits, no-load rate limits and dynamics of the ICE control effectors are listed in Table 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000738_tpas.1967.291749-Figure11-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000738_tpas.1967.291749-Figure11-1.png",
        "caption": "Fig. 11. Regions of instability for different rotor resistances. 1) rdT' = 0.030 p.u.; r' = 0.015 p.u. 2) rd7' = 0.150 p.u.; r6r' = 0.030 p.u. 3) rdr' = 0.060 p.u.; r67' = 0.075 p.u. 4) rd7' = 0.075 p.u.; rqr' =0.060 p.u.",
        "texts": [
            " 9 show an increase in the region of instability with an increase in the ratio Xad/ X,q. In other words, an increase in the maximum steadystate torque is accompanied by a larger region of !instability. With the machine parameters given in Table I, it was found that instability did not occur with Xad/ Xaq = 2. The 'increase in the region of instability due to an increase in stator resistance is shown in Fig. 10. The influence of the rotor resistances, rqr'I and rdT', on the region of instability is shown in Fig. 11. Regions of instability for several values of machine leakage reactances are shown in Fig. 12. In this study the leakage reactances of the machine were maintained equal, that is, X1S = XldT' = XI,,'. The contours shown in Fig. 12 illustrate that the region of instability decreases as the leakage reactances of the machine increase. This characteristic is also demonstrated in Fig. 13. In this study, however, the leakage reactances of the rotor circuits were maintained at 0.10 p.u. and machine stability was investigated for several values of stator leakage reactance"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002154_1.4037570-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002154_1.4037570-Figure2-1.png",
        "caption": "Fig. 2 Facet angle computation",
        "texts": [
            " Using this method, each mechanical property (ultimate tensile strength, elongation, and Vickers hardness) was defined by different equations according to heat treatments. Surface Roughness. Mezzetta [6] studied the surface roughness on Ti6Al4V samples. Different tests were performed using a constant layer thickness of 0.03 mm to study the roughness of upfacing and side-facing surfaces. Within this work, a model was developed based on polynomial regression linking the surface roughness with the surface orientation Ra \u00bc 9:4148\u00fe 0:0389 h (5) where [0 deg, 90 deg] represents the angle between the surface normal and the XY plane of the machine as shown in Fig. 2. Currently, the graphic standard for AM is the STL format, in which the surface of the 3D part is split into small triangles called facets. The surface roughness of each facet is calculated after estimating the normal of each triangle using the right-hand rule and evaluating the angle h with the vertical axis of the machine using the given equation h \u00bc arcsin jA : u1 \u00fe B : u2 \u00fe C : u3jffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi A2 \u00fe B2 \u00fe C2 p : ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u2 1 \u00fe u2 2 \u00fe u2 3 p (6) Where n\u00bc (A, B, C) is the facet normal and u\u00bc (u1, u2, u3) is the vertical axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000236_j.mechmachtheory.2010.06.004-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000236_j.mechmachtheory.2010.06.004-Figure1-1.png",
        "caption": "Fig. 1. Cutting profile geometric definition and the basic profile based on the ISO profile,M is the gear module that defines the teeth size in the gear. The two sides of the tool are termed drive and coast side respectively. Pressure angles \u03b1d and \u03b1c are shown here with the same value. The coordinate system used is shown.",
        "texts": [
            "With apressure angledecrease, theprimaryadvantage is the increase of the contact ratio and a possible increase of the tooth height that will have a positive influence on the noise level. A disadvantage is an increase in the maximum teeth sliding speed that has a negative influence on the lubrication. A further listing of advantages and disadvantages of increasing or decreasing the pressure angle can be found in Ref. [2]. Almost all gears are symmetric and defined according to the standard cutting tool. The cutting tool definition used in the present paper is based on the ISO profile and seen in Fig. 1. The shown profile has, as the ISO profile, an added top with the height of M/4, whereM is the gear module which controls the gear teeth size and subsequent also the gear size (the pitch diameter dp is given by dp=Mzwhere z is the number of teeth on the gear). Top radius \u03c1 is chosen such that there is no jump in the slope. The bottom of the true cutting tooth profile is not identical to the bottom of the shown cutting profile based on the ISO profile. For the real cutting profile, the top of the cut teeth is assumed given by the initial steel blank diameter, which is equal to the addendum diameter. The shown profile has as envelope the full cut tooth, i.e., the envelope of the bottom part of the profile is the finished cut tooth top. Teeth cut with the ISO profile and teeth cut with the profile shown in Fig. 1 are therefore identical. Gears become symmetric when the cutting tool tooth is symmetric with respect to the y-axis as defined in Fig. 1. Symmetry of the two involutes of a tooth follows a choice of identical pressure angles, \u03b1d=\u03b1c. Subscript d is used for drive side and subscript c is used for coast side. Two identical pressures angles imply that the two straight lines have opposite gradient, and that they go through the points (\u2212\u03c0M/4, 0) and (\u03c0M/4, 0) respectively (the envelope of the straight side are the tooth involute). If the object of gear design is to minimize the stresses, it follows from the listed advantages and disadvantages of changing the pressure angle that the pressure angle should be as large as possible",
            " The tooth is fixed at a depth of size M and at two symmetry lines to the two adjacent teeth, see Fig. 2. If the support is moved to the tooth root it would complywith the Lewis formula for bending stress calculation, see e.g. Ref. [24]. By moving the support closer to the gear center the tooth becomes more flexible. Fixing the tooth at a depth larger than M has a negligible influence on the stress we want to minimize, i.e., the maximum bending stress at the root. The basic ISO profile has an added top with a height of M/4 as seen in Fig. 1. The top on the basic profile is added to make a clearance for the lubricating oil. It is however also the top that controls the bottom shape of the gear teeth. This is the case which can be seen e.g. for the rackwhere the teeth are the counter part of the profile as shown in Fig. 1. In Ref. [1] the tool tip is the design domain because the symmetric design was kept and the focus was on the stress concentrations at the tooth root. Root stress is directly controlled by the tool tip shape. In the present paper the parameterization used in Ref. [1] is extended to include asymmetric cutting teeth that give asymmetric gear teeth. The straight side of the cutting tool is no longer fixed to have the pressure angle \u03b1 but the idea is to change this value without interfering with a lower constraint on the tooth top thickness(top land)",
            " The involute part should be kept unchanged to allow the optimized gears to have the same functional qualities as the original involute gears. A distinction is made between the tool top part that cuts the tooth root of the drive side (drive top) and the other part that cuts the tooth root of the coast side (coast top). As indicated in Fig. 4 the coast side top is a simple circle (part of a full circle). The radius of the circle is given as \u03c1c = \u03baM = 4\u03bc + \u03c0\u22125tan\u00f0\u03b1c\u00de 4\u00f0cos\u00f0\u03b1c\u00de\u2212\u00f0sin\u00f0\u03b1c\u00de\u22121\u00detan\u00f0\u03b1c\u00de\u00de M \u00f09\u00de ight be greater than or smaller than the ISO standard \u03c1\u22480.38 M (see Fig. 1). This also means that the involute on the costs and m sidemight not be as long as it would have been using the ISO cutting tooth, but this is ignored because of the unidirectional loading assumption. he design domain for the optimization shown as the hatched part. The coast side pressure angle and drive side pressure angle are shown together with the dius on the cutting tool coast side. Final part to be parameterized is the drive top, this is done by a modified super elliptic shape. The design domain is shown as the hatched part in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000807_j.mechmachtheory.2013.06.013-Figure16-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000807_j.mechmachtheory.2013.06.013-Figure16-1.png",
        "caption": "Fig. 16. Illustration of the process position of station 1 and station 2.",
        "texts": [
            " 15, a tool slide is funded on the machine and the installation solutions for grinding face-gear based on the disk wheel are mentioned above. The range of swing angle \u0394\u03c8w of the disk wheel is [\u2212 \u03c8w \u2217 ,\u03c8w \u2217 ] combined with Eq. (21). Whereas, the movement of B-axis of PHOENIX\u00ae 800G Bevel Gear Grinding Machine is limited to [0, 90]. Therefore, the whole process is implemented in two steps: (1) Move the disk wheel to the process station of station 1, where tooth surfaces 1 of face-gear is in-process (shown in Fig. 16) until all the gear teeth are done. (2) The face-gear rotates around A-axis at 180\u00b0. Then the disk wheel is moved to the process position of station 2, where the tooth surfaces 2 of face-gear is in-process (shown in Fig. 16). The test platform is established with the NC simulation software Vericut which is developed by CGTECH Company in the United States [16]. An overview of the simulation processing test is as the following steps: (1) Use CATIA software to establish the machine model, stock model of the face-gear, the theoretical face-gear model (Fig. 17 (b)) and the disk wheel model, and then put the model files into Vericut software. (2) Calculate the NC code file based on the parameters represented in Table 3 and the grinding method mentioned above, and then put it into Vericut software"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001742_0954406214531943-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001742_0954406214531943-Figure2-1.png",
        "caption": "Figure 2. The statics experiment system.",
        "texts": [
            " Statics experiments of linear guideway The SHS-35R linear guideway with middle preload was used in the statics experiment to obtain the vertical stiffness of guideway in this section. The guideway is shown in Figure 1 and consists of rail, carriage, retainer, balls, and other accessories. There are four grooves in the guideway. According to the handbook of guideway provided by THK Corporation,11 the relative parameters guideway are listed in Table 1. These parameters will be used in analytical and finite element analysis in the next sections. The test instruments are shown in Figure 2, including a universal testing machine, two dial indicators, and accessories. First, the linear guideway is fixed on the bed of testing machine. The vertical load FV applied to the carriage of guideway varies from 0 to 30 kN using the universal testing machine, and the load step is 5 kN. Then, the relative deformation of guideway is measured by two dial indicators. To reduce the measurement error, only the deformations corresponding to load range of 10 to 30 kN are recorded, and the average values of the two dial indicators are the final results"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003346_j.mechmachtheory.2019.103671-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003346_j.mechmachtheory.2019.103671-Figure4-1.png",
        "caption": "Fig. 4. Two-DOF auxiliary mechanism of path-generation.",
        "texts": [
            " Based on the afore-mentioned theoretical analysis, a prescribed path can be specified as a function of the input angle \u03d5, i.e., Eq. (2), when it is given by a sequence of discrete points. This continuous curve can provide a good approximation to the prescribed path. By substituting \u03d5i (\u03d5i = \u03c0 64 i, i = 1, 2, \u00b7 \u00b7 \u00b7, 128) into Eq. (2), 128 points can be obtained and form a relative smooth curve. A two-DOF (degree of freedom) auxiliary mechanism will be used to build the relationship between the points and the input angle, as shown in Fig. 4. Crank AB can rotate around the fixed pivot A. Curve PPiPj is the closed path formed by the 128 points. It is known that when crank AB rotates through the full turn, the point P traces the whole closed path PPiPj. Based on this fact, the relationship between the points and the input angle can be obtained if the coordinates of fixed pivot A (Ax, Ay), the length lAB of crank AB, and the length lBP of the floating bar BP are obtained. Based on this observation, when crank AB rotates through a full turn and point P traces the closed curve, link AB is collinear with link BP twice"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001702_j.automatica.2014.03.001-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001702_j.automatica.2014.03.001-Figure1-1.png",
        "caption": "Fig. 1. The planar double pendulum hung from a random vibrating ceiling.",
        "texts": [
            " , 5) large enough. Remark 6. Applying Chebyshev\u2019s inequality, for any \u03b5 > 0 and \u03b50 > 0, there exists a moment T > 0 such that when t > T , P{|z1(t)| > \u03b5} \u2264 1 \u03b52 (\u03b50 +  d ck1  1 2 ) \u2264 \u03b5\u2032. \u03b5\u2032 can be made small enough by tuning design parameters, which implies that the asymptotically tracking in probability in some sense can be achieved. 5. Application to mechanical systems To illustrate the efficiency of the control scheme, we consider a planar double pendulum hung from a random vibrating ceiling (see Fig. 1). The \u2018\u2018upper\u2019\u2019 pendulum has mass m1 and length l1, the \u2018\u2018lower\u2019\u2019 pendulum has mass m2 and length l2, whose units are kg (kilogram) and m (meter), respectively. g is the acceleration of gravity whose unit is m/s2. Suppose that the double pendulum moves in a vertical plane, and there is no air resistance acting on it. As in Section 8.2.4 of Zhu (2003), let \u03be1 and \u03be2 denote the accelerations of hanging point O in horizontal and vertical directions, respectively, which can be seen as independent white noises"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001770_j.apsusc.2016.09.009-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001770_j.apsusc.2016.09.009-Figure6-1.png",
        "caption": "Fig. 6 (a) Snap shot of contact pattern (at t = 0) in the HCR spur gear pair; (b)MDOF spur system for HCR gear pair, \ud835\udc58( ) and \ud835\udc50\ud835\udc5aare in the LOA direction here.",
        "texts": [
            "1\ud835\udc45\ud835\udc4e (22) Thus, the simulation of \ud835\udc67(\ud835\udc65) for different surface roughness can be easily conducted. Fig. 5 shows results with \ud835\udc46 varying from 0.1 \ud835\udc5a to 1.5 \ud835\udc5a. Then, STE for a teeth pair will be the synthetic of each tooth. The system model for a spur HCR gear can be established with the following assumptions: (i) pinion and gear are rigid disks; (ii) shaft-bearing stiffness elements in the line-of-action (LOA) and OLOA directions are modeled as lumped springs which are connected to a rigid casing; (iii) the nonlinear backlash is not considered for simplicity, as shown in Fig. 6. Overall, an improved linear time-varying system formulation can be obtained with time-varying sliding friction and STE. The sliding friction coefficient and STE are a function of surface roughness. The governing equations for the torsional motions \ud835\udc5d and \ud835\udc54 are as follows: \ud835\udc5d ?\u0308? = \ud835\udc5d \u2212 \u2211 \ud835\udc3f\ud835\udc5d \ud835\udc5b= \ud835\udc52 \ud835\udc59( ) =1 (\ud835\udc58 (\ud835\udc5f\ud835\udc4f\ud835\udc5d \ud835\udc5d \u2212 \ud835\udc5f\ud835\udc4f\ud835\udc54 \ud835\udc54 + \ud835\udc5d \u2212 \ud835\udc54 \u2212 \ud835\udc52) + \ud835\udc50\ud835\udc5a(\ud835\udc5f\ud835\udc4f\ud835\udc5d ?\u0307? \u2212 \ud835\udc5f\ud835\udc4f\ud835\udc54 ?\u0307? + ?\u0307? \u2212 ?\u0307? \u2212 ?\u0307?)) \u2212 \u2211 \ud835\udc5f\ud835\udc4f\ud835\udc5d (\ud835\udc58 (\ud835\udc5f\ud835\udc4f\ud835\udc5d \ud835\udc5d \u2212 \ud835\udc5f\ud835\udc4f\ud835\udc54 \ud835\udc54 + \ud835\udc5d \u2212 \ud835\udc54 \u2212 \ud835\udc52) \ud835\udc5b= \ud835\udc52 \ud835\udc59( ) =1 + \ud835\udc50\ud835\udc5a(\ud835\udc5f\ud835\udc4f\ud835\udc5d ?\u0307? \u2212 \ud835\udc5f\ud835\udc4f\ud835\udc54 ?\u0307? + ?\u0307? \u2212 ?\u0307? \u2212 ?\u0307?)) (23) \ud835\udc54 ?\u0308? = \u2212 \ud835\udc54 + \u2211 \ud835\udc3f\ud835\udc54 \ud835\udc5b= \ud835\udc52 \ud835\udc59( ) =1 (\ud835\udc58 (\ud835\udc5f\ud835\udc4f\ud835\udc5d \ud835\udc5d + \ud835\udc5f\ud835\udc4f\ud835\udc54 \ud835\udc54 + \ud835\udc5d \u2212 \ud835\udc54 \u2212 \ud835\udc52) + \ud835\udc50\ud835\udc5a(\ud835\udc5f\ud835\udc4f\ud835\udc5d "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002213_j.mechmachtheory.2014.06.006-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002213_j.mechmachtheory.2014.06.006-Figure3-1.png",
        "caption": "Fig. 3. Screw system of the derivative queer-square mechanism.",
        "texts": [
            " For the purpose of analysis, a coordinate system O(x, y, z) is built up as shown in Figs. 2 and 3. The origin point O of the system is located at a distance of l2 / 2 away from point O\u2032 in the direction of A1O0. The x-axis points in the direction of OA1. The z-axis is perpendicular to the plane OA1A2, and points upwards. The y-axis is defined by the right hand rule. All of the angles \u03b11, \u03b81, \u03b211, \u03b212, \u03b12, \u03b82, \u03b221 and \u03b222 are defined by rotating from the extended line of the former bar to the latter bar, as demonstrated in Fig. 3. Each of the twelve revolute joints of the derivative queer-squaremechanism is expressed by a screw, denoted as Si, which belongs to a six-dimension linear vector spacewith transformation features [21]. The unit vector in the direction of the screw axis is presented in the first three components. In some postures, S3, S4, S5 and S6 and S9, S10, S11 and S12 can form two parallelograms. When the derivative queer-square mechanism changes to some other postures, S3, S4, S5 and S6 or S9, S10, S11 and S12 only build up one parallelogram"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000679_j.ymssp.2010.02.003-Figure18-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000679_j.ymssp.2010.02.003-Figure18-1.png",
        "caption": "Fig. 18. Qualitative behaviour of the floating bearing blocks in operational conditions.",
        "texts": [
            " (35) and (36) is W \u00bc 0:150 ~E 2 \u00fe ~G 2 1=2 \u00f01 a0\u00de3=2 1 \u00f037\u00de where the parameters ~E; ~G; a0 that depend on the eccentricity ratio are defined in [12]. It is worth noting that the eccentricity of the journal axis with respect to the bearing block (of modulus e and azimuth G, Fig. 16) is different from the eccentricity of the gear axis with respect to the case (of modulus ~e and azimuth ~G, Fig. 6), due to the relative position of the bearing blocks into the case. In fact, there is a radial backlash hb between the bearing blocks and the case as shown in Fig. 18, where the backlash is enlarged for better highlighting. Thus, the bearing blocks are floating and consequently the eccentricity of the gears with respect to the case depends not only on the relative position of the journals into the bearings but also on the relative position of the bearing blocks into the case. It is very difficult to estimate the dynamic behaviour of the floating bearing blocks; hence let us suppose that the pressure distribution around the bearing blocks is the same as around the gears. Therefore, the bearing blocks will be subjected to a global pressure force that pushes them in a static position with zero backlash at the low pressure side, as shown in Fig. 18. The relationship between the journal-bearing block eccentricity and the gear-case one is evaluated on the basis of this assumption. Based on the above-described formulation, the bearing reactions depend on the gear centre position and velocity as well as the gear angular velocity. In order to introduce these reactions in the equations of motion (1)\u2013(6), expressions (28) have to be multiplied by two, since each gear is supported by two bearings, and finally the reactions have to be reduced in the reference frames OkXkYk of Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000648_978-3-642-17531-2-Figure1.23-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000648_978-3-642-17531-2-Figure1.23-1.png",
        "caption": "Fig. 1.23. Laboratory demonstration of a motion-compensated matrix camera with moving image sensor (Janschek et al. 2007): a) camera configuration, b) hardwarein-the-loop test stand",
        "texts": [
            " For each of the two orthogonal axes X and Y, an inner control loop\u2014the platform control loop\u2014 adjusts the platform position locally to a reference value generated by the outer control loop\u2014the imaging control loop. Due to its position control, the elastomechanical properties of the piezo platform are no longer visible to the outer control loop, so that the control accuracy is primarily determined by the delay for image processing. Fig. 1.22 presents typical time evolutions; a laboratory demonstration and a hardware-in-the-loop test stand are shown in Fig. 1.23. Methods, models, concepts This textbook imparts fundamental knowledge concerning the systems oriented treatment of mechatronic systems. It presents methods appropriate to design tasks (e.g. modeling, dynamic analysis, and configuration), develops representative dynamic models to aid in understanding applicable physical phenomena, and discusses illustrative mechatronic solution concepts for selected examples from practice. What is covered? Subject canon The tasks of systems design for heterogeneous systems\u2014 here, the subject is mechatronic systems\u2014are very broad in their nature"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003919_j.apor.2020.102053-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003919_j.apor.2020.102053-Figure1-1.png",
        "caption": "Fig. 1. AUV coordinate systems.",
        "texts": [
            " One of the typical AUV systems has 6 DOFs having 3 coordinate for the position and 3 coordinate for the orientations in space. The dynamical model contains hydrodynamic features and the unmodeled dynamics which makes the dynamic model more complex and highly nonlinear. Therefore, in this section, firstly the generalized kinematic and dynamic model of AUV are derived and after this, for the feasibility of the proposed control scheme, a 4-DOF reduced dynamic model is derived. To obtain the kinematic model of the autonomous underwater vehicle system, we commonly consider two reference frames as shown in Fig. 1, namely inertial/earth-fixed frame(A) and the body-fixed frame(B). In the body-fixed frame, = u v w p q r[ , , , , , ]T is the linear and the angular velocities vector such that u, v, w \u2208 R describe the surge, sway and heave velocities and p, q, r \u2208 R describe the angular velocities, whereas in the earth-fixed frame, = x y z[ , , , , , ]T is the position and orientation vector of the vehicle such that x, y, z \u2208 R involves the position of the vehicle and \u03d5, \u03b8, \u03c8 \u2208 R involves the roll, pitch, and yaw"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003496_tec.2020.3006098-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003496_tec.2020.3006098-Figure1-1.png",
        "caption": "Fig. 1. Configuration of a three-phase 48-stator-slot/ 52-rotor-pole MSTPM machine. (a) 3D view. (b) 2D view.",
        "texts": [
            " To further verify the advantage of the coupled model, a 3D-FEM thermal analysis is performed and the predicted results are compared with those from the coupled model in section VI. In section VII, experimental validation on a prototyped machine is conducted to confirm the effectiveness of the coupled model. Finally, important conclusions are highlighted in section VIII. The configuration of a three-phase 48-stator-slot/ 52-rotorpole (48s/52p) MSTPM machine for in-wheel electric motorcycle is shown in Fig. 1, where the dimensions and specifications are the same as those of a commercial 3-phase SPM machine in electric motorcycles [8]. Three-phase concentrated tooth-wound armature windings are distributed evenly in the 48 stator slots, which means each stator tooth is wound by an armature coil with the coil pitch of 1. For the outer rotor, it is composed of 26 rotor elements, and each rotor element is a combination of a piece of spoke-type magnet and two pieces of magnetic conductive blocks (iron teeth)",
            " Therefore, the thermal resistance in the air gap can be calculated as Rstator, rotor=0.84101K/W. In addition to conduction, convection heat transfer appears between solid surface and fluid. Normally, there are two types of convections: natural convection and forced convection. Consequently, the convection thermal resistance R(j, k) between nodes j and k with different states can be defined as: (15) where, h is the heat transfer coefficient modeled in region where the solid and fluid contact, and A defined in equ. (14). Except for the end caps shown in Fig. 1(a), the convection thermal resistances of other components of the MSTPM machine can be determined easily by the guidance in [9-10], [21, 23]. To calculate the heat transfer coefficient of end caps, a rotating disc model is established in Fluent, and the heat transfer coefficient hec of end caps is 63.9 W/(m2\u00b7K). The key components thermal resistances of the MSTPM machine are listed in Table VII. According to the magnetic field and loss model in section III as well as the LPTN model in section IV, a coupled magnetic field-thermal network model is constructed to investigate both EM and thermal characteristics of the MSTPM machine"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000236_j.mechmachtheory.2010.06.004-Figure17-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000236_j.mechmachtheory.2010.06.004-Figure17-1.png",
        "caption": "Fig. 17. New standard asymmetric elliptic cuter AE2.",
        "texts": [],
        "surrounding_texts": [
            "For the discussions and suggestions I wish to thank Prof. Pauli Pedersen."
        ]
    },
    {
        "image_filename": "designv10_5_0000831_j.humov.2011.06.009-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000831_j.humov.2011.06.009-Figure3-1.png",
        "caption": "Fig. 3. The average Euclidean norm angle trajectory as well as the average standard deviation (SD) at each point in the lifting cycle under both loading conditions: zero load (0%) and 10% of each subject\u2019s maximum back strength. Note that the average angle and standard deviation curves were first calculated for each subject, and then ensemble averaged across subjects.",
        "texts": [
            " Both short- (kmax s) and long- (kmax l) term maximum finite-time Lyapunov exponents were computed to estimate the neuromuscular control of stability, over a short and long period, during repetitive lifting from the floor to waist height. There was a significant main effect of load on kmax s (p < .001), and a near significant main effect of load on kmax l (p = .055). Thus, kmax s was statistically lower when lifting a load equivalent to 10% of each participant\u2019s maximum back strength, indicating less rapidly diverging (more stable) short-term dynamics. Conversely, there was a trend for decreased long-term local dynamic stability (kmax l), and increased kinematic variability (p = .164) (Fig. 3), when lifting this 10% load. There were no significant effects of sex, or significant interactions between load lifted and sex. These results suggest that dynamic stability during lifting is similar between females and males, and that both sexes react similarly to the addition of an external load in the hands. To the best of the authors\u2019 knowledge, this was the first study to characterize and quantify changes in the neuromuscular control of spinal stability resulting from changing the load in the hands during a dynamic lifting task",
            " Second, because the spine is in a more mechanically-stable state when lifting a load (due to increased muscular demand), there would also be a decreased need for feedbackinduced muscular contraction following a perturbation, where a time delay (EMG onset or electromechanical) can cause a destabilization of the control system (Ogata, 2002). Third, previous research has found that empirically-measured antagonistic cocontraction, which can alter loading and stability, is recruited less in high-moment conditions and more in low-moment conditions (Granata & Marras, 2000); here this may have been destabilizing. Lastly, principal component analyses (PCA) of this dataset have shown that movement range of motion is decreased when lifting the heavier load (Sadler, Graham, & Stevenson, in press) (Fig. 3). Thus, it is possible that this change in lifting technique contributed to the findings. However, repeating the present analyses after standardizing the Euclidean norm angle to unit variance produced nearly identical results, showing the dynamic equivalence of the state spaces (Kang & Dingwell, 2009a,b). There were no significant differences in the long-term neuromuscular control of stability between the zero load and loaded groups, though there was a trend for decreased local dynamic stability when lifting the 10% load (p = "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000491_c1sm06354e-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000491_c1sm06354e-Figure8-1.png",
        "caption": "Fig. 8 Stress localization in the",
        "texts": [
            " As the shrinkage of the core reaches the second critical value, d(2)crit, another bifurcation occurs: one wrinkle grows in amplitude at the expense of its two neighbors and d2 deviates from d1 gradually. This bifurcation creates a period-doubling morphology, as shown in Fig. 5e. The system enters into the region III in Fig. 6. In comparison with the sinusoidal pattern, the folding patterns can release more elastic strain energy in this stage. Finally, the system evolves into a pitchfork morphology 560 | Soft Matter, 2012, 8, 556\u2013562 caused by the constraint effect of the outer hard layer and is also a process of stress localization.39 As can be seen from Fig. 8, the stress focuses in narrow ridges of the patterns. Similar perioddoubling buckling is also observed in growing tubular biological tissues, e.g., esophageal mucosas.20 It should be pointed out that the period-doubling folding phenomenon reported here is different from that observed in cylindrical voids in osmotic elastomers or growing single-layers,42,50 in which the surface evolves into crack-like patterns following the buckle-to-crease transition. We further examine the condition for the occurrence of the observed wrinkle-to-fold transition phenomena"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001082_tasc.2014.2361932-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001082_tasc.2014.2361932-Figure2-1.png",
        "caption": "Fig. 2. (a) Geometry of the iron core for a laboratory-scale dc induction heater prototype. (b) B\u2013H curve of the iron used in the experiments.",
        "texts": [
            " Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. The self-field critical current the tape is 170 A at 77 K. Except for a small difference in the number of turns, two coils have approximately the same inner and outer diameters and other configuration parameters. The INS coil is insulated by Kapton. Both coils are immersed in liquid nitrogen in the experiments (see Fig. 1). Fig. 2 shows the geometry and specification of the iron core for a laboratory-scale dc induction heater. It has the same shape as the industry-scale one being built in Shanghai Jiao Tong University, China. This structure can heat two aluminum billets simultaneously in the two air gaps. The core is built with steel ASTM 1045, whose B\u2013H curve is shown in Fig. 2. The two coils are set around the central cylindrical pillar of the iron core. Fig. 3 shows the electromagnetic characteristics of the coils with the iron core. A Hall probe is used to measure the magnetic field induced by the coils. For the coils without the iron core, it is placed at the center of the coil. For that with the iron core, the hall sensor is placed at the center of the iron core\u2019s air gap, where the billets are rotated and heated. An equivalent circuit model is coupled with a FEM model to analyze the electromagnetic characteristics of the NI coil with iron core"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002476_j.ymssp.2019.106342-Figure24-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002476_j.ymssp.2019.106342-Figure24-1.png",
        "caption": "Fig. 24. The gear before and after the run-to-failure experiment.",
        "texts": [
            " 23 shows two segments of baseline vibration, as well as their corresponding speed profiles of the input shaft acquired by the zebra-strip shaft encoder. Sampling frequency equals to 6.4 kHz. The left- side baseline vibration and its corresponding speed profile are used as training data, whereas the right-side as testing data. Except for this baseline vibration, 30 additional baseline data files are collected. Each data file follows the speed signal as shown in Fig. 23(c). The experiment considers an initial tooth crack fault as shown in the left side of Fig. 24. The initial crack was machined with spark erosion and had the following dimensions: approximately 0.3 mm high, 50% of the tooth width deep, and through the entire face of the tooth. After initiation, a run-to-failure experiment was conducted which lasted around 21 days of continuous running. At last, the tooth was missing, as shown in right side of Fig. 24. During this process, 170 faulty data files are collected with a time interval of 3 h. Each data file contains a 6.5 s of vibration signal as well as speed signal. The right side of Fig. 25 shows the time waveforms of faulty vibrations from datafile #30, #100, and #170, whereas the left side their corresponding speed profile. We visually observe that the faulty vibration from datafile #170 is peakier than the other two. During the sparse FP-AR modeling, the training and testing signals as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000898_j.mechmachtheory.2011.08.010-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000898_j.mechmachtheory.2011.08.010-Figure1-1.png",
        "caption": "Fig. 1. Typical slewing bearing loads and assembly.",
        "texts": [
            " Keywords: Slewing bearing Rolling contact fatigue Stress-life approach Strain-life approach Slewing bearings are machine elements that enable relative rotation of two structural parts. They are widely used in the construction of transport devices (cranes, transporters, turning tables, etc.), wind turbines production, and other fields of mechanical engineering. Slewing bearings can accommodate axial force Fa, radial force Fr and tilting momentM, acting either single or in combination and in any direction, as shown in Fig. 1a. Usually they are made of inner and outer rings, rolling elements, seals and spacers, which prevent rolling elements from hitting against each other. The rings are typically available in one of three executions: a) without gears, b) with an internal gear, and c) with an external gear. Slewing bearings can perform both oscillating (slewing) and rotating movements. The rotational speed usually ranges from 0.1 to 5 rpm. The procedure for calculation of the load capacity for standard rolling bearings is widely known and standardised [1,2], but it does not take into account several aspects, such as [3]: a) non-parallel displacement of the rings, b) clearance of the bearing, c) rotational speed and consequently centrifugal forces, d) irregular ring geometry, etc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002098_j.enzmictec.2014.02.004-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002098_j.enzmictec.2014.02.004-Figure4-1.png",
        "caption": "Fig. 4. Cyclic voltammograms of bare GCE (a), AuNPs/GCE (b), GN/GCE (c), GN-",
        "texts": [
            " After CLDHChE composite was immobilized on GN-AuNPs/GCE, the Rct value f CLDH-AChE/GN-AuNPs/GCE (curve e) increased to about 550 . his increase of Rct value is attributed to the fact that most biologcal molecules, including enzymes, are poor electrical conductors t low frequencies (at least <10 kHz) and could cause hindrance to he electron transfer. These results were supported by the cyclic oltammogram study. CV of the ferricyanide system is a convenient and valuable tool o monitor the characteristics of the surface of each modified elecrode [32]. In Fig. 4, after the bare GCE was modified by the AuNPs, N, especially GN-AuNPs nanocomposite, an obvious increase of AuNPs/GCE (d), CLDH-AChE/GN-AuNPs/GCE (e)in pH 7.5 phosphate buffer solutions containing 5 mM [Fe(CN)6]3\u2212/4\u2212 and 0.1 M KCl. peak current (curve b\u2013d) could be observed compared to bare GCE electrode (curve a). Finally, the immobilization of CLDH-AChE composite resulted in a decrease in the peak current (curve c), which was the direct evidence of successful binding of enzyme on the electrode surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001873_j.apacoust.2014.03.018-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001873_j.apacoust.2014.03.018-Figure3-1.png",
        "caption": "Fig. 3. Test rig.",
        "texts": [
            " The Hilbert Transform h(t) of a function x(t) is defined as: h\u00f0t\u00de \u00bc Hfx\u00f0t\u00deg \u00bc 1 p Z 1 1 x\u00f0s\u00de t s ds \u00f01\u00de The HT of x(t) (H{x(t)}) is the convolution of x(t) with the signal 1/pt. Hence, it can be interpreted as the output of a system linear time-invariant system with input h(t) and impulse response 1/pt. When the envelope is extracted, the time domain signal is transformed into frequency domain using the Fast Fourier Transform (FFT) to obtain the frequency spectrum of the enveloped AE signal, which is used to define peaks which will lead on to misalignment detection [22]. The test rig used in this work (Fig. 3) was developed by Romax Technology Ltd (Intelwind project participant, see acknowledgement) in order to investigate bearing skidding and its effect on the bearing useful life. The test rig was designed to represent the shaft arrangement in a typical 2 MW wind turbine. The shaft was supported by three test bearings; one cylindrical roller bearing and two tapered roller bearings. Gear load was simulated by hydraulic actuators, applying axial and radial loads through the slave bearings. A thrust bearing was used as the axial slave bearing and a spherical bearing as the radial slave"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000782_j.mechmachtheory.2012.11.006-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000782_j.mechmachtheory.2012.11.006-Figure9-1.png",
        "caption": "Fig. 9. Location of the LOA direction according to transmission error sign.",
        "texts": [
            " To identify the plane of action two directions are needed: the direction for the line of action and the one for the axis of rotation of the gears. The former must be calculated in relation to the contacting tooth flanks; the latter is already available in the reference frame. The LOA direction (unit vector) is calculated in the reference frame, rotating the x axis around the z axis of a quantity complementary to the transverse pressure angle: LOAr \u00bc cos \u03c0 . 2 \u2212\u03c6t sign DTE\u00f0 \u00desin \u03c0 . 2 \u2212\u03c6t 0 8>< >: 9>= >; : \u00f017\u00de Contacting tooth flanks are identified by the sign of the DTE, which is also used for the rotation around the reference z axis (Fig. 9). Once the line of action is found, misalignments in the POA can be calculated. LOA parallel misalignment directly translates into a transmission error therefore it can be seen as a displacement excitation. This misalignment component is due to the relative displacement of the gears along the LOA and is already considered, scaled along the transverse direction, in Eq. (4). POA angular misalignment is calculated through the following procedure: 1) Each axis of rotation is projected on the POA in the reference frame; 2) Angles between the projected axes and the reference axis are calculated in the reference POA; 3) Misalignment is obtained by the difference of the rotations (since same rotation in the same direction implies aligned gears)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001842_s00170-015-7647-4-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001842_s00170-015-7647-4-Figure8-1.png",
        "caption": "Fig. 8 Concept for a hybrid mandrel of an extrusion die with cooling channels (cut)",
        "texts": [
            " The large-volume, geometrically simple basic body will be manufactured by conventional manufacturing methods quickly and economically. The basic requirement for the manufacturing of such dies is a good bonding between the additively manufactured area and the basic body. In plastic injection molding, hybrid dies with near-surface cooling are successfully applied even in industrial applications [17]. However, in the field of hot metal forming and, especially, in hot metal extrusion, where the tools are exposed to high mechanical tensile loads (Fig. 8), such a hybrid structure has not been tested yet. Because of this, first of all, the bonding was tested on specially designed tensile specimens consisting both of a conventionally manufactured basic body and a part fabricated by selective laser melting. As materials for the characterization of the hybrid properties for the basic bodies manufactured conventionally, the following two materials were used: & 1.2343/H11 (X37CrMoV5-1), carbon martensite hardening [18], as the alloy most commonly used for the manufacturing of hot aluminum extrusion dies, & 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000811_j.matdes.2012.12.062-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000811_j.matdes.2012.12.062-Figure7-1.png",
        "caption": "Fig. 7. (a) CAD model of Batch 2 Tensile Samples and (b) the fabricated vertical and horizontal SC420 builds.",
        "texts": [
            " This resulted in poor elongation of 2\u20134% only. The yield strength and tensile strength were similar irrespective of the deposition direction (Fig. 6b). This result is in contrast with the literature data that suggested that the tensile strength and yield strength were reported to be lower after annealing [2], as it does not seem that the annealing effect in the vertical builds resulted in poorer strength. In Batch-2 the build size was 25 35 70 mm and 70 35 30 mm for the vertical and horizontal samples, respectively. From each build (Fig. 7) 6 samples were extracted using Electro Discharge Machining (EDM); among these, 3 samples were tested in the asdeposited condition and 3 samples were HIPped. The build volume was at least 5 times bigger than the Batch-1 samples, which resulted in a significant scatter in tensile properties (strength and elongation %) especially the horizontal builds (Fig. 8a). Both orientations had considerably reduced elongation % (Fig. 8) in the as-deposited conditions ( 2\u20133%), compared to Batch-1. The fracture surfaces of samples which failed at very low (0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001268_tmag.2012.2224358-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001268_tmag.2012.2224358-Figure6-1.png",
        "caption": "Figure 6 IPM FEA model cross section",
        "texts": [
            " (a) armature reaction field comparison of two models with 5th stator MMF (b) armature reaction field comparison of two models with 7th stator MMF Fig. 5 armature reaction field comparisons of two models with different high order stator MMF IV. VALIDATION WITH FINITE ELEMENT ANALYSIS To validate the proposed analysis model, the armature reaction field obtained by the proposed model and traditional model are compared with FEA results. In the FEA model, the stator is smooth, winding is modeled by current sheet in the air-gap, and the length and height of magnet bridge is close to zero. Fig. 6 shows the cross section of IPM FEA model, the coils are equivalent to infinitesimal current sheet in the air-gap. Fig. 6 IPM FEA model cross section To validate the pole-cap effect in IPM motor, different current sheet placements are employed to structure different Copyright (c) 2011 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org. stator MMF harmonic component. Square-wave stator MMF is employed to take the place of sinusoidal MMF. With different current sheet placements, the dominant harmonic component of total MMF is changed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002413_s00170-017-1059-6-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002413_s00170-017-1059-6-Figure1-1.png",
        "caption": "Fig. 1 Specimen dimensions in mm (a); built orientations (b)",
        "texts": [
            " An experimental plan has been carried out in order to investigate the effect of the local stratification angle and the rotational speed. The first one is related to the SLM process fabrication: it is the slope of the fabricated surface with respect to the stratification direction. Since it is well known that horizontal and vertical surfaces have deeply different morphologies and 45\u00b0 one shows a mixed behavior [5, 16, 26], for this experimentation, three different local stratification angles are considered: 0\u00b0, 45\u00b0, 90\u00b0. The considered parts (Fig. 1a) are standard flat unmachined tension test specimens [27]. In Fig. 1b, the three considered built orientations are shown: for the sake of simplicity, the specimens are indicated with the capital letters A (0\u00b0 local stratification angle), B (45\u00b0 local stratification angle), and C (90\u00b0 local stratification angle). The employed SLMmachine is an EOSINT\u00aeM290with a 400-W ytterbium fiber continuum laser, a beam diameter of 100 \u03bcm, and a building volume of 250 \u00d7 250 \u00d7 325 mm3. The used material is the Ti6Al4V supplied by EOS GmbH. The process parameters have been chosen according to the \u201cOriginal EOS Parameters set for Ti6Al4V\u201d: 30-\u03bcm layer thickness, 140-\u03bcm hatch spacing, 1200 mm/s scan speed, 280-W laser power. As provided for EOS GmbH, the scanning strategy has been of the island type on each layer and the scanning direction has been rotated between consecutive layers by 67\u00b0 in order to minimize the out-of-plane distortion induced by transient and residual thermal stresses. After the fabrication, no thermal treatment has been performed. As shown in Fig. 1b, the specimens A and B have support structures that are removed by mechanical operations after the fabrication. The supported surfaces are not considered in the measurement campaign. The used BF machine is a Rotar EMI 47, an inclined octagonal barrel 400 mm in diameter moved by an asynchronous motor with an electronic speed control. The employed media are angled cut cylindrical 15 mm in diameter and 25 mm in height. Their composition is a mixing of a synthetic resin as matrix and powder of alumina, silica, and silicon carbide as abrasive"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002266_tie.2017.2688963-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002266_tie.2017.2688963-Figure4-1.png",
        "caption": "Fig. 4. Full 3\u2013D representation of zMFs correspond to proposed zGT2FFM. (a) First input zMFs (Accuracy). (b) Second input zMFs (Distance). (c) Output zMFs.",
        "texts": [
            " Due to the use of k\u2013fold cross validation manner, the fitness function is chosen as the mean of the k-folds misclassification rate as follows: kCVMR = 1 k k\u2211 i=1 MRi (25) where k is the number of folds. In this paper, it is supposed that the fusion model consists of three SVMs with different polynomial or RBF kernels. The accuracies and the distances are then calculated by means of SVM classification of each test samples. zGT2FFM then uses these six inputs and generates an output representing the class of each sample. The full 3\u2013D representation of input and output zMFs correspond to this fusion model are depicted in Fig. 4. To achieve more accurate results with the input MFs, minimum and maximum accuracies are set as the left and right endpoints (instead of usual 0% to 100%). Furthermore, for the same reason, minimum and maximum distances are chosen as the left and right endpoints of distance MFs. The proposed zGT2FFM has been constructed by means of 64 rules, which is due to the six inputs, i.e., 26 = 64. General structure of each rule is considered to be as follows: IF a1 is A\u0303i1 and a2 is A\u0303i2 and a3 is A\u0303i3 and d1 is D\u0303i 1 and d2 is D\u0303i 2 and d3 is D\u0303i 3, THEN gi is O\u0303i (i=1,2,"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000127_nme.1620100603-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000127_nme.1620100603-Figure4-1.png",
        "caption": "Figure 4. Harmonically vibrating undamped frame. Displacement components at joint 2 and load components at joint 4. These components are amplitudes which are to be multiplied by the common time factor sin cot or exp iot",
        "texts": [
            " New elements K , to K , in the member stiffness matrix F in (1) are found by taking kGA and E l as constants, putting W = 0 and I/ = 0, assuming w = X(x') sin cot and u = Y(x')sin cot PFVIBAT-A PROGRAM FOR PLANE FRAME VIBRATION ANALYSIS 1225 and solving for the mode functions X and Y by use of (5) and the boundary conditions (Figure 1) X ( 0 ) = t , Y(0) = - m , X ( L ) = t , Y ( L ) = - m 2 (6a-d) For instance, the function K , in (3) is replaced by r 2 where X and Y in (7a) shall belong to the case t , = t , = 0 = rn, and m, = 1 and where Y in (7b) shall belong to the case t , = 0 = rn, = m, and t , = 1 (the alternative (7b) was found to be the numerically most favourable one and was programmed in PFVIBAT). The functions K , , and K , , in (1) pertaining to the longitudinal vibration of the member 12 (Figure 1) do not change. Required condensation of F is performed as before. STRUCTURE-FORCED VIBRATION The global translational and rotational amplitudes of the joints of a harmonically vibrating frame (Figure 4) are collected in a column matrix p termed the structure displacement. The amplitudes of the vectorially associated external loads upon the joints are collected in a column matrix P termed the structure load. The condensed and transformed local stiffness matrices F = F(o) of all members (Figure 1) are assembled to form the global stiffness matrix E = E(w) of the frame structure. The governing matrix equation is Ep = P (8) Rigid, hinged and rolling (in the x- and/or z-direction) supports of the frame are considered in PFVIBAT by special procedures in handling (8)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003394_j.compstruct.2020.112698-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003394_j.compstruct.2020.112698-Figure5-1.png",
        "caption": "Fig. 5. Application of external conditions: (a) fixed constraints (in blue) on seat contours and pillar bases; b) applied load as a three directional force (46kN) transmitted by an infinitely rigid plate (in red).",
        "texts": [
            " Numerical modeling was limited to the central and upper sections of the safety cage (Fig. 4b), in which the four seats also performed structural functions. These parts are rigidly anchored to underlying elements of the structure, specifically the monocoque and central tunnel, sections of the vehicle that can be considered infinitely rigid in relation to the applied external forces. The result is a simplified model with interlocking constraints where the seats and uprights are in contact with the vehicle (Fig. 5a). A total weight of 750 kg was adopted for the investigation, including the mass of the frame, batteries, photovoltaic panels, engines, driver, passengers and all other kinematic elements (e.g. wheels, suspension, etc.). This overall weight is higher than in the past due changes in the race configuration (larger battery pack, heavier engines, etc.), but also represents a more conservative approach to design validation. The static loading system was applied by placing an infinitely rigid plate in contact with the roof of the vehicle. Given the geometry, initial contact between the plate and structure only occurred within the central section of the middle safety cage roll bar. The plate was then loaded with a force in accordance with regulations in terms of magnitude and direction (Fig. 5b). Specifically, compression equivalent to 5 g downwards (Z direction), 4 g backwards (Y direction) and 1.5 g sidewards (X direction) was applied, with a resultant force of 46 kN. The choice of using a rigid obstacle (the plate), instead of directly applying forces to nodes was intended to provide better correspondence of loading conditions to the case of a real rollover. In particular, the plate allowed other sections of the structure, not engaged during initial contact, to be progressively included during impact progression and structure deformation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002325_icra.2015.7139915-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002325_icra.2015.7139915-Figure2-1.png",
        "caption": "Fig. 2. Hexapod robot model showing legs 1, 5 and 3 in stance phase and legs 2, 4 and 6 in swing phase during an alternating tripod gait. LB is the body length, WA and WB are the lower and upper bounds on the body width, and S is the stride length. The robot\u2019s centre of mass is at O, and the positive direction of the x axis corresponds to forward motion.",
        "texts": [
            " Section IV describes the experimental setup and procedure and Section V present experimental results showing overall system performance across concrete, grass, and leaf litter. Section VI concludes the paper with insights in to the significant results of this work. The approach presented in this paper is applicable to legged locomotion in general. However, we will focus on a hexapod robot where each leg has three actuated joints (thus resulting in 18 degrees of freedom (DOFs)). The actuators link the coxa, femur and tibia segments. For clarity of discussion, we consider the operation of the robot in statically stable modes. The dimensions of the robot (Fig. 2) are given by the body length LB and the body widths WA and WB (lower and upper bounds on the width). The forward direction corresponds to the positive x axis and up corresponds to the positive z axis forming a right handed coordinate frame. The lengths of the femur and the tibia links are given by LF and LT , respectively. The stride length is given by S. A typical triangular foot trajectory is shown in Fig. 3, and corresponds to the motion T1 \u2192 T2 \u2192 T3. Smoother trajectories can be defined by interpolating over a larger number of points (for example, T1 \u2192 T4 \u2192 T2 \u2192 T5 \u2192 T3)",
            " The duty factor \u03b2 for a leg is defined as \u03b2 = Tstance/Tstride (1) where Tstance is the duration of the stance phase and Tstride is the stride period. As noted by Nishii in [7], assuming the same duty factor for all legs, n\u03b2 gives the average number of legs in stance phase when n is the total number of legs. Since hexapods require at least three legs on the ground to walk statically, lowest value for \u03b2 is 0.5. Typical gaits for an hexapod are wave, diagonal amble and alternating tripod. The duty factors of these gait patterns are given in Fig. 4, while the leg motions during the gait are described next. The leg numbers in examples refer to Fig. 2. 1) Wave gait: The wave gait has one leg in \u201cswing phase\u201d (off the ground) with all other five legs in \u201cstance phase\u201d (on the ground). This pattern is repeated for each leg, leading to a six step gait common among insects. An example wave gait would have the swing phase progress as Leg 3\u2192 Leg 2 \u2192 Leg 1 \u2192 Leg 6 \u2192 Leg 5 \u2192 Leg 4. 2) Amble gait: The diagonal amble gait has two legs in swing phase at a time with four legs in stance phase. This is more common among quadruped animals such as lizards and salamanders"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000127_nme.1620100603-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000127_nme.1620100603-Figure5-1.png",
        "caption": "Figure 5. Rigid body (a) connected to two beams of a frame. First calculation model (b): rigid body is assigned to and connected at a joint J which is placed where the (extended) beam axes meet. Second calculation model (c): rigid body is assigned to a joint J which is placed in the mass centre MC of the body. Rigid body is connected to .two beam members at separate (auxiliary) joints J1 and 52 the displacements of which are governed by the displacement of J",
        "texts": [
            " For any given angular frequency o of a forced vibration case, unknown components of p (free displacements) and unknown components of P (support reactions and loads imposing prescribed non-zero displacements) can be found by (8). When all components of p are known, all displacements n and forces N at the member ends (Figure 1) and all (longitudinal, rotational, transversal) displacements u(x\u2019), u(x\u2019), w(x\u2019) and sectional forces N(x\u2019), T(x\u2019), M(x\u2019) along the members can be calculated. PFVIBAT prints p, P, n, N and plots [u2(x\u2019)+w2(x\u2019)]* and M(x\u2019). Joints must be placed in positions where rigid bodies (Figure 5a) are connected to a frame. In PFVIBAT, the actual connection can be modelled in two ways (Figs. 5b and 5c). The exact contribution to the structure stiffness matrix E in (8) from a rigid body attached to the joint J (Figure 5b) is given by Here, M , is the total mass of the body, i, its radius of gyration with respect to a y-axis through the mass centre MC, a and c the x- and z-distances (with sign) between J and MC, p J x , pJz and p,, the translational and rotational displacements of joint J , and AP,,, APJZ and AP,, those parts of the total external force and moment loads P J x , P,, and P,, on the rigid body at J which are required to make the body perform the displacement described. In the refined second calculation model (Figure k ) , J must be placed in MC and thus u = c = 0",
            " Normalized eigenmodes p\" (sum of squares of components of p\" made equal to unity) and pertinent modal masses m,, are also obtainable by PFVIBAT. From the information contained in p\", the program calculates the local displacements ~ \" ( x ' ) , ~ \" ( x ' ) , w\"(x') along each beam member. The contribution Am,, to m,, from one member 12 (Figure 1) is determined by Am,, = m [ { U ~ ( X ' ) } ~ + { W \" ( X ' ) } ~ + ~ ~ ( ~ \" ( X ' ) } ~ ] dx' (10) I Numerical integration is employed in PFVIBAT to evaluate (10). The contribution Am,, to m,, from one rigid body (Figure 5 ) with global mass centre translations uLc and wLc and rotation u i B is determined by Am,, = M , [ { uLc) + { wLc} + i f { u\",} 2] (1 1) TRANSIENT VIBRATION The undamped angular eigenfrequencies a,, the normalized eigenmodes (represented by p\") and the pertinent modal masses m,, of a frame can be calculated by PFVIBAT as mentioned above. Let q,,(t) be the modal displacements (normal co-ordinates), Q,(t) the modal loads, and in the (estimated) relative linearly viscous modal dampings of the frame"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000831_j.humov.2011.06.009-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000831_j.humov.2011.06.009-Figure1-1.png",
        "caption": "Fig. 1. Experimental setup used for repetitive lifting from a target on a table positioned at half of each participant\u2019s height to a target on the floor. Each of the 30 lifts consisted of moving from position 1 (solid lines) to position 2 (dashed lines) and back, to the beat of a metronome.",
        "texts": [
            " Subjects completed three maximum back extensor exertions against a calibrated uniaxial load cell, and the average value of the three trials was recorded for use in the testing session. During this orientation session subjects\u2019 standing heights were also recorded in order to determine the required table height for the lifting task. The testing session required participants to perform two trials of 30 continuous freestyle box lifts from a target positioned at half of their standing height to a target on the floor (Fig. 1) (Graham et al., 2011). Participants were asked to perform several practice lifts until targeting could be completed comfortably, and then their feet were outlined with chalk to ensure identical foot positioning between lifts and trials. The box made contact with the targets synchronous to a periodic tone from a metronome, establishing a movement pace of 10 lift cycles per minute. Each trial lasted 3 min. Ten lifts per minute was chosen to ensure a continuous movement pattern, and to minimize the effects of fatigue, which can increase the variability of muscular efforts (Ng, Parnianpour, Richardson, & Kippers, 2003)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000035_tie.2010.2095392-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000035_tie.2010.2095392-Figure4-1.png",
        "caption": "Fig. 4. Structure of an active compliance joint.",
        "texts": [
            " Because the lead screw can activate two screw nuts to move farther or closer to each other, the robot is able to expand or contract the pantograph mechanism. In addition, the gear train transfers the power of a dc motor to the three lead screws so that they can rotate synchronously. Each track module is composed of two parts: frontal and rear tracks. A compliance active joint connects the tracks. The compliance active joint is composed of a radio-controlled (RC) servomotor and a torsion spring as shown in Fig. 4. The RC servomotor is attached to the rear tracks, and the torsion spring is connected to the motor and the frontal track. The compliance active joint allows the robot to be adaptive to uneven surfaces. Fig. 5 shows the performance of an active compliance joint when the robot travels over an uneven surface. When the robot passes over a protrusion, the RC servomotor adjusts the rotating angle to maintain contact between the frontal track and the pipe, as shown in Fig. 5(a). In contrast, the joint causes the track module to fold, so that it remains in contact with the surface, as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000236_j.mechmachtheory.2010.06.004-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000236_j.mechmachtheory.2010.06.004-Figure3-1.png",
        "caption": "Fig. 3. Il the driv",
        "texts": [
            " Since the lengths are different on the two sides we distinguish between drive side and coast side. Tooth thickness at the pitch diameter is given by where s = spd + spc \u00f01\u00de spd and spc are the tooth pitch thickness at the pitch diameter for the drive and coast side, respectively. These are given by spd = 1 4 \u03c0 + pstan\u00f0\u03b1d\u00de M \u00f02\u00de spc = 1 4 \u03c0 + pstan\u00f0\u03b1c\u00de M \u00f03\u00de ps is a possible cutting tool shift. This shift is inmany cases not identical on the twomatinggears. The lengths related to the drive where side are indicated in Fig. 3 where we have used the known involute function definition given by inv(\u03b1)=tan(\u03b1)\u2212\u03b1. In Fig. 3 only the part that relates to the coast side is shown for clarity. A similar figure can be made for the drive side, the only difference is that the base diameter is different, in the shown case the base radius for the drive side rbd is smaller than the base radius for the coast side rbc. At the top diameter dt=2rt the tooth thickness for the drive and coast side is given by lustration of the tooth top thickness for an asymmetric tooth related to only one side, here the coast side. The coast side pressure angle is here \u03b1c=20\u00b0 and It shou center ld be noted that one of the length std or stcmight be negative, indicating that all of the tooth top lies to one side relative to the line, see Fig. 3. Total tooth top length is given directly by st = std + stc \u00f06\u00de It remains to determine the drive top angle, \u03b1td, and the coast top angle, \u03b1tc, these are given by cos\u00f0\u03b1td\u00de = dp dt cos\u00f0\u03b1d\u00de \u00f07\u00de cos\u00f0\u03b1tc\u00de = dp dt cos\u00f0\u03b1c\u00de \u00f08\u00de From the input: 1. Module M. 2. Shift values for the two gears ps1 and ps2. 3. Number of teeth on the two gears z1 and z2. 4. A given pressure angle, \u03b1d or \u03b1c. 5. A lower limit on the tooth top thickness, e.g., st=0.25M. The limiting value of the other pressure angle can be found by the use of Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003040_j.ijfatigue.2019.03.022-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003040_j.ijfatigue.2019.03.022-Figure4-1.png",
        "caption": "Fig. 4. Geometry of the fatigue specimens for load increase and constant amplitude tests.",
        "texts": [
            " To characterize the cyclic deformation behavior, the plastic strain amplitude \u03b5a,p was determined during the fatigue tests by using an extensometer. The fatigue specimens were manufactured by turning the additively manufactured bars and polishing the gauge length to explicitly exclude the influence of surface imperfections resulting from the additive manufacturing process. Hence, only the properties of the additively manufactured material volume was investigated. The geometry of fatigue specimens is given in Fig. 4 and was designed in accordance with DIN 50100 [30]. Note that the loading direction in fatigue as well as tensile tests for SLM-H is perpendicular, for SLM-V is parallel and for SLM-45 specimens is in an angle of 45\u00b0 to the building direction. For rating the influence of the austenite-\u03b1\u2019-martensite transformation, measurements of the magnetic fraction in the gauge length of the specimens before and after the tensile and fatigue tests were performed with a FERITSCOPE\u2122 MP 30E device. An increase of magnetic fraction correlates to a transformation from paramagnetic austenite to ferromagnetic \u03b1\u2019-martensite [20]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001232_s1006-706x(11)60014-9-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001232_s1006-706x(11)60014-9-Figure4-1.png",
        "caption": "Fig. 4 Synchronous powder feeding and topography of surface and section metallograph",
        "texts": [
            " The tem perature changes large in cladding area, so the mesh is fine where more precision is needed. Contrari wise, the mesh is coarse. The mesh of the transition zone is between the cladding and the base given by Fig. 2 (b). The thermal property parameters of H13 are listed in Table 3 and those of P20 are given by Fig. 3. Issue 1 Effect of Laser Power on the Cladding Temperature Field and the Heat Affected Zone \u2022 75 \u2022 2. 2 Results and discussion In practice, laser cladding is carried out by syn chronized powder feeding. So the element which is irradiated by laser is given by Fig. 4 (a). The c1added layer can be set to the surface of thermal convection. To realize a load moving in laser cladding, the continuous movement of space is transformed into discrete time domain using APDL of ANSYS soft ware, and then the moving load is loaded for circular statement at a certain time step. The analysis is carried out under v= o. 006 m/sand P=1. 2,1. 8, and 2. 2 kW, respectively. E=P/D= 300,450, and 550 kW/m, respectively (E: laser en ergy density, P: power, D: diameter of laser spot). The temperature field at the fifth step is given by Fig. 4 (a). Fig. 4 (b) gives the cladded layer topog raphy and cross-section metallograph of the heat af fected zone by experiment. As can be seen from the figure, as the laser power is small, the decalescence of cladded layer is also small and the alloy powder of surface melts incompletely, and the size of the heat affected zone is small. With the laser power increas ing, the heats and pool temperatures increase, the alloy powder melts completely, the surface is rela tively smooth, and the heat affected zone enlarges"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001968_978-94-007-6101-8-Figure5.3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001968_978-94-007-6101-8-Figure5.3-1.png",
        "caption": "Fig. 5.3 Anthropomorphic robot in initial reference pose",
        "texts": [
            "12) sx = \u2212c6(s1c4 + c1c23s4)+ s6(s1s4c5 + c1(s23s5 \u2212 c23c4c5)) (5.13) sy = c1(c4c6 \u2212 s4c5s6)\u2212 s1(\u2212s23s5s6 + c23(s4c6 + c4c5s6)) (5.14) sz = \u2212s23s4c6 \u2212 s6(s23c4c5 + c23s5) (5.15) ax = s1s4s5 \u2212 c1(s23c5 + c23c4s5) (5.16) ay = \u2212s1s23c5 \u2212 s5(s1c23c4 + c1s4) (5.17) az = \u2212s23c4s5 + c23c5 (5.18) px = d6s1s4s5 \u2212 c1(\u2212a2c2 + s23(d4 + d6c5)+ d6c23c4s5) (5.19) py = a2s1c2 \u2212 s1s23(d4 + d6c5)\u2212 d6s5(s1c23c4 + c1s4) (5.20) pz = c23(d4 + d6c5)+ a2s2 \u2212 d6s23c4s5 + d1 (5.21) The anthropomorphic robot is in Fig. 5.2 displayed in an arbitrary pose. In Fig. 5.3 the same robot mechanism is shown in its initial reference pose, when all joint variables equal zero and the x axes of the neighboring coordinate frames overlap. When developing the inverse geometric model of robot mechanism, we know the position and orientation of robot end-segment, while it is our aim to calculate the joint variables [2, 3]. With another words, we know all nine elements of matrix (5.9) and it is our task to write the expressions for the variables \u03d11 . . . \u03d16. Beside the elements of matrix (5",
            "22) 78 5 Geometric Model of Anthropomorphic Robot with Spherical Wrist z6 For the sake of more simple developing of inverse model, we shall lift the base coordinate frame x0, y0, z0 to the level od the second joint. In this way we shall limit our consideration to the second and third segment representing \u201cupper arm\u201d and \u201cforearm\u201d of the anthropomorphic robot. From the situation presented in left Fig. 5.4, we shall calculate the angles \u03d11, \u03d12, and \u03d13. In Fig. 5.4 the joint variables \u03d11, \u03d12, and \u03d13 are defined with respect to the initial pose shown in Fig. 5.3. From the right Fig. 5.4 we first determine the distance between the origin of the shifted coordinate frame x0, y0, z0 and the center of the wrist Q: r = \u221a q2 x + q2 y + (qz \u2212 d1)2 (5.23) We write the cosine rule for the triangle from the right Fig. 5.4 with the sides r, a2, and d4: r2 = a2 2 + d4 2 \u2212 2a2d4 cos\u03b1 (5.24) With St\u00e4ubli robot as well as in general with anthropomorphic robots and also with human arm, the length of the forearm is equal to the length of the upper arm, i.e. a2 = d4. The ratio of the segment lengths 1 : 1 at selected constant collective length of both segments, results in maximal volume of the robot workspace [1]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002521_tec.2016.2590988-Figure12-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002521_tec.2016.2590988-Figure12-1.png",
        "caption": "Fig. 12. 12/10-pole PS-SFPM machine having alternate poles wound armature windings.",
        "texts": [
            " In the previous analysis, PS-SFPM machines with all poles wound winding were analyzed and it was found that they operate based on the magnetic gearing effect. Here, the magnetic gearing effects in the 12/10-pole alternate poles wound, 6/10-pole E-core and C-core PS-SFPM machines are analyzed. Their dimensional parameters are the same as those in the 12/10-pole all poles wound PS-SFPM machine as given in Table I. The winding type in the 12/10-pole alternate poles wound PS-SFPM machine is A1- C1- B1- A2- C2- B2 anti-clockwise, as shown in Fig. 12. This is doubled in the previously analyzed 12/14-pole all poles wound PS-SFPM machine, Fig. 1(d), i.e. A1- C1- B1- A2- C2- B2- A3- C3- B3- A4- C4- B4 anti-clockwise. Consequently, pea in the 12/10-pole alternate poles wound PS-SFPM machine is half of that in the 12/14- pole SFPM machine with all poles wound, i.e. 4 and 8 respectively. With consideration of pPM=6 and nr=10, it is found that (11) can also be matched in the 12/10-pole PSSFPM machine with alternate poles wound. Figs. 13(a) and (b) illustrate the cross-sections of 6/10-pole E-core and C-core PS-SFPM machines, respectively. The 6/10-pole E-core PS-SFPM machine, Fig. 13(a), also has 6 alternate pole wound coils in the outer stator, similar to 12/10- pole alternate pole wound PS-SFPM machine Fig. 12, albeit with different winding layouts. However, the PM number in the E-core machine is half, i.e. 6. In 6/10-pole E-core and C- 0885-8969 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. core PS-SFPM machines, the outer air-gap armature reaction MMF is given in Fig. 14, which can be expanded to Fourier series as, { \ud835\udc39\ud835\udc34\ud835\udc35\ud835\udc36(\ud835\udf03, \ud835\udc61) = \u2211[ 3\ud835\udc49\ud835\udc34\ud835\udc35\ud835\udc36 2 \ud835\udc40\ud835\udc34\ud835\udc35\ud835\udc36\ud835\udc5e sin(\ud835\udf09)] \u221e \ud835\udc5e=1 \ud835\udc49\ud835\udc34\ud835\udc35\ud835\udc36 = 4\u221a2\ud835\udc41\ud835\udc50\ud835\udc3c\ud835\udc5f\ud835\udc5a\ud835\udc60 \ud835\udf0b \ud835\udf09 = { \u2212\ud835\udc5e\ud835\udf03 + \ud835\udc5b\ud835\udc5f\ud835\udefa\ud835\udc5f\ud835\udc61, \ud835\udc5e = 6\ud835\udc5f \u2212 5 \ud835\udc5e\ud835\udf03 + \ud835\udc5b\ud835\udc5f\ud835\udefa\ud835\udc5f\ud835\udc61, \ud835\udc5e = 6\ud835\udc5f \u2212 1 0, \ud835\udc5e = \ud835\udc52\ud835\udc59\ud835\udc60\ud835\udc52 (15) where MABCq for the E-core PS-SFPM machine is \ud835\udc40\ud835\udc34\ud835\udc35\ud835\udc36\ud835\udc5e = (1/\ud835\udc5e) [1 + 2 cos ( \ud835\udc5e\ud835\udf0b 6 )] sin(\ud835\udc5e\ud835\udf033) (16) and MABCq for the C-core PS-SFPM machine is It can be concluded from (12) with j=-1 and (15)-(17) that the 6/10-pole E- and C-core PS-SFPM machines shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003199_j.mechmachtheory.2019.103576-Figure26-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003199_j.mechmachtheory.2019.103576-Figure26-1.png",
        "caption": "Fig. 26. Pinion profile modification.",
        "texts": [
            " The approach presented in this paper is based on the profile modification of the pinion by applying reliefs at tip and root of all teeth. The realization of tip and root reliefs is standard for spur and helical gears and is typically realized by grinding. The applied reliefs ( C \u03b1a , C \u03b1f ) are realized by circle segments which do not refer to the tooth height, but refer to the working length ( L ca , L cf ). The use of the working length is advantageous regarding the resulting transmission characteristics, which correlates better with the working length than the tooth height. Fig. 26 shows the applied approach schematically. According to Litvin [1] the function of transmission errors is given by \u03c62 (\u03c61 ) = \u03c62 (\u03c61 ) \u2212 N 1 N 2 \u03c61 (64) The function of transmission errors related to the pinion is therefore defined as follows: \u03c61 (\u03c61 ) = N 2 N \u03c62 (\u03c61 ) \u2212 \u03c61 (65) 1 The determination of the required quantities of face-gear crowning and pinion profile modification is based on the resulting contact pattern for the given range of alignment errors. The resulting contact ellipses should be completely within the usable flank"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001652_s00170-017-0760-9-Figure19-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001652_s00170-017-0760-9-Figure19-1.png",
        "caption": "Fig. 19 Transverse residual stress contours for specimen A from simulation (the highest and lowest values shown on the figures) a before heat treatment and b after the heat treatment",
        "texts": [
            " The experimental and simulation results show the good agreement, and in most parts, simulation curves are within the calculated upper and lower tolerance limits (using a 90% confidence interval, and the collected experimental data). The heattreated samples show stresses of lower magnitude. In the non-heat-treated specimen A, the transverse stress magnitude changed from tensile value of 71 ksi (490 MPa) at the substrate surface to a compression value of \u2212145 ksi (\u22121000 MPa) at the mid-depth area. Toward the bottom of the substrate, the transverse stress becomes tensile (18 ksi (124 MPa)) again. Figure 19 depicts a 3D view and a section view of the transverse (xx) residual stress in the specimen before and A after the 1-h heat treatment. The numerical model reveals the transverse tensile residual stress along the clad bead except at the start and end regions. The transverse tensile stresses in regions near the clad beads were balanced by equilibrating compressive stresses toward the edges, which is shown in the 3D contour plot views for specimen A (Fig. 19a). The zone with the higher transverse tensile stress is located below the clad track. Below, there is a compression area, and in the bottom, the model predicts an area of tensile stresses. The residual stress contours from the simulation in the longitudinal (zz) and out-of-plane (yy) directions after the workpiece cooled down are presented in Fig. 20. In laser cladding, the substrate material is heated up to the melting point rapidly, and a molten clad material is deposited on it. Therefore, the heat is conducted into the substrate material and the clad material solidifies and shrinks due to thermal contraction, while the substrate first expands and later contracts"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003073_j.jmrt.2019.12.075-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003073_j.jmrt.2019.12.075-Figure2-1.png",
        "caption": "Fig. 2 \u2013 Surface morphology of Inconel 718 pre-alloyed powder. (a) At low magnification. (b) At high magnification.",
        "texts": [
            " To this end, the flow behaviour f the pre-alloyed powder was characterized by the following ethods. ) The pre-alloyed powder particle size distribution curve was measured by a Mastersizer laser-diffraction diameter tester (model: ms3000) (as shown in Fig. 1). The pre-alloyed powder particle size was in the range of 30\u201365 u m, and the median particle diameter was 55 um. Therefore, the selected powder presented a sufficient particle size. ) SEM (model: Philip-Quanta 400 F) was used to observe the microstructural characteristics of the pre-alloyed powder (as shown in Fig. 2). The pre-alloyed powder was found to be dense and spherical in general, and only a few of the powder particles were ellipsoids during the extrusion of the powder particles around them. Therefore, the dense and smooth powder surface guaranteed good flow characteristics, which were beneficial for the powder feeding process. ) According to ASTM D6393-99, to measure the apparent density/tap density of alloy powder particles, the apparent density, tap density and corresponding compression ratio of Inconel 718 pre-alloyed powder were obtained by means of an apparent density measuring instrument (model: FT102B) and a tap density measuring instrument (FT100A)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001176_1.4007693-Figure10-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001176_1.4007693-Figure10-1.png",
        "caption": "Fig. 10 Illustration of contact between gears at s 5 19.4 mm; z is the pitch point",
        "texts": [
            " Positive values of s correspond to contact taking place on the addendum part of the pinion tooth and negative values correspond to contact on the addendum of the wheel tooth. A typical raw profile trace of the tooth from root to tip is shown in Fig. 9. The location of the tooth tip is clearly evident and is used to establish the origin for co-ordinate x. The simulations were, therefore, carried out at selected positions on the path of contact using profiles from the two gears corresponding to the desired s-value. Four different s-values were selected: 9.4, 5.0, \u00fe5.0, and \u00fe9.4 mm. Figure 10 shows an illustration of the meshing position s\u00bc\u00fe9.4 mm, which corresponds to contact occurring close to the pinion tip/wheel root. The raw profiles from the teeth were filtered using a standard Gaussian filter with a cutoff of 0.25 mm prior to micro-EHL simulation. Micro-EHL simulations were carried out using the modeling techniques described in detail in Refs. [7\u20139]. The aim was to model conditions under which micropitting was initiated and the emphasis was, therefore, on the earlier (lighter) load stages in the tests",
            " The conditions analyzed corresponded to a nominal maximum Hertzian contact pressure of 1.0 GPa at four positions chosen 011501-4 / Vol. 135, JANUARY 2013 Transactions of the ASME Downloaded From: http://tribology.asmedigitalcollection.asme.org/ on 01/29/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use on the path of contact (s\u00bc 9.4, 5.0, \u00fe5.0, \u00fe9.4 mm). The entraining and sliding speeds at these positions were calculated corresponding to a pinion speed of 314 rad/s, as used in the tests. The positive values of s (as defined in Fig. 10) therefore corresponded to the pinion tooth surface being the faster-moving surface relative to the contact and negative values corresponded to the wheel tooth surface being faster. At each s value, sample lengths of the wheel and tooth profiles were selected of a length 4a (where a was the corresponding semidimension of the Hertzian contact), centered on the profile position corresponding to s. The values of a, pinion and wheel surface velocities Up and Uw relative to the contact point, and the slide roll ratio (SRR) are given in Table 3 for the different mesh positions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003811_j.commatsci.2020.109752-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003811_j.commatsci.2020.109752-Figure1-1.png",
        "caption": "Fig. 1. Schematic representation of solution domain with substrate, powder bed and solidified build part.",
        "texts": [
            " The tendency to form lack-of-fusion defects and resulting discontinuity between adjacent tracks are examined and compared with similar experimentally observed behaviour. A comparative analysis of the computation time and memory necessity for an adaptive remeshing based analysis with that for a uniform mesh is carried out to provide an insight on the relative computational needs to model L-PBF with multiple tracks and layers. A schematic representation of the solution domain consisting of the substrate, powder bed with loose powder and the solidified build part is shown in Fig. 1. The axes X, Y and Z refer to the scanning, hatching and build directions, respectively. The bidirectional hatching strategy is also shown Fig. 1 in which the laser beam starts along the positive X direction and is rotated by 180\u00b0 for every alternate track. The energy from the laser beam is absorbed by the powder particles and conducted through the powder bed, substrate and the previously solidified build. The governing equation of transient heat conduction is written in 3D Cartesian coordinate system as \u239c \u239f \u2202 \u2202 \u239b \u239d \u2202 \u2202 \u239e \u23a0 + \u2202 \u2202 \u239b \u239d \u2202 \u2202 \u239e \u23a0 + \u2202 \u2202 \u239b \u239d \u2202 \u2202 \u239e \u23a0 + = \u2202 \u2202x k T x y k T y z k T z Q H tv (1) where k, H, T and t are the thermal conductivity, enthalpy, temperature and time variable, respectively",
            " The elements that experienced melting temperature of the powder alloy were considered as a continuous build for the subsequent analysis. The length of the fine mesh region (1 mm) is optimized through trials and error to reduce error due to mapping and to avoid any increase in preand post-processing computational costs. Once the entire track length is scanned, the fine mesh region is moved in the hatching direction by an amount equal to the hatch spacing and the direction of the laser beam is reversed as per the alternate direction scan pattern (as shown in Fig. 1). Fig. 3 shows the schematic representation of the mesh adaption in the hatching directions for the first and fifth tracks. This process of mesh adaption in the hatching direction continues till all the tracks in a layer are simulated. Once a layer is completed, the elements for the next layer is added, and the mesh is adapted in the build direction keeping the total node number as constant. The elements of the previous layer are assigned with appropriate material properties. The stored temperature field from the last time step is mapped onto the entire domain as an initial condition"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002064_s11661-018-4788-8-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002064_s11661-018-4788-8-Figure3-1.png",
        "caption": "Fig. 3\u2014Schematic illustration of possible hypothesis for asymmetric cracking of cylindrical parts with overhang geometries based on spatial differences in heat transfer condition that may lead to variations in thermal gradients, which in turn results in spatial variations of thermal gradients.",
        "texts": [
            " METALLURGICAL AND MATERIALS TRANSACTIONS A Any simulation exercise should start with the question to evaluate a hypothesis. In this regard, we have proposed the following scenario for our modeling activities based on spatial and temporal changes in thermal distribution due to variations in beam scanning strategy and variations in mechanical constraints due to changes in section modulus. Since the titled parts are surrounded by powder particles, thermal conditions on the left (solid) and right (overhang) side of the part would be different. This condition is explained schematically in Figure 3. Since the conductivity of the powder is approximately 0.3 to 1.5 pct of the bulk material,[29] the heat rapidly conducts out through the solid region on the left side such that the layer cools faster on the left. Also, the left region is restrained by the solid below. It can be hypothesized that asymmetric temperature distribution is produced due to the powder particles and leads to inhomogeneous thermal stresses. Consequently, the mechanical driving force for cracking may be satisfied only on one side of the cylinder and thereby inducing the asymmetric cracking"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003386_j.ast.2020.105974-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003386_j.ast.2020.105974-Figure1-1.png",
        "caption": "Fig. 1. Quadrotor transportation system with four-cable-suspended payload.",
        "texts": [
            " As a nonsingular attitude parameterization, quaternions have ambiguity, which may cause the unwinding phenomenon. Hence, the proposed controller can be used to deal with antiunwinding large attitude maneuvers. The remainder of this paper is organized as follows. The system analysis of the proposed quadrotor transportation system is given in Section 2. Sections 3 and 4 present the proposed controller and experimental results, respectively. Conclusions are drawn in Section 5. The schematic of the quadrotor with a four-cable-suspended payload is shown in Fig. 1. A cable of length l is attached at each of the four corners of the quadrotor\u2019s frame. Two coordinate frames are used to describe the system motion, i.e., the inertial coordinate frame xI yI zI and the body-fixed frame xb yb zb . The inertial frame is the Earth-fixed West-South-Up frame in our laboratory. The body-fixed frame is at the mass center of the quadrotor, xb is parallel to the symmetry plane of the rotor hubs, zb is in the local up direction when the quadrotor is at a hover and the yb-axis completes a right-handed frame",
            " By treating the effect of the suspended payload as unknown, but bounded disturbances, the dynamics model of the quadrotor can be expressed as Eqs. (1) and (3) together with M v\u0307q = \u2212Mgz I + f Rzb + d1 (5) J \u0307 = \u2212 \u00d7 J + \u03c4 + d2 (6) where d1 and d2 represent the disturbances on the translational and angular motions, respectively. To analyze the bounds of d1 and d2, the following two subsections will discuss the possible payload positions in stable configurations and the transient payload motion. In this section, the possible equilibriums of the suspended payload with different quadrotor attitude will be analyzed. For the system shown in Fig. 1, a fast spin in the yaw direction may cause the cable to twist [30,31]. However, in a general aerial transportation mission, the main objective is to move a payload from an initial position to an expected position. Hence, it is not desirable to drive the quadrotor with fast spin and the cable twisting will be negligible in the transportation mission. Furthermore, as shown in Assumptions (ii) and (iv), the payload is treated as a point mass and the cable mass is neglected. Therefore, it is reasonable to omit the effect of the payload on quadrotor in the yaw direction. As shown in Fig. 1, the view of the transportation system in yb zb and xb zb planes are similar. Both cases may have the possible configurations shown in Fig. 2 with different roll or pitch angles. Without loss of generality, the motion is restricted to yb zb plane in the following analysis. That is, the effect of the roll angle on the stable configuration of the four-cable-suspended payload will be investigated. Since the stable configurations are symmetric with the roll angles \u03c6 and \u2212\u03c6, only the situation where \u03c6 \u2265 0 is discussed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003729_s10763-020-10129-y-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003729_s10763-020-10129-y-Figure3-1.png",
        "caption": "Fig. 3 Learning activities developed for the engineering project. Note: the central figure is retrieved from Fan, Yu, and Lou (2018).",
        "texts": [
            " Finally, it was necessary to assign various roles and weights to pieces of knowledge from various subject areas based on the curriculum theme. To help students acquire the STEM subject knowledge necessary to complete the vehicle design project, two design components, the \u201ccar body structure\u201d and \u201cbody shape design,\u201d were positioned as the main axes. Based on this focus, four learning activities that revolve around \u201cinquiry and experiment\u201d and \u201cdesign and making\u201d have been developed to help students explore the relationship between theory and practice. The design of the learning activities is shown in Fig. 3, and the teaching process is shown in Table 1 in the Electronic Supplementary Material (ESM). This course consists of a one hour lesson per week, for a total of 18 weeks. Learning Activity 1 (Inquiry and Experiment): Rolling Experiment of Landslide Resistance. \u201cInquiry and experiment\u201d activities should help students understand important scientific concepts or mathematical principles with the aim of strengthening their skills in observation, data recording and analysis, reflection and evaluation, and data-based communication"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000648_978-3-642-17531-2-Figure5.14-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000648_978-3-642-17531-2-Figure5.14-1.png",
        "caption": "Fig. 5.14. Example of a characteristic force map of an electrostatic transducer with variable electrode separation and voltage drive (e.g. a plate transducer, see Sec. 6.4): a) force map, b) force-displacement curves for a constant transducer voltage",
        "texts": [
            "4 The Loaded Generic Transducer 319 behavior to be described using a characteristic force map ( , ) T F x , where describes the applicable electrical working variable for a particular case. Mathematically, the characteristic force map is a higher-dimensional surface. The transducer force-displacement curve shown in Fig. 5.13 is just a section curve 0 ( , ) T F x of the transducer characteristic map at a constant value 0 of the electrical working variable. As a demonstrative example of a transducer implementation, the characteristic force map of an electrostatic transducer (a plate transducer) is depicted in Fig. 5.14a. For this case, let the plate voltage be controllable. The corresponding section for a constant transducer voltage can be seen in Fig. 5.14b. Three equilibrium positions can be seen, of which only two 1 3 ( , ) R R x x are stable. In the end, however, only the equilibrium posi- tion 1R x is actually useable as an operating point, as 3R x lies outside the operating regime. Geometric interpretation of equilibrium position equations The equilibrium position equations (5.40), (5.41) can be interpreted concretely as defining the intersection of the transducer map with the spring force plane (Fig. 5.14b). 320 5 Functional Realization: The Generic Mechatronic Transducer Initializing operating points Given a fixed stiffness k of the elastic suspension and a steady-state mechanical excitation (external force), the active operating point (equilibrium position) depends solely on the electrical drive variable (voltage or current). For example, consider the electrostatic transducer in Fig. 5.14. As the transducer force in the electrically nonactive state is equal to zero (see Eq. (5.22)), increasing values of the electrical drive variable (here the voltage) cause the operating point to move along the voltage-force curve as shown in Fig. 5.14a (the solid intersection of the transducer force surface with the spring force plane). This voltageforce curve forms the set of all stable equilibrium positions (quasistatically) reachable from the electrically inactive state (see Fig. 5.14a,b). Critical electrical drive As can be seen in the example of the electrostatic transducer in Fig. 5.14, there is a critical voltage crit U beyond which there are no more reachable equilibrium positions. It can be seen in Fig. 5.14b that this is due to precisely the previously-mentioned marginally stable case. The bounding value crit U represents the maximum operat- ing drive value; the corresponding crit x characterizes the maximum controllable armature displacement. As the intersection curve changes with the angle of the spring force plane, these operational bounds also depend on the elastic suspension k . The dashed intersection curve indicated in Fig. 5.14a represents the set of all unstable equilibrium positions (cf. the middle equilibrium position 2R x in Fig. 5.14b). Nonlinear transducer model The nonlinear equations of motion in Table 5.6 in the preferred coordinates for voltage and current drive each consist of only one second-order nonlinear differential equation in the mechanical coordinate x . This differential equation has the following general form: ( , / ) T S S ext m x k x F x u i F , (5.45) where the transducer force T F depends on the electrical source variables. In addition, there is also one algebraic output equation for the dependent electrical terminal variable\u2014 T i for voltage drive, or T u for current drive (see Table 5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000288_tmag.2010.2044417-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000288_tmag.2010.2044417-Figure7-1.png",
        "caption": "Fig. 7. Cross sections of 8-pole/9-slot and 10-pole/9-slot machines. (a) 8-pole/9-slot. (b) 10-pole/9-slot.",
        "texts": [
            " INVESTIGATION OF UNBALANCED MAGNETIC FORCE IN 8-POLE/9-SLOT AND 10-POLE/9-SLOT MACHINES The general expression for UMF is derived in Section IV. It is validated against experimental results for a 2-pole/3-slot machine in Appendix 1 and against FE results in this section. In Section IV, the cancellation and additive effects between the UMF components resulted from the radial and tangential force waves are revealed by the analytical model. In order to further illustrate this important phenomenon, the analytical model is employed to analyze the UMF in 8-pole/9-slot and 10-pole/9-slot machines, Fig. 7, whose main parameters are given in Table VI. With sinusoidal current excitation, the generation and harmonic contents of UMFs by the armature reaction only in the 8-pole/9-slot and 10-pole/9-slot machines are shown in Table II, while those by mutual interaction are shown in Tables III\u2013IV. The results confirm the foregoing analyses and conclusions obtained in Section IV. The analytically predicted UMFs are compared with FE prediction for the 8-pole/9-slot and 10-pole/9-slot machines in Figs. 8 and 9, respectively, and good agreement is obtained"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001551_icuas.2015.7152306-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001551_icuas.2015.7152306-Figure2-1.png",
        "caption": "Fig. 2: Axis Definitions",
        "texts": [
            " These differential equations will be in the following form x\u0307 = f (x,u) (1) where x is the state vector which is defined as [x u y v z w \u03c6 p \u03b8 q \u03c8 r]T and u is the input vector which is defined as [Fz Mx My Mz] T, where Fz is the vertical force and M is the rotational moment along the aircraft\u2019s body axes. A quadrotor can be modeled as a rigid body. We can consider a fixed inertial frame, {i}, and a body frame, {b}, placed with an origin at the center of mass of the quadrotor 978-1-4799-6009-5/15/$31.00 \u00a92015 IEEE 320 as shown in Fig. 2. Using Newton\u2019s equations expressed in the body frame, the translational motion is governed by mv\u0307+m\u03c9\u00d7v = \u03a3F (2) where v are the body-frame translational velocities [u v w]T and \u03c9 are the body-frame rotational velocities [p q r]T. The forces considered are the gravitational force Fg, the thruster force Ft, and the aerodynamic force Fa. This summation is written as \u03a3F = Fg +Ft +Fa (3) The gravitation force can be expressed as Fg = T [ 0 0 mg ] (4) where T is the rotation matrix from the body frame to the inertial frame"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003989_j.jallcom.2020.155019-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003989_j.jallcom.2020.155019-Figure9-1.png",
        "caption": "Fig. 9. Schematic diagram of EBS-LST 718 solidification process.",
        "texts": [
            " The SDAS of EBS-LST 718 is significantly smaller than that of conventional technologies, and the RC of the EBS-LST 718 ingot is faster than that of conventional methods [4,7,24]. Furthermore, the SDAS decreases with the cooling rate as shown in Fig. 8, indicating that such a fast RC is responsible for the formation of fine dendrites [25]. Smelting occurs between the layers during the preparation of EBS-LST 718, leading to the formation of a so-called mushy zone ahead of the solidification interface before solidification begins as shown in Fig. 9. New free-oriented grains and/or dendrites are already formed and grow in the mushy zone during the initial solidification due to the constitutional supercooling [26]. Therefore, the dendrite-cellular morphology is formed under such a fast RC at the onset of solidification. As the solidification progresses, certain dendrites with a particular orientation are gradually formed due to the presence of a temperature gradient in a certain direction. In brief, the crystals of EBS-LST 718 mainly grow in the form of dendrites, which are mainly mass transferred in the dendrite scale, as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003450_j.jfranklin.2019.08.038-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003450_j.jfranklin.2019.08.038-Figure2-1.png",
        "caption": "Fig. 2. The flexible joint actuated by DC-motor.",
        "texts": [],
        "surrounding_texts": [
            "2 M. Cui and Z. Wu / Journal of the Franklin Institute xxx (xxxx) xxx\npassivity-based control [11] . However, most of them perform torque-based control strategies to achieve the desired results, which have the drawbacks of involving practical problems and excluding the role of actuators. Due to the high controllability of electric actuator, engineers pay their more attention to the electrically driven manipulators. Since the DC-motor has many outstanding advantages such as small volume, light weight and high efficiency, it has been widely used in the robot control. For the rigid-link robots driven by DC-motors, Guldner et al. [12] introduced a framework for the tracking controller design. Fateh [13] presented a novel approach with fast response and robust. For the flexible joint robots driven by DC-motors, a high-performance controller was designed in [14] by using backstepping. In [15] , the set-point regulation control design method was proposed. Chien and Huang [16] developed an adaptive controller. A novel robust adaptive control was developed in [17] . For the case of unmeasured velocity, Chang and Yen [18] designed a novel observer-based robust dynamic feedback tracking controller such that the closed-loop system is locally stable. An adaptive fuzzy output feedback approach is proposed in [19] . However, the existing references mainly focus on the deterministic case. It is naturally expected that robots can work in many random vibration environment with the development of the robot technology and stochastic theory [20\u201323] . How to describe the random disturbances and introduce them to the system is the key for modeling and control. The traditional research thinking is to set the random noise as white noise which is regarded as the formal derivative of wiener process, and establish It\u00f4 type stochastic differential equation systems (SDEs). In [24\u201327] , the stochastic modeling and the controller design methods were studied for different mechanical systems. For a class of rigid manipulators in random vibration environment, Cui et al. [26] constructed a stochastic Hamiltonian dynamic model and designed a tracking controller. Owing to the mildness of actual random disturbances, it is more reasonable to describe random disturbances as stationary processes.\nFor mechanical systems with colored noise disturbances, the results of random modeling and control are very few. In [28] , a theoretical framework on stability of random differential equation systems (RDEs) was given where stochastic disturbances are stationary processes. In [29] , a random Lagrangian equation of a benchmark system was constructed and a tracking controller with tunable parameters was designed. For automobile suspension systems in rough road, Cui et al. [30] established a random dynamic model and designed a stabilization controller. But for the modeling and tracking control of flexible joint manipulators actuated by DC-motors under random disturbance, to the authors\u2019 knowledge, there is no any related result.\nThe objective of this paper is to solve this problem, the main work consists of the following aspects:\n(1) How to describe random noises and transform them to the system is the main difficulty for modeling. By describing random vibration in environment as random acceleration, according to relative motion, the influence of random vibration is transformed to mass points along links as torque disturbed by stationary processes. By the equivalent circuit, the thermal noise of DC-motors is transformed to the system as voltage disturbed by stationary processes. Then it leads to a random model by using Lagrangian mechanics and the electromagnetic.\n(2) Since random noises affect the whole system through the integral chain, how to deal with random noises is the main difficulty for tracking controller design. By using the vectorial backstepping and the technique of separating out random noises from coupled terms, a state feedback tracking controller with tunable parameters is designed such that the mean square of the tracking error converges to an arbitrarily small neighborhood.\nPlease cite this article as: M. Cui and Z. Wu, Trajectory tracking of flexible joint manipulators actuated by DCmotors under random disturbances, Journal of the Franklin Institute, https:// doi.org/ 10.1016/ j.jfranklin.2019.08.038",
            "M. Cui and Z. Wu / Journal of the Franklin Institute xxx (xxxx) xxx 3\nd a b i\nn o i i r s s\n2\nm\n(3) Considering the established model (see Eq. (5) ) described by RDEs rather than SDEs, ifferent from [24\u201327] , the Lyapunov function in this paper is the quadratic rather than quartic, nd there is no Hessian term to deal with in the controller design. Compared with [24\u201327] , the ound of the tracking error does not depend on the reference signal, which is more reasonable n actual application.\nNotations: The following notations are used throughout the paper: For a vector x , x T deotes its transpose; for a matrix X , X\n\u22121 denotes its inverse; I n \u00d7n denotes the identity matrix f dimension n ; | \u00b7 | denotes the usual Euclidean norm of \u201c \u00b7\u201d; diag( \u00b7 ) transforms a vector nto a diagonal matrix; for matrices A and B , A \u2264B means that B \u2212 A is a positive semidefnite matrix; E denotes the mathematical expectation; R +\ndenotes the set of all nonnegative eal numbers; R n denotes the real n -dimensional space; R\nn\u00d7m denotes the real n \u00d7m matrix pace; C\ni denotes the set of all functions with continuous i th partial derivative. For simplicity, ometimes the arguments of functions are dropped.\n. Problem formulation\nIn this paper, consider a n -link planar manipulator with flexible joints actuated by DCotors in a random vibration environment, which is shown in Figs. 1 and 2 with parameters\nPlease cite this article as: M. Cui and Z. Wu, Trajectory tracking of flexible joint manipulators actuated by DCmotors under random disturbances, Journal of the Franklin Institute, https:// doi.org/ 10.1016/ j.jfranklin.2019.08.038",
            "4 M. Cui and Z. Wu / Journal of the Franklin Institute xxx (xxxx) xxx\nThe manipulator is connected to O on the floor. The manipulator is affected by the random vibration environment. As in [24] , the random vibration is described by the random accelerations of the point O and let \u03be 1 , \u03be 2 denote the random accelerations in horizontal and vertical directions, respectively (see Fig. 1 ), which can be seen as independent stationary processes.\nWith the development of sensor technology, for i = 1 , 2, . . . , n, the states q i , \u02d9 qi , \u03b8 i , \u02d9 \u03b8i and I i can be easily measured by adding some sensors. Given a smooth reference signal q r = (q r1 , q r2 , . . . , q rn )\nT , in the absence of air resistance, the objective of this paper is to design a state feedback tracking controller u = (u 1 , u 2 , . . . , u n )\nT such that trajectory tracking error q \u2212 q r as small as possible where q = (q 1 , q 2 , . . . , q n )\nT , while keeping all the other signals in the closed-loop system bounded in probability.\n3. Random model For manipulator\nIn order to establish the model, the following assumption is imposed.\nAssumption 1. It is used permanent magnet DC motors and the rotors of DC-motors and the gear are symmetric about their axis of rotation in this paper.\nBy using robot dynamics, Lagrangian mechanics and the electromagnetic, the random\nmodel is to be constructed by two steps. Step 1: Modeling in the deterministic case\nPlease cite this article as: M. Cui and Z. Wu, Trajectory tracking of flexible joint manipulators actuated by DCmotors under random disturbances, Journal of the Franklin Institute, https:// doi.org/ 10.1016/ j.jfranklin.2019.08.038"
        ]
    },
    {
        "image_filename": "designv10_5_0003504_rpj-12-2019-0320-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003504_rpj-12-2019-0320-Figure2-1.png",
        "caption": "Figure 2 Machine standard laser scanning strategy and layer rotation",
        "texts": [
            " The powder morphology and powder particle diameter distribution are shown in Figures 1(a) and 1(b), respectively. A commercial laser powder-bed-fusionmachine (3D systems ProXDMP320) was used for sample fabrication. Themachine was equipped with a fiber laser having a focused beam diameter of 80 mm and a high purity argon-filled chamber. Specimens were fabricated using the machine standard skin core scanning strategy with a layer rotation angle of 67\u00b0 relative to the previous layer. A graphical representation of the adopted scanning strategy can be observed in Figure 2. Process parameters used for sample fabrication are reported in Table 2. Two HT processes with different cooling rates, i.e. heating up to 1,050\u00b0C for 1 h followed by furnace cooling (HT 1) and Post-heat treatment SaadWaqar et al. Rapid Prototyping Journal heating up to 1,050\u00b0C for 1 h followed by relatively higher cooling rate, i.e. air cooling (HT 2) were selected. HT conditions were selected considering the standard 316L annealing conditions and recrystallization temperature. Table 3 states the conditions for HTprocesses",
            " For phase analysis, 316L powder and the TD1\u2013TD2 planes of as-built (AB), HT 1 and HT 2 samples were subjected to XRD diffraction. XRD analysis was conducted on an Ultima IV X-ray diffractometer with Co-Ka radiation at 40 kV and 40mA in range of 2u from 10\u00b0 to 90\u00b0, using a step size of 0.02\u00b0. Phase distribution maps were also acquired for AB, HT 1 and HT 2 samples from EBSDdetectors attached to SEM. The cross-sectional planes parallel to built direction (BD-TD1) plane of all samples, as shown in Figure 2, were observed for microstructural investigation. Sectioned 5mm samples were ground with 600, 1,200 and 2,000 grit sandpapers, followed by polishing to a mirror finish of 3 mm. Polished samples were etched using a 1:1:1 solution of HCl, HNO3 and distilled H2O for 90 s. The microstructure was investigated through FEI QUANTA FEG 250 SEM. For EBSD, mirror polished specimens of the cross-sectional plane were also electrochemically polished in a 10% oxalic acid solution at 6V for 90 s. EBSD analysis was done on SEM attached detectors at a step size of 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003735_j.jmapro.2020.10.065-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003735_j.jmapro.2020.10.065-Figure2-1.png",
        "caption": "Fig. 2. Schematization of the cutting of the specimens for metallographic observations and microhardness measurements.",
        "texts": [
            " Standard metallographic techniques were used for the microstructural observations. The microstructure observations and analysis were carried out by following the methods reported in the literature [53]. The specimens were sectioned, mounted in resin, ground with SiC papers up to the grit size of 1200, and then lapped using diamond suspension down to 0.05 \u03bcm. The microstructure was analysed, observing the cross-sections of samples. In particular, it was observed the surface x\u2013z, i.e. a surface parallel to the build direction, as sketched in Fig. 2. The polished specimens were then etched with a hydrofluoric acid-based solution (1 mL hydrofluoric acid, 50 wt.%, and 3 mL nitric acid, 60 wt.%, in 7 mL of distilled water). The etched samples were analysed using both an optical microscope (Zeiss Axioscope) and a scanning electron microscope (SEM, Hitachi TM3000). The samples were observed at fixed distances from the build plate to guarantee the consistency of the measurements. To measure the hardness of the specimens, Vickers microindentation tests were executed using a test load of 0.5 kgf and a loading time of 20 s. The samples for the microhardness measurements were prepared following the same procedure used for metallographic specimens, of course the etching was not performed on these specimens. The hardness measurements were performed on the z-x plane defined in Fig. 2; referring to the prior work of Tan et al. [12] that suggested a graded microstructure along the building direction. In this perspective, to investigate the variation of hardness during the build, three lines of indentations (along the x-axis) were performed at different distances from the build plate (300\u2013750\u20131200 \u03bcm, hereinafter referred respectively as bottom, core and top) and five valid measures were taken for each line. The roughness was measured by using a Leica DCM3D contactless confocal microscope, this microscope is able to acquire surfaces and the correlated software calculates the surface roughness parameters as defined by ISO 25178-2:2012 (Geometrical product specifications (GPS) \u2014 Surface texture: Areal \u2014 Part 2: Terms, definitions and surface texture parameters)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001155_j.measurement.2014.02.029-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001155_j.measurement.2014.02.029-Figure6-1.png",
        "caption": "Fig. 6. Time signal averaging arrangement for synchronous and asynchronous speed.",
        "texts": [
            " The input shaft of the gear box is powered by a three phase, 3 HP, 0\u20135000 rpm variable speed motor. 3. The output shaft is connected with 4\u2013220 lb.in capacity magnetic particle brake. It can be seen from the schematic of gearbox test rig Fig. 5 that, more than one test gears can be mounted on shaft 1 at a time to save time in changing the gears. The gears to be tested can be engaged with gear 2 easily by loosing and tightening the screw of pinion gear 1 collar. The uni-axial accelerometer will be fixed at the bearing housing of input shaft to the gearbox as shown in Fig. 6a. Output shaft is connected with Magnetic Particle Brake for applying required load/torque. The simulator is used to carry out the experiments on a single stage parallel shaft gearbox with constant or varying input speed from a synchronous motor. The load can also be varied as required with the help of a programmable magnetic brake. A tachometer is installed just above the input shaft outside the motor. A multi-pulse tacho signal generator arrangement as shown in Fig. 6b is installed on the input shaft before coupling to produce tacho-pulse at constant or varying speed of motor. The motor is connected with a PC and can be programmed to run at a constant speed or a varying speed of specified speed profile. The output of the motor is the input shaft of the gear box on which the gear in consideration is placed. The pinion in consideration can be directly meshed to a gear on the output shaft (single stage). On the output shaft, a magnetic brake is placed, which can be programmed to give a constant load or varying load of specified profile. The accelerometer sensor can be place on either of the shafts or on the gear box to record the vibrations, which is interfaced to the PC via DAQ (Data Acquisition system) instruments as shown in Fig. 6c. The vibration signals were recorded and analysed using MATLAB programming. The crack propagation path at a pinion tooth root has been predicted using finite element analysis [13\u201315] followed by the generation of crack trajectory on actual pinion. A 2-D involute gear tooth geometry of pinion used in this study is generated using the parameters of gear listed in Table 1. A single tooth two-dimensional model is used in the present study for the ease of computation. The mesh is then imported to FRacture Analysis Code (FRANC)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001155_j.measurement.2014.02.029-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001155_j.measurement.2014.02.029-Figure7-1.png",
        "caption": "Fig. 7. (a) Finite element mesh of pinion tooth and (b) cracked tooth.",
        "texts": [
            " A single tooth two-dimensional model is used in the present study for the ease of computation. The mesh is then imported to FRacture Analysis Code (FRANC). FRANC is a finite element code which uses principles of linear elastic fracture mechanics (LEFM) for static analysis of cracked structure. It has unique automatic crack propagation capabilities after an initial crack is inserted in a mesh [13]. The tooth is rigidly held at the edges of the rim and the load is applied at the highest point of single tooth contact (HPSTC), normal to the surface as shown in Fig. 7a. The point of largest stress has been identified using finite element analysis and the crack has been introduced at the fillet region of tooth root. The crack propagation path has been obtained for different crack lengths viz. 10%, 20%, 30%, 40% and 50%. The crack trajectory is shown in Fig. 7b. The crack trajectory obtained can be used to introduce the crack in the specimen for experimental study of the cracked tooth. The specimen material used in the experimental study in the subsequent section is, a 32 teeth pinion made of steel. The cracks will be induced in the specimens on one of the pinion tooth at the location identified by finite element analysis. The predicted crack trajectory (Fig. 7b) obtained via finite element analysis described in previous section has been programmed in ELCAM CNC part programming facility available in ECOCUT \u2013 CNC Wirecut Electrode Discharge Machining (WEDM) as shown in Fig. 8b. The successive crack lengths have been generated on pinion, as shown in Fig. 8a, up to 50% of fully developed crack in the steps of 10% (see Fig. 9). In order to evaluate the effectiveness of the proposed method, multiple experiments on gear box setup with cracked pinion with different crack level at tooth root have been tested under different conditions of load and speed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002453_s11071-019-04780-6-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002453_s11071-019-04780-6-Figure1-1.png",
        "caption": "Fig. 1 Gear pair dynamic model",
        "texts": [
            " This study established an enhanced spur gear dynamic model by considering the stiffness and damping of both the gear tooth and oil film, and the models for oil film stiffness and damping in normal and tangential directions are developed. The combined stiffness is deduced from the stiffness of both the gear tooth and oil film, while the combined damping is derived from the damping of these parts. Effects of oil film stiffness and damping in normal and tangential directions on spur gear dynamics are investigated. Finally, the comparison of dynamic response between the developedmodel and the conventional model is discussed. 2.1 Enhanced dynamic model for spur gear pairs The dynamic model for a spur gear pair is sketched in Fig. 1, and the gear geometry is shown in Fig. 2. In the present study, an enhanced dynamic model for spur gear pairs including the backlash and static transmission error and stimulatingly incorporating the combined stiffness in the normal direction as well as the combined damping both in normal and tangential directions is developed from a conventional model [6,7]. And the conventional model refers to the spur gear dynamicmodel inwhich theoil filmstiffness anddamping are not considered and the friction is not included as well"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003740_physrevb.102.174106-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003740_physrevb.102.174106-Figure1-1.png",
        "caption": "FIG. 1. Schematic of the formation of a GMS by pattern-based hydrogenation of a graphene sheet. (a) Folding pattern showing the areas where the graphene sheet is hydrogenated (magenta, top side; cyan, bottom side). (b) GMS with Lx,0 = Ly,0 = 36.7 nm, w = 3.7 nm, and \u03c1 = 15% (GMS 1) in the equilibrium state at 300 K. (c) Definition of geometrical parameters. (d) Potential energy of GMS 1 as function of the simulation time at 300 K.",
        "texts": [
            " While auxeticity was proposed previously for Miura-origami structures [33\u201335], we introduce in the present paper a method to obtain simultaneously superflexibility (under both tension and compression). This unique combination of extraordinary mechanical properties, e.g., can be used to strongly enhance the sensitivity of strain sensors [20]. We carry out MD simulations of the formation of GMSs by pattern-based hydrogenation of graphene sheets to evaluate the response under mechanical loading. Figure 1(a) shows schematically the hydrogenation by random distribution of H atoms in predefined areas on top (magenta) and on bottom (cyan) of a graphene sheet. The interaction between the atoms is modeled by the second generation reactive empirical bond order (REBO-II) potential, using the parameters of Ref. [36]. The hydrogenation locally perturbs the planar sp2 bonding 2469-9950/2020/102(17)/174106(6) 174106-1 \u00a92020 American Physical Society and thus induces pseudo surface stress acting as a driving force to fold the graphene sheet at the hydrogenated areas, resulting in the formation of a GMS. The pattern is characterized by the unit cell dimensions Lx,0 and Ly,0, fold width w, and density of hydrogen atoms \u03c1 [ratio of the numbers of hydrogen and carbon atoms in the magenta and cyan areas of Fig. 1(a)]. We apply periodic boundary conditions in the zigzag (x) and armchair (y) directions to eliminate possible edge effects. A 2 \u00d7 2 supercell is considered after confirming that the difference in the obtained structure with respect to a 4 \u00d7 4 supercell is negligible for a GMS with Lx,0 = Ly,0 = 36.7 nm, w = 3.7 nm, and \u03c1 = 15% (GMS 1). Initially, a molecular statics simulation is conducted for each GMS (with the supercell dimensions fixed) using the conjugate gradient method with an energy tolerance (relative change of the total energy between successive iterations) of 10\u221216. The GMS then is relaxed at 300 K under a canonical (NVT) ensemble for 100 ps and afterwards under an isothermal-isobaric (NPT) ensemble (in which the stress components along the in-plane directions are controlled to be zero). According to Fig. 1(d) the relaxation process is well converged. The equilibrium state of GMS 1 is shown in Fig. 1(b). To simulate the mechanical response of a GMS under uniaxial stress in the x direction, starting from the fully relaxed state, the GMS is stretched/compressed in the x direction with a strain rate of \u00b1108 s\u22121 under a NPT ensemble (in which the stress component in the y direction is controlled to be zero). In all MD simulations the temperature and pressure are controlled by a Nos\u00e9-Hoover thermostat [37] and barostat [38], respectively, and a time step of 1 fs is chosen. The opensource LAMMPS code [39] is used to perform the molecular statics and MD simulations, and the OVITO software [40] is used to visualize the simulation results",
            " In particular, Young\u2019s modulus in the x direction (Yxx), which is calculated as the slope of the stress-strain curve in the small strain interval from \u22121 to 1%, turns out to be 4.6 MPa, which is much smaller than that of pristine graphene (777 GPa, obtained in the strain interval from 0 to 2%). Under the loading the GMS is deformed without significant changes in the atomic distances, while flapping of the graphene pieces connecting at folds [according to Fig. 2(a) the changes of the angles \u03b8 and \u03c6 defined in Fig. 1(c) are large] results in high flexibility and low stiffness. The atomic distances increase significantly when the strain approaches 68% [point B in zone 3 of Fig. 2(a)], where \u03b8 becomes zero (flat GMS) according to Fig. 2(b). Similarly, the compressive stress increases significantly when the strain approaches \u221278% [point A in zone 1 of Fig. 2(a)], where the flapping is largely constrained due to the fact that \u03b8 approaches \u03c0 according to Fig. 2(b). Our MD simulations confirm that the deformation is reversible in the strain interval from \u221278 to 68%, implying excellent mechanical resilience",
            " Turning to the effect of w on Es and Ec, we consider GMSs with w in the range from 1.2 to 3.7 nm and \u03c1 in the range from 5.0 to 17.5% (common Lx,0 = Ly,0 = 36.7 nm). We find that the effect of w is similar to that of \u03c1 [Fig. 3(b)]. Furthermore, Yxx falls in the range from 1.5 to 1287.7 MPa [Fig. 3(c)], which is about three orders of magnitude larger than reported for typical cellular graphene structures with similar Ec [54]. For the ideal Miura-origami structure (flapping without deformation and w Lx,0) Poisson\u2019s ratio is given by [33] \u03bdxy = \u2212 tan2 \u03c6/2. (5) As Fig. 1(c) implies \u03b8 = arccos (2 sin2(\u03c6/2) sin2 \u03b2 \u2212 1), we obtain \u03bdxy = \u2212 ( sin2 \u03b2(1 + cos \u03b8 ) 2 \u2212 sin2 \u03b2(1 + cos \u03b8 ) ) . (6) Figure 3(d) compares \u03bdxy obtained by Eq. (6), using \u03b8 from our MD simulations for the equilibrium state, with the MD results of the negative slope of \u03b5xx(\u03b5yy) for the GMSs of Fig. 3(a), both showing that \u03bdxy increases for increasing w and \u03c1. The fact that the two approaches provide closely related results indicates that the model behind Eq. (6) describes the fundamental physics very well"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002962_j.jmatprotec.2016.12.020-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002962_j.jmatprotec.2016.12.020-Figure5-1.png",
        "caption": "Fig. 5. Groove dimensions used for Type",
        "texts": [
            " e with extended clad and surface ground. 250 Y. Chew et al. / Journal of Materials Processing Technology 243 (2017) 246\u2013257 ended clad-surface grind) test specimens (unit:mm). T i r e fl T l w t w a 2 i W b c i a a h e a c t e r c t s a m n 2 t I t ype II specimen with the clad layer fabricated in the groove and ts expected fatigue failure mode initiating from the intersection egion where the clad material meets the substrate material at the nds of the groove. The schematic of the groove details is given in Fig. 5, and the ow chart for fabrication of Type II specimens is shown in Fig. 6. he substrate dimension and cladding parameters including clad ength is similar to the Type I (as-clad) specimen. The groove depth as determined such that the remaining clad layer thickness after he clad surface was ground down to flush with substrate surface ill be comparable to the clad layer thickness for Type III specimen fter surface grinding. .1.3. Type III specimen design and fabrication The main feature of Type III specimen is that the clad region s extended beyond the gage section of the fatigue test specimen"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002912_s00170-019-04456-w-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002912_s00170-019-04456-w-Figure6-1.png",
        "caption": "Fig. 6 Schematic illustrations of laser spot and scan track directions in a uni-directional scanning mode, and b bidirectional scanning mode",
        "texts": [
            " Notably, the details of finding optimal processing window of laser power and scanning speed can be found in our study in [1]. It is noted that different from the optimized parameters at the laser power and scanning speed for studying the single-scanning track SLM process, here in this study mainly the optimized parameters at the hatch space and scan length are chosen for studying the double-scanning track SLM process. Double-scanning track simulations were performed in both the unidirectional mode and the bi-directional mode (see Fig. 6). Figure 7 a shows the result of circle packing design algorithm in dimensionless unit. Accordingly, the simulated coordinates of each circle are converted to the corresponding values of hatch space and scan length as shown in Fig. 7b. For ensuring the results of FE heat transfer simulation to reach steady value, the minimum length of scan track was chosen as 1 mm [24]. Experimental results in literature [8] indicated that longer scanning length would result in higher residual stress in SLM processed components",
            " In implementing the volumetric heat source given in Section 2.1, the radial distance r in the laser energy intensity distribution given in Eq. (3) was formulated as r \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x\u2212a\u00f0 \u00de2 \u00fe y\u2212b\u00f0 \u00de2 0\u2264r\u2264r0\u00f0 \u00de q \u00f012\u00de where a and b are the center coordinates of the laser spot on the irradiated surface. For the uni-directional scanning pattern (see Fig. 6a), variables a and b in Eq. (11) were given as follows: a; b\u00f0 \u00de \u00bc vt \u00fe 0:1; 0:875\u00f0 \u00de 0\u2264 t\u2264 L v vt \u00fe 0:1; 0:875\u00fe H\u00f0 \u00de L v \u2264 t\u2264 2L v 8>< >: \u00f013\u00de Meanwhile, for the bi-directional scanning pattern (see Fig. 6b), variables a and b were given as a; b\u00f0 \u00de \u00bc vt \u00fe 0:1; 0:875\u00f0 \u00de 0\u2264 t\u2264 L v L\u2212vt \u00fe 0:1; 0:875\u00fe H\u00f0 \u00de L v \u2264 t\u2264 2L v 8>< >>: \u00f014\u00de where v is the laser scanning speed, L is the scan track length, H is the hatch space, and t is the simulation time. The COMSOL simulations were performed to determine the peak temperature and melt pool dimensions of the two scanning tracks for each of the hatch space and scan length parameters identified using the circle packing design method. Note that the remaining simulation parameters were given as shown in Table 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002213_j.mechmachtheory.2014.06.006-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002213_j.mechmachtheory.2014.06.006-Figure5-1.png",
        "caption": "Fig. 5. State 1 of the derivative queer-square mechanism (\u03b11 N 0, \u03b12 N 0, \u03b211 = \u03b212, \u03b221 = \u03b222).",
        "texts": [
            " The angle ranges of\u03b11,\u03b12 (in state 2) and\u03b211, \u03b221 (in state 1) can also be extended less than\u2212 \u03c0 2 until the geometry touches constraint whose angles are always greater than\u2212 \u03c0. In state 1, the angles \u03b11 and \u03b12 are positive which leads limb1s and limb2s relatively higher than the base. Angle ranges for state 1 are demonstrated as \u03b11N0;\u03b211 \u00bc \u03b212b0 \u03b12N0;\u03b221 \u00bc \u03b222b0 : \u00f024\u00de In state 1, the limb1s, limb1p, limb2s and limb2p have a higher location with regard to the base, and the platform is located lower than the limb1s, limb1p, limb2s and limb2p, as illustrated in Fig. 5. In state 2, the angles \u03b11 and \u03b12 both are negative that lead to limb1s and limb2s relatively lower than the base. The angle ranges of the derivative queer-square mechanism in state 2 satisfy \u03b11b0;\u03b211 \u00bc \u03b212N0 \u03b12b0;\u03b221 \u00bc \u03b222N0 : \u00f025\u00de In state 2, the limb1s, limb1p, limb2s and limb2p are lower than the base, and the platform occupies a higher altitude compared to the limb1s, limb1p, limb2s and limb2p, as illustrated in Fig. 6. By combining the reciprocal screw of the platform constraint\u2013screw system in Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000218_1.3063817-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000218_1.3063817-Figure7-1.png",
        "caption": "Fig. 7 Cage reference frame",
        "texts": [
            " The cage components, i.e., discrete eleents and cage pockets, must remain coplanar. Additionally, each f the cage components may rotate only about an axis that is erpendicular to the plane on which the cage components lie. In order to maintain the planar flexibility and allow the overall age to experience 3D motion, the deformable cage assembly ranslates along the cage axis and tilts as a rigid body. Defining he positions of all the blocks and pockets on a single plane of a oating cage reference frame enables this. Figure 7 illustrates the oating cage reference frame that contains the plane of the blocks nd pockets. Note that the cage reference frame has 5DOFs, two otational and three translational. Tilting of the cage reference rame takes place about its Y- and Z-axes, while translation occurs long its X-axis. Initially, the X-axis of the cage is coincident with hat of the inertial reference frame, but tilting of the cage reorients ts axis with respect to the inertial reference frame. Therefore, the hree inertial directions describe the cage translation along its -axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003556_j.jmmm.2019.165754-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003556_j.jmmm.2019.165754-Figure4-1.png",
        "caption": "Fig. 4. A part of magnetic shielding structure mode for FOG (a) and its object of Permalloy via SLM directly out of Ni-15Fe-5Mo powder (b) using the optimized SLM parameters.",
        "texts": [
            " Thus, the properly controlling of the intervals between the adjacent laser-induced molten passes is conducive to ensuring a good top surface roughness of the as-printed samples. Finally, one group of the tailored SLM process parameters was thus determined as follows: laser powder 200W, laser scan speed 400mm/s, hatch-spacing 80 \u03bcm and layer thickness 35 \u03bcm. As a result, a high bulk density and a very low surface roughness were then achieved under the optimized SLM conditions. Employing the optimal parameters, a part of magnetic shielding structure (Fig. 4a) for a FOG was successfully printed in 3D by SLM (Fig. 4b). The prealloyed powder for SLM, as-printed and subsequently annealed Permalloy Ni-15Fe-5Mo samples were all determined as a single Austenite phase, according to the XRD spectra as exhibited in Fig. 5a, with the enlargements in 2\u03b8 ranges of 43.5\u00b0~45.5\u00b0 (Fig. 5a-1) and 50.5\u201352.5\u00b0 (Fig. 5a-2). Furthermore, they implied the effect of annealing on the internal stress relief in the as-printed sample, due to that the Austenite spectrum shifts to a high diffraction angle direction after SLM fabrication without annealing, by comparison with that of the powder or the annealed SLM sample"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003887_j.etran.2020.100080-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003887_j.etran.2020.100080-Figure6-1.png",
        "caption": "Fig. 6. Rotor shape of flat, V-shape, and circular arc flux barrier and PM poles [55].",
        "texts": [
            " [52] optimized the length and thickness of PMs, and proved that with similar rotor structure, reduced PM thickness can still attain similar performance, though with a slightly lower power factor. A 40 kW traction motor was presented with 26 Nm/L torque density [53], but it was still inferior to NdFeB IPM machine. The shape of the PMs and flux barriers also showed great importance to the PMASynRM design. S. Musuroi et al. in Ref. [54] presented a V-shape ferrite PMASynRM since it has simple flux barriers and rectangular PM poles. K. Hayakawa et al. investigated the influence of different flux barrier shape, as shown in Fig. 6, and results revealed that circular arc structure could substantially improve the maximum torque and power output with three flux barriers [55]. It should be noted that ferrite PM was brittle especially when large thin arc shape was used. Y. Matsumoto et al. in Refs. [56] proposed a structure cutting the third flux barrier into three parts, so as to reduce the mechanical stress on the rotor. But due to the flux leakage in the ribs, demagnetization could be observed the PM edge near the ribs. When taken massive production in consideration, long arc shape PMs were more expensive to produce and difficult to assemble"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000644_j.1538-7305.1965.tb04141.x-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000644_j.1538-7305.1965.tb04141.x-Figure4-1.png",
        "caption": "Fig. 4 - Series connection of two voltage-controlled resistors.",
        "texts": [
            " Indeed, the well known characterization of continuous functions of bounded variation\" implies that any voltage-controlled resistor characteristic, i (t) = CR (v(t),t), that is continuousand of bounded variation in v can beobtained by connecting in parallel two one-to-one resistors whose characteristics arecontinuousand strictlymonotonic. (Oneresistor is monotonically increasing and the other is monotonically deereasing.) A dual statement holds for current-controlled resistors. In fact, there are combined series and parallel connections of oneto-one two-poles that are neither voltage-controlled nor current-controlled. Refer to Fig. 4, which shows the series connection of 91 and 92 . Fig. 5 shows how a voltage-controlled characteristic such as 91 may be obtained by connecting in parallel two one-to-one resistors. Putting the two resistors of characteristic 91 and 92 in series, we obtain (see Fig. 4) the characteristic 93, which is neither voltage-controlled nor currentcontrolled. A (possibly time-varying) fiue-cordrotled. inductor is a voltage-controlled two-pole and, dually, a (possibly time-varying) charge-controlled capacitor is a current-controlled two-pole. If the inductor is flux-controlled, the current i is a function of the flux \u00a2: i(t) = r(lp(t),t). If v(;) is the voltage applied to the inductor and lpo is the flux through it at the initial time to, then by Lenz's law tp(t) = jt v(t')dt' + tpo to hence, i(t) = r (1: v(t')dt' + tpo, t) for all t"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000058_s0022112077001669-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000058_s0022112077001669-Figure2-1.png",
        "caption": "FIGURE 2. The geometry of the model in a meridian plane, illustrating the body of the organism, the cilia layer and the control surface S.",
        "texts": [
            " (3) In this formulation of the problem, the effect of the cilia on the fluid is represented by certain prescribed boundary conditions on the radial component of velocity u, and on the tangential component of velocity us a t the control surface S. Axisymmetry about the z axis is assumed. Guided by physical observation and mathematical hindsight, we consider the boundary conditions u = -Ue, as 1x1 -+a, (4) u, = u . n = -K(n.e,) on S, (5) us = u . s = -V,(s.e,) on S , ( 6 ) where x is the position vector, the constants V , and are regarded as parameters of the problem, and n and s are unit outward-normal and tangential vectors respectively with the sense of s indicated in figure 2. It is a simple matter to show that n and s are related to e, and the unit radial vector e, by n = [( i - e2)t ze, + (a2 - z2)J e,] (a2 - e2z2)-*, s = ( - (a2 - 22)) e, + (1 - e2)t ze,] (a2 - e2z2)-). (7) (8) Porous spheroidal model for ciliated micro-organisms 263 Physically, for V, > 0 and V, > 0, the situation described by ( 5 ) and (6) is one in which the lateral cilia impart a tangential slip velocity while fluid is sucked into the cilia layer on the anterior and expelled on the posterior side of the organism"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000603_s11460-009-0065-3-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000603_s11460-009-0065-3-Figure7-1.png",
        "caption": "Fig. 7 Type III RC rotorcraft. (a) Trex-450; (b) Lama-V4; (c) PD-100 Black Hornet; (d) Draganflyer",
        "texts": [
            " [5,7\u20139]). Their validity on short-endurance aerial photography has recently been explored by a number of commercial companies (see, for example, AutoCopter Express UAV1) and Flying-Cam2)). 3) Type III forms the smallest group of the RC rotorcraft. Besides small single-rotor helicopters such as Trex-4503) of Align, multiple-rotor helicopters such as coaxial LamaV44) of ESky, PD-100 Black Hornet5) of Proxdynamics, quadrotor Draganflyer6) of Draganfly Innovations, are named brands in this category (see Fig. 7). Because it is tiny in size, ultra light in weight and has very limited payload, constructing the avionic system for this type of rotorcraft is extremely difficult. Special care needs to be taken into consideration on the selection of its power supply, layout of the avionic system, choice of its processing and sensing units, and vibration isolation. The key features of these three types of the RC rotorcraft platforms are intentionally summarized together in Table 1 for easy comparison and reference"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001842_s00170-015-7647-4-Figure18-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001842_s00170-015-7647-4-Figure18-1.png",
        "caption": "Fig. 18 a Detail mandrel top with integrated thermocouples horizontal cut through cooling channel in mandrel top and b detail mandrel top with integrated thermocouples",
        "texts": [
            " Figure 17 shows one example from the extrusion of the aluminum alloy EN AW-6082 with a relatively high profile\u2019s exit speed of 18 m/min. The extrusion ratio is R=50. Despite the high speed, the profile\u2019s exit temperature can be reduced by approximately 15 \u00b0C by water cooling of the mandrel. At the same time, the extrusion forces increase moderately by 0.3 MN in maximum (approx. 10 %). The coolant exits the die with a constant temperature of 60 \u00b0C. The die temperatures can be reduced significantly from around 590 \u00b0C (without cooling) down to values between 400 \u00b0C (measured close to the coolant outlet, Fig. 18) and 240 \u00b0C (measured close to the coolant inlet Fig. 18) by the concentrated and localized die cooling (Fig. 17). In order to have a more uniform die temperature around the die bearings, a cooling channel with variable cross sections (in this case, with a widening of the cooling channel close to the coolant outlet in order to counter the preheated coolant) can be used in future. This little change in geometry, which could not be manufactured by conventional manufacturing methods, will not lead to any additional costs when using additive manufacturing technologies"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000369_iros.2010.5649095-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000369_iros.2010.5649095-Figure2-1.png",
        "caption": "Fig. 2. The geometry for the intersection set",
        "texts": [
            " It thus follows that the geometry of the intersection problem is invariant with respect to the orientation of the line joining the centres of the two spheres. The geometric solution for the possible poses is thus calculated with the normalized wrist position placed vertically above the base joint. Solutions for other orientations can be easily obtained by applying an appropriate normalizing rotation matrix. The geometry of the \u201dgenerating circle\u201d can be easily computed. Given two links of length L1 (line OA) and L2 (line BA), separated by a distance \u2018d\u2019 between them as shown in Figure 2. Then, the intersection set (denoted in the plane by the point A, or the elbow-joint) is described by the centre lying at point C, at a distance dC from point O and the radius RC (line CA). The angles 6 COA & 6 CBA subtended by the intersection point A at the wrist position and the base from the vertical axis are represented by \u03b11 and \u03b12 respectively. From the geometry of the problem, these angles can be easily obtained as \u03b12 = cos\u22121 [ (d2 + L2 2 \u2212 L2 1)/(2dL2) ] , and \u03b11 = sin\u22121 [L2sin(\u03b12)/(L1)] (3) Further, the dC and RC follow as dC = L1cos(\u03b11) = d\u2212 L2cos(\u03b12) and RC = L1sin(\u03b11) = L2sin(\u03b12) (4) It is obvious that if [ (d2 + L2 2 \u2212 L2 1)/(2dL2) ] > 1, no solutions are possible for \u03b12, implying a null set condition",
            " The constraints on \u03c6 for the second variable can be determined from (Crot(RLJ , DLJ , \u03c6)/d3) \u2265 cos(\u03b82L) = cos(\u03b82U ) (22) The fourth joint variable is the elbow angle and it depends only on the normal distance between the base joint and the wrist joint as discussed in Fact 2. From the earlier developments it is seen that the elbow angle for the outelbow pose can be simplified to get \u03b84 = \u03b8U + \u03b8L, = (\u03b11 + \u03b12) + tan\u22121(a3/d3) + tan\u22121(|a4|/d5) (23) Then the possible minimum and maximum values for (\u03b11 + \u03b12) can be obtained as (\u03b11 + \u03b12)min = \u03b84L \u2212 [ tan\u22121(a3/d3) + tan\u22121(|a4|/d5) ] , (\u03b11 + \u03b12)max = \u03b84U \u2212 [ tan\u22121(a3/d3) + tan\u22121(|a4|/d5) ] (24) The normal distances for which these conditions would be met can be evaluated by applying the Lambert\u2019s cosine law for 6 BAO in Figure 2. d = \u221a L2 1 + L2 2 \u2212 2L1L2cos(\u03c0 \u2212 (\u03b11 + \u03b12)) (25) The corresponding minimum and maximum values for the normal distance d can be easily obtained as 0.2721m and 0.7343m respectively. It can be shown that the out-elbow poses are feasible only for 0.2721 \u2264 d \u2264 0.8552; and the in-elbow poses are possible only for 0.7343 \u2264 d \u2264 0.8552. As mentioned earlier, the wrist elevation angle can also be computed as the in-plane angle between the tool z-axis (TRz) and the vector from the upper-joint to the wrist position"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000050_nme.2959-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000050_nme.2959-Figure5-1.png",
        "caption": "Figure 5. One-dimensional solidification of a semi-infinite elastic\u2013perfectly plastic body.",
        "texts": [
            " In order to share the same nodes in both problems, a mesh of hexahedra for the mechanical model is generated. Then, the thermal FE mesh is obtained by splitting each hexahedron into six tetrahedra. Thermal stresses calculated by this model have been validated by comparison with the thermal stresses computed in the semi-analytical solution developed by Weiner and Boley [17] for one-dimensional solidification of a semi-infinite elastic\u2013perfectly plastic body after a sudden decrease in surface temperature. These conditions are typical of those appearing in a continuous casting machine (see Figure 5). Copyright 2010 John Wiley & Sons, Ltd. Int. J. Numer. Meth. Engng 2011; 85:84\u2013106 DOI: 10.1002/nme The thermal problem corresponds to the Neumann classical phase change one-dimensional problem with uniform initial temperature Ts (solidification temperature) and fixed temperature Tw<Ts on one end, with T o =Ts \u2212Tw being defined as the temperature drop. An elastic\u2013perfectly plastic material model has been used for the mechanical problem, with a constant Young\u2019s modulus E and yield stress y varying linearly with temperature: y(T )= o y Ts \u2212T T o , T Ts (19) where o y is the yield stress at temperature T w"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000892_tie.2013.2257135-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000892_tie.2013.2257135-Figure2-1.png",
        "caption": "Fig. 2. Forces and moments acting on the UH.",
        "texts": [
            " In Section IV, the AGA is utilized to fine-tune the parameters of the dynamic model based on the actual flight data. Verification of frequency and time domains, as well as flight control experiments, is implemented to test the validity of the identified model in Section V. Finally, conclusions are provided in Section VI. As shown in Fig. 1, the UH used in this paper is upgraded from a radio-controlled hobby helicopter. The physical parameters of the UH are depicted in Table I. The UH is powered by a piston engine running on a mixed-model engine fuel. The UH is free to rotate and translate in the air. Fig. 2 shows the key forces acting on the six-DOF UH [23]. Origin O is the center of gravity of the UH, and XB , YB , and ZB form the body reference frame; u, v, and w are the velocities in the XB , YB , and ZB directions, respectively; \u03c6, \u03b8, and \u03c8 are the Euler angles; p, q, and r are the angular rates along the XB , YB , and ZB axes, respectively; X , Y , and Z are the forces acting on the center of gravity of the UH, whereas L, M , and N are the moments in XB , YB , and ZB , respectively; and x, y, and z form the displacement of the center of gravity of the UH from OI in the XI , YI , and ZI axes of the inertial frame, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001130_j.jsv.2011.12.025-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001130_j.jsv.2011.12.025-Figure7-1.png",
        "caption": "Fig. 7. Gear immersion.",
        "texts": [
            " This dissipative source is controlled by the gear geometry, the lubricant properties and quantity, and the operation speed. The power losses are well documented in the literature [38,39] and a detailed investigation certainly exceeds the scope of the present paper. Consequently, the churning losses are integrated in the model by means of Eq. (36), derived from the Changenet and Velex [39] formulation Ci \u00bc 0:5rl _yi R 3SCl (36) where rl is the fluid density (kg/m3) and S is the wet surface of the gear wheel (m2) S\u00bc R2 \u00f02bi sin\u00f02bi\u00de\u00de\u00fe2RFbi\u00fe 2NiFbihtooth \u00f0pcosj\u00de htooth is tooth height (m), bi (rad) is illustrated in Fig. 7, Cl is a dimensionless torque (Eq. (37)) Cl \u00bcc1 F 2R c2 ht 2R c3 V0 \u00f02R\u00de3 !c4 Rec5 Frc6 (37) Re\u00bc _yR2 u (38) where Re is the Reynolds number, Fr is the Froude number, ht is the immersion depth of the gear (m), Vo is the lubricant volume (m3), ci are constant coefficients (Table 2), g is the gravity (m/s2), n is the kinematic viscosity (m2/s), and the n value is corrected to account for the temperature. Table 2 gives the ci factor values. Two sets of factors referring to different speed ranges are needed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003698_j.addma.2020.101134-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003698_j.addma.2020.101134-Figure1-1.png",
        "caption": "Fig. 1. Schematic illustration of the test samples: BD, ND, and TD are the building direction, normal direction, and transverse direction respectively. V and H samples were used for tensile testing and I samples were used for in vitro corrosion tests.",
        "texts": [
            " The key processing parameters included the laser power P, scanning speed Vs, hatch spacing Hs, and layer thickness Ds, which together determine the laser energy input. Based on our previous studies, pure Zn slabs measuring 10\u00d710\u00d750mm were built in the vertical and horizontal directions using the following optimized parameters: P=80W, Hs=70 \u03bcm, and Ds=30 \u03bcm. Three different scanning speeds were used (300, 500, and 700mm/s). Further details regarding the powder and LPBF processing methods can be found in our previous works [25\u201327]. As shown in Fig. 1, the Zn slabs were cut into tensile specimens with a width of 5mm and gauge length of 25mm, according to the ASTM 8E standard. The tensile samples were labeled as V1, V2, V3 and H1, H2, H3, where V and H indicate vertical and horizontal BD, and 1, 2, and 3 correspond to the scanning speeds of 300, 500, and 700mm/s, respectively. The surfaces of the samples were cleaned and polished before testing. A tensile test was conducted using a universal testing machine (MTS C45105) at a constant speed of 1.5mm/min at room temperature (\u223c20 \u00b0C). Three samples were tested to obtain the average value for each condition. After tensile testing, the fresh facture surfaces were observed using a scanning electron microscope (SEM; Zeiss Gemini). An electrochemical workstation (Metrohm AG, Switzerland) was used to perform electrochemical tests of AM samples. The test samples were cut into square sheet (10\u00d7 10\u00d72mm). The exposed circle faces (diameter of 6mm) were perpendicular to the ND direction as Fig.1 shows, and were carefully polished by emery papers and then by plasma. A three-electrode system with a working electrode (pure Zn sample, 10\u00d710\u00d72mm3), reference electrode (saturated calomel), and counter electrode (platinum) was used. The open-circuit potential was measured as the sample was immersed for 1 h in Hank\u2019s solution. Electrochemical impedance spectroscopy (EIS) was performed over a frequency range of 10\u22122\u2013105 Hz with a perturbation of 10mV. The potentiodynamic polarization (PDP) was determined at a scan rate of 1mV/s. After testing, a CrO3 solution was used to remove the corrosion products, and SEM was used to examine the corrosion morphology. Immersion tests were performed on AM samples in Hank\u2019s solution (at 37 \u00b0C, pH 7.4) for 21 days, in accordance with ASTM-G31-72. The test sample were cut into square sheets (10\u00d7 10\u00d72mm3). The square surfaces (10\u00d7 10mm2) were perpendicular to the ND direction as Fig.1 shows, and the exposure ratio was 20mL/cm2. The pH was recorded using a pH meter (Mettler FiveEasy pH FE20 K) at selected times. After immersion, the samples were cleaned using distilled water, and the corrosion surface was observed using SEM. The corrosion products were further examined using energy-dispersive spectroscopy (EDS) and X-ray diffraction (XRD). Inductively coupled plasma optical emission spectroscopy (ICP-OES; iCAP6300, Thermo Scientific, USA) was used to examine the ion concentration of the Hank\u2019s solution"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002007_j.phpro.2015.11.052-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002007_j.phpro.2015.11.052-Figure3-1.png",
        "caption": "Fig. 3. 3D models of single track test piece (A) and hatch test piece (B).",
        "texts": [
            " The high speed camera took 5000 fps and the resolution of the images was 600 x 400 pixels. Polished sections were made from the single track test pieces such that the pieces were first cut in half in the longitudinal direction and then polished. Etching of the test pieces was made with electro etching using Kalling\u2019s 2 reagent as etchant. The polished sections were photographed with an Infinity digital camera in Olympus optical microscope. The penetration depth and width of the single track beads were measured with AxioVision LE64 microscopy software. The test pieces (shown in Fig. 3) were fabricated for altering the heat input of single tracks and one single layer to be able to determine the effect of heat input on the single track and layer formation and penetration depth. Single tracks were made on top of 20 x 40 x 15 mm plane surfaced bulk piece, test piece A in figure 3. Different heat input values used in this test are marked as St-3 to St3 and they are explained in Table 2 and 3. The single hatched layer tests were made with 200 W laser power. The test piece for this test is shown in figure 3 B. Hatch tests on cube shaped test piece are 5 mm x 5mm squares which were exposed with input values shown in Table 2. The energy density input in this study was calculated according to equation 1. (Schleifenbaum et al. 2010) hLTv P ED (1) In case of single tracks, the hatch distance is set equal as laser beam spot size. (Ciurana et al. 2013) The intensity of the laser beam was defined according to equation 2. (Steen, Mazumder 2010) LaserA P I (2) The laser interaction time was defined as equation 3 shows"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000083_j.mechmachtheory.2009.01.010-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000083_j.mechmachtheory.2009.01.010-Figure6-1.png",
        "caption": "Fig. 6. Geometric conditions for the line contact of a cylindrical gear pair.",
        "texts": [
            " The condition of line contact, which is necessary for designing gear drives in approximate line contact, can be obtained by substituting sinw = 0 in Eq. (17), whereby the parameter bL for positioning the line of action cannot be determined definitely. This means geometrically that there are an infinite number of lines of action with the same direction, i.e. we may have a plane of action, and the teeth are engaged in line contact. When sinw = 0, Eqs. (16) and (17) are rewritten as R \u00bc bCb2 \u00fe bCb1; \u00f030\u00de a \u00bc rCb1 \u00fe rCb2: \u00f031\u00de The geometric meaning of Eqs. (30) and (31) is explained in Fig. 6, where a common tangential plane (the plane of action), and the base cylinders of the skew gear drive, are tangential to each other [5,13]. Another design condition is the consideration of edge contact. Edge contact occurs when the line of action is shifted outside of the face-width from the theoretical position caused either by the assembly errors or by the manufacturing errors. The shift of the line of action along the gear axis can be served as an evaluation criterion for edge contact. As the definition in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003313_j.mechmachtheory.2019.03.012-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003313_j.mechmachtheory.2019.03.012-Figure3-1.png",
        "caption": "Fig. 3. Schematic representation of the simulated system. DOF locations and numbers are noted, with DOFs 3 to 6 referring to equivalent tooth angles.",
        "texts": [
            " Shafts are described using a single torsion finite element per shaft, incorporating mass, damping and elasticity properties. As far as damping is concerned, a typical damping ratio of 2% is selected, for the single eigenmode of each shaft [7] . This value refers to an isolated shaft, i.e. it does not take into consideration other modeling elements (gear stages, flywheels) that are attached to it. Flywheels on the other hand are modeled using their moment of inertia. The proposed modeling methodology is utilized to examine the response of a typical, medium power transmission, which is described in Fig. 3 , both through linear analysis and non-linear simulation. The system comprises the motor, which is modeled as an angular velocity source imposed on the first DOF, the input shaft, a gear stage, the output shaft, and the flywheel, on which an opposing torque is applied. Two variants of the proposed system are considered, in order to further investigate the influence of tooth eigenvibrations on its response. In the first variant, gears with a high number of smaller size teeth are used (drivetrain A), while in the second variant, tooth number is reduced and tooth size is increased (drivetrain B)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001249_s10544-014-9876-y-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001249_s10544-014-9876-y-Figure2-1.png",
        "caption": "Fig. 2 The microfluidic device at a glance; (a) Expanded view of the device comprising of the top and bottom plexiglass support layers, a third plexiglass layer for supporting the PDMS layer covering the hydrogel device layer. The hydrogel device consists of three parallel channels, each 500 \u03bcm wide and spaced 500 \u03bcm apart; (b) Photograph of the hydrogel device layer (top view) with a U.S. 25 \u00a2 coin for comparison; (c) Functional testing of the assembled microfluidic device using colored test fluids",
        "texts": [
            " An inverted fluorescence microscope with a 63\u00d7DIC objective was used to verify co-localization of bacteria and microparticles and count the number of bacteria attached to the microparticles (Fig. 1d). 2.2 Microfluidic device fabrication and assembly We have recently reported a diffusion-based poly (ethylene glycol) diacrylate (PEG-DA) microfluidic chemotaxis assay device that is fabricated through a one-step photolithography process (Traore andBehkam 2013). A schematic of the device is illustrated in Fig. 2a. Briefly, 10 % (v/v) PEG-DA hydrogel (MW 700 Da) precursor solution in phosphate buffered saline (PBS) was mixed with 10 % (w/v) Irgacure\u00ae 2959 photoinitiator solution (in 70 % ethanol) at a 1:20 ratio to make the hydrogel solution. Polydimethylsiloxane (PDMS, Sylgard 184), prepared according to manufacturer\u2019s instructions, was spin-coated on a clean 1 mm glass slide to make a 300 \u03bcm thick PDMS layer. The PDMS-coated glass slide was cured on a hot plate at 100 \u00b0C for 45 min and then the PDMS was cut into a square shape frame to build an enclosure for the hydrogel solution",
            " The hydrogel device was then soaked in DI water overnight to remove any excess photoinitiator. A 4 mm thick square shape PDMS layer was made in a petri dish, punched to pass the tubes through and placed directly on top of the hydrogel pattern in the PDMS frame to provide sufficient support for the hydrogel and prevent fluid leaking. Two plexiglass support layers on top and one underneath the glass slide were used to provide sufficient pressure for the assembly of the device. The hydrogel device layer and the assembled microfluidic platform are shown in Fig. 2b and c, respectively. 2.3 Bacteria/bacteriabot chemotaxis assay To eliminate the effect of fluid flow on the bacteria and BacteriaBot chemotaxis, the flow-free microfluidic device described above was used to generate quasi-steady chemical concentration gradients. L-aspartic acid, a known chemoattractant for E. coli K-12, at spatially varying and temporally constant concentration gradients was used to direct the motility of bacteria and BacteriaBots. First, motility buffer solution was manually loaded in the center channel and the corresponding tube was clamped after filling up the channel to prevent any fluid flow and liquid evaporation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002004_1.4028532-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002004_1.4028532-Figure5-1.png",
        "caption": "Fig. 5 Rigid subdivision of CC pattern. (a) S 5 1, 2, and 4 divisions, (b) straight-line segments between subdivided points, and (c) K rigid strips.",
        "texts": [
            " This is demonstrated next for a CC-Miura pattern. The CC pattern is split into S strips for every row of panels in the prismatic base pattern, where S is termed the division number. Divisor lines are straight and parallel to straight-crease lines on the base Miura pattern. The pattern now possesses a total of s longitudinal crease lines where s\u00bc S(m \u2013 1)\u00fe 1. Specifying S\u00bc 1 creates a geometry corresponding to the prismatic base pattern. A higher S gives a closer approximation of the curved surface, shown in Fig. 5(a). Unless otherwise stated, all CC-patterns in this paper have S\u00bc 4. The spacing distribution between split crease lines can be chosen as desired. In the simplest case, the lines can be set to be equidistant in the y direction. However, this paper adopts a slightly more complex spacing scheme in which crease lines split the elliptical curve into regular tlim/S angular divisions of the parameter t, shown in Fig. 5(b). This was seen to give a more regular approximation of the original elliptical surface than a laterally equidistant division scheme. Vertices Wk,j are calculated at the intersection of the kth divided longitudinal crease lines and the jth zigzag crease (k\u00bc 1, 2,\u2026, s, j\u00bc 1, 2,\u2026, n). Note that the k, s, and Wk,j terms have replaced the i, m, and Vi,j terms used to define prismatic pattern vertices in Ref. [21]. In a 3D Cartesian coordinate system with origin and orientation shown in Fig. 5(a), the coordinate vector (xk,j, yk,j, zk,j) of Wk,j can be given as xk;j \u00bc \u00f0j 1\u00dea sin\u00f0gA;set=2\u00de \u00fe u0\u00f0tk\u00de (16) yk;j \u00bc \u00f0k k 1\u00de b sin\u00f0gZ;set=2\u00de S \u00fe v0\u00f0tk\u00de (17) zk;j \u00bc 0 for odd j a cos\u00f0gA;set=2\u00de for even j (18) where u0(tk) and v0\u00f0tk\u00de are coordinates of the subdivided elliptical curve obtained by substituting tk\u00bc tlim(k*/S \u2013 1) into Eqs. (9) and (10). Note that the subdesignation k*\u00bcmod(k \u2013 1, 2S), giving 0 k*< 2S, is used where it gives a more concise parametrization. The subscript \u201cset\u201d denotes a pattern variable obtained from prismatic base geometry at the folded configuration used to set the CC pattern",
            " Fortunately, these parameters can be simply derived. Each Miura strip is one-plate wide, that is to say has mK\u00bc 2, and possesses the same number of panels in the longitudinal direction as the prismatic base pattern, nK\u00bc n. Here, the superscript K denotes a parameter for the Kth rigid strip, and nonsuperscripted parameters denote a parameter from the prismatic base geometry. All strips share two additional parameters with the prismatic base pattern: longitudinal edge angle gK A \u00bc gA and side length aK\u00bc a, shown in Fig. 5(c). The remaining two parameters for each segment, lateral sector angle /K and side length bK can be calculated from the vertex coordinates with the following equations: bK \u00bc Wk\u00fe1;1 Wk;1 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0xk\u00fe1;1 xk;1\u00de2 \u00fe \u00f0yk\u00fe1;1 yk;1\u00de2 q (19)Fig. 4 Crease pattern unrolled from a folded configuration. (a) Perpendicular projected ellipse and (b) unrolled pattern"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002270_tmag.2017.2706764-Figure12-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002270_tmag.2017.2706764-Figure12-1.png",
        "caption": "Fig. 12 Rotor and stator of the series VFM prototype machine.",
        "texts": [
            " The z-axis flux density tends to grow with the increase of current, as the saturation in laminations is more severe and thus the flux is more likely to flow through the end shaft. Meanwhile, the ratios between 3-D FE and 2-D FE predicted average torques are included in Fig. 11. The difference between 3-D and 2-D predictions becomes larger with current increasing, which corresponds to the variation of end leakage flux and reveals that the end effect is more significant. In order to verify the foregoing FE analyses, a prototype machine is manufactured, as shown in Fig. 12, in which the stator and armature windings of Prius2010 IPM machine are inherited but a new rotor with CPMs and VPMs is employed. The CPMs have been fully magnetized while the VPMs are non-magnetized before fitting into the rotor. Id= +430A, which 0018-9464 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. is the maximum available current of the inverter, is applied to magnetize the VPMs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001449_s10846-013-9955-y-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001449_s10846-013-9955-y-Figure3-1.png",
        "caption": "Fig. 3 Pure rolling motion",
        "texts": [
            " where Cx0,Cy and Cn are the aerodynamic coefficients involved for the lateral dynamics. These coefficients are obtained by considering small angles and with low airplane speed. The following equations describe the dynamics for the roll motion: \u03c6\u0307 = p (16) p\u0307 = L\u0304 Ixx (17) V\u0307y = Fy m + pVx (18) V\u0307x = Fx m \u2212 pVy (19) where p denotes the roll angular rate, L\u0304 is the rolling moment, Ixx represents the inertia for the x-axis and \u03c6 describes the roll angle. The aerodynamic effects on the airplane are obtained as they have been obtained in the yaw motion. In the Fig. 3, it is observed that \u03b4a represents the deviation of the ailerons. In the case of the roll moment, this corresponds the expression L\u0304 = q\u0304SbCL, where b is the wing span of the airplane and CL represents the aerodynamic coefficient of the roll moment [3]. In this section, we describe the nonlinear controllers that have been designed in order to control the fixed-wing UAV. 3.1 Altitude Control In order to design the altitude control law, we consider the equations that define the longitudinal dynamics, except the Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000887_tbme.2012.2216262-Figure10-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000887_tbme.2012.2216262-Figure10-1.png",
        "caption": "Fig. 10. Position of pressure sensor assembly inside a stainless steel tip.",
        "texts": [
            " The telemetric unit is then entirely covered with epoxy adhesive to protect the CMOS components from light incidence and damage (d). D. Implant Housing The tip chip is integrated into a stainless steel capsule with an outer diameter of 1 mm before a small tube made from polyurethane is attached to the housing. By placing the pressure sensor ASIC exactly below laser cut pressure inlets, it is ensured that the pressure transfer inside the capsule toward the sensitive membrane is optimal. The CAD drawing in Fig. 10 exemplarily shows the pressure sensor assembly on the polyimide connection tape inside a metal form with three circular openings above the pressure sensing region. The damping of the pressure signal between pressure inlet and capacitive membranes is reduced to a minimum because of the thin silicone filling in this location. Afterward, the polyurethane tube holding the microcable and the steel form are filled with silicone from proximal to distal. Air-free filling of the implant is crucial to enable highly dynamical measurements and to prevent the circuitry on the implant from being corroded by electrochemical processes in humid or liquid environment which will shorten the lifetime of the implant"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001758_jrproc.1956.275102-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001758_jrproc.1956.275102-Figure3-1.png",
        "caption": "Fig. 3-The prototype transfluxor.",
        "texts": [
            " The primning pulses must be of sufficient magnitude to provide the required magnetizing force around the small aperture, but insufficient to provide it around both apertures. Inherent Characteristics The core of the transfluxor for which the characteristics are given below was made of magnetic ceramic material (manganese-magnesium ferrospinel-30 per cent MnO, 30 per cent MgO, 40 per cent F203), of composition and processing identical to those used for memory cores. The dimensions are shown on Fig. 3. The knowledge of the actual amounts of flux set in leg 2 and leg 3 by a pulsed magnetomotive force applied to leg 1 can be used to evaluate the idealized explanation of the operation given above as well as to predict the detailed operation. These inherent setting properties, illustrated on Fig. 4, were obtained as follows: leg 1 was subjected first to a relatively large blocking pulse of 5 ampere turns (AT) of magnetomotive force and then to a setting pulse the amplitude of which is the abscissa of the plot",
            " 4 only approximate the sectioixally linear curves predicted by the above idealization, because the real material is characterized by a family of hysteresis loops deviating appreciably from the ideal rectangular shape. The \"rounding-off\" of the corners and the asymptotic saturation characteristics are, therefore, not surprisinig. It is worth noting that leg 3 exhibits a substantial flux setting before leg 2 reaches saturation and also that its saturated value is smaller because the width of this leg happens to be somewhat narrower than that of leg 2 (see Fig. 3). OPERATING CHARACTERISTICS The amount of flux which is interchanged between legs 2 and 3 for a given setting by priming and driving The setting characteristics for asymmetrical energization shown in Fig. 5, can be explained as follows: the flux change 4ls in leg 1, set into it by the setting pulse, will divide itself, in general, between legs 2 and 3 where the changes of flux 42s and 43s will be produced (01is =-2sS+03S). When the set flux 4ls is smaller than the maximum flux containable in the narrowest leg (in this case leg 3, which is slightly narrower than leg 2), the setting is referred to as \"normal"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002291_s11071-018-4364-1-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002291_s11071-018-4364-1-Figure1-1.png",
        "caption": "Fig. 1 North-east-down frame and vessel-fixed frame [26]",
        "texts": [
            " Not only is the requirement for differentiations of intermediate control function vectors removed due to introducing command filters, but also the filtering errors of intermediate control vectors caused by command filters are compensated by means of designed dynamic systems, such that the developed DP control law is computationally simple and the DP control performance is improved. The rest of the paper is organized as follows. Section 2 gives the motion mathematical model of vessels in the DP mode and the control objective. Section 3 details the DP robust nonlinear control design. Section 4 provides the simulations based on a MSS toolbox. Section 5 draws the conclusions. Denote the vessel\u2019s position and orientation in northeast-down frame (Fig. 1) as \u03b7 = [x, y, \u03c8]T and the vessel\u2019s velocities in vessel-fixed frame as \u03c5 = [u, v, r ]T, respectively. The motion mathematical model of the vessel with thruster system dynamics in the DP mode is [27\u201329] \u03b7\u0307 = J(\u03c8)\u03c5 (1) M\u03c5\u0307 = \u2212D\u03c5 + \u03c4 + d(t) (2) \u03c4\u0307 = \u2212Atr\u03c4 + Atr\u03c4 p (3) where J(\u03c8) is the following transformation matrix J(\u03c8) = \u23a1 \u23a3 cos\u03c8 \u2212 sin\u03c8 0 sin\u03c8 cos\u03c8 0 0 0 1 \u23a4 \u23a6 (4) with J\u22121(\u03c8) = JT(\u03c8) and ||J(\u03c8)|| = 1. || \u00b7 || represents the two-norm. M = MT \u2208 R3\u00d73 denotes the positive-definite inertial matrix with hydrodynamic added mass"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001968_978-94-007-6101-8-Figure4.1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001968_978-94-007-6101-8-Figure4.1-1.png",
        "caption": "Fig. 4.1 Geometric model of a robot",
        "texts": [
            " The position of a rotational joint will be described by angle \u03d1i , while the position of a translational joint will be denoted as distance di . The structure of segments and joints represents an open robotic chain. One end of the chain is attached to the robot base. On the other side of the chain, there is the robot end-point with robot end-effector, which is usually robot gripper enabling manipulation of object in space. Let us consider a manipulator consisting from (n+1) segments which are connected by n joints (Fig. 4.1). The aim of the geometric robot model is to determine the pose (position and orientation) of the robot end-effector as a function of joint variables. The description of the position and orientation of the gripper with respect to the reference coordinate frame was already discussed in the second chapter. The position of the robot end-point is described by a positional vector connecting the origin of the reference frame to the frame attached to the gripper. We have also learned, how the orientation of the gripper can be expressed either by RPY or Euler angles or quaternions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003800_s40430-020-2208-7-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003800_s40430-020-2208-7-Figure1-1.png",
        "caption": "Fig. 1 The position relationship of cycloidal-pin gear",
        "texts": [
            " In view of this, in order to improve the meshing characteristics and motion accuracy of RV transmission, a meshing contact analysis method of cycloidal gear of RV reducer is proposed by constructing the cycloidal-pin gear meshing transmission model including manufacturing error. This method can accurately obtain the real meshing state of cycloidal-pin gear transmission process, thus providing certain theoretical support and technical means for the profile modification, motion accuracy improvement and bearing contact analysis of RV transmission. According to the working principle of RV cycloidal-pin gear [6], the position relationship of cycloidal-pin gear is shown in Fig.\u00a0 1. The coordinate system Sf (xf , yf ) is introduced that is fixed on the frame, coordinate systems Sp(xp, yp) and Sc(xc, yc) are, respectively, defined for the pin gear and the cycloid gear, and angles 1 and 2 are the rotation angles of the pin gear and the cycloid gear, respectively. Among them, the yc axis passes through the tooth root point T on the cycloid profile, and the yp axis passes through the roller center A of the pin tooth. The coordinate system Sc2(xc2, yc2) is connected with the second cycloid gear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001842_s00170-015-7647-4-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001842_s00170-015-7647-4-Figure9-1.png",
        "caption": "Fig. 9 a Hybrid tensile specimens and cubes in holding device and b hybrid tensile specimen with zoom in the transition zone",
        "texts": [
            " In order to fix and to position the specimens in the selective laser melting machine, holding devices were built. The holding device enables to position all specimens in one horizontal level for the additive manufacturing process and to build them up for each material simultaneously. Besides the hybrid specimens, also entire tensile specimens as references made of the hot working steels 1.2343 and 1.2709 as well as completely additively manufactured tensile specimens made of 1.2344 powder (vertically manufactured, 3800 layers in 28 h, approx. 6 cm3/h) were manufactured. Figure 9a shows the hybrid specimens in the holding device. The parts manufactured additively were fabricated with a small allowance (approx. 0.3 mm) in order to enable, for some specimens, a machining post-processing for avoiding a notching effect by the rough surface resulting from the additive manufacturing process (Fig. 9b). Figures 10 and 11 show micrographs taken from the cubeformed hybrid samples after the additive manufacturing. The samples were cut transverse to the built-up direction, grinded, polished, and etched. The middle pictures show the transition zone. The neighboring images to the left and to the right are each extracted from the middle of the additively or conventionally manufactured half of the specimen. For the materials 1.2343 and 1.2344, the microstructure was exposed with a nitric acid of 5%. According to Yasa et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001150_j.mechmachtheory.2011.10.001-Figure10-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001150_j.mechmachtheory.2011.10.001-Figure10-1.png",
        "caption": "Fig. 10. Physical prototype.",
        "texts": [
            " The output mechanism is floating plate mechanism, which is composed by the quadrate hole in the floating plates, the rollers and the protrudent parts on the cycloid gear and double supporting plates. Compared to the conventional pin-hole output mechanism, the floating plate mechanism has the following advantages: higher efficiency, larger load capacity, continuous motion; simple structure, easy to be manufactured and assembled; the output torque is moment of couple and no force on the eccentric bearing, which can extend the lifetime of the bearing. The 3D model of double-enveloping cycloid drive is as Fig. 9, and the physical prototype is as Fig. 10. The success of trial production of the physical prototype shows that double-enveloping theory can be applied for cycloid drives. Fig. 11 is the experimental test rig for the transmission error test. The test method is using static testing under no load operation condition. The polyhedron prism is connected to the output shaft of the gear reducer, and the output rotation angle can be tested by autocollimator. The rotation angle of the input shaft can be obtained from the stepper motor. During the test, the input shaft is given a certain rotation angle, then the actual rotation angle of the output shaft is tested, and the difference between the actual and the theoretical rotation angle of the output shaft is calculated as the transmission error of this measuring position, which can be represented as Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001114_s10846-015-0231-1-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001114_s10846-015-0231-1-Figure2-1.png",
        "caption": "Fig. 2 The UPAT tri-tiltrotor mechanical configuration and coordinate frames",
        "texts": [
            " The features presented consist substantial improvements or expansions of the progressive work presented in [20, 21], and mark the completion of the required framework for a high-end tiltrotor aerial vehicle w.r.t. its autonomous hovering operation. 2.1 Mechanical Design The system\u2019s mechanical design was realized with the use of Computer-Aided Design (CAD)-software. The body framework which consists of aluminum and carbon-fiber parts ensures structural robustness. The platform, including all on-board components has a mass of m = 2.35 kg. Figure 2 illustrates the utilized North-East-Down (NED) [22] Local Tangential coordinates Plane (LTP) W = {N, E, D}, the BodyFixed coordinates Frame (BFF) B = {Bx, By, Bz}, and the morphology of the platform. As depicted, i \u2192 [1, 2, 3] mark the right, left and tail rotor with respect to the Bx positive axis, dij marks the BFF-j -direction component of the geometric distance from the COM to the i-th rotor\u2019s tilt axis, and hi the height of the i-th rotor\u2019s propeller hub from its tilt axis. Table 1 presents the respective values of the aforementioned geometrical parameters",
            " Thus, in the rotor design, propellers (fixed-blade) are selected, with higher-pitch blades than common hovering multirotors (the sizing is derived for efficient slow-cruising in fixed-wing operation). Additionally, it is noted that the tail rotor requires smaller sizing w.r.t the main rotors, as its usefulness is to provide a counter-acting torque for pitch control while hovering, and its torque lever arm is d3x (d1x = d2x ) w.r.t the COM. Regarding the rotor-tilting mechanism which is highlighted in Fig. 2, it is designed to be easily accommodated on a single-pieced wing axis. The gearreduction implementation provides a sufficiently wide range for the rotor-tilt angle \u03b3i \u2208 [\u221215, 90] deg, and more importantly a low required torque from the servomotor while traveling, and an even lower required holding torque for a static tilt angle (compared to hinged designs). 2.3 Autopilot Design The basis for the UPAT-TTR\u2019s autopilot are its onboard sensorial equipment, consisting of the Global Positioning System (GPS)-enabled XsensMTi-G Attitude and Heading Reference System (AHRS), a MaxSonar HRLV-EZ4 Sonar high-precision distance sensor, 3 USDigital EP4 rotary speed encoders for \u03c9i rotational speed measurement, 3 ADXL345 3-axis accelerometers for \u03b3i rotor-tilt angle measurement, and a downwards-pointed USB camera used for translational velocity estimation via optical flow calculation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002031_tec.2016.2637311-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002031_tec.2016.2637311-Figure4-1.png",
        "caption": "Fig. 4. VFRM winding configurations. (a) External field winding. (b) Dual three-phase winding.",
        "texts": [
            " However, due to the coil back-emf, A2, B2, and C2 have a different 0885-8969 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. polarity between the field and armature windings [4]. Therefore, in order to utilize the integrated windings, they should be divided into two winding sets due to the opposite polarity between the armature winding sets, while the polarities of the dc component are the same. Fig. 4 shows the external field winding and integrated winding configurations. The field windings are connected in series for the external field current control scheme, and the armature windings are connected in Y-connection. For the integrated windings, the divided two winding sets have 180\u030a shift due to the opposite back-emf as shown in Fig. 4(b). To derive the voltage and torque equations in the synchronous dq-axis frame, some assumptions have been made. For simplicity, the dc and fundamental components in inductances are only considered. The magnetic saturation effect is neglected in this paper, but the derived equations can provide a better understanding of the operating principle of VFRMs. A. Voltage and Torque Equations with External Current Configuration In the VFRMs with external field excitation, the voltage equations in the synchronous dq-axis frame can be represented as 0 0 0 0 0 0 d d d d q q q e fa q f f f f v i di dt L i v R i L di dt L M i v i di dt i                                               (1) where vd, vq are the dq-axis voltages; id, iq are the dq-axis currents in the synchronous dq-axis frame; vf and if are the field voltage and current respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000402_1.2959106-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000402_1.2959106-Figure9-1.png",
        "caption": "Fig. 9 Dent location on outer race",
        "texts": [
            " In this investigation, the bearing dynamic simulation starts with having the inner race at rest and exponentially increasing the inner race speed such that after a period of 5 ms the inner race achieves the desired steadystate speed. In order to explicitly describe the effects of dents, the results are divided into different sections dealing with effects of dent size, inner race speed, dent location, and dent cluster. Dent Model The effect of a dent in the dynamic bearing model is demonstrated by simulating a ball bearing containing ten balls with a dent located on the outer race. The dent is positioned to have its axis Fig. 1 on the Y-Z plane at 30 deg from the Y-axis Fig. 9 . In order to clearly demonstrate the effect of a dent on bearing operation, a case of a bearing with 5 m interference was considered i.e., the radius of the inner race plus the ball diameter is 5 m larger than the outer race radius . In this configuration the balls experience the same contact loading condition, as shown in Fig. 10 a . However, in the presence of a dent on the outer race, the contact force exhibits fluctuations indicating vibrations excited due to the dent Fig. 10 b . Note that Figs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000050_nme.2959-Figure11-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000050_nme.2959-Figure11-1.png",
        "caption": "Figure 11. Finite element mesh.",
        "texts": [
            " The x , y and z axes are oriented along the width, thickness and length of the plate, respectively. The coordinate y =0 corresponds to the top surface of the sample, and x =0 corresponds to the symmetry plane. The mesh model has 28 000 eight-node mechanical hexahedral elements with 33 383 nodes and 140 000 thermal tetrahedra sharing nodes with the hexahedra mesh. The heat affected zone (HAZ) was refined locally and coarsened gradually along the transversal and vertical directions, as shown in Figure 11. Copyright 2010 John Wiley & Sons, Ltd. Int. J. Numer. Meth. Engng 2011; 85:84\u2013106 DOI: 10.1002/nme Copyright 2010 John Wiley & Sons, Ltd. Int. J. Numer. Meth. Engng 2011; 85:84\u2013106 DOI: 10.1002/nme A thermoelastic/perfectly-plastic model was used in the analysis. The tensile deformation curves for this material showed extensive plastic deformation with limited work hardening, therefore validating the application of this model [29]. We remark that solid state phase change effects were neglected"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001923_icra.2017.7989452-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001923_icra.2017.7989452-Figure4-1.png",
        "caption": "Fig. 4. Landing cases",
        "texts": [
            " Let equation (1) equals to (2) to get the maximum first order natural frequency. Substitute the known parameter, we can roughly calculate that the length of Beam2 is 2.5 times the length of Beam-1. The effectiveness of this design is verified empirically through our past experiments on older prototypes. When a cross wind is present for hovering or landing, the vehicle needs to tilt its whole body by a proper angle \u03b8 in order to compensate the wind disturbance and maintain its hovering or landing point. Fig. 4 shows three landing cases: on the left is the normal case without cross wind, in the middle is a successful landing case with moderate wind, and on the right is a failed landing case with too strong wind disturbance. If the body is tilted at landing, the whole aircraft pivots around the landing gear contact point due to the moment produced by gravity. The resulting landing will remain stable if the tilt angle \u03b8 is within \u03b3, elsewhere unstable. In our design, \u03b3 = 35\u25e6. Simulation results shown in section III imply that a tilting angle of 35\u25e6 corresponds to wind speed of 6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001150_j.mechmachtheory.2011.10.001-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001150_j.mechmachtheory.2011.10.001-Figure1-1.png",
        "caption": "Fig. 1. Coordinate system.",
        "texts": [
            " In this paper, the new cycloid drive whose conjugated tooth pair is composed by cycloid gear and double-enveloping tooth profile is called double-enveloping cycloid drive, whereas the conventional cycloid drive is also called single-enveloping cycloid drive; the motion which generates the cycloid tooth profile using cylindrical pin tooth as the cutting tool is called the first enveloping motion, whereas the motion which generates the double-enveloping tooth profile using cycloid gear as the cutting tool is called the second enveloping motion. 3. Double-enveloping tooth profile The coordinate systems are established according to the right-hand rule and shown in Fig. 1, where member 1 is the internal wheel andmember 2 is the planetary cycloid gear. The moving coordinate systems ObX1Y1Z1 and OgX2Y2Z2 are rigidly connected to the centers of internal wheel and the planetary cycloid gear, respectively. The fixed coordinate system OXY is connected to the center of internal wheel. In the initial position, the axes X1 and X are coincident, X2 is parallel with X. The axes Z, Z1 and Z2 are parallel with each other. The radius of pin teeth distributed circle is Rz, and the radius of pin tooth is rz",
            " During the first enveloping motion, the pin tooth is used as the cutter tool: when the internal wheel rotates by angle \u03b21 about the axis Z1 in counterclockwise direction, the cycloid gear will rotate by angle \u03b11 about the axis Z2 in the same direction according to the motion relation. During the second enveloping motion, the cycloid gear is used as the cutter tool: when the cycloid gear rotates by angle \u03b12 about the axis Z2 in counterclockwise direction, the internal wheel will rotate by angle \u03b22 about the axis Z1 in the same direction according to the motion relation. The rotation speeds of the internal wheel and the cycloid gear are \u03c91 and \u03c92 , respectively. In Fig. 1, p is the subscript of \u03b1 and \u03b2, where p=1 and p=2 represent the first and second enveloping motion, respectively. According to transmission ratio of the transform mechanism, the rotation speeds and rotation angles have the relationship as the following equation: i \u00bc \u03c92 \u03c91 \u00bc \u03b11 \u03b21 \u00bc \u03b12 \u03b22 \u00bc zb zg : The equation of the original cylindrical pin tooth profile \u03a3(1) can be described in the coordinate system ObX1Y1Z1 as x1 \u00bc rz cos \u03b8 y1 \u00bc Rz \u00fe rz sin \u03b8 z1 \u00bc v 8< : \u00f02\u00de where \u03b8 and v are the parameters of the tooth surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001394_tec.2016.2597059-Figure15-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001394_tec.2016.2597059-Figure15-1.png",
        "caption": "Fig. 15. a) Vector diagram of the PMSM at 1500 rpm with Uph = 180 VRMS, E = 150 VRMS, Iph = 185 ARMS. Per unit values in the figure are Us = 1 p.u., is = 1 p.u., U\u2032s = 0.97 p.u., IsRs = 0.03 p.u., \u03a8s = 0.97 p.u., \u03a8PM = 0.86 p.u., IsLs = 0.46 p.u., b) Vector diagram of the PMSM with the same base values as in (a). Per unit values in the figure are Us = 1 p.u., is = 2 p.u., U\u2032s = 0.95 p.u., IsRs = 0.07 p.u., \u03a8s = 0.95 p.u., \u03a8PM = 0.86 p.u., IsLs = 0.92 p.u.",
        "texts": [
            " \u0394T is the temperature change of tubes\u2019 inlet and outlet temperatures. According to the measurements, cooling oil removed app 3.8 kW heat power at 766 Nm load. The higher torque measurements (above 400 Nm) were performed at a lower speed (300 rpm) because a high load current produces a very high armature reaction. This armature reaction, even at a moderate synchronous inductance absolute value, can lead to a situation where there is not enough voltage at the nominal speed to increase the torque any further, as it can be seen in the vector diagrams shown in Fig. 15. In Fig. 15a we can see that at the speed of 1500 rpm, the PMSM works with the id = 0 control (MTPA control for a non-salient PMSM) and with a sufficient overload capability, whereas in Fig. 15b it is shown that with a higher supplied phase current, a field weakening control should be applied (after the maximum supply voltage has been reached). Further, the armature reaction becomes too high, which reduces the overload capability of the motor to an insufficient value. Thus, with a direct-cooling approach that allows using a very high 0885-8969 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003277_tmag.2018.2839740-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003277_tmag.2018.2839740-Figure8-1.png",
        "caption": "Fig. 8. Prototype of the analyzed machines. (a) Traditional 27-slot/30-pole SPM machine. (b) Stator together with the four-layer winding and CP SPM rotor.",
        "texts": [
            " For the third-harmonic torque component, the CP PM machine with the four-layer winding is reduced by 67% compared with the CP PM machine with the doublelayer winding due to the reduction of the second and fourth harmonics in the back EMFs. Ultimately, the torque ripple of the CP PM machine with four-layer winding is 0.98% higher than that of the traditional SPM machine while 5% lower than the double-layer CP PM machine. In order to verify the suppression principle of even-order harmonics in back EMFs, the 27-slot/30-pole traditional SPM machine and CP SPM machine with the four-layer windings are manufactured and tested. The traditional 27-slot/30-pole SPM machine is shown in Fig. 8(a), while Fig. 8(b) shows the 27-slot stator together with the four-layer winding and CP SPM rotor. Fig. 9 shows the measured cogging torque without armature excitation by locking the rotor at different positions. The measured experiment waveforms and FE waveforms are represented by the suffix MEA and FE, respectively. As shown in Fig. 9, good agreement between the measured and 2-D FE predicted cogging torque can be observed. The phase back EMFs of the 27-slot/30-pole SPM and 27-slot/30-pole four-layer CP SPM machines at 300 r/min without armature excitation are measured and compared with FE results in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001267_tmag.2011.2178100-Figure13-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001267_tmag.2011.2178100-Figure13-1.png",
        "caption": "Fig. 13. The boundary-element model constructed by importing the mesh of the motor from ANSYS 12.1into SYSNOISE 5.6.",
        "texts": [
            " As a result, the accelerations at the frequencies of , , and are almost not affected by the rotor eccentricity. Similarly, in Fig. 12(b), this phenomenon can be observed at the frequencies of (3078 Hz), (4104 Hz), (5129 Hz), and (6155 Hz), respectively. Based on the results in Section IV, this section builds a 3-D boundary-element model to analyze the electromagnetic noise of the motor. An indirect boundary-element model is constructed by importing the mesh of the motor model produced by ANSYS 12.1 into the commercial software SYSNOISE 5.6, as shown in Fig. 13. After skinning the imported mesh to make the boundary-element model more adaptive to calculate the acoustic noise [26], the numbers of the nodes and the elements in the model are reduced to be 4906 and 4788, respectively. The longest length of the elements is meshed to be 3.8 mm to assure that the upper frequency limit of the acoustic model is over 6400 Hz by the rule of six elements per wavelength [26]. As the motor was hung above the ground in the measurement, a symmetry plane reflecting the noise is defined in the boundary-element model to represent the ground (see Fig. 13 ). The sound pressures distributing around the motor can be calculated by applying the accelerations onto the nodes of the boundary-element model in the frequency domain. Moreover, according to the ISO standard [27], the sound pressures were measured in a hemi-anechoic room with dimensions . And the background noises in the room are lower than 10 dB in the frequency range of 120 Hz to 6400 Hz. As shown in Fig. 14, four microphones (B&K type 4187) were located on a hemispherical measurement surface with a radius of 1 m"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000395_j.ymssp.2011.10.014-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000395_j.ymssp.2011.10.014-Figure2-1.png",
        "caption": "Fig. 2. 3D dynamic gear model: (a) global model; (b) pinion and gear degrees of freedom; (c) mesh stiffness modeling in the base plane.",
        "texts": [
            " Lm: Magnetizing (synchronous) inductance. os: Synchronous speed. osl\u00bcos om : where om is the (electrical) angular rotor speed. The electromagnetic torque equation is developed from the electric power supplied to the rotor in the dq0 frame. In relation to the different electrical and magnetic parameters, the electromagnetic torque of the multi-polar induction motor is obtained independently of the angle defining the dq frame as Cem \u00bc pLm Lr \u00f0Cdriqs Cqrids\u00de \u00f03\u00de where p is the number of pole-pairs. The model, described in Fig. 2a is composed of five basic elements: (a) the input and output shafts simulated by twonode classic elements (Timoshenko beam element for bending), (b) a specific pinion-gear element [8], (c) bearings introduced as additional lumped stiffness elements, (d) a motor applying the electromagnetic torque described in (3) to one node of the pinion shaft (input), and (e) a load machine that, for the sake of simplicity, is assimilated to a torsional stiffness element placed at one node of the gear shaft (output). The system dynamic behavior is therefore accounted for by 36 degrees-of-freedom (DOFs), which correspond to the infinitesimal generalized elastic displacements superimposed on rigid-body motions. The pinion-gear pair DOFs are shown in Fig. 2b. Following [8] and [9], the pinion and the gear are assimilated to rigid cylinders connected to flexible shafts. Mesh elasticity is simulated by a distribution of independent stiffness elements along the theoretical lines of contact in the base plane (Wrinckler foundation) as illustrated in Fig. 2c. Each stiffness element is time-dependent as the relative positions of the meshing teeth vary during the pinion-gear rotation. The results of Weber and Banascheck [15] for tooth bending and base displacements have been employed while contact deflections have been introduced via Lundberg\u2019s formula for semiinfinite half-spaces [16]. The equations of motion point to a non-linear parametrically excited differential system of the form [8,17]: M \u20acY\u00feC _Y\u00feK\u00f0t,Y\u00deY\u00bc F0\u00f0t\u00de\u00feFe1\u00f0t,Y\u00de\u00feFe2\u00f0t\u00de \u00f04\u00de with Y\u00bc fv1,w1,u1,f1,c1,y1,v2,w2,u2,f2,c2,y2,v3,w3,u3,f3,c3,y3, v4,w4,u4,f4,c4,y4,v5,w5,u5,f5,c5,y5,v6,w6,u6,f6,c6,y6g T : DOF\u2019s vector M,C,K(t,Y): total mass, damping and time-dependent non-linear stiffness matrix, respectively",
            " The time-dependent possibly non-linear global stiffness matrix comprises the constant stiffness elements associated with the shaft-bearing assembly and more specifically the contributions of mesh elasticity, which are detailed below. Following Velex and Maatar [8], the non-linear gear stiffness matrix can be expressed in terms of a structural vector V(Mij) as K\u00f0t,q\u00de \u00bc X i,j k\u00f0Mij\u00dede\u00f0Mij\u00deV\u00f0Mij\u00deV\u00f0Mij\u00de T \u00f05\u00de and the forcing term generated by tooth shape deviations and errors (including tooth spalls) reads: Fe1\u00f0t,q\u00de \u00bc X i, \u00bc j k\u00f0Mij\u00dede\u00f0Mij\u00deV\u00f0Mij\u00de \u00f06\u00de with: k(Mij): elemental stiffness at cell ij: segment j of contact line i (Fig. 2c). V(Mij): structural vector associated with point Mi j [8]. q\u00bc v2 w2 u2 f2 c2 y2 v5 w5 u5 f5 c5 y5 n oT , pinion and gear DOFs. de(Mij)\u00bce(Mij) e(Mn), (Fig. 2c), which represents the equivalent normal deviation at point Mi j with respect to ideal flanks and accounts for geometrical errors and deviations possibly produced by tooth flank modifications, pits, spalls, etc. The instantaneous contact line positions are determined at every time step and the actual stiffness and shape/error distributions are updated [8]. Following [18] and [19], local faults such as tooth pits or spalls are assimilated to distributions of shape errors in the base plane in both the contact line direction (face width) and the profile direction (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000749_tmag.2011.2169805-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000749_tmag.2011.2169805-Figure3-1.png",
        "caption": "Fig. 3. Static field distribution of the 24/32-pole DSEG. (a) ; (b)",
        "texts": [
            " The slot leakage flux is effectively weakened because of the distance increase of the adjacent stator poles. Fig. 2 shows the typical structure of a 6N/4N-pole DSEG and a 3N/4N-pole DSEG, respectively. A. 2-D FEA The magnetic field distribution and steady-state performance of the machine are analyzed by using 2-D FEM. In the 24/32-pole DSEG, the stator pole-width is no longer equal to the stator slot-width, which is different from the conventional DSEG. Table I gives key parameters of the generator. . Fig. 3 shows the electromagnetic field distribution of the DSEG with different rotor positions when the excitation current is 8 A. In Fig. 3(a), the rotor position angle is zero , and the B-phase flux linkage is at its maximum. While in Fig. 3(b), the B-phase flux linkage has reached the minimum. The variation of the phase flux linkage in the 24/32-pole DSEG is similar to that of the conventional DSEG. Fig. 4 shows the variation curves of the excitation winding inductance of a 24/32-pole DSEG under the different load conditions. It can be seen that the inductance fluctuation of the excitation windings is very little and satisfactory, so high induced voltage of the excitation windings could not be produced. In a load condition, the excitation winding inductance is slightly smaller due to the magnetic saturation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000940_j.aca.2011.11.053-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000940_j.aca.2011.11.053-Figure1-1.png",
        "caption": "Fig. 1. The manufactured CoPC-SPCE electrode on a glass-epoxy substrate.",
        "texts": [
            " Hydrogen peroxide solutions and l-lactate solutions were prepared from 30% and 98% stock solutions, respectively. 2.2. Apparatus and electrochemical measurements Cyclic voltammetric (CV) and amperometric measurements were performed with a PalmSens handheld potentiostat (Palm Instruments BV, Netherlands) at room temperature (25 \u25e6C). All electrochemical experiments were carried out with a sampling unit attached to the manufactured screen-printed carbon electrodes (SPCEs) containing 90 L of 0.1 M phosphate buffer (pH 7.4). A picture of the manufactured electrode is presented in Fig. 1. CV experiments were performed with and without l-lactate solution; the potential range used was \u22120.4/+0.6 V, at a scan rate of 10 mV s\u22121. The amperometric experiments were carried out by applying a constant potential to the working electrode of the biosensor. After the transient current had settled (t = 150 s), 10 L aliquots of known concentrations of l-lactate standard solutions were injected into the sampling unit by micropipette and the sensor response was measured until the resulting current reached a steady state value",
            " Fabrication took place in four rinting steps: (1) carbon ink was printed to form a conducting ayer that also acted as the counter electrodes, (2) Ag/AgCl ink as printed in the positions for the reference electrodes, (3) caron ink containing CoPC was printed on the working electrode o form an activated surface, (4) insulating ink was printed to over the non-working and non-conducting region of the SPCE to efine the working area. After each deposition, the electrodes were ried at 60 \u25e6C for 30 min. The individual CoPC-SPCE was cut from he sheets into size 12 mm \u00d7 25 mm rectangles and the sampling nit composed of white PET (\u2205 9.0 mm, 12 mm \u00d7 12 mm \u00d7 1.6 mm), hich defined the working area and sample volume of 100 L, as bonded on top of each CoPC-SPCE with an epoxy adhesive. n a batch process, inexpensive CoPC-SPCEs with consistent quality ere prepared (Fig. 1). As can be seen from Fig. 1, the working elecrode was a 4 mm-diameter disk, and the auxiliary electrode and g/AgCl reference electrode were large and small portions of a \u2205 .8 mm \u00d7 1.0 mm curved line, respectively. .5. Fabrication of the l-lactate biosensor LOD-FSM8.0/Naf/CoPC-SPCEs) The LOD-immobilized FSM8.0, LOD-FSM8.0 conjugate, was preared as follows [41]: An FSM8.0 powder (100 mg) was added to .0 mL of 10 mg mL\u22121 LOD solution (citrate buffer, pH 4.3). The s oxidized on the CoPC-SPCE surface resulting in a flow of electrons to the working suspension was then shaken for 24 h at 4 \u25e6C to establish an adsorption equilibrium"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002920_tbme.2019.2960530-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002920_tbme.2019.2960530-Figure2-1.png",
        "caption": "Fig. 2. A microrobot navigation platform. (a) A general schematic of the microrobot navigation system. (b) Magnetic field intensity. (c) Magnetic field gradient.",
        "texts": [
            " Section IV presents the experimental results to demonstrate the effectiveness of the proposed approach. Section V presents an overview of translating the proposed research into clinical applications for humans. Lastly, Section VI presents the conclusion of this work. 0018-9294 (c) 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. The microrobot navigation platform is mainly composed of an electromagnetic actuation system and an OCT imaging system (Fig. 2(a)). The electromagnetic actuation system uses selfdesigned iron cores in the gradient magnetic field that ranges from 0 T/m to 20 T/m in the workspace to enable the navigation of microrobots in complex environments. The OCT imaging system detects the position of microrobots in in vivo environments, such as the portal vein of mice. A controller can adjust the current input to each coil and the power-on time in driving a microrobot toward the target position based on the feedback of the detected position information"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003346_j.mechmachtheory.2019.103671-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003346_j.mechmachtheory.2019.103671-Figure2-1.png",
        "caption": "Fig. 2. Left dyad of a four-bar linkage.",
        "texts": [
            " (6) yields the following relations: c\u2032 0 = c0 \u2212 rei\u03bc f e\u2212i(\u03b1+\u03b2), (7-1) c\u2032 1 = c1 \u2212 aei\u03d50 f e\u2212i(\u03b1+\u03b2), (7-2) c\u2032 n = cn e\u2212i(\u03b1+\u03b2); n = 0, 1. (7-3) f In general, the problem of path synthesis for a four-bar mechanism involves nine design variables [a, b, c, d, r, f, \u03bc, \u03b2 , \u03b1] as well as the initial angle \u03d50 of the input link. Therefore, in the analysis of the whole four-bar mechanism, one must solve a complex system of non-linear equations [26]. As is well known, the four-linkage can be divided into two dyads. The left dyad consists of the design variables r, a, f, \u03bc, \u03d50, as shown in Fig. 2. This way of dividing the mechanism allows a system of five equations describing the left dyad to be built and solved, which contains five out of the ten design variables: r, a, f, \u03bc, \u03d50. Substitution of these solutions into the loop closure equations describing the four-bar mechanism yields another system of five equations in the five remaining design variables. As a result, new synthesis equations can be established in two steps. The vector loop equation for left dyad can be written as follows: r + a + f = rP"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000083_j.mechmachtheory.2009.01.010-Figure15-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000083_j.mechmachtheory.2009.01.010-Figure15-1.png",
        "caption": "Fig. 15. Contact stress distribution for the case with end-relief (a/b = 526; applied torque 350 Nm; or total normal force 5173 N): (a) on the contact region (be = 4 mm; ce = 0.02 mm); (b) along the major axis of the contact ellipse.",
        "texts": [
            " Such a contact pattern can be regarded as line contact. According to Eqs. (4) and (5), we analyzed contact stresses for the two different end-relieved cases: (a) the length be = 4 mm, and the amount ce = 0.01 mm; (b) the length be = 4 mm, and the amount ce = 0.02 mm. The corresponding separation of the engaged tooth surfaces can be seen in Fig. 14. The contact stress is analyzed under the load condition: torque 350 Nm or total normal force 5173 N. The numerical results from the presented method are represented in Fig. 15. The contact stress distribution of the end-relieved teeth over the whole contact area in Fig. 15a illustrates the results of the case with be = 4 mm, and ce = 0.02 mm. Fig. 15b shows a comparison of the contact stress distribution along the major axis of the contact ellipse of gear drives end-relieved with different amounts. The results indicate that the end-relief can effectively reduce the concentration of stress at the tooth edges; the overall stress increases about 8% due to the smaller usable face-width. The results enable us to draw the following conclusions: (i) An efficient LTCA approach for gear drives in (approximate) line contact has been developed. This approach has the following advantages: (a) A comparison of the calculated results from the presented method with those obtained by FEM analysis has a relative deviation of less than 5%"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001331_tmag.2014.2310179-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001331_tmag.2014.2310179-Figure3-1.png",
        "caption": "Fig. 3. Open-circuit magnetic field distributions of machines without tooth tips. The rotor position is where the phase A has its maximum flux linkage. (a) UNET (12/10). (b) Modular (12/10). (c) UNET (12/14). (d) Modular (12/14).",
        "texts": [
            " Similar phenomena can be observed for the UNET machines with the slot number higher than the pole number, that is, 12-slot/10-pole, except that its slot pitch is lower than its pole pitch. This in turn explains why the windings must be wound on the wider teeth to achieve a higher winding factor. Apart from the influence of flux gaps and UNET on winding factors, they also have a significant impact on air-gap flux density towing to the PMs. This is particularly the case for flux gaps, which modify both the air-gap permeance and the flux paths in the stator iron core (Fig. 3). By way of example, only the open-circuit magnetic field distributions of the UNET and modular machines without tooth tips are given. However, those of the UNET and modular machines with tooth tips are similar. Moreover, the open-circuit magnetic field distributions of the equal teeth machines are similar to that of the UNET ones. Therefore, they are not shown here to avoid duplication. For different \u03b20, the flux densities because of the PMs against angular position, in the middle of the air-gap, have been calculated",
            " The previously mentioned influences of flux gaps and UNET widths on winding factor and air-gap flux density owing to the PMs will be mainly reflected in the flux linkage. Without considering the flux leakage and flux focusing/defocusing effect, the flux linkage is directly determined by the winding factor and the air-gap flux density because of the PMs [15]. However, as a consequence of the flux gaps in the modular machines, the flux path in stator iron core is significantly modified. Therefore, the flux gaps will have an extra influence on flux linkage compared with UNET widths. With the results shown in Fig. 3, different phenomena have been observed for modular machines with different slot/pole combinations. For the modular machines with the slot number higher than the pole number, that is, 12-slot/10-pole [Fig. 3(b)], the flux gaps prevent part of flux of adjacent phases (phase B) from getting into the phase A. As a result, compared with the UNET (or ET) machine [Fig. 3(a)], less flux crosses through phase A and its flux linkage decreases. Therefore, the flux gaps have a flux defocusing effect. Besides, this effect is independent of \u03b20. On the contrary, for the modular machines with the slot number lower than the pole number, that is, 12-slot/14-pole [Fig. 3(d)], the effect is opposite. The flux gaps push an extra part of flux to get into the phase A. However, without flux gaps, this extra part of flux either does not cross through stator yoke (flux leakage) or gets into adjacent phases (phase B) [Fig. 3(c)]. As a result, the flux linkage of the phase A increases and a flux focusing effect can be achieved. However, the flux focusing effect depends on \u03b20. This is because a too large flux gap will ultimately prevent flux from getting into the phase A. Therefore, the flux focusing effect will become a flux defocusing effect. To illustrate the direct influence of flux gaps and UNET widths, the flux linkages versus rotor position and \u03b20 have been calculated for the investigated machines. By way of example, only the results for 12-slot/10-pole and 12-slot/14-pole modular machines without tooth tips are shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001590_s12239-012-0052-1-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001590_s12239-012-0052-1-Figure2-1.png",
        "caption": "Figure 2. Oscillatory impacts of a gear pair (a, b - forward rotation contact points; A, B - backward rotation contact points) when (a) double-tooth contact occurs in both directions and (b) both single-tooth and double-tooth contacts are present.",
        "texts": [
            " In the forward tooth contact geometry, the position a is the contact point where a tooth pair just enters the mesh zone; a second tooth pair simultaneously contacts at position c. When the second tooth pair is about to exit the meshing zone at position d, the first pair is making contact at position b. The position p is the pitch point where the tooth surface friction force changes its direction. The same definitions can be applied to the backward contact case, corresponding to positions A, B, C, D and P in Figure 1(b). Two types of forward and backward oscillatory impact behaviors of a meshing spur gear pair are shown in Figure 2. The gear denoted by the black solid curve represents forward contact, and the dotted curve represents backward contact. The letters a, b, A and B refer to contact points. One type of oscillatory impact involves double-tooth contact for both forward (points a and b) and backward (points A and B) oscillations as shown in Figure 2(a). The other type of impact causes double-tooth contact in one direction (points a and b) and single-tooth contact in the opposite direction (point A) as shown in Figure 2(b). Note that a third type of impact behavior, in which single-tooth contacts occur in both directions, is not shown here for brevity. The phase relationship for the forward and backward contacts is also shown in Figure 2(b). Here, \u03b8p(t) is the rotational angle and Op is the geometric center of the pinion. The positions where the gear pair contacts at point a for forward contact in Figure 1(a) and point A for backward contact in Figure 1(b) are chosen to be the origins of the mesh stiffness curves in this paper. Thus, in Figure 2(b), the magnitudes of the mesh stiffness are dependent on the angle \u03b8 (t)= \u03b8 p(t)=\u2220BOpD-\u03b80 for forward contact and \u03b8 (t)=\u2220EOpC-\u03b80 for backward contact. The pinion rotational angle \u03b80 shown in Figure 1a is the rotational angle between the position of the pinion where a tooth is just rotating into the LOA (point X) and the position where it just engages with its mating tooth at contact point a. \u03b80 can be calculated using Equation (1): . (1) As described above, the mesh stiffness values corresponding to the same pinion angular position are different in the forward (drive side) and backward (coast side) tooth contact conditions",
            " In the regions of \u03b8a-\u03b8b and \u03b8c-\u03b8d, there are two pairs of teeth in mesh. However, only a single gear tooth pair is in contact in the \u03b8b-\u03b8c region. \u03b8p is the pinion angular position at which the gear tooth pair in contact is at the pitch point. When the gear pair rotates in the reverse direction, the corresponding regions are denoted by \u03b8A, \u03b8B, \u03b8C, \u03b8D and \u03b8P. When the two rotational cases are plotted simultaneously as a function of the pinion angular position, as shown in Figure 3 based on the definitions used in Figure 2, a phase differential between the forward and the backward gear rotations can be clearly seen. This phase shift results in two types of contact behavior, producing different gear mesh stiffness on the drive and coast sides for a given pinion angular position. Taking into account the different contact behavior of the gear pair in forward and backward rotation, the positiondependent mesh stiffness for the gear pair can be written as, . (2) On the drive side, when the teeth are in contact, . (3a,b,c) When the teeth disengage, . (4a,b) According to the angular relationship in Figure 2b, , (5) where . (6a,b,c) The relationship between the phase angle \u03b8 (t) and the pinion angular position \u03b8p(t) can be obtained by the substitution of (6) into (5) as shown as equation (7c). Thus, for the coast side, when the teeth are in contact, \u03b80 Rpp Rgp+( )sin\u03b1 Rga 2 Rgb 2 \u2013\u2013 Rpb --------------------------------------------------------------= Km K \u03b8 t( ) \u03be t( ) \u03b7 e t( ), , ,( )= \u03be t( ) e t( ) \u03b7+> Km K \u03b8 t( )( ) \u03b8 t( ) \u03b8p t( )=,=, \u03be t( ) e t( ) \u03b7+< Km 0=, BOpD\u2220 EOpC\u2220 COpD\u2220 BOpE\u2220=\u2013+ BOpD\u2220 \u03b80 \u03b8p t( ) COpD\u2220 \u03c0 zp --- 2 \u03b1tan \u03b1\u2013( ) BOpE\u2220 2\u03b1=,+=,+= engagements; , : mesh stiffness curves for forward and backward tooth contacts)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000749_tmag.2011.2169805-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000749_tmag.2011.2169805-Figure9-1.png",
        "caption": "Fig. 9. Field-circuit coupled model of the 24/32-pole DSEG.",
        "texts": [
            " Hence, we pay attention to the DSEG applied in the semi-direct driven wind power generation system. The following simulations and experiments of the DSEG have been done under a rotation speed of 500 rpm. The 3N-4N-poles DSEG with a half-wave rectified output can provide DC power, which is called the switched reluctance generating mode. The armature reaction may enhance the magnetic field produced by the excitation MMFs in this mode [16], [17]. The 2-D FEA model of DSEG and circuit model of rectification are built in MAXWELL2D, as shown in Fig. 9. A 3-D FEA model of the 24/32-pole DSEG based on transient field analysis is also built to further verify the effectiveness. Fig. 10 shows the phase voltage simulation waveforms performed by 2-D FEA and 3-D FEA of the 24/32-pole DSEG at no-load with 6 A excitation current. The 2-D FEA results agree well with the 3-D FEA results. As far as the structure topology is concerned, the 24/32-pole DSEG is constructed from a 48/32-pole DSEG, so we have performed the comparisons between these two generators by 2-D FEA"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000035_tie.2010.2095392-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000035_tie.2010.2095392-Figure3-1.png",
        "caption": "Fig. 3. Side view of a pantograph mechanism.",
        "texts": [
            " PAROYS-II consists of active pantographs with actuators and passive springs. The active pantograph mechanism adjusts PAROYS-II to the radius change of the pipe. Because the pantograph mechanism moves in the radial direction, no distortion forces are applied when the robot passes over uneven surfaces [5]. The length ratio between the links of the pantograph is 2 : 1 to provide a maximum range of its motion [6]. This mechanism is connected to a lead screw that has both rightand left-hand threads, as shown in Fig. 3. Compressible springs located between the connectors and the screw nuts assist in the surmounting of obstacles. Because the lead screw can activate two screw nuts to move farther or closer to each other, the robot is able to expand or contract the pantograph mechanism. In addition, the gear train transfers the power of a dc motor to the three lead screws so that they can rotate synchronously. Each track module is composed of two parts: frontal and rear tracks. A compliance active joint connects the tracks"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001423_j.jsv.2017.07.030-Figure12-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001423_j.jsv.2017.07.030-Figure12-1.png",
        "caption": "Fig. 12. Experimental test rig.",
        "texts": [
            " An accelerometer (with sensitivity of 100 mV/g and frequency range 0\u201310 kHz) and a shaft encoder (produced by Encoder Products Co. with 1 pulse/revolution) are used for capturing vibration and Tacho signals simultaneously. The data are captured under speed up conditions from 0 rpm to 3000 rpmwithin 8 s and 4.3 s data is used for the following analysis. The sampling frequency was set to be 7680 Hz to accommodate all interested frequency contents of this test rig. The whole set-up arrangement is shown in Fig. 12 [27]. In the experiment, tooth-missing and healthy condition sun gears are used for the following analysis. While, gear with a crack tooth, distributed and a broken tooth are used for further demonstrating the fault detection capability of the proposed scheme. The pictures of experimental sun gears are depicted in Fig. 13. The physical parameters of planetary gearbox are listed in Table 4 in which gear teeth, number of planet gears and the transmission ratios are given and calculated. In the experimental set-up, the ring gear of planetary gearbox is stationary and the sun gear is the input of the planetary gearbox system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000024_0278364909104296-Figure11-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000024_0278364909104296-Figure11-1.png",
        "caption": "Fig. 11. Phase portrait (left) and trajectories (right) of failed turning maneuver using partial feedback linearization with large PD gains.",
        "texts": [
            " This is not surprising, as we are essentially replacing the four-DOF hipped biped\u2019s dynamics with that of a planar hipless biped and two decoupled linear PD systems, all of which are known to be stable. However, when we instruct this controlled biped to perform a 90 turn as before, it always fails. Choosing small critically damped PD gains, k p 5, k p 20, kd 2 k p , kd 2 k p , the biped makes loose sloppy turns and eventually trips (Figure 9). With large critically damped gains, k p 150, k p 250, etc., we see immediate failure in Figure 11: the quick turning motion destabilizes the sagittal-plane limit cycle, causing a strange back- at TEXAS SOUTHERN UNIVERSITY on October 15, 2014ijr.sagepub.comDownloaded from wards misstep and subsequent fall. The inputs for both cases are shown in Figure 10. We see that feedback linearization/decoupling is sufficient for straight-forward walking, when the actual hipped dynamics are closer to the desired planar hipless dynamics, but this method is clearly not robust for highly dynamic motions such as turning, when the hip induces a strong coupling between the yaw, lean, and pitch modes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000148_s00202-007-0073-3-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000148_s00202-007-0073-3-Figure1-1.png",
        "caption": "Fig. 1 Diagram of the electromechanical system",
        "texts": [
            " An experimental application is performed such that SMC + I controller is designed for the speed control of an electromechanical system, a DC motor connected to a load using belt mechanisms via shafts. The feasibility and effectiveness of the proposed sliding mode controller is experimentally demonstrated and the system is controlled using a computer. The results obtained from the present study are compared with the traditional PID control system and conventional SMC system in dynamic responses of the closed-loop control. Electromechanical system is given in Fig. 1 and its block diagram is presented in Fig. 2. Electrical and mechanical equations of the system can be given as: va(t) = La d dt ia(t) + Raia(t) + Km\u03c9m(t) (1) Jm ( d\u03c9m(t) dt ) =Tm(t)\u2212Ts1(t)\u2212Rm\u03c9m(t)\u2212Tf(\u03c9m) (2) J1 ( d\u03c91(t) dt ) = Tb1(t) \u2212 Ts2(t) \u2212 R1\u03c91(t) \u2212 Tf(\u03c91) (3) JL ( d\u03c9L(t) dt ) = Tb2(t) \u2212 RL\u03c9L(t) \u2212 Td(t) \u2212 Tf(\u03c9L) (4) Ts1(t)=ks1(\u03b8m(t)\u2212Kb1\u03b81(t))+Bs1(\u03c9m(t)\u2212Kb1\u03c91(t)) (5) Ts2(t)=ks2(\u03b81(t)\u2212Kb2\u03b8L(t))+Bs2(\u03c91(t)\u2212Kb2\u03c9L(t)) (6) d\u03b8m(t) dt =\u03c9m(t), d\u03b8L(t) dt =\u03c9L(t), d\u03b81(t) dt =\u03c91(t) (7) where va is the motor armature voltage, Ra and La are the armature coil resistance and inductance, respectively, ia is the armature current, Km is the torque coefficient, Tm is the generated motor torque, \u03c9m, \u03c91, \u03c9L, are the rotational speeds of the motor, Jm, J1, JL are the moments of inertia, Rm, R1, RL are the coefficients of viscous-friction, Td is the external load disturbance, Tf is the nonlinear friction, Ts1, Ts2 are the transmitted shaft torques, Tb1, Tb2 are the transmitted torques from the belts, and Kb1, Kb2 are the belt constants"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000922_j.mechmachtheory.2013.11.001-Figure15-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000922_j.mechmachtheory.2013.11.001-Figure15-1.png",
        "caption": "Fig. 15. Best constructive solution of the 5-link PGT in terms of efficiency and attainable transmission ratio.",
        "texts": [
            " For greater multiplications, the efficiency decreases rapidly, and for smaller multiplications the 4-link PGT 3,1\u20132 in the configuration 10 offers a simpler alternative that is essentially just as efficient. Finally, in the range of transmission ratios 1/15 b |R| b 1/12, or 12 b |R| b 15, the constructive configuration which has the greatest efficiency, i.e., the one whose efficiency corresponds to the point of the upper envelope, is 5310-132-10123 as reducer, and the inverse train, i.e., 5310-312-10123, as increaser. This train, which is usually called a Wolfrom gear drive, is shown schematically in Fig. 15. 10. Efficiency of six-link PGTs In this section we analyze the efficiency that PGTs of 6 links can attain. In Section 6, we obtained the ranges of transmission ratios achievable by different trains in their three constructive solutions: two simple planets, one simple and one double planet, and two double planets. Figs. 9 and 10 show the transmission ratios achievable with two simple planets. Figs. 11 and 12 show the same but for one simple and one double planet, and for two double planets, respectively",
            " It was also observed that the efficiency upper envelope showed a sharp fall in the maximum achievable efficiency when the transmission ratio exceeded a certain value. Obtaining the efficiency upper envelope of the 5- and 6-link trains allowed us to identify a set of trains which have a suitable combination of efficiency and transmission ratio, and therefore constitute potentially attractive designs for both speed reducer and speed increaser gear drives. In the 5-link case, the most efficient constructive solution was that shown in Fig. 15. For the 6-link case, we identified the set of 13 trains shown in Fig. 20. Only 5 of these 13 trains had also been noted as trains of high efficiency in [5]. The completeness with which the present analysis was carried out ensures that the set of trains represented schematically in Figs. 20 and 15 constitutes the principal source of possibilities for the election of constructive alternatives in the design of planetary transmission drives. Supplementary data to this article can be found online at http://dx"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003450_j.jfranklin.2019.08.038-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003450_j.jfranklin.2019.08.038-Figure1-1.png",
        "caption": "Fig. 1. n -link planar manipulator.",
        "texts": [
            " Wu, Trajectory tracking of flexible joint manipulators actuated by DCmotors under random disturbances, Journal of the Franklin Institute, https:// doi.org/ 10.1016/ j.jfranklin.2019.08.038 4 M. Cui and Z. Wu / Journal of the Franklin Institute xxx (xxxx) xxx The manipulator is connected to O on the floor. The manipulator is affected by the random vibration environment. As in [24] , the random vibration is described by the random accelerations of the point O and let \u03be 1 , \u03be 2 denote the random accelerations in horizontal and vertical directions, respectively (see Fig. 1 ), which can be seen as independent stationary processes. With the development of sensor technology, for i = 1 , 2, . . . , n, the states q i , \u02d9 qi , \u03b8 i , \u02d9 \u03b8i and I i can be easily measured by adding some sensors. Given a smooth reference signal q r = (q r1 , q r2 , . . . , q rn ) T , in the absence of air resistance, the objective of this paper is to design a state feedback tracking controller u = (u 1 , u 2 , . . . , u n ) T such that trajectory tracking error q \u2212 q r as small as possible where q = (q 1 , q 2 , "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001902_17452759.2016.1210483-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001902_17452759.2016.1210483-Figure1-1.png",
        "caption": "Figure 1. (a) Schematic of an EBM A2XX system. (b) SEM micrograph of Ti\u20136Al\u20134V ELI Powder.",
        "texts": [
            " The study aims to establish the synthetical influence of 2D planar build geometry and in-fill hatching strategy on the SEBM process. An understanding of the geometrical-based microstructure and mechanical properties obtained from this investigation could aid in the better understanding of the powder bed fusion process. The material used for this investigation is the extra low interstitial grade of Ti\u20136Al\u20134V powder (Grade 23) supplied by Arcam AB, M\u00f6lndal, Sweden. The powders are spherical in shape with a size distribution ranging from 45 to 106 \u00b5m, as shown in Figure 1. After each built job, the recycling of non-melted and sintered powder was achieved via the powder recovery system and a vibrating sieve (mesh size \u2264150 \u00b5m). All parts made in this study were fabricated using the powder bed fusion AM system (A2XX, Arcam AB).The STL data were generated and prepared using Magics, a commercial STL software, and were sliced using the Build Assembler software by Arcam AB. A schematic of the system is shown in Figure 1. The build conditions are: pre-heating stainless steel start plate to 600\u2013650\u00b0C, a controlled vacuum pressure of \u223c2e-3 mBar and build layers of 50 \u00b5m. High-purity helium was used to regulate the vacuum and to prevent powder charging due to the electronbased process. Figure 2 shows the two parts with different 2D-planar geometries, namely the block part and the curve part, respectively. The built height of these two parts is \u223c30 mm. Each part has a fin structure with thicknesses of 1 mm, 5, 10 and 20 mm, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003720_j.addma.2020.101491-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003720_j.addma.2020.101491-Figure7-1.png",
        "caption": "Fig. 7. Variations of the temperature and velocity fields during ten-layer laser DED for the 10th layer during unidirectional scanning. Laser power 1500W, scanning speed 8mm/s, mass feed rate 20 g/min. (a) and (d) scanned distance 5mm. (b) and (e) scanned distance 20mm. (c) and (f) scanned distance 25mm. The contours in (d), (e) and (f) represent the temperature distributions of 2200 K, 2000 K, and 1928 K, respectively.",
        "texts": [
            " This is reasonable as the layer height would not increase unlimited. On the contrary, it would enter a quasi-steady state as shown in Fig. 6(c) and (d). This means that the latest layer is printed via contributing a net increment on the build top, and meanwhile remelting the adjacent previous layers within its coverage associated with the total layer height. Results on the molten pool scale are interpreted in this section to reveal the underlying mechanisms for the strikingly different features of layers presented above. Fig. 7 shows the spatiotemporal variations of the temperature and velocity fields during printing of the 10th layer for unidirectional scanning, with molten pool boundaries depicted by the solidus temperature of Ti-6Al-4 V. The liquid metal in the molten pool flows dynamically, driven by forces including the Marangoni force, surface tension, buoyancy, and recoil pressure. The predominant backward and sideward flow of the liquid metal observed from Fig. 7(d) indicates that the local fluid flow in the rear region of the molten pool is mainly driven by the Marangoni stress resulting from the gradient distribution of surface tension [52,53]. Such a flow pattern drives the liquid metal to the rear of the molten pool, spreading on the preceding layer. In a recent article [23], a prominent bulge at the beginning part of a single track was observed. Similarly, the protrusion at the track head was observed in single track laser powder bed fusion samples [54]",
            " 8 shows the spatiotemporal variations of temperature fields during ten-layer laser DED for the 1st, 8th, 9th, and 10th layers, respectively. Significantly lager molten pools for upper layers compared with those for lower layers can be observed. Similar experimental observations have also been reported for thin wall structure printing using laser wire DED [37,55]. As demonstrated in Fig. 8(c), a declining zone which has progressively smaller build height was generated at the end of the 8th layer. The 9th layer subsequently started from this zone. Although the molten pool metal flows in a similar pattern as described for Fig. 7(d), the starting condition for the bidirectional scanning case changed layer wisely compared with the unidirectional case shown in Fig. 7. Thus, the different features of the starting and ending zones are counteracted via the opposite scanning directions of adjacent layers for the bidirectional scanning cases. In contrast, the accumulation at the starting zone and the decline at the ending zone are reinforced layer wisely during unidirectional scanning, resulting in a final unequal height build. The interlayer idle time was 1 second between two consecutive layers for the bidirectional cases. The idle time was about 36 seconds for the unidirectional cases considering that the sample was deposited as a part of a ten-layer and six-track build with a large hatch spacing so that adjacent tracks were isolated",
            " The peak temperatures were significantly different upon the start of a new layer for different scanning cases. The peak temperature increased from 850 K when the 2nd layer started to 1520 K when the 10th layer started using bidirectional scanning. In contrast, the peak temperature increased from 560 K when the 2nd layer started to 730 K when the 10th layer started using unidirectional scanning. The greater heat accumulation occurred during bidirectional scanning caused larger molten pools and thus a wider build and higher powder catchment efficiency. The molten pool shown in Fig. 7(e) demonstrates a typical near saddle shape profile during multi-layer metal printing. Such a profile is significantly different from that obtained during deposition of a single layer build [10]. The depressed feature of the molten pool is generated due to the recoil pressure and the absence of the side support, with downward flow of the local liquid metal in the front region as shown in Fig. 7(d)\u2013(f). Moreover, a trend of a stretching longer molten pool can be observed from Fig. 7. The mushy zone confined by the temperature range between the solidus and liquidus temperatures enlarges significantly along the scanning direction due to the linear scanning of the heat source. The heat transfer and fluid flow in the molten pool was studied using dimensionless numbers including Peclet number (Pe), Prandtl number (Pr) and Marangoni number (Ma) [9,26,34,56]. Pr is the ratio of the momentum to thermal diffusivity, and can be used to assess the fluid flow patterns affecting the molten pool shape [34,57,58]: =Pr \u03bcC k p (2) where \u03bc is the viscosity of the liquid metal, Cp is the specific heat, and k is the thermal conductivity",
            " The measured experimental and computational data of the build height along the build length direction are further shown in Fig. 12. For the 10th layer, the build could be divided into three zones, i.e., the bump beginning zone from 0mm to 12mm, the flat middle zone from 12mm to 27mm, and the declining zone from 27mm to 42mm. One interesting point is that a valley exists between the bumped head zone and the flat middle zone of the layer. Such a variation originates from the liquid metal flow within the molten pool as depicted in Fig. 7. Such a near staircase build profile is undesired for uniform deposition, and may cause serious termination of the printing process. Considering the significant influences of the most basic patterns of unidirectional and bidirectional scanning for laser DED, the selection of scanning strategies should be cautious for the deposition of thin wall builds. In this work, the complex transport phenomena during multi-layer laser DED of Ti-6Al-4 V are quantitatively explored considering the spatiotemporal variations of the temperature and velocity fields"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002283_j.rcim.2017.10.003-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002283_j.rcim.2017.10.003-Figure7-1.png",
        "caption": "Fig. 7. CMM measurement and its data-driven programming.",
        "texts": [
            " It needs to evaluate hether its ease-off is in accordance with the prescribed requirement or ot. In proposed modification model, according to the ease-off which is equired by the user, a controllable and flexible design schemes is proosed. Incidentally, the ease-off is a very popular concept to represent he geometric shape derivation of the theoretical flank form the actual r master one [13,23] . Generally, ease-off [23,24] can be prescribed ccording to the measurement by coordinate measuring machines CMMs) [13,15,24] . Fig. 7 represents the data-driven programming for he universal measurement with CMMs. Here, the tooth flank is made iscretization by a typical 5 \u00d79 points grid. It generally takes 9 data oints along the face width (FW) direction and 5 data points along he tooth height (TH) direction according to the Gleason measurement ethod [24,41] , respectively. To this end, ease-off values h ij ( i \u2208[1,9], \u2208[1,5]) and three-dimensional coordinates of the measured flank grid oints can obtained. They are used to construct the prescribed ease-off opography by interpolation fitting method [15,24] ",
            " With the application of UMC, the given set of nitial machine settings can be transformed with the universal machine FEM MODEL del for TCA of hypoid gear. s o d 6 a fl w a i t c t i H b a l fl s 2 t 6 p t i t c c t fl g s R f \ud835\udefd t s h s v t c m o ettings. With the given machine tool settings \ud835\udf430 , a target flank can be btained [49] . To this end, there are 11 machine settings as main data riven in programming for the HCIs in collaborative system. .2. HCI 2: measurement Before modification, a universal CMM measurement (see Fig. 7 ) is pplied to obtain the actual processed pinion flank. It is a basic tooth ank in modification model which can represented by a flank grid ith data points [23,24] . The prescribed ease-off value is identified ccording to the precision requirement of the user. Once a basic flank is dentified, any required ease-off values can be identified to obtain the arget flank topography by polynomial fitting. In the industrial appliations, there generally is a master flank which is determined through he experienced or skilled operators"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003848_j.jmatprotec.2020.117032-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003848_j.jmatprotec.2020.117032-Figure4-1.png",
        "caption": "Fig. 4. a) Tool for orbital forming b) Scheme for tumbling angle over tumbling rounds c) cavities to be filled in forming operation for layout R40 and R35.2.",
        "texts": [
            " Thus the part height primarily depends on the maximum forming force. The control of the material flow was identified as one of the main challenges in SBMF processes in previous investigations. In this case, the buckling of the cup wall has to be prevented as it causes an insufficient die filling and poor part properties. Schulte et al. (2017a) showed, that the application of tailored blanks is an expedient measure to enhance the material flow control in SBMF. Therefore, an orbital forming process (Fig. 4a) is used to manufacture tailored blanks with preformed gear M. Merklein et al. Journal of Materials Processing Tech. 291 (2021) 117032 teeth. By tilting the lower tool, the contact zone between punch and work piece is reduced, which results in higher contact pressure. The tilting increase in the first process phase (Uh) and is kept constant in the second phase (Uk), as shown in Fig. 4b. In the last phase (Ur) the tumbling angle \u0398 is set back to the initial position. The force for orbital forming is set to the maximum possible value 4000 kN. The number of tumbling cycles in all three phases is set to five in regard to Schulte et al. (2017b). The initial sheet thickness is 2.0 mm. The tool features gear cavities analogue to the target geometry, yet oriented in the direction of the sheet plane as indicated in Fig. 4c. The examples in Fig. 4c show tooth alignment radii of R40 and R35.2. A radius of R35.2 mm needs a much higher form filling. In this work, the layout R35.2 is used to receive a higher effective tooth length, which is beneficial for the use case as a functional gear component. The combination of sheet bulk metal forming operations, orbital forming, deep drawing and upsetting results in a process chain of subsequent forming operations to realize a gear component. The process chain is shown in Fig. 5. By comparing the process chain of PBF-LB and forming (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001486_j.1151-2916.1970.tb12142.x-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001486_j.1151-2916.1970.tb12142.x-Figure3-1.png",
        "caption": "Fig. 3. When two wedges are in face-to-face contact, there",
        "texts": [
            " Since Rr is zero all along the wedge, Ra is a constant, and the result of the determination of Rz for the is a shear force independent of liquid volume. Fig. 2. Unsymmetric wedge-on-plane geometry exhibits normal force independent of liquid volume and torque that increases with liquid volnme. cone-on-plane case still applies. Thus - (y/L) (cotp,cose-sine) (11) Fn'veedsc=LY(CQtPi+COtP2)COSe (12) ,Jp- r d 6 C =: In this case t I cancels out, so that the interparticle force between a wedge and a plane is independent of the volume of liquid. Analysis of the case of two particles in face-to-face contact (Fig. 3) is also simple. The derivation is identical to that for each side of the wedge contact. If p does not vary along either side of the contact, Lycosecotp is the contribution to F, from that side; F, is given by the sum of these contributions around the perimeter or an integral if p varies along the perimeter. F, = ycoseJcotpdL (13) For an irregular convex particIe, R2 is determined approximately by the construction of Fig. 4. As the liquid volume increases, the angle p varies, and F , changes accordingly",
            " ( 4 ) Shear The shear is always zero when the contact on one of the particles is a plane large enough that the liquid does not reach its edge. This result can be seen by evaluating the shear term at the plane surface. The A P term has no shear component, and there is always an opposite and equal ycose term for the opposite side of the particle. With the mathematics outlined above, shear cases where both of the particles were curved at the point of contact could be treated. However, only the simplest possible case is considered here to confirm the existence of a shearing force. Figure 3 shows two wedges in contact along the flat faces. By considering forces along the common plane, the shearing force F t is Ft = 2yLcose (18) and is independent of the wedge angles pi, the area of solidsolid contact, and the amount of liquid. Since torques tend to bring the flat sides together, this geometry is a reasonable model for demonstrating the shear that might actually occur. If one of the particles is tilted slightly, the liquid fills the gap and recedes. The shear is somewhat reduced. The shear disappears when the liquid recedes to the point where it no 1onge",
            " It is of interest to compare the magnitude of the shears and torques for a single contact with those exerted on the particle a s a result of the normal forces from the several contacts it has in a compact. For equilibrium with respect to rearrangement, these shears and torques at one contact must be balanced by forces a t other contacts of the same particle. Conversely, for rearrangement to occur, the forces on a particle must be unbalanced. For the shear to operate it may, for instance, have to exert enough force either to break the contact at A in Fig. 3 or to drag the particle along. Similarly, it may have to push the particle at B along. However, these other contacts do not necessarily oppose rearrangement. The particles a t A and B may experience forces from the other contacts that will aid the shear. The important point is that for the shear to be effective, it must be of the same magnitude as FvL. The shear must also overcome friction. This too requires F t to be of magnitude F,, times a friction coefficient. Equations (13) and (18) show that F t can be comparable to FTL"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003310_17452759.2019.1565596-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003310_17452759.2019.1565596-Figure4-1.png",
        "caption": "Figure 4. Numerical models of test to retrieve plastic strain at fracture (svM), from left to right compression, butterfly, round smooth, round notched.",
        "texts": [],
        "surrounding_texts": [
            "constitutive law (looking for the best match between measured and numerical force\u2013displacement curves).\nThe constitutive law can be represented with the Voce law (1948, 1955) as\ns = k0 + Q(1\u2212 e\u2212b1p ) (1)\nFor the currentmaterial, the calibration on a smooth specimen in tension gives the parameters reported in Table 2.\nSeveral different ductile damage models are available in the literature and the most common ones are Mae et al. (2007), Gilioli et al. (2015) and Cortese, Nalli, and Rossi (2016) which try to relate the maximum plastic strain at fracture with the triaxiality: a parameter representing the state of stress and defined as\nh = \u2211si\n3 1 2 \u2211 (si \u2212 sj) 2 [ ]\u221a (2)\nAmong others, Rice and Tracey (1969) proposed an exponential decreasing function. This model was first extended by Hancock and Mackenzie (1976) and successively by Johnson and Cook (1983) in order to take into consideration the effects of temperature and strain rate. Bao and Wierzbicki (2004) proposed three separate branch relations between strain to failure and triaxiality. In this study, the Johnson\u2013Cook model was used:\n1peq = [D1 + D2 exp(D3h)][1+ D4 ln(1\u0307\u2217p)][1+ D5T \u2217] (3)\nwhere Di are parameters that have to be calibrated for each material, h is the triaxiality, 1\u0307 is the strain rate and T\u2217 express the dependence on temperature.\nIn the present paper, in order to calibrate the damage model, four different sample geometries, already developed for a previous research (Concli and Gilioli 2018) (Figure 3), were experimentally tested. The goal is to determine the relation between the plastic strain at failure and triaxiality over a large range of the latter. The reason is because in the trabecular structure, the stress state is complex, and therefore, it is necessary to have a damage criterion reliable over a wide range of triaxialities. A comparison between the measurements and the numerical reproduction of the experiments on the various shape specimens allowed to determine the evolution of the plastic strain up to failure as a function of triaxiality for four different scenarios. In such a way, then it is possible to calibrate the Johnson\u2013Cook damage model.\nIn the FE simulations, the measured displacement at failure was applied, and the values of h and 1peeq were calculated. The results are shown in Figures 4 and 5.\nAs shown in Figure 5, the actual results are comparable with those available in the literature (Karpanan and Thomas 2016).\nDespite the capability of the Johnson\u2013Cook model to take into account the strain rate and the temperature effect, in the present research, the fracture strain was assumed to be independent of these parameters. Therefore, the constants D4 and D5 result in zero. According to the results presented in Figure 6 and Table 3, the other constant results are shown in Table 4.\nThe plastic behaviour of AM structures was investigated testing a trabecular geometry under compression. An FE simulation of such test was performed in order to assess the capability to predict themechanical responseof the trabecula up to the collapse. The sample geometry is shown in Figure 6. The diameter of the trusses is f = 1.5 mm.\nSamples were produced using a Renishaw AM250. The quasi-static compression tests were performed using an MTS Criterion 45 testing machine available at\nFigure 2. Round samples for the identification of the stress\u2013strain curve; vM stresses at failure.",
            "the Free University of Bozen \u2013 Bolzano. It is a 2-column, floor-standing frame equipped with an electromechanical actuator capable of applying up to 100 kN. Tests were conducted using displacement control (1 mm/ min) and without extensometer. It is reasonable to assume that the displacement of the upper plate is representative of the compression of the sample, its stiffness being much lower than the stiffness of the testing machine itself.\nFigure 7 reports the experimental measurements in terms of force magnitude\u2013displacement magnitude. Despite the trabecular samples not being treated (Hot Isostatic Pressing), the measurements result was repeatable.\nFE simulations of the experimental setup were performed. The geometrical model was simplified exploiting the symmetry of the trabecula modelling only onequarter of the cell. The nominal geometry of the trabecula has been used even if some recent studies have\nFigure 3. Sample geometries for the calibration of ductile damage criterion.",
            "shown that the real geometry of AM produce structures that differ significantly from the nominal one (Leary et al. 2018; Sing, Wiria, and Yeong 2018). A mesh sensitivity analysis was conducted. The final grid consists in about 100,000 cells (Figure 8).\nFigure 6. Geometry of the trabecular structure.\nTable 3. Results of the calibration procedure: triaxiality vs. strain at fracture.\nCompression Butterfly Round smooth Round notched\nh \u22120.33 0.16 0.53 0.76 1 peeq 2.41 0.54 0.15 0.10\nTable 4. Johnson\u2013Cook calibrated parameters.\nD1 D2 D3 D4 D5 0 0.9323 \u22122.911 0 0"
        ]
    },
    {
        "image_filename": "designv10_5_0003966_j.jmatprotec.2020.117036-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003966_j.jmatprotec.2020.117036-Figure4-1.png",
        "caption": "Fig. 4. The Z-axis cladding lift calculation model.",
        "texts": [
            " \u0394Z should be consistent with the thickness of the single-pass cladding layer to ensure the same cladding process conditions for each layer; however, in actual multi-layer cladding, thermal deformation of parts and other factors will cause a certain deviation between \u0394Z and the thickness of a single cladding layer. As a result of the cumulative effect, the accuracy of the multi-layer cladding is decreased; therefore, it is necessary to ensure the accuracy and reasonableness of lifting amount \u0394Z. According to the cladding strategy in this article, the value of \u0394Z is determined according to the calculation model of multi-layer cladding over a single track, as shown in Fig. 4, and then adjusted accordingly according to specific experiments. This model makes the following assumptions: (1) The cross-section of each cladding layer is a circular arc, and the cross-sectional area is equal; (2) The curvature of the track remains unchanged after cladding (Zhu et al., 2010). In theory, it is necessary to ensure that after cladding a layer, it remains flat relative to the previous layer, so SABH = SBCD + SGHF 3a) SCDFG = SOAFD \u2212 SOFD (3b) FD = W,AE = h,CD = \u0394Z (3c) \u0394Z = ( 4h2+w2 8h )2 arcsin ( 4Wh 4h2+w2 ) \u2212 W(W2 \u2212 4h2) 16h W (3d) where r is the radius of the arc, h represents the height of a single cladding, and W is the width of a single track"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002735_3242587.3242659-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002735_3242587.3242659-Figure6-1.png",
        "caption": "Figure 6. Horizontal connection is achieved by a pair of rotatable sphere magnets.",
        "texts": [
            "5 mm thickness) disc-shaped magnet in both top and bottom faces. Each block has four studs (\u03c61 mm x 1 mm thickness) on the top and mating cylindrical holes (\u03c61.4 mm x 1.2 mm thickness) on the bottom. These studs prevent horizontal rotation between vertically stacked blocks. Next, we describe the mechanism for connection and disconnection using the shape-display. The block elements of Dynablock are stacked on top of the pin arrays. As described in the design section, each pin can push the vertically connected stacked blocks. Figure 6 illustrates the mechanical design. As described above, each block has a 0.5 mm deep slit, which receives a 1 mm thick spacer attached to the bottom of the plate that serves as an obstacle to horizontal connection. Although there is still magnetic attraction between blocks, it is too weak to connect the blocks. This horizontal separation mechanism allows each pin to individually push the stacked blocks without interfering with nearby stacks. For stable connection and disconnection, a careful design must be considered"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001482_j.asoc.2012.02.016-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001482_j.asoc.2012.02.016-Figure1-1.png",
        "caption": "Fig. 1. Quanser 2 degree of freedom helicopter.",
        "texts": [
            " / Applied Soft Computing 12 (2012) 2462\u20132469 w c g H w a I a e 3 m m h t T w p t y w c hich each entry Hij is the derivative of the neural network virtual ontrol, i(k), with respect to one neural network weight, wij(k), iven as follows: ij(k) = [ \u2202 i(k) \u2202wij(k) ] (10) here i = i, . . ., r and j = 1, . . ., Li. Usually Pi and Qi are initialized s diagonal matrices, with entries Pi(0) and Qi(0), respectively. t is important to remark that Hi(k), Ki(k) and Pi(k) to the EKF re bounded, i.e. \u2016H(k)\u2016 \u2264 H, \u2016K(k)\u2016 \u2264 K, \u2016P(k)\u2016 \u2264 P, for a detailed xplanation of this fact see [10]. . Description of the system The Quanser 2-DOF helicopter consists of a helicopter model ounted on a fixed base with two propellers that is driven by DC otors, see Fig. 1. The front propeller controls the elevation of the elicopter nose about the pitch axis, and the back propeller controls he side to side motions of the helicopter about the yaw axis [17]. he model is described in continuous-time, however in the present ork a discrete-time approach is considered. Therefore, we proose below the discretization of the helicopter model using Euler echnique [18]: x1(k + 1) = x1(k) + x3(k)T x2(k + 1) = x2(k) + x4(k)T x3(k + 1) = x3(k) \u2212 c1 cos(x1(k))T \u2212 c2x3(k)T \u2212c3 sin(x1(k)) cos(x1(k))x2 4(k)T + c4TVmp + c5TVmy(k) x4(k + 1) = x4(k) \u2212 c6x4(k)T + c7 sin(x1(k)) cos(x1(k))x3(k)x4(k)T +c8TVmp + c9TVmy(k)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002809_taes.2015.150046-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002809_taes.2015.150046-Figure1-1.png",
        "caption": "Fig. 1. Reference frames.",
        "texts": [
            " Four reference frames are defined: the inertial frame, the target frame, the desired frame, and the body frame. The inertial frame is the Earth-centered inertial frame. The body frame is some frame fixed to the chaser satellite and centered at its center of mass. The target frame is defined as I\u0304T = r\u0304T/I/\u2016r\u0304T/I\u2016, J\u0304T = K\u0304T \u00d7 I\u0304T, and K\u0304T = \u03c9\u0304T/I/\u2016\u03c9\u0304T/I\u2016. The desired frame is defined as I\u0304D = r\u0304D/T/\u2016r\u0304D/T\u2016, J\u0304D = K\u0304D \u00d7 I\u0304D, and K\u0304D = \u03c9\u0304D/T/\u2016\u03c9\u0304D/T\u2016 [7]. The target satellite is assumed to be fixed to the target frame. The different frames are illustrated in Fig. 1. The control objective is to superimpose the body frame onto the desired frame. The target spacecraft is assumed to be in a highly eccentric Molniya orbit with initial orbital elements given in [7] and nadir pointing. The relative motion of the desired frame with respect to the target frame is defined as an ellipse in the I\u0304T-J\u0304T plane with semimajor axis equal to 20 m along J\u0304T and semiminor axis equal to 10 m along I\u0304T. The relative orbit has constant angular speed equal to the mean motion of the target satellite"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002721_j.ceramint.2018.05.036-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002721_j.ceramint.2018.05.036-Figure3-1.png",
        "caption": "Fig. 3. Sample structures: (a) thin-walled structure; (b) cylindrical structure.",
        "texts": [
            " Compared to the conventional forming-sintering method, there is no need to add any binders and sintering aids in the powder. Taking into account physical compatibility and chemical compatibility with the original powder material, a sintered Al2O3 ceramic plate (Fig. 2(b)) was selected as the substrate for the shaping experiment. Size of the substrate was 150mm\u00d7100mm\u00d715mm and the Al2O3 content was 95%. Two kinds of structural samples were prepared in this study. One kind is thin-walled structure (as shown in Fig. 3(a)) for microstructure analysis and the other kind is cylindrical structure (as shown in Fig. 3(b)) for macro property testing. The thin-walled structures with size of 15mm\u00d74mm\u00d710mm were fabricated using reciprocal deposition trajectory. During the fabricating procedure, process parameters for each layer, such as laser power, scanning speed, and powder feed rate, remained the same. After each layer was deposited, the CNC table was lowered by a layer thickness (\u0394z) to prepare for deposition of next layer. The value of \u0394z was determined by the above three process parameters. Size of the cylindrical structure for macro properties testing was about \u00f86 mm\u00d740mm, and the deposition trajectory of each layer was clockwise circular trajectory"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002706_978-3-319-68801-5_7-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002706_978-3-319-68801-5_7-Figure4-1.png",
        "caption": "Fig. 4 Schematic of direct deposition a blown powder system, b wire feed system",
        "texts": [
            " DLD is used as an AM of metal and functionally graded parts. In DLD, there is not a pre-deposited layer of powder and that is why it can be used as a method to coat or repair parts by cladding. Blown powder and wire feed systems are the two common processes for DLD [15]. In blown powder, the powder is sprayed through a nozzle under inert atmosphere gas such as argon. The powder is then melted on a focal point to create dense 3D structures or to coat the surface and/or specific feature of a part (see Fig. 4a). Blown powder is a precise process as it uses an automated robotic arm for the deposition of the metal materials with a thickness ranging from 0.1 mm to few millimetres [16, 17]. This offers the freedom in design in the production of complex structures. Moreover, the focused laser energy of blown powder process reduces the effect of the thermal effects when compared to other welding procedures. On the other hand, wire feed systems replace metal powder used in blown powder with a metal wire. The metal wire is extruded through a nozzle and melts using an energy source, typically a laser beam (see Fig. 4b). In a similar way to blown powder systems, an inert gas shielding is utilised either in an enclosed chamber or in an open environment. This process offers superior deposition rate in comparison with other AM techniques. Moreover, wire feed systems are cost-effective as they use metal wires that are cheap and more easily available than metal powders [18]. The AM techniques as explained above can process wide range of metals, their number continues to expand as improved technologies, and optimised operation parameters emerge to cover new applications"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002396_tac.2016.2644379-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002396_tac.2016.2644379-Figure1-1.png",
        "caption": "Fig. 1. Underactuated system with weak coupling under zero-gravity or micro-gravity circumstance",
        "texts": [
            " Besides, we replace rn + \u03c4 in [7] by \u033an+1, which contributes to constructing C1 controllers and even smooth controllers for high-order SNSs. Owing to the presence of noise terms and the high power pn, a more general system is considered in our paper. Remark 3: System (1) with Assumptions 1 and 2 can describe many practical models. In what follows, we will take an underactuated system with weak coupling [12], [18] as an example. Throughout this paper, we assume that this system is under zero-gravity or micro-gravity circumstance (e.g., in space or underwater). As demonstrated in Fig. 1, the mechanical system with two degrees of freedom is composed of two masses and two springs. The mass m1 is connected 0018-9286 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. to the wall by an unstretched spring on a smooth horizontal surface, and the mass m2 is supported by a massless rod. The two masses are jointed with each other by an unstretched spring"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001880_j.applthermaleng.2014.02.008-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001880_j.applthermaleng.2014.02.008-Figure7-1.png",
        "caption": "Fig. 7. The loss density distribution of the healthy and faulty motor.",
        "texts": [
            " The core loss of the tooth may be expressed as: Pfet \u00bc K 0 GfetPfe10 B2 fN 1:3 (15) d =50 t1=2 50 The core loss of the yoke may be expressed as: Pfej \u00bc KdGfejPfej10=50 B2j fN 50 1:3 (16) where, K 0 d and Kd are the loss increase coefficients of the tooth and yoke respectively, Pfe10=50 and Pfej10=50 are the unit loss of the tooth and yoke respectively, Gfet and Gfej are the weight of the tooth and yoke respectively, Bt1/2 and Bj are the maximum flux density of the tooth and yoke respectively, and fN is the frequency. Fig. 7 is the loss density distribution of the motor, and the dissymmetry in the machine produce a change in the core loss distribution, and the regions in the vicinity of broken bars have a much higher core loss density compared to the healthy situation, which is mainly due to deformation of electromagnetic field deduced by broken bar faults, and the magnetic saturation level within the stator and rotor laminations in the region surrounding the broken bars. The rotor iron loss at rated load is relatively small, so it can be ignored"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001006_s10846-014-0143-5-Figure13-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001006_s10846-014-0143-5-Figure13-1.png",
        "caption": "Fig. 13 Air velocity components relative to the blade element [155]",
        "texts": [
            " These components are defined in relation to the plane perpendicular to the rotor shaft, known as the hub plane. The plane hub frame is defined as Fh = {Oh, ih, jh, kh} where ih points backwards towards the tail, jh points to the right of the helicopter, and kh points up. Two components are in the hub plane while the third is out of the plane. All three components are normal to the hub plane. The out of plane component is perpendicular to the hub plane pointing downward and is denoted by UP , as seen in Fig. 13c. The next component, UT , is parallel to the hub plane and tangential to the blade in the direction of the blade rotational motion as seen in Fig. 13a and d. The last component, UR , lies on the hub plane and points radially pointing outward in the direction of and parallel to the blade, as seen in Fig. 13a and c. The total air velocity seen by the blade is given as U = \u221a U2 T + U2 P . At any time during flight, the blade experiences a pitch angle, \u03b6 = \u03b1b +\u03c6b, related to the angle of attack \u03b1b of the blade with respect to the airstream U , which approaches the blade at an inflow angle \u03c6b, as seen in Fig. 14. The lift and drag on the blade are determined through blade element analysis. By considering the blade as a two-dimensional airfoil, the lift and drag vectors at each blade element may be determined"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000857_j.cma.2013.12.017-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000857_j.cma.2013.12.017-Figure4-1.png",
        "caption": "Fig. 4. Blade profiles of a spread-blade cutter.",
        "texts": [],
        "surrounding_texts": [
            "The main generating profile will generate the main active part of curvilinear gear tooth surfaces and will be provided with a straight profile. The range of variation of the profile parameter u (see Figs. 4 and 5) is bm qm 1 sinan\u00f0 \u00de cos an < u < am cos an \u00f03\u00de The vector position of a point P laying on the main generating profile is given in coordinate systems Sib and Sob for the inner and outer blades, respectively, by r\u00f0P\u00de\u00f0u\u00de \u00bc r\u00f0P\u00deib \u00f0u\u00de \u00bc r\u00f0P\u00deob \u00f0u\u00de \u00bc 0 u 0 1 2 6664 3 7775 \u00f04\u00de Generating profiles will be expressed for both, spread-blade or fixed-setting cutters, in coordinate system Sb as previously described. The coordinate transformation between coordinate systems Sib and Sob, fixed to the inner and outer cutting profiles, respectively, and reference coordinate system Sb, are as follows: Mb;ib \u00bc cos an sin an 0 p 4 m sinan cos an 0 0 0 0 1 0 0 0 0 1 2 6664 3 7775 \u00f05\u00de Mb;ob \u00bc cos an sin an 0 p 4 m sin an cos an 0 0 0 0 1 0 0 0 0 1 2 6664 3 7775 \u00f06\u00de Finally, if we denote point Pib as a point on the inner blade profile, Pib is represented in coordinate system Sb as r\u00f0Pib\u00de b \u00f0u\u00de \u00bcMb;ibr\u00f0Pib\u00de ib \u00f0u\u00de \u00bc u sin an \u00fe p 4 m u cos an 0 1 2 6664 3 7775 \u00f07\u00de On the contrary, if we denote point Pob as a point on the outer blade profile, Pob is represented in coordinate system Sb as r\u00f0Pob\u00de b \u00f0u\u00de \u00bcMb;obr\u00f0Pob\u00de ob \u00f0u\u00de \u00bc u sin an p 4 m u cos an 0 1 2 6664 3 7775 \u00f08\u00de"
        ]
    },
    {
        "image_filename": "designv10_5_0003440_s11071-019-05056-9-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003440_s11071-019-05056-9-Figure1-1.png",
        "caption": "Fig. 1 Schematic of the finite element model and mesh of a cylindrical roller bearing (dimensions detailed in Table 1)",
        "texts": [
            " 5, perturbation andnumerical integrationmethods are applied to explain the dynamic response from a theoretical viewpoint. The unstable (i.e., resonant) combinations of stiffness fluctuation amplitude and frequency are predicted by themethod ofmultiple scales and compared with the resonant peaks obtained by numerical integration. Conclusions are given in Sect. 6. The number of contacting rolling elements changes periodically as a bearing spins, which results in variation of the bearing stiffness. A FE/CM model of a cylindrical roller bearing, as shown in Fig. 1, is established to calculate this time-varying bearing stiffness. The contact condition between the bearing rollers and races, which changes kinematically corresponding to the bearing rotation speed, is calculated by a combined method that applies a semi-analytical method near the contact region and the FE method away from the contact region [30\u201333]. The computational efficiency and accuracy of this approach to bearing stiffness calculation have been verified in the literature [34,35]. The bearing inner and outer races are rigidly attached to the shaft and gear surfaces, respectively, so the innermost and outermost cylindrical surfaces in Fig. 1 remain circular. All other components are deformable and modeled using FE, including the bearing rollers. A radial force is applied on the bearing inner ring to simulate the loading. Two typical instantaneous roller positions in a spinning bearing are shown in Fig. 2. One is where the radial force points through the center of the bottom roller, and the other iswhere the radial force is applied between two rollers. To investi- Fig. 2 a Instantaneous position where the radial force points through the center of one roller",
            " The sudden jumps in stiffness represent changes in the number of rollers in contact. The maximum number of rollers in contact increases with bearing load. For the specific case with external radial force Fr = 33,500 N , the number of rollers in contact varies between three and four; for the case of Fr = 9500 N , the number of rollers in contact varies between two and three. In order to investigate the influence of time-varying bearing stiffness on the vibration of a gear-bearing system, a spur gear pair system supported by the cylindrical roller bearing in Fig. 1 is introduced. The gear pair consists of the sun and planet gears split from a planetary gear system used in a helicopter transmission. The Fig. 3 Time-varying bearing stiffness under different external loads Fr in the radial direction calculated by FE/CMmodel. The curves with marks of circle and square correspond to Fr = 9500 N and Fr = 33,500 N, respectively. The regions A, B, C, and D represent conditions with different numbers of rollers in contact. A: four bearing rollers in contact; B: three rollers in contact; C: two rollers in contact; D: three rollers in contact system contains a sun gear (Gear 1) that has only rotational vibration and a bearing-supported pinion gear (Gear 2) that is able to move translationally and rotate, as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003304_j.jsv.2019.01.048-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003304_j.jsv.2019.01.048-Figure1-1.png",
        "caption": "Fig. 1. The diagram of faulty shape (enlarged view).",
        "texts": [
            " The surface failures may occur on the outer race, inner race and rolling elements when the rolling bearing continuously running, whichwould lead to a severe increase of the bearing vibration, especially in the case of high speed or heavy load. This research will focus on the analysis of faults on the outer ring raceway, since the dynamics analysis of faults in other places is similar. This study focuses on such bearing faults that spalling, pitting, etc. For the convenience of derivation, the geometry of the fault is predigested as a cube. As shown in Fig. 1(a), the cube's length, width and height are defined as L, B and H respectively, where L is along the rolling direction of the rolling elements; as shown in Fig.1(b), the rolling element impacts point Awhen it enters the fault area, and impacts point D when it exits the fault area. The effective circumference angle of faulty region qd is calculated by the fault length L and the bearing geometric parameters. The maximum displacement of the impact excitation DH is calculated by the size of the fault and the bearing geometric parameters, DH0 is the theoretic value of the maximum displacement determined by the relationship between the rolling element and the fault"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002476_j.ymssp.2019.106342-Figure14-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002476_j.ymssp.2019.106342-Figure14-1.png",
        "caption": "Fig. 14. Model of a spur gear tooth with tooth root crack.",
        "texts": [
            " We configure the speed profiles similar as the profile in simulation study. Load motor generates a constant load level of 80Nm during the experiment. Fig. 13 shows two segments of baseline vibration, as well as their corresponding speed profiles acquired by an encoder. Sampling frequency equals to 6.4 kHz. The left-side baseline vibration and its corresponding speed profile are used as training data, whereas the right-side as testing data. The experiment considers a tooth crack fault as shown in Fig. 14 given that the tooth crack fault propagates along gear face width and crack depth simultaneously after its initiation [51]. In the figure,w denotes gear tooth face width; wo denotes the width of tooth crack; q denotes a half-length of the tooth chordal thickness (e.g., circular tooth thickness); q0 denotes the depth of tooth crack; ac is the crack angle. In total 5 levels of tooth crack are considered, as listed in Table 4. Electric discharge machine is used to induce such crack. The left side of Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001586_j.mechmachtheory.2013.07.015-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001586_j.mechmachtheory.2013.07.015-Figure2-1.png",
        "caption": "Fig. 2. Schematic of DexTAR's calibration model.",
        "texts": [
            " In the actual prototype, there are both geometric errors and non geometric errors (such as elasticity and thermal expansion). However, in this work, as in [26], the non geometric errors are neglected as their components in the xy plane were measured and found to be negligible. Furthermore, the non parallelism among the axes of the revolute joints is also negligible and not taken into account. Finally, the robot has direct drive motors with high accuracy absolute encoders, so no backlash or encoder nonlinearity is considered. Therefore, the DexTAR calibration model includes twelve geometric parameters (Fig. 2), namely: \u2219 the link lengths l1,1, l1,2, l2,1, l2,2 and the distance d between the axes of the base joints; \u2219 the offset of the TCP (the TCP is denoted by E) with respect to the axis of the joint between the two distal links, represented by distance l2,3 and angle \u03b3, as shown in Fig. 2; \u2219 the angular offsets \u03b41 and \u03b42 in actuators 1 and 2 respectively; \u2219 the pose of the base frame, O-xy, with respect to the world frame (WF), W\u2013xwyw. Our parameter identification process is based on minimizing the forward kinematics residuals by using the TCP coordinates with respect to the WF. The optimization problem is solved by the lsqnonlin Matlab optimization toolbox function. This calls for the direct kinematic equations of the calibrationmodel. Given the active joint variables \u03b81 and \u03b82, the position pE = rOE = [x,y]T of the TCP is calculated as follows: where with \u03be end-ef rOE \u00bc rOB2 \u00fe l2;3 l2;2 cos\u03b3 \u2212 sin\u03b3 sin\u03b3 cos\u03b3 rOC\u2212rOB2 ; \u00f010\u00de rOB2 \u00bc l2;1 cos\u03b82 \u00fe d 2 ; l2;1 sin\u03b82 T ; \u00f011\u00de rOC \u00bc rOB1 \u00fe b1 dB1B2 rB1B2 \u00fe \u03be h dB1B2 0 \u22121 1 0 rB1B2 ; \u00f012\u00de rOB1 \u00bc l1;1 cos\u03b81\u2212 d 2 ; l1;1 sin\u03b81 T ; \u00f013\u00de = \u00b11 being the index that defines the robot's assembly mode (changing the assembly mode leads to a different fector's pose), and h \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi l21;2\u2212b21 q ; b1 \u00bc l21;2\u2212l22:2 \u00fe d2B1B2 2dB1B2 ; \u00f014\u00de dB1B2 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rTB1B2rB1B2 q ; \u00f015\u00de rB1B2 \u00bc rOB2 \u2212rOB1 : \u00f016\u00de The TCP position with respect to the WF (pE WF) is calculated as follows: pWF E \u00bc xWF yWF \u00bc xO \u00fe x cos\u03b1\u2212y sin\u03b1 yO \u00fe x sin\u03b1 \u00fe y cos\u03b1 ; \u00f017\u00de pO WF = [xO,yO]T and \u03b1 are the position and orientation of the base frame with respect to the WF respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001006_s10846-014-0143-5-Figure10-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001006_s10846-014-0143-5-Figure10-1.png",
        "caption": "Fig. 10 Helicopter blade flapping motion",
        "texts": [],
        "surrounding_texts": [
            "where \u03c9\u0302B is the skew-symmetric matrix representation of the angular rate vector. The orientation dynamics are derived using Eq. 10 [70, 138, 155, 177] as: \u0307 = \u23a1 \u23a3 \u03c6\u0307 \u03b8\u0307 \u03c8\u0307 \u23a4 \u23a6 = ( )\u03c9B (11) where ( ) is given as: ( ) = \u23a1 \u23a3 1 sin \u03c6 tan \u03b8 cos \u03c6 tan \u03b8 0 cos \u03c6 \u2212 sin \u03c6 0 sin \u03c6/ cos \u03b8 cos \u03c6/ cos \u03b8 \u23a4 \u23a6 (12) 3.3 Complete Helicopter Dynamics The position and velocity dynamics together with the orientation dynamics form the complete helicopter equations of motion in terms of the helicopter\u2019s bodyfixed frame forces and moments, and are given as: p\u0307I = vI v\u0307I = 1 m Rf B R\u0307 = R\u03c9\u0302B I \u03c9\u0307B = \u2212\u03c9B \u00d7 (I\u03c9B) + \u03c4B (13) with pI and vI denoting the position and linear velocity of the helicopter center of gravity (CG) with respect to an earth-fixed reference frame. In addition to the forces acting on the body, the effect of gravity on the body frame is considered by transforming the gravity vector from the inertial frame, gI = [0 0 g]T , to body-frame, gB = RT (t)gI . Expanding the Newton-Euler equations of motion in Eq. 7 and adding the force of gravity, the translational velocity and angular rate equations of motion with respect to the body-fixed frame are given as: u\u0307 = rv \u2212 qw + R31g + X/m (14) v\u0307 = pw \u2212 ru + R32g + Y/m (15) w\u0307 = qu \u2212 pv + R33g + Z/m (16) p\u0307 = qr(Jyy \u2212 Jzz)/Jxx + L/Jxx (17) q\u0307 = pr(Jzz \u2212 Jxx)/Jyy + M/Jyy (18) r\u0307 = qp(Jxx \u2212 Jyy)/Jzz + N/Jzz (19) The position and orientation trajectory dynamics may be obtained by integrating the rigid body dynamics in Eqs. 14 \u2013 19 through the kinematic equations in Eq. 13. The inertial position can be found given the body velocities through p\u0307I = vI = RvB . The Euler rates can be found through the relationship \u0307 = ( )\u03c9b in Eq. 11. The final position and orientation dynamics are given as: x\u0307I = c\u03b8 c\u03c8u + (s\u03b8 s\u03c6c\u03c8 \u2212 c\u03c6s\u03c8 )v + (s\u03b8 c\u03c6c\u03c8 + s\u03c6s\u03c8 )w (20) y\u0307I = c\u03b8 c\u03c8u + (c\u03c6c\u03c8 + s\u03c6s\u03c8s\u03b8 )v + (c\u03b8 s\u03c8s\u03b8 \u2212 c\u03c8s\u03c6)w (21) z\u0307I = \u2212s\u03b8u + c\u03b8 s\u03c6v + c\u03c6c\u03b8 x (22) \u03c6\u0307 = p + s\u03c6t\u03b8 q + c\u03c6t\u03b8 r (23) \u03b8\u0307 = c\u03c6q \u2212 s\u03c6r (24) \u03c8\u0307 = s\u03c6 c\u03b8 q + c\u03c6 c\u03b8 r (25) 3.4 Forces and Torques A result of the main and tail rotor rotation is the generation of thrust and torques acting on the helicopter body. Gravity is also acting on the helicopter body, and must be taken into account while determining the total body forces on the helicopter. The forces and torques acting on the helicopter are functions of the main rotor thrust, TMR , tail rotor thrust, TT R , and the main rotor cyclic angles, a1 and b1 [70]. The torques acting on the helicopter body are a result of the forces being offset from the center of gravity. The relation below defines the relationship between the force (F ), distance (d) and the resultant torque: \u03c4 = Fd (26) The thrust generated by the main rotor results in a translational force on the helicopter. This thrust is perpendicular to the Tip-Path-Plane (TPP) which is the plane formed by the blade tips. This force vector can be decomposed into components along the bodyframe x, y, and z axis. The magnitude of the thrust vector is represented as TMR . The components of the main rotor forces as a result of the blade flapping and thrust are given by: FB MR = \u23a1 \u23a3 XMR YMR ZMR \u23a4 \u23a6 = \u23a1 \u23a3 \u2212TMR sin a1 \u2212TMR sin b1 \u2212TMR cos a1 cos b1 \u23a4 \u23a6 (27) Unlike the main rotor, the tail rotor generates a force perpendicular to the rotor hub. The pilot has no control of the flapping angles. As a result, the resulting force component is in the y-direction only. The components of the tail rotor thrust are given by: FB T R = \u23a1 \u23a3 XT R YT R ZT R \u23a4 \u23a6 = \u23a1 \u23a3 0 TT R 0 \u23a4 \u23a6 (28) The gravitational force on the helicopter is represented in the inertial Earth-fixed frame in the downward direction given as FI g = [0 0 mg]T . This force may be expressed as components with respect to the body-fixed frame, given as follows [13, 70, 106]: FB g = \u23a1 \u23a3 Xg Yg Zg \u23a4 \u23a6 = R( )F I g = \u23a1 \u23a3 \u2212 sin \u03b8mg sin \u03c6 cos \u03b8mg cos \u03c6 cos \u03b8mg \u23a4 \u23a6 (29) For the main rotor torque, the main rotor offset distance from the helicopter center of gravity is defined as [lm, ym, hm]T [154]. The resulting torque contributed by the main rotor is given as: \u23a1 \u23a3 LMR MMR NMR \u23a4 \u23a6 = \u23a1 \u23a3 YMRhm \u2212 ZMRym \u2212XMRhm \u2212 ZMRlm XMRym + YMRlm \u23a4 \u23a6 (30) For the tail rotor torque, the distance offset of the tail rotor from the helicopter center of gravity is defined as [lt , 0, ht ]T . The resulting torque contributed by the main rotor is given by: \u23a1 \u23a3 LT R MT R NT R \u23a4 \u23a6 = \u23a1 \u23a3 YT Rht 0 \u2212YT Rlt \u23a4 \u23a6 (31) The main rotor generates an aerodynamic drag as it rotates. This drag results in a torque, QMR [70, 100], which is perpendicular to the TPP and can be decomposed into components along the body frame by projecting the torque vector on to the hub plane. The resultant components are given as: \u23a1 \u23a3 LD MD ND \u23a4 \u23a6 = \u23a1 \u23a3 QMR sin a1 \u2212QMR sin b1 QMR cos a1 cos b1 \u23a4 \u23a6 (32) 3.5 Main and Tail Rotor The helicopter receives most of its propulsive force from the main and tail rotors. The aerodynamics of the rotors, especially that of the main rotor, are highly nonlinear and complex. In order to reduce the complexity and simplify the dynamics for modeling and control design purposes, a number of assumptions are considered [13, 32, 33, 154, 155] as follows: rotor blades are rigid in both bending and torsion, small flapping angles, uniform inflow across rotor blade, no inflow dynamics used, effects of coning, due to flapping angles, is constant, forward velocity effect omitted, coupling ratio for pitch-flap is disregarded, and constant rotor speed. The dynamics of the main and tail rotors are controlled by input control commands. However, they are also affected by the motion of the helicopter. These control commands are represented by uc = [\u03b4lon \u03b4lat \u03b4ped \u03b4col]T . The thrust magnitudes of the main and tail rotors are controlled by the collective commands \u03b4col and \u03b4ped , respectively. The main rotor blade flapping dynamics is controlled by the cyclic inputs \u03b4lon and \u03b4lat , which control the tilt of the TPP. Control of the propulsive forces is achieved by controlling the direction and inclination of the TPP. Thrust produced by the rotor blades is perpendicular to the TPP. The orientation of the TPP is dependent on main rotor blade flapping dynamics. During rotation, the blades exhibit a flapping motion, a lead-lagging motion, and a pitching motion of the blade, as shown in Figs. 10, 11, and 12 respectively. These motions make-up the rotor blade DOF and are denoted by \u03b2, \u03be , and \u03b6 , respectively. The aerodynamic forces on the rotor blade depend on the orientation of the blade at any time. The blade\u2019s pitch angle, \u03b6 , affects the lift and drag of the blade elements. The flapping angle of the blade affects the inertial forces on the blade along the direction of the main rotor thrust vector. Determining the lift and drag generated by the main rotor requires consideration of the blade\u2019s flapping motion, \u03b6 , helicopter forward velocity with respect to the air, also known as free stream velocity denoted by V\u221e, rotation of the blade about the shaft in the form of angular velocity, , and also the inflow velocity of air through the rotor [155]. This total air velocity on the blade, U , can be decomposed into three components. These components are defined in relation to the plane perpendicular to the rotor shaft, known as the hub plane. The plane hub frame is defined as Fh = {Oh, ih, jh, kh} where ih points backwards towards the tail, jh points to the right of the helicopter, and kh points up. Two components are in the hub plane while the third is out of the plane. All three components are normal to the hub plane. The out of plane component is perpendicular to the hub plane pointing downward and is denoted by UP , as seen in Fig. 13c. The next component, UT , is parallel to the hub plane and tangential to the blade in the direction of the blade rotational motion as seen in Fig. 13a and d. The last component, UR , lies on the hub plane and points radially pointing outward in the direction of and parallel to the blade, as seen in Fig. 13a and c. The total air velocity seen by the blade is given as U = \u221a U2 T + U2 P . At any time during flight, the blade experiences a pitch angle, \u03b6 = \u03b1b +\u03c6b, related to the angle of attack \u03b1b of the blade with respect to the airstream U , which approaches the blade at an inflow angle \u03c6b, as seen in Fig. 14. The lift and drag on the blade are determined through blade element analysis. By considering the blade as a two-dimensional airfoil, the lift and drag vectors at each blade element may be determined. The infinitesimal lift and drag of the blade element dr are given as: dL = 1/2\u03c1aU 2cbCl\u03b1\u03b1bdr (33) dD = 1/2\u03c1aU 2cbCddr (34) The forces perpendicular and parallel to the hub plane can be expressed in terms of the lifting and drag forces as follows: dF\u2016 = dL sin \u03c6b + dD cos \u03c6b (35) dF\u22a5 = dL cos \u03c6b \u2212 dD sin \u03c6b (36) Following the procedures from [13, 155], the total force on the blades parallel (F\u2016) and perpendicular (F\u22a5) to the hub plane can be expressed in terms of the air stream velocity components as: dF\u2016 \u2248 1 2 \u03c1cbCl\u03b1 ( \u03b6UT UP \u2212 U2 P ) dr + 1 2 \u03c1cbCDU2 T dr (37) dF\u22a5 \u2248 1 2 \u03c1cbCl\u03b1(\u03b6U2 T \u2212 UT UP )dr (38) The total pitch of the blade is given as \u03b6 = \u03b60 \u2212 \u03b61 cos \u03c8b\u2212\u03b62 sin \u03c8b, where \u03b60 is the collective pitch to control the thrust of the rotor and \u03b61 = Alon\u03b4lon, \u03b62 = Blat \u03b4lat are the linear functions of the pilot\u2019s lateral and longitudinal cyclic control stick inputs (\u03b4lat , \u03b4lon) and lateral and longitudinal control derivatives (Alon, Blat ). As seen in Fig. 15, the blade is modeled as a rigid thin plate rotating about the shaft at an angular rate of . The angular position of the blade in the hub plane is denoted as \u03c8b measured from the tail axis. The blade flapping hinge is modeled as a torsional spring with stiffness K\u03b2 . The moments acting on the blade are due to the lifting force described in Section 3.5, weight of the blade, the inertial forces acting on the blade, and the restoring force of the spring. Equating all the moments acting on the blade results in: \u03b2\u0308 \u00b7 ( 2 \u00b7 K\u03b2 Ib \u00b7 1 2Ib mbgR2 b)\u03b2 = 1 2Ib \u03c1cbCl\u03b1 \u222b RB 0 r(\u03b6U2 T \u2212 UT UP )dr (39) where the blade\u2019s inertia is given by Ib =\u222b Rb 0 mbr 2dr . The flapping dynamics, \u03b2(t) in Eq. 39, can be expressed as a Fourier series neglecting the higher order terms, only keeping the first order harmonics, as: \u03b2(t) = a0 \u2212 a1 cos \u03c8b \u2212 b1 sin \u03c8b (40) Differentiating Eq. 40 and substituting \u03b2, \u03b2\u0307, and \u03b2\u0308 into Eq. 39, the flapping dynamics can then be written as a system of the form x\u0308 + Dx\u0307 + Kx = F . Here, the state vector x = [a0 a1 b1]T , a0 is the coning, a1 is the longitudinal tilt, and b1 is the lateral title angle of the TPP. The state space representation, where x1 = x and x2 = x\u0307, is given as: [ x\u03071 x\u03072 ] = [ 0 I \u2212K \u2212D ] [ x1 x2 ] (41) The TPP dynamics are simplified [13, 155] by assuming a constant coning angle, disregarding the hinge offset, assuming a zero pitch-flap coupling ratio, and disregarding the effects of forward velocity. The simplified dynamics are given in Eq. 42 for the longitudinal dynamics and Eq. 43 for the lateral dynamics as follows: \u03c4f a\u0307 = \u2212a \u2212 \u03c4f q + Abb + Alon\u03b4lon (42) \u03c4f b\u0307 = \u2212b \u2212 \u03c4f p + Bba + Blat \u03b4lat (43) Here, the time rotor constant, \u03c4f = 16 \u03b3 , is a function of the angular velocity, , and the Lock number, \u03b3 = 16 \u03b3 . Additionally, Ab = \u2212Ba = 8 \u03b3 (\u03bb2 b \u2212 1), are the rotor cross coupling terms, and \u03bb\u03b2 = K\u03b2 2Ib + 1 is the flapping frequency ratio. The total thrust and counter-torque produced by the main rotor is a function of the forces acting on the blades perpendicular and parallel to the hub plane. The expressions are given as: Tmr = Nmb 2\u03c0 \u222b 2\u03c0 0 \u222b Rt 0 dF\u22a5,t cos \u03b2d\u03c8m (44) Qmr = Nmb 2\u03c0 \u222b 2\u03c0 0 \u222b Rt 0 ldF\u2016,t d\u03c8m (45) Unlike the main rotor, the tail rotor only has a collective pitch, \u03b6t . The tail rotor blade experiences induced air velocity and has flow components similarly to the main rotor. The perpendicular and parallel force components resemble Eqs. 37 and 38 of the main rotor. The tail rotor thrust and counter-torque can be found using Eqs. 46 and 47 [13] and are given as: Ttr = Ntb 2\u03c0 \u222b 2\u03c0 0 \u222b Rt 0 dF\u22a5,t d\u03c8t (46) Qtr = Ntb 2\u03c0 \u222b 2\u03c0 0 \u222b Rt 0 rdF\u2016,t d\u03c8t (47) 3.6 Complete Set of Helicopter Equations of Motion The key equations that describe the helicopter motion and are necessary for flight controller design are summarized in Table 1."
        ]
    },
    {
        "image_filename": "designv10_5_0002520_j.optlastec.2016.06.008-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002520_j.optlastec.2016.06.008-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram of LSF equipment (a); the selection of transverse sections (b); the testing region of Vickers microhardness (c).",
        "texts": [
            " The mentioned above means that the heat input should be a critical factor influencing the formation of the cracks during high energy beam processing of nickel-based superalloy. In this paper, DZ4125, as a typical nickel-based superalloy with the high sensitivity for hot cracking, is used to further investigate the effect of the heat input on the cracks formation during laser solid forming. The characterization of the cracks is examined in detail. The formation and suppression mechanisms of the cracks during laser solid forming are also discussed. Fig. 1(a) schematically shows the LSF system used in present research. It mainly consists of a fiber laser with a maximum power of 3000 W, a numerical controlled working table, an induction heating system, a controlled atmosphere chamber and a powder feeding system with a coaxial nozzle. Argon gas was used to protect the molten pool from oxidation and was also used to carry the alloy powder. The induction heater was used to preheat the substrate. DZ4125 superalloy powder with spherical shape and a diameter of 147\u2013250 mm was used",
            " The normal chemical composition of the DZ4125 superalloy powder and substrate is shown in Table 1. Prior to the LSF experiment, the powers were dried for 3 h at 120 \u00b0C under the vacuum, and the substrates were polished with the sand papers and then were cleaned by acetone. Single trace LSFed samples with about 55 mm in length were fabricated and totally 20 layers were deposited. The LSF parameters were listed in Table 2. The samples were first sectioned perpendicular to the laser scanning direction, as shown in Fig. 1(b). Then, they were prepared for microstructure observation and microhardness testing through the metallographic practice. The OLYMPUS-GX71 optical microscope (OM) and TESCAN VEGA IILMH scanning electron microscope (SEM) were used to characterize the microstructures. Duramin-A300 Vickers microhardness tester with a load of 1.96 N and a dwelling time of 15 s was used to test the microhardness in the LSFed samples. The microhardness was measured with an interval of 0.2 mm along the line 1 and line 2 as shown in Fig. 1(c). Line 1 distributes from the as-deposited layers to the substrate, which is used to characterize the longitudinal hardness. Line 2 distributes at the center of the remelted zone in the substrate, which is used to characterize the hardness in the remelted zone of the substrate. The INSTRON11-96 universal material testing machine was used to get the stress-strain curve of LSFed DZ4125 alloy with the strain rate of 1 mm/min. To clarify the effect of thermal stresses on the formation of the liquation cracking, the Vickers micro-indentation method [21] was applied with the assumption that the residual stresses is equalbiaxial and the stress-strain curve obeys the power-law function (that is \u03c3 \u03b5= K p n, where K and n are the constants obtained from the uniaxial stress-strain curve)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001491_iros.2015.7354129-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001491_iros.2015.7354129-Figure3-1.png",
        "caption": "Fig. 3. Direction of hip joint angle and coordinates of IMU integrated at the lower back in hip exoskeleton: V vertical, AP anterior-posterior, ML medial-lateral",
        "texts": [
            " If gait task inference is completed (TC2 is satisfied), then state DGT is activated. Transition to a sub-state in DGT is determined by investigating tid conveyed. If transition condition TC4 in any state among SA, LE, or SD is satisfied, then state EX can also be activated. If a transition condition TC3 in state DGT is satisfied, then state ST is activated. Foot contact estimation is achieved by processing the vertical acceleration value (V) given from the inertial measurement unit (IMU) integrated at the lower back in hip exoskeleton as described in Fig. 3. At initial standing upright, we set the vertical acceleration value as zero to eliminate the bias. Mean value of receding prediction horizon (RPH: black rectangle) of the acceleration is compared to the threshold (TH) to determine foot contact as seen in Fig. 4. We introduce the freeze horizon (FH: blue rectangle) from a prior knowledge that some duration between foot contacts should be required. During the freeze horizon, foot contact estimation is not performed. The freeze horizon is useful because it enforces only one foot contact detection in the same step"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000679_j.ymssp.2010.02.003-Figure12-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000679_j.ymssp.2010.02.003-Figure12-1.png",
        "caption": "Fig. 12. Length of action IF along the DLA.",
        "texts": [
            " In particular, in the first part of the meshing period, for 0rtr\u00f0~e 1\u00deT , the antecedent tooth pair, denoted as pair b, is contemporary in contact on the length of action, a base pitch in advance with respect to the subsequent one, denoted as pair a. Thus, the radii of the contact point of this subsequent pair a are evaluated through Eqs. (19) of the companion paper giving r1(t), r2(t), while the radii of the contact point of the antecedent pair b is evaluated through Eqs. (20) of the companion paper giving r1(t+T), r2(t+T). Fig. 12 depicts the length of action, highlighting some important points in the calculus of the pressure torque; in particular, points I and F are the starting and the ending points of the length of action, while points B and A represent the positions where the number of meshing tooth pairs changes, in B from two to one and in A from one to two. When a new tooth pair starts the contact in I, the antecedent one is in contact in A, see Figs. 12 and 13. As the contact point of the new subsequent tooth pair (second pair in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001651_s1023193517050123-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001651_s1023193517050123-Figure4-1.png",
        "caption": "Fig. 4. CVs for oxidation of 50.0 \u03bcM droxidopa at the surface of 2PHCZNCPE at different scan rates of 10, 25, 50, 75, 100 and 150 mV s\u20131. Insets: variation of (a) anodic peak current versus the square root of scan rate. (b) Variation of the scan rate normalized current (Ip/v1/2) with scan rate.",
        "texts": [
            " However, 2PHCZNCPE shows much higher anodic peak current for the oxidation of droxidopa compared to 2PHCCPE, indicating that the combination of ZnO nanorods and the mediator (2PHC) has significantly improved the performance of the electrode toward droxidopa oxidation. In fact, in the absence of droxidopa 2PHCZNCPE exhibited a wellbehaved redox reaction (Fig. 3, curve c) in 0.1 M PBS (pH 7.0). However, there was a drastic increase in the anodic peak current in the presence of 100.0 \u03bcM droxidopa (curve f), which can be related to the strong electrocatalytic effect of the 2PHCZNCPE towards this compound [49]. The effect of scan rate on the electrocatalytic oxidation of droxidopa at the 2PHCZNCPE was investigated by cyclic voltammetry (CV) (Fig. 4). As can be observed in Fig. 4, the oxidation peak potential shifted to more positive potentials with increasing scan rate, confirming the kinetic limitation in the electrochemical reaction. Also, a plot of peak height (Ip) vs. the square root of scan rate (v1/2) was found to be linear in the range of 10\u2013150 mV s\u20131, suggesting that, at sufficient over potential, the process is diffusion rather than surface controlled (Fig. 4a). A plot of the scan rate-normalized current (Ip/v1/2) vs. scan rate (Fig. 4b) exhibits the characteristic shape typical of an EC' process [49]. Figure 5 shows the Tafel plot for the sharp rising part of the voltammogram at the scan rate of 10 mV s\u20131. If deprotonation of droxidopa is a sufficiently fast step, the Tafel plot can be used to estimate the number of electrons involved in the rate determining step. A Tafel slope of 0.0854 V was obtained which agrees well with the involvement of one electron in the rate determining step of the electrode process [49], assuming a charge transfer coefficient, \u03b1 of 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001918_j.precisioneng.2017.05.014-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001918_j.precisioneng.2017.05.014-Figure5-1.png",
        "caption": "Fig. 5. Distortion deviations in mm for the impeller.",
        "texts": [
            " However, the implementation f CT scans was not in the scope of the current research, but it ould be valuable to determine its applicability and accuracy in uture research. As an addition to the 3D optical scanning meaurement method, future research can be conducted to incorporate ifferent surface measurement techniques into the proposed disortion compensation methodology, including: fringe projection; hotogrammetry; Moir\u00e9 interferometry; coherence scanning intererometry; confocal microscopy and focus variation microscopy 16\u201320]. Fig. 4 shows the distortion deviations of the as-built turine blade and the 100% distortion inversion using the proposed ethodology. Fig. 5 shows the same data for the impeller compo- Please cite this article in press as: Afazov S, et al. A methodology for Eng (2017), http://dx.doi.org/10.1016/j.precisioneng.2017.05.014 ent. The results show that the mathematical models for distortion nversion and interpolation from the methodology work for the two omplex geometries. m for the turbine blade. Once the coordinates of the reference surface meshes for both components were inverted, the components were built and measured using the same steps from the methodology with the modified reference mesh"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000679_j.ymssp.2010.02.003-Figure11-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000679_j.ymssp.2010.02.003-Figure11-1.png",
        "caption": "Fig. 11. Unbalanced tooth space (gear 1).",
        "texts": [
            " The pressure forces depend on the same quantities as the pressure distribution around the gears, namely, the axis eccentric position (coordinates xk and yk) that influences the radial clearances between tooth tips and case, the gear angular position yk over one pitch, and the gear angular speed (see Eq. (20)). Thus, fpxk \u00bc fpxk\u00f0xk; yk;yk; _yk\u00de fpyk \u00bc fpyk\u00f0xk; yk; yk; _yk\u00de \u00f025\u00de On the other hand, the pressure torques are due to the pressure difference in the tooth spaces of the meshing teeth, which are the only unbalanced spaces. In fact, the contact point separates two volumes, at the outlet and inlet pressure (Fig. 11(a)). The other tooth spaces have a constant pressure, giving a zero resulting torque. Here the method for the computation of the pressure torques is outlined, taking into account the possibility of meshing contact along the direct (DLA) or the inverse line of action (ILA). First of all the contact along the DLA is considered. The region between the outside radius and the radius of the contact point P, shown in Fig. 11(a), has to be taken into account in order to calculate the resultant pressure torque in the unbalanced space; in fact both the pressure acting on the region between S and P in Fig. 11(b) and the pressure acting on the tooth tip determine a radial force that gives no torque. The pressure torque is just created by the difference between the pressure acting in arcs SR and PQ, that is to say, the arcs of the tooth profile between the outside radius and the radius corresponding to the contact point along the line of action. In the case of two tooth pairs in contact, the contact point will be selected that actually separates the volumes at the outlet and inlet pressure, taking into account the effect of the relief grooves"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003358_j.neucom.2020.01.072-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003358_j.neucom.2020.01.072-Figure1-1.png",
        "caption": "Fig. 1. The description of input deadzone.",
        "texts": [
            " Problem formulation Considering a robotic system with n degrees of freedom, the model of which can be described as [54] M(q ) \u0308q + C(q, \u02d9 q) \u0307 q + G (q ) = N(\u03c4 ) (1) where q, \u02d9 q, q\u0308 \u2208 R n are position vector, velocity vector and acceleration vector of the robot respectively, \u03c4 \u2208 R n is the vector of joint torques supplied by actuators, N ( \u03c4 ) is the deadzone function of the input torque, which is denoted by N(\u03c4 ) = \u03c4 \u2212 \u03c4 and \u03c4 is the error, M(q ) \u2208 R n \u00d7n is the symmetric positive definite inertia matrix, C(q, \u02d9 q) \u2208 R n \u00d7n is the Coriolis and centrifugal matrix, G (q ) \u2208 R n is the gravitational force. Property 1 [55] : The inertia matrix M ( q ) is symmetric and posi- tive definite. Property 2 [55] : The matrix \u02d9 M \u2212 2 C(q, \u02d9 q) is skew-symmetric. The nonlinear function of the deadzone can be described as N(\u03c4 ) = \u23a7 \u23a8 \u23a9 h r ( \u03c4 \u2212 b r ) , \u03c4 \u2265 b r 0 , b l < \u03c4 < b r h l ( \u03c4 \u2212 b l ) , \u03c4 \u2264 b l (2) where parameters of the deadzone b l and b r satisfy the condition that b l < 0 and b r > 0, h r (.) and h l (.) are functions of the deadzone. The function of the input deadzone is shown in Fig. 1 . If we set x 1 = [ q 1 , q 2 , . . . , q n ] T and x 2 = [ \u0307 q1 , \u02d9 q2 , . . . , \u02d9 qn ] T , then the model of robot dynamics can be described as \u02d9 x1 = x 2 (3) \u02d9 x2 = M \u22121 ( x 1 ) [ N(\u03c4 ) \u2212 C ( x 1 , x 2 ) x 2 \u2212 G ( x 1 ) ] (4) Assumption 1 : The desired trajectory is known, continuous and bounded. .2. Useful technical lemmas emma 1 [56] . If a i \u2208 R , (i = 1 , 2 , . . . n ) and 0 \u2264 x \u2264 1, then the fol- owing inequality is valid: ( | a 1 | + \u00b7 \u00b7 \u00b7 + | a n | ) x \u2264 | a 1 | x + \u00b7 \u00b7 \u00b7 + | a n | x "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000874_j.wear.2013.01.047-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000874_j.wear.2013.01.047-Figure2-1.png",
        "caption": "Fig. 2. Load of the roller linear guide.",
        "texts": [
            " When the roller linear guide is used in machine tools and machining centers, the load mainly includes the vertical load on the upper surface of the slider, the horizontal load on the side surface of the slider, and the turning torque around the motion direction of the load. Deformation is generally applied to the roller to form a pre-load on the roller linear guide and eliminate the gap between the roller and raceway, thus increasing the stiffness of roller linear guides. We calculate the magnitude of deformation of each column of the roller under loading based on contact mechanics to obtain the stiffness calculation model of the roller linear guide. Fig. 2 shows the applied load on the roller linear guide and the contact load on the roller from the contact surface of the slider. We establish the coordinate system O-XYZ at the symmetrical center point O of the roller columns, which are denoted by numbers 1, 2, 3, and 4 (Fig. 2). The vertical load FV and horizontal load FH both pass through point O, and the turning torqueMZ is exerted on the slider around the Z-axis. The normal load on each roller of the ith column from the contact surface of the slider is Qi(i\u00bc1, 2, 3, 4). The initial deformation of the rollers in each column is d0 under pre-load F0. The center distance between two rollers in the X-axis and the Y-axis direction are lx and ly, respectively. The angle between the normal direction of the contact surface and the Y-axis direction is a"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003496_tec.2020.3006098-Figure10-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003496_tec.2020.3006098-Figure10-1.png",
        "caption": "Fig. 10. 3-D FEM predicted results of the MSTPM machine @ 480rpm && 42Nm. (a) 3D meshed model, (b) 3D temperature distribution.",
        "texts": [
            " The ambient temperature during the simulation is set 30C for the 3-D FEM model, which is consistent with the bidirectional coupled electromagnetic-thermal analysis model and experiment. Since the machine cooling method is air natural cooling, an air circle, which is 10 times of the size of the simulated 3-D machine model, is specifically introduced to contain the machine to simulate the actual air around the machine. To reduce the amount of computation load, only a smallest symmetric model shown in Fig. 10 is referenced from [14-15]. The total node number and the element number of the smallest symmetric model is 178907 and 165468, respectively as shown in Fig. 10(a). An equivalent single-turn winding coil is used to predict the temperature instead of the actual coil composed of multi-strand copper wires, since the number of meshed elements can be significantly reduced and the calculation time can be effectively saved. Here, the single-turn winding coil is just modeled as the solid with anisotropic thermal conductivity. The conductivity nqn  Th Authorized licensed use limited to: University College London. Downloaded on July 07,2020 at 03:38:46 UTC from IEEE Xplore",
            " along the axial direction is set to be 300W/(mC) and the conductivity perpendicular to the axial direction is 0.15W/(mC), which are the same as those in [14-15, 30]. Other parameters are set to be the same as those in the LPTN model. The losses in each component of the machine obtained from the 2D-magnetic field solutions and the formula calculation are applied as the heat sources in the thermal 3D-FEM model. The temperature distribution of the MSTPM machine and a coil solved by 3D-FEM is shown in Fig. 10. The predicted results from both coupled model and FEM are compared in Table IX. In Fig. 10, the temperature in the winding end-part is higher than that in other components. The reason is that the end-part winding dissipates the heat through air dominantly, while the inner part mainly exchanges heat with the stator and has a larger heat transfer coefficient. In Table IX, the predicted temperature deviations are small, which confirms the coupled LPTN method. To further verify the feasibility of the coupled model, experiments on a prototyped MSTPM machine with rated power of 2.1kW are conducted"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001961_j.jclepro.2018.10.109-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001961_j.jclepro.2018.10.109-Figure7-1.png",
        "caption": "Fig. 7. Schematic of the pin-on-disc rig and the dimensions of the samples.",
        "texts": [
            " Torsional samples were tested using a torsion testing machine (NJ-100B) with a 30 /min velocity before a 20 torsional angle, a 50 /min velocity between 20 and 60 , and a 100 /min velocity after 60 . The gauge lengthwas 30mmwhen the overall length was 54mm, and the gauge cross-section is a 6-mm-diam circle, see Fig. 6. Each test was repeated three times. Dry wear tests were performed using a pin-on-disk rig (Langzhou Zhongkekaihua Tech. Co., China). The round-head pins were made of SLMed 316 L stainless steel. The diameter of each pin was 6mm. A schematic of the rig and the dimensions of the samples are shown in Fig. 7. Discs were made of 38CrMoAl, which were hardened to a depth of 0.5mm using ion-nitriding technology with hardness of 1000 HV. The contacting surfaces of the pins and discs were finished by polishing with a root-mean-square (RMS) value Ra\u00bc 0.02 mm. Each test lasted for 30min and was repeated three times. The speed was set to 400 rpmwith a rotation radius of 8mm and the applied load was 8 N. The wear rate was obtained using the Archard equation (Archard, 1953). The mass loss was measured by weighing the pin before and after the tests"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000648_978-3-642-17531-2-Figure8.35-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000648_978-3-642-17531-2-Figure8.35-1.png",
        "caption": "Fig. 8.35. Electrodynamic (ED) voice coil transducer",
        "texts": [
            " The flux-guiding iron armature induces a radial magnetic field across the air gap and thus always ensures a relative angle 0 ( , ) 90 C A B , i.e. maximum torque independ- ent of displacement (and constant transducer parameters with 0 R in Eq. (8.119)). Furthermore, the significantly smaller air gap as compared to Fig. 8.34a results in a noticeably greater flux density 0 B , enabling higher torque for the same electrical and magnetic parameters. Electrodynamic voice coil transducer Translational transducers, configuration One of the most widely distributed electrodynamic transducer types is the voice coil transducer. Fig. 8.35 shows a schematic configuration with vertical motion. Compared to the reference configuration in Fig. 8.30, the voice coil configuration makes much better use of space. The cylindrical magnetic field ensures maximum flux linkage with the coil. The minimum air gap is limited only by the winding wire width and the need for a small amount of clearance. This results in a high magnetic air gap flux density 0 B and thus a large ED force constant 0 0 0 2 ED B K N B r , (8.120) where 0BN represents the number of coil windings linked to the magnetic flux of the pole shoes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002325_icra.2015.7139915-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002325_icra.2015.7139915-Figure4-1.png",
        "caption": "Fig. 4. Three standard gait types with the corresponding duty factor \u03b2 = Tstance/Tstride is the ratio between the duration of the stance phase and the stride period. The numbers alongside the legs denote the relative phase of each leg w.r.t the rear right leg taken as the reference [7].",
        "texts": [
            " The duty factor \u03b2 for a leg is defined as \u03b2 = Tstance/Tstride (1) where Tstance is the duration of the stance phase and Tstride is the stride period. As noted by Nishii in [7], assuming the same duty factor for all legs, n\u03b2 gives the average number of legs in stance phase when n is the total number of legs. Since hexapods require at least three legs on the ground to walk statically, lowest value for \u03b2 is 0.5. Typical gaits for an hexapod are wave, diagonal amble and alternating tripod. The duty factors of these gait patterns are given in Fig. 4, while the leg motions during the gait are described next. The leg numbers in examples refer to Fig. 2. 1) Wave gait: The wave gait has one leg in \u201cswing phase\u201d (off the ground) with all other five legs in \u201cstance phase\u201d (on the ground). This pattern is repeated for each leg, leading to a six step gait common among insects. An example wave gait would have the swing phase progress as Leg 3\u2192 Leg 2 \u2192 Leg 1 \u2192 Leg 6 \u2192 Leg 5 \u2192 Leg 4. 2) Amble gait: The diagonal amble gait has two legs in swing phase at a time with four legs in stance phase",
            "These tests on concrete show that the tripod gait is the fastest on hard ground. The highest frequency plotted for each gait corresponds to the maximum achievable frequency and consequently maximum speed the hexapod can achieve in that specific gait. The maximum achievable frequency is related to the maximum speed the servos can reach during the swing phase. The shorter the time of the swing phase the quicker the leg must move through it to maintain the proper gait. The duration of the swing phase relates to both the stride frequency 1/Tstride and duty factor \u03b2 (Fig. 4), \u03b2 = 1\u2212 (Tswing/Tstride). This means that for a given stride frequency the wave gait must move its legs three times as fast during the swing phase compared to the tripod gait and is why the tripod can reach stride frequencies three times that of the wave gait. Leaf Litter: As mentioned in the experiment description, the tripod gait was ineffective at all tested speeds on this terrain type. Therefore, we only report results for the wave and amble gaits in Fig. 7(d), Fig. 7(e) and Fig. 7(f). These tests on leaf litter show that the wave gait is the fastest on soft, slippery ground"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000079_s0022-0728(79)81047-5-FigureI-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000079_s0022-0728(79)81047-5-FigureI-1.png",
        "caption": "Fig. I.",
        "texts": [
            " All the potentials are given relative to a hydrogen electrode in the same solution. Oxygen electroreduction with laccase was initially catalyzed with the use of a mediator couple. Laccase accelerates the homogeneous oxidation of hydroquinone by molecular oxygen. The electrode reaction lies in the reduction of quinone. The electrode potential depends on the ratio of the oxidized and reduced form of the carrier. The thermodynamic equilibrium constant of this reaction is high and it proceeds almost up to the formation of quinone, which is reduced on the electrode (Fig. I, curve 3). The wave observed on the polarization curve plot ted for a rotat ing pyrographi te electrode represents hydroquinone oxidation (Fig. I, curve 2). On the pyrographite electrode the quinone-hydroquinone system exhibits a reversible behaviour and OU/O log I is equal to o.o3 V. From the results obtained it follows that laccase in the quinonehydroquinone system decreases the overvoltage of oxygen electroreduction b y o.o3 V. Redox systems with a higher potential than that of quinone-hydroquinone pair (o.7I V) did not yield any desirable result either because of low solubility in water, or because of instabil i ty of the oxidized form"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000691_j.snb.2012.05.073-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000691_j.snb.2012.05.073-Figure1-1.png",
        "caption": "Fig. 1. Schematic diagram of the electrochemical flow cell (A) used in the amperometric measurements in the flow injection system. (A) PB, polyurethane resin block; RE, reference electrode; CE, counter electrode; WE, working electrode; CF, contact field; PT, polyethylene tubing (flow). Schematic diagram of the flow system (B) used",
        "texts": [
            "9) for data acquisition and experimental control. The measurements were performed in a conventional electrochemical cell of 10.0 mL capacity, where the screen-printed carbon electrode (Oxley Developments UK) was coupled. The pH measurements were carried out using a Metrohm pH-meter with a Metrohm combined pH reference electrode. All experiments were performed at a temperature of 25 \u25e6C. The measurements were taken in a flow cell specially developed to adapt the screen-printed carbon electrode; the design of the cell is shown in Fig. 1A. The body of the electrochemical flow cell was fabricated with polyurethane resin (20 mm \u00d7 40 mm \u00d7 50 mm). The effective volume of the flow cell was 95 L. The design of the screenprinted carbon electrode used in all the electrochemical experiments is also shown in Fig. 1A. The screen-printed electrode is based on an alumina ceramic base with dimensions of 50 mm length, 10 mm width, and 0.85 mm thickness, and on this surface are lined up the working (W), the reference (R), and the auxiliary (CE) electrodes, printed with carbon ink. The contacting region (CF) at the upper side of the electrode designed in Fig. 1 is connected to the potentiostat by cable using the active part formed by the ink carbon lines. The measurements of the electric current were performed by chronoamperometry in association with flow injection analysis. The electrochemical flow cell was inserted in a one-channel flow injection analysis system, which is schematically represented in Fig. 1B. The system was assembled with a peristaltic pump (Ismatec, model 78001-00, Switzerland) and a manual injector made of acrylic with two fixed sidebars and a sliding central bar. The manifold connections were made with polyethylene tubing (0.8 mm i.d.). Potassium nitrate solution 0.10 mol L\u22121 (adjusted in pH 3.0) was used as the carrier solution. The analytical path was 30 cm and the entire flow injection system was kept at room temperature. Actuators B 171\u2013 172 (2012) 795\u2013 802 797 2 t d p ( f T b s r o i S t ( T m o 2 Q u a t w t I h w d 1 t s e 5 r 3 3 c t e O s 0 a p e e f a I f P"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000391_robot.2010.5509183-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000391_robot.2010.5509183-Figure4-1.png",
        "caption": "Fig. 4. Aircraft body coordinates and control surfaces.",
        "texts": [
            " \u2022 A micro-SD card module to record flight data and other information for postexperiment analysis. \u2022 A R/C receiver to control aircraft by a human in emer- gency. The main computer receives commands from an R/C transmitter, but these are not used in control calculation. A configuration diagram of the electronic system is shown in Fig. 3. The earth fixed coordinate system defines X axis as true north, Y axis as east, and Z axis as perpendicular downward. The fuselage fixed coordinate system is defined as shown in Fig. 4 as a principal axis of inertia. The attitude of the fuselage is expressed with respect to the earth fixed coordinate system. Because the tail-sitter maneuver covers a wide range of attitudes, quaternion expression which theoretically has no singularity is used as a method of describing the attitude. Quaternion expresses the attitude by a three dimensional unit vector r and its rotation angle \u03b6 , as follows: q = [ cos(\u03b6/2) rsin(\u03b6/2) ] = [q0 q1 q2 q3] T . (1) Quaternion feedback is generally used for UAVs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000782_j.mechmachtheory.2012.11.006-Figure11-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000782_j.mechmachtheory.2012.11.006-Figure11-1.png",
        "caption": "Fig. 11. Separation (Mb0) and extra penetration (M>0) caused by POA angular misalignment.",
        "texts": [
            " POA angular misalignment is calculated through the following procedure: 1) Each axis of rotation is projected on the POA in the reference frame; 2) Angles between the projected axes and the reference axis are calculated in the reference POA; 3) Misalignment is obtained by the difference of the rotations (since same rotation in the same direction implies aligned gears). The axis OLOAr defines the positive rotation for the misalignment angle \u03b1i as shown in Fig. 10. POA angular misalignment is finally expressed in terms of slope coefficient, to enter the look-up tables, as: M \u00bc tan \u03b11\u2212\u03b12\u00f0 \u00de: \u00f018\u00de POA angular misalignment causes increased separation, if negative, or extra penetration, if positive, of teeth surfaces towards one side of the active face width (Fig. 11). Since DTE and its time derivative are calculated in the reference transverse plane, which is positioned on one gear face, the other gear face remains to be considered. If extra penetration is caused on the opposite side, an additional contribution to DTE Eq. (1) and its time derivative Eq. (5) must be added according to Eqs. (19) and (20); if instead separation is increased, there is no need for correction. Eq. (19) is scaled by the cosine of the transverse pressure angle, since DTE is calculated on the pitch circles in the tangential direction while the plane of action is tangent to the base circles"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002920_tbme.2019.2960530-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002920_tbme.2019.2960530-Figure4-1.png",
        "caption": "Fig. 4. Simulation results of microrobot motion with fluid structure interaction method. (a) The microrobot moving inside microfluid channel, the fluid speed gradient is shown with different colors. The red dotted line represents a guideline for the local magnification. (b) Tracking the microrobot\u2019s movement and measuring the degree of deviation from 0s to 0.4s. The coordinate in the left-hand side represents the microrobot position and that in the right-hand side represents the dimension of the system.",
        "texts": [
            " When a microrobot deviates from the centerline, it rotates because of the nonuniform velocity field, thereby causing the 0018-9294 (c) 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. microrobot to move toward the wrong direction. This tendency is verified through numerical simulations that aimed at investigating the dragging mechanism of microrobots in fluid. The simulation results are shown in Fig. 4. The diameter of the microfluid channel and the microrobot are 400 and 80 \u00b5m, respectively. The pipe is filled with pure water with 1000 kg/m3 density and 1e\u22123viscosity at room temperature. The microrobot is lashed and dragged by water during movement. The motion of the microrobot also affects the fluid environment. This condition is regarded as a fluid\u2013structure interaction problem. The centerline of the pipe corresponds to the X-axis, and the original starting point of the microrobot is (100, \u2212150) \u00b5m"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001963_robio.2017.8324682-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001963_robio.2017.8324682-Figure4-1.png",
        "caption": "Fig. 4: Trajectory and ZMP plot for Task 1",
        "texts": [
            " The trained IK solver is tested in the dynamic simulator of MSC Adams environment. The joint trajectories generated by the solver are given as input to the simulator for testing the solution. A set of three experiments which have high probability of losing balance are chosen in order to demonstrate the efficiency of the learnt IK solver and also to explore the advantages of an articulated torso. In the first task, it had to reach a point in the far right end where it needs to use its spine to bend towards the right, as Fig. 5: Trajectory and ZMP plot for Task 2 shown in Fig. 4a. In the second task, as shown in Fig. 5a, it has to reach a point in the left-back side, where the chest motion is tested. In the last task, it had to reach a point below its knee where it tried to explore the limitation of the pelvis and abdomen joints which is shown in Fig. 6a. Figs. 4a, 5a and 6a show the end effector trajectories along with the final posture of the robot. The corresponding ZMP plots for tasks are shown in Figs. 4b, 5b and 6b. It was observed that the ZMP stays within the support polygon while performing each of these tasks"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000492_tie.2011.2168795-Figure13-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000492_tie.2011.2168795-Figure13-1.png",
        "caption": "Fig. 13. Magnitude of the (left) fifth and (right) seventh harmonics of magnetic flux density for motor B.",
        "texts": [],
        "surrounding_texts": [
            "For that purpose, the Opera-2d/RM was chosen with the transient eddy-current solver extended to include the effects of rigid body (rotating) motion and connection of external circuits. The mesh was refined to minimize the solution errors and achieve reasonable compromise between accuracy and calculation times. The final mesh consists of 41 872 elements and is shown in Fig. 7. The application of the field-circuit method to the modeling of the magnetic field distribution in an induction motor, taking into account the movement of the rotor, requires the introduction of a special element into the model, which suitably connects the stationary and moving parts. In the rotating machine module of Opera-2d, this element takes the form of a gap element. The gap region (Fig. 8) is divided quite uniformly into 528 elements along the circumference of the gap. This yields the time of displacement of one element that is equal to about 7.5 \u00d7 10\u22125 s at synchronous speed, comparable with the average time step of computation. The gap region subdivision is essential to avoid erroneous oscillations in the field solution due to meshing. The machine was operated at synchronous speed and fed by a sinusoidal voltage. The computation accounts for the conductance of the rotor bars. The start of the modeling period is related to the instant of switching on the voltage while the rotor rotates with synchronous speed. Despite the fact that the voltage in the first two cycles increases linearly, there is an initial transient; hence, computation continues up to 0.2 s when the transient has disappeared (this is monitored by watching the phase currents and electromagnetic torque). Several snapshots were taken over the voltage cycle that followed. Fig. 9 shows the magnetic field distribution after the 0.2-s time. A number of sample points were chosen to allow for the subsequent DFT analysis. Eighty points were in fact used, and it was found important that the subdivision angle of the air gap and the angle between sample points were not the same or multiples of each other. Using the values of x and y components of magnetic flux density in each element calculated at sample points, the DFT analysis was performed in order to assess the contribution of higher harmonics Bpk = N\u22121\u2211 n=0 Bp(n)e \u2212i2\u03c0kn N , p=x and y; k=0, 1,. . ., N 2 (6) where k is the harmonic order and N is the number of sample points. The components of the flux density were calculated in the stationary frame of reference. The DFT applied to elements of the rotor moving with the rotor necessitates a simple transformation in terms of the rotor position angle Bx(rf) =Bx(sf) cos(\u03b1) + By(sf) sin(\u03b1) By(rf) = \u2212Bx(sf) sin(\u03b1) + By(sf) cos(\u03b1) (7) where \u03b1 describes the position of the rotor in a given time instant. The number of calculated harmonics was selected according to the Nyquist\u2013Shannon sampling theorem as half of the number of sample points. The core losses in each element were evaluated using the specific core loss expression, in which the parameters\u2014dependent on frequency\u2014and flux were derived from a test conducted on a sample laminated ring core. To highlight the importance of motion of the rotor, calculations were done with and without including the rotor movement. Detailed results may be found at the end of the section. Figs. 10\u201313 show the distribution of calculated magnitudes of the flux density harmonics for motors A and B. More results can be found in Appendix A. Core losses were calculated as a sum of losses due to individual harmonics and are based on specific losses measured on a ring sample at a given frequency. The superposition of losses constitutes the main simplifying approximation of the method. In reality, the higher harmonic losses are related to the resultant saturation of the magnetic circuit as influenced primarily by the first harmonic and the phase displacement of the first and higher harmonics [17]. Notwithstanding this simplification, the approach used gives quite realistic results because of the dominating influence of eddy-current losses at higher frequencies, which are less sensitive to the changes in the saturation level due to the fundamental harmonic. The DFT analysis was conducted for each element of the mesh separately using the time samples. As a result, we can construct as many tables as the computed harmonics are, each containing the results of the DFT analysis for each element in the form of sine and cosine components of the flux density. This allows color zone maps to be produced, employing the built-in procedures of a standard software package but using the relevant table as a source. This makes it also possible, for each element, to calculate the lengths of the major and minor axes of the elliptic hodograph of vector B in time and define its axis ratio (the degree of roundness of the ellipse). Loci of magnetic flux density for motor B can be found in Appendix C. Another problem that we often encounter when calculating core losses is related to rotational losses. At low and medium flux density values, the rotational losses may be several times higher than the alternating flux density losses. There are two possible approaches to resolve the difficulties. The first, presented in [18], introduces correction coefficients for hysteresis and excess losses, while the second applies correction to the total loss computed for a purely alternating flux [19], [20]. The second approach, which is more convenient in our case, was used to correct the calculated losses. The correction was made only for the first harmonic. The model of loss increase derived in [19] and [20] only applies to 50 Hz and cannot be directly used at higher frequencies. Moreover, the correction is mainly applied to the hysteresis losses as their contribution to the total losses decreases significantly as frequency increases. For the machine examined, this problem is not critical because only a small volume of the core is subjected to the rotational flux (less than 12% for the first harmonic). For high-power machines, on the other hand, about 60%\u201370% of the stator core volume is subjected to an alternating flux and about 30\u201340% to a rotational flux [21]. The degree of rotation is expressed in terms of the axis ratio, which is defined as the ratio of the minor and major axes \u03bb = Bmin Bmaj (8) where Bmaj and Bmin are the peak flux density values along the major and minor axes of the field loop. The rotational losses were calculated as follows [19], [20], [22]: Prot = [Palt(Bmaj) + Palt(Bmin)] \u03b3(\u03bb,Bmaj) (9) where Palt denotes the measured alternating iron losses. The values of \u03b3 as a function of \u03bb and Bmaj are shown in Fig. 14. Furthermore, the average aspect ratio is about 0.2, and in regions where the ratio is higher, the amplitude of flux density is close to 1.5 T for motor A, for which the correction is quite small. Fig. 15 shows the aspect ratio for the first harmonic for motors A and B. Fig. 16 shows the flux density magnitude for motor A. A rotor cage, even when rotating at synchronous speed, is subjected to magnetic flux density changes due to slotting effects. Therefore, additional losses will occur. These losses are relatively high, up to a significant percentage of total losses. This part of losses was calculated as an average value taken from all time snapshots [23], [24]. To emphasize the need to take into account the motion of the rotor in the calculation of losses, Figs. 17 and 18 show a comparison between losses calculated with and without the rotor movement. More results can be found in Appendix B. From these results, it is clear that including motion of the rotor is crucial for accurate loss calculation. Figs. 19 and 20 show the iron loss components, from the fundamental to the 40th harmonic, according to the harmonic order. One can notice significant contribution of slotting harmonics to the total losses. Fundamental losses amount to only about a half of the total losses. Thus, the losses in the rotor are dominated by the losses in the tooth tips. Despite the similarities between the constructions of both motors, the distributions of harmonics for motors A and B differ due to a significant difference in the magnetic circuit saturation level [25]. The no-load core losses calculated using the field-circuit method for motors A and B are presented in Table I."
        ]
    },
    {
        "image_filename": "designv10_5_0002387_9781118773826-Figure13.25-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002387_9781118773826-Figure13.25-1.png",
        "caption": "Figure 13.25 M~H curve of Bi 1-x La x FeO 3 (x=0.2 and x=0.3) measured at RT.",
        "texts": [
            " It gives a clear cut indication of the antiferromagnetic nature consistent with our report [110] and other literature reports [111\u2013113]. Figure 13.24(b) shows the magnetization curve (M~H) for 10% La-substituted bismuth ferrite Bi 1-x La x FeO 3 (x=0.1) sample. It is evident from Figure 13.24 that pure BiFeO 3 compound behaves like an antiferromagnet, whereas the 10% La-substituted compound shows very small remanence (M r ) of 0.588 emu/g. Structural, Electrical and Magnetic Properties 485 With a further increase of La concentration from x=0.1 to x=0.2, the M~H curve (Figure 13.25a) gives a straight thin loop behavior without saturation with remanence (M r ) value of 0.934 emu/g. With a further increase of concentration from x=0.2 to x=0.3, the area of the M~H loop (Figure 13.25b) is slightly increased. Th is indicates that the canted spin moment increases from antiferro to ferromagnetic ordering. A surprising increase in M r around 2.209 emu/g was observed in this case. Further increase of concentration from x=0.3 to 0.4 indicates that the area of the M~H loop (Figure 13.26a) increased more without saturation. Similar behavior has been observed in the case of x=0.5 (Figure 13.26b) 486 Biosensors Nanotechnology with increased area without saturation. Th e observed values of remnant magnetization were 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003697_s40192-020-00170-8-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003697_s40192-020-00170-8-Figure1-1.png",
        "caption": "Fig. 1 The bridge structure geometry used in this study and for AM-Bench challenge AMB2018-01",
        "texts": [
            " Select legs are cross-sectioned to measure the location-specific microstructure [20] and phase evolution [21]. Since cross sections from only select legs of the part are analyzed, the cooling rate analysis presented herein is used to explore the possibility of using these legs as proxies for the other features that are not cross-sectioned. The experiments were performed using a commercial LPBF machine to manufacture 3D metal alloy bridge structures while measuring the temperature in\u00a0situ. The bridge structure, shown in Fig.\u00a01, is 12.5\u00a0mm tall, 75.0\u00a0mm long, and 5\u00a0mm wide. The bottom half of the geometry consists of twelve 5.0-mm-tall legs of varying size and a larger base. The twelve legs consist of four sets of three different sizes: the largest legs (L1, L4, L7, and L10) measure 5.0\u00a0mm \u00d7 5.0\u00a0mm, the medium sized legs (L3, L6, L9, and L12) measure 2.5\u00a0mm \u00d7 5.0\u00a0mm, and the smallest legs (L2, L5, L8, and L11) measure 0.5\u00a0mm \u00d7 5.0\u00a0mm. A subset of the largest and smallest legs is cross-sectioned and analyzed by Phan et\u00a0al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000526_tac.2009.2017962-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000526_tac.2009.2017962-Figure2-1.png",
        "caption": "Fig. 2. A point mass planar satellite.",
        "texts": [
            " -/ 0 - 1 2 / / ./ - 1- (23) where - is the radial displacement, 2 is the angle measured from the horizontal line, and are the radial and tangential thrusts, respectively, 1 is the mass which is unknown but the bound is known (i.e., 1 1 1), and are bounded disturbances, and 0 is a constant related to the force field. Assume that - and 2 can be measured. Suppose and are realized by the relation 3 3 3 3 4 3 (24) where represents the actual control input and 3 the rotation angle of thrust direction (see Fig. 2). It is assumed that 3 is given by 3 3 3 , where 3 is known while 3 is unknown but satisfies 3 , , with a known constant 5\" . Note that, without control, the system admits a solution - - and 2 / with 0 - / , where - and / are constants [16]. The problem is to design a controller which transfers the point mass into the desired orbit described above despite the plant uncertainties and disturbances. At first, the system is rewritten in new coordinate system defined by - - , ., - 2 / , - / / % $ % - / / $ 4 3 ( (25) Note that 6 6 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003089_j.jmrt.2020.06.015-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003089_j.jmrt.2020.06.015-Figure2-1.png",
        "caption": "Fig. 2 \u2013 (a) Jigs for tensile testing (b) schematic diagram of a miniature specimen (c) EBSD/SEM observation position (marked",
        "texts": [
            " Three orthogonal coordinate system, namely building direction (BD), in the first (SD1) and second scanning directions (SD2), were set based on the scanning direction in the SLM process. The density of the specimens was measured using Archimede\u2019s method (RADWAG-AS-R-series) [66]. Three samples for each condition were used to obtain the average density of SLM specimens. The average densities of the SLMI and SLM-II specimens were 7.95 g/cc (99.57%) and 7.55 g/cc (94.57%), respectively, with a standard deviation of 0.0038 and 0.0173. Tensile tests were conducted using an electronic universal testing machine (Exceed, E44 MTS, USA), as shown in Fig. 2(a). Miniature tensile specimens with a total length of 18 mm, a width of 2 mm, and a thickness of 1.5 mm were fabricated via the SLM process directly. The miniature specimen is not yet standardized but widely used in several literature [67\u201371] where it is impossible to use standard specimens due to the limited size of the material produced. An important consideration in the design of miniature specimens is to keep the ratio of gauge length and width similar to ASTM standard and subsize specimens (5:1 and 4.17:1). In this study, we followed the 5:1 ratio according to the ASTM E8 standard. Prior to the tensile test, mechanical polishing was performed using SiC paper for the purpose of removing the roughness of the surface of the tensile specimen. A schematic diagram of the miniature tensile specimens is shown in Fig. 2(b) along with the reference sample coordinates: loading direction (LD), transverse direction (TD), and normal direction (ND). The relationship between the coordinate system of the SLM process based on the scanning direction and the coordinate system of the tensile specimens is as follows: LD//SD2, TD//SD1, ND//BD. The digital image correlation (DIC) technique was used to measure the stress\u2013strain curve and strain distribution of SLM specimens under the uniaxial tension testing [71]. The DIC technique is based on the calculation of the strain distribution by measuring the displacement of the speckles scattered on the surface of the tensile specimen [72,73]",
            " In this study, the deformation heterogeneities of SLM pecimens was evaluated by the spatial distribution of KAM alues. SLM specimens deformed to different engineering strains ere prepared to observe the microstructural changes under niaxial tension: e = 0.15, e = 0.20, e = 0.25 and ef for SLM-I speciens, and e = 0.05, e = 0.10, e = 0.15 and ef for SLM-II specimens, espectively. The deformation behavior of the SLM specimens nder different strain levels was experimentally analyzed t the center of the TD section via FE-SEM and EBSD, as hown in Fig. 2(c). The deformed specimens were polished nder the same conditions as the as-fabricated specimen entioned above. EBSD analysis was examined by selecting 300 \u00d7 300 m2 scanning area at a step size of 0.5 m. Addiional analyses of the fracture surfaces of the fractured tensile pecimens were conducted on the LD section. . Results .1. Microstructure characterization icrostructures of the as-fabricated SLM specimens analyzed sing OM and FE-SEM appear in Fig. 3. In the SLM process, he microstructure of SLM specimens depends on processing arameters such as initial powder size, laser power, scanning peed, scanning strategy, the thickness of the powder layer, using OM and FE-SEM: (a\u2013d) SLM-I and (e\u2013g) SLM-II, (h) a and the size of the focusing laser beam [55]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001286_tec.2017.2651034-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001286_tec.2017.2651034-Figure1-1.png",
        "caption": "Fig. 1. Motor structure. (a) stator. (b) rotor.",
        "texts": [
            " The highefficiency MSM and noise transfer function (NTF) are respectively employed to predict the vibration and noise during run-up. The calculated results are all validated by test. Moreover, independent of noise test, some commonly used psychoacoustical indices are predicted based on the calculated noise result, which can further contribute to annoyance evaluation. Based on the proposed model, the influence of current harmonics on SQ is also investigated. The motor studied in this paper is a FSCW PMSM with 6 poles/9 slots and its structure is shown in Fig. 1. Most of analytical electromagnetic force models are suitable for surface-mounted PMSM with tile shape PMs. Because the PMs of the motor in this research are not purely surface- mounted, FE method is employed for force calculation. Fig. 2 shows the 2-D electromagnetic FE model which is validated by the back electromotive force test [20]. The motor speed under investigation varies from 1500 rpm to 5000 rpm, which covers the common operation range. To analyze the vibration and noise in the whole speed range, the radial force with uniform acceleration from 1500 rpm to 5000 rpm is calculated"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003848_j.jmatprotec.2020.117032-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003848_j.jmatprotec.2020.117032-Figure8-1.png",
        "caption": "Fig. 8. Geometry of a) hybrid part after PBF-LB/M, b) conventional part after orbital forming and c) deviation to target.",
        "texts": [
            " Beside mechanical properties of hybrid parts, the geometry of tooth geometries on a sheet metal is investigated. The geometry is analysed after PBF-LB to evaluate deviations of the tooth geometry to the target geometry. In order to illustrate the potential of the approach, the tooth geometry of a tailored blank after orbital forming representing the state of reference is also considered. The part is formed from a 316L sheet metal of t0 = 2 mm with the upper limit of 4000 kN. The geometry of the as built part (Fig. 8a), the tailored blank after orbital forming (Fig. 8b) and the deviation to the target geometry (Fig. 8c) are discussed in the following. The deviation to the target geometry is evaluated by a cross section of a tooth (A-A) in Fig. 8c. The maximum deviation to the target geometry for the whole AM part is 0.10 mm at the upper side of the tooth. At this point, the AM part is smaller than the target geometry. Whereas at the flank of the tooth, the as built geometry is wider than the target geometry. For additive manufacturing using PBF-LB/M, these geometric deviations are common as investigations of Kaliamoorthy et al. (2019) show. Even though the as built geometry deviates from the target geometry, it is much closer to the target geometry than after orbital forming",
            " In a first step, the geometries of cross-sections of tailored blanks made by orbital forming of radii R40 and R35.2 (Fig. 11) and hybrid parts (Fig. 12) after deep drawing in radial direction are presented. The geometries are compared to the target tooth depth, which represents the depth of tooth cavity in the forming die. In case of orbital formed tailored blanks, the form filling after deep drawing is low. This results from insufficient material being formed. As investigations on the cross section after orbital forming show (Fig. 8), the pre-formed teeth are comparatively small. Therefore, the low form filling was expected after deep drawing. The comparison of R40 and R35.2 show only small difference between the form filling. The tooth height indicated by the length of the tooth is M. Merklein et al. Journal of Materials Processing Tech. 291 (2021) 117032 smaller for R40. The tooth terminates at the border to the cup radius. In case of R35.2 the teeth are drawn around the radius of the cup resulting in a higher tooth height",
            " Based on this result, both process chains lead to a geometry close to the target depth of the tooth. However, the part manufactured by orbital forming, deep drawing and upsetting has the smallest cup height. The cup height correlates with the force for upsetting as investigated for sheet metals by Schneider (2016). In contrary, the forming operation of the hybrid part can be used for calibrating the geometry, when the tooth geometry after additive manufacturing is already close to the target as shown in Fig. 8. When comparing the cup height of the tailored blank part with t0 = 2.5 mm and the hybrid part of layout R35.2 mm, the volume of the whole component should be considered. The volume of the tailored blank VTB = 19625 mm3 resulting from a sheet metal of t0 = 2.5 mm with a diameter of d = 100 mm is higher than for the hybrid part with t0 = 1.5 mm and AM tooth geometries (VHP = 16274 mm3). The comparison of volume shows, that more material is available for forming the tooth by using the tailored blank"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000492_tie.2011.2168795-Figure12-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000492_tie.2011.2168795-Figure12-1.png",
        "caption": "Fig. 12. Magnitude of the (left) fifth and (right) tenth harmonics of magnetic flux density for motor A.",
        "texts": [],
        "surrounding_texts": [
            "For that purpose, the Opera-2d/RM was chosen with the transient eddy-current solver extended to include the effects of rigid body (rotating) motion and connection of external circuits. The mesh was refined to minimize the solution errors and achieve reasonable compromise between accuracy and calculation times. The final mesh consists of 41 872 elements and is shown in Fig. 7. The application of the field-circuit method to the modeling of the magnetic field distribution in an induction motor, taking into account the movement of the rotor, requires the introduction of a special element into the model, which suitably connects the stationary and moving parts. In the rotating machine module of Opera-2d, this element takes the form of a gap element. The gap region (Fig. 8) is divided quite uniformly into 528 elements along the circumference of the gap. This yields the time of displacement of one element that is equal to about 7.5 \u00d7 10\u22125 s at synchronous speed, comparable with the average time step of computation. The gap region subdivision is essential to avoid erroneous oscillations in the field solution due to meshing. The machine was operated at synchronous speed and fed by a sinusoidal voltage. The computation accounts for the conductance of the rotor bars. The start of the modeling period is related to the instant of switching on the voltage while the rotor rotates with synchronous speed. Despite the fact that the voltage in the first two cycles increases linearly, there is an initial transient; hence, computation continues up to 0.2 s when the transient has disappeared (this is monitored by watching the phase currents and electromagnetic torque). Several snapshots were taken over the voltage cycle that followed. Fig. 9 shows the magnetic field distribution after the 0.2-s time. A number of sample points were chosen to allow for the subsequent DFT analysis. Eighty points were in fact used, and it was found important that the subdivision angle of the air gap and the angle between sample points were not the same or multiples of each other. Using the values of x and y components of magnetic flux density in each element calculated at sample points, the DFT analysis was performed in order to assess the contribution of higher harmonics Bpk = N\u22121\u2211 n=0 Bp(n)e \u2212i2\u03c0kn N , p=x and y; k=0, 1,. . ., N 2 (6) where k is the harmonic order and N is the number of sample points. The components of the flux density were calculated in the stationary frame of reference. The DFT applied to elements of the rotor moving with the rotor necessitates a simple transformation in terms of the rotor position angle Bx(rf) =Bx(sf) cos(\u03b1) + By(sf) sin(\u03b1) By(rf) = \u2212Bx(sf) sin(\u03b1) + By(sf) cos(\u03b1) (7) where \u03b1 describes the position of the rotor in a given time instant. The number of calculated harmonics was selected according to the Nyquist\u2013Shannon sampling theorem as half of the number of sample points. The core losses in each element were evaluated using the specific core loss expression, in which the parameters\u2014dependent on frequency\u2014and flux were derived from a test conducted on a sample laminated ring core. To highlight the importance of motion of the rotor, calculations were done with and without including the rotor movement. Detailed results may be found at the end of the section. Figs. 10\u201313 show the distribution of calculated magnitudes of the flux density harmonics for motors A and B. More results can be found in Appendix A. Core losses were calculated as a sum of losses due to individual harmonics and are based on specific losses measured on a ring sample at a given frequency. The superposition of losses constitutes the main simplifying approximation of the method. In reality, the higher harmonic losses are related to the resultant saturation of the magnetic circuit as influenced primarily by the first harmonic and the phase displacement of the first and higher harmonics [17]. Notwithstanding this simplification, the approach used gives quite realistic results because of the dominating influence of eddy-current losses at higher frequencies, which are less sensitive to the changes in the saturation level due to the fundamental harmonic. The DFT analysis was conducted for each element of the mesh separately using the time samples. As a result, we can construct as many tables as the computed harmonics are, each containing the results of the DFT analysis for each element in the form of sine and cosine components of the flux density. This allows color zone maps to be produced, employing the built-in procedures of a standard software package but using the relevant table as a source. This makes it also possible, for each element, to calculate the lengths of the major and minor axes of the elliptic hodograph of vector B in time and define its axis ratio (the degree of roundness of the ellipse). Loci of magnetic flux density for motor B can be found in Appendix C. Another problem that we often encounter when calculating core losses is related to rotational losses. At low and medium flux density values, the rotational losses may be several times higher than the alternating flux density losses. There are two possible approaches to resolve the difficulties. The first, presented in [18], introduces correction coefficients for hysteresis and excess losses, while the second applies correction to the total loss computed for a purely alternating flux [19], [20]. The second approach, which is more convenient in our case, was used to correct the calculated losses. The correction was made only for the first harmonic. The model of loss increase derived in [19] and [20] only applies to 50 Hz and cannot be directly used at higher frequencies. Moreover, the correction is mainly applied to the hysteresis losses as their contribution to the total losses decreases significantly as frequency increases. For the machine examined, this problem is not critical because only a small volume of the core is subjected to the rotational flux (less than 12% for the first harmonic). For high-power machines, on the other hand, about 60%\u201370% of the stator core volume is subjected to an alternating flux and about 30\u201340% to a rotational flux [21]. The degree of rotation is expressed in terms of the axis ratio, which is defined as the ratio of the minor and major axes \u03bb = Bmin Bmaj (8) where Bmaj and Bmin are the peak flux density values along the major and minor axes of the field loop. The rotational losses were calculated as follows [19], [20], [22]: Prot = [Palt(Bmaj) + Palt(Bmin)] \u03b3(\u03bb,Bmaj) (9) where Palt denotes the measured alternating iron losses. The values of \u03b3 as a function of \u03bb and Bmaj are shown in Fig. 14. Furthermore, the average aspect ratio is about 0.2, and in regions where the ratio is higher, the amplitude of flux density is close to 1.5 T for motor A, for which the correction is quite small. Fig. 15 shows the aspect ratio for the first harmonic for motors A and B. Fig. 16 shows the flux density magnitude for motor A. A rotor cage, even when rotating at synchronous speed, is subjected to magnetic flux density changes due to slotting effects. Therefore, additional losses will occur. These losses are relatively high, up to a significant percentage of total losses. This part of losses was calculated as an average value taken from all time snapshots [23], [24]. To emphasize the need to take into account the motion of the rotor in the calculation of losses, Figs. 17 and 18 show a comparison between losses calculated with and without the rotor movement. More results can be found in Appendix B. From these results, it is clear that including motion of the rotor is crucial for accurate loss calculation. Figs. 19 and 20 show the iron loss components, from the fundamental to the 40th harmonic, according to the harmonic order. One can notice significant contribution of slotting harmonics to the total losses. Fundamental losses amount to only about a half of the total losses. Thus, the losses in the rotor are dominated by the losses in the tooth tips. Despite the similarities between the constructions of both motors, the distributions of harmonics for motors A and B differ due to a significant difference in the magnetic circuit saturation level [25]. The no-load core losses calculated using the field-circuit method for motors A and B are presented in Table I."
        ]
    },
    {
        "image_filename": "designv10_5_0002436_j.ymssp.2018.06.034-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002436_j.ymssp.2018.06.034-Figure1-1.png",
        "caption": "Fig. 1. Photograph of actual test bearing and schematic view of ball bearing with design parameters [25].",
        "texts": [
            " Actually, the cage of the ball bearing used in turbo pump for space launch vehicle includes not only the orbital vibration of the ball but also the vibration component generated in the combustion chamber by transient vibration. Thus, the transient vibration affecting the cage can cause partial wear loss, which increases the imbalance mass of the cage, thereby increasing the radial force of the cage. In this paper, the dynamic behavior of a cage was experimentally investigated according to its rotational speed and mass imbalance through the signal analysis of the whirling motion of the cage, frequency distribution of whirling of the cage, and wear loss of the ball bearing elements in a cryogenic environment. Fig. 1 shows a schematic view of the ball bearing used in the experiment. It is a deep-groove ball bearing (model 6214), and the bore diameter is 70 mm. It is made using SUJ2 material, which is used as a general bearing material. The precision of the ball bearings is class 5 according to the International Standards Organization standard 492, and the internal clearance grade is C5. The precision class of the balls was higher than grade 25 (Standards of the American Bearing Manufactures Association-ABMA Std"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000176_1.4001485-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000176_1.4001485-Figure1-1.png",
        "caption": "Fig. 1 Outside blade of the grinding wheel",
        "texts": [
            " Mathematical Model of the Hypoid Tooth In the present paper, the adopted mathematical model of the eneration process for face-milled hypoid gears is based on the ecently proposed invariant approach 9,10 . Without the loss of enerality, the invariant approach is employed here to model the ooth surface of a spiral bevel pinion, ground by a curved blade ool according to the Gleason face-milling, fixed-setting method. 2.1 Tool Surface and Machine Kinematics. The grinding heel employed has a standard curved profile. A schematic repesentation of it is depicted in Fig. 1. It consists of three portions: art I is a straight line while parts II and III are portions of two ircles with radii f edge radius and R1 spherical radius . Rp is he point radius and p is the blade angle. The position vector of he points belonging to the generating tool surface is indicated as e , . The parameters and are the arc length on the blade rofile and the rotation angle about the tool axis, respectively. The proposed mathematical model of the machine kinematics eproduces the universal generation model UGM developed by he Gleason Works 11 , and it is based on the virtual cradle-style achine, Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001641_j.optlastec.2016.12.021-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001641_j.optlastec.2016.12.021-Figure3-1.png",
        "caption": "Fig. 3. Sampling method of microstructure and hardness samples.",
        "texts": [
            " Changing the pulse laser parameters (T_pulse and T_pause) can completely change the energy distribution within the fabrication process that results in the changing of melting behavior of material. As shown in Table 2, the peak power keeps constant of 1000 W in all experiments. However, the average power is discriminated as 500 W (item 1), 650 W (item 2), 750 W (item 3), 500 W (item 4) and 1000 W (item 5) because of the varying pulse length (T_pluse) and pause length (T_pause). Type 1 and 2 samples for microstructure of LMD parts which were fabricated with different laser pulse parameters were obtained as shown in Fig. 3. Fig. 4 presents the microstructures of central region in type 1 and 2 with different items. It can be seen that the grain size of type 2 region is smaller than the type 1 regardless of the experimental conditions. Tabernero et al. revealed that due to the edge effect in which temperature gradients on the edges are higher than those on the internal areas of the parts, the grain size near the central zone is smaller than outer zone [23]. In addition, the region of type 1 is close to the edge of the parts in which the interval time between two layers for cooling is less than the time in type 2 which is near the central region that attributes to the reciprocated laser scan path as shown in Fig",
            " Say lower single pulse energy and more number of pulses in item 4 and higher single pulse energy and less number of pulses in item 1that contributes to the smaller grain size in item 4 than 1. Furthermore, the grain size increases with the increase of T_pulse from 25 ms to 75 ms when the T_pause is 25 ms as shown in Fig. 4(a)\u2013(f) due to the increase of inputted powder and decrease of cooling rate of molten pool. Four types samples (1\u22124) for hardness indentations of LMD parts which were fabricated with different laser pulse parameters were made as shown in Fig. 3. In order to investigate the distribution of hardness, many sampling points were measured in each LMD part. Type 1 and 2 samples include nine sampling points along the surface of vertical planes in the Z-direction, 10 mm from the edge and crossing the central line respectively. Type 3 and 4 samples include thirteen sampling points along the surface of transverse planes in the Ydirection, 8 mm from the top surface and 8 mm from the substrate respectively. A step size between two sampling point is 5 mm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002424_j.mechmachtheory.2017.12.003-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002424_j.mechmachtheory.2017.12.003-Figure1-1.png",
        "caption": "Fig. 1. UGM based on virtual cradle-type universal generator: (a) Gleason\u2019s cradle-style machine tool; (b) geometric arrangement.",
        "texts": [
            " The tooth flank is determined by enveloping curve family of cutting path of the cutter blade in its continuous cutting of gear blank [20,21] . Recently, a so-called universal generation model (UGM) represented by universal machine settings has been developed by Gleason Works. It is applied for the geometric description of the tooth flank for both face-milled or face-hobbed hypoid gear [22] . Whether for a mechanical machine tool or the Six-axis CNC free-form one, and whether for a Gleason\u2019s machine or a Klingelnberg\u2019s one, the generation process can be executed [23] by application of universal machine settings. Shown in Fig. 1 is a schematic representation of the UGM based on a virtual cradle-type universal generator (e.g., the well known Gleason\u2019s cradle-style machine tool is typical one, as shown in Fig. 1 (a)). Generally, there are 8 basic machine tool settings [24,25] , known as the universal machine tool settings, as follows: \u23a7 \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23a8 \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23a9 R a = R a 0 + R a 1 \u03c6 + R a 2 \u03c6 2 + R a 3 \u03c6 3 + \u00b7 \u00b7 \u00b7 + R a n \u03c6 n S r = S r0 + S r1 \u03c6 + S r2 \u03c6 2 + S r3 \u03c6 3 + \u00b7 \u00b7 \u00b7 + S r n \u03c6n E M = E M0 + E M1 \u03c6 + E M2 \u03c6 2 + E M3 \u03c6 3 + \u00b7 \u00b7 \u00b7 + E Mn \u03c6 n X B = X B 0 + X B 1 \u03c6 + X B 2 \u03c62 + X B 3 \u03c63 + \u00b7 \u00b7 \u00b7 + X Bn \u03c6n X D = X D 0 + X D 1 \u03c6 + X D 2 \u03c6 2 + X D 3 \u03c6 3 + \u00b7 \u00b7 \u00b7 + X Dn \u03c6 n \u03c3 = \u03c30 + \u03c31 \u03c6 + \u03c32 \u03c6 2 + \u03c33 \u03c6 3 + \u00b7 \u00b7 \u00b7 + \u03c3n \u03c6n \u03b3m = \u03b3m 0 + \u03b3m 1 \u03c6 + \u03b3m 2 \u03c62 + \u03b3m 3 \u03c63 + \u00b7 \u00b7 \u00b7 + \u03b3mn \u03c6n \u03b6 = \u03b60 + \u03b61 \u03c6 + \u03b62 \u03c6 2 + \u03b63 \u03c6 3 + \u00b7 \u00b7 \u00b7 + \u03b6n \u03c6n (1) They can be used to vary the polynomial expression during generation process. They can be converted the into the any types of machine settings in the actual manufacturing by applying the higher-order polynomial functions with respect to the basic motion parameter, namely the cradle rotation angle \u03c6. Each machine setting is analytically described as a motion element associated with a coordinate system ( i , j , k ). After establishing the main coordinate systems rigidly fixed at the blank and the cutter head, their related generation motion can be determined (see Fig. 1 ) to represent the machine kinematics. With some calculated transformation matrices representing the kinematic chain from the cutter to the blank [10] , the universal mathematical model of the tooth flank can be obtained as { r b (\u03bc, \u03b8, \u03c6) = M bc ( R a , S r , E M , X D , X B , \u03b3m , \u03c3, \u03b6 ;\u03c6) \u00b7 r c (\u03bc, \u03b8 ) n b (\u03bc, \u03b8, \u03c6) = M bc ( R a , S r , E M , X D , X B , \u03b3m , \u03c3, \u03b6 ;\u03c6) \u00b7 n c (\u03bc, \u03b8 ) n b (\u03bc, \u03b8, \u03c6) \u00b7 v(\u03bc, \u03b8, \u03c6) = 0 . (2) where n b v = 0 represents the well-known theory of gearing, and ( \u03bc, \u03b8 , \u03c6) collects the Gaussian parameters \u03bc and \u03b8 , and motion parameter \u03c6"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002200_admt.201800486-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002200_admt.201800486-Figure2-1.png",
        "caption": "Figure 2. a) Schematic diagram showing the mechanism of introducing strain gradient in heteroepitaxial crystalline bilayer. Reproduced with permission.[70] Copyright 2000, Elsevier. b) Schematic diagram illustrating the rolling-up process of the Cr/SGOI nanomembranes system. c) Optical microscopy showing the rolled-up microtubes utilizing Cr as the strained layer. (b,c) Reproduced with permission.[75] Copyright 2008, American Institute of Physics. d) SEM image of two suspended SiGe/Si/SixNy/Cr (10/10/10/18 nm) microtubes with a diameter of 3.8 \u00b5m. Reproduced with permission.[73] Copyright 2004, American Institute of Physics.",
        "texts": [
            " According to different mechanisms, the internal strain gradient can be introduced by the following methods:[17,45] (a) utilizing lattice mismatch in heteroepitaxial crystalline bilayer, (b) via nonepitaxial deposition methods, (c) utilizing different swelling properties or (d) thermal response properties of different materials, (e) utilizing lattice mismatch resulted from topochemical transformation, or (f) via surface reconstruction of ultrathin nanomembranes. In the following sections, the mechanisms of the above six methods along with the corresponding advantages and disadvantages will be discussed in details with specific examples. The strain gradient in the heteroepitaxial grown bilayer originates from the different lattice constant of different materials.[17] This method was first reported in 2000,[70] where epitaxially grown GaAs/InAs bilayer rolled up into microtubes upon the etching of the sacrificial layer (AlAs), as shown in Figure 2a. In details, the lattice constant of In is larger than that of Ga. Thus, when a layer of GaAs is epitaxially grown on the crystalline InAs, the upper layer would be stretched in order to fit the lattice constant of the lower layer at the interface, while the lower layer will shrink. In this way, a tensile strain is introduced in the GaAs layer, while the InAs layer is in compression. For such heteroepitaxial crystalline bilayer system, upon strain relaxation via etching of the sacrificial layer, the upper layer tends to shrink and the lower layer tends to expand, causing a bending moment which eventually results in the rolling up of GaAs/InAs bilayer",
            "[72] Besides heteroepitaxial grown bilayer, nanomembranes deposited via nonepitaxial methods such as electron beam evaporation, magnetron sputtering, and ion plating can also contain built-in strain gradient even though those nanomembranes are either polycrystalline or amorphous.[17,41,51] Cr deposited by electron beam evaporation is a commonly used strained metal nanomembrane,[73\u201375] and is often incorporated with semiconductor layers. For example, researches have shown that the Cr layer deposited onto silicon is highly tensile strained.[73] Figure 2b,c presents a Cr/SiGe-on-insulator system fabricated via Ge condensation.[75] Once the top Cr/SiGe bilayer is released from the substrate via selective etching, the Cr layer and the SiGe layer would relax inward and outward, respectively, resulting in a bending moment that causes the bilayer to roll upward. Furthermore, the strain gradient inside the Cr layer can be controlled by the evaporation rate.[17] It should be noted that as the bending moment linearly depends on the distance between the mean positions of the forces applied to the upper and lower layers,[76] the rolling process of nanomembranes system also depends on the thickness of Cr layer, and Changhao Xu received his B",
            "[73,77,78] Depending on the deposition parameters, the strain inside SixNy can be either compression or tension. For example, a 10 nm thick SixNy layer deposited by low-pressure CVD (250 mTorr) at 800 \u00b0C from a dichlorosilane/ammonia gas mixture with a growth rate of 3.5 nm min\u22121 exhibits a considerable residual tensile strain,[73] while the SixNy film obtained under similar conditions except higher pressure (600 mTorr) presents a compressive strain.[79] The microtube fabricated with the aid of SixNy strained layer is shown in Figure 2d. The advantages of the above mentioned methods are obvious: nonepitaxial deposition methods exhibit a significant reduction in cost when compared with epitaxial methods. However, this way of introducing internal strain requires a layer of strained nanomembranes besides the functional material. The existence of strain layer might influence the characterization of the functional layer, or even erode its properties, limiting the usage of this method. To overcome this problem, strained single-layer nanomembranes were introduced by changing the deposition parameters during growth, such as the substrate temperature and growth rate, and no additional prestrained layer is needed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002941_j.ymssp.2016.07.007-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002941_j.ymssp.2016.07.007-Figure3-1.png",
        "caption": "Fig. 3. A schematic of the low-degree-of-freedom model for the dynamics of an epicyclic gearbox with three planets. The schematic focusses on the tooth meshing dynamics; for clarity, the fluid damping coefficient, which acts on the elements at all time, cfluid, has been omitted.",
        "texts": [
            " A number of authors have described models considering both translational and rotational degrees of freedom [27\u201329] when investigating the influence of aspects such as planet phasing, gyroscopic effects, mesh stiffness variation and transmission error excitation on dynamic response. Other authors have presented purely rotational models [30\u201332]. Despite the fact that these low degree-of-freedom models are simpler in their formulation, incorporated nonlinearities still allow various interesting, sometimes chaotic, dynamic phenomena to be simulated. In our model we similarly adopt a low-degree-of-freedom approach. Fig. 3 shows a schematic of an epicyclic gearbox with three planets, with each gear subject to an independent torsional loading. Resolving moments acting on each element in the epicyclic gearbox yields the equations of motion \u2211 \u2211\u03b8 \u03b8 \u03b8 \u03b8 \u03b2 \u03b8 \u03b8 \u03b8 \u03b8 \u03b8 \u03b8 \u03b2\u00a8 + ( ) + \u02dc ( ) ( ) = ( )= = J r C e r k B e T, , , , , , , , , , , 1a s s s n N sn s n c sn sn s n N sn s n c sn s n c sn sn s 1 1 \u03b8 \u03b8 \u03b8 \u03b8 \u03b2 \u03b8 \u03b8 \u03b8 \u03b8 \u03b8 \u03b8 \u03b2 \u03b8 \u03b8 \u03b8 \u03b2 \u03b8 \u03b8 \u03b8 \u03b8 \u03b8 \u03b8 \u03b2 \u00a8 + ( ) + \u02dc ( ) ( ) \u2212 ( ) \u2212 \u02dc ( ) ( ) = ( ) J r C e r k B e r C e r k B e T , , , , , , , , , , , , , , , , , , , , , 1b n n n sn s n c sn sn n sn s n c sn s n c sn sn n nr n r c nr nr n nr n r c nr s n c nr nr n \u2211 \u2211\u03b8 \u03b8 \u03b8 \u03b8 \u03b2 \u03b8 \u03b8 \u03b8 \u03b8 \u03b8 \u03b8 \u03b2\u00a8 + ( ) + \u02dc ( ) ( ) = ( )= = J r C e r k B e T, , , , , , , , , , 1c r r r n N nr n r c nr nr r n N nr n r c nr n r c nr nr r 1 1 ( ) ( ) ( ) ( ) \u2211 \u2211 \u2211 \u2211 \u2211 \u03b8 \u03b1 \u03b8 \u03b8 \u03b8 \u03b2 \u03b1 \u03b8 \u03b8 \u03b8 \u03b8 \u03b8 \u03b8 \u03b2 \u03b1 \u03b8 \u03b8 \u03b8 \u03b2 \u03b1 \u03b8 \u03b8 \u03b8 \u03b8 \u03b8 \u03b8 \u03b2 + \u00a8 \u2212 ( ) \u2212 \u02dc ( ) ( ) \u2212 ( ) \u2212 \u02dc ( ) ( ) = ( ) = = = = = \u239b \u239d \u239c\u239c \u239e \u23a0 \u239f\u239fJ m r r C e r k B e r C e r k B e T cos , , , , cos , , , , , , cos , , , , cos , , , , , , , 1d c n N n n c c s n N sn s n c sn sn c s n N sn s n c sn s n c sn sn c r n N nr n r c nr nr c r n N nr n r c nr n r c nr nr c 1 2 1 1 1 1 where \u03b8 is angular position, J is moment of inertia, m is mass and r is the radius",
            " (1) leads to the following equations of motion for an epicyclic gearbox \u2211 \u2211\u03b8 \u03b2 \u03b8 \u03b8 \u03b2\u00a8 + ( ) + \u02dc ( ) ( ) = ( )= = J r C x r k B x T, , , , 6a s s s n N sn sn sn s n N sn s c sn sn sn s 1 1 \u03b8 \u03b2 \u03b8 \u03b8 \u03b2 \u03b2 \u03b8 \u03b8 \u03b2\u00a8 + ( ) + \u02dc ( ) ( ) \u2212 ( ) \u2212 \u02dc ( ) ( ) = ( )J r C x r k B x r C x r k B x T, , , , , , , 6bn n n sn sn sn n sn s c sn sn sn n nr nr nr n nr s c nr nr nr n \u2211 \u2211\u03b8 \u03b2 \u03b8 \u03b8 \u03b2\u00a8 + ( ) + \u02dc ( ) ( ) = ( )= = J r C x r k B x T, , , , 6c r r r n N nr nr nr r n N nr s c nr nr nr r 1 1 ( ) ( ) ( ) ( ) \u2211 \u2211 \u2211 \u2211 \u2211 \u03b8 \u03b1 \u03b2 \u03b1 \u03b8 \u03b8 \u03b2 \u03b1 \u03b2 \u03b1 \u03b8 \u03b8 \u03b2 + \u00a8 \u2212 ( ) \u2212 \u02dc ( ) ( ) \u2212 ( ) \u2212 \u02dc ( ) ( ) = ( ) = = = = = \u239b \u239d \u239c\u239c \u239e \u23a0 \u239f\u239fJ m r r C x r k B x r C x r k B x T cos , cos , , cos , cos , , . 6d c n N n n c c s n N sn sn sn c s n N sn s c sn sn sn c r n N nr nr nr c r n N nr s c nr nr nr c 1 2 1 1 1 1 Tooth profile defects may be incorporated into the model as part of a periodic no-load STE function. From Fig. 3, an individual tooth on the sun gear will mesh with a particular planet gear at a frequency, \u03b8S\u0307unMesh, of \u03b8 \u03b8 \u03b8\u0307 = \u0307 \u2212 \u0307 ( ). 7s cSunMesh For an epicyclic gearbox with N planets, the tooth will mesh with a planet gear at a frequency of \u03b8 \u0307N SunMesh rad s 1. An individual tooth on the ring will mesh with a particular planet gear at a frequency, \u03b8R\u0307ingMesh, of \u03b8 \u03b8 \u03b8\u0307 = \u0307 \u2212 \u0307 ( ), 8r cRingMesh which, similar as in the case of a tooth on the sun gear, indicates that a tooth on the ring gear will mesh with a planet gear at a frequency of \u03b8 \u0307N RingMesh rad s 1"
        ],
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    },
    {
        "image_filename": "designv10_5_0002687_tmag.2017.2665580-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002687_tmag.2017.2665580-Figure7-1.png",
        "caption": "Fig. 7. Schematic of the optimized rotor structure. (a) Initial rotor. (b) Optimized rotor.",
        "texts": [
            " 6 shows the simulated average torque variation with the DC current ratio when the phase current is 12 A. It can be seen that the torque increases with the DC ratio, then reaches a maximum value, and after that the torque begins to decrease. Under the constant phase current, that is constant copper loss, from Eq. (9), the optimum DC ratio for maximum torque is related to the PM flux linkage, \u03c8PM, and the magnetizing inductance, Lm. For this designed machine, the optimal value of k is 0.36. The structure of uneven rotor tooth distribution is adopted to reduce the torque ripple. As shown in Fig. 7, all the rotor teeth have the same width and length, but the odd number rotor teeth are rotated 1.5 mech. degree clockwise. The electromagnetic torque waveforms with pure and with a DC ratio of 0.36 are compared in Fig. 8 (a). The average torque increases from 3.22 Nm to 3.57 Nm, about 11% improvement, 0018-9464 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001973_b978-0-12-417049-0.00005-5-Figure5.2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001973_b978-0-12-417049-0.00005-5-Figure5.2-1.png",
        "caption": "Figure 5.2 Schematic of the armature controlled DC motor (\u03b8m 5 rotation angle, \u03c9m 5motor angular speed, IL 5 load moment of inertia).",
        "texts": [
            "1 In this example, we derive the dynamic models (transfer function, state-space model) of the direct current (DC) electrical motor which is used in mobile robots to provide the torques that lead to the desired acceleration and velocity of them. DC motors are distinguished into motors controlled by the rotor (armature controlled), and motors controlled by the stator (field controlled). Both the motors will be considered. Armature Controlled DC Motor The rotor involves the armature and the commutator. A schematic of this motor is shown in Figure 5.2, where Ra and La are the resistance and inductance of the rotor, IL is the load moment of inertia, and \u03b2 is the linear friction coefficient. The mechanical torque is given by: Tm\u00f0t\u00de5 Kaia\u00f0t\u00de \u00f05:7\u00de where Ka is the motor\u2019s torque constant. The back electromotive force (emf) eb which is subtracted from the input voltage \u03c5a is proportional to \u03c9m, that is: eb 5 Kb\u03c9m\u00f0t\u00de; \u03c9m\u00f0t\u00de5 d\u03b8m\u00f0t\u00de=dt \u00f05:8\u00de 0.33eb \u03c9m (rad/min)0 Tm eb 0.67eb ia=const Rf if Stability is a binary property of a system, that is, a system cannot be simultaneously stable or not stable"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002419_j.jmatprotec.2017.11.026-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002419_j.jmatprotec.2017.11.026-Figure2-1.png",
        "caption": "Fig. 2. Schematic of coaxial powder feeding with four tips, (a) top view of nozzle, (b) photograph of powder flow on symmetric plane.",
        "texts": [
            " (5), the deposition height increment of the point W within time dt can be represented as = \u2212 \u2212 = \u2026+dh C x v dt y z dh v dt \u03c1 i ( , , ) 0, 1, 2,i i b i i i p p 1 (6) Based on this iterative relation, once the powder flow mass spatial distribution and the melt pool boundary are obtained, deposited growth at any point on a single-layer deposition path can be described. 2.2. Defining the powder flow mass spatial distribution In this study, a coaxial nozzle was used with typical powder feed situation. This consisted of four tips uniformly orientated about the optical axis of the laser. The relation of orientation of nozzle tips and scanning direction is shown in Fig. 2(a). Powder flow mass spatial distribution can be obtained from an effective model developed using analytical methods. This model has also been previously developed and validated (Tan et al., 2012, 2016). The powder flow mass spatial distribution of a four-tip coaxial nozzle C(x, y, z) can be given as; = +C x y z C x y z C x y z( , , ) ( , , ) ( , , )13 24 (7) \u239c \u239f \u239c \u239f = \u00d7 \u23a1 \u23a3 \u23a2\u2212\u239b \u239d \u239e \u23a0 \u23a4 \u23a6 \u23a5 + \u00d7 \u23a1 \u23a3 \u23a2\u2212\u239b \u239d \u239e \u23a0 \u23a4 \u23a6 \u23a5 + \u2212 + \u2212 + \u2212 + + \u2212 + \u2212 + \u2212 \u2212 + \u2212 \u2212 + \u2212 + + \u2212 \u2212 + \u2212 C x y z( , , ) exp exp m a \u03c0v l z \u03c6 x S z \u03c6 \u03c6 x S z \u03c6 \u03c6 y a l z \u03c6 x S z \u03c6 \u03c6 m a \u03c0v l z \u03c6 x S z \u03c6 \u03c6 x S z \u03c6 \u03c6 y a l z \u03c6 x S z \u03c6 \u03c6 13 4 { csc [ ( )cot ]cos } {[ ( )cot ]sin } { csc [ ( )cot ]cos } 2 4 { csc [ ( )cot ]cos } {[ ( )cot ]sin } { csc [ ( )cot ]cos } 2 p p f f f p p f f f 2 0 2 2 2 2 0 2 2 2 (7-1) \u239c \u239f \u239c \u239f = \u00d7 \u23a1 \u23a3 \u23a2\u2212\u239b \u239d \u239e \u23a0 \u23a4 \u23a6 \u23a5 + \u00d7 \u23a1 \u23a3 \u23a2\u2212\u239b \u239d \u239e \u23a0 \u23a4 \u23a6 \u23a5 + \u2212 + \u2212 + \u2212 + + \u2212 + \u2212 + \u2212 \u2212 + \u2212 \u2212 + \u2212 + + \u2212 \u2212 + \u2212 C x y z( , , ) exp exp m a \u03c0v l z \u03c6 y S z \u03c6 \u03c6 y S z \u03c6 \u03c6 x a l z \u03c6 y S z \u03c6 \u03c6 m a \u03c0v l z \u03c6 y S z \u03c6 \u03c6 y S z \u03c6 \u03c6 x a l z \u03c6 y S z \u03c6 \u03c6 24 4 { csc [ ( )cot ]cos } {[ ( )cot ]sin } { csc [ ( )cot ]cos } 2 4 { csc [ ( )cot ]cos } {[ ( )cot ]sin } { csc [ ( )cot ]cos } 2 p p f f f p p f f f 2 0 2 2 2 2 0 2 2 2 (7-2) where C 13(x, y, z) is the powder flow mass concentration from nozzle tip1 and tip3, C 24(x, y, z) is the powder flow mass concentration from nozzle tip2 and tip4, a and l stand for the characteristic parameters of powder flow, \u03c6 is the angle between the center line of the single powder stream and the horizontal, and Sf shows the distance between the theoretical focus position and the nozzle exit plane (as shown in Fig. 2(b)). Similarly, this method of powder stream superposition can also be applied to obtain powder flow mass spatial distribution of the multi-tip or annular coaxial feeding nozzle. 2.3. Defining the melt pool boundary In the proposed strategy, the melt pool boundary is first obtained in the absence of powder injection, and then the deposition process can be considered as interaction between the melt pool and powder flow in the absence of the laser beam. To simply the process, some assumptions should be made",
            " From the geometric relation, spot diameter D= 2Ltan \u03b8, where L is the distance from laser focus to deposited surface, \u03b8 is the divergence angle of laser beam. So spot diameter Dj after layer j deposition can be calculated as; = + \u2212\u2212D D \u0394Z h \u03b82( )tanj j layer j1 (18) Experimental investigation of single-pass deposition was performed using a DMD system, consisting of a 5 kW continuous wave CO2 laser (multi-mode laser), a powder delivery unit, and a CNC machine. Fig. 4 shows a schematic of the DMD system. A coaxial nozzle with four tips (as shown in Fig. 2) was used to feed the powders into the melt pool by argon gas. The theoretical focus position of the powder flow of the nozzle is at 13.5 mm below the nozzle exit plane, the nozzle tips are included at 65\u00b0to the horizontal plane, and the diameter of the nozzle tube is 1.5 mm 316L stainless steel was used for both the powder and substrate (plate with dimension of 120 \u00d7 60 \u00d7 6 mm) for the experiments. The powder particle diameter was limited by the separation of the molecular sieve to simplify the analysis, and the equivalent diameter of the as 150 \u03bcm in this study",
            " This influences the deposition characteristics of different scanning directions, making it necessary to create a method to investigate the effects of the orientation relationship between the nozzle tip and laser scanning direction. In this study, a four-tip coaxial nozzle is used, and the deposition tracks were along the two symmetrical planes of the nozzle, respectively (as shown in Fig. 11). Fig. 11(a) shows a 90\u00b0 powder feeding configuration (is the same as the above subject investigated shown in Fig. 2), and Fig. 11(b) shows a 45\u00b0 powder feeding situation. To analyze the deposition layer growth at 45\u00b0 powder feeding configuration, the powder flow mass concentration of 45\u00b0 powder feeding configuration must first be determined. It can be described as; \u2032 \u2032 \u2032 = \u2032 \u2032 \u2032 + \u2032 \u2032 \u2032C x y z C x y z C x y z( , , ) ( , , ) ( , , )45 45 13 45 24 (19) Where C45(x', y', z') is the powder flow mass concentration in moving coordinate system of 45\u00b0 powder feeding configuration. According to geometrical relations between powder flow coordinate systems at 45\u00b0 powder feeding configuration and at 90\u00b0 powder feeding configuration, the coordinate transformation relation can be obtained from \u2032 = + \u23a1\u23a3 + \u23a4\u23a6 \u2032 = + \u23a1\u23a3 + \u23a4\u23a6 \u2032 = ( ) ( ) x x y y x y z z cos arctan sin arctan \u03c0 y x \u03c0 y x 2 2 4 2 2 4 (20) So, the powder flow mass concentration at 45\u00b0 powder feeding configuration can be obtained from Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003459_d41586-019-03363-0-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003459_d41586-019-03363-0-Figure1-1.png",
        "caption": "Figure 1 | Magnetic soft microbots morph on cue. a, Cui et al.1 have fabricated microscopic components consisting of magnetized panels connected by flexible hinges. When an external out-of-plane magnetic field is applied, the panels move in a direction that depends on the panels\u2019 direction of magnetization (red arrows) and on the direction of the applied field. For example, this two-panel system bends at the hinge. b,\u00a0Robots assembled from panels that have different magnetization directions can thus be made to undergo complex movements when a sequence of magnetic fields is applied, such as this bird producing flapping movements.",
        "texts": [
            " This, in turn, meant that it was easier to re-magnetize thicker magnets \u2014 to \u2018over-write\u2019 the strength and direction of their magnetization \u2014 using relatively weak fields. Cui and colleagues could therefore selectively tune the magnetization of the nano magnets so that an actuating magnetic field (much weaker than the fields that initially magnetized them) caused different panels to fold in different ways. The resulting multi-panelled components were thus \u2018programmed\u2019 to morph into specific configurations in an actuating magnetic field (Fig.\u00a01). These components could, in turn, be assembled to produce complex shapes, such as letters, and even to make a microscopic \u2018bird\u2019 that produces motions such as turning, flapping and slipping across a surface. Much work must still be done to achieve the full potential of magnetic soft robots for biomedical applications across various length scales. They must be designed using quantitative models to optimize their performance for specific tasks in relatively weak magnetic fields \u2014 that is, to work out which reconfigurations are needed, the sizes of the forces that the robot must exert on its environment, and the speeds at which reconfigurations should occur and with which the forces should be applied"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001114_s10846-015-0231-1-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001114_s10846-015-0231-1-Figure5-1.png",
        "caption": "Fig. 5 The tri-tiltrotor platform hovering\u2013navigation control principles",
        "texts": [
            " In order to maintain a tractable model of the rotor-tilting mechanisms for control, the identified models (17) are reformulated to have the same dynamics, and their dc-gain is set as: \u03b4\u03b3i \u03b4\u03b3 r i |t\u2192\u221e = 1. It is consequently left to a properly synthesized Low-Level Control structure (elaborated in Section 4.2) to handle the proper manipulation of the low-level commandUsi and account for this non-linearity. 3.3 Modeling for Control The control principles of the UPAT-TTR for hovering navigation -i.e. near-zero attitude translation control- are illustrated in Fig. 5. The aerial vehicle\u2019s attitude, as well as its lateral and vertical dynamics, are considered along the usual tri-rotor configuration approach: Fig. 5a) indicates the roll\u03c6 control authority, achieved via differential thrusting of the main rotors, Fig. 5b) shows the pitch-\u03b8 control principle, which exploits differential thrusting of two main (front) rotors and the tail (back rotor), Fig. 5c) illustrates the yaw-\u03c8 control authority, which relies on lateral tilting/lateral thrust projection of the tail rotor\u2019s thrust to create a yawing moment w.r.t. the COM, Fig. 5e) presents the standard underactuated approach employed to control the vehicle\u2019s lateral-y motion, via \u03c6-projection of its thrust force, and Fig. 5f) indicates the use of the total rotor thrust force to control the altitude-z. The longitudinal-x DoF motion however, illustrated in Fig. 5d), exhibits the exceptional trait that it can be driven by two actuation principles, namely either via main rotor-tilting/longitudinal projection of their com- bined thrust, or via (underactuated) body \u03b8 -pitching. Within this work the exploitation of this unique feature is regarded as a compound control authority, utilizing both principles in order to maximize the aerial system\u2019s performance w.r.t. its longitudinal dynamics. The attitude dynamics are of crucial importance to the platform\u2019s flight stability",
            " This model incorporates the effect of the differentiated main and tail rotor internal dynamics on the evolution of the vertical motion. However, it accounts for an asymmetrically generated moment only in the steady-state sense (via the coefficients {c1,2, c3}), as for the specific rotor scaling of the UPAT-TTR platform it was experimentally found to provide sufficient performance. The actuation allocation of the translation control authorities is provided in overview, consistently with the principles described in the beginning of Section 3.3 and illustrated in Fig. 5d, e, f), with \u03b4\u03c6r , \u03b4\u03b8r being used as reference inputs for the cascaded attitude control [28] structure: Ulon = [ U \u03b3 lon U\u03b8 lon ] = [ \u03b4\u03b3 r x \u03b4\u03b8r ] , Ulat = \u03b4\u03c6r , Uvert = \u03b4T r (48) \u0394UX a = \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 \u03b4T X 1 \u03b4\u03b3 X 1 \u03b4T X 2 \u03b4\u03b3 X 2 \u03b4T X 3 \u03b4\u03b3 X 3 \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 = \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 c1,2(\u2212Uvert ) U \u03b3 lon c1,2(\u2212Uvert ) U \u03b3 lon c3(\u2212Uvert ) 0 \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 . (49) The necessary complete setup in order to achieve the accurate and autonomous operation of the UPAT-TTR platform consists of multiple subsystems. The most crucial parts of this synthesis are: a) the onboard State Estimation scheme, b) the Low-Level actuation control scheme, c) the Attitude Control scheme, d) the (Feedforward) Compensation scheme, and e) the Explicit Model Predictive Control scheme"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002279_s00170-017-1179-z-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002279_s00170-017-1179-z-Figure6-1.png",
        "caption": "Fig. 6 a Filling contour using longest line as vector. b Filling contour from MAT curve toward outside [16]. c Proposed filling pattern",
        "texts": [
            " As can be concluded from building up the blocks, the startand-stop of deposition made the surfaces at the two ends rough, where extra material had to be added for post-machining. It also had a stair-step effect along the boundary when building free-form contour as shown in Fig. 7g. To get a good surface and minimize the amount of additional material, the number of start-and-stops of deposition along the contour should be minimized. Traditionally, the longest straight line inside the contour was chosen as the vector to fill the contour. This method resulted in start-and-stops of deposition existing along the whole contour (see Fig. 6a). Another filling method proposed in ref. [16] filled the con- (a) (b) (c) \u2026 = (h)(e) (f) (g) (d) \u2212 \u2212 Sliced contour (a) Sort points (b) Find longest segment (c-d) Offset curve (e-f) Generate robot code Compensation& lead-in/lead-out (g-h) Fig. 7 Procedure of the proposed process planning method tour from a MAT curve toward the outside. This method also resulted in start-and-stops of deposition existing along the whole contour (see Fig. 6b). In this study, a long smooth curve was extracted from the boundary curve. The contour was filled by offsetting the smooth curve with a certain y offsetting until it completely covered the contour. In this way, no start-and-stop of deposition existed along the extracted curve (see Fig. 6c). The surface along the extracted curve was smooth with no need to add material for post-machining. This method was significantly effective for walled free-form structures like propeller, blade, and impeller, because the extracted smooth curve could be very long. Consequently, a large fraction of the surface was smooth and needed a very small amount of additional material for post-machining. The schematic presentations of the proposed filling process are shown in Fig. 7. It consists of five steps that are detailed as follows: 1",
            " To compensate for the voids, the start-and-stop points of deposition tracks are extended along the tangential direction until the voids disappear (see Fig. 7h). The voids are compensated based on local geometries instead of considering the machining allowance on the original model. This compensation saves material at the smooth places where only a small amount of additional material is needed for post-machining. 5. Generate the robot code in MATLAB For each track, the lead-in and lead-out points are determined by extending the start-and-stop point along their tangential directions with a lead-in/lead-out distance (see Fig. 6h). The TCP position and orientation of the laser head at a point is TCPpi = [xpi, ypi, zpi, api, bpi, cpi, E1pi, E2pi]. The command to reach this position and orientation can be generated by fprintf(fid, 'LIN{E6POS: X %4.4f, Y %4.4f, Z %4.4f, A %4.4f, B %4.4f, C %4.4f, E1%4.4f, E2%4.4f} C_DIS%n', TCPpi). fid is the defined file handle fid = fopen(['name of src file', '.txt'],'wt'). The command for laser/wire control is defined in the subfunction as fprintf fid; 0 LASERON\u00f0\u00de%n 0 ; fprintf fid; 0 WIREON\u00f0\u00de%n 0 ; fprintf fid; 0 LASEROFF\u00f0\u00de%n 0 ; fprintf fid; 0 WIREOFF\u00f0\u00de%n 0 ; A free-form enclosed 2D contour sliced from a blade was built using the proposed process planning method"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002200_admt.201800486-Figure15-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002200_admt.201800486-Figure15-1.png",
        "caption": "Figure 15. a) Illustration of shallow etching method to eliminate the poor rolling behavior at the corners. Reproduced with permission.[207] Copyright 2002, IOP Publishing. b) Tilted deposition method utilizing the ballistic shadow effect and SEM image of rolled-up Ti/Au microtubes exhibiting well-defined direction. Reproduced with permission.[51] Copyright 2008, Wiley-VCH. c) SEM images showing nanomembranes with long-side rolling behavior. Reproduced with permission.[210] Copyright 2010, American Chemical Society. d) Schematic diagram showing the structures of initial wrinkle layer, tube at wrinkled edge, and tube at flat edge. e\u2013h) Optical microscopy image showing the rolling process of flat and wrinkled nanomembranes. The flat nanomembrane exhibits long-side rolling behavior while the wrinkled nanomembrane rolls from the short side. (d\u2013h) Reproduced with permission.[208] Copyright 2018, American Chemical Society.",
        "texts": [
            " However, when considering etching process (such as wet etching), the patterned nanomembranes are not released from the substrate immediately but rather gradually, because the sacrificial layer starts to dissolve upon contacting with etchants. Thus, all sides of patterned nanomembranes would bend initially once they are released from the substrate and final rolling behavior is hard to control (i.e., the poor rolling behavior at the pattern corners).[207,208] Several methods have been proposed to manipulate the rolling behavior of patterned nanomembranes and induce the nanomembranes to roll along the desired direction with accurate positioning. The first method is shallow etching,[207] as shown in Figure 15a. A deep mesa structure was created on the top of InGaAs/GaAs bilayer grown on a GaAs (100)-oriented substrate via MBE. Then certain part of the upper GaAs layer was removed in a second lithography step and a shallow mesastructure was obtained. Upon releasing the nanomembranes from GaAs substrate, the strain-free single InGaAs layer would not bend and only the shallow mesastructure area could roll due to strain relaxation. The adjacent InGaAs layer at the boundary was ruptured during the rolling process as a result of mechanical stresses concentration. In this way, the pattered bilayer would roll along the desired direction without any poor rolling behavior at corners. The other method is glancing angle deposition (GLAD) techniques,[51] which could be used in normal physical vapor deposition methods such as electron beam or thermal evaporation as well as sputtering. As shown in Figure 15b, the sacrificial layer (photoresist) was patterned into rectangles by photolithography and strained nanomembranes were deposited onto the tilted substrate. In this case, a narrow gap remained open after deposition at the far end of the patterned sacrificial layer due to the ballistic shadow effect that always occurs in GLAD.[209] Thus, the etchants would enter the gap and the etching process started only from this gap, leading to the formation of microtubes array with well-defined direction. Furthermore, the rolling process and final morphology of nanomembranes with rectangular patterns are of great interest, as rectangle is a basic shape and many other complex pattern could be regarded as a combination of rectangles. The rolling behavior of rectangle nanomembranes upon isotropic etching has been investigated both experimentally and theoretically.[210,211] Generally, nanomembranes with rectangular shapes would preferably roll along the direction perpendicular to the long side. As shown in Figure 15c, though both the long side and the short side of rectangle start to roll at the beginning due to the simultaneously and isotropic etching process, the curved short side compromises by opening itself up to allow continued rolling from the long side as the etching proceed with increasing portion of free nanomembranes. Such preferable rolling direction could be explained by the larger bending force to roll perpendicular to the long side than the bending force to roll parallel to the long side, which has been justified by the simulation with finite element method",
            " The deformation history, which could influence the experimental process such as etching rate in different directions, might also determine the rolling direction depending on the intermediate status. Nevertheless, long-side rolling is still dominant for rectangularpatterned nanomembranes. Moreover, anisotropic etching process kinetically created via lithographical patterning could force the rectangle nanomembranes to exhibit long-side rolling with 100% yield.[210] To change such long-side rolling dominance and make the rectangle nanomembranes roll along the short side, a method utilizing wrinkles has been proposed.[208] As shown in Figure 15d, when a rectangular prestrained wrinkled nanomembrane is gradually released from its substrate, it would either roll along the wrinkled edge and form a tube at wrinkled edge (TWE) or roll along the flat edge and form a tube at flat edge (TFE). Theoretical study showed that TFE is the energetically favorable morphology as bending from the wrinkled edge would be suppressed by an energy barrier arising from the need to flatten the wrinkles. Experiments based on such wrinkled structures have also been performed, as shown in Figure 15e\u2013h. The wrinkled rectangle nanomembranes were prepared by deposition of metallic CuNiMn alloyed nanomembranes on wrinkled surfaces of photoresist and the lithographic step afterward. Adv. Mater. Technol. 2019, 4, 1800486 www.advancedsciencenews.com \u00a9 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim1800486 (17 of 26) www.advmattechnol.de Upon contacting with droplets of N-methyl-2-pyrrolidone to selectively remove the sacrificial layer, the wrinkled nanomembranes would roll along the flat edge (short side) and eventually form a TFE"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003831_tia.2020.3029997-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003831_tia.2020.3029997-Figure3-1.png",
        "caption": "Fig. 3. 3-D LPTN modelling of active-winding. The equivalent slot thermal conductivities in \ud835\udc5f - and \ud835\udf03 - directions \ud835\udf06\ud835\udc5f/\ud835\udf03, and in \ud835\udc67- direction \ud835\udf06\ud835\udc67 are calculated as [21]:",
        "texts": [
            " 2, in which the main parts are included. In order to restrain the overestimated error caused by simplified \u201cI-type\u201d thermal network, the LPTN is modelled based on the \u201cT-type\u201d elementary network. The detailed description of the thermal model is tabulated in Table II. The active-winding region is built by the homogeneous composite 3-D hollow cylinder segment, including copper, impregnation and wire insulation, in which the heat flow path in axial (\ud835\udc67-), radial (\ud835\udc5f-) and circumferential (\ud835\udf03-) directions are taken account. Fig. 3 shows the 3-D winding thermal network, in which the \ud835\udc67- and \ud835\udc5f- thermal resistances are determined by the method in [7]. The \ud835\udf03- thermal resistances describe the heat flow path between the stator teeth and the active-winding and can be expressed as: \ud835\udc45\ud835\udf03 = (\ud835\udf032 \u2212 \ud835\udf031) 2\ud835\udf06\ud835\udf03\ud835\udc3f \u2219 \ud835\udc5f1 + \ud835\udc5f2 \ud835\udc5f2 \u2212 \ud835\udc5f1 (1) \ud835\udc45\ud835\udf03,\ud835\udc5a= \u2212 5(\ud835\udf032 \u2212 \ud835\udf031) 24\ud835\udf06\ud835\udf03\ud835\udc3f \u2219 \ud835\udc5f1 + \ud835\udc5f2 \ud835\udc5f2 \u2212 \ud835\udc5f1 (2) where \ud835\udf06\ud835\udf03 is the circumferential thermal conductivity. The negative \ud835\udc45\ud835\udf03,\ud835\udc5a is the \u201ccompensation resistance\u201d to set the midpoint temperature to be equal to the mean value in the \ud835\udf03 direction",
            " The boundary conditions are adopted from Table IV. The average and maximum temperatures calculated by different methods against the experimental results are given in Table V. The experimental average and maximum temperatures are obtained by the 14 inserted thermocouples. It can be observed that the first terms of the Fourier series (19), (21), (34) and (35) are qualified to calculate average and maximum temperatures with high accuracy. The results from the \u201cT-type\u201d elementary thermal model (see Fig. 3) are larger than the results from the analytical model and the experiments. The reason can be interpreted as: the \u201cT-type\u201d thermal model in either direction can only guarantee that the node temperature equals the average temperature in this direction, it will reduce the precision in the 2-D thermal analysis. Since the LP and the analytical methods are established from different perspectives, the values of estimation error depend on the several factors, i.e. the boundary conditions, the generated heat losses, the geometric size and the material thermal properties"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001742_0954406214531943-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001742_0954406214531943-Figure4-1.png",
        "caption": "Figure 4. Contact model of the ball bearing.",
        "texts": [
            " Figure 3(b) shows that the measured vertical stiffness increases slightly with the increase of the load, and the slope of the curve also decreases slightly. Analytical modeling of statics for the linear guideway In this section, the statics model of linear guideway with four grooves was created using the Hertz contact theory. Furthermore, to obtain the accurate analytical model, the experimental results were used to revise the analytic model. Contact modeling for a single ball bearing To analyze the contact characteristics between a single ball and grooves, the model is created and shown in Figure 4. To enhance the accuracy of model, the contact of ball bearing is regarded as elastic contact. In Figure 4, R1 is the radius of the ball, R2 is the radius of grooves of the rail and carriage, is the contact angle, and F is the contact force. According to the Hertz contact theory,12 the relation between the contact force and the elastic deformation is expressed as F \u00bc 2 ffiffiffi 2 p 3=2 3=2 3 2 1 v2 1 E1 \u00fe 1 v2 2 E2 h i P 1=2 \u00f02\u00de where is the elastic deformation between ball and groove, E1, E2, 1, and 2 are elastic modulus and Poisson ratio of the material of ball, rail, and carriage, respectively, is named as Hertz coefficient related with the geometry of the ball bearing, and P is the curvature of the ball bearing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001653_tie.2017.2733442-Figure14-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001653_tie.2017.2733442-Figure14-1.png",
        "caption": "Fig. 14 The prototype of the 12s/10p SPM-FS machine.",
        "texts": [
            " asivWvve lDABT 2cos 4   (17) where Bv and AWv is are the magnetic loading and armature winding electrical loading of the harmonic with v-pole-pair, respectively. Dsi is the stator inner diameter, and la is the stack length. AWv=m(Npkwv)Imax/(\u03c0Dsi) (18) where Np is the turns of series conductors per phase, kwv is the winding factor of v-th order, Imax is the maximum armature current value. 0278-0046 (c) 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. For the typical 12s/10p SPM-FS machine as shown in Fig. 14, the total torque is contributed by 6 dominating harmonics, i.e. 4- (28.5%), 6- (18%), 8- (14%), 16- (29.2%), 18- (28.9%) and 28-pole-pair (9.5%), respectively, as shown in Fig. 16. It is worth noting that the magnetic loading contains static fundamental harmonics (jPPM) and other modulated harmonic orders (kPr\u00b1jPPM). Moreover, the torque components are not only produced by the primitive armature reaction MMF with 4i pole pairs, but also attributed by the modulated MMF harmonics |4i\u00b1pPr|. The prototype topology and the electromagnetic torque decomposition of typical 24s/10p RPM-FS machine are shown in Figs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003890_j.ymssp.2020.107280-Figure10-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003890_j.ymssp.2020.107280-Figure10-1.png",
        "caption": "Fig. 10. Experimental samples for variations of mesh stiffness: (a) normal pinion, (b) pinion with 1 mm circumferential crack, and (c) enlarged view of (b).",
        "texts": [
            " Therefore, the parameter uncertainties are implemented by certain variability of the parameters in the present experimental investigation. And the certain variability of dynamic parameters is achieved by changing the geometric feature parameters of the dynamic parameters to be studied. Specifically, the uncertainties of mesh stiffness, bearing support stiffness, and the hybrid uncertainties of mesh stiffness and mass are studied respectively. The variation of mesh stiffness is mainly realized by changing the effective tooth thickness of the pinion. The normal pinion and the pinion with circumferential crack are given in Fig. 10. The pinion with circumferential crack is achieved by machining a circumferential crack with the depth of 1 mm and the direction of 45 near the base circle of the pinion. The variation curves of the mesh stiffness by installing the normal pinion and the pinions with different depth cracks are shown in Fig. 11. The results are implemented by the potential energy method [31]. The mesh stiffness of a pair of external\u2013external spur gears is calculated by considering Hertzian contact stiffness, bending stiffness, shear stiffness and axial compressive stiffness"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002436_j.ymssp.2018.06.034-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002436_j.ymssp.2018.06.034-Figure5-1.png",
        "caption": "Fig. 5. Schematic view of cryogenic chamber.",
        "texts": [
            " The flow rate of liquid nitrogen supplied from an external liquid nitrogen tank (170 L) is measured through a Coriolis-type mass flow meter at the inlet. To check the phase of liquid nitrogen, the temperature and pressure of liquid nitrogen entering the test ball bearing through the axial rod arm is measured at the inlet and outlet. In addition, the chamber can visually confirm the level of the cryogenic fluid through a double-windowed sight glass. The axial rod arm is constructed as a hollow shaft to allow the cryogenic fluid to flow in the direction of the ball-bearing center to minimize the effects of fluid forces. Fig. 5 shows a schematic cross-sectional view of the inside of the cryogenic chamber. The test ball bearing housing is equipped with an optical displacement sensor protected by a flexible metal hose to measure the whirling motion of the cage at 90 intervals, and the sensor measures the motion of the metal ring on both ends of the cage. To measure the temperature of the test ball bearing, a T-type thermocouple is placed in point contact with the outer ring of the bearing, and the thermocouple is surrounded by a flexible pipe filled with a low-thermal-conductivity material to minimize the effects of cryogenic fluids"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002225_j.mechmachtheory.2014.02.016-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002225_j.mechmachtheory.2014.02.016-Figure1-1.png",
        "caption": "Fig. 1. Geared rotor system on moving base with various co-ordinate systems.",
        "texts": [
            " Considering the time-varying base movements and gear meshing, the second order differential equations of the system will not only have time-periodic gyroscopic and stiffness coefficients, but also have the multi-frequency external excitations. Numerical method is utilized to obtain the lateral and torsional responses of the geared system under transmission error and unbalanced mass excitations. The effects of various base angular motions on both frequency response and response spectra are discussed in detail. Finally, some conclusions are given. The configuration of the geared rotor-bearing system is shown in Fig. 1. Two uniform flexible shafts are of the same length L. The gear pair is modeled as two rigid disks mounted at the mid-span, and ac represents the gear center distance. The flexible shafts are assumed to be simply supported and mass-less. The base of the geared rotor is assumed to be sufficiently rigid, and its mass center is at the left support, as shown in Fig. 1. Four co-ordinate systems are defined in the paper: inertial frame of reference X0\u2013Y0\u2013Z0, frame of moving base Xb\u2013Yb\u2013Zb and rotor frames X1\u2013Y1\u2013Z1 (for driving gear) and X2\u2013Y2\u2013Z2 (for driven gear), which are fixed to the gear disks and non-rotating. The driven and driving gears rotate about its own axiswith constant speed\u03a91,\u03a92, and one hasNt1\u03a91 = Nt2\u03a92, whereNt1 andNt2 are the numbers of teeth of driving and driven gears, respectively. Three angular rotations of the base about frame Xb\u2013Yb\u2013Zb, i.e",
            " (26) that both the gyroscopic and stiffness coefficients of the geared rotor system are time-variable due to the periodic base angular motions. In addition, the external excitations also contain multiple frequencies, i.e. \u03c9b,\u03a9m,\u03a91,\u03a92 and \u03a91 \u00b1 \u03c9b,\u03a91 \u00b1 2\u03c9b. In this case, it is difficult to obtain the dynamic behaviors analytically. In this paper, the numerical integration method (Runge\u2013Kutta method) is utilized to compute the dynamic responses of the system under both angular base and gear meshing excitations. For the geared rotor system shown in Fig. 1, the values of system parameters, which are given by Choi and Mau [18], are adopted as: md1 = 2.91 kg, Id1 = 0.0125 kg m2, Ip1 = 0.0022 kg m2, md2 = 2.83 kg, Id2 = 0.0125kg m2, Ip2 = 0.0022 kg m2, mu1e1 = mu2e2 = 7.38 \u00d7 10\u22126 kg m, \u03c6d1 = \u03c6d2 = 0, r1 = r2 = 0.0445 m, R = 0.0185 m, Ri = 0.005 m (inner radius for the driven shaft), L = 0.254 m, ma = 1 \u00d7 10\u22126 s, \u03c2c = 0.005, e t \u00bc 9:3\u00f110\u22128 m, Nt1 = Nt2 = 28 and \u03d5p = 20\u00b0. The modulus of elasticity is E = 2.07 \u00d7 1011 N/m2, shearmodulus isG = 8.28 \u00d7 1010 N/m2, and Poisson's ratio is v = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000888_j.oceaneng.2011.07.006-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000888_j.oceaneng.2011.07.006-Figure1-1.png",
        "caption": "Fig. 1. Motion state variables for a marine vessel.",
        "texts": [
            " Section 3 develops the control scheme including the observer design, the SHLNN implementation and the design of the robust term. Section 4 contains the stability analysis. Section 5 provides simulation results for the proposed output feedback tracking control scheme. Finally, conclusions are made in Section 6. A ship can be viewed as a rigid body with a 6-DOF attitude motion-surge, sway, heave, roll, pitch and yaw. The definition of the six degree-of-freedom motion of a marine vessel is shown in Fig. 1. However, the influence of roll and pitch motions on the dynamics of the ship is often neglected in the horizontal plane. Furthermore, since gravity and buoyancy is vertical to the horizontal plane, which have little influence on the motion of the horizontal plane, heave motion can also be neglected. Hence a simplified 3-DOF ship moving in the horizontal plane is discussed, whose schematic diagram is shown in Fig. 2. In the horizontal plane, a 3-DOF ship is modeled as follows in Fossen (2002): _Z \u00bc J\u00f0Z\u00deu M _u\u00feC\u00f0u\u00deu\u00feD\u00f0u\u00deu\u00fetd \u00bc t Y \u00bc Z 8>< >: \u00f01\u00de where u\u00bc \u00bdu,v,r T denotes the linear velocities in surge, sway and angular velocity in yaw"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001449_s10846-013-9955-y-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001449_s10846-013-9955-y-Figure2-1.png",
        "caption": "Fig. 2 Pure yawing motion",
        "texts": [
            " CD,CL and CM are the aerodynamic coefficients for drag force, lift force and pitch moment respectively. 2.2 Lateral Dynamic The lateral dynamic generates the roll motion and, at the same time, induces a yaw motion (and vice versa), then a natural coupling exists between the rotations about the axes of roll and yaw [11]. In our case, we solve it by considering that there is a decoupling of yaw and roll movements [4]. Thus, each movement can be controlled independently. Generally, the effects of the engine thrust are also ignored [11]. In the Fig. 2, the yaw motion is represented, which can be described with the following equations: \u03c8\u0307 = r (9) r\u0307 = N Izz (10) V\u0307y = Fy m \u2212 rVx (11) V\u0307x = Fx m + rVy (12) where\u03c8 represents the angle of yaw and r denotes the yaw angular rate, with respect to the centre of gravity of the airplane. N is the yawing moment and Izz represents the inertia in the z-axis. \u03b4r is the rudder deflection. Vx corresponds to the speed of the airplane in the longitudinal x-axis, Vy is the speed in the lateral y-axis, Fx describes the thrust force in the longitudinal x-axis and Fy denotes the component of the resultant lateral force on the y-axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002618_j.addma.2019.100848-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002618_j.addma.2019.100848-Figure2-1.png",
        "caption": "Fig. 2. An illustration of the LENS deposition head and powder nozzles.",
        "texts": [
            " The DED under consideration was performed with Optomec LENS 450 Workstation (Optomec, Albuquerque, NM, USA). The system has a chamber of 254\u00d7 254\u00d7254 (mm) and a maximum laser power output of 400W. A pneumatic powder delivery system and a computer-controlled motion system are integrated with the LENS system. The powder material is injected into the molten pool created by a focused fiber laser beam. Argon was used as a protective and carrier gas. The four-jet exit nozzles were positioned around the main nozzle and aimed at the molten pool, as shown in Fig. 2. A cross-section through the powder stream through the four-jet nozzle is shown in Fig. 3. The outlet plane of the nozzle is defined as the reference plane and the intersection point of the plane and laser beam Nomenclature MA, MB, MC, and MD Mass flow rate below nozzle (A, B, C, and D) before the converging point (g/mm2s) Dr,z Distance of a single point P (r, z) to the center line of powder stream (mm) m Powder feeding rate (g/min) rs Powder stream radius (mm) Density of the powder (g/cm3) Vp Volume of a single powder (cm3) mp Mass of a single powder (g) St The area occupied by the laser beam (mm2); V Carrier gas volumetric flow rate (L/min) r0 Powder nozzle outlet radius (mm) a,b, c, and d Distance of a single point P (r, z) to the center line of each powder stream below nozzle (A, B, C, and D) (mm) Nr,z Powder flow at point P (r, z) before the converging point (units/mm3) vp Velocity of the powder (mm/s) dp Distance from nozzle outlet to the beam center (mm) dc Distance from the consolidation plane to nozzle outlet (mm) L Radius of the powder stream at the consolidation plane (mm) dh Distance from the nozzle outlet to the bottom of nozzle holder (mm) dn Distance from the intersection point of nozzle centerline and the bottom of nozzle holder to the beam center (mm) rp Average radius of the particles in the powder stream (\u03bcm) wf Laser beam radius at the consolidation plane (mm) focus are defined as the origin point O (0, 0)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000807_j.mechmachtheory.2013.06.013-Figure17-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000807_j.mechmachtheory.2013.06.013-Figure17-1.png",
        "caption": "Fig. 17. Models of face-gear (a) simulation results, (b) theoretical model.",
        "texts": [
            " (2) The face-gear rotates around A-axis at 180\u00b0. Then the disk wheel is moved to the process position of station 2, where the tooth surfaces 2 of face-gear is in-process (shown in Fig. 16). The test platform is established with the NC simulation software Vericut which is developed by CGTECH Company in the United States [16]. An overview of the simulation processing test is as the following steps: (1) Use CATIA software to establish the machine model, stock model of the face-gear, the theoretical face-gear model (Fig. 17 (b)) and the disk wheel model, and then put the model files into Vericut software. (2) Calculate the NC code file based on the parameters represented in Table 3 and the grinding method mentioned above, and then put it into Vericut software. (3) Start the simulation processing test. (4) Overlap the simulation results model (Fig. 17(a)) and the theoretical face-gear (Fig. 17(b)) together (Fig. 18(a)), and then analyze the tooth surface error between them. The analyses of tooth surface error are shown in Fig. 18(b) and (c). The theoretical tooth profile of face-gear is denoted by shadow profile, and the spots denote to tooth surface errors which are larger than 1 \u03bcm (see Fig. 18(b)). Overall, the maximum error is 2.62 \u03bcm, which is within the theoretical precision of face-gear at AGMA 12 (see Fig. 18(c)). The manufacturing time of a single tooth lasts for about 1.5 min derived by the estimation of the manufacturing time in Vericut software"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003887_j.etran.2020.100080-Figure10-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003887_j.etran.2020.100080-Figure10-1.png",
        "caption": "Fig. 10. Ferrite spoke-type design with more PM poles.",
        "texts": [
            " However, the amount of ferrite used is usually doubled or even tripled to add axially magnetized PM poles. Moreover, due to the existence of axial flux, soft magnetic composite (SMC) cores were necessary because of the 3-dimensional (3D) flux distribution, which would increase the material costs. For more cost-effective ways of increasing PM excited field, more ferrite was inserted by making full use of the space inside the rotor. I. Seo et al. presented segmented spoke type poles with certain angles [80], as demonstrated in Fig. 10(a). By adjusting the angles of the segmented PMs, larger amount of PM material could be inserted, and open-circuit flux density was improved. Moreover, cogging torque could be reduced by optimized design. However, this uneven PM distribution would bring in unwanted harmonics. H. Kim et al. in Ref. [81,82] presented a ring-type assistant pole in the inner rotor part to increase the torque density with 3.8%. Wingtype and wing-shaped spoke-type configurations were proposed to place more and more PM poles in the rotor [83,84]. Compared to spoke-type only structure, the airgap flux density could be enhanced by 25%, as depicted in Fig. 10(b) and (c). Slightly higher torque output was also achieved compared to the initial rare-earth IPM machine. These designs utilised most of the space in the rotor to house the PM poles, so the assembly of rotor with more PM than steel lamination would be an issue. Moreover, although the wingshaped spoke-type machine maximized the PM torque, the reluctance torque was significantly reduced. Thus, these structures may not be very practical nor material-effective for industrial use. Other than PM torque, reluctance torque is also a very important component in total torque production"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000492_tie.2011.2168795-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000492_tie.2011.2168795-Figure7-1.png",
        "caption": "Fig. 7. Finite-element mesh consisting of 41 872 elements.",
        "texts": [
            " The thickness of the air gap used in calculations was assumed to be 0.225 mm. Therefore, both machines are characterized by a completely different level of saturation of the magnetic circuit. For that purpose, the Opera-2d/RM was chosen with the transient eddy-current solver extended to include the effects of rigid body (rotating) motion and connection of external circuits. The mesh was refined to minimize the solution errors and achieve reasonable compromise between accuracy and calculation times. The final mesh consists of 41 872 elements and is shown in Fig. 7. The application of the field-circuit method to the modeling of the magnetic field distribution in an induction motor, taking into account the movement of the rotor, requires the introduction of a special element into the model, which suitably connects the stationary and moving parts. In the rotating machine module of Opera-2d, this element takes the form of a gap element. The gap region (Fig. 8) is divided quite uniformly into 528 elements along the circumference of the gap. This yields the time of displacement of one element that is equal to about 7"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002558_j.ins.2017.08.085-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002558_j.ins.2017.08.085-Figure7-1.png",
        "caption": "Fig. 7. Position servo control system [54] .",
        "texts": [
            " The simulation results are shown in Figs. 5 and 6 . From Fig. 5 , it can be seen that the control scheme without the \u03c3 -modification method still achieves the control objective. However, from Figs. 2 and 6 it is obvious that the control signal becomes larger by using the control scheme without the \u03c3 -modification method. This paper introduces the use of \u03c3 -modification method to avoid this phenomenon. Example 2. Consider a dynamic position servo control system [54] using a mechanical transmission device as shown in Fig. 7 , and the dynamic can be described by M \u0308y = w \u2212 f K (y ) \u2212 f B ( \u0307 y) + (t) , where M denotes the mass of the platform subjected to the force w, y is the system displacement, f B (y ) = B \u0307 y denotes the viscous friction with B a constant coefficient, f K (y ) = K(y ) y denotes the elastic load with its coefficient K ( y ) being a nonlinear function of the displacement, and (t) = 0 . 5 sin (y ) is the disturbance. In this example, the force u exhibits backlash-like hysteresis because of the mechanical transmission device, and \u03c9 is the control of the servomotor to be designed"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002784_j.jmrt.2019.11.063-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002784_j.jmrt.2019.11.063-Figure3-1.png",
        "caption": "Fig. 3 \u2013 The production method of the test sample by the additive DMLS.",
        "texts": [
            " The first group of samples were samples made of an annealed drawn bar with a diameter of 12 mm in the turning process. The phys- i o u w p p u t s s d f m e t a cal form of the sample is shown in Fig. 2a. The second group f samples were made by the additive method DMLS (Fig. 2b) sing the EOS M280W machine with the dimensions of the orking platform 250 mm \u00d7 250 mm \u00d7 325 mm. The printing rocess was characterized by the following parameters: laser ower 200 W, minimum layer thickness 30 m, scanning speed p to 7 m / s. The sample print direction was consistent with he Z axis (Fig. 3). The laser beam path sintering the powder is hown in Fig. 4. Each layer of the element was created in the ame way. After the DMLS sample was build, it was annealed. A round sample in which the load distribution is evenly istributed during the tensile test was adopted. One of the actors affecting the load even distribution is the repeatable ounting method on the testing machine\u2019s handles, which nsures that the symmetry axis of the sample coincides with he axis of the machine\u2019s handles symmetry. Due to the aim of the paper, the elements made with the dditive DMLS method and samples made of a round drawn bar in the turning process were compared"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001968_978-94-007-6101-8-Figure3.12-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001968_978-94-007-6101-8-Figure3.12-1.png",
        "caption": "Fig. 3.12 Image formation by the lens",
        "texts": [
            "11), three zeros and a one were written into the fourth line. It appears that their aim is only to make the homogenous matrix quadratic. In this section we shall learn that the last line of the 3.5 Perspective Transformation Matrix 53 matrix means perspective transformation. The perspective transformation [3] has no meaning in robotics, it is however interesting in computer graphics and designing of virtual environments. The perspective transformation can be explained by formation of the image of an object through the lens with focal length f (Fig. 3.12). The lens equation is: 1 a + 1 b = 1 f (3.26) Let us place the lens into the x, z plane of cartesian coordinate frame (Fig. 3.13). The point with coordinates [x, y, z]T is imaged into the point [x \u2032, y\u2032, z\u2032]T. The lens equation is in this particular situation as follows: 1 y \u2212 1 y\u2032 = 1 f (3.27) The rays passing through the center of the lens remain undeviated: z y = z\u2032 y\u2032 (3.28) Another equation for undeviated rays is obtained by exchanging z and z\u2032 with x and x \u2032 in Eq. (3.28). When rearranging the equations for deviated and undeviated rays, we can obtain the relations between the coordinates of the original point x , y, and z and its image x \u2032, y\u2032, z\u2032: x \u2032 = x 1\u2212 y f (3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002912_s00170-019-04456-w-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002912_s00170-019-04456-w-Figure3-1.png",
        "caption": "Fig. 3 Geometry and mesh of: a first scanninning tracks; b second scanning tracks",
        "texts": [
            " (11), it can be inferred that the specific heat of powder layer is almost equal to that of solid material. Additionally, the simulation model took into account two phase change events. The first phase change occurs at melting temperature of SS 316L material (1648 K) and is associated with a latent heat of fusion of 300 kJ/kg [18]. The second phase changes take place at evaporation point (3273 K [3]) and are related to a latent heat of evaporation of 600 kJ/kg [21]. The FEM heat transfer simulations were performed using COMSOL Multiphysics commercial FE software based on the 3D model shown in Fig. 3. The model consisted of a 316L SS powder layer deposited on a 316L SS substrate. The powder layer measured 0.29 mm in the y-direction and had a thickness (z-direction) of 0.05 mm. The substrate also measured 0.29 mm in the y-direction, but had a greater thickness of 0.19 mm. The powder bed and substrate had the same length in the x-direction, where this length varied depending on the scan length used in the particular simulation. The formula to calculate the length in x-direction of the domain is specified in Fig. 3. Since the simulations involve two scanning tracks, the simulation time increases significantly with an increasing scan track length. Accordingly, to maintain the accuracy of the simulation results, while minimizing the computational time, a finer mesh was used in the laser scanning zone of the powder bed. In particular, through a series of convergence trials, the mesh size in scan region was set as 8 \u03bcm. Furthermore, a coarser mesh was used in the non-scanning region of the powder bed and substrate and the mesh size in this region was set as 30 \u03bcm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002254_s00170-016-9523-2-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002254_s00170-016-9523-2-Figure4-1.png",
        "caption": "Fig. 4 The speed reducer design problem",
        "texts": [
            " As it can be seen, the best feasible solution obtained for the pressure vessel design example using the above methods is 6059.71433, which is also provided by AMDE. In addition, it is observed from the statistical results that the proposed algorithm is more robust in solving this problem with 8.2267E\u221212 standard deviation. So, it can be said that AMDE outperforms the four compared approaches in terms of robustness. SD standard deviation, NA not available The objective is to optimize the total weight of the speed reducer [38]. The problem (Fig. 4) is subjected to constraints on bending stress of the gear teeth, surfaces stress, transverse deflections of the shafts, and stresses in the shafts. The variables are the face width (b), module of teeth (m), number of Table 1 Pressure vessel problem: comparison of AMDE results with literature Design variables PSO-DE ABC CS MOCoDE AMDE Ts 0.8125 0.8125 0.8125 0.812500 0.8125 Th 0.4375 0.4375 0.4375 0.437500 0.4375 R 42.098445596 42.098446 42.0984456 42.09844559585 42.098445595854919 L 176.636595842 176"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001501_tia.2016.2532289-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001501_tia.2016.2532289-Figure2-1.png",
        "caption": "Fig. 2: The average of nodal forces between two neighboring nodes.",
        "texts": [
            " Through implementation of (7) for multiple time steps up to one rotation of the rotor, the mean torque and torque harmonics can be calculated. Through analyzing the time-dependent torque, the effect of the tangential force densities wave can be studied. C. Implementation The first step of the approach is to perform FE-simulations to determine the nodal forces on the air gap side of the stator\u2019s surface. The force density waves acting on the stator are calculated through averaging two neighboring nodal forces (Fig. 2) and dividing its value by the distance between the two nodes and the axial length of the machine. The force densities should be decomposed in radial and tangential components. Through 2D Fourier transformation, the force densities can be decomposed in temporal and spatial order. As shown in Fig. 2, the average of nodal forces and thus the force density waves point mainly in radial direction. The value of the force densities in radial direction is greater than its value in the tangential direction. The acoustic noise, which is emitted from the stator, are induced by the radial force densities. The tangential forces excites structures, which are attaches to the rotor. The noise emitted from the attached structures, e.g gear, can be suppressed through minimizing the torque ripple. The next step is to determine the radial force density waves, which have major contribution to the acoustic radiation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001564_j.triboint.2013.06.017-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001564_j.triboint.2013.06.017-Figure8-1.png",
        "caption": "Fig. 8. Spindle-bearing experimental setup.",
        "texts": [
            " This study is a foundation for the future development of an optimum preload technique for high-speed ball bearings in machine tool spindle. 3. Experiment and verification Fig. 7 illustrates the setup of the spindle-bearing experiment. The oil\u2013air lubrication system for the test shaft used in this study is an integrated oil\u2013air mixer generator. The outlets of the mixers are connected to two separate lubrication channels that terminate at the front and rear bearings, respectively. The cooling system keeps the temperature of the driving motor sufficiently low. In Fig. 8, the shaft of the spindle bearing is driven by a motorised high-speed spindle at 0\u201320,000 rpm. The shaft is supported by two pairs of angular contact ball bearings, which are preloaded by a hydraulic chamber. The motorised high-speed spindle housing around the power zone is cooled by a compulsive cooling water circuit to disseminate the generated heat. To verify the validity of the analytical method presented in Section 2, a B7007C ball bearing is studied, with dimensions of rb\u00bc3.25 mm, dm\u00bc24.255 mm, \u03b11\u00bc151, ri\u00bc3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002838_978-3-319-54169-3-Figure5.9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002838_978-3-319-54169-3-Figure5.9-1.png",
        "caption": "Fig. 5.9 Model of the cutting mechanism on the elastic support",
        "texts": [
            " For the non-ideal case the steady-state dynamics of the system is examined by introducing the approximate analytical solution of the averaged differential equations of motion for the case of primary resonance. Parameters of the system are varied and their influence on the motion is tested. The analytically obtained solution is compared with exact numerical one and shows a good agreement. The ideal forcing case, when the motion of the mechanism is with constant angular velocity, is also analyzed. For this case the steady-state motion is obtained analytically, too. Cutting mechanism connected with the support is shown in Fig. 5.9. The considered mechanism contains two slider-crank mechanisms O1AB and O2DE connectedwith a rod BC . Rotation of the driving element O1A is transformed into the straightforward motion of the slider E which represents the cutting tool. During the contact between the slider E and the object in G, the cutting tool cuts 5.4 Dynamics of the Cutting Mechanism with Flexible Support \u2026 157 the sheet in G. The kinematic properties of the mechanism are widely discussed in previous section. In order to obtain the more realistic description of the dynamics of the mechanism it is necessary to include its interaction with the support",
            " If the mass moment of inertia of motor is J , the kinetic energy of the mechanism has three terms: kinetic energy of the motor (due to rotation), Tm , kinetic energy of the support, T1, and of the slider, T2, respectively, T = Tm + T1 + T2, (5.51) i.e., T = 1 2 J \u03d5\u03072 + 1 2 m1 S\u0307 2 + 1 2 m2v 2 E , (5.52) where vE is the velocity of the slider E . To determine the velocity vE some geometric properties of the mechanism have to be considered. Let us determine the coordinate yE as a function of the generalized coordinates \u03d5 and S. From Fig. 5.9. the coordinate yE in the fixed coordinate system x \u2032Oy\u2032 is yE = S + p + g cos \u03b3 + h cos\u03c8, (5.53) where the lengths of the elements are g = O2D and h = DE . Using the geometric properties of the mechanism O2DE we have g sin \u03b3 = h sin\u03c8. (5.54) 158 5 Dynamics of Polymer Sheets Cutting Mechanism The relation (5.53) transforms into yE = S + p + g cos \u03b3 + h \u221a 1 \u2212 ( g sin \u03b3 h )2 . (5.55) For the known distances l and w we have cos \u03b8 = l \u2212 a cos\u03d5 b \u2264 1, (5.56) and cos\u03c7 = w \u2212 r sin \u03b3 c \u2264 1, (5.57) where a = O1A, b = AB, r = O2C , c = BC ",
            " As the force F is required to be constant during the cutting (F = F0 = const . for \u03d5 \u2208[\u03d5K , \u03d5M ]) and otherwise to be zero (F = 0 for \u03d5 \u2208 [0,\u03d5K ) \u222a (\u03d5M , 2\u03c0]), it is modeled as a UnitStep function: F = F(\u03d5) = F0 F\u0304(\u03d5), (5.70) where F\u0304(\u03d5) = F0(Unit Step(mod(\u03d5, 2\u03c0) \u2212 \u03d5K ) \u2212Unit Step(mod(\u03d5, 2\u03c0) \u2212 \u03d5M)). (5.71) Using (5.69) and (5.70), the expression of the virtual work of the force and the torque in the system is \u03b4A = M\u03b4\u03d5 + F(\u03b4yE \u2212 \u03b4yG), (5.72) where \u03b4yE is the variation of the coordinate yE , (see Eq. (A.10)), and \u03b4yG is the variation of the coordinate yG . From Fig. 5.9 it is evident that yG = S + p + (O2G) and (O2G) is a fixed distance. Substituting the variation of the coordinates \u03b4yE and \u03b4yG : \u03b4yE = \u03b4S + a f \u03b4\u03d5, \u03b4yG = \u03b4S, into (5.72) we have \u03b4A = (M + Fa f (\u03d5))\u03b4\u03d5. (5.73) The generalized forces of the system are according to (5.73) Q\u03d5 = M + Fa f (\u03d5), (5.74) QS = 0. (5.75) Employing the relations (5.65)\u2013(5.67), (5.74) and (5.75) the Lagrange\u2019s equations (5.50) yield the equations of motion of the mechanism in the form 0 = (m1 + m2)S\u0308 + m2a f \u03d5\u0308 + (q1 + q2)S\u0307 + m2a f \u2032\u03d5\u03072 + q2a f \u03d5\u0307 (5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000710_j.jsv.2011.04.008-Figure14-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000710_j.jsv.2011.04.008-Figure14-1.png",
        "caption": "Fig. 14. The reference frame for the oil squeeze model.",
        "texts": [
            " Moreover, on an actual plant, by monitoring TE with the present measurement technique, the model may help in preventing an eventual incipient gear rattle operating condition. During the phase in which the gear teeth are not in contact but are approaching each other, a damping force is exerted by the oil film \u2018\u2018squeezed\u2019\u2019 in the gap. Such force is indicated by S x,W1\u00f0 \u00de _x in (6). With reference to a single tooth pair meshing in correspondence of the pitch point the \u2018\u2018oil squeeze\u2019\u2019 effect in the gap can be modeled under the following tribological assumptions: the teeth are rigid bodies of cylindrical shape, whose axes are parallel to the gear axis. In Fig. 14 it can be noted the reference frame with the z-axis parallel to the gear axis; as the radius of each cylinder it is assumed the involute radius at the pitch point; the cylinders approach each other along the Z direction without any slip velocity in the x direction; the fluid is assumed to be incompressible with constant viscosity. The gap height h(x,t) between the teeth assumes then the following expression: h\u00f0x,t\u00de \u00bc x\u00f0t\u00de\u00fer1 1 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 x r1 2 s2 4 3 5\u00fer2 1 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 x r2 2 s2 4 3 5 (1-A) in which, x(t) is the instantaneous value of the minimum gap while x takes value in the interval: (\u2013addendum, \u00feaddendum)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002983_b978-0-12-811820-7.00008-2-Figure6.8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002983_b978-0-12-811820-7.00008-2-Figure6.8-1.png",
        "caption": "FIGURE 6.8 Morphology of a single \u03b1 variant in \u03b2 matrix with the consideration of the anisotropic energy contributions.",
        "texts": [
            " The stress equilibrium is assumed to be much faster than the microstructure evolution [81]. Due to the anisotropic interfacial energy and SFTS, the morphology of \u03b1 products, both diffusional and diffusionless ones, are generally anisotropic with lath or acicular shape and habit planes [52,82\u201386]. With these anisotropies considered, the morphologies of \u03b1 product are reconstructed, which quantitatively agrees with the experimentally reported {3 3 4}, {8 8 11}, {8 9 12} or {11 11 13} habit planes [52,82\u201384,86], as shown in Figure 6.8, with a maximum deviation of only 3 \u25e6. With the energy anisotropies and the temperature-dependent thermodynamic and kinetic coefficients, the non-isothermal growth behavior of \u03b1 products can be accounted for. To further consider the temperature-dependent nucleation behavior, the classical nucleation theory [59,87,88] is applied: j = ZN0\u03b2 \u2217 exp ( \u2212 G\u2217 RT ) exp ( t \u03c4 ) (6.17) where j is the nucleation rate, Z is Zeldovich\u2019s factor, N0 is the number of available nucleation sites in the corresponding system (here a simulation cell), \u03b2\u2217 is atomic attachment rate, G\u2217 is nucleation barrier, t is elapsed time and \u03c4 is incubation time for nucleation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000069_ichr.2005.1573583-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000069_ichr.2005.1573583-Figure3-1.png",
        "caption": "Fig. 3. At heel strike the velocity of the point mass is redirected. All velocity along the length of the new stance leg is lost, so that \u03b8\u0307+ = \u03b8\u0307 \u2212 cos \u03c6.",
        "texts": [
            " An additional requirement is that the foot must make a downward motion, resulting in an upper limit for the forward swing leg velocity \u03c6\u0307 < \u22122\u03b8\u0307 (note that \u03b8\u0307 is always negative in normal walking, and note that swing leg retraction happens when \u03c6\u0307 < 0). In our simulation, we use a third order polynomial to interpolate between two simulation data points in order to accurately find the exact time and location of heel strike. The transition results in an instantaneous change in the velocity of the point mass at the hip, see Fig. 3. All of the velocity in the direction along the new stance leg is lost in collision, the orthogonal velocity component is retained. This results in the following transition equation: \u03b8\u0307+ = \u03b8\u0307 \u2212 cos\u03c6 (2) in which \u03b8\u0307 \u2212 indicates the rotational velocity of the old stance leg, and \u03b8\u0307+ that of the new stance leg. At this instant, \u03b8 and \u03c6 flip sign (due to relabeling of the stance and swing leg). Note that in Eq. 2 \u03c6 could equally well be replaced with 2\u03b8. The instant of transition is used as the start of a new step for the swing leg controller; in the case that a disturbance would make step n last longer than usual, then the start of the swing leg trajectory for step n + 1 is postponed accordingly"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003810_j.addma.2020.101251-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003810_j.addma.2020.101251-Figure3-1.png",
        "caption": "Fig. 3. (top) View of the cyclic plane bending testing machine including specimen location, actuating mechanism and load cell; bottom) loading scheme of the miniature specimen for smooth fatigue testing.",
        "texts": [
            " In terms of test flexibility, the plane cyclic bending with R = Mmin/ Mmax = 0 loading condition applied to the mini specimen geometry shown in Fig. 2 offers the possibility of testing either the flat specimen surface, thus determining the un-notched fatigue behavior, or the surface with the round-notch, determining the notch fatigue behavior, upon selecting the direction of application of the cyclic bending moment M. The cyclic plane bending fatigue experiments at a frequency of 25 Hz were performed on an electro-mechanical testing machine applying a fixed rotation range to the specimen ends. Fig. 3a shows a local view of the cyclic plane bending testing machine including specimen location, grips, electro-mechanical actuating mechanism and load cell for continuous load monitoring during the experiment. The scheme of Fig. 3b explains how the oscillation of one grip (whose amount linked to the rotation angle \u03b8) translates in a cyclic bending moment applied to the miniature specimen. When the load cell detects a 10% drop of the bending moment with respect to its initial value, cycle counting is interrupted and the test ends. Alternatively, the test is terminated at 2 \u00d7 106 load cycles (i.e. run-out) if no appreciable load change is detected, [33]. The maximum nominal stress \u03c3max in the miniature specimen is given by \u03c3max = M/W where M is the maximum plane bending moment and W is the section modulus of the minimum square cross-section (i.e. W = (bxh2)/6 = 21 mm3 because b and h are the section thickness and height, respectively). When the cyclic tensile stress is applied in the longitudinal direction as shown in Fig. 3 (bottom) the effective maximum stress value is achieved at the center of the specimen, opposite to the notch because of the local cross section reduction. This is quantitatively demonstrated by the finite element stress analysis of Fig. 4 (top). The effective maximum tensile stress at the top flat surface is determined as \u03c3max = Cmg M/W where Cmg = 0.91 is a miniature specimen geometry-dependent coefficient that corrects the maximum nominal bending stress. It means that the local stress on the flat surface is overestimated by the nominal stress of about 9%. The Cmg coefficient should be included especially when comparing fatigue behavior obtained with mini specimens and fatigue behavior obtained with standard smooth specimen geometries. While the presence of the correction coefficient Cmg may be considered a weakness of the test method, it is counterbalanced by the many benefits of specimen miniaturization. On the other hand, when the specimen in the loading apparatus of Fig. 3 (bottom) is flipped vertically, the stress distribution due to the applied bending loading M is presented in Fig. 4 (bottom). The peak tensile stress occurs at the notch root and its value can be used to compute the stress concentration factor Kt of the miniature specimen geometry as follows: Kt = \u03c3max,FE /(M/W) = 1.63, where \u03c3max,FE is the maximum principal stress computed by elastic finite element analysis. Fig. 5 shows four orientations of the mini specimen on the build plate that were used in this experimental campaign and their respective denominations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000679_j.ymssp.2010.02.003-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000679_j.ymssp.2010.02.003-Figure8-1.png",
        "caption": "Fig. 8. Volume variation at the tooth tip.",
        "texts": [
            "5 times the pitch on the root circle and the meatus length ld the difference between the radius of the root circle and the radius of the drainage circle (rd). In this case, the term related to the \u2018drag flow rate\u2019 has been neglected because its radial component is zero; therefore the volumetric flow rate becomes Qd;i \u00bc bdh3 f 12mld \u00f0pi pd\u00de \u00f018\u00de The last term to be calculated in Eq. (10) is the volume variation dVi; such a term for an angle rotation dy of the gear is obtained by the difference of the shaded areas in Fig. 8 multiplied by the face width bk of the gear: dVi dy \u00bc rextbk\u00f0hi\u00fe1 hi\u00de \u00f019\u00de So, taking all the previous terms into account and substituting in Eq. (10), considering the volume Vi as constant and equal to the nominal volume of the tooth space V0, the following equation for the generic tooth space i can be obtained: dpi dy \u00bc Boil okV0 \u00bdCh\u00f0h 3 i\u00fe1Dpi\u00fe1 h3 i Dpi\u00de Kh\u00f0hi\u00fe1 hi\u00de\u00fe2Cf \u00f0Dpi\u00fe1 Dpi\u00de 2CdDpd;i \u00f020\u00de where Dpi\u00fe1 \u00bc pi\u00fe1 pi; Dpd;i \u00bc pi pd; Dpi \u00bc pi pi 1 Ch \u00bc bk 12mlt ; Cf \u00bc bf h3 f 12mlf ; Cd \u00bc bdh3 f 12mld Kh \u00bc bkokrext 2 ; dVi dy ok \u00bc bkokrext\u00f0hi\u00fe1 hi\u00de \u00bc 2Kh\u00f0hi\u00fe1 hi\u00de Vi \u00bc V0; 8i Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001653_tie.2017.2733442-Figure15-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001653_tie.2017.2733442-Figure15-1.png",
        "caption": "Fig. 15 The prototype of the 24s/10p RPM-FS machine.",
        "texts": [],
        "surrounding_texts": [
            "From the armature reaction MMF harmonic components analysis, it can be found that the spoke number Nsp is a key parameter to determine the dominant harmonic PPN in both rotor PM machines and stator PM machines. On the other hand, Nsp can be utilized to provide a powerful guidance for the combination of stator slots Ps and rotor pole pairs Pr. It should be emphasized that Nsp must be an integer multiply of the phase number m. For the RPM-FS machines with 24-slots as shown in Fig. 1(c), the GCD number can be determined to be four cases easily, i.e. 1, 2, 4, 8. Hence, the rotor pole number can be analyzed and determined from the four GCD cases as shown in Table IV. Similarly, for the 12-slots SPM-FS machine shown in Fig. 1(a), and the rotor pole number can be identified in Table V from the three GCD cases. It should be emphasized that one Pa value deduces two cases of Pr number in SPM-FS machines, due to Pa=|Pr\u00b1PPM|. It can be found that the values of harmonic components HC and the distribution factor kd are the same between different Pa under one GCD case, due to the same slot-conductors back-EMF vectors distribution. Hence, the eligible combination of Ps and Pr can be obtained preliminarily by referring to the winding factor kw. Then the optimized combination cases with the same kw can be further analyzed based on the influence of magnetic loading by the geometric parameters."
        ]
    },
    {
        "image_filename": "designv10_5_0002004_1.4028532-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002004_1.4028532-Figure1-1.png",
        "caption": "Fig. 1 Straight-crease Miura-base unit geometries and relevant parameters. Crease pattern, on left and folded configuration, on right. (a) Miura, (b) tapered Miura, (c) Arc, and (d) Arc-Miura.",
        "texts": [
            " Compared to the previous work investigating the discretization of curved folds [19], it is seen that the new method discretizes CC patterns into piecewise assemblies of self-similar straight-crease patterns, allowing their understood geometric behaviors, including simulation of rigid folding motion and pattern closure conditions, to be utilized. The Miura pattern is a planar, rectilinear pattern that deploys with a single-DOF rigid mechanism. It is formed from a single repeated parallelogram plate, shown in Fig. 1(a), but by altering characteristics of this plate, Miura-derivative geometries are formed with different global curvatures. For instance, removing pattern rectilinearity produces the tapered Miura pattern with a polar form, shown in Fig. 1(b). Changing alternate zigzag crease lines produces the longitudinally curved Arc and Arc-Miura patterns, shown in Figs. 1(c) and 1(d), and changing alternate straight-crease lines produces the laterally curved nondevelopable and nonflat foldable Miura derivatives (not shown). Numerous parametrizations exist for these patterns but this paper adopts the consistent parametrization for straight-crease Miura-derivative geometries presented in Ref. [21]. Numerous straight-crease pattern geometric parameters are used directly and with minimal explanation. These include Miura pattern parameters a, b, /, m, n, gA, and gZ; Tapered Miura parameters ac, af, b1, bj, /c;/f , q, q, gfZ, gcZ, gcA, gfA, and Rc,j; Arc parameters a1, a2, n1, n2, R, and h; and Arc-Miura parameters a1, a2, b1, b2, /1;/2, gVA, gVZ, gMZ, n, na2, nb1, nb2, R1, and h. These parameters are shown in Fig. 1, 1Corresponding author. Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received November 5, 2013; final manuscript received September 1, 2014; published online October 20, 2014. Assoc. Editor: Karthik Ramani. Journal of Mechanical Design DECEMBER 2014, Vol. 136 / 121404-1Copyright VC 2014 by ASME Downloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use with complete definitions available in Ref"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003202_ab39c9-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003202_ab39c9-Figure2-1.png",
        "caption": "Figure 2. Thermo-mechanical analysis of bilayer structure actuator: (a) structure of a typical bilayer structure actuator, and (b) bilayer structure actuator after heating.",
        "texts": [
            " In section 3, a constitutive model with five main deformation programming parameters including the line width, the print height, the print temperature, the filled form, and the stimulation temperature is developed, and the orthogonal experiment is designed to fit the constitutive model. In section 4, a typical temperature shape memory material polylactic acid (PLA) is used as a case study to illustrate the methodology and a desired programmed deformation is achieved. The paper concludes in section 5 with a discussion on further research. A typical SMP bilayer structure actuator is composed of two layers SMP, as shown in figure 2(a). The deformation of the SMP bilayer structure actuator stimulated by heating is shown in figure 2(b). Static equilibriums of the are actuator concluded as follows: r = = = + = + P P P Ph M M Ph E I E I 2 2 , 1 1 2 1 2 1 1 2 2 \u23a7 \u23a8\u23aa \u23a9\u23aa ( ) ( ) ( ) where E1 and E2 represent the elastic modulus of each layer. a1 and a2 are the thickness of each bilayer, and h is the total thickness of the structure. P1, P2 are the axial tensile forces of each bilayer, andM1 andM2 are the bending moments of each bilayer. \u03c1 is the radius of curvature of the strip, and E1I1 and E2I2 are the bending stiffness of each bilayer"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002941_j.ymssp.2016.07.007-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002941_j.ymssp.2016.07.007-Figure1-1.png",
        "caption": "Fig. 1. Experimental rig. A 1.5 kW, 8 pole squirrel-cage induction motor drives an epicyclic, speed increasing gearbox which in turn is loaded by a 1.5 kW, 2 pole squirrel-cage induction motor. The 8-pole drive motor was supplied via an autotransformer whilst the 2-pole load motor was connected to an ABB ACS800 drive (neither of which are pictured). The components are attached to a common base of large mass, standing on 8 vibration isolators. The gearbox was instrumented with accelerometers and the drive motor included current, voltage and angular displacement sensors.",
        "texts": [
            " In Section 5 the synchronous average of electrical signals is introduced along with the special considerations necessary in order for the method to be applied to epicyclic gearboxes. In Section 6 experimental results are presented, initially highlighting the results of basic vibration analysis and subsequently giving the results of the synchronous averaging of motor current. In Section 7 discussions on the accuracy of the derived model and the influence of operating conditions are given. Additionally, indications on how the methods might be incorporated into a condition monitoring system are provided. Finally in Section 8 conclusions are stated. Fig. 1 shows a photograph of the experimental rig. The system was driven by a 1.5 kW, 8-pole Kacperek Y3-112M-8 B5 three phase induction motor with a nominal speed of 700 RPM. The motor was supplied with 430 VRMS direct on line via an autotransformer. The motor was connected via a ROTEX 48 coupling to the carrier of a Bonfiglioli 301 L1 PC 5.77 B3 in-line epicyclic gearbox with ratio 5.77. The gearbox was comprised of a 13 tooth sun gear, a 62 tooth fixed ring gear and three planets, each with 24 teeth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000142_j.tsf.2010.08.106-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000142_j.tsf.2010.08.106-Figure1-1.png",
        "caption": "Fig. 1. Schematic illustration of the fabrication process.",
        "texts": [
            " The contoured substrate comprises a wavy stiff thin SiOx film on a PDMS substrate, formed by ultraviolet/ozone (UV/O) treatment on pre-stretched PDMS substrate followed relaxation. The metal thin film/contoured substrate is stretchable and has been demonstrated as stretchable electrical conductors. PDMS was prepared by mixing silicone elastomer base and curing agent (Sylgard 184, Dow Corning) at the ratio of 10:1 by weight, followed by degas and polymerization at 80 \u00b0C for 2 h. The polymerized PDMS slab (1 mm thick, 1 cm wide, and 2 cm long) is stretched by a stage to desired pre-strain \u03b5pre, as shown in step (i) in Fig. 1. The pre-strained PDMS substrate is subject to a flood exposure by a UV lamp (low pressure mercury lamp, BHK), which generates 185 nm and 254 nm radiations to react and change the chemistries of PDMS at the presence of atmosphere oxygen, as shown in step (ii) in Fig. 1. The distance between the lamp and the sample is constant 5 mm, which is chosen in order to maintain high radiation intensity 0.51 mW/cm2, but not to introduce much perturbation by the heat from the lamp. The exposing time varies from 40 min to 140 min, and the pre-strain on PDMS varies from 10% to 40%. The PDMS exhibits creep behavior after subjected to a fixed deformation for a significant amount of time, and it becomes more dramatic when PDMS is heated up. For example, there is around 5% permanent strain on PDMS after a 20% pre-strain is held for 120 min during UV/O treatment. Once the desired exposure time is reached, the pre-strained PDMS is slowly relaxed to generate wavy surfaces, as illustrated by step (iii) of Fig. 1. The fabricated wavy PDMS sample surface is characterized by optical microscopy and scanning electron microscopy (SEM). A 3 nm-thick gold/palladium layer is sputtered for discharging purpose prior to SEM imaging. The amplitude and wavelength are characterized by profilometer. To demonstrate the application for stretchable electrodes, chromium/gold (Cr/Au) films are directly deposited on the sinusoidally contoured surface by thermal evaporation through a shadowmask. Cr serves as adhesive promoter between SiOx and gold"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002776_j.jmapro.2019.09.012-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002776_j.jmapro.2019.09.012-Figure6-1.png",
        "caption": "Fig. 6. Simulated thermal contours of IN625 2Cone-0.5 sample tested at (a) 200 \u00b0C and (b) 500 \u00b0C at different times.",
        "texts": [
            " The encapsulated powder together with the interstitial gas was treated as a continuum and assumed to have the following unknown properties: density (\u03c1) and conductivity (k). Besides, two contact conductance values: (1) between the powder and the top solid shell (kt), and (2) between the powder and the bottom solid shell (kb), needed to be determined as well. Additionally, the specimen-holder contact conductance (kp) at testing temperatures was obtained by analyzing the thermal response of the solid sample testing using the same laser flash system and the FE simulations, and then included in the laser flash simulation for the specimens with encapsulated powder. Fig. 6 illustrates two examples of temperature contours of the cut-off sectional area at different times for a 2Cone-0.5 IN625 powder-enclosed sample at 200 \u00b0C and 500 \u00b0C with assumed material properties. At the beginning, the heat flux is applied at the bottom surface of the sample, and the irradiation time period is 0.003 s as in testing. The temperature of the irradiation region of the sample can increase by about 29 \u00b0C for the 500 \u00b0C testing case, for instance. Then, the heat flows upward through the sample"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000754_j.mechmachtheory.2013.10.006-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000754_j.mechmachtheory.2013.10.006-Figure5-1.png",
        "caption": "Fig. 5. A range of bevel gear with (a) chipped tooth, (b) missing tooth, and (c) worn gear.",
        "texts": [
            " This machine could be used for the simulation of a range of machine faults like in the gearbox, shaft misalignments, rolling element bearing damages, resonances, reciprocating mechanism effects, motor faults, and pump faults. In the MFS experimental setup, 3-phase induction motor was mounted to the rotor that was connected to the gear box through a pulley and belt mechanism. The gear box and its assembly are illustrated in Fig. 4. In the study of faults in gears, three different types of faulty pinion gears namely the chipped tooth (CT), missing tooth (MT) and worn tooth (WT) along with normal gear (or no defect, i.e. ND) gear were used (see Fig. 5). The real time data in frequency domain were measured using a tri-axial accelerometer (sensitivity: x-axis: 100.3 mV/g, y-axis: 100.7 mV/g, z-axis: 101.4 mV/g) mounted on the top of the gearbox (see Fig. 6) and the data acquisition hardware. Measurements were taken for the rotational speed of 10 Hz to 30 Hz at the interval of 2.5 Hz for each of the four gear conditions. For each measurement set, 300 cycles of data with 10000 samples each were taken. Total 10000 \u00d7 300 samples (FFT) were collected for each of three directions (i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001126_s12555-011-9214-6-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001126_s12555-011-9214-6-Figure3-1.png",
        "caption": "Fig. 3. Multiplicative uncertainties in a pole. pn, pa, and w are a nominal pole, an actual pole, and the relative magnitude of maximum uncertainty, respectively.",
        "texts": [
            " When the open-loop system is unstable, it can be stabilized by a feedback controller first, and the DOB may be applied to the stabilized system. 3.1. Multiplicative uncertainties in poles Suppose that a closed-loop pole of the DOB loop, pa, is subjected to an uncertainty such that the location of the pole is changed from its nominal location. Suppose an actual pole is located at (1 ), a n p p w\u03b4= + (12) where pn\u2208C is the location of nominal pole, w + \u2208\u211c is the relative magnitude of maximum uncertainty, and \u03b4\u2208C is any complex number with bounded magnitude, |\u03b4| < 1. Fig. 3 shows the graphical representation of (12). If \u03b4 = 0, the actual pole is located at the nominal pole, which is the center of the disk. When \u03b4 is non-zero, pa is placed on an arbitrary point on the disk. In the continuous time domain, the actual pole should have negative real part for asymptotic stability, i.e., Re[ (1 )] 0 for all , | | 1 n p w C\u03b4 \u03b4 \u03b4+ < \u2208 < (13) Graphically, (13) is satisfied if w is less than ,w where Re[ ] . n n p w p + \u2212 = \u2208\u211c (14) In (14), it is assumed that the nominal model is stable (i.e., Re[pn] < 0). Recall that w|pn| represents the radius of uncertainty disk, shown in Fig. 3. Therefore, | | n w p is the maximum radius of the disk that satisfies the sta- bility condition. Note that \u2013Re[pn] is the distance from the nominal pole to the imaginary axis. When w = ,w the disk in Fig. 3 contacts the imaginary axis, which implies that an actual pole may cross the imaginary axis for some \u03b4. Note that w is in the range of 0 and 1. When pn is on the real axis, w is equal to one. If it is on the imaginary axis, w is zero. Since the larger the disk, the better the expected robustness, it is desired to maximize .w Therefore, w is regarded as a measure of stability ro- bustness, or uncertainty margin, in this paper. Since the DOB loop includes multiple closed-loop poles, w is calculated separately for each pole",
            " In a mathematical sense, GD(z) and Gn(z) cancel each other, and therefore pole-zero cancelation takes place in the closed- loop transfer functions in (2)-(4). Assuming that the closed-loop poles are subjected to pole location uncertainty in (12), all the closed-loop poles affect the response. In Fig. 10, one pole is located at \u2013 0.9007, which results in w = 0.03327. The other poles are located where w is close to one. Therefore, it is a reasonable expecta- tion that instability shown in Fig. 8 was caused by this small uncertainty margin. Due to the small ,w the radius of the disk in Fig. 3 was small, and therefore the entire system became easily unstable even by a small perturbation. Therefore, the DOB should be redesigned such that all the closed-loop poles have large uncertainty margin. 4.3. Nominal model manipulation Table 1 shows the parameters optimized by the pro- posed method. The unconstrained nonlinear program- ming function in Matlab (fmincon.m) was used for opti- mization. The initial guess and the structure of GD(z) were the same as Gn \u20131(z). Note that a0 became close to zero"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003940_s40964-020-00140-8-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003940_s40964-020-00140-8-Figure1-1.png",
        "caption": "Fig. 1 High frame rate (HFR) camera viewing track processing during laser powder bed fusion",
        "texts": [
            " Each stripe on a particular layer was scanned for melting and fusing the powder material by following a hatching strategy that begins and ends on 4\u00a0mm-wide stripe patterns in a serpentine manner (looking like a serpent or a snakelike). Each stripe consists of laser scanned tracks separated by a hatch distance where each one of them is processed with the laser scanning moving at a constant velocity. At the end of each track, the laser is turned off (laser-off condition) for about 0.042\u00a0ms and the laser scan direction is reversed by realigning scanning mirrors and the processing of the next unprocessed track begins (see Fig.\u00a01). It should be noted that the videos acquired were processed for removal of the laser-off condition. The size of the meltpool in the powder bed is affected by LPBF operational parameters, powder material size and distribution, and ambient gas concentration. Once a layer is processed, a new layer of powder is spread over the surface of the powder bed with a predefined thickness. To obtain a fully dense build with no anomalies, the meltpool shape and size should remain consistent so that each track is processed with same energy density absorbed and each layer is fused and bonded with the previous layer by deep enough meltpool"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000751_tmech.2012.2209673-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000751_tmech.2012.2209673-Figure3-1.png",
        "caption": "Fig. 3. Setup of the experiment shows the gripper grasping on the right side of tissue and pulling in the direction of the arrow. Sixteen fiducials apart are marked on the tissue. Spacing between rows in both direction is 20 mm.",
        "texts": [
            " The first simulation scenario assumed that the tissue and manipulation geometries were acquired accurately. The second scenario considered the case when the tissue geometry was not perfectly modeled. The third scenario considered the case when there were uncertainties in positioning of the end effector on the target tissue. The fourth scenario considered uncertainties in the robot\u2019s motion. And finally, the fifth scenario considered the case when the robot performs nontrivial manipulations. In the simulations, a tissue model in the shape of a square patch, shown in Fig. 3, with dimensions of 10 cm \u00d7 10 cm \u00d7 1 cm was used. The center of the tissue was (0.0, 0.0, 0.0) in x\u2013y\u2013z coordinates. The end-effector gripper was assumed to grasp a 2 cm \u00d7 2 cm area on the tissue without any slip. This was modeled by anchoring the grabbed part of the tissue rigidly to the gripper by position boundary conditions. The size of the gripper was 2 cm in width and initially at (0.04, 0.0, 0.0) m. The tissue was assumed to be anchored on the left side (x = \u22125 cm) and the gripper retracted the tissue by pulling in the direction of the arrow shown in Fig. 3 (+x-direction). The stress and strain of the tissue are assumed to be in the zero state at the beginning of the experiment including the effect of gravity. The Salmon [12] open source finite element modeling and simulation package was used as the underlying FEM simulation engine, after custom modifications. The Salmon package offers FEM simulation with geometric and material nonlinearities. The meshing of the geometric models to be used in the FEM simulations was done by TetGen [29]. The SQP algorithm using the quasi-Newton line search, as provided by the MATLAB\u2019s fmincon function, was used to find minimum of the objective function"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001286_tec.2017.2651034-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001286_tec.2017.2651034-Figure2-1.png",
        "caption": "Fig. 2. 2-D electromangtic FE model",
        "texts": [
            " Moreover, independent of noise test, some commonly used psychoacoustical indices are predicted based on the calculated noise result, which can further contribute to annoyance evaluation. Based on the proposed model, the influence of current harmonics on SQ is also investigated. The motor studied in this paper is a FSCW PMSM with 6 poles/9 slots and its structure is shown in Fig. 1. Most of analytical electromagnetic force models are suitable for surface-mounted PMSM with tile shape PMs. Because the PMs of the motor in this research are not purely surface- mounted, FE method is employed for force calculation. Fig. 2 shows the 2-D electromagnetic FE model which is validated by the back electromotive force test [20]. The motor speed under investigation varies from 1500 rpm to 5000 rpm, which covers the common operation range. To analyze the vibration and noise in the whole speed range, the radial force with uniform acceleration from 1500 rpm to 5000 rpm is calculated. The time history of three phase currents is recorded during the test to serve as the current source of the electromagnetic model. Fig. 3 is the time-frequency map of Bphase current during run-up",
            " See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. (2), the force components around fc in Fig. 4(a) can find their corresponding current harmonics in Fig. 3. (a) (b) Fig. 4. Time-frequency map of radial force density during run-up. (a) with current harmonics. (b) without current harmonics. III. VIBRATION AND NOISE PREDICTION The flowchart of vibration and noise calculation during runup is shown in Fig. 5. First, 2-D electromagnetic model shown in Fig. 2 is built to calculate the electromagnetic force, which is extended to 3-D space under the assumption that the force distributes uniformly along the axial direction. STFT is employed to obtain the frequency spectrum of force at different rotational speeds. Then, by nodal force transfer method, the force on electromagnetic mesh is transferred to structural mesh in frequency domain. MSM is adopted to calculate the stator surface vibration. Next, acoustic transfer vector (ATV) between vibration and sound pressure at acoustic field point is obtained via BEM"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001115_j.wear.2015.01.047-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001115_j.wear.2015.01.047-Figure2-1.png",
        "caption": "Fig. 2. Single contact features.",
        "texts": [
            " Wear tracks and forces measurement data are analyzed. The PRS consists of a screw and a threaded nut of the same pitch (Fig. 1), with rollers in between. The thread profile of the screw and the nut is straight and usually cut to 901 for best efficiency. Threaded rollers are set between the two components, and their profile is curved to further reduce friction. The axial load is transmitted through multiple contacts between the threaded components. Then, these contacts can be described as ellipsoidon-flat contacts (Fig. 2) that are characterized by three radii: the pitch radius of the screw (or the nut) and the roller, and the roller's radius of curvature. They are subjected to a single normal force Fn that is the 451 projection of the single axial load Ftot. The resulting contact area is an ellipse whose characteristics can be calculated using the Hertz theory. For unique loading direction, only one side of the thread works because of axial backlash. The overall motion is similar to that of an epicyclic gear train: the rotation of the screw drives the orbital motion of the rollers",
            " Nomenclature i screw, nut or roller Ftot axial load on a single contact (N)\u00bctotal axial load/ number of contact points Fn normal force (N)\u00bc Ftot= cos \u03b2 Ft tangential friction force (N) Rcurv radius of curvature of the roller profile (mm) Ri pitch radius of the component i (mm) R radius of the track on the disc (mm) \u03c4 creep ratio (\u00bcVsliding/Vrolling\u00bctan\u0398) \u0394 axial shift on the test rig \u0398 creep angle (1) pi pitch of the component i (mm) \u03b1i helix angle of the component i (1) \u03b2 tilt angle (1) generally equal to 451 Vrolling in-plane rolling speed of the PRS roller (m s 1) Vsliding in-plane sliding speed of the PRS contact (m s 1) Vax.sliding axial sliding speed of the PRS contact (m s 1) Vdisc speed of the contact point on the disc (m s 1) vrolling speed of the contact point on the roller (m s 1) vsliding sliding speed of the roller sample (m s 1) po maximum Hertz pressure (MPa) p local normal stress (MPa) q local shear stress (MPa) m friction coefficient (\u00bcFt/Fn) Since the contacting threads are tilted from the axis to an angle \u03b2, the actual sliding speed at the contact point and the creep ratio are (cf. Fig. 2). Vsliding \u00bc Vrolling\u00f0 tan \u03b1screw\u00fe tan \u03b1roller\u00de cos \u03b2 \u00f010\u00de \u03c4\u00bc Vsliding Vrolling \u00bc \u00f0 tan \u03b1screw\u00fe tan \u03b1roller\u00de cos \u03b2 \u00f011\u00de The creep ratio and the rolling speed are directly related to the PRS design: for small pitches PRS, helix angles are smaller than for large pitches PRS, but applied speeds are usually higher. Then, the wear behavior would be different from one design to another. Typically, the creep may vary from 5% to 10%. Finally, since the contact is not punctual and is tilted from the rotation axis, the constant sliding lines inside the contact describe a class of circles whose centers may or may not lie within the contact area"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003987_tmech.2020.2979027-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003987_tmech.2020.2979027-Figure5-1.png",
        "caption": "Fig. 5. da Vinci PSM robotic arm with the force sensor placed at the end of the trocar\u2014kinematic frames description.",
        "texts": [
            " (6) Two off-diagonal terms K12Q and K21Q have been introduced in the calibration matrix (6) to capture the nonperfect symmetry of the sensor and the residual cross-talk effects. Authorized licensed use limited to: University of Exeter. Downloaded on June 22,2020 at 20:21:40 UTC from IEEE Xplore. Restrictions apply. A software calibration procedure was implemented to compensate the residual bias due to the nonnegligible differences between the parameters of each sensor and their asymmetry. The force fS measured by the trocar sensor is influenced by the external force acting on the instrument shaft, but also by gravity and inertial forces due to the instrument motion. Fig. 5 shows the sensing system mounted on the patient side manipulator (PSM) of a da Vinci surgical robot. The PSM is a 7-DOF actuated arm, which moves the attached instrument with respect to a remote center of motion (RCM), i.e., a mechanically fixed point that is invariant with respect to the configuration of the PSM joints. The position of the instrument tip depends only on the first three joint variables, corresponding to revolute (R) and prismatic (P) joints in an RRP sequence. The corresponding joint axes are shown in Fig. 5, where they are denoted as Ji, i = 1, 2, 3. The last four joints allow the opening/closure and reorientation of the gripper mounted on the tip [29]. A counterweight, not represented in the figure, is used to balance the weight of the mass which translates with respect to the RCM. The sensor is mounted on the terminal part of the trocar, in proximity of the RCM of the robot, which is located at the intersection of axes J1 and J2. Fig. 6 represents a planar view of the system, where the RCM is at point R in the center of the two yellow semicircles. In this figure, the shaft of the instrument (blue segment) is linked to point O, which corresponds to the intersection of axes J4 and J5 of Fig. 5, and can translate with respect to the RCM along axis J3. The rotational motion of the shaft about the axes J1 and J2 is described by joint variables q1 and q2, while the translational motion along axis J3 is described by q3. The joints J1, J2, and J3 are actuated by the motors of the PSM, and the corresponding joint variables are collected in the vector q = [q1, q2, q3] T . It is assumed that the external force fE \u2208 R3 is applied to the end point of the shaft. The sensing element is placed on pointS of Fig. 6, at a distance LS from the RCM R. The sensor measures the displacement of the shaft with respect to its rest position under the action of the external force, gravity, and inertial forces, and fS \u2208 R2 is the reaction force of the deformable part of the sensing element. To model this displacement, we assume that the shaft (a carbon fiber tube) is rigid and can rotate with respect to the pivot point O about the orthogonal axes J4 and J5 of Fig. 5, modeled as passive revolute joints. The corresponding joint variables are collected in the vector qS = [q4, q5] T . In static conditions and in the absence of gravity, the relationship between the force fS applied to the sensor and the external force fE depends only on the distance of the end point from point S as explained in Section III-A. This relationship is used in Section III-B for sensor calibration and in Section III-C for sensor characterization. In dynamic conditions, the weight and inertia of the instrument shaft must be suitably taken into account to estimate the external forces from sensor readings, as illustrated in Section III-D",
            " The experimental results presented in the next section show that the resolution that can be achieved using the residual-based approach alone is about 1 N, making this method unsuitable to measure small interaction forces. The idea here is to improve the estimation of the external forces by combining the measurements obtained by the trocar sensor with the residual-based approach, which takes into account the dynamic interaction between the PSM arm and the sensor. For this purpose, the dynamic model of the PSM arm and of the instrument can be computed by considering the kinematic chain composed by the actuated joint J1, J2, and J3 of the PSM and the two passive joints J4 and J5 (see Fig. 5). The dynamic model can be computed using a Lagrangian approach, by taking the following into account: 1) the instrument can rotate with respect to the RCM about the axes J1 and J2, with joint variables q1 and q2, respectively; 2) the instrument can translate along the axis J3, with joint variables q3; Authorized licensed use limited to: University of Exeter. Downloaded on June 22,2020 at 20:21:40 UTC from IEEE Xplore. Restrictions apply. 3) the instrument is modeled as a rigid cylinder which can rotate about the two passive revolute joints J4 and J5",
            " (18) The vector r45 collecting the last two components of the residual vector (12) can be expressed as r45 = K45I ( Bxy(q)q\u0307\u2212 \u222b t 0 (r45(\u03c3) + \u03c4S + nxy(q, q\u0307)) , d\u03c3 ) Authorized licensed use limited to: University of Exeter. Downloaded on June 22,2020 at 20:21:40 UTC from IEEE Xplore. Restrictions apply. In the abovementioned equations, mpxS is a first moment of the instrument shaft, and IxxS , IyyS , IzzS are the elements of its inertia matrix. The numerical values of these parameters, for a standard da Vinci needle driver instrument, were derived using CAD and are reported in Table I. The quantities are referred to frame O5-x5y5z5 of Fig. 5 and expressed in SI basic standard measurement units that are omitted here for brevity. The third component of the residual vector (12) can be expressed in the form r3 = k3I ( bTz (q)q\u0307 \u2212 \u222b t 0 (r3(\u03c3) + \u03c43R + nz(q, q\u0307) ) d\u03c3 ) with bTz (q) = [bz1 bz2 bz3] nz(q, q\u0307) = cz1q\u03071 + cz2q\u03072 \u2212 gz \u2212 fz and bz1 = mpyIc2 bz2 = mpxI bz3 = mI +mC cz1 = 2mpyIs2q\u03072 \u2212 0.0312mIc 2 2q\u03071 + 0.4mCc 2 2q\u03071 +2mpzIc 2 2q\u03071 + 2(mI +mC)q3c 2 2q\u03071 + 2mpxIc2s2q\u03071 cz2 = 0.4mC q\u03072 \u2212 0.0312mI q\u03072 \u2212 2mpzI q\u03072 +2(mI +mC)q3q\u03072 gz = \u22129"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001740_s00170-015-7974-5-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001740_s00170-015-7974-5-Figure4-1.png",
        "caption": "Fig. 4 Schematic description of computation domain",
        "texts": [
            " The mixed thermocapillary gradient\u2013temperature relationship depends on sulfur content of the material. Sulfur concentrations of 6 and 10 ppm are assumed in this study. The temperatures at which the peak of thermocapillary occurs are 1818 and 1941 K, respectively. More details of the mixed thermocapillary\u2013temperature calculation have been given in a previous publication [4]. The simulation was conducted in a 3D computation domain with dimensions of 2.8 cm (X-direction), 1.5 cm (Y-direction), and 0.9 cm (Z-direction) as shown in Fig. 4 below. The substrate occupies the region 0<Z<0.5 cm, and void occupies the region 0.5<Z<0.9. The region 0< Z<0.4 is meshed with coarse mesh blocks to reduce computational load. The upper fine mesh block has 262,500 cubic cells with edge length of 200 \u03bcm, and the lower block contains coarse mesh block 26,600 cubic cells with edge length of 400 \u03bcm. Thermophysical properties and manufacturing parameters used in this simulation are given in Table 1. The powder particles and substrate material are both Ni-based superalloy IN718"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003076_tmag.2019.2955884-Figure10-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003076_tmag.2019.2955884-Figure10-1.png",
        "caption": "Fig. 10. Prototype of the exterior-rotor PM-SRM.",
        "texts": [
            " 9(c), the phase rms current of the PM-SRM is lower than that of the PMless and 12/10 SRMs. The rated speed of the PM-SRM is 600 r/min with the rated power of 290 W. Moreover, the copper losses of the three motors are compared in Fig. 9(d). It can be inferred that the PM-SRM has lower copper losses since it draws lower rms current. Consequently, the proposed PM-SRM offers higher efficiency than the two other motors in a wide speed range, as illustrated in Fig. 9(e). To validate the simulation results, a prototype of the proposed PM-SRM is manufactured and tested. Fig. 10 shows the stator and rotor structures of the prototyped PM-SRM. The test setup of the proposed PM-SRM is shown in Fig. 11. A position encoder is used to determine the position of the rotor in the switching process. The measured static torque and flux linkage of the PM-SRM are illustrated in Fig. 12. It is obvious that there is a very small difference between the measured values and results of the finite-element method (FEM) analysis. The dynamic performance of the proposed motor under the nominal speed of 600 r/min is conducted using a CCC strategy with the chopping current of 8 A"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002216_00207179.2014.974675-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002216_00207179.2014.974675-Figure1-1.png",
        "caption": "Figure 1. Inverted Pendulum on a Cart",
        "texts": [
            " One can convert the kinematics and dynamics to the state space form: q\u0307 = v, v\u0307 = M\u22121(q){\u2212C(q, v)v \u2212 G(q) + F (q, v)} = f(q, v). (4) This state space form is used for constructing control schemes for stabilizing the simple mechanical system. The remainder of this section describes two simple mechanical systems that are representative of this large class of systems that occur in several practical applications. Two illustrative examples of simple mechanical systems are considered next. 2.1 Inverted Pendulum on a Cart The first example system considered is an inverted pendulum on a cart, a schematic of which is shown in Fig. 1. This system has two degrees of freedom. The generalized coordinates are chosen as the horizontal displacement of the cart, x, and the rotational displacement of the pendulum from the upward vertical, \u03b8; thus, q = [x \u03b8]T . The kinetic and potential energy for the inverted pendulum on a cart are obtained in terms of these generalized coordinates and their generalized velocities as T = 1 2 mcx\u0307 2 + 1 2 mp(x\u0307 2 + 2dx\u0307 cos \u03b8\u03b8\u0307 + d2 \u03b8\u03072) + 1 2 I\u03b8\u03072, (5) U = mpgd cos \u03b8, (6) where mc and mp are the mass of the cart and the pendulum respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003301_j.mechmachtheory.2019.01.014-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003301_j.mechmachtheory.2019.01.014-Figure8-1.png",
        "caption": "Fig. 8. Deflection and deformation of j th ball at angular location \u03c8 j .",
        "texts": [
            " When the ball bearing is under load, the relative displacement between inner and outer rings shifts the inner groove curvature center to O i \u2019 . Then, the distances A j and A j \u2019 between the inner and outer groove curvature centers are given by A j = \u221a ( A 0 b sin \u03b30 \u2212 x j )2 + ( A 0 b cos \u03b30 ) 2 (30) A j \u2032 = \u221a ( A 0 b sin \u03b30 + x j )2 + ( A 0 b cos \u03b30 ) 2 (31) where x j is the relative displacement along the X axis between the inner and outer rings for j th ball. According to Eqs. (30) and (31) , with the increase of load, the distances A j and A j \u2019 have opposite tendency. As shown in Fig. 8 , the relative displacement x j is caused by the displacement and deformation along the X axis, which can be expressed as follows: x j = x b + \u03b4x j = x b + R j \u03d5 sin \u03c8 j (32) where x b is the relative displacement between inner and outer rings, and \u03b4xj is the deformation caused by the deflection of inner ring. The attitude angle \u03c8 j for j th ball can be calculated as \u03c8 j = 2 \u03c0( j \u2212 1) n (33) b where n b is the number of balls in a ball bearing; this can be referred to the technical manual of ball bearing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000218_1.3063817-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000218_1.3063817-Figure3-1.png",
        "caption": "Fig. 3 Simplified stamped cage model",
        "texts": [
            " The bearing components begin in some initial configuration. After calculating the net force and moment acting on each component, Newton\u2019s laws of motion determine the accelerations of the balls, inner and outer races, and cage. The accelerations and velocities are integrated in time using a fourthorder Runge\u2013Kutta method to predict the velocities and positions, respectively. The states of the bearing components are recorded periodically, and the simulation ends once a criterion for stopping has been reached. Figure 3 illustrates the stamped-style cage modeled in this analysis. Manufacturing this style of cage involves riveting together two stamped pieces of sheet metal. This analysis neglects some of the features of the cage resulting from the manufacturing process. The cage model assumes that the two halves of the cage are fixed along the mating surfaces of the bridges, thereby ignor- Transactions of the ASME of Use: http://www.asme.org/about-asme/terms-of-use i n m e r d m b r i R fi F f i a c C o m r e t d i c a e b i f b J Downloaded Fr ng the effects of the rivets"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001711_s1560354713060166-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001711_s1560354713060166-Figure9-1.png",
        "caption": "Fig. 9. The Poincare\u0301 section formed by the intersection of the flow u\u0307, \u0307v, y\u0307 with the plane v = 0 for I1 = 0.8,",
        "texts": [
            "5), it suffices to plot the trajectories with initial conditions lying on one straight line, for example, y0 = 0. All the other trajectories will be obtained from the given trajectories by means of a drift along the axis Oy. It is obvious that the unboundedness of the Poincare\u0301 map implies the unboundedness of the ball\u2019s rolling motion in the direction of Oy. The type of this unboundedness (linearity or nonlinearity of the mean motion) can be qualitatively determined from the appearance of the map. Examples of the Poincare\u0301 maps for various values of the integral \u0394 are given in Fig. 9 and will be described below. 5.2. Transverse Motion for Nonresonant Tori As is well known (see the Appendix), if a torus is nonresonant (i.e., Tu/Tv \u2208 Q), then y(\u03c4) = \u3008V\u0303y\u3009\u03c4 + \u03b4y(\u03c4), where \u3008V\u0303y\u3009 is the velocity averaged over the invariant torus (5.2), which can be found as \u3008V\u0303y\u3009 = \u03c0\u222b \u2212\u03c0 \u03c0\u222b \u2212\u03c0 Vy(u, v\u0303)\u03a6u(u)\u03a6v(v\u0303) du dv\u0303 TuTv , (5.7) and the remainder satisfies the equality lim \u03c4\u2192\u221e \u03b4y(\u03c4) \u03c4 = 0. According to the Appendix, in the initial time t the average velocity differs from \u3008V\u0303y\u3009 only by a constant multiplier",
            " After the above-mentioned change of time t \u2192 \u03c4 , the function y(\u03c4) = \u03b4y(\u03c4) can be represented as a formal series y(\u03c4) = \u2211 n1,n2 Vn1n2 i(\u03c9un1 + \u03c9vn2) ei(\u03c9un1+\u03c9vn2)\u03c4 , n1, n2 \u2208 Z, (5.8) where Vn1n2 are the coefficients of the Fourier decomposition of velocity Vy(\u03d5u, \u03d5v). This series converges absolutely and uniformly at \u03c4 \u2208 (\u2212\u221e,+\u221e) for almost all rotation numbers r = \u03c9u \u03c9v , and y(\u03c4) is a quasiperiodic function. In this case the Poincare\u0301 map is a family of curves bounded in y, filled everywhere densely with points of the trajectories (see Fig. 9a). It follows from the above translation symmetry of mapping that the curves are mapped into each other by a parallel translation along the axis Oy. It is seen in the figure that the totality of trajectories above and below is bounded by curves which only touch (but do not intersect) the straight line y = y0, i.e., for the corresponding solutions the difference y \u2212 y0 is either nonnegative or nonpositive for all t (see the Appendix, Theorem 3). If the series (5.8) converges absolutely, but nonuniformly at \u03c4 \u2208 (\u2212\u221e,+\u221e), then y(\u03c4) is not a bounded function",
            "1) is everywhere transverse to the plane v\u0303 = 0 for 0 < \u0394 < 1) and construct a graph showing the value of the drift for one period of motion on the torus \u0394y = y(t + T )\u2212 y(t) depending on u0. An example of such a graph for Tu Tv = 4 3 is given in Fig. 10. By symmetry V\u0303y(u, v\u0303 + \u03c0) = \u2212V\u0303y(u, v\u0303), each trajectory with a positive mean motion corresponds to a trajectory with the same mean motion in the negative direction, as can be seen well in Fig. 11b. In this case the trajectories of the Poincare\u0301 map with initial conditions lying on the straight line y0 = 0 are n vertical straight lines ( for Tu Tv = n m ) filled with points spaced apart at distances \u0394y(u0) (see Fig. 9b). Depending on the sign of \u0394y, the vertical straight lines are filled in the positive or negative direction along the axis Oy (see Fig. 9b). Remark. We note that the velocity of the mean motion along the axis Oy, even for the most large resonances such as Tu Tv = 4 3 , is two orders less than the velocity of motion along the axis Ox (see Fig. 11). Thus, an experimental detection of this effect by means of immediate measurement is a fairly complicated problem (due to the presence of friction). When it comes to practical observation of the mean motion, it is also appropriate to raise the question of nonzero mean motion on finite (albeit rather large) times"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003451_j.measurement.2019.107043-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003451_j.measurement.2019.107043-Figure6-1.png",
        "caption": "Fig. 6. Hertzian contact zone.",
        "texts": [
            "375 m Module (m) 16 mm CSPA (ac) 20 Tooth number (z) 40 DSPA (ad) 20 /25 /30 /35 Face width (b) 8 mm Surface treatment Induction heating Addendum (ha) 1 m Surface hardness 55\u201365 HRC Dedendum (hf) 1.25 m bh \u00bc 2:15 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi F 2 qp qd=qp \u00fe qd E vuut \u00f03\u00de where F is the applied load per unit length, E is Young\u2019s modulus of the gear material, and qp and qg denote the radii of curvature at the mating points for pinion and gear, respectively. The Hertzian contact zone is seen in Fig. 6. Boundary conditions of the FEA were defined to be consistent with the experimental test setup. A single static force was applied on the tooth surface from the 5 mm inside of the addendum circle. The body of the gear sample, which was clamped to the rigid body with the bolts, were fully fixed as seen in Fig. 7. Four different single static forces (750, 1000, 1250 and 1500 N) were applied on the tooth surface from the 5 mm inside of the addendum circle. The yield strength of the material was taken into account in determining the static loads used in the experiments, and numerical stress analyzes"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002518_s00170-016-9135-x-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002518_s00170-016-9135-x-Figure2-1.png",
        "caption": "Fig. 2 Sketch of the cross section of a multilayer specimen",
        "texts": [
            "2 \u22c5arcsin 2\u22c5 W 2 \u22c5H W 2 2 \u00fe H2 0 BB@ 1 CCA \u2212 W 2 \u22c5 W 2 2\u2212H2 2\u22c5H2 \u00f03\u00de O% \u00bc W\u2212Sx W \u22c5 100 \u00f04\u00de In these equations,H (mm) is the maximum height reached by the single track, W (mm) is the value of the maximum width, AABC (mm2) is the area of the cross section, and O% represents the degree of overlap between two tracks. In order to apply these equations, it was necessary to measure the width and the height of the preliminary track, which was determined based on the experimental plan. The model suggested by Angelastro et al. was used [30]. As shown in Fig. 2, the centre of the laser spot of the first track in even layers was displaced of Sx / 2 with respect to the first one of odd layers, so the odd layers had one extra track with respect to Sample Real average dimension (mm) even ones. The laser was focused on the intersection of the two ideal circumferences, which is indicatedwith the letter G in Fig. 1. After having calculated the circumference radius by Eq. 5, it is possible to determine optimal values of the laser step height, Sz (Eq. 6), for multilayer manufacturing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001885_j.matpr.2015.10.028-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001885_j.matpr.2015.10.028-Figure6-1.png",
        "caption": "Fig. 6. a) Billet for visioplastic analysis (drawing), b) real billet with pins",
        "texts": [
            " Hence, possible local changes in the material flow can be attributed only to local differences in the surface roughness [8]. In order to facilitate the ejection of the aluminum, the prechamber in the die is tapered by 3\u00b0 in extrusion direction. The infeed to the die bearings has additionally a die opening angle of 45\u00b0. By this, the dead zone shall be minimized and the contact surfaces with relative movement between workpiece and the die shall be enlarged additionally. For visualizing the material flow, the billets were prepared by the indicator pin method (Fig. 6 a)). A finite element simulation (DEFORM 2D) was used to determine a suitable position of the indicator pins as well as the length to be extruded. Billets of 175 mm in length and 62.5 mm in diameter were prepared, fitting to the prechamber of the die. Indicator pins of EN AW-4043A (AlSI5) with a diameter of 3.1 mm were placed axially and radially in the billet symmetry plane at the tip of the billet. The billet geometry is adapted to the geometry of the die\u2019s prechamber (Fig. 6 b)). By this, directly from starting the process, the indicator pins are in contact with the die surfaces to be investigated. The prepared billets were preheated to 540 \u00b0C and put into the container of the extrusion press in this kind, that the indicator pins are placed perpendicular to the transition plane between the machined and the rough surface in the prechamber. The billets were extruded at a ram speed of 0.5 mm/s. After extrusion the billets were ejected and cut in the plane containing the indicator pins"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001198_j.ijsolstr.2014.06.023-Figure17-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001198_j.ijsolstr.2014.06.023-Figure17-1.png",
        "caption": "Fig. 17. Film/Sub III under the first step of compression along the x direction. The left c determined by bifurcation indicators. The right column presents the associated instabili",
        "texts": [
            " The film is meshed with 26 50 shell elements, while the substrate is compatibly discretized by 6500 block elements with five layers. Totally, the film/substrate system contains 53,235 DOF including the Lagrange multipliers. The uniaxial compression in the first step generates the same type of sinusoidal wrinkles as in Section 4.1. In Fig. 16(a), two bifurcation points have been found. The sequence of wrinkling modes Dv corresponding to the bifurcation loads and their associated instability modes Dv3 are illustrated in Fig. 17. The first mode is modulated in a sinusoidal way while the second one corresponds to a quasi-uniformly distributed oscillation. During the second step of compression along the y direction, two bifurcations have been captured by computing bifurcation indicators (see Fig. 16(b)). The erboard pattern v in the final step, (b) the final shape v3. first mode shows aperiodic wrinkles (see Fig. 18(a) and Fig. 18(b)), where the perfect periodicity in Fig. 17(d) has been broken by the new bifurcation. Such a loss of periodicity had been previously discussed in Sun et al. (2012), Cao and Hutchinson (2012a,b), Cao et al. (2012), Zang et al. (2012) and Xu et al. (submitted for publication), where period-doubling or even period-quadrupling is observed. Here, the periodicity is broken by the appearance of 3D wrinkling patterns and one can wonder in which cases the sinusoidal modes lose their stabilities by the occurrence of period-doubling or 3D wrinkling modes. The herringbone mode (see Fig. 17(d) and olumn shows a sequence of wrinkling modes Dv corresponding to its critical load ty modes Dv3 at the line Y \u00bc 0:5Ly: (b) the 1st mode, (d) the 2nd mode. Fig. 18(d)) appears around the second bifurcation with an in-plane wave occurring along the y direction in order to satisfy the minimum energy states (Chen and Hutchinson, 2004; Audoly and Boudaoud, 2008b). Apparently, the wavelength ky is larger than the sinusoidal wavelength kx, which is consistent with the experimental results in Yin et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000747_s12283-013-0117-z-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000747_s12283-013-0117-z-Figure8-1.png",
        "caption": "Fig. 8 Reverse swing on a high-speed cricket ball that moves left to right. This figure is adapted from Mehta\u2019s work [54]",
        "texts": [
            " Mehta [54] provides a nice qualitative description of the phenomenon. Ball spin and orientation are just as described for ordinary swing, only now the ball must be thrown fast enough that the boundary layer is turbulent over the entire ball. In that situation, the seams enhance the thickness of the boundary layer, which weakens it, causing it to separate sooner than if there were no seams. The asymmetric boundary-layer separation is now opposite to the ordinary case, leading to a force in the direction of the non-seam part of the ball. Figure 8 illustrates how the boundary layer separates from a cricket ball with reverse swing. Mehta notes that speeds must be upwards of 40 m/s = 144 kph = 89 mph to see reverse swing, meaning only the elite bowlers could do this. Lower-speed bowlers could still achieve reverse swing if they used a worn ball, meaning the surface is rougher than a new one, which pushes the drag crisis to a lower speed. Mehta suggests that speeds around 30 m/s = 108 kph = 67 mph would give reverse swing with a worn ball. Beyond normal aerodynamics, playing surface and atmospheric conditions may influence cricket play"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001468_j.isatra.2015.02.008-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001468_j.isatra.2015.02.008-Figure4-1.png",
        "caption": "Fig. 4. Flowchart of control program for trajectory tracking.",
        "texts": [
            " Recalling generalized coordinate (18), the state vector is selected as x\u00f0t\u00de \u00bc \u00bdqT \u00f0t\u00de; _qT \u00f0t\u00de T . The state-space form of equation of motion (19) is presented as _x\u00f0t\u00de \u00bc \u00bd xn\u00fe1\u00f0t\u00de; :::; x2n\u00f0t\u00de;M 1\u00f0x\u00f0t\u00de\u00de u\u00f0t\u00de c\u00f0x\u00f0t\u00de\u00de g\u00f0x\u00f0t\u00de\u00de T : \u00f020\u00de After forming the state-space Eq. (20), SDC matrices are made. The details of SDC parameterization ought to be found in [20]. The control program is presented in Fig. 3 as a flowchart. For trajectory tracking the desired output should be provided as a function of time where the details are reported in Fig. 4. The point-to-point motion benefits from the Lyapunov-based method using negative root of related SDRE which has a singleround forward solution. The tracking problem employs the backward integration method and two differential equations are solved to complete the answer. Regarding the general formulation peculiar to flexible joint manipulators [20], considering flexibility in joint does not need new derivation for dynamics equation and augmented equation can be structured using rigid joint equation of dynamics",
            " It receives the desired velocity of end-effector in Cartesian coordinate and solves the following first order differential equation: _q\u00f0t\u00de \u00bc J 1\u00f0q\u00f0t\u00de\u00de _X\u00f0t\u00de; \u00f024\u00de where _X\u00f0t\u00de \u00bc \u00bd_xdes;e\u00f0t\u00de; _ydes;e\u00f0t\u00de; _zdes;e\u00f0t\u00de is the desired velocity of the end-effector and J\u00f0q\u00f0t\u00de\u00de is Jacobian matrix of robot (using a Jacobian in square form is considered; so for manipulators with more than three DoFs, the orientation of the end-effector must be augmented to _X\u00f0t\u00de to omit the redundancy situation). The desired value r\u00f0t\u00de must be saved as a continuous function of time; command \u201cfit\u201d with \u201clinearinterp\u201d option in MATLAB software can be used. This option for trajectories with sudden jump and deviation is suitable which in that case polynomials would not provide a proper answer. The rest of the program is based on \u201cFlowchart C: Trajectory tracking\u201d in Fig. 4 with two rounds, backward solution and storing the results and then solving the problem forward. The tracked trajectories with two methods SDRE and SDDRE via backward integration accompanied by configuration of links are shown in Fig. 27. The errors of tracking in end-effector are also presented in Fig. 28. The maximum error of conventional SDRE is 22.11 mm and this value for SDDRE is gained 6.4 mm which reduced the error 71.05% by the proposed controller. Now by defining 22.11 mm error as a new allowable bound for end-effector, the external load on endeffector will be increased for SDDRE to find the maximum acceptable load"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001842_s00170-015-7647-4-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001842_s00170-015-7647-4-Figure4-1.png",
        "caption": "Fig. 4 Three-dimensional FE simulations of an extrusion process at a die stroke of 60 mm: a without die cooling, b notisolated die cooling, and c isolated cooling",
        "texts": [
            " As an example, a mandrel with a volume of 116 cm3 manufactured additively was fabricated in around 30 h while the conventional manufacturing with subtractive methods took approximately 5.5 h [7]. But, even if the pure die manufacturing costs are higher, the use of additively manufactured dies with conformal cooling channels can be economically beneficial when balancing the production costs of the whole manufacturing process due to a higher productivity. The effect of the not-isolated and the isolated cooling during hot aluminum extrusion was firstly investigated by finite element simulations and compared to the non-cooled extrusion trial (Fig. 4). The process of hot extrusion of squared tube profile was simulated by a quarter model of bridge die using the simulation software DEFORM 3D. The initial temperature of the container and the die was set to 450 \u00b0C, and the temperature of the billet was set to 540 \u00b0C. The ram speed is 1 mm/s. The extrusion ratio for the extrusion of a profile with 3 mm wall thickness is R=15. The aluminum alloy EN AW-6060 and the hot working steel 1.2343/H11 were selected as billet and die material, respectively",
            " Between container and billet, as well as between die and billet, sticking friction condition was set except from the area of the die bearings, where a shear friction factor ofm=1 was used [16]. The different simulations do not differ in the boundary conditions or process parameters, except from the applied cooling strategy. In case of cooling, the surface of the cooling channel (with a cross section of 1.6 mm) was modeled with a constant temperature of 275 \u00b0C as a boundary condition, which corresponds to the coolant exit temperature measured in the experiments while applying compressed air as coolant. In case of \u201cnot-isolated cooling\u201d (Fig. 4b), all nodes in the whole cooling channel were selected, and in case of \u201cisolated cooling,\u201d only the nodes in the area of the die bearings were selected and allocated with the coolant temperature (Fig. 4c). By this, the cooling effect is concentrated on the top of the mandrel and, thereby, in the area of the die bearings, respectively, the main forming zone. The coolant does not experience a preheating before reaching the area of the die bearings, whereby the cooling effect in the target area is increased. The cooling was started 20 s after starting the process. Due to the size of the 3D simulations, all simulations were carried out up to a die stroke of 90 mm. Figure 5 shows the profile\u2019s exit temperatures and the extrusion forces for the three previously mentioned conditions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002687_tmag.2017.2665580-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002687_tmag.2017.2665580-Figure2-1.png",
        "caption": "Fig. 2 No load flux plot distributions with different excitations by the FEA. (a) DC current is 4.3 A, PM is assumed to be vacuum. (b) PM excitation without DC current. (c) Both PM and DC current of 4.3 A excitation.",
        "texts": [
            " The maximum torque per current control of the proposed machine is zero d-axis current control. The electromagnetic torque expression under Id=0 control is ( )em r pm dc q r pm ac r dc m acT N I N I N I L I      (9) where \u03c8pm, \u03c8dc are the flux linkage by PM and DC current, respectively. Lm is the equivalent magnetizing inductance. It can be found that with the proposed DC-biased current configuration, in addition to the PM torque component, another torque component which is proportional to the square of current is introduced. Fig. 2 compares the no load flux distributions with different excitations simulated by the FEA. In Fig. 2 (a), the PMs are removed, the main flux produced by DC current bypasses the PMs, but through the adjacent iron shoe, this condition is similar to the no load situation in VRM. Another condition is the sole PM excitation in Fig. 2 (b) which is similar to the no load situation in FRPM, when the stator PM aligns with the center of the rotor slot, the magnetic flux forms mostly leakage flux, while when the stator PM aligns with the rotor tooth, the magnetic flux leakage is the least. It can be inferred that, due to the large flux leakage, the open circuit back-EMF will be small, which is helpful for the short circuit current reduction during short-circuit condition. To some extent, when both the DC current and PM are excited, the flux distribution at this time can be roughly considered to be a superposition of the two cases, as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002387_9781118773826-Figure13.16-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002387_9781118773826-Figure13.16-1.png",
        "caption": "Figure 13.16 Ionization curve.",
        "texts": [
            " Heating through dielectric loss is widely used in industry for heating thermosetting glues, for drying lumber and other fi brous materials, for preheating plastics before molding and for fast jelling and drying of foam rubber, etc. Th e dielectric loss of dielectric materials depends upon the following factors: \u2022 Eff ect of Voltage: Th e dielectric loss increases in proportion to the square of the voltage applied to the insulation. However, the dependence of tan \u03b4 on voltage is almost invariable with same values of voltage, but the curves of tan \u03b4 vs voltage (V) abruptly rise when voltage grows above a defi nite limit V ion . Th e curve shown in Figure 13.16 is known as an ionization curve and a point on the curve where ionization starts to increase is called the ionization point (point A in Figure 13.16) and confi rms the beginning of ionization in the insulation of air or other gases inside the insulation. \u2022 Frequency: At low frequencies of applied ac voltage, dipoles are able to keep in phase with changes in electric fi eld, and power losses are low. As the frequency is increased, space charge, orientation and ionic polarization become 470 Biosensors Nanotechnology inoperative and dipoles become out of phase. When several polarization processes such as ionic, orientation, space charge, etc., occur in a material, it follows that the dielectric loss decreases with increasing frequency"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000679_j.ymssp.2010.02.003-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000679_j.ymssp.2010.02.003-Figure4-1.png",
        "caption": "Fig. 4. Volumetric flow rates for the generic isolated tooth space i.",
        "texts": [
            " In fact, it is well-known that for a fluid film element with height h, length l and width w, the volumetric flow rate due to the pressure drop Dp can be calculated using Poiseuille\u2019s equation that supposes laminar flow: Qp \u00bc wh3 12m Dp l \u00f08\u00de On the other hand, the volumetric \u2018drag flow rate\u2019 has a linear distribution from zero to u, where u is the relative velocity of the upper part of the fluid film element with respect to the bottom part and it can be calculated using the wellknown relation Qu \u00bc wuh 2 \u00f09\u00de Relations (8) and (9) will be used hereafter in order to calculate the flow rate gain DQ in four kinds of control volumes while the volume variation dV/dy is obtained from geometrical considerations. Once the flow rate gain and the volume variation is obtained for all the control volumes, the resulting equation system can be numerically integrated in order to obtain the pressure distribution around the gears. Fig. 4 shows the generic tooth space i, edged between two consecutive tooth flanks (i and i+1) and the case. Each tooth space is connected with the next tooth spaces by the corresponding clearances between the case and the tooth tip, hi, hi +1, and between the bearing blocks and the tooth lateral flanks, hf; in addition, it is connected with the drainage circle through the clearances hf between the bearing blocks and the lateral surfaces of the gears (see also Figs. 3 and 5). So, Eq. (7) applied to the generic tooth space i becomes Qh;i\u00fe1 Qh;i\u00fe2\u00f0Qf ;i\u00fe1 Qf ;i\u00de 2Qd;i \u00bc Vi Boil dpi dy \u00fe dVi dy o \u00f010\u00de It can be noted that the flow through the clearance hf is double because of the two sides of the gear; moreover the flow rates Qh,i, Qf,i, Qd,i are taken as positive when coming out of the tooth space i, whilst Qf,i+ 1 and Qh,i +1 are considered as positive when coming into the tooth space i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002930_j.triboint.2016.03.017-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002930_j.triboint.2016.03.017-Figure1-1.png",
        "caption": "Fig. 1. Geometrical relation for mixed EHL model of spiral bevel and hypoid gears.",
        "texts": [
            " Besides, the prediction method is validated by comparing its results with experimental measurements by means of a roughness ellipsoid-on-disc contacts considering the surface velocity directions under severe operating conditions. In addition, numerical simulations are conducted to systematically study the influence of surface velocity directions corresponding to different sliding velocity on friction coefficient and flash temperature distribution in wide ranges of speed and load. The geometrical relation of spiral bevel and hypoid gears is well descripted in Fig. 1. The difference of contact zone is obvious from cylindrical gear or bearing. Note that in the contact ellipse, both the surfaces velocity direction, u1, and u2, do not coincide with the x or y direction. As a result, oblique angles occurs in the contact zone between the principal axis of ellipse and entraining velocity vectors u!e, as well as sliding velocity vectors u!s. In order to compute the friction and flash temperature, it is essential first to obtain the detailed information of film and pressure distribution based on a mixed EHL model"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000845_j.scient.2012.01.004-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000845_j.scient.2012.01.004-Figure3-1.png",
        "caption": "Figure 3: (a) Conduction between rings and individual rolling elements. (b) Clearance fitting of bearing rings.",
        "texts": [
            " \u2022 Convection between bearing and lubricant/surrounding fluids, lubricant and shaft/housing and between housing and surrounding air. Heat transfer by radiation is not expected to be very significant at the range of temperatures common to bearings. At higher temperatures, it could be included by linearizing the radiation equation, and adding it to the terms related to convective heat transfer. In general, rings and rolling elements have different temperatures, and a thermal contact resistance exists between them (Figure 3(a)) that depends on contact properties. Thermal resistance for a half-space is calculated as [9]: R = 1 2\u03c0\u03bba  \u03c0/2 0 d\u03b8 1 \u2212  1 \u03ba2  sin2 \u03b8 . (11) In which \u03bb is the conductivity of the half-space, a is the major axis of the elliptical contact area and \u03ba is the ratio of its minor to major axis. The above integral is in the form of the elliptical integral of the 1st kind, F, and, thus, becomes: R = F 2\u03c0\u03bba , (12) where F represents the elliptical integral of the 1st kind over the contact zone [10]. For the two-body contact of balls and the two rings, we have: Rbr = F 2\u03c0\u03bbba + F 2\u03c0\u03bbra . (13) Due to high rotational speeds, all balls are assumed to have similar thermal conditions and, therefore, are regarded as a unit. The thermal resistance at inner and outer contact zones is: Rbi = Rbi Z , Rbo = Rbo Z . (14) Bearing rings and the housing/shaft are usually attached by clearance fitting. The gap between fitted bodies, denoted as h in Figure 3(b), depends on body temperatures and also initial clearance, h0. Heat transfer through the gap is characterized by thermal conductance as below [9]: \u03a0 = 1 hring \u03bbring + hgap \u03bbair A. (15) hgap and \u03bbair are width of gap and conductivity of gap air, respectively, and hring and \u03bbring are the mean width and conductivity of the ring. A is the contact surface area. The temperature dependence of the gap width for outerring/housing and inner-ring/shaft contacts is given as: hgo = h0 \u2212 (To \u2212 Th) \u03b1rh, hgi = h0 \u2212 (Ts \u2212 Ti) \u03b1rs, (16) respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001442_romoco.2015.7219710-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001442_romoco.2015.7219710-Figure5-1.png",
        "caption": "Fig. 5. Workspace for the tested Pick & Place scenario (left). A and B denote the initial and goal position of the end-effector. The real robot (right).",
        "texts": [
            " The service internally calls forward kinematics to compute the orientations and positions of all n links and then performs collision detection between the links and workspace and also between pairs of links. The obvious advantage of this service is the smallest size of the messages, as only 8n bytes need to be transmitted. The disadvantage is, that the service needs to utilize forward kinematics and it has to be ensured, that both the planner and the service uses same forward kinematics. The three studied types of collision detection services have been experimentally verified in the Pick & Place scenario (Fig. 5). The workspace is represented by simple boxlike objects, that were converted to a 3D triangular mesh (with 150 triangles) for the purpose of collision detection. The geometry of the 6-link manipulator is described by a detailed CAD model with \u223c 105k triangles. The real robot is depicted in Fig. 5. The collision detection was implemented by the Rapid [22] library. The planner and the services Servicelinks,Servicearm and Serviceangles communicate with the planner using IP sockets. The performance of the services was compared with the collision detection called as a normal function without need to communicate using sockets. This version is referred to as Servicenone in the rest of the paper. The planners were tested with and without end-effector pose constraints (denoted Con=0/1 in the tables)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000842_00220345720510026301-FigureI-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000842_00220345720510026301-FigureI-1.png",
        "caption": "FIG I.-Schematic drawing metallic strip. of curved bi-",
        "texts": [],
        "surrounding_texts": [
            "Shear Stress Measurements at a Dental Porcelain-Gold Bond Interface\nJOSEPH J. TUCCILLO and JOHN P. NIELSEN J. F. Jelenko & Co., New Rochelle, New York 10801 USA, and New York University, New York, New York\nIn this study a method of measuring interfacial shear stresses from the curvatures of bimaterial dental porcelain-gold strips is described. Stresses were calculated for different porcelain thicknesses and as a function of temperature. The interfacial stresses found ranged from 1,000 psi tensile stress to 3,000 psi compressive stress on the porcelain side of the interface for porcelain thicknesses commonly used in dental restorations.\nDental porcelains adhere tenaciously to dental porcelain-gold alloys when applied and fired properly. The strength of adherence and the nature of the bond has been described in papers by Shell and Nielsen,' Leone and Fairhurst,2 and others.3-5 In recent years, there has been interest in learning the factors that tend to weaken the intrinsic porcelain-to-metal bond. For example, investigations are underway to determine the effect of thermal stresses that may occur in dental restorations.6'7 It is recognized generally that a mismatch in the coefficients of expansion between the two materials should generate thermal stresses in the composite on cooling from the porcelain firing temperature and that such stresses lower the intrinsic bond strength. It is of interest, therefore, to know the degree of interfacial shear stress that results from this mismatch. In addition, it would be worthwhile to know whether there are ways of decreasing internal stresses by controllable technique factors, such as, specimen geometry and rate of cooling. Possible porcelain strengthening effects that could come from controlled thermal stresses should not be\nPresented at the 49th general session of the IADR in Chicago, 111, March 1971. Received for publication March 18, 1971.\n626\noverlooked. A compression stress at the porcelain surface, as in a tempered-glass effect, might be desirable in dental restorations. The specific aim of this investigation was to determine experimentally the magnitude of the interfacial shear stress developed in an actual bonded dental porcelain* and gold alloyt composite.\nStress Calculations In a previous investigations the interfacial shear stress as a function of the coefficient mismatch was calculated for a porcelaingold bimetallic composite. These calculations were based on the Timoshenko bimetallic strip equation9 as follows:\nS - KmAwAXT (1)\nwhere Km is a function containing only G the modulii of elasticity (E) of the two materials and the geometry parameters of the specimen; Aa is the coefficient of expansion mismatch; and AT is the temperature range through which the porcelain behaves as a rigid solid (less than about 1,100 F). For example, for a bimetallic strip having a Aa corresponding to the mismatch between the porcelain and metal used in this investigation (0.15 X 10-6 inch/inch/0C), the theoretical interfacial shear stress is 1,800 psi (for equal thicknesses of metal and porcelain). The value of 1,800 psi, however, probably has a precision no better than about +20%, which is probably a high systematic error caused by a number of factors. The fictive temperature, although considered constant in the calculations, is affected by processing\n* Ceramco opaque porcelain, Ceramco, Inc., Long Island City, NY.\nt Ceramco \"O\" alloy, J. F. Jelenko & Co., New Rochelle, NY.\nat East Carolina University on April 23, 2015 For personal use only. No other uses without permission.jdr.sagepub.comDownloaded from",
            "SHEAR STRESS MEASUREMENTS 627\nvariables such as cooling rate. By definition (for this paper), fictive temperature is the temperature below which the porcelain behaves as a rigid solid. The mean mismatch coefficient depends on this fictive temperature. In addition, the effect of viscous flow in either or both materials, and the change in elastic moduli with temperature, are not accounted for in the equation. Because of the uncertainty caused by these factors, a calculation of stresses from experimental data immune to some of these uncertainty factors is desirable.\nIf a sufficiently thin strip of porcelaingold is porcelainized on one side and then heated to the firing temperature, the thermal stresses set up on cooling to room temperature will cause deflections of the composite strip. For equilibrium to exist in the system, any force set up in the porcelain at the interface must be balanced by an equal and opposite force in the metal at the interface. Thus, if the deflection or curvature in a porcelain-metal composite strip can be measured at room temperature, the stress at the interface between the metal and porcelain can be calculated free of such factors contributing to the uncertainties described.\nFigure 1 is a schematic drawing that shows a composite strip exhibiting the arc of a circle as a result of thermal deflection caused by different contraction rates in the porcelain and metal.\nThe interfacial stress in the porcelain of such a thermally deflected strip is related to the radius of curvature, P, by the following formula'0:\n-1 F2 E) alEl]S =[h (EII, +r E,-,1) + 2 PO ha1 11+ 22-\n(2)\nwhere subscript 1 refers to porcelain; subscript 2 refers to metal; s is interfacial stress; P0 is radius of curvature; h is composite thickness; E is modulus of elasticity; and I is moment of inertia = ba3/ 12; a is material thickness; and b is specimen width. The radius of curvature can be determined by direct measurement and the remaining factors (except E), based on specimen geometry, also are measurable with considerable precision. The value of the room temperature modulus of elasticity for both materials used in this study was taken as 12 X 106 psi. Young's modulus for the\nmetal was obtained directly from stress strain tensile tests in our laboratory, and it was close to 12.6 X 106 psi. The same modulus for porcelains is not obtained as easily. However, the technical literaturell-'3 indicates that the glassy matrix can be assumed to be more than 9 X 106 psi for dental porcelain; this value is enhanced with the feldspar, silica, and other crystallites residing in the matrix. Inasmuch as the stress values as calculated from equation 2 are affected mildly by the porcelain modulus values, it is permissible for the stress value precision sought in this paper to use an average modulus value of 12 x 106 psi for both materials.\nMaterials and Methods Plastic strips 0.312 inches wide by 2.25 inches long and 0.021 inches thick were invested and cast of Ceramco \"O\". An eighth inch hole was punched through one end of the cast specimen to provide means for freely suspending the strip during firing. The strips were sandblasted and degassed by heating to 1,950 F (1,065.6 C) and then cooled to room temperature under glass.\nVol 51 No. 2\nat East Carolina University on April 23, 2015 For personal use only. No other uses without permission.jdr.sagepub.comDownloaded from",
            "628 TUCCILLO AND NIELSEN\nBefore applying the opaque porcelain, the strips were cleaned ultrasonically for ten minutes in a detergent followed by a water rinse, and then an alcohol rinse. The porcelain slurry was applied over a 2 inch length as an even thickness on one side of the strip (Fig 2). The thickness of the porcelain was controlled by a jig that could be varied to give the required total composite thickness. The strips then were suspended from a horizontal Inconel arm by placing a ceramic rod through the arm and the hole at the end of the specimen. A platinum-wound resistance furnace was then rolled horizontally into position to house the specimen. A schematic drawing of the experimental setup is shown in Figure 3. In\nFigure 4, the specimen is shown suspended freely inside the furnace. The end from which the photograph was taken had been fitted with a 5 inch diameter, three-eighths inch thick quartz glass. This allowed viewing of the specimen during firing. It also was possible to measure the deflection change as the temperature varied by use of a calibrated telescope.\nAfter firing to 1,850 F at a rate of approximately 57 F/minute, the power was shut off and the specimen furnace was cooled. The heating and cooling cycle is shown in Figure 5. On heating, the rate was maintained somewhat constant by means of a Powerstat* control. The temperature was measured by a chromel-alumel thermocouple suspended alongside the specimen and hooked to a portable potentiometer.t To reduce the possible temperature\n* Superior Electric Co., Bristol, Conn. 1 Leeds and Northrup, Philadelphia, Pa.\nmeasurement error, a strip of pure silver also was suspended next to the test specimen and when it melted (1,760 F) a millivolt reading was noted on the potentiometer. To this was added 1.95 millivolts (90 F), and the power was shut-off when the new millivolt reading was reached. The estimated accuracy with this method was -+10 F (95% certain that the true temperature was within t10\u00b0 of the reading). The final fired porcelain thicknesses were measured by taking nine point-micrometer readings: three across the top, middle, and bottom of the specimen. These nine readings (minus the metal thickness) were averaged to determine the moment of inertia (I) of the porcelain. Nine readings were necessary because during fusion the volume shrinkage of porcelain was greater along the middle region of the specimen than near the edges. Figure 6 is a photograph of the cross section\ndimensions. Fio 4. Specimen suspended inside furnace.\nJ Dent Res March-April 1972\nat East Carolina University on April 23, 2015 For personal use only. No other uses without permission.jdr.sagepub.comDownloaded from"
        ]
    },
    {
        "image_filename": "designv10_5_0002464_ffe.13029-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002464_ffe.13029-Figure1-1.png",
        "caption": "FIGURE 1 Specimen orientation related to the build platform (A) and specimen geometry (B)",
        "texts": [
            " Cuboid specimens (10\u00d710\u00d7100 mm3) made of the austenitic chromium\u2010nickel stainless steel AISI 316L (X2CrNiMo17\u201012\u20102, 1.4404) were fabricated in one run with a M2 Cuising SLM system (Concept Laser, Germany) with an integrated 200\u2010W fiber laser on a standard platform size (250 \u00d7 250 \u00d7 350 mm3). The chemical composition for the alloy measured by spark optical emission spectroscopy (OES) is listed in Table 1. In total, three different batches of specimens with different relative orientation to the build platform (0\u00b0, 45\u00b0, and 90\u00b0) according to Figure 1A were manufactured for further investigations. Microstructural characterizations were conducted on the as\u2010built samples whereas for the fatigue tests specimens with a geometry according to Figure 1B were subsequently machined out of the cuboids. To prevent failure induced by the surface quality, the specimens were ground and polished to Rz \u2264 0.8 \u03bcm in the gauge section. 2.2 | X\u2010ray micro\u2010computed tomography (\u03bc\u2010CT) To detect the process\u2010induced porosity of certain specimens, nondestructive micro\u2010computed tomography (\u03bc\u2010 CT) was utilized by using the system Nikon XT H 160 (Nikon, Japan) with a maximum acceleration voltage of 160 kV. The scanned volumes correspond to the fatigue specimens' gauge length with a diameter of 5 mm",
            " The microstructure of the as\u2010built material as well as the morphology of the fracture surfaces after fatigue testing was additionally analyzed by scanning electron microscopy (SEM) Tescan Mira3 XMU (Tescan, Czech Republic). To evaluate the fatigue behavior of the three building orientations, two different fatigue tests, load increase tests (LIT) and constant amplitude tests (CAT), were performed on a servohydraulic testing system Schenck PSB100 (75\u2010kN load cell, Instron 8800 controller) (Instron, USA) under force control. The specimen's geometry can be found in Figure 1B. The material was tested at a frequency of f = 10 Hz and a load ratio of R = \u22121. The LIT is used to identify firstmaterial reactions under a stepwise increasing stress amplitude.23 Specimens were tested at a starting stress amplitude of \u03c3a,start = 200 MPa. This corresponds to approximately 36% of the yield stress for the 0\u00b0 specimens and 34% and 41% for the 45\u00b0 and 90\u00b0 specimens, respectively. The stress amplitude was increased by \u0394\u03c3 = 20 MPa every\u0394N= 104 cycles. Thematerial reaction wasmeasured in terms of strain measurements by using a tactile extensometer with a gauge length of 10 mm to record the stress strain hysteresis and calculate the plastic strain amplitude \u03b5a,p which is an indicator for plastic deformation and irreversible fatigue damage in thematerial"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000531_j.triboint.2012.03.006-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000531_j.triboint.2012.03.006-Figure2-1.png",
        "caption": "Fig. 2. Finite element model of contact stresses applied to an elastic half-space.",
        "texts": [
            " The rolling contact fatigue model presented in this investigation was developed to simulate subsurface initiated spalling in cylindrical roller bearings. The normal contact between a roller and a raceway can be modeled as an equivalent contact between two cylinders, which produces a pressure distribution given by p\u00bc pmax ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 x a 2 r \u00f01\u00de that acts over a rectangular region of length, l, and half-width, a. To compute the subsurface stress history in the raceway of a cylindrical roller bearing, a finite element model of a 3D elastic half-space, depicted in Fig. 2, is constructed using the microstructure model generator developed in [16]. The dimensions are limited to (10 1 12)a in the rolling (X), transverse (Y), and vertical (Z) directions, respectively. All displacements on the lower boundary of the model are fixed, and periodicity constraints are enforced in the rolling and transverse directions in order to effectively simulate the response of a semi-infinite, elastic half-space. The topology of the material microstructure is modeled by randomly created Voronoi tessellations",
            " Grains are discretized into tetrahedra by placing a node at the centroid of each face to divide the faces into triangles forming the bases of tetrahedra that share a common apex at the grain centroid as shown in Fig. 3. Each tetrahedron is meshed with either linear or quadratic elements depending on its proximity to the applied loads as described in [16]. The microstructure model is subjected to a sequence of surface tractions to simulate the action of a bearing element rolling over the raceway. The pressure distribution of Eq. (1) is applied at a sequence of 21 discrete locations from 2a to 2a as depicted in Fig. 2 using the equation tz\u00f0x\u00de \u00bc pmax ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 \u00f0x xc\u00de a 2 s \u00f02\u00de where x is the coordinate where the traction is evaluated, and xc is the location of the center of the pressure. Varying xc enables the traction distribution to translate over the surface of the halfspace. Shear surface traction in the rolling direction is defined by a constant ratio of the normal traction: tx\u00f0x\u00de \u00bc ms9tz\u00f0x\u00de9 \u00f03\u00de where m is the coefficient of friction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001137_j.robot.2014.10.009-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001137_j.robot.2014.10.009-Figure8-1.png",
        "caption": "Fig. 8. A mobile manipulator mounted on a platform suspended from a chassis moving across an uneven terrain.",
        "texts": [
            " In this section, we consider the context of amobilemanipulator for which the unactuated and actuated dynamics are strongly coupled. In addition, the platform oscillates with much higher frequency than in the case of the ship, as the disturbances from a rough terrain are transmitted to the platform via a suspension. In the control design, we again consider the system dynamics as being completely unmodeled. A slight twist is the inclusion of a nonholonomic constraint on the platform kinematics. The model of a mobile manipulator of interest is sketched in Fig. 8, in which w := (w1,w2,w3) is an inertial reference triad and the triad b := (b1, b2, b3) is obtained by rotatingw an angle\u03c6h about the vertical axis w3. The position of the platform\u2019s center of mass B relative to the inertial reference frame is represented by the displacements xv and yv along w1 and w2, respectively. The triad a := (a1, a2, a3), attached to the platform, is obtained by rotating b an angle \u03c6p about b2. The point A represents the joint connecting link 1 of the manipulator to the platform, such that rBA := LBAa1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002447_tie.2018.2878131-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002447_tie.2018.2878131-Figure4-1.png",
        "caption": "Fig. 4. Configuration of the proposed DWPMM.",
        "texts": [
            " If the electrical flight surface actuator system operates under the four-quadrant condition without adopting the corresponding four-quadrant control strategy, the electrical flight surface actuator system will exist the pump voltage. The pump voltage will lead to the bus voltage occurs over-voltage and damage to the electrical flight surface actuator system [15]-[16].The electrical flight surface actuator system based on the DWPMM consists of two sets of rectifier circuits and half-bridge drive circuits, the DWPMM, two sets of braking unit circuits (R1\u3001S1and R2\u3001 S2), gearbox, and flight surface actuator. The 115V AC bus supplied powers for two sets of rectifier circuits and half- bridge drive circuits, respectively. Fig.4 shows the structure of the proposed DWPMM. The DWPMM is a 12/10-pole motor. Its PM rotor is optimized by changing the shape of PMs and its centrifugal height h=10mm. The stator consists of the independent ABC and independent XYZ windings [8],[10]. The DWPMM has the merits of high efficiency and power density. In addition, it has the advantages of magnetic and thermal isolation, and it can inhibit the short- circuit current by adopting a big self-inductance [8],[10]. The self-inductance has a big leakage inductance by using deep and narrow slot notch (slot notch thickness h0 is biggish and slot notch width b0 is smallish) as shown in Fig.4. Fig.5 shows the four quadrant diagram of the DWPMM. It can be shown that the DWPMM will operate at energy consumption brake state when the system operated under the four-quadrant operational condition. The direction of the speed and the direction of the torque is the opposite. The bus voltage will increase due to energy accumulation of bus capacitance. When the DWPMM operations in the 101 switching mode, as shown in Fig.6(a), T1\u3001T4\u3001T5 will be turned on and T2\u3001 T3\u3001T6 will be turned off. The inductance of the DWPMM will be in the charging state"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001968_978-94-007-6101-8-Figure4.3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001968_978-94-007-6101-8-Figure4.3-1.png",
        "caption": "Fig. 4.3 SCARA robot manipulator",
        "texts": [
            " The transformation between the i th coordinate frame and the frame (i\u22121) is described by the following four displacement: i\u22121Ai (qi ) = T rans(0, 0, di )Rot (zi\u22121, \u03d1i )T rans(ai , 0, 0)Rot (xi , \u03b1i ) = = \u23a1 \u23a2\u23a2\u23a3 c\u03d1i \u2212s\u03d1i 0 0 s\u03d1i c\u03d1i 0 0 0 0 1 di 0 0 0 1 \u23a4 \u23a5\u23a5\u23a6 \u23a1 \u23a2\u23a2\u23a3 1 0 0 ai 0 c\u03b1i \u2212s\u03b1i 0 0 s\u03b1i c\u03b1i 0 0 0 0 1 \u23a4 \u23a5\u23a5\u23a6 = \u23a1 \u23a2\u23a2\u23a3 c\u03d1i \u2212s\u03d1i c\u03b1i s\u03d1i s\u03b1i ai c\u03d1i s\u03d1i c\u03d1i c\u03b1i \u2212c\u03d1i s\u03b1i ai s\u03d1i 0 s\u03b1i c\u03b1i di 0 0 0 1 \u23a4 \u23a5\u23a5\u23a6 (4.3) The transformation matrix is function of only one variable, \u03d1i for rotational joint and di for translational joint. At this stage it appears to be most appropriate to study few examples of developing a geometric robot model by using the DH parameters. Let us consider a robot arm with only three degrees of freedom. Figure 4.3 shows SCARA industrial manipulator with one translational and two rotational joints. The distance variable d1 belongs to the first joint, while the angle variables \u03d12 and \u03d13 appertain to the second and third joint. First we shall draw the coordinate frames into the schematic presentation of the SCARA robot. As the first joint is translational, we shall in accordance with the 5th exception place the origin of the base reference frame into the starting point of the translational displacement. In accordance with the 1st DH rule, we shall place the z0 axis along the translation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000351_09544062jmes1844-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000351_09544062jmes1844-Figure2-1.png",
        "caption": "Fig. 2 Geometry partitioning and mesh",
        "texts": [
            " The resulting geometry is then subdivided into quadrilateral regions, paying particular attention to their form, avoiding shapes that could lead the software to generate unacceptably distorted quadrilateral elements (Figs 2(a) and (b)). Furthermore, in order to reduce the computational requirements, only five pair of teeth are modelled, assuming that the effects on the meshing of the other pairs are negligible. The teeth and the gear bodies are then meshed, refining the contact zones and the zones where a high stress gradient is expected (Fig. 2(c)). After defining the material properties, the gear and the pinion are assembled (Fig. 3) and the contact surfaces are defined. The contact between the teeth flanks is handled by ABAQUS using a general purpose contact algorithm: the actual contact areas and stresses are then determined, without introducing any simplification based on some particularity of gear geometry. The constraints are defined so that it will be possible to automatically run a sequence of static analyses. The procedure can then be summarized as the following key points"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002832_tie.2017.2677330-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002832_tie.2017.2677330-Figure2-1.png",
        "caption": "Fig. 2. The 3 horizontal degrees-of-freedoms of surface vessel.",
        "texts": [
            " Therefore the risk of damaging gangway is significantly reduced. iii) By applying the H\u221e control strategy, the good system robustness corresponding to the exogenous disturbances is guaranteed . Finally, a simulation is carried out on a scale-down replica of AV to further demonstrate effectiveness of the proposed scheme. A. Problem Formulation Consider the surface vessel modeled by the following dynamic, which is depicted in 3 degree-of-freedom (DOF) that are surge, sway and yaw respectively (shown in Fig.2) [19], \u03b7\u0307 (t) = J (\u03b7) v (t) ,Mv\u0307 (t) = \u2212C (v) v (t)\u2212D(v)v (t) \u2212 g (\u03b7 (t))\u2212\u2206(t) + \u03c4 (t) , (1) where \u03b7 (t) = [x (t) , y (t) , z (t)] T \u2208 R3 is the state vector, of which x (t) , y (t) and z (t) are the position and head states respectively; v (t) = [vx (t) , vy (t) , vz (t)] T \u2208 R3 is the velocity vector, of which vx (t) , vy (t) , vz (t) are the surge, sway, yaw velocities respectively; J (\u03b7) = cos (z) \u2212 sin (z) 0 sin (z) cos (z) 0 0 0 1  \u2208 SO(3), i.e. J\u22121 (\u03b7) = JT (\u03b7), is the rotation matrix for coordinate transforming between the vessel-fixed and earthfixed frames; g (\u03b7) \u2208 R3 is the restoring force vector in the presence of gravity and buoyancy; \u2206(t) \u2208 R3 is the external disturbances, which has the property of \u2206(t) \u2208 L2[0, tp], where \u2200tp \u2208 [0,\u221e) is the operating time for the system; \u03c4 (t) \u2208 R3 is the control input"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000842_00220345720510026301-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000842_00220345720510026301-Figure2-1.png",
        "caption": "FIG 2.--Schematic drawing of cast specimen",
        "texts": [
            " The strips were sandblasted and degassed by heating to 1,950 F (1,065.6 C) and then cooled to room temperature under glass. Vol 51 No. 2 at East Carolina University on April 23, 2015 For personal use only. No other uses without permission.jdr.sagepub.comDownloaded from 628 TUCCILLO AND NIELSEN Before applying the opaque porcelain, the strips were cleaned ultrasonically for ten minutes in a detergent followed by a water rinse, and then an alcohol rinse. The porcelain slurry was applied over a 2 inch length as an even thickness on one side of the strip (Fig 2). The thickness of the porcelain was controlled by a jig that could be varied to give the required total composite thickness. The strips then were suspended from a horizontal Inconel arm by placing a ceramic rod through the arm and the hole at the end of the specimen. A platinum-wound resistance furnace was then rolled horizontally into position to house the specimen. A schematic drawing of the experimental setup is shown in Figure 3. In Figure 4, the specimen is shown suspended freely inside the furnace"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002270_tmag.2017.2706764-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002270_tmag.2017.2706764-Figure6-1.png",
        "caption": "Fig. 6 Illustration of path for unipolar end leakage flux.",
        "texts": [
            " Substituting (3)-(7) into (10), it yields: \u03a6 = _ _ _ __ _ \u2219 (11)= _ _ (12). 0018-9464 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. From (11), it can be clearly seen that the magnetization ratio of VPM (km) can regulate the resultant flux through air-gap. The unbalanced rotor poles cause unipolar end leakage flux via the path illustrated in Fig. 6. As can be seen, the end shaft together with air and rotor provides a path for the z-axis leakage flux. When the rotor poles are not perfectly balanced, the redundant flux will flow through this path and the shaft magnetization may occur. The 3-D finite element (FE) analysis is used to evaluate the end leakage flux. Fig. 7(a) illustrates the flux density vectors on shaft when the CPMs and VPMs are remarkably unbalanced, where the significant unipolar flux is observable. Alternatively, according to (9) in aforementioned analysis, another model with balanced poles is evaluated in Fig. 7(b) and the end leakage flux is negligible. Further, a monitor line located on the joint curve between the end shaft and the rotor, Fig. 6, is employed to assess the unipolar leakage flux. The z-axis flux densities on the monitor line of the two models are compared in Fig. 8, where a high amplitude is observed in the model with unbalanced poles while it is almost zero in the model with balanced poles. In order to further verify (9), the variations of z-axis flux density on the monitor line versus PM cross section area ratio (Avpm/Acpm) is shown in Fig. 9. The minimum unipolar leakage flux occurs when the area ratio is close to 1.05, which is exactly Br_cpm/Br_vpm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001006_s10846-014-0143-5-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001006_s10846-014-0143-5-Figure5-1.png",
        "caption": "Fig. 5 Body-fixed frame coordinate system, [155]",
        "texts": [
            " However, establishing a reference frame fixed to the helicopter body significantly simplifies the analysis of forces acting on the helicopter. The set of equations describing helicopter motion is derived based on two Cartesian reference frames as follows: \u2013 The body-fixed Cartesian frame is defined as FB = {OB, iB, jB, kB}; the origin is fixed at the helicopter center of mass. The unit vector iB points from the origin toward the helicopter nose. The unit vector jB points from the origin to the right of the fuselage. The unit vector kb points downward. The orientation of these vectors in relation to the helicopter body is seen in Fig. 5. \u2013 The inertial Earth-fixed Cartesian frame follows the North-East-Down (NED) directional convention, defined as FI = {OI , iI , jI , kI }. The unit Fig. 4 Helicopter dynamics vectors iI , jI , and kI , point North, East and Down towards the center of the Earth, respectively, as shown in Fig. 6. Rigid body dynamics are governed by the following Newton-Euler laws of motion: Fnet = d dt G(t) (1) MCM net = d dt HCM(t) (2) These equations provide information on translational and angular velocities as a result of forces acting on the rigid body"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001267_tmag.2011.2178100-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001267_tmag.2011.2178100-Figure8-1.png",
        "caption": "Fig. 8. Section-view of the 3-D finite-element model of the PMDC commutator motor (Different colors represent different material types).",
        "texts": [
            " Moreover, the established electromagnetic model used to calculate the flux density and the magnetic forces is validated by comparing the measured cogging torque [3] with that calculated from the finite-element model, as shown in Fig. 7. This section builds a 3-D finite-element model to accurately calculate the dynamic responses of the motor excited by the magnetic forces from Section III. Furthermore, the effects of the glue and the eccentricity on the modal parameters and the dynamic responses of the motor are analyzed respectively. A 3-D structural model shown in Fig. 8 is constructed in ANSYS 12.1 with the end-shield structure involved for predicting accurately the modal parameters of the motor. The reason to build such a 3-D model is that the end-shield structure and the boundary conditions, as pointed by Wang in [20] and [24], can considerably affect the modal parameters of the motor structure. In the modal testing, the PMDC motor was suspended by the soft rubber ropes to approximate to the free support-condition [25]. Therefore, the 3-D model in Fig. 8 is supported by eight spring-elements (COMBIN14) located at the end-shields of the motor. A total of 8390 nodes and 5857 SOLID45-type elements are contained in the model. The structural finite-element model is constructed according to the geometric dimensions and the material properties of the motor. The materials of the stator, the rotor, the permanent magnet, the glue, the right end-shield, and the commutator are low-carbon steel, cold-rolled silicon steel, ferrite magnet, epoxide-resin, hard plastic, and copper, respectively, of which the mechanical properties are given in Table I",
            " Although the two motors have the identical geometric dimensions and material parameters, the natural frequencies of Motor 2 are unexpectedly lower than those of Motor 1. The discrepancy of the natural frequencies is thought to be caused by the glue because the thicknesses of the manually glued epoxide-resins can hardly keep uniform in the two motors. Thus, the thicker glue can act as a \u201cmore soft\u201d spring, which can decrease the stiffness of the motor and lead to the lower natural frequencies. This judgment has been proved by increasing the thickness of the glue between the stator and permanent-magnets (see Fig. 8). After increasing the thickness of the glue from 0.1 mm to 0.4 mm, the calculated natural frequencies of the modes 1 to 4 were reduced to 3055 Hz, 4159 Hz, 5088 Hz, and 5669 Hz, respectively. The calculated natural frequencies with the thicker glue agree well with those measured from Motor 2 in Table II. The relative errors between the calculated and the measured are 5.2%, 1.5%, 0.8%, and 1.8%, respectively. On the other hand, by analyzing the effects of other parts of the motor on the natural frequencies, the glue can also be identified as the reason of causing the discrepancy of the natural frequencies"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000679_j.ymssp.2010.02.003-Figure16-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000679_j.ymssp.2010.02.003-Figure16-1.png",
        "caption": "Fig. 16. Sketch of the generic journal bearing; P is the centre of the shaft and O the centre of the bearing; ue ! and uG ! are the unit vectors, respectively, along and orthogonal to the eccentricity e ! .",
        "texts": [
            " Since their application ranges do not coincide, the \u2018short\u2019 solution and \u2018long\u2019 one of the Reynolds equation can be combined together, obtaining an approximate solution with extended validity range for general finite-length bearings with both large and small eccentricity ratios. The vectorial composition of the results obtained with the \u2018short\u2019 and \u2018long\u2019 theories called \u2018finite impedance formulation\u2019 has been proposed by Childs et al. [12]. Such a theory has been chosen in order to calculate the reacting forces of the journal bearings in the pump under study. In the following, the reacting force fb ! will be obtained for the generic journal bearing shown in Fig. 16 in reference frame OkXk 0 Yk 0 . In particular, the bearing reactions can be defined as a function of the bearing impedance, the position and velocity of the shaft: fbx0 \u00bc 2vsmbb Rb Cr 3 Wx0 fby0 \u00bc 2vsmbb Rb Cr 3 Wy0 8>>< >>: \u00f028\u00de The kinematical quantities of Eq. (28) are expressed as illustrated in the following (more details can be found in [12]). With reference to Fig. 16 and Nomenclature, let us consider e\u00bc e Cr \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffi x2 P\u00fey2 P q Cr \u00f029\u00de G\u00bc arctan yP xP \u00f030\u00de o\u0302 \u00bc o 2 \u00f031\u00de In order to calculate the squeeze velocity vS ! some steps have to be followed; the velocity of the journal centre relative to reference frame OkXk 0 Yk 0 is v ! \u00bc d\u00f0Cr~e\u00de dt \u00f032\u00de and v ! S is the derivative of vector Cre ! with respect to a coordinate system that has an angular velocity of o\u0302~K : v ! S \u00bc v ! o\u0302~K Cr e ! \u00bc vSe~ue\u00fevSG~uG \u00bc Cr _e~ue\u00feCre\u00f0 _G o\u0302\u00de~uG \u00f033\u00de where K ! is the unit vector normal of Zk 0 -axis (axial direction) and vSe and vSG are, respectively, the components of v ! S along the direction of the eccentricity (of unit vector ~ue) and the direction orthogonal to the eccentricity (of unit vector ~uG), see Fig. 16. From Eq. (33) the pure-squeeze-velocity modulus is vS \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0Cr _e\u00de2\u00fe\u00bdCre\u00f0 _G o\u0302\u00de 2 q \u00f034\u00de where the quantities _e and _G are the time derivatives of e and G. The impedance components in direction X0 and Y0 are, respectively, Wx0 \u00bcW cos\u00f0z\u00fe ~a c\u00de \u00f035\u00de Wy0 \u00bcW sin\u00f0z\u00fe ~a c\u00de: \u00f036\u00de Angle z is the attitude angle of vS ! relative to I ! , angle ~a is the attitude angle of e! relative to vS ! (see Fig. 17) and angle c is commonly obtained by an approximate expression (more details are given in [12]). The impedance modulus of Eqs. (35) and (36) is W \u00bc 0:150 ~E 2 \u00fe ~G 2 1=2 \u00f01 a0\u00de3=2 1 \u00f037\u00de where the parameters ~E; ~G; a0 that depend on the eccentricity ratio are defined in [12]. It is worth noting that the eccentricity of the journal axis with respect to the bearing block (of modulus e and azimuth G, Fig. 16) is different from the eccentricity of the gear axis with respect to the case (of modulus ~e and azimuth ~G, Fig. 6), due to the relative position of the bearing blocks into the case. In fact, there is a radial backlash hb between the bearing blocks and the case as shown in Fig. 18, where the backlash is enlarged for better highlighting. Thus, the bearing blocks are floating and consequently the eccentricity of the gears with respect to the case depends not only on the relative position of the journals into the bearings but also on the relative position of the bearing blocks into the case"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001880_j.applthermaleng.2014.02.008-Figure11-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001880_j.applthermaleng.2014.02.008-Figure11-1.png",
        "caption": "Fig. 11. The path along radial and axial of the motor.",
        "texts": [
            " It indicates that the temperature-rise at the same position of the motor is increased when the broken bar fault appears, and the increase of the temperature-rise is directly related to the number of broken bars, that is the more serious the fault is, the higher the temperature rise. From Table 2, we also can see that the most obvious increase of the temperature-rise is located in the rotor; therefore, the rotor bar temperature increase could become more susceptible to thermal stress and eventually lead to further rotor bar degradation, which will reduce the motor\u2019s lifetime and reliability directly. The temperature-rise comparisons along radial and axial paths are given in Fig. 11, path L1 and path L2 are in radial direction, L3 and L4 are in axial direction, and they all go through the center of the stator and rotor slot. Fig. 12 describes the temperature-rise variations on the four paths. By comparing Fig. 12(a) with (b), it can be found that there are some distinct differences at the stator area. Firstly, the downward gradient of the temperature-rise on stator yoke in L2 is a little steeper than L1, and this is because the bad heat transfers capability of the connecting box"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000648_978-3-642-17531-2-Figure7.10-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000648_978-3-642-17531-2-Figure7.10-1.png",
        "caption": "Fig. 7.10. Piezoelectric strip transducer",
        "texts": [
            "15) through (7.23) can be applied directly. Due to the increased stiffness, there is a favorable increase in the transducer eigenfrequency, but simultaneously a decrease in the transducer gain or sensitivity. Another disadvantage is the concomitant reduction in the maximum displacement x , as can be seen in Fig. 7.9d. Strip transducers: contractors Laminated structures: transverse effect The piezoelectric transverse effect can be advantageously employed in a spatially distributed architecture. Fig. 7.10 shows such a laminated structure: the piezoelectric material (active material) takes the form of a strip element tightly bound to a substrate. By applying an electrical voltage along the 3-coordinate, the transverse effect 31 31 ( , )e d can be used to generate a change in length along the or- thogonal 1-coordinate. It follows from the constitutive material equations in ( , )S D form that 31 T d u . (7.26) As in the disk transducer (exploiting the longitudinal effect), the realizable displacement depends on the transducer geometry; in particular, it is proportional to the strip length . Since, when subjected to a positive electrical voltage (i.e. an electric field along the polarization direction), the transverse effect induces a contraction ( 31 0e and 31 0d ), strip transducers also often called contractors. Unimorphs, bimorphs Strip transducers in the layout shown are commonly employed in laminated structures. The arrangement shown in Fig. 7.10 is termed a unimorph, as only one piezoelectric laminated layer is fused to the substrate. A bimorph consists of two active laminate layers, optionally separated by a substrate (only suggested in Fig. 7.10). Electrode shape Using a suitable electrode shape, the type and manner of force generation can be precisely selected. Fig. 7.11 shows two common variants. With a rectangular electrode geometry, an applied voltage induces mechanical bending moments at the electrode edges (Fig. 7.11a). With a triangular electrode geometry, a voltage induces a point force at the triangle tip (Fig. 7.11b). Note further that only the piezo material covered by the electrode area actively contributes to the force/moment"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001394_tec.2016.2597059-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001394_tec.2016.2597059-Figure2-1.png",
        "caption": "Fig. 2. Electrical and liquid cooling terminations for the proof-of-concept machine.",
        "texts": [
            " Temperature (\u00b0C) Neodymium magnets, 40SH-type 120 Winding Insulation material 155 To reduce rotor eddy current losses, each magnet in the pole was divided into 12 equal segments, and the magnets were embedded below laminated iron parts supported by a composite rotor frame. The rotor has a yokeless structure. Fig. 1 illustrates the construction of one stator. The twelve tooth coils are configured as six pairs forming half of a phase winding each. Each pair has a single inlet and outlet cooling conduit. Fig. 2 shows how the stainless steel cooling conduit arrays pass through the motor housing. Because the proof-of-concept machine was a retrofit into an existing machine, this rudimentary approach was necessary. Table IV summarizes the main dimensions and parameters for the electrical machine. Parameter Value Stack (physical) iron length re-ri = lFe [mm] 70 Total stack length ltot [mm] 70 Stator inner diameter Dsi [mm] 250 Stator outer diameter Dse [mm] 390 Original rotor tangential tension stan (at rated torque) [kPa] 28"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002848_s00773-017-0486-2-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002848_s00773-017-0486-2-Figure3-1.png",
        "caption": "Fig. 3 LOS guidance for path following",
        "texts": [
            " When setting system states and input as x = [ x1 x2 x3 x4 ]T = [ \ud835\udf13 r r\u0307 \ud835\udeff ]T and u = C, respectively, we transform (2) and (3) into the following state-space form: where g1(x, u) can be denoted by Due to the presence of disturbances, model (4) is rewritten as follows: where E \u2208 \u211d4\u00d74 is the disturbance input matrix, and w(t) \u2208 \u211d4\u00d71 is an unknown but bounded random disturbance vector. The proposed model (5) can be categorized according to Table\u00a01 as an nonlinear model with disturbances of which the input and one DOF is the rudder angle and yaw, respectively. In this section, we will design the two key components of the decision system in Fig.\u00a01: the adaptive LOS guidance algorithm and the nonlinear MPC controller based on model (5). A typical reference path, as shown in Fig.\u00a03, can be considered as several straight line segments generated by connecting waypoints Pn(xn, yn), Pn+1(xn+1, yn+1), Pn+2(xn+2, yn+2), etc. The ship actual position is Ob(xb, yb). In LOS guidance, an underactuated vessel controlled only with a rudder tracks the reference path based on the difference between the heading angle and the LOS angle LOS that can be calculated with a LOS point PLOS(xLOS, yLOS). There are three ways to generate the LOS points on the path: 1. to set the waypoint Pn+1 as the LOS point PLOS [9]; (4)x\u0307 = f (x, u) = \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a3 x2 x3 g1(x, u) 1 TC \ufffd KCu \u2212 x4 \ufffd \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a6 , g1(x, u) = 1 T1T2 [Kx4 + KT3 TC ( KCu \u2212 x4 ) \u2212 ( T1 + T2 ) x3 \u2212 x2 \u2212 x3 2 ]",
            " The first approach results in large cross errors in the presence of environmental disturbances. The second approach may increase difficulties in converging to the path when there exist large cross errors. Therefore, the third approach is employed in this paper as in [6]. The LOS point PLOS is calculated by solving the following equations [12]: Two solutions corresponding to the two intersections between the circle and the path can be obtained by solving the above equations. The closer intersection to the current waypoint, i.e., Pn+1 in Fig.\u00a03, is selected as PLOS. The transformation for the body-fixed velocities to the inertial velocities is as follows: Define the ship heading relative to the path as ?\u0303? = \ud835\udf13 \u2212 \ud835\udf13P, where P is the path direction. Then, differential equations of e and ?\u0303? can be denoted by [38]: In (9), e is the cross-tracking error, i.e., the vertical distance from Ob to the objective path PnPn+1. The surge speed u is assumed to be constant as u0 (u0 > 0), and the sway speed v (6)(xLOS \u2212 xb) 2 + (yLOS \u2212 yb) 2 = R2 LOS , (7) yLOS \u2212 yn xLOS \u2212 xn = yn+1 \u2212 yn xn+1 \u2212 xn "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001471_j.mechmachtheory.2014.07.013-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001471_j.mechmachtheory.2014.07.013-Figure1-1.png",
        "caption": "Fig. 1. Dynamic model of two-stage straight bevel gear.",
        "texts": [
            "tn 3 Notation i Gear indice j Block indice k Stage indice Fji Below of the spherical involute on the base circle of bevel gear (i) of the block (j) Oji Center of bevel gear (i) of the block (j) Q1 Crossing point of the two bevel gears (12) and (21) Q2 Crossing point of the two bevel gears (22) and (31) S1 Intersection of the arc of meshing with the circle head of the driving gear S2 Intersection of the arc of meshing with the circle head of the driving gear I 1 Point slip-free rolling of pitch circles of the two bevel gears (12) and (21) Te1, Te2 Gearing periods of the first stage and the second stage respectively r12 Radius of the sphere which contains two bevel gears (12) and (21) r21 Radius of the sphere which contains two bevel gears (12) and (21) (r12 = r21) r22 Radius of the sphere which contains two bevel gears (22) and (31) r31 Radius of the sphere which contains two bevel gears (22) and (31) (r22 = r31) Tji Tangent point between plane of pressure and base circle of bevel gear (i) of the block (j) Zji Tooth number of bevel gear (ji) \u03b11, \u03b12 Pressure angle of the first and the second bevel gears stages respectively \u03a612S1 Angle between the planes (ts1, O12, S1) and (ts1, O12, O21) \u03a612S2 Angle between the planes (ts1, O12, S2) and (ts1, O12, O21) \u03bbji Angle Tji ts\u0302k S1 \u03c7ji Angle Tji ts\u0302k S2 \u03b7ji Angle Oji ts\u0302k S2 \u03b3ji Angle Tji ts\u0302k Ik \u03b4ji Half-angle of the pitch circle of bevel gear (i) of the block (j) \u03b4bji Half-angle of the base circle of bevel gear (i) of the block (j) \u03b4aeji Half-angle of the tip circle of bevel gear (i) of the block (j) \u03b5\u03b11, \u03b5\u03b12 Contact ratio of the first and second bevel gears stages respectively Caeij Effective outside diameter of bevel gear (i) of the block (j) deflection. Then numerical results for the dynamic response are obtained by using Newmark algorithm. Finally, eccentricity defect, profile error and tooth crack are investigated on the dynamic behavior. 2. Model of two-stage straight bevel gear Fig. 1 presents the lumped parametermodel developed to study the dynamic behavior of the two-stage straight bevel gear system composedwith three blocks. Thefirst block (j=1) is constituted of the drivewheel (11)which is connected to the bevel gear (12) via a shaft (1)which is supposedmassless and torsional rigidity k\u03b81. Thebevel gear (21) is linked in the onehand to the bevel gear (12) via a teethmesh stiffness k1(t) and it is linked to the bevel gear (22) via a shaft (2)which ismassless and has stiffness of torsion k\u03b82 in the other hand"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001101_1350650111409517-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001101_1350650111409517-Figure1-1.png",
        "caption": "Fig. 1 A purely torsional dynamic model of a spur gear pair",
        "texts": [
            " In this study, the effect of the lubrication characteristics on the dynamic response in terms of lubricant stiffness and damping is not considered, such that the dynamic solver and the EHL solver are uncoupled. The investigation is also kept limited to spur gear pairs with no significant lead modifications to allow a line contact formulation. Other types of gear pairs such as helical and hypoid gears were beyond the scope of this study. In order to predict the dynamic loading on the teeth of a spur gear pair, a single-degree-of-freedom (DOF) discrete model similar to that of Tamminana et al. [15] is employed. This torsional dynamic model, shown in Fig. 1, consists of two rigid discs of radii rb1 and rb2 (to represent the base circle radii of gears 1 and 2) and polar mass moments of inertia I1 and I2, respectively. The gear mesh interface model consists of (a) a parametrically time-varying gear mesh stiffness k\u00f0t \u00de, (b) a constant viscous damper c, and (c) an externally applied gear mesh displacement excitation Proc. IMechE Vol. 000 Part J: J. Engineering Tribology at Eindhoven Univ of Technology on June 26, 2014pij.sagepub.comDownloaded from e\u00f0t \u00de, all of which are applied along the line of action (line tangent to the base circles of the gears)",
            " The displacement excitation e\u00f0t \u00de represents the motion transmission deviation caused by intentional tooth profile modifications as well as the manufacturing errors under unloaded condition. Bulk of the non-linear behaviour observed in spur gear pairs occurs at instances when the dynamic force amplitude exceeds the static load (preload) transmitted by the gear pair. With the presence of gear backlash, the gear teeth lose contact at such instances and the gear mesh stiffness drops to zero instantaneously. As proposed earlier [12, 15], the mesh stiffness k\u00f0t \u00de is subjected to a piecewise linear clearance function, d as illustrated in Fig. 1. This function is composed of a dead zone (backlash) of size 2b bounded by two unity slope regions representing the linear and back contact conditions (no contact loss). With the positive directions of the alternating rotational displacements, #1 and #2, and the applied torque, T1 and T2, defined as shown in Fig. 1, the dynamic equations read I1 \u20ac#1\u00f0t \u00de \u00fe rb1k\u00f0t \u00de \u00f0t \u00de \u00fe crb1\u00bd_s\u00f0t \u00de _e\u00f0t \u00de \u00bc T1 \u00f01a\u00de I2 \u20ac#2\u00f0t \u00de rb2k\u00f0t \u00de \u00f0t \u00de crb2\u00bd_s\u00f0t \u00de _e\u00f0t \u00de \u00bc T2 \u00f01b\u00de where s\u00f0t \u00de \u00bc rb1#1\u00f0t \u00de rb2#2\u00f0t \u00de is the dynamic transmission error and \u00f0t \u00de \u00bc s\u00f0t \u00de e\u00f0t \u00de b, s\u00f0t \u00de e\u00f0t \u00de4b 0, s\u00f0t \u00de e\u00f0t \u00de b s\u00f0t \u00de e\u00f0t \u00de \u00fe b, s\u00f0t \u00de e\u00f0t \u00de5 b 8< : \u00f01c\u00de Since the generalized parameters of the two-DOF model of Fig. 1 are semi-definite with a rigid body mode at zero natural frequency, a new relative displacement parameter is defined as \u00f0t \u00de \u00bc s\u00f0t \u00de e\u00f0t \u00de. With this, the equation of motion of the resultant definite single-DOF model is derived as me \u20ac \u00f0t \u00de \u00fe c _ \u00f0t \u00de \u00fe k\u00f0t \u00de \u00f0t \u00de \u00bc F me \u20ace\u00f0t \u00de \u00f02a\u00de where me is the equivalent mass defined as me \u00bc I1I2 \u00f0I1r2 b2 \u00fe I2r2 b1\u00de. The constant force transmitted by the gear mesh F \u00bc me rb1T1=I1\u00f0 \u00ferb2T2=I2\u00de, where T1 and T2 are the constant external torques applied to gears 1 and 2, respectively. The overdot denotes the differentiation with respect to time t. The non-linear restoring function in Fig. 1 has the form of \u00f0t \u00de \u00bc \u00f0t \u00de b, \u00f0t \u00de4b 0, \u00f0t \u00de b \u00f0t \u00de \u00fe b, \u00f0t \u00de5 b 8< : \u00f02b\u00de It is noted that the mesh stiffness k\u00f0t \u00de consists of a mean component, k, and an alternating component, ka\u00f0t \u00de, i.e. k\u00f0t \u00de \u00bc k \u00fe ka\u00f0t \u00de. With this, a set of dimen- sionless parameters can be defined as \u0302\u00f0t \u00de \u00bc \u00f0t \u00de b, e\u0302\u00f0t \u00de \u00bc e\u00f0t \u00de b, \u0302\u00f0t \u00de \u00bc \u00f0t \u00det=b, \u00bc c=\u00f02 ffiffiffiffiffiffiffiffiffi me k q \u00de and F\u0302 \u00bc F=\u00f0b k\u00de, leading to a dimensionless form of equa- tion (2a) as d2\u0302\u00f0t \u00de dt 2 \u00fe 2 !n d\u0302\u00f0t \u00de dt \u00fe !2 n 1\u00fe ka\u00f0t \u00de k \u0302\u00f0t \u00de \u00bc "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001813_j.ijheatmasstransfer.2018.04.164-Figure14-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001813_j.ijheatmasstransfer.2018.04.164-Figure14-1.png",
        "caption": "Fig. 14. Temperature distribution of various phase transition regions during the deposition process.",
        "texts": [
            " The melting temperature (Tm), solid-solution temperature (Tsol), austenitizing temperature (Ac1), and aging temperature (Ta) of the FV520B maraging steel are 1675, 1323, 989, and 693 K, respectively. Based on the characteristic phase-transition temperatures of the material, the temperature field of the deposited material during the laser hot-wire deposition process can be divided into four regions: (1) the fusion zone ([Tm, Tmax]), (2) the solid-solution zone ([Tsol, Tm]), (3) the austenitizing zone ([Ac1, Tsol]), and (4) the aging zone ([Ta, Ac1]), as shown in Fig. 14. The effective depths of various phase transition regions at different times were determined from the simulations and the values are presented in Table 5. As the deposition process progresses, the effective depth of each phase transition region increases and eventually stabilizes as the deposition time approaches 1.08 s. It is found that the predicted effective depths of the solid-solution zone, austenitizing zone, and aging zone are 0.65, 1.13, and 1.72 mm, respectively. Table 5 Effective depth of various phase-transition regions during the deposition process"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003753_s12206-019-0140-5-FigureA.1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003753_s12206-019-0140-5-FigureA.1-1.png",
        "caption": "Fig. A.1. Equilibrium of a ball: (a) Local coordinate system defined at a particular ball; (b) free-body diagram of a ball.",
        "texts": [
            " Hong, Improved formulation for running torque in angular contact ball bearings, International Journal of Precision Engineering and Manufacturing, 19 (1) (2018) 47-56. [25] NSK Ltd., Rolling Bearing Catalogue, CAT. No. E1102m, Japan (2013). [26] SKF Group, SKF General Catalogue, 6000/I EN, Sweden (2008). [27] E. V. Zaretsky, W. J. Anderson and R. J. Parker, The effect of contact angle on rolling-contact fatigue and bearing load capacity, ASLE Transactions, 5 (1) (1962) 210-219. Appendix The displacements of the inner ring cross-section and contact load are defined, respectively, by (see Fig. A.1(a)) {u}T = {ur, ux, q} (A.1) {Q}T = {Qr, Qx, T} (A.2) where {u} depends on the global displacement by {u} = [Rf]{d} (A.3) where the transformation matrix is given by cos sin 0 sin cos 0 0 1 sin cos . 0 0 0 sin cos P P P P z z R r r -\u00e9 \u00f9 \u00ea \u00fa= -\u00e9 \u00f9\u00eb \u00fb \u00ea \u00fa \u00ea \u00fa-\u00eb \u00fb f f f f f f f f f (A.4) The ball center displacement is indicated by {v}T = {vr, vx}. (A.5) The ball loading including the ball\u2013race contact forces, centrifugal force, and gyroscopic moment is shown in Fig. A.1(b). The equilibrium equations of a ball are given as follows: cos cos sin sin sin sin cos cos 0 0 i g e g i i e e c i e a a i g e g i i e e i e a a M M Q Q F D D M M Q Q D D l l a a a a l l a a a a \u00ec \u00fc - + - +\u00ef \u00ef \u00ef \u00ef \u00ed \u00fd \u00ef \u00ef- + -\u00ef \u00ef\u00ee \u00fe \u00ec \u00fc = \u00ed \u00fd \u00ee \u00fe (A.6) where li and le indicate the distribution parameters for the gyroscopic moment. The effects of gyroscopic moment on each raceway are assumed equal, i.e., li = le = 1. The centrifugal force and gyroscopic moment of a ball are calculated by 21 2c m mF md w= (A"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003394_j.compstruct.2020.112698-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003394_j.compstruct.2020.112698-Figure3-1.png",
        "caption": "Fig. 3. External schematic of the vehicle. The metal r",
        "texts": [
            " These sections, which represent holes in the support panel, not only reduced the weight of the structure, but also helped dissipate heat. Photovoltaic panels, in fact, suffer rapid reductions in efficiency with temperature increases. Almost all of the sections described thus far were redesigned and modified as a consequence of the present work. The monocoque structure in which all elements are housed, comprising the central beam (battery holder) and lower bathtub structure (visible externally in Fig. 3) instead remained unchanged. Replacement of the metal safety cage (Fig. 4a) was achieved by conceiving an alternative able to exploit the marked anisotropy of reinforced composites. Several options were considered, both in terms oll cage is shown together with its critical zones. of geometry and materials. The present discussion is limited the final solution (Fig. 4b). The study was carried out considering the safety requirements defined within the WSC 2019 race regulations, comprising static analysis at pre\u2010established loads and verification of maximum deformation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001739_j.bios.2013.10.035-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001739_j.bios.2013.10.035-Figure2-1.png",
        "caption": "Fig. 2. Image of the strip sensor: (a) working electrode, (b) counter electrode, (c) reference electrode, (d) counter electrode connection, (e) working electrode connection, and (f) reference electrode connection.",
        "texts": [
            " Both electrodes were subsequently connected to the power supply and a predetermined voltage was applied for a prescribed time under the stirring condition. When the extraction was completed, the hollow fiber was taken from the sample vial and the AP was collected using a micro syringe. In this step, screen-printed electrochemical strips (DS 110, DropSens, Spain) including a screen-printed carbon electrode (SPCE) as the working electrode, a carbon counter electrode, and a silver pseudoreference electrode were used for the electrochemical determination of concentrated morphine in the AP. As it is shown in Fig. 2, all of the electrodes are printed in a small area and the strip is suitable for working with micro-volumes. A specific connector was used to connect the electrochemical strip to the m-Autolab potentiostat/galvanostat type III. The SPCE was first activated in the blank solution (NaOH 0.1 M (20 mL)\u00feHCl 0.1 M (20 mL)) by cyclic voltammetric sweeps between 0.0 and \u00fe0.6 V, until stable cyclic voltammograms were obtained. Then, as the extraction was completed, the collected AP (20 mL HCl 0.1 M containing extracted morphine) was mixed with 20 mL of NaOH (0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003303_j.addma.2019.02.006-Figure11-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003303_j.addma.2019.02.006-Figure11-1.png",
        "caption": "Fig. 11. Canonical part used in the case study (a) CAD model, (b) part mesh, and (c) mesh with powder elements.",
        "texts": [
            "5 mm to 24mm, which represents most of the real-world scenarios. However, for more complex small features in close proximity and trapped powder, such as small holes and lattice structures, modeling heat conduction into the power bed as convection may not be suitable, and thus the powder model would be best suited as the heat is easily accumulated at the trapped powders and conducted to the nearby structures. A case study of this new convection boundary condition is presented in the following section. Fig. 11(a) and (b) show the CAD model and the cutaway view of the voxel mesh for the square canonical part used for this case study. This geometry has thin and thick walls with a varying cross-sectional thickness and a significant overhang structure, which make ideal for testing the thickness-dependent thermal boundary condition. The four representative probing points for investigating interlayer temperature history are highlighted in Fig. 11. Nodes 1\u20133 are located in the inner wall of the part at locations with 3 different thicknesses. Nodes 3 and 4 have an identical build height, which is just above the overhang structure, with each node located on the inner and outer walls, respectively. The thermal histories of these 4 points should represent that of the canonical part during LPBF construction. Fig. 11(c) illustrates the mesh when powder elements are used, again shown with a cutaway view. Two materials, poorly conducting Ti6Al4V and highly conductive AlSi10Mg are used to verify the thickness-dependent convection coefficients. Four square canonical models are run for each material with differing thermal boundary conditions at the part side surface: \u2022 Case 1: Material dependent average, which is the averaged value of convection coefficient for each material from the 5 modeled wall thicknesses. Ti6Al4V: 6W/m2/\u00b0C AlSi10Mg: 37W/m2/\u00b0C \u2022 Case 2: uniform 25 which applies the convection value of 25W/m2/ \u00b0C [24] to part side surfaces \u2022 Case 3: Thickness dependent convection"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003003_tie.2018.2811383-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003003_tie.2018.2811383-Figure3-1.png",
        "caption": "Fig. 3: A Series Elastic Actuator System",
        "texts": [
            " A Practical Control Implementation Note that various of the practical system models could be expressed as the form (1), and the nonsmooth feature of the designed controller will yield a better active disturbance rejection ability. Hence Theorem 4.1 is easily-applicable to a wide class of real-life systems. In what follows, we show, by a practical control implementation to a Series Elastic Actuator (SEA) system, the practical nature and control performance improvements of the proposed control strategy. As depicted by Fig. 3, the studied SEA system has two series elastic elements: a linear spring with a low stiffness and a torsional spring with a high stiffness. In this paper, we verify the proposed controller using only the torsional spring. Borrowed from [20], the mathematical model for the considered SEA system can be represented by the following model    x\u03071 = x2 x\u03072 = k ml x3 \u2212 k ml x1 + d1 x\u03073 = x4 x\u03074 = 1 mm Fm \u2212 k mm (x3 \u2212 x1) + d2, (32) where mm,ml are the inertia/mass of the motor and link, respectively; x1, x3 are angle/position of the link and motor, respectively; k is the stiffness of the SEA; Fm is the motor torque/force and d1, d2 are the lumped mismatched disturbance torque/force which might consist of the unknown viscous friction effects, and external disturbances, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003881_j.mechmachtheory.2020.104047-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003881_j.mechmachtheory.2020.104047-Figure2-1.png",
        "caption": "Fig. 2. The diagram of defect profile.",
        "texts": [
            " Via the transformation matrix, u ib is computed as u ib = T ib U i (1) where T ib = [ cos \u03c6k sin \u03c6k 0 0 0 0 0 1 r i sin \u03c6k \u2212r i cos \u03c6k 0 0 0 sin \u03c6k \u2212 cos \u03c6k ] (2) where \u03c6k is the angle position of the k th ball at time t;r i is the radius of curvature of inner raceway. The localized fault may occur on the outer raceway, inner raceway or even the rolling element. During the running of a faulty bearing, the defect can cause the change of bearing vibration. In this study, we will focus on the defect on the outer raceway, because the analysis of other cases is similar. And the defect shape is simplified as a cube [12] , as shown in Fig. 2 . The maximum value of displacement impact can be obtained according to the defect size and bearing\u2019s parameters, which is written as: H = { H \u2032 H \u2032 < H H H \u2032 \u2265 H (3) H \u2032 = 0 . 5 D \u2212 ( ( 0 . 5 D ) 2 \u2212 ( 0 . 5 min ( L, B ) ) 2 )0 . 5 (4) where L, B and H are the length, width and depth of the defect respectively; and D is the diameter of the rolling element. When the rolling element passes through the defect area, an additional impulse is added to the bearing system. The half-sine displacement excitation function is used to represent the impact of defect"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000648_978-3-642-17531-2-Figure7.3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000648_978-3-642-17531-2-Figure7.3-1.png",
        "caption": "Fig. 7.3. Anisotropic piezo material: a) longitudinal effect (here 33 0e , 33 0d ), b) transverse effect (here due to contraction: 31 0e , 31 0d )",
        "texts": [
            " This implies that, in the general case, the variables and coefficients in the constitutive equations (7.1), (7.2) must be interpreted as tensors (Bronshtein et al. 2005). Further, it should be noted that the two effects described by Eqs. (7.1), (7.2) are always active simultaneously, as can be seen from the coupling factor e . Thus, the coupled system of equations must naturally also always be considered as a whole. The transducer is customarily set in a Cartesian coordinate system (1,2, 3) such that the polarization direction (and the electric field) points along the 3 -axis (see Fig. 7.3). The ( , )T D -tensor form of the constitutive material equations corresponding to Eqs. (7.1), (7.2) is then ( ) - , ( ) , T S,E c S e E D S,E e S E E S Ec : YOUNG\u2019s modulus when 0E , i.e. electrical short circuit; S : permittivity when 0S , i.e. mechanically braced; e : piezoelectric force constants 2[As/m =N/Vm] . (7.3) Equivalently to Eq. (7.3), the ( , )S D -tensor form of the constitutive material equations are found to be ( ) , ( ) , S T,E T d E DT,E d T E E T s Es : compliance when 0E , i",
            " This means that there is anisotropy only in the polarization direction while all orthogonal directions are isotropic (cylindrical symmetry). This implies that a number of the material tensor components are zero (Jordan and Ounaies 2001). Luckily, for cases important to implementation, only a few of the directional dependencies are significant, so that for further considerations in this book, the entire tensor description can be ignored and only scalar equations such as Eqs. (7.1), (7.2) employed. Longitudinal effect, transverse effect The two directional dependencies most important in practice are shown in Fig. 7.3: the longitudinal effect, where the electric field and corresponding mechanical quantities ,T S act in parallel directions (Fig. 7.3a); and the transverse effect, where the electrical and mechanical directions of action are orthogonal (Fig. 7.3b). The piezoelectric behavior is described by the tensor components 33 e and 33 d for the longitudinal effect, and the tensor components 31 e and 31 d for the transverse effect2 (the remaining components are all zero). These parameters, like the remaining material parameters, can be determined from data sheets for the piezo material (or transducer), generally also directly with the indicated superscript designation. 2 The first index of the d-parameters and e-parameters indicates the respective \u201celectrical\u201d component (E or )D , the second index specifies the \u201cmechanical\u201d component (T or )S "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000896_wst.2012.957-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000896_wst.2012.957-Figure1-1.png",
        "caption": "Figure 1 | (a) Front view; and (b) Side view of the MFC biosensors.",
        "texts": [
            " The objective of this study was to optimize the design of the MFC-based toxicity sensor that could provide: (i) a stable baseline in the absence of toxicity (Stein et al. ); (ii) high sensitivity when exposed to toxicity; and (iii) good recovery capability following the toxic event. Different configurations, membranes and external resistances were compared to develop the optimal MFC-based toxicity sensor. Finally, the reliability of our biosensor was evaluated with the occurrence of an acidic toxic event (HCl at various pHs). MFC construction and configurations The MFCs used in this study were single-chambered air-cathode designs (Liu & Logan ) (Figure 1). The anode chamber was 1 cm deep and had a diameter of 6 cm, resulting in an empty volume of 28 mL. Both the anode (surface area of 28 cm2) and the cathode were made of carbon cloth (E-Tek, USA) and the cathode was coated with platinum catalyst on one side at a load of 0.5 mg cm 2. Two different configurations were tested: (i) a membrane electrode assembly (MEA, Figure 2, Type A); and (ii) separated anode and cathode. In the latter case, the wastewater flowed between the electrodes and two types of wet proofing method were tested, utilizing either a polytetrafluoroethylene (PTFE) layer on the air-side of the cathode (Figure 2, Type B) as suggested by Cheng et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001880_j.applthermaleng.2014.02.008-Figure10-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001880_j.applthermaleng.2014.02.008-Figure10-1.png",
        "caption": "Fig. 10. The temperature distribution of rotor bar and end-ring (unit: C).",
        "texts": [
            " The temperature distribution of the stator winding with healthy cage is shown as Fig. 9(a). Because the connecting box and the fan in the motor model are considered, the temperature of the stator winding closed to the junction box is higher, and the highest temperature is not in the midpoint of the winding, but slightly a little close to load side. Fig. 9(b), (c) are the temperature distribution of stator windingwith broken bar fault. Compared to the healthy motor, we can know that the temperature increases in the case of broken bar fault. Fig. 10(a)e(c) are the steady rotor temperature distributions at the above three states. The temperature of the rotor with broken bars increases obviously comparedwith the healthy rotor. The rotor temperature distribution is also not complete symmetry. From the electromagnetic field analysis, we can know that no currents pass though the broken bars and no losses are generated, and the currents of the bars near to the broken bars are dramatically increased and the losses of the bars are increased a lot. But in fact, the temperature difference of the whole rotor is quite small, which can be found from Fig. 10(b) and (c). That is because of the large thermal conductivities of the rotor materials, and when the heat transfer reaches to balance, the temperature of the rotor is almost the same. The temperature of measured points is given in Table 1, which includes the test values and calculated values. For comparison, the calculated and tested temperature-rise are also listed in it. It indicates that the temperature-rise at the same position of the motor is increased when the broken bar fault appears, and the increase of the temperature-rise is directly related to the number of broken bars, that is the more serious the fault is, the higher the temperature rise"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003199_j.mechmachtheory.2019.103576-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003199_j.mechmachtheory.2019.103576-Figure8-1.png",
        "caption": "Fig. 8. Face-gear pointing line and chamfering to avoid pointing: Above: Symmetrical teeth; Below: Helical teeth.",
        "texts": [
            " \u2022 When shaper rotation angle \u03c6s \u2217 is known, all position vectors for the whole flank line can be calculated from Eq. (20) , where u s is determined by Eq. (19) of meshing. Points defined by shaper rotation angles ahead \u03c6s max can be calculated by determination of higher roots of the equation of meshing. This becomes practically relevant for large helix angles only. 2.6. Avoidance of pointing The face-gear tooth is limited due to the intersection of flank surfaces of both sides of the tooth which is shown in Fig. 8 . In comparison to a cylindrical gear, the top width of a face-gear is not constant. The knowledge about the intersection line of both tooth flank surfaces is practically relevant since the top of the tooth generated by pointing is prone to fracture and it must be avoided by cutting the tooth addendum below that intersection line (pointing line). The exact determination requires the simultaneous consideration of the equations of surfaces of both flanks of the tooth. So, taking Eq. (20) for both, the left and the right-side involute flank surfaces, a system of three linear equations of four unknowns is obtained"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003130_s00170-016-8950-4-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003130_s00170-016-8950-4-Figure9-1.png",
        "caption": "Fig. 9 The model designed and sample",
        "texts": [
            " In addition, the influence of the shielding gas on the molten pool is reflected on the viscous drag force. The shielding gas pressure can indirectly increase the viscous drag force, and it can also counteract the part of the gravity. Thus, the shielding gas pressure weakens the influence of gravity on the molten pool. So, the whole displacement offset is less than 0.06 mm, as shown in Fig. 8. To verify the process viability, a geometrical model with continuously variable postures of coaxial powder nozzle was designed, as shown in Fig. 9a. The scanning path was from A point to B point, and the axis direction of powder feeding nozzle is always coincident with curved surface normal direction. The sample coated by laser cladding was shown in Fig. 9b under the process parameters in Table 3 with the overlapping rate of 30 %. It can be seen from Fig. 9b that the surface quality of the sample is good without sticky powder. Meanwhile, it proves the process feasibility. Adopting the technology of \u201chollow laser beam and internal powder feeding\u201d and investigating the influence rules of the substrate inclines angles on the section sizes of cladding layers, some of conclusions can be summarized as follows: 1. The substrate-inclined angles from 0\u00b0 to 150\u00b0 and continuously variable postures of coaxial powder nozzle can been achieved by changing the programming to control the laser processing robot"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000414_s026357470999083x-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000414_s026357470999083x-Figure3-1.png",
        "caption": "Fig. 3. Simplified model of the sheath compared with a generic sheath.",
        "texts": [
            " Since the tendon thickness is close to the inner diameter of the sheath and the segment of tendon sheath is significantly small, the angle of both tendon and sheath is assumed to be the same. Therefore we have C = \u2212T , dC = \u2212dT . (2) The compressive force measured at the proximal end of the sheath is the same as the tension measured from the tendon at the same end. This result is easily verified by experiments. The theory presented so far applies only to sheath and tendon with a fixed curvature throughout its length, as shown in Fig. 3(a). In general, the sheaths are free to move and the curvature is different throughout the whole length, as shown in Fig. 3(b). This is modeled as a sheath having n sections, each having a different radius of curvature R1\u2212Rn and a displacement of x1\u2212xn from the housing. In this case Eq. (1) becomes T (x) = Tin ( e\u2212 \u03bc R1 x1\u2212 \u03bc R2 (x2\u2212x1)\u2212 \u03bc Rn\u22121 (xn\u22121\u2212xn\u22122)\u2212 \u03bc Rn (x\u2212xn\u22121)) \u00d7 (xn\u22121 < x < xn). (3) To predict the tension at the end of the sheath, expression (3) can be simplified as Tout = Tine\u2212K, (4) where K = \u03bc( x1 R1 + x2\u2212x1 R2 + \u00b7 \u00b7 \u00b7 + xn\u2212xn\u22121 Rn ) represents the effective friction between the tendon and sheath. It is important to note that, if the sheath does not change its shape, K is a constant"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000402_1.2959106-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000402_1.2959106-Figure8-1.png",
        "caption": "Fig. 8 Unit contact force vector sc",
        "texts": [
            " Therefore, the contact forces for a ented contact, from Eq. 2 , are smaller than the contact forces alculated using the classic Hertzian relationship, expressed in Eq. 1 . For contact between a ball and race, the unit vector along the irection of the normal contact force lies along the line joining the all center to the race groove center. However, in the presence of dent, the normal force direction is disrupted by the discontinuity t the dent edges and is dependent on the dent geometry in addiion to the race geometry. Figure 8 a illustrates an exaggerated ection of the dent along a plane in which the dent edge is re- 41103-4 / Vol. 130, OCTOBER 2008 om: http://tribology.asmedigitalcollection.asme.org/ on 01/29/2016 Terms placed by a torus of negligible tube radius and, thus, the unit normal force fnzx in the sectional plane under consideration is along the line joining the tube section center and ball center. When the ball is in simultaneous contact with both edges of a dent, fnzx is calculated by taking an overlap-weighted sum of the vectors corresponding to each edge of the dent. In Fig. 8 b , the overlap with Edge 1 is greater than the overlap with Edge 2, and thus the vector fn1 dominates the weighted sum. The weights of fn1 and fn2 are linearly dependent on l1 and l2, the distance from the ball center to the respective contacting edges projected onto the horizontal plane, as shown in Fig. 8 b . Considering the small size of dents, the linear relationship assumption is a reasonable approximation for determining the contact direction. A similar approach is used to find fnyz, the unit force vector projection on a plane perpendicular to the plane containing fnzx. The two projections of the force unit vector, fnzx and fnyz, are then combined by superposition to form the normal force unit vector fn. hematics: \u201ea\u2026 Case I; \u201eb\u2026 Case II Transactions of the ASME of Use: http://www.asme.org/about-asme/terms-of-use J Downloaded Fr ournal of Tribology om: http://tribology",
            " This an be accredited to the increased deflection overlap in the presnce of the dent. The ball impact with dents results in an impulse, exciting a ide range of vibration frequencies as compared to wavy bearings 20\u201322 , which excite the bearing at a single frequency correponding to a number of waves. Thus, the waviness, unlike dent, s detrimental only when the resulting exciting frequency equals o harmonic frequencies of bearing 20 . The dent also significantly affects the cage motion. Under noral operation without dent, fn1 and fn2 Fig. 8 have equal weights nd thus their X-axis components cancel out each other and comonents along the Z-axis add up to give fnzx. Nevertheless, when he ball rolls over the edges of the dent, fn1 or fn2 dominates the ther and thus the resulting contact force has a nonzero compoent along the X-axis. This component results in ball-cage imacts, which can be clearly seen in Fig. 12. ent Size The size of the dent directly affects the value of exponent n and hus the magnitude of fluctuations observed in dent-affected reions, which is also dependent on dent size"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000050_nme.2959-Figure21-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000050_nme.2959-Figure21-1.png",
        "caption": "Figure 21. Longitudinal stress distribution at t =55s.",
        "texts": [],
        "surrounding_texts": [
            "In this section, the simulation of the construction of a titanium wall by SMD is presented. The same geometry, material properties and process parameters than in the previous example were Copyright 2010 John Wiley & Sons, Ltd. Int. J. Numer. Meth. Engng 2011; 85:84\u2013106 DOI: 10.1002/nme used, which were validated by comparison to experiments. The only difference is the number of layers that are deposited to form the wall. The image sequences given in Figures 25 and 26 show the addition of filler material for each layer in four time instants with temperature plots. Figure 27 shows the residual longitudinal stresses that were developed 500 s after the beginning of the process."
        ]
    },
    {
        "image_filename": "designv10_5_0000492_tie.2011.2168795-Figure34-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000492_tie.2011.2168795-Figure34-1.png",
        "caption": "Fig. 34. (Left) Positions of points at which the trajectories of vector B are shown in Fig. 35 and (right) positions of points at which the trajectories of vector B are shown in Fig. 36.",
        "texts": [
            " However, the field-circuit timestepping method is quite time consuming, so for optimization, the rapid analytical method is to be recommended. APPENDIX A FLUX DENSITY HARMONICS See Figs. 25\u201327. APPENDIX B CORE LOSS SPECTRUM See Figs. 28 and 29. The higher field harmonics in the rotor are superimposed on the constant field rotating synchronously with the rotor (assuming synchronous speed of rotation), as shown in Figs. 30\u201338. Fig. 38 shows the sample time waveforms of the radial and tangential flux density components for point 7 defined in Fig. 34. ACKNOWLEDGMENT The authors would like to thank J. Szulakowski from the Technical University of Lodz for his work on core loss measurements and A. Michaelides from Vector Fields Software Cobham Technical Services for the valuable help. REFERENCES [1] M. A. Saidel, M. C. E. S. Ramos, and S. S. Alves, \u201cAssessment and optimization of induction electric motors aiming energy efficiency in industrial applications,\u201d in Proc. ICEM, 2010, pp. 1\u20136. [2] E. Dlala, A. Belahcen, J. Pippuri, and A. Arkkio, \u201cInterdependence of hysteresis and eddy-current losses in laminated magnetic cores of electrical machines,\u201d IEEE Trans"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000616_s0022112010000108-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000616_s0022112010000108-Figure1-1.png",
        "caption": "Figure 1. Examples of swimming micro-organisms, in which the swimming apparatus exerts a thrust T backwards on the fluid, while the body or head exerts an equal and opposite drag force, in the forwards direction, e. The distance between the effective points of application of these forces is . The force dipole system is equivalent to a stresslet S of magnitude T . (a) A biflagellate algal cell, for which S > 0 (a \u2018puller\u2019); (b) a spermatozoon and (c) a bacterium, for both of which S < 0 (\u2018pushers\u2019).",
        "texts": [
            " Some of these were the \u2018Batchelor stresses\u2019, present in any particulate suspension, but these proved to have a negligibly small effect on the predicted most unstable wavenumber and growth rate. However, one additional term was not negligible. This term arises because the swimming motion of each cell has an effect on the fluid that, in the far field, is equivalent to a force-dipole or \u2018stresslet\u2019 (it is assumed that the cell Reynolds number is very small, so locomotion is dominated by viscosity). Figure 1 shows three examples of swimming micro-organisms, in which a cell\u2019s swimming apparatus exerts a thrust T backwards on the fluid, while its body or head exerts an equal and opposite drag force in the forwards direction. If the distance between the effective points of application of these forces is , then the magnitude of the equivalent stresslet is T . For a biflagellate algal cell, such as C. nivalis, depicted in figure 1(a), the stresslet strength, S = T , is positive. Such cells can be thought of as \u2018pullers\u2019, pulling themselves along by their breast-stroke-like flagellar action. The effect on the fluid is to pull it in along the axis of symmetry and push it out sideways in the perpendicular plane. Figure 1(b) represents a spermatozoon, pushed from behind by a waving flagellum, while figure 1(c) represents a bacterial cell, pushed from behind by a rotating flagellar bundle. In these two cases, S = \u2212T and is negative; the cells may be termed \u2018pushers\u2019. Such cells push fluid out along the axis of symmetry, and suck it in from the sides. When there are n identical cells per unit volume, then the sum of the stresslets makes a contribution to the bulk stress tensor of \u03a3 (p) = n S ( \u3008ee\u3009 \u2212 1 3 I ) , (1) where I is the identity tensor and \u3008X\u3009 represents the average of X over e-space (the unit sphere)",
            " (40) If we take S\u0302 of the same (large) order as \u03bd\u0302, then in the above discussion \u03bd\u0302 is replaced by \u03bd\u0302 \u2212 S\u0302B1(\u03bc), these S\u0302 terms being due to the perturbation in \u3008ee\u3009, not in n. Hence, if S\u0302B1(\u03bc) > \u03bd\u0302, the stable and unstable modes change round. Since B1(\u03bc) < 0 in virtually all realistic cases, and always for \u03bc close to 1, it follows that strong pushers can drive instability for such modes even for g\u0302 < 0. Conversely, since B1(\u03bc) can be >0 for \u03bc close to zero when \u03b10 is small and strong, nearly spherical pullers can drive instability even for g\u0302 < 0 (although the existence of head-heavy pullers is questionable; see figure 1), but only if |S\u0302|/\u03bd\u0302 is large enough to make them happen. For the cases listed in table 2 and Appendix B, |S\u0302|/\u03bd\u0302 is not larger than 1/|B1(\u03bc)| (see Discussion). A little more insight can be gained by performing a small-\u03ba \u2032 expansion with all other parameters (including \u03bd\u0302 and S\u0302) taken to be O(1), so inertia is not totally neglected. Now the three roots of (25) are, approximately, \u03c3\u0303 = \u22122D\u0302R and \u03c3\u0303 \u2248 \u03ba \u2032 2 { iV\u0302 \u03bc \u00b1 [ \u2212V\u0302 2\u03bc2 + 2(1 \u2212 \u03bc2)B2(\u03bc)g\u0302 D\u0302R ]1/2 } . (41) As long as B2 is positive and \u03bc is taken small enough, this always gives instability if g\u0302 > 0, and this is the gyrotactic instability of PHK; B2 is positive, for all \u03bc, in all the cases listed in table 2, and in general for small \u03bb unless \u03b2\u0302 is very large (Appendix B), which is unrealistic"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003800_s40430-020-2208-7-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003800_s40430-020-2208-7-Figure2-1.png",
        "caption": "Fig. 2 Tooth profile model of cycloidal gear with parabolic modification",
        "texts": [
            " However, we should note that the parabolic modification is another important method in the modification design of cycloid gear, it is a single tooth non-backlash mismatch modification method, which can ensure that the main meshing area is close to the conjugate profile, the non-meshing area has the appropriate backlash, and the transmission error is reasonable under the influence of installation error, manufacturing error and other factors [22]. According to the meshing characteristics of cycloidal-pin gear transmission, the profile geometry of cycloid gear with parabolic modification mainly depends on six parameters [6]: the teeth number of cycloidal gear zc , the eccentricity a, the roller radius rrp , the roller position rp , the parabolic modification coefficient ac and the parameter angle 0 of mismatching reference point. The tooth profile model with parabolic modification is shown in Fig.\u00a02. In Fig.\u00a02, K is the meshing point and M is the center of pin tooth. KC is the curvature radius of the theoretical tooth profile of cycloid gear. P is the meshing pitch point. Oc is the center of cycloidal gear, and Op is the center of pin gear. ra and rb are, respectively, the pitch radius of cycloid gear and pin gear. Therefore, the tooth profile of cycloidal gear with the parabolic modification in coordinate system Sc(xc, yc) can be deduced as follows [22]: (3) \u23a7\u23aa\u23a8\u23aa\u23a9 xc = rp sin zc \u2212 a sin(1 + iH) + \ufffd rrp + ac \ufffd\ufffd r2 p + r2 b \u2212 2rprb cos \u2212 \ufffd r2 p + r2 b \u2212 2rprb cos 0 \ufffd\ufffdn k1 sin(1+i H ) \u2212sin zc s yc = rp cos zc \u2212 a cos(1 + iH) \u2212 \ufffd rrp + ac \ufffd\ufffd r2 p + r2 b \u2212 2rprb cos \u2212 \ufffd r2 p + r2 b \u2212 2rprb cos 0 \ufffdn\ufffd\u2212k1 cos(1+i H ) +cos zc s where subscripts c indicates the coordinate system Sc(xc, yc) "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000492_tie.2011.2168795-Figure30-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000492_tie.2011.2168795-Figure30-1.png",
        "caption": "Fig. 30. Positions of points at which the trajectories of vector B are shown in Fig. 31.",
        "texts": [],
        "surrounding_texts": [
            "This paper has presented a no-load core loss analysis of three-phase energy-saving small-size induction motors fed by sinusoidal voltage, using a combination of the timestepping FEM and an analytical approach, which offers rapid computation. In this field-circuit approach, the distribution and changes in magnetic flux densities of the motor are computed using a time-stepping FEM. A DFT is then used to analyze the magnetic flux density waveforms in each element of the model obtained from several snapshots taken over a voltage cycle of the time-stepping solution. Rotational aspects of the field are accounted for by introducing a correction to the first harmonic of the alternating losses. The core losses in each element are evaluated using the specific core loss expression, in which the frequency-dependent parameters and flux are derived from a test conducted on a sample laminated ring core. The results are compared with measurements, and good agreement is observed for both methods. However, the field-circuit timestepping method is quite time consuming, so for optimization, the rapid analytical method is to be recommended. APPENDIX A FLUX DENSITY HARMONICS See Figs. 25\u201327. APPENDIX B CORE LOSS SPECTRUM See Figs. 28 and 29."
        ]
    },
    {
        "image_filename": "designv10_5_0003394_j.compstruct.2020.112698-Figure14-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003394_j.compstruct.2020.112698-Figure14-1.png",
        "caption": "Fig. 14. Comparison of stress values in the most critical zones for: a) metal (von Mises) and b) CFRP (Maximum Principal stresses).",
        "texts": [
            " For the same reason, the zone with highest stress on the top rail is on the right (~380 compared to ~240 MPa) and shifted ~50 mm to the right with respect to the plane of symmetry (Fig. 12a). Fig. 13 shows a distribution map of the MPS for each separate section for the most stressed layer. The highest value of MPS for each layer is reported in Table 4. The seats are not shown since they are subject to negligible stress under these test conditions. Considering these values, the material stress limits for T800 or T1000 are not exceeded at any point. Principal stresses are useful for comparing metal and composite cages in the case of a rollover. In Fig. 14, the structural response of these structures in the above\u2010mentioned conditions is represented in terms of von Mises equivalent stress for Ti\u2010alloy and Maximum Principal stress for CFRP. In particular, the comparison highlights the fact that: - the Ultimate Tensile Strength (UTS) of Ti\u2010alloy (1030 MPa) is exceeded in several zones, implying structural failure. Large zones exceeding the plastic limit (>970 MPa) are also visible. On the contrary, in the case of CFRP, the maximum (principal) stress in the T1000 is much lower than the material UTS (~1000 MPa compared to 2200 MPa)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003394_j.compstruct.2020.112698-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003394_j.compstruct.2020.112698-Figure4-1.png",
        "caption": "Fig. 4. Safety cage before and after redesign with all subsections: a) original metal roll-cage structure, as inserted in the composite structure (not visible); b) final structure in reinforced composite.",
        "texts": [
            " These sections, which represent holes in the support panel, not only reduced the weight of the structure, but also helped dissipate heat. Photovoltaic panels, in fact, suffer rapid reductions in efficiency with temperature increases. Almost all of the sections described thus far were redesigned and modified as a consequence of the present work. The monocoque structure in which all elements are housed, comprising the central beam (battery holder) and lower bathtub structure (visible externally in Fig. 3) instead remained unchanged. Replacement of the metal safety cage (Fig. 4a) was achieved by conceiving an alternative able to exploit the marked anisotropy of reinforced composites. Several options were considered, both in terms oll cage is shown together with its critical zones. of geometry and materials. The present discussion is limited the final solution (Fig. 4b). The study was carried out considering the safety requirements defined within the WSC 2019 race regulations, comprising static analysis at pre\u2010established loads and verification of maximum deformation. In particular, with the aim of protecting occupants from the potential risk of vehicle rollover, the regulation requires that a multidirectional load is applied in static conditions. This load must be equivalent to 5 times the weight of the vehicle in the vertical direction, 4 times in the longitudinal direction and 1.5 times in the transverse direction, applied to a section of the roof with a diameter smaller than 150 mm. Physical conditions were reproduced with a finite element (FE) simulation using the commercial software ANSYS Workbench Ver. 18.2. A description of this modeling approach applied metal structures is presented in [51]. Numerical modeling was limited to the central and upper sections of the safety cage (Fig. 4b), in which the four seats also performed structural functions. These parts are rigidly anchored to underlying elements of the structure, specifically the monocoque and central tunnel, sections of the vehicle that can be considered infinitely rigid in relation to the applied external forces. The result is a simplified model with interlocking constraints where the seats and uprights are in contact with the vehicle (Fig. 5a). A total weight of 750 kg was adopted for the investigation, including the mass of the frame, batteries, photovoltaic panels, engines, driver, passengers and all other kinematic elements (e"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003080_j.automatica.2020.108932-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003080_j.automatica.2020.108932-Figure2-1.png",
        "caption": "Fig. 2. States of the robot.",
        "texts": [
            " Thus, d(t) > 0 holds for all t \u2265 t0 if d(t0) > 0. Firstly, we show that there exists a t1 \u2265 t0 such that \u03c6(t) \u2208 [\u03b3 , \u03c0 \u2212 \u03b3 ] for any t \u2265 t1 if \u03c6(t0) \u2208 [0, \u03c0]. Particularly, if \u03c6(t) \u2208 [0, \u03b3 ), it follows from (15) that \u03c6\u0307(t) \u2265 (vc\u03b5)\u22121k1 (vc cos \u03b3 + k2sat ((d(t) \u2212 rc)/k3)) \u2265 (vc\u03b5)\u22121k1(vc cos \u03b3 \u2212 k2) > 0. (17) Thus, \u03c6(t) will finally go beyond \u03b3 . Similarly, \u03c6(t) \u2208 (\u03c0 \u2212 \u03b3 , \u03c0] leads to that \u03c6\u0307(t) \u2264 (vc\u03b5)\u22121k1(k2 \u2212 vc cos \u03b3 ) < 0. Then, we show that \u03c6(t) enters the region [0, \u03c0] in finite time for any \u03c6(t0) \u2208 (\u2212\u03c0, 0). To this end, four cases in Fig. 2 are considered. In Fig. 2(a), i.e., d(t0) \u2208 [rc, \u221e) and \u03c6(t0) \u2208 [\u2212\u03c0/2, 0), it follows from (3) and (15) that d\u0307(t0) \u2265 0 and \u03c6\u0307(t0) > 0. For a sufficiently small \u03b4 > 0, i.e., t = t0 + \u03b4, we have that 0 > \u03c6(t) > \u2212\u03c0/2 and d\u0307(t) > 0. This implies that d(t) > rc and from (15) that \u03c6\u0307(t) > k1 vc \u03b1\u0302(t) ( d\u0307(t) + k2sat ( d(t) \u2212 rc k3 )) > k1cos\u03c6(t) > 0. Thus, \u03c6\u0307(t) \u2265 k1cos\u03c6(t0 + \u03b4) and there exists a finite time t1 such that \u03c6(t1) \u2265 0. In Fig. 2(b), i.e., d(t0) \u2208 [rc, \u221e) and \u03c6(t0) \u2208 (\u2212\u03c0, \u2212\u03c0/2), it follows from (15) that{ \u03c6\u0307(t) > 0, if \u03c6(t) = \u2212\u03c0/2, \u03c6\u0307(t) < 0, if \u03c6(t) = \u2212\u03c0. Then, there are three possible cases after some finite time \u03b4 > 0: (i) \u03c6(t0 + \u03b4) < \u2212\u03c0 and d(t0 + \u03b4) \u2265 rc , i.e. \u03c6(t0 + \u03b4) \u2208 [0, \u03c0]; (ii) \u03c6(t0+\u03b4) > \u2212\u03c0/2 and d(t0+\u03b4) \u2265 rc , which is the case in Fig. 2(a); (iii) d(t0 + \u03b4) < rc which is to be shown for the cases in Fig. 2(c) and (d). If d(t0) \u2208 (0, rc), it contains cases in Fig. 2(c) and (d). When \u03c6(t) = \u2212\u03c0/2 and d(t) > 0, it follows from (15) \u03c6\u0307(t) = d2(t) \u2212 rcd(t) + 2rcv2 c /(k1k2) rcvcd(t)/(k1k2) . (18) Consider the numerator of (18) in a quadratic form of d(t). \u2022 If k1k2 < 8v2 c /rc , it can be easily verified that r2c \u2212 4 \u00d7 (2rcv2 c )/(k1k2) < 0 and \u03c6\u0307(t) > 0 for \u03c6(t) = \u2212\u03c0/2 and d(t) \u2208 (0, rc). This implies that (18) is unstable in Fig. 2(c) and (d). \u2022 If k1k2 \u2265 8v2 c /rc , there exists an equilibrium y\u0303e := [d\u2217, \u2212\u03c0/2]\u2032 such that \u03c6\u0307(t) = 0, where d\u2217 \u2208 (0, rc). However, the equilibrium y\u0303e is unstable. To prove it, we define y(t) := [d(t), \u03c6(t)]\u2032 and linearize the closed-loop system in (3) around y\u0303e as follows y\u0307(t) = F (y(t) \u2212 y\u0303e), F = \u23a1\u23a3 0 vc k1k2 rcvc \u2212 2vc d2 \u2217 k1 \u23a4\u23a6 . It is clear that F at least has one unstable eigenvalue. Specifically, (i) when k1k2 = 8v2 c /rc , the unique equilibrium is y\u0303e = [rc/2, \u2212\u03c0/2]\u2032 and the other eigenvalue of F is zero; (ii) when k1k2 > 8v2 c /rc , the equilibrium lying in the region (rc/2, rc) is a saddle, and the other equilibrium lying in (0, rc/2) is an unstable node or focus",
            " When y2(t) \u2208 (\u2212\u03c0 + \u03b3 , \u2212\u03b3 ) and y1(t) \u2208 (0, rc), it follows from (3), (14) and (15) that \u2202(h(y)y\u03071) \u2202y1 + \u2202(h(y)y\u03072) \u2202y2 = 4k1 sin y2(t) < 0. Thus, there is no closed orbit in the region y2(t) \u2208 (\u2212\u03c0 + \u03b3 , \u2212\u03b3 ) and y1(t) \u2208 (0, rc). In any case, all trajectories starting near y\u0303e would diverge from it in finite time (Khalil, 2002, Chapter 2.1). Overall, there are only two possible results for d(t0) \u2208 (0, rc) and \u03c6(t0) \u2208 (\u2212\u03c0, 0) after some finite time \u03b4 > 0: (i) \u03c6(t0+\u03b4) \u2208 [0, \u03c0]; (ii) d(t0 + \u03b4) \u2208 [rc, \u221e) and \u03c6(t0 + \u03b4) \u2208 [\u2212\u03c0/2, 0), which is Fig. 2(a). \u25a0 Lemma 3. Under the conditions in Proposition 1, it holds that lim t\u2192\u221e |d(t) \u2212 rc | = lim t\u2192\u221e |d\u0307(t)| = 0. (19) Proof. By Lemma 2, it follows from (15) that \u03c6\u0307(t) = k1 vc sin\u03c6(t) ( d\u0307(t) + k2sat ( d(t) \u2212 rc k3 )) . (20) Consider a Lyapunov function candidate as V3(x) = k1k2 \u222b x1(t) rc sat ( \u03c4 \u2212 rc k3 ) d\u03c4 + 1 2 x22(t). Taking the time derivative of V3(x) along with (7), (9) and (20) leads to that V\u03073(x) = k1k2sat((x1(t) \u2212 rc)/k3)x2(t) \u2212 x2(t) (k1x2(t) + k1k2sat ((x1(t) \u2212 rc)/k3)) = \u2212k1x22(t) \u2264 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000857_j.cma.2013.12.017-Figure19-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000857_j.cma.2013.12.017-Figure19-1.png",
        "caption": "Fig. 19. Tip relief geometry definition.",
        "texts": [
            " Avoidance of areas of severe contact stresses increases the endurance and life of gear transmissions. In this work, tip relief is applied by modifying the face-milling cutter cross section geometry. A parabolic tip relief geometry for blade profile, due to its tangency with active generating profile, avoids the appearance of edges on the contacting gear tooth surfaces and assure a smoother load transition [13\u201315]. In this work, tip relief height htr and tip relief parabola coefficient apf have been considered as design parameters for the parabolic tip relief geometry, which is shown in Fig. 19. Table 5 shows the design parameters for the search of the optimal tip relief. Tip relief height htr has been kept constant, while tip relief parabola coefficient apf has been increased gradually in each numerical case until the optimal value is found. Table 6 shows the optimal parabola coefficients for each case of design. Based on the the obtained results, the following remarks can be made: Fig. 20 shows the evolution of the contact and bending stresses with respect to the parabola coefficient of the tip relief profile for example of design 16"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000083_j.mechmachtheory.2009.01.010-Figure13-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000083_j.mechmachtheory.2009.01.010-Figure13-1.png",
        "caption": "Fig. 13. Contact stress distribution for the case of approximate line contact (a/b = 83; applied torque 300 Nm; total normal force 4434 N): (a) on the contact region and (b) along the major axis of the contact ellipse.",
        "texts": [
            " The relative deviation of the calculated values from the FEM analyzed values does not exceed 5 % (Fig. 11b). When the gear drive is loaded with a larger torque, 300 Nm, or a total normal force of 4434 N correspondingly, the length of the major axis of the contact ellipse is enlarged about 1.5 times the face-width of the conical gear. The contact stress on the tooth can be analyzed, not by the conventional Hertz\u2019s analytical method, but by the presented numerical method. The analysis results from FEM and the presented method are shown in Fig. 12a and b, and Fig. 13a and b, respectively. A comparison of the results from FEM analysis and the presented method (Fig. 13b) gives a relative error at the contact point of about 3%. The results from both methods indicate that the contact stress distribution remains as a half ellipsoid near the middle of the face-width. They also show concentrated stress at the face-end of the tooth. The region of contact therefore shows a saddle shape and the calculated stress distribution near the tooth end is only approximate. The face-width of the gear drive in case 2 is enlarged to 40 mm for the purpose of the end-relief effects"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000467_0954406212470363-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000467_0954406212470363-Figure2-1.png",
        "caption": "Figure 2. Fabrication stages. (a) Flat plate, (b) After bending to radius, (c) Applied clamping force, and (d) Deposition in progress.",
        "texts": [
            " The deposition pattern in a complex 3D geometry is expected to significantly influence the transient temperature distribution and distortion in the base plate, which may not be the case with simple geometries. The investigation made use of the commercial software, ABAQUS for solving the FE analysis (FEA) equations. The FE model (FEM) predicts the respective distortions arising from the different plate thicknesses and deposition patterns. Manufacture of aero-engine component with the DLD process The manufacture of this component followed a series of steps which is shown in Figure 2. The first of these steps is the bending of the initially flat plate of aged Inconel 718 (Figure 2(a)), which measured 250 250 3mm3 into a curved shape with a radius 300mm (Figure 2(b)). To provide structural support during the DLD process (simulating the cladding process over actual aero-engine tubular ring), the curved plate was placed on two L-shaped channels along their straight sides and then constrained by clamping these sides onto the channels, as shown in Figure 2(c). Followed then was the deposition process, as shown in Figure 2(d). The deposited build on the curved base plate is located at a radius of 50mm from the centre of the plate and has a width of 25mm and height that varies from 28mm at the periphery to 20mm at the inside. During the DLD process, a continuous spray of water at room temperature was provided on the underside of the base plate to serve as a cooling mechanism with which heat dissipation could be enhanced. To estimate the distortion induced on the base plate, 81 points, in a (9 9) equally spaced matrix layout were marked underneath the plate and the corresponding x-, y- and z-coordinates of each point were recorded using a coordinate measuring machine before and after the DLD process (with reference to a plane tangent to the edge of the base plate)",
            " Each step in this analysis corresponded to a time step in the thermal analysis, with the fusion zone elements incrementally activated in strain-free states to simulate the continuous deposition of powder. The materials were assumed to follow thermo-elastic behaviour and the temperature-dependent material properties of elastic modulus, Poisson\u2019s ratio, coefficient of thermal expansion and yield stress were used in the analysis and are adopted from Kamara et al.18 The applied structural boundary conditions were such that the nodes on the sides of the base plate along the straight edge (as shown in Figure 2(c)) were constrained in all directions to simulate clamping effect on the base plate (simulating the process over actual aero-engine tubular ring). The FEM investigation was carried out in two stages. The first stage was to develop a basic model, capable of predicting the distortion values to a reasonable accuracy in comparison with the experimental results. The second stage of the investigation dealt with a parametric study of base plate thickness and deposition patterns, focusing on identifying the combination of these parameters that will give rise to least distortion on the base plate",
            " The FE simulation results show a maximum distortion of 5.9mm at the centre of the plate while the corresponding experimentally measured value is 2.1mm. Although the FE simulation and the experimental results show similar profiles (i.e. least distortion along the edges and maximum distortion at the centre of the base plate) their magnitudes, however, differ substantially. This effect is speculated to have resulted from the internal pre-stress that existed in the experimental base plate. This speculation can be further justified by the bending (Figure 2(b)) of base plate by rolling,37 which induces a pretension/pre-stress within the baseplate that was not taken into account during the initial FEA. After further analysis of all the factors in simulation, it was revealed that the substantial variation between the experimental and simulation results is possibly due to the internal pre-stress found in the experimental base plate. A further analysis was carried out considering a uniform pre-stress of 841MPa on the base plate. The pre-stress values are computed using plate bending equations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000324_j.ijengsci.2008.01.007-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000324_j.ijengsci.2008.01.007-Figure3-1.png",
        "caption": "Fig. 3. Vertical and horizontal point-load configurations.",
        "texts": [
            " Point-load Green\u2019s functions In the preceding sections, the general solution has been formulated for an arbitrary source distributed on the plane z \u00bc s. To obtain the point-load Green\u2019s functions, which are useful for integral formulations of boundary value problems, one may define the body force field as fh\u00f0r; h; z\u00de \u00bcFh d\u00f0r\u00de 2pr d\u00f0z s\u00deeh; fv\u00f0r; h; z\u00de \u00bcFv d\u00f0r\u00de 2pr d\u00f0z s\u00deez; \u00f031\u00de with the harmonic time factor eixt omitted for brevity. In (31), d is the one-dimensional Dirac delta function; eh is the unit horizontal vector in the h \u00bc h0 direction given by eh \u00bc er cos\u00f0h h0\u00de eh sin\u00f0h h0\u00de; \u00f032\u00de (see also Fig. 3); er, eh, and ez are the unit vectors in the radial, angular and vertical directions, respectively; and Fh and Fv are the load magnitudes. By virtue of the angular expansions of the stress discontinuities across the plane z \u00bc s and the orthogonality of the angular eigenfunctions feimhg1m\u00bc 1, one finds P 1\u00f0r\u00de \u00bcFhe ih0 d\u00f0r\u00de 4pr ; P m\u00f0r\u00de \u00bc 0; m 6\u00bc 1; Q 1\u00f0r\u00de \u00bc Fhe ih0 d\u00f0r\u00de 4pr ; Qm\u00f0r\u00de \u00bc 0; m 6\u00bc 1; R0\u00f0r\u00de \u00bcFv d\u00f0r\u00de 2pr ; Rm\u00f0r\u00de \u00bc 0; m 6\u00bc 0; \u00f033\u00de for the point loads in (31). Subsequently, the transformed loading coefficients X m, Y m and Zm can be expressed as X 1 \u00bc Fh 2p e ih0 ; X m \u00bc 0; m 6\u00bc 1; Y 1 \u00bc Fh 2p eih0 ; Y m \u00bc 0; m 6\u00bc 1; Z0 \u00bc Fv 2p ; Zm \u00bc 0; m 6\u00bc 0: \u00f034\u00de Upon inverting the transformed expressions (26) and (27), the displacement and stress point-load Green\u2019s functions may be written as u\u0302 r \u00f0r; h; z; s\u00de \u00bc 1 4pc44 2Fv Z 1 0 c3nJ 1\u00f0rn\u00dedn Fh cos\u00f0h h0\u00de Z 1 0 \u00f0c1 \u00fe c2\u00denJ 0\u00f0rn\u00dedn Z 1 0 \u00f0c1 c2\u00denJ 2\u00f0rn\u00dedn ; u\u0302 h\u00f0r; h; z; s\u00de \u00bc 1 4pc44 Fh sin\u00f0h h0\u00de Z 1 0 \u00f0c1 \u00fe c2\u00denJ 0\u00f0rn\u00dedn \u00fe Z 1 0 \u00f0c1 c2\u00denJ 2\u00f0rn\u00dedn ; u\u0302 z \u00f0r; h; z; s\u00de \u00bc 1 2pc44 Fv Z 1 0 X2nJ 0\u00f0rn\u00dedn\u00feFh cos\u00f0h h0\u00de Z 1 0 X1nJ 1\u00f0rn\u00dedn : \u00f035\u00de s\u0302 zz\u00f0r; h; z; s\u00de \u00bc 1 2pc44 Fv Z 1 0 c33 dX2 dz c13nc3 nJ 0\u00f0rn\u00dedn \u00feFh cos\u00f0h h0\u00de Z 1 0 c33 dX1 dz c13nc1 nJ 1\u00f0rn\u00dedn ; s\u0302 zr\u00f0r; h; z; s\u00de \u00bc 1 4p 2Fv Z 1 0 nX2 \u00fe dc3 dz nJ 1\u00f0rn\u00dedn Fh cos\u00f0h h0\u00de Z 1 0 nX1 \u00fe dc1 dz \u00fe dc2 dz nJ 0\u00f0rn\u00dedn Z 1 0 nX1 \u00fe dc1 dz dc2 dz nJ 2\u00f0rn\u00dedn ; s\u0302 zh\u00f0r; h; z; s\u00de \u00bc 1 4p Fh sin\u00f0h h0\u00de Z 1 0 nX1 \u00fe dc1 dz \u00fe dc2 dz nJ 0\u00f0rn\u00dedn \u00fe Z 1 0 nX1 \u00fe dc1 dz dc2 dz nJ 2\u00f0rn\u00dedn ; s\u0302 rr\u00f0r; h; z; s\u00de \u00fe 2c66 r fu\u0302 r \u00fe i\u00f0u\u0302 h1 eih u\u0302 h 1 e ih\u00deg \u00bc 1 2pc44 Fv Z 1 0 c13 dX2 dz c11nc3 nJ 0\u00f0rn\u00dedn \u00feFh cos\u00f0h h0\u00de Z 1 0 c13 dX1 dz c11nc1 nJ 1\u00f0rn\u00dedn ; s\u0302 hh\u00f0r; h; z; s\u00de 2c66 r fu\u0302 r \u00fe i\u00f0u\u0302 h1 eih u\u0302 h 1 e ih\u00deg \u00bc 1 2pc44 Fv Z 1 0 c13 dX2 dz c12nc3 nJ 0\u00f0rn\u00dedn \u00feFh cos\u00f0h h0\u00de Z 1 0 c13 dX1 dz c12nc1 nJ 1\u00f0rn\u00dedn ; s\u0302 rh\u00f0r; h; z; s\u00de \u00fe 2c66 r fu\u0302 h i\u00f0u\u0302 r1 eih u\u0302 r 1 e ih\u00deg \u00bc 1 2pa2 Fh sin\u00f0h h0\u00de Z 1 0 c2n 2J 1\u00f0rn\u00dedn : \u00f036\u00de In the above, the symbols \\u\u0302 i \" and \\s\u0302 ik\" \u00f0i; k \u00bc r; h; z\u00de denote, respectively, the displacement and stress Green\u2019s functions, with the superscript \u2018\u2018*\u201d denoting the direction of the point load upon appropriate speci- fications of Fh, Fv, and h0 in Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000782_j.mechmachtheory.2012.11.006-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000782_j.mechmachtheory.2012.11.006-Figure4-1.png",
        "caption": "Fig. 4. Gear angle calculation scheme for displaced gear frames.",
        "texts": [
            " This relative displacement accounts for the following two contributions (Fig. 3): where and D DTE \u00bc DTEr \u00fe DTEt \u00f01\u00de DTEr is due to relative rotation of the gears and is given by: DTEr \u00bc \u03b81rpo1 \u00fe e\u03b82rpo2 \u00f02\u00de rpi \u00bc zi ez1 \u00fe z2 CD xrj j \u00f03\u00de TEr is due to relative translation in the tangential direction and is given by: DTEt \u00bc \u2212eCD\u00fe yr: \u00f04\u00de Angles \u03b8i in Eq. (2) are calculated between the actual x axes of the gear frames and the reference x axis, positive in the direction of the reference z axis, in the reference transverse plane (xryr) as shown in Fig. 4. The variable e in Eq. (2) is used to account for internal or external gears. Variable e is equal to 1 for external gears, since angles have opposite sign and Eq. (2) converts into a difference. Variable e is equal to \u22121 for internal gears, since gear 2 rotates in the same direction of gear 1. The variable e is also used in Eq. (3) since center distance is given by the sum of the operating pitch radii for external gears, while by the difference for internal gears. The operating pitch radii, rpoi, are calculated projecting the actual center distance CD on the reference x axis and splitting it keeping constant the gear ratio",
            " When dynamic effects of center distance are disabled, mesh stiffness is calculated using the nominal value; when they are enabled the actual center distance is used to interpolate the look-up tables. In this case, effects on mesh stiffness due to changes in contact ratio and active tooth height are included together with alterations on the effects of profile modifications, since teeth profiles become displaced relatively to each other. The actual center distance is calculated projecting the vector connecting the origins of the gear frames on the reference transverse plane (Fig. 4), according to: where CDxyr \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi CD xr\u00f0 \u00de2 \u00fe CD yr\u00f0 \u00de2 q : \u00f014\u00de This value is also used to calculate the actual operating transverse and normal pressure angles (Fig. 5), respectively \u03d5t and \u03d5n: \u03c6t \u00bc arccos rb1 rpo1 \u00f015\u00de \u03c6n \u00bc arctan tan\u03c6tcos\u03b2\u00f0 \u00de \u00f016\u00de rb1 is the base radius of gear 1. Misalignments in the plane of action are calculated with respect to the reference frame"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003793_j.mechmachtheory.2019.103764-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003793_j.mechmachtheory.2019.103764-Figure5-1.png",
        "caption": "Fig. 5. Dynamics model of GTF star gearing system.",
        "texts": [
            " 4 shows the dynamic model of the GTF gearbox transmission system, a pure torsional nonlinear dynamic model of the input and output shaft and spline pairs is established by the lumped mass method. Since the gears of the star gearing system are fixed-axis rotation, an absolute coordinate system OXYZ is established for central floating components (sun gear, ring gear, planet carrier), and coordinate systems o i x i y i z i are built for each star gear, in which the coordinate center is the rotational center of each star gear, the direction of X \u2212 axis is along the radial direction of the floating member, and the Y \u2212 axis is tangential along the center floating member. Fig. 5 (a) shows the schematic diagram of the left end face of the dynamic model of the star gearing system. Fig. 5 (b) is a three-dimensional schematic diagram of the engagement, where the X \u2212 axis is perpendicular to the meshing line of the sun gear and the first star gear, and the counterclockwise direction is the positive direction. Fig. 5 (c) shows coupled dynamics model of star gear and planet carrier. Fig. 6 shows the relationship of internal and external meshing phase. Each side of gear has four degrees of freedom (movement in X, Y, Z direction and rotation around Z axis). Different gears are marked with upper and lower marks. The subscripts s, p, r represent the sun gear, star gears and ring gear respectively. Superscript L, R represent the gear in left end and right end. In the dynamic model of star gearing system, the sun gear and ring gear float axially, assume that all the star gears have same support stiffness and damping"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003623_17452759.2020.1818917-Figure10-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003623_17452759.2020.1818917-Figure10-1.png",
        "caption": "Figure 10. (a) Natural frequencies of the original (red bar), topologically optimised (green bar), and lattice-structured (cyan bar) parts according to the vibrations at the first, second, and third vibration orders. (b) A photograph of the lattice-structured part additively manufactured.",
        "texts": [
            " If the element is not highly stressed, the density is decreased to indicate that the element is not necessary for structural strength; if the element is highly stressed, its density is increased until the initial volume (full density). Comprehensive reviews of topology optimisation can be found in various references (Aboulkhair et al. 2019; Greer et al. 2019; Yoder et al. 2018; Yu et al. 2018). Vibrations from internal or external disturbances occurring in the substances were caused by the uneven and asymmetric shapes between the flat plate and the curved board, when considering the different vibration modes (orders) of the substances affixed to the four pin-locking holes and bolt-fastening nuts at the bottom sheets. Figure 10(a) shows the natural frequencies of the substances according to the agitations; they are deformed differently at each vibration order. As shown, deforming the substance in the original part was the most difficult at the highest natural frequency of 11163 Hz at the third order, while deforming the substance in the topologically optimised part was easiest at the lowest natural frequency of 4623 Hz at the first order. Because the original part exhibits full density, the natural frequencies of the substances at each order must become the maximum with the least solid deformation (the highest vibration resistance). The topologically optimised part exhibited the lowest density, and thus the natural frequencies at the same order were the smallest with significant deformation, which could lead to increased fatigue damage in the shift block and the turbine blade in the hovercraft as well as its components. Hence, the topologically optimised part must adopt the lattice structure for vibration absorption, as shown in Figure 10(b). In principle, it is better to combine a topologically optimised substance that is a dense solid with a lattice structure of low density even though it has been assumed in some studies that for the substance used, the adoption of a lattice structure as a vibration resonator only affects the vibration resistance at low frequency (Aboulkhair et al. 2019; Banhart 2001; Kang et al. 2019; Matlack et al. 2016; Mukhopadhyay, Adhikari, and Alu 2019; Wang et al. 2018c). Furthermore, although the vibration resistance of the combined structure can be improved simply by increasing the mass/stiffness ratio of the whole structure, the vibration resistance of the shift block modified with topology optimisation and the lattice structure improved compared to that of the shift block modified only with topology optimisation, as shown in Supplementary Figure 8"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001606_jestpe.2013.2284096-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001606_jestpe.2013.2284096-Figure5-1.png",
        "caption": "Fig. 5. Two-mass model of wind turbine drivetrain.",
        "texts": [
            " The resonance causes undesired fluctuations in the transmitted torque, resulting in large fatigue loads. Controllers, such as the one presented in this paper, can be designed and implemented to mitigate or prevent the resonant loads and hence to preserve the design life of the drivetrain. This paper focuses on a commonly used modular drivetrain configuration in operating wind turbines [8]. Fig. 4 shows the building blocks of the configuration. The GRC multistage gearbox consists of a planetary gear stage and two parallel gear stages, with two intermediate shafts. Fig. 5 shows the configuration of the two-mass model commonly used to model the dynamics of drivetrains in wind turbine aeroelastic tools, such as FAST [1]. Inputs into this model are the five parameters: Jrot, kd , cd , N , and Jgen. This simple model lumps the rotor (i.e., the hub and blades) into an inertial body and the rest of the drivetrain as another one. Jrot and Jgen are, respectively, the inertia of the rotor and generator, \u03b8rot and \u03b8gen are, respectively, the angular position of the rotor and generator"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003887_j.etran.2020.100080-Figure11-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003887_j.etran.2020.100080-Figure11-1.png",
        "caption": "Fig. 11. Spoke type designs to increase rotor saliency [78,86,88].",
        "texts": [
            " [76] proposed a 50 kW ferrite machine with air holes and triangular cut-outs to increase the salient pole ratio and up to 80% torque of Prius rare-earth motor was achieved with same frame size at the current density of 20 A/mm2. Auxiliary radial magnetized poles were applied in between two spoke-type main poles to increase flux density as well as reluctance torque in Refs. [78,85]. An improved spoke-type design was proposed by dividing each of the conventional spoke-type pole into two parts shown in Fig. 11(b) [86,87]. The reactance torque could benefit from this design and an 25 Nm/L torque density was achieved. However, there are still more room to develop a rotor design sustaining certain airgap flux density and higher rotor saliency. B. Xia et al. in Ref. [88] proposed a novel designwith multi-layer configuration for traction applications. The reluctance torque was maximized with acceptable PM torque component, and the final design was able to deliver up to 95% of the Prius rare-earth IPMmachines as shown in Fig. 11(c). W. Fei et al. further investigated the influence of the number of layers on the machine performance, and shown that two-layer configuration was the most cost-effective design compromise in terms of performance and rotor complexity [89]. To fully utilize the machine space and gain higher torque density, a 3D trench airgap configuration with double-stators was proposed in Ref. [85] to increase flux density, as illustrated in Fig. 12. The proposed machine consisted of double stators and a spoke type rotor with side rotor poles sandwiched in between"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000648_978-3-642-17531-2-Figure5.19-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000648_978-3-642-17531-2-Figure5.19-1.png",
        "caption": "Fig. 5.19. Lossy generic mechatronic transducer",
        "texts": [
            " However, the inherent instability of the transducer must then be actively countered with suitable control measures (see Ch. 10). 330 5 Functional Realization: The Generic Mechatronic Transducer Dissipative phenomena In contrast to the ideal assumptions made so far, in real transducers, dissipative phenomena on both the mechanical and electrical sides must be accounted for. Inside the mechanical subsystem, viscous friction phenomena appear. Such effects can be incorporated into the load as additional mechanical damping (Fig. 5.19). This maintains the order (number of states) of the system, and, relative to the undamped case, only the eigenfrequencies change slightly: the purely imaginary pairs of poles at the eigenfrequencies move slightly into the left half-plane (see Sec. 4.5.3). This behavior can easily be qualitatively taken into account in the complete model without requiring much additional calculation. Resistive losses For real electrical systems, resistive losses must always be accounted for. These arise from non-negligible internal resistances in the controlled auxiliary energy sources, resistance in the conductors, or insulation losses (Fig. 5.19). Normally, resistive losses are considered unwelcome parasitic effects, and they are brought as close to idealized conditions as possible. Resistive feedback From a system theoretical point of view, electrical resistance in certain system configurations induces (analog) electrical feedback. This property can be exploited in a targeted manner in a mechatronic transducer by cleverly manipulating the physical feedback properties to advantageously influence the dynamic frequency response at a local level. 5.5 Lossy Transducer 331 This choice of electrical resistance makes available an important design degree of freedom for optimizing the system behavior with minimal implementation effort. Resistive configurations Resistive losses can be fundamentally modeled as a serial resistance on a terminal lead (lossless at 0R ) or as a parallel resistance across a terminal pair (lossless as R ) (Fig. 5.19). The resulting effect on the system dynamics and the model description fundamentally depends on the choice of auxiliary energy source. Serial resistance, voltage drive For the electrical configuration shown in Fig. 5.20a, the transducer voltage T u is no longer\u2014as in the lossless case\u2014equal to the independent source voltage. Rather, it now depends on the load current T i . This behavior, which differs from the lossless trans- ducer, must be incorporated into the dynamic model and leads to loaddependent feedback via the electrical subsystem of the transducer"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003652_j.ymssp.2019.04.029-Figure19-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003652_j.ymssp.2019.04.029-Figure19-1.png",
        "caption": "Fig. 19. Three dimensional schematic of pitting.",
        "texts": [
            " When the gear pitting occurs, the results between the two methods can be well matched, but the time-consuming of the method proposed in this paper is much less than that of FEM. The multiple teeth damage on pinion and wheel have been studied in this subsection. Table 1 shows the number of three types of pits including slight pitting, moderate pitting and severe pitting. The distribution of pitting and the method of determining the coordinates of each pit has been given in Section 2.1. The model of a gear is established using CAD software, while these pits can be dug out based on the former determined coordinates. The damaged pinion and wheel can be found in Fig. 19(a) and (b), respectively. It can be found five consecutive teeth have slight pitting, moderate pitting, severe pitting, moderate pitting and slight pitting, respectively, while the other teeth are all health. Fig. 20(a)\u2013(f) shows the six engagement stages between pinion and wheel, representing six different meshing conditions. The mesh stiffness obtained under six meshing conditions have been separately shown in Fig. 21(a)\u2013(f). Under the meshing order shown in Fig. 20(a), the TVMS of 10 pairs of teeth is affected by pitting corrosion",
            " 20, it can be concluded that the reduction of mesh stiffness depends mainly on the gear with serious pitting damage. When the pitting degree of a pair of meshing gears is identical, such as Fig. 20(f), two gears will play a decisive role simultaneously. It can be found in Fig. 16 as well as the adjacent regions of A and B in Fig. 21 that similar pitting appears on the pinion and wheel, which has small effect on the overall stiffness. Therefore, the reduction of mesh stiffness is mainly related to the degree of pitting damage. Pitting occurs on both pinion and gear in the model as shown in Fig. 19, while the engagement system of the model is referred to as Fig. 20(f). Then a three-dimensional finite element model shown in Figs. 22 and 23 is established. The health teeth and gear body are mapped using hexahedral elements and the pitting teeth are mapped with tetrahedral elements in the finite element model. The tetrahedral shape is chosen for the pitting teeth as it can simulate the complicated pitting profile. Then, the pitting teeth are mapped further refined. Fig. 24 shows the results of grid stiffness comparison between the proposed method and the FEM"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002944_iet-rpg.2016.0236-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002944_iet-rpg.2016.0236-Figure4-1.png",
        "caption": "Fig. 4 Vector relationship of the vibration components (a) (m = 1, h = 0), (b) (m = 1, h = \u2212 1, n = \u2212 1), (c) (m = 1, h = 1, n = 1)",
        "texts": [
            " Due to the feature that the third term of (19) only influences the amplitudes of the two spectral lines around the meshing frequency, the response collected by the sensor, which satisfies the equations below, is generated from the former two terms of in (19) (path 1 and path 2) xi(t) = xri(t)wi(t) + axsi(t)wi(t) + bxsi(t) = \u2211 m = \u2212 M M \u2211 k = \u2212 K K \u2211 n = \u2212 1 1 CrimF\u0304rimWkVn ej2\u03c0(mzr + k + n) f cte\u2212 j(mzr + k + n)\u03c8 i + \u2211 m = \u2212 M M \u2211 k = \u2212 K K \u2211 n = \u2212 1 1 aCsimF\u0304simWkVn ej\u03c0ej2\u03c0(mzr + k + n) f ctej(mzs \u2212 k \u2212 n)\u03c8 i + \u2211 m = \u2212 M M \u2211 n = \u2212 1 1 bCsimF\u0304simVn ej\u03c0ej2\u03c0(mzr + n) f ctej(mzs \u2212 n)\u03c8 i (17) x(t) = \u2211 i = 1 N xi(t) = \u2211 i N xri(t)wi(t) + axsi(t)wi(t) + bxsi(t) = \u2211 m = \u2212 M M \u2211 k = \u2212 K K \u2211 n = \u2212 1 1 CrimF\u0304rimWkVn ej2\u03c0(mzr + k + n) f ct \u2211 i = 1 N e\u2212 j(mzr + k + n)\u03c8 i + \u2211 m = \u2212 M M \u2211 k = \u2212 K K \u2211 n = \u2212 1 1 aCsimF\u0304simWkVn ej\u03c0ej2\u03c0(mzr + k + n) f ct \u2211 i = 1 N ej(mzs \u2212 k \u2212 n)\u03c8 i + \u2211 m = \u2212 M M \u2211 n = \u2212 1 1 bCsimF\u0304simVn ej\u03c0ej2\u03c0(mzr + n) f ct \u2211 i = 1 N ej(mzs \u2212 n)\u03c8 i (18) Table 1 Structural parameters of the planetary gear train of wind turbine gearbox Type Number of planet gears N Tooth number of ring gear zr Tooth number of sun gear zs Mesh manner IET Renew. Power Gener., 2017, Vol. 11 Iss. 4, pp. 425-432 \u00a9 The Institution of Engineering and Technology 2016 429 Q11 = Xr10 e\u2212 j0 = Xr10ej0 Q12 = Xr10 e\u2212 j101(2\u03c0 /3) = Xr10ej(2\u03c0 /3) Q13 = Xr10 e\u2212 j101( \u2212 2\u03c0 /3) = Xr10ej(\u22122\u03c0 /3) Q21 = aXs10 ej\u03c0 ej0 = aXs10 ej\u03c0 Q22 = aXs10 ej\u03c0 ej22(2\u03c0 /3) = aXs10 ej(\u2212\u03c0 /3) Q23 = aXs10 ej\u03c0 ej22( \u2212 2\u03c0 /3) = aXr10 ej(\u03c0 /3) (24) The vector relationship of the components in the plane \u2018XOY\u2019 is demonstrated in Fig. 4a, from which we can infer that the amplitude of frequency f10 is zero. 1. When m = 1, h = \u2212 1 and n = \u2212 1, the corresponding frequency is f1\u22121 = 100 Hz, which is the first spectral line in the left of the first-order meshing frequency of the planetary gear train. Its amplitude is generated from all the three terms (vibration through three paths) in (19) and satisfies the equations below Q11 = Xr1 \u2212 1 e\u2212 j0 = Xr1 \u2212 1 ej0 Q12 = Xr1 \u2212 1 e\u2212 j100(2\u03c0 /3) = Xr1 \u2212 1 ej( \u2212 2\u03c0 /3) Q13 = Xr1 \u2212 1 e\u2212 j100( \u2212 2\u03c0 /3) = Xr1 \u2212 1 ej(2\u03c0 /3) Q21 = aXs1 \u2212 1 ej\u03c0 ej0 = aXs1 \u2212 1 ej\u03c0 Q22 = aXs1 \u2212 1 ej\u03c0 ej23(2\u03c0 /3) = aXs1 \u2212 1 ej(\u03c0 /3) Q23 = aXs1 \u2212 1 ej\u03c0 ej23( \u2212 2\u03c0 /3) = aXr1 \u2212 1 ej(\u2212\u03c0 /3) Q31 = bCsF\u0304s1V\u22121 ej\u03c0ej0 = bCsF\u0304s1V\u22121 ej\u03c0 Q32 = bCsF\u0304s1V\u22121 ej\u03c0 ej23(2\u03c0 /3) = bCsF\u0304s1V\u22121 ej(\u03c0 /3) Q33 = bCsF\u0304s1V\u22121 ej\u03c0ej23( \u2212 2\u03c0 /3) = bCsF\u0304s1V\u22121 ej(\u2212\u03c0 /3) (25) The vector relationship of the components is shown in Fig. 4b, from which we can infer that the amplitude of frequency f1\u22121 is zero. 1. When m = 1, h = 1 and n = 1, the corresponding frequency is f11 = 102 Hz, which is the first spectral line right to the firstorder meshing frequency of the planetary gear train. Its amplitude is generated from all the three terms in (19) and satisfies the equations below Q11 = Xr11 e\u2212 j0 = Xr11 ej0 Q12 = Xr11 e\u2212 j102(2\u03c0 /3) = Xr11 ej0 Q13 = Xr11 e\u2212 j102( \u2212 2\u03c0 /3) = Xr11 ej0 Q21 = aXs11 ej\u03c0 ej0 = aXs11 ej\u03c0 Q22 = aXs11 ej\u03c0 ej21(2\u03c0 /3) = aXs11 ej\u03c0 Q23 = aXs11 ej\u03c0 ej21( \u2212 2\u03c0 /3) = aXr11 ej\u03c0 Q31 = bCsFs1V1 ej\u03c0 ej0 = bCsFs1V1 ej\u03c0 Q32 = bCsFs1V1 ej\u03c0 ej21(2\u03c0 /3) = bCsFs1V1 ej\u03c0 Q33 = bCsFs1V1 ej\u03c0 ej21( \u2212 2\u03c0 /3) = bCsFs1V1 ej\u03c0 (26) The vector relationship of the components in the plane \u2018XOY\u2019 is demonstrated in Fig. 4c, from which we can infer that the amplitude of frequency f11 is not zero. Take other values of m and h, repeat the process above and normalise the amplitude of the overall vibration Q to obtain the results, as listed in Table 2. It can be seen that the response amplitude of the type 1 planetary gear train equals to 0 except that the frequency f is integral multiples of N (the number of the planet gears). Therefore, the amplitudes of the meshing frequency component and its harmonics are not equal to 0, when the frequency and its harmonics are integral multiples of N"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001590_s12239-012-0052-1-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001590_s12239-012-0052-1-Figure4-1.png",
        "caption": "Figure 4. Spur gear pair system having six degrees of freedom.",
        "texts": [
            " Note that the effects of the support bearings and the shafts are implicitly included in the above equation as the lateral restraints on the pinion and the gear (Fujimoto and Kizuka, 2001). Additionally, the vibrations transmitted through the bearings excite the housing structure, which in turn radiates acoustic noise (Wang et al., 2001). 2.3. Spur Gear Pair System Using the proposed mesh stiffness and enhanced mesh force formulations, a dynamic lumped-parameter model is developed for a spur gearbox system in the idling condition comprising six degrees of freedom. A schematic of the dynamic gear model is shown in Figure 4. The system equations of dynamic motion are derived here. The equations of motion governing torsional vibration are represented by (14a) . (14b) The equations of motion describing the translational vibration are as follows: , (15a) , (15b) , for drive-side contact (15c) \u03be t( ) e t( ) \u03b7+( )\u2013< Km K \u03b8 t( )( )= \u03b8 t( ) \u03c0 zp --- 2tan\u03b1 2\u03b80 \u03b8p t( )\u2013\u2013+=, , Fk Km \u03be \u03b7\u2013( ) \u03be \u03b7\u2013 2\u03b7 ---------- \u2206 1\u2013 = Fc Cm\u03be for \u03be \u03b7 \u03b5+\u2265=, Fk Km 2 ----- 1( \u03b5 2 -- \u03b6 \u03b7\u2013+\u239d \u23a0 \u239b \u239e \u03c0 \u03b5 --\u239d \u23a0 \u239b \u239e )sin \u03be \u03b7\u2013( ) \u03be \u03b7\u2013 2\u03b7 ---------- \u2206 1\u2013 \u2013= Fc Cm 2 ----- 1 \u03b5 2 -- \u03be \u03b7\u2013+\u239d \u23a0 \u239b \u239e \u03c0 \u03b5 --\u239d \u23a0 \u239b \u239e sin\u2013\u239d \u23a0 \u239b \u239e\u03be for \u03b7 \u03be \u03b7 \u03b5+\u2264 \u2264= Fk Km 2 ----- 1 \u03b5 2 -- \u03be \u03b7+ +\u239d \u23a0 \u239b \u239e \u03c0 \u03b5 --\u239d \u23a0 \u239b \u239esin\u2013\u239d \u23a0 \u239b \u239e \u03be \u03b7+( ) \u03be \u03b7+ 2\u03b7 ---------- \u2206 1\u2013 = Fk Cm 2 ----- 1 \u03b5 2 -- \u03be \u03b7+ +\u239d \u23a0 \u239b \u239e \u03c0 \u03b5 --\u239d \u23a0 \u239b \u239esin\u2013\u239d \u23a0 \u239b \u239e\u03be for \u03b7 \u03b5 \u03be \u03b7\u2013\u2264 \u2264\u2013\u2013= Fk Km \u03be \u03b7+( ) \u03be \u03b7+ 2\u03b7 ---------- \u2206 1\u2013 = Fc Cm\u03be \u00b7 for \u03be \u03b7 \u03b5\u2013\u2013\u2264=, \u03be \u03b8pRpb \u03b8gRgb\u2013 yp yg\u2013+= J\u03b8 \u00b7\u00b7 T= J Jp 0 0 Jg = \u03b8 \u03b8p \u03b8g T Tp MpN Mpf+\u2013 Tg MgN Mgf\u2013 Cg\u03b8 \u00b7 g\u2013+\u2013 =,=, MX \u00b7\u00b7 F= M mp mg mp mg X xp xg yp yg =,= F Ff K\u2013 pBxxp C\u2013 pBx x \u00b7 p Ff\u2013 K\u2013 pBx xg CgBx\u2013 x \u00b7 g N\u2013 N KpBy\u2013 KgByyg\u2013 yp CpBy\u2013 CpBy\u2013 y \u00b7 p y \u00b7 g = , for coast-side contact (15d) Here, N is the net contact force due to the elastic and dissipative forces presented earlier"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000014_j.triboint.2008.11.003-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000014_j.triboint.2008.11.003-Figure2-1.png",
        "caption": "Fig. 2. Bearing dimensions.",
        "texts": [
            " Photographs were taken and investigated in order to find out the cause of severe vibrations. 2. Experimental setup The experimental test rig shown in Fig. 1 is designed to investigate failure and vibration characteristics of ball bearings. The spindle is driven by a variable-speed AC motor equipped with a frequency converter in order to control motor speed. Both sides of the spindle are force fitted with a new pair of standard 6205 deep groove ball bearings whose dimensions and characteristic frequencies are given in Fig. 2 and Table 1, respectively. A flywheel is installed at the free end of the spindle in order to apply load as well as to minimize speed oscillations of the spindle. The angular speed of the spindle is set around 3200 rpm and vibration signals are acquired with three B&K 4384 charge-type accelerometers. The accelerometers are placed at both the horizontal and vertical directions on the right-hand side bearing support and at a vertical direction on the left hand-side bearing support. Spindle speed is also measured with a B&K photoelectric tachometer probe"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000815_j.rcim.2010.07.001-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000815_j.rcim.2010.07.001-Figure2-1.png",
        "caption": "Fig. 2. Inverse kinematic model of 2-RRR manipulator.",
        "texts": [
            " , E22 \u00bc 2l1 x\u00fe hcosa 2 \u00fe ffiffiffi 3 p hsina 6 a ! ators: (a) 4-RRR manipulator and (b) 3-RRR manipulator. E32 \u00bc x\u00fe hcosa 2 \u00fe ffiffiffi 3 p hsina 6 a !2 \u00fe y\u00fe hsina 2 ffiffiffi 3 p hcosa 6 !2 \u00fe l21 l22 E13 \u00bc 2l1 y\u00fe ffiffiffi 3 p hcosa 3 ffiffiffi 3 p 2 a ! , E23 \u00bc 2l1 x ffiffiffi 3 p hsina 3 1 2 a ! E33 \u00bc x ffiffiffi 3 p hsina 3 1 2 a !2 \u00fe y\u00fe ffiffiffi 3 p hcosa 3 ffiffiffi 3 p 2 a !2 \u00fe l21 l22 2.3. Inverse kinematics of 2-RRR manipulator The kinematic model of the 2-RRR manipulator is shown in Fig. 2. From Fig. 2 it can be concluded that rC1 \u00bc rB1 \u00fe l2 cos\u00f0y1\u00fey u 3\u00de sin\u00f0y1\u00fey u 3\u00de \" # \u00f07\u00de where yu3 is the angle between links A1B1 and B1C1. Combining Eqs. (2) and (7) lead to tan\u00f0y1\u00feyu3\u00de \u00bc y h=2sina h=2cosa l1 siny1 x\u00feh=2sina h=2cosa l1 cosy1 \u00f08\u00de Joint variables y1 and y2 of the 2-RRR manipulator are the same as those of the 4-RRR manipulator. y1 and y2 are determined by Eq. (5). Then, yu3 can be determined by Eq. (8). 3. Jacobian matrix 3.1. Jacobian matrix of 4-RRR manipulator Taking the time derivative of Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000738_tpas.1967.291749-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000738_tpas.1967.291749-Figure8-1.png",
        "caption": "Fig. 8. Regions of instability for different values of inertia.",
        "texts": [
            " The values of the system parameters and the quantities which were varied in each case are given in Table I. Variation in the region of instability due to a change in the amplitude of the stator applied voltages are shown in Fig. 7. The applied stator voltage V is decreased linearly with fR. That is V = fRVm, wherein the voltage Vm is normally 1.0 p.u. Figure 7 shows the contours for Vm = 0.8 p.u., 1.0 p.u., and 1.2 p.u. The effect upon machine stability due to a change in the inertia of the machine or machine-load combination is given in Fig. 8. Regions of instability are shown for H = 0.5 s,1.0 s, and 1.5 s. Te 0.5- 0 - -0.5- -0.5. 0.- 0.51 831 IEEE TRANSACTIONS ON POWER APPARATUS AND SYSTEMS JULY 1967 The contours given in Fig. 9 show an increase in the region of instability with an increase in the ratio Xad/ X,q. In other words, an increase in the maximum steadystate torque is accompanied by a larger region of !instability. With the machine parameters given in Table I, it was found that instability did not occur with Xad/ Xaq = 2. The 'increase in the region of instability due to an increase in stator resistance is shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002930_j.triboint.2016.03.017-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002930_j.triboint.2016.03.017-Figure2-1.png",
        "caption": "Fig. 2. Grid of flash temperature calculation.",
        "texts": [
            " As the surfaces velocity direction, u1 , and u2 , do not coincide with the x or y direction, the temperature distribution in two surfaces can be estimated with the stripes parallel to velocity direction of u1 and u2, respectively. The temperature profile along any stripe is same as that of an infinitely long band heat source which has a width equal to the stripe length and has the same heat flux profile along the stripe. Hence, the following mesh grids are taken to predict the surface temperature as illustrated in Fig. 2. In the present study, a newly developed ball-on-disc tribometer by Sichuan University is used to measure friction coefficient of mixed lubrication in elliptical contacts with arbitrary velocity vector, as shown in Fig. 3. Both the disc and ball can be independently driven by motorized spindle. The ball-spindle has two degrees of freedom that can move back and forth, and achieve pivot angle at 730\u00b0 around its axis. The disk-spindle always has two degrees of freedom including up-down and left-right"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003767_j.conengprac.2019.03.012-Figure12-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003767_j.conengprac.2019.03.012-Figure12-1.png",
        "caption": "Fig. 12. Quadrotor used for experiments.",
        "texts": [
            " Attitude and position tracking results are then presented for the same desired trajectories used for simulations. Finally, flipping of the quadrotor is shown to demonstrate the capabilities of the developed nonlinear robust control law. A brief description of the vehicle and the associated electronics is given here along with some details about the software (flight stack) used to finally implement the proposed control law. A modified version of a commercial-off-the-shelf (COTS) variablepitch quadrotor Assault Reaper 500 is used for carrying out experiments (see Fig. 12). It consists of a motor geared to the main drive shaft (gear ratio 14:90) and four rubber belts connected to the shaft that drive the four rotors. The commercial version comes with its own flight controller, radio control transmitter and receiver, and an electronic speed controller (ESC). The aforementioned hardware components are replaced with electronics that are relevant for this work. The ESC used in this set up is Castle Creations Phoenix Edge Lite 75A, 34 V ESC with built in 5 V battery eliminator circuit (BEC)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003831_tia.2020.3029997-Figure18-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003831_tia.2020.3029997-Figure18-1.png",
        "caption": "Fig. 18. (a) Measurement window drilled in end-cap, (b) Experimental platform.",
        "texts": [
            " The reason can be interpreted as: the \u201cT-type\u201d thermal model in either direction can only guarantee that the node temperature equals the average temperature in this direction, it will reduce the precision in the 2-D thermal analysis. Since the LP and the analytical methods are established from different perspectives, the values of estimation error depend on the several factors, i.e. the boundary conditions, the generated heat losses, the geometric size and the material thermal properties. The hybrid thermal model is further validated on the prototype machine with a rotor, as shown in Fig. 18. The ambient temperature is 24\u2103. The K-type probe thermocouples are installed in the winding, the end-winding, the stator yoke, the stator tooth and the frame. The noncontact infrared thermometer (Raynger ST80) is used to measure the PM temperatures through the measurement window drilled in the end-cap. The measurement window is sealed during the experiments to ensure the machine is totally enclosed. The data from the thermocouples are recorded by thermocouple data logger (Pico TC08) and thermometers (Fluke 52II)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002983_b978-0-12-811820-7.00008-2-Figure6.2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002983_b978-0-12-811820-7.00008-2-Figure6.2-1.png",
        "caption": "FIGURE 6.2 Illustration of the multi-scale phase-field framework for AM of alloys: (A) finite-element-based thermal model; (B) grain growth phase-field model; (C) sub-grain-scale phase-field model for solid phase transformation.",
        "texts": [
            " To highlight the major governing factors of the microstructure evolution and simplify the numerical model, the following overall assumptions are made: (1) The microstructure evolution processes have negligible effect on heat transfer and temperature distribution in the build, while the heat transfer is mainly affected by the heat conductivity and capacity of the material, as well as the AM parameters such as power, scanning probe size and scanning speed of the heat source; (2) The solidification and the development of grain structures take place in the high temperature regime followed by possible solute segregation and inclusions occur near grain boundaries, while the phase transformation and microstructure evolution inside grains take place in the low temperature regime with negligible grain structure change. With the assumptions above, the entire microstructure evolution model can be decoupled into three different sub-models on different length scales, as illustrated in Figure 6.2: (i) the macroscopic thermal model to obtain the temperature distribution and thermal history in the build sample during the whole AM process; (ii) the grain-scale solidification or grain growth phase-field model to study the grain morphology and texture development and/or solute distribution and segregation; (iii) the sub-grain-scale phase-field model to simulate the intra-granular phase transformations which may include diffusional transformations such as precipitation and diffusionless structural transformations, depending on the specific materials system"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003841_1.j059216-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003841_1.j059216-Figure6-1.png",
        "caption": "Fig. 6 FE model of the seat (a); LSTC Hybrid III model (b) and FE model of the belt (c).",
        "texts": [
            " Details of internal surfaces (b) and cargo and cabin zones (c) [43]. D ow nl oa de d by 1 93 .2 03 .9 .4 3 on O ct ob er 2 6, 2 02 0 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /1 .J 05 92 16 Concerning the seats, having a total mass of 34 kg [43,44], Quad4 and Tria3 shell element types have been used to model the seats\u2019 support system (entirely made of 70xx aluminum alloys), whereas Tetra4 3D element type has been used to model the polyurethane foam cushions [39], for a total of 53,932 nodes and 64,752 elements (Fig. 6a). Rigid connections have been used to link seats and rails. As aforementioned, a 50% Hybrid II and a 50% FAA Hybrid III male ATDs were used in the experiment. Features that distinguish a standard Hybrid III from a Hybrid II include a slouched spine sitting posture, a curved lumbar spine, and themass [54]. The slouched spine adapter in the standard Hybrid III resulted in a lower measured lumbar load than the Hybrid II. Generally, FAA Hybrid III results are more accurate and with lower variability in the measurements when compared with Hybrid II [55]",
            " Nevertheless, all the Hybrid II body parts and joints worked, allowing performing the comparison between recorded data and numerical dummy ones. The Hybrid III numerical dummy model has been found to be the most suitable for the current work purposes as it includes all human body parts that are useful, in the postprocess phase, for calculating the indices to assess the injury criteria provided by the reference standards. The LSTC/NCAC Hybrid III 50th percentile male dummy model [56,57], illustrated in Fig. 6b, has been used. This FE model consists of 276,008 nodes, 452,598 elements, solids, and shells. Both the experimental dummies have been modeled using the Hybrid III numerical dummy, and they have been correctly positioned following the AC25.562-1B (FAA (2006)) [46]. Moreover, it is imperative that, during an emergency landing, all passengers wear safety belts to ensure that they are not violently projected toward fuselage parts or other passengers, with fatal consequences. Aircraft safety belts\u2019 performance criteria are similar to those specified by the Federal Motor Vehicle Safety Standards for automobiles but also include a limit on pelvic force to prevent spinal injuries thatmay be caused by thevertical component of impact force. Therefore, the ATDs have been restrained on the seats by a torso belt oriented almost horizontally, thus avoiding any kind of dangerous movement. The modeled safety belt, Fig. 6c, consists of 305 nodes and 480 2D shell elements. The belts\u2019 material and properties are those supplied with the manikin model, which are valid for safety belts normally used in the automotive industry. As aforementioned in Sec. II, skin, stringers, and frames are made of carbon fibers infused in thermosetting matrix; instead a Fig. 3 Positioning of passengers\u2019 seat system (a), DAS (b), balancing mass (c), and accelerometers (d) [43]. D ow nl oa de d by 1 93 .2 03 .9 .4 3 on O ct ob er 2 6, 2 02 0 | h ttp :// ar c"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001423_j.jsv.2017.07.030-Figure13-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001423_j.jsv.2017.07.030-Figure13-1.png",
        "caption": "Fig. 13. Sun gear.",
        "texts": [
            "3 s data is used for the following analysis. The sampling frequency was set to be 7680 Hz to accommodate all interested frequency contents of this test rig. The whole set-up arrangement is shown in Fig. 12 [27]. In the experiment, tooth-missing and healthy condition sun gears are used for the following analysis. While, gear with a crack tooth, distributed and a broken tooth are used for further demonstrating the fault detection capability of the proposed scheme. The pictures of experimental sun gears are depicted in Fig. 13. The physical parameters of planetary gearbox are listed in Table 4 in which gear teeth, number of planet gears and the transmission ratios are given and calculated. In the experimental set-up, the ring gear of planetary gearbox is stationary and the sun gear is the input of the planetary gearbox system. Another very important calculation to the planetary gearbox is its characteristics orders. The characteristics orders [19,28,29] are listed in Table 5. Firstly, the tooth-missing fault of sun gear vibration response and corresponding rotational speed is plotted in Fig",
            " This result agrees well with the simulation conclusions and tells that the proposed phase angle based scheme is promising for fault detection under non-stationary operational conditions. Table 8 Sample entropy values of cosine phase angles for different faults. Conditions Healthy (30 Hz speed) Healthy & Speed-up 30 Crack (30 Hz speed) Crack & Speed-up 30 0.3307 0.3310 0.4399 0.4201 Conditions Broken (30 Hz speed) Broken & Speed-up 30 Wear (30 Hz speed) Wear & Speed-up 30 0.6291 0.6897 0.8555 0.8493 Fig. 24. Evaluation results of different faults. Furthermore, other types of faults, such as sun gear with a crack tooth, broken tooth and distributed wear, see the Fig. 13 (c)\u2013(e), are introduced to further test and verify the fault detection capability of the proposed scheme. The evaluation results of sample entropy are listed in Table 8 and Fig. 24. From Table 8 and Fig. 24, it can be found that the proposed scheme has promising abilities to detect other faults on planetary gearbox as well. For different faults scenarios in both constant (30 Hz) and speed-up cases, sample entropy results with cosine phase angles signals are well classified the different fault types"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002283_j.rcim.2017.10.003-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002283_j.rcim.2017.10.003-Figure9-1.png",
        "caption": "Fig. 9. Hypoid gear solid modeling by simulation process.",
        "texts": [
            " Generally, ABAQUS [44] is used for LTCA and ANSYS/LS_DYNA 45] is used for DTCA in this work. Before LTCA using FEM simulation oftware, the establishment of an accurate and efficient FEM model is o e m b a fl a o s g s t i h i d t L a w c 5 p 3 I c h m a o T w I m t [ 6 a t f I t 6 d s p w t m a v a r a o T m i f paramount importance to computation of the tooth contact strength valuations. This modeling mainly includes i) three-dimensional solid odel and ii) finite element meshing. To obtain a solid model, modeling y simulation process (as Fig. 9 ) based on the virtual machine tool is lways a main method. To get a high geometric accuracy, an accurate ank reconstruction is needed to be performed by some surface fitting nd optimization approaches [24,46,47] . Fig. 10 represents a general establishment of FEM model for LTCA f hypoid gear. The hexahedral finite element mesh and the entity egmentation technique are applied to maintain the effective contact earing of hypoid gear drive. To distinguish with the structured grid or wept mesh, above methods can divide the hypoid gear geometry into he simple geometric regions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001968_978-94-007-6101-8-Figure4.7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001968_978-94-007-6101-8-Figure4.7-1.png",
        "caption": "Fig. 4.7 Look at the cylindrical robot from above",
        "texts": [
            "2 Examples of Geometric Robot Models 67 0A1 = \u23a1 \u23a2\u23a2\u23a3 c1 \u2212s1 0 0 s1 c1 0 0 0 0 1 0 0 0 0 1 \u23a4 \u23a5\u23a5\u23a6 1A2 = \u23a1 \u23a2\u23a2\u23a3 1 0 0 0 0 0 1 0 0 \u22121 0 d2 0 0 0 1 \u23a4 \u23a5\u23a5\u23a6 2A3 = \u23a1 \u23a2\u23a2\u23a3 1 0 0 0 0 1 0 0 0 0 1 d3 0 0 0 1 \u23a4 \u23a5\u23a5\u23a6 The geometric model of the cylindrical robot mechanism with three degrees of freedom has the following form: 0A3 = 0A1 1A2 2A3 = \u23a1 \u23a2\u23a2\u23a3 c1 0 \u2212s1 \u2212d3s1 s1 0 c1 d3c1 0 \u22121 0 d2 0 0 0 1 \u23a4 \u23a5\u23a5\u23a6 The geometric robot model represents the pose (position and orientation) of the robot end-point coordinate frame with respect to the base reference frame. Let us displace our cylindrical robot for an angle \u03d11 in the positive direction and let us look at it from above as shown in Fig. 4.7. In this way we can only see the horizontal segment with the length d3. Let us draw also the base coordinate frame and the end-point frame, as determined in the DH procedure. The orientation of the robot end-point frame with respect to the base frame will be described by the matrix (2.19), where we have stressed that the elements of the rotation matrix are cosines of the angles between the pairs of axes appertaining to both coordinate frames. Let us remember that the three columns of the rotation matrix belong to the axes of the coordinate frame whose orientation is to be determined with respect to the frame with its axes belonging to the lines of the rotation matrix. Now we can simply read the angles between the corresponding pairs of the axes of both frames from Fig. 4.7 and write them into the homogenous transformation matrix: 68 4 Geometric Robot Model 0A3 = x3 y3 z3 \u23a1 \u23a2\u23a2\u23a3 cos\u03d11 cos 90\u25e6 cos(90\u25e6 + \u03d11) \u2212d3 sin \u03d11 cos(90\u25e6 \u2212 \u03d11) cos 90\u25e6 cos\u03d11 d3 cos\u03d11 cos 90\u25e6 cos 180\u25e6 cos 90\u25e6 d2 0 0 0 1 \u23a4 \u23a5\u23a5\u23a6 x0 y0 z0 The first two elements of the fourth column can be also simply read from Fig. 4.7, while the third element is evident from Figs. 4.5 or 4.6. In this way the same matrix was obtained as after multiplying the three DH matrices. Of course, this is only possible with such simple mechanism as the cylindrical robot. When developing geometric model of a robot with six degrees freedom, the Denavit-Hartenberg approach is advantageous. From this example we have clearly learned the meaning of the geometric model of a robot mechanism. As the third example we shall consider a spherical robot mechanism shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003090_j.mechatronics.2020.102388-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003090_j.mechatronics.2020.102388-Figure2-1.png",
        "caption": "Fig. 2. Parallel leg-wheeled mechanism.",
        "texts": [],
        "surrounding_texts": [
            "Mechatronics 69 (2020) 102388\nContents lists available at ScienceDirect\nMechatronics\njournal homepage: www.elsevier.com/locate/mechatronics\nAdaptive impedance control with variable target stiffness for wheel-legged\nrobot on complex unknown terrain\n\u2606\nKang Xu a , b , c , Shoukun Wang a , b , c , \u2217 , Binkai Yue a , b , c , Junzheng Wang a , b , c , Hui Peng a , b , c ,\nDongchen Liu a , b , c , Zhihua Chen a , b , c , Mingxin Shi a , c\na School of Automation, Beijing Institute of Technology, No. 5 South Zhongguancun Street, Haidian District, Beijing, 100081, PR China b Key Laboratory of Intelligent Control and Decision of Complex System, Beijing Institute of Technology, No. 5 South Zhongguancun Street, Haidian District, Beijing, 100081, PR China c Key Laboratory Ministry of Industry and Information Technology, Beijing Institute of Technology, No. 5 South Zhongguancun Street, Haidian District, Beijing, 100081, PR China\na r t i c l e i n f o\nKeywords: Wheel-legged robot Adaptive impedance control Variable target stiffness Force tracking Unknown terrain\na b s t r a c t\nWheel-legged robots operating on the ground experience real-time interactions with the complex unknown terrain, which may lead to tilting of the whole body and instability if no regulated effort is made. Maintaining a horizontal posture of the whole body with changes in the terrain geometry via impedance control (IC) that is widely used in many fields is desirable to be realized. However, because the stiffness and location of the terrain relative to the robot are not known in advance, the force-tracking error occur when using IC, which is the main cause of robot tilting. In this paper, an adaptive variable impedance control (AVIC) method is proposed to minimize the force-tracking error for the forces of each leg that are exerted on the body, thereby maintaining a horizontal posture of the whole body and improving the stability. This control method is applied by adjusting the target stiffness to compensate for terrain uncertainties. In terms of the existence of the dynamic force tracking error, the proposed control method also allows the robot to adapt to changes to track the desired force. The theoretical analysis of the stability of the AVIC was demonstrated through a stable force-tracking application. The numerical and experimental results were compared to those obtained using IC, and the proposed control method was validated on complex, unknown terrain.\n1\nl t i u i a i h\ns H f s w s\no t e i\nt u [ m\ns [ t i f r v p\nh R 0\n. Introduction\nThe wheel-legged robot combines the strengths of wheeled and egged robots, and this hybrid robot has many advantages over both ypes of robots [1\u20133] , including high motion efficiency, more flexibilty, and low energy consumption. Robots that operate on complex and\nnknown terrain while maintaining a horizontal body and stability are\nn great demand in many applications, such as material transportation, nd disability assistance [ 4 , 5 ]. These robots must be capable of adaptng to unknown terrain geometries, because interactive tasks cannot be\nandled well by pure position or force control [6\u20138] .\nThe impedance control method has been widely employed for the tability control of robots after the pioneering work of Hogan [9\u201311] .\nowever, the force-tracking error exist due to the unknown terrain inormation [ 12 , 13 ]. For a wheel-legged robot, this error prevents the deired force of each leg exerted on the body from being tracked well,\nhich may result in body tilting and instability [14] . Under this circumtance, the robot cannot maintain a relative horizontal posture when it\n\u2606 This paper was recommended for publication by Associate Editor Prof. Feliu Vice \u2217 Corresponding author.\nE-mail address: bitwsk@bit.edu.cn (S. Wang).\nttps://doi.org/10.1016/j.mechatronics.2020.102388 eceived 6 May 2019; Received in revised form 4 April 2020; Accepted 25 May 2020 957-4158/\u00a9 2020 Published by Elsevier Ltd.\nperates on complex unknown terrain [15] , which may cause damage to he carried load. Therefore, to ensure the body level in unknown terrain, liminating the force-tracking error arising from impedance control (IC) s of great significance for robots [ 16 , 17 ].\nTo this end, many efforts have been made to minimize the forceracking error and enhance the force-tracking performance of IC against ncertainties (i.e., the unknown stiffness and location of the terrain) 18] . These efforts can be roughly divided into two classes: (1) adjust-\nent of the reference trajectory, and (2) variable impedance adaption.\nTo adjust to the reference trajectory, some studies have focused on traightforward adjustment to the reference trajectory. For instance, in 19] , a nonlinear model reference adaptive controller was used to esimate the reference trajectory and provide a desired stable impedance n Cartesian coordinates for the robot end-effector to track the desired orce. The other studies were mainly conducted to indirectly adjust the eference trajectory by identifying the stiffness and location of the enironment to reduce the force tracking error. Villani and Canudas pro-\nosed a control law by scaling the trajectory as a function of the esti-\nnte.",
            "m a m a u b t [\np a p a a w c t c m d [ m o a r p b t t\nl p r i o c i o\n2 e\n2\ns s u o w T\np\nw b t i t\nt o\nated environment stiffness [20] . Estimating the environment stiffness\nnd adjusting the controller gain to compensate for unknown environ-\nent stiffness were proposed in [21] . In addition, some researchers have\nlso made efforts to offer intelligent force control to compensate for the ncertainties by using neural network [ 22 , 23 ]. These approaches were ased on estimations. Thus, force-tracking error was is unavoidable, and he dynamic physical properties at the time of contact were not reflected 24] .\nVariable impedance adaption aims to modify the target impedance arameters based on the force feedback [25\u201328] . For example, voltage daptive impedance force control was proposed in which the impedance arameters were adaptively regulated by a gradient descent algorithm to djust the human force when performing therapeutic exercises [29] . Gan nd Duan [30] proposed an adaptive variable impedance control scheme\nhere the unknown environment and robot dynamic uncertainties were\nompensated for by adjusting the damping parameter for a zero-stiffness arget impedance scenario. Furthermore, the optimal variable stiffness ontrol strategies of impedance control based on the utility of an opti-\nal control formulation were demonstrated for exploiting the system\nynamics to enhance the force-tracking performance by Braun et al. 31] . These methods of variable impedance adaptation aimed to mini-\nize the force-tracking errors while considering the physical properties\nf the contact. However, adaptive control methods via online adaptive djustment of the impedance parameters to reduce the error have been arely reported [ 32 , 33 ]. Therefore, based on the discussion above, we ropose adaptive impedance control with the variable target stiffness to etter track the desired force and minimize the force-tracking error in erms of the unknown terrain information. The primary contributions of his paper are summarized as follows.\n(1) In the case of an unknown stiffness and position of the terrain,\nthe force-tracking error is reduced by using adaptive variable impedance control (AVIC). For a wheel-legged robot, the force from each leg exerted on the body can track the desired force well. (2) The desired dynamic force can be tracked sufficiently with the\nproposed control algorithm, which allows the robot to adapt to the load changes. (3) The effectiveness of the proposed control algorithm was verified\nby simulations and experiments, and thus, the robot could be applied in exigent fields to stably carry a load.\nThe rest of this paper is organized as follows. In Section 2 , the wheelegged robot and the system model of the robot and environment are\nresented. The existence of force-tracking errors on the unknown terain is demonstrated in Section 3 . Section 4 introduces the adaptive mpedance control with variable stiffness, and the theoretical analysis n the stability of the proposed control method is also clarified. This ontrol algorithm is verified by a series of simulations and experiments n Section 5 . Finally, conclusions are made to summarize the main work f this paper in Section 6.\n. Wheel-legged robot and system model of robot and nvironment\n.1. BIT-NAZA\nThe wheel-legged robot used in this study, called BIT-NAZA (as hown in Fig. 1 ), is an electric parallel wheel-legged robot, which conists of four 6-DOF (six-degree-of-freedom) parallel platforms that are sed as legs of the robot, and four actuated wheels that are mounted n the above top of the platform as end-effectors. The presence of both\nheel and leg enables the robot more flexible and diverse movements. he main parameters of BIT-NAZA are listed in Table 1 .\nThe goal of BIT-NAZA is to execute a transportation task with comliant interaction and maintain a level posture through the expansion of\nIt is mainly composed of an inverted parallel 6-DOF platform and a heel. Each electric cylinder in the platform is connected to the robot ody through the upper Hooke joint, and the wheel is fixed to the base hrough the lower Hooke joint. The driving motor of the foot-end wheel s fixed to the robot body, and the motor drives the wheel and reducers o move through the drive link.\nCompared with the previous prototype, we improved the structure of his parallel leg-wheeled mechanism in two main aspects: 1) The length f the outer two electric cylinders were reduced such that the foot-end",
            "p m t d t t\n2\ne m i t a {\n\ud835\udc39\nw i i t m t f\n\ud835\udc39\nw a\n3\nc\np t o n\nt l t t P q t T t\n3\nt m g o l q h l o f w c i l r I\nz m l s t\nosition of the leg extends 8 cm outside; 2) the wheel drive motor is\noved to the body. The purpose of the first improvement is to increase he support area of the robot, thereby improving the stability margin uring the movement of the robot. The second improvement is to reduce he weight of the legs by moving the motor to the body, which increases he flexibility of the robot during locomotion.\n.2. Equivalent interaction model of the robot leg and environment\nThe interaction system model of the robot leg and environment is stablished and simplified in this section. The robot and environment are\nodeled by a second order mass-spring-damper system, which is shown n Fig. 3 . Since the forces on the robot in all directions are decoupled, he force in the vertical direction (z-axis) is obtained. The frame { B } is\nreference coordinate system that is attached to the robot. The frame\nI } is the inertial coordinate system.\nThe contact force between robot and terrain can be expressed as\n\ud835\udc52 \ud835\udc67 = \ud835\udc40 \ud835\udc52 \ud835\udc67 \u0394?\u0308? + \ud835\udc35 \ud835\udc52 \ud835\udc67 \u0394?\u0307? + \ud835\udc3e \ud835\udc52 \ud835\udc67 \u0394\ud835\udc4b, (1)\nhere \ud835\udc40 \ud835\udc52 \ud835\udc67 , \ud835\udc35 \ud835\udc52 \ud835\udc67 , and \ud835\udc3e \ud835\udc52 \ud835\udc67 are the mass, damping, and stiffness matrices\nn z direction, respectively, and \ud835\udc39 \ud835\udc52 \ud835\udc67 is the environment-to-robot force n z direction with respect to { I }. During actual motion, the speed of he environment deformation \u0394?\u0307? and the acceleration of the environ-\nent deformation \u0394?\u0308? approach zero. The interaction model between he robot and terrain can then be simplified into a spring system, as ollows:\n\ud835\udc52 \ud835\udc67 =\n{\n\ud835\udc3e \ud835\udc52 \ud835\udc67\n( \ud835\udc4b\n\ud835\udc51 \ud835\udc67 \u2212 \ud835\udc4b \ud835\udc52 \ud835\udc67\n) , \ud835\udc4b\n\ud835\udc51 \ud835\udc67 > \ud835\udc4b \ud835\udc52 \ud835\udc67\n0 , \ud835\udc4b \ud835\udc51 \ud835\udc67 \u2264 \ud835\udc4b \ud835\udc52 \ud835\udc67\n, (2)\nhere the force of the environment \ud835\udc39 \ud835\udc52 \ud835\udc67 with respect to (w.r.t) { I } can be\nccurately obtained by the external sensor.\nAVIC1\nAVIC2\nAVIC3\nAVIC4\nLeg1\nLeg2\nLeg3\nLeg4\nPostu\nEventdriven\n+ \u2212\n+\n+\nRobot Kinematics\nSingle Leg\niN iN\n,\u03b1 \u03b2\nid zF\nie zF iF zE\n1c zX\n2c zX\n3c zX\n4c zX\niAtt zX\n1c zX\n2c zX\n3c zX\n4c zX\nF\n( 1,2,3,4)ie zF i =\n. Control framework based on AVIC\nThe control framework of BIT-NAZA mainly consists of event-driven ontroller, AVIC controller and posture controller, which is shown Fig. 4 .\nBased on the force information \ud835\udc39 \ud835\udc52 \ud835\udc56 \ud835\udc67 ( \ud835\udc56 = 1 , 2 , 3 , 4) in z direction and ostural angles (i.e., roll \ud835\udefc, pitch \ud835\udefd), event-driven controller is designed o detect the relative leg that is disturbed by the terrain geometries. After btaining the force-tracking error \ud835\udc38\n\ud835\udc39 \ud835\udc56 \ud835\udc67 ( \ud835\udc56 = 1 , 2 , 3 , 4) in z direction and leg\number of motion \ud835\udc41 \ud835\udc56 ( \ud835\udc56 = 1 , 2 , 3 , 4) , four AVIC controllers are employed o track the desired force \ud835\udc39 \ud835\udc51 \ud835\udc56 \ud835\udc67 ( \ud835\udc56 = 1 , 2 , 3 , 4) in z direction by control the egs with the commanded position trajectory ?\u0304?\n\ud835\udc50 \ud835\udc56 \ud835\udc67 ( \ud835\udc56 = 1 , 2 , 3 , 4) in z direc-\nion. But for the quadruped robot, when one leg operates, it will induce he affects to the other legs, which also lead to the robot body titling. osture controller is applied to eliminate the affect with the command uantity \ud835\udc4b\n\ud835\udc34\ud835\udc61 \ud835\udc61 \ud835\udc56 \ud835\udc67 ( \ud835\udc56 = 1 , 2 , 3 , 4) in z direction. The final commanded posi-\nion trajectory \ud835\udc4b \ud835\udc50 \ud835\udc56 \ud835\udc67 ( \ud835\udc56 = 1 , 2 , 3 , 4) in z direction are as input of each leg.\nhe measured position trajectory \ud835\udc4b \ud835\udc4e \ud835\udc56 \ud835\udc67 ( \ud835\udc56 = 1 , 2 , 3 , 4) in z direction control\nhe posture of robot body in real time.\n.1. Event-driven control for BIT-NAZA\nEvent-driven controller aims to detect the relative leg that is disurbed by the terrain geometries. In practical application, an inertial\neasurement unit (IMU), which measured the roll, pitch, and yaw an-\nles of the body, was mounted on the robot body. When robot moved n uneven terrain, the posture angle and the generalized force of each eg exerted on the body was altered if no adjustment was made. For the\nuadruped robot and force tracking of each leg on the body, achieving a orizontal posture by simultaneously tracking the desired force on each\neg is difficult due to the particularity of the force changes while driving ver uneven terrain. For example, if LF(2) is subjected to an increase in orce due to environmental geometric changes, then the force on RH(4)\nill also increase accordingly, and the forces of LH(1) and RF(3) will be\norrespondingly reduced. Thus, achieving a force balance by performng force-tracking control on each leg is difficult. Hence, detecting which eg caused the body tilt is not only the key to eliminating the tilt, it also educes the energy waste. There are four special scenarios based on the MU information, described as follows.\n(1) pitch > 0 & roll > 0\nFor a quadruped robot, the pitch and roll angles are greater than ero, which is caused by LH(1) driving on the raised terrain. At this\noment, the forces of LH(1) and RF(3) exerted on the body become arger, and the forces of LF(2) and RH(4) exerted on the body become maller. Hence, the force of LH(1) is regulated, and the desired force is racked to lower the body tilt.\nre Control\nRobot Body\n,\u03b1 \u03b2\n1e z\n2e zF\n3e zF\n4e zF\n1a zX\n2a zX\n3a zX\n4a zX"
        ]
    },
    {
        "image_filename": "designv10_5_0002260_tmag.2017.2668845-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002260_tmag.2017.2668845-Figure2-1.png",
        "caption": "Fig. 2. On-load field and flux density distributions at d-axis under different temperature. (a) Field distributions. (b) Flux density distributions.",
        "texts": [
            " Characteristics of the Magnets In the linear part of the B-H curve of the magnets employing NdFeB materials, for temperature below about 100\u00b0C, the PM remanence Br and coercive force Hc vary linearly with temperature, which can be expressed as [7], [8]:  aBrAr TTsBB  (1)  aHcAc TTsHH  (2) where, BrA and HcA are the remanence and coercive force at normal ambient temperature TA, and sB and sH are the slope of Br- and Hc-temperature characteristics, respectively. The typical values of sB and sH of NdFeB magnets are \u22120.11%/\u00b0C and \u22120.62%/\u00b0C, respectively. The temperature in the magnets of 25\u00b0C (ambient temperature), 63\u00b0C and 75\u00b0C, respectively, will be discussed in this paper. Overall, the raise of temperature will degrade Br and Hc, thus cause the variation of field distributions and flux density distributions, especially when armature currents are applied, as shown in Fig. 2. This will further lead to different electromagnetic performances, e.g., armature reactions, leakage fluxes, et al. Especially, the flux density distributions are directly related to iron losses, which in return, show influences on the temperature. B. Phase Fluxes and Torque Outputs Firstly, the influences of temperature on the no-load phase fluxes and cogging torque can be neglected. Secondly, under the on-loaded condition, the phase-A flux values increase slightly with the raise of temperature as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003833_j.triboint.2020.106710-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003833_j.triboint.2020.106710-Figure3-1.png",
        "caption": "Fig. 3. Schematic diagram of the ball-on-disc device for friction measurement.",
        "texts": [
            " The curves of shear stress versus shear rate for grease Li/ 32, Li/460, PU/85 and PU/220 were obtained by using the DHR-3 rheometer at 40 \u25e6C, as shown in Fig. 2. The Herschel-Bulkley model (Eq. (1)) was used to fit the experimental results by the least square method to determine the rheological parameters of the grease. For more detailed experimental methods and procedures, please refer to Ref. [28]. Other grease properties were provided by the grease supplier. The friction tests for grease lubrication were measured on ball-ondisc apparatus, illustrated schematically in Fig. 3(a), where a steel ball with a radius of 15 mm was loaded and rubbed against a steel disc in rolling/sliding conditions. The geometry, material and surface roughness parameters of ball and disc in this study are shown in Table 2. This device allows the measurement of grease friction coefficient in ball-ondisc configuration, covering different ranges of entrainment speed, load and slide/roll ratio (SRR). The definitions of entrainment speed and SRR are as follows: u= uball + udisc 2 (10) SRR= 2\u22c5 |uball + udisc| uball \u2212 udisc (11) Before the friction tests, a certain thickness of grease is applied to the disc on a predetermined track with a grease bar",
            " Then the relevant experimental conditions, such as entrainment speed, load and SRR, are set. It should be noted that after the grease has been cut through the disk for 1 turn, most of the grease will be squeezed to both sides of the lubrication area, and the recirculation effect of the grease is not obvious. Therefore, as the number of disk rotations increases, insufficient grease supply in the inlet area will be formed. Aimed at ensuring full film lubrication condition, a grease scoop to channel the grease into the contact track is used as shown in Fig. 3(b) The test conditions for the friction coefficient versus SRR curves (traction curves) and the friction coefficient versus entrainment speed Fig. 1. Initial surface profile of ball. J. Yang et al. Tribology International 154 (2021) 106710 curves (Stribeck curves) are listed in Table 3. The relating average values calculated from the two measurements are then plotted into curves. Above all some preliminary sample cases have been analyzed to validate the correctness of the grease EHL model in point contact. And the results acquired from simulation are compared with the available J. Yang et al. Tribology International 154 (2021) 106710 results found in the referring literatures. The central film thickness and the minimum film thickness solved by the present model are compared with those obtained by available numerical solutions from Refs. [13] demonstrated in Fig. 3. The same main input parameters referring to Ref. [13] are listed in Table 4. The present model is based on a solution domain of \u2212 2\u2264X \u2264 2 and \u2212 2\u2264Y \u2264 2, and the computational grid of the solution domain is set to be 257 * 257. From the comparisons in Fig. 4, we can see that the minimum film thickness and the central film thickness solved by the present model fit well with the results obtained from Refs. [13]. The difference between the simulation results of the two model is basically within the error range of 20 nm"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003079_s00521-020-04821-x-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003079_s00521-020-04821-x-Figure1-1.png",
        "caption": "Fig. 1 Furuta pendulum system",
        "texts": [
            " The structure is composed of an arm, attached to a motor, rotating in the horizontal plane. At the end of the arm, a pendulum is attached with a free rotational movement in the vertical plane. The motion control of such systems becomes difficult because the control of the overall system should be achieved from the actuated joints to the nonactuated joints [3]. Moreover, the presence of extraneous disturbance in the system has made the control design more complicated. The rotary inverted pendulum (Fig. 1), which was first introduced by Furuta et al. [4], contains well-known underactuated dynamics, and many reports about its stabilization can be found. Most of the controls of the rotary inverted pendulum fall into one of the several categories. For example, some have considered the problem of Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00521-020-04821-x) contains supplementary material, which is available to authorized users. & Seyed Hassan Zabihifar zabihifar@student",
            " The dynamic model of the Furuta pendulum in Euler\u2013Lagrange form [25, 26] can be written as: M\u00f0q\u00de\u20acq\u00fe C\u00f0q; _q\u00de _q\u00fe Gm\u00f0q\u00de \u00bc U \u00f01\u00de where q \u00bc \u00bdq0 q1 T 2 IR2 is a vector of joint positions, M\u00f0q\u00de 2 IR2 2 is the symmetric positive definite inertia matrix, c\u00f0q; _q\u00de _q 2 IR2 is the vector of centripetal and Coriolis torques, Gm\u00f0q\u00de 2 IR2 is the vector of gravitational torques, and U \u00bc \u00bdu 0 T 2 IR2 is the vector of input torques, with u 2 IR being the torque applied to the arm. In particular, the model of the Furuta pendulum has the following components: q \u00bc q0 q1 ; M\u00f0q\u00de \u00bc I0 \u00fe m1\u00f0L20 \u00fe l21 sin 2 q1\u00de m1l1L0 cos q1 m1l1L0 cos q1 J1 \u00fe m1l 2 1 \" # C\u00f0q; _q\u00de \u00bc 1 2 m1l 2 1 sin\u00f02q1\u00de _q1 m1l1L0 sin q1 _q1 \u00fe 1 2 m1l 2 1 sin\u00f02q1\u00de _q0 1 2 m1l 2 1 sin\u00f02q1\u00de _q0 0 2 64 3 75 Gm\u00f0q\u00de \u00bc 0 m1gl1 sin q1 ; U \u00bc u 0 The coordinate system and notations are described in Fig. 1. We will assume that friction is negligible. I0 Inertia of the arm L0 Total length of the arm m1 Mass of the pendulum l1 Distance to the center of gravity of the pendulum J1 Inertia of the pendulum around its center of gravity q0 Rotational angle of the arm q1 Rotational angle of the pendulum u Input torque applied on the arm g The gravity The controller is required to serve a twofold control objective. The first objective is to stabilize the pendulum in its upright position at the origin from an initial condition in the upper half plane (i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002213_j.mechmachtheory.2014.06.006-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002213_j.mechmachtheory.2014.06.006-Figure6-1.png",
        "caption": "Fig. 6. State 2 of the derivative queer-square mechanism (\u03b11 b 0, \u03b12 b 0, \u03b211 = \u03b212, \u03b221 = \u03b222).",
        "texts": [
            " Angle ranges for state 1 are demonstrated as \u03b11N0;\u03b211 \u00bc \u03b212b0 \u03b12N0;\u03b221 \u00bc \u03b222b0 : \u00f024\u00de In state 1, the limb1s, limb1p, limb2s and limb2p have a higher location with regard to the base, and the platform is located lower than the limb1s, limb1p, limb2s and limb2p, as illustrated in Fig. 5. In state 2, the angles \u03b11 and \u03b12 both are negative that lead to limb1s and limb2s relatively lower than the base. The angle ranges of the derivative queer-square mechanism in state 2 satisfy \u03b11b0;\u03b211 \u00bc \u03b212N0 \u03b12b0;\u03b221 \u00bc \u03b222N0 : \u00f025\u00de In state 2, the limb1s, limb1p, limb2s and limb2p are lower than the base, and the platform occupies a higher altitude compared to the limb1s, limb1p, limb2s and limb2p, as illustrated in Fig. 6. By combining the reciprocal screw of the platform constraint\u2013screw system in Eq. (21) and the specific angle relations in Eq. (23), platform motion\u2013screw system in states 1 and 2 is obtained as S f n o \u00bc S f1 \u00bc 0 0 0 1 1 0\u00bd T n o : \u00f026\u00de Since the cardinal number of the platform motion\u2013screw system, as the dimension of the spanned subspace, equals to one, the platform of the derivative queer-square mechanism has mobility one in states 1 and 2. Furthermore, the first three components in the platform motion\u2013screw system in states 1 and 2 are equal to zero"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001867_j.msec.2014.03.012-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001867_j.msec.2014.03.012-Figure9-1.png",
        "caption": "Fig. 9. CVs of Hb-PSMA-g-3ABA/MWCNTs/CPE in 0.1 M PBS (pH 7.0) containing different concentrations of H2O2 0.0 (a), 30.0 (b), 40.0 (c), 60.0 (d), 80.0 (e) and 100.0 (f) \u03bcM at a scan rate of 0.1 V s\u22121.",
        "texts": [
            " The Hb-PSMA-g-3ABA/MWCNTs/CPE was stored at 4 \u00b0C, and the stability was investigated by measuring the cyclic voltammogram periodically. The results indicated that the peak potentials and currents of Hb-PSMA-g-3ABA/MWCNTs/CPEwere stable for twoweeks and then decreased gradually. Also, the cyclic voltammetric peak potentials appeared at the same position with the peak current decreased 20% compared with the initial response after 1 month. 3.4. Electrocatalytic reactivity of modified electrode The electrocatalytic activity of the Hb-PSMA-g-3ABA/MWCNTs/CPE towards reduction of H2O2 was first investigated by CV (Fig. 9). When H2O2was added in the solution, therewas a disappearance of the oxidation peak and an increase of the reduction peak depending on the concentration of H2O2 in solution. This result confirms that Hb adsorbed on PSMA-g-3ABA/MWCNTs/CPE had a pseudo peroxidase activity. A possible mechanism of reaction of H2O2 catalyzed by the Hb-PSMA-g3ABA/MWCNTs/CPE is postulated as follows: [HbFe(III)] + H+ + e\u2212 \u2194 [HbFe(II)] 2[HbFe(II)] + H2O2 + 2H+ + 2e\u2212 \u2194 2[HbFe(III)] + 2H2O According to above proposedmechanism, HbFe(II) generated on the electrode was chemically oxidized by H2O2, and the produced HbFe(III) was reduced again at the electrode in a catalytic cycle"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000317_1.2890112-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000317_1.2890112-Figure1-1.png",
        "caption": "Fig. 1 Coordinate systems f",
        "texts": [
            " The faceobbing cutter head, which is more complicated than the faceilling cutter head, has z0 sets of blade groups, each consisting of t least an inner and an outer blade that generate convex and oncave flanks, respectively, and are arranged in a strictly defined elative position for continuous indexing. In a two-blade group pplication, the pitch points of the inner and outer cutter edges are n the same circle, but for a three-blade group cutter head, the adii of the pitch points must be modified for appropriate tooth hickness. Figure 1 shows the coordinate systems for a faceobbing cutter head that can be used to simulate Oerlikon\u2019s FS, PIRON\u00ae cutter heads or Gleason\u2019s TriAC\u00ae cutter head. Even though the cutting edge is generally straight lined, ircular-arc blades may also be used for profile crowning. Assumng that the blade edge rl u is represented as a function of the ariable u in the coordinate system Sl, the position vector of the utter blade in the coordinate system of cutter head St is repre- ented as 62604-2 / Vol. 130, JUNE 2008 om: http://mechanicaldesign"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002838_978-3-319-54169-3-Figure5.2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002838_978-3-319-54169-3-Figure5.2-1.png",
        "caption": "Fig. 5.2 Slider-crank mechanisms: a simple, b eccentric",
        "texts": [
            ", \u03d5 \u2212 \u03b3 expression is obtained as ( c2 \u2212 w2 \u2212 r2 \u2212 (p \u2212 yB)2 \u2212 2r(p \u2212 yB) cos \u03b3 )2 = 4w2r2(1 \u2212 cos2 \u03b3), (5.10) i.e., A2 cos 2 \u03b3 \u2212 A1 cos \u03b3 + A0 = 0, (5.11) 5.1 Structural Synthesis of the Cutting Mechanism 145 where A = c2 \u2212 w2 \u2212 r2 \u2212 (p \u2212 yB)2, A0 = A2 \u2212 4w2r2, A1 = 4Ar(p \u2212 yB), A2 = 4r2 ( (p \u2212 yB)2 + w2 ) , (5.12) and p is a constant distance between fixed points O1 and O2 in y direction. Solving the quadratic equation (5.11) for cos\u03b3 and substituting into Eqs. (5.7) with (5.6), the y \u2212 \u03d5 relation follows. In Fig. 5.2a the simple and in Fig. 5.2b the eccentric slider-crank mechanisms are plotted. The mechanisms differ as the distance between the fixed point O and the piston position is different. In Fig. 5.3 the displacement-angle relations for: (a) simple (5.6), (b) eccentric (5.3) and (c) two slider-crank (5.7) mechanisms are plotted. It is assumed that for the simple and eccentric slider-crankmechanism the length of the leading shaft and of the connecting rod are equal for the both mechanisms. The dimensions of the two joined slider-crank mechanisms are: a = 0.08, b = 0.32, c = 0.14, r = 0.20, g = 0.24, h = 0.18, l = 0.20, p = 0.12, w = 0.16 and the cutting depth is \u03b4 = 0.12. In our consideration the common assumption used for comparing the three mechanisms is that the cutting depth has to be equal and the cutting angle is calculated from the lowest position of the slider. In Fig. 5.2 the full line indicates the motion of the slider in the sheet (where the shaded area is for cutting) and the dotted line shows the 146 5 Dynamics of Polymer Sheets Cutting Mechanism Fig. 5.3 yB \u2212 \u03d5 diagrams for a simple slider-crank mechanism (Fig. 5.2a), b eccentric slider-crank mechanism (Fig. 5.2b), and c yE \u2212 \u03d5 diagram for two-joined slider-crank mechanism (Fig.5.1) with following notation: shaded area - cutting, dotted line - slider in the sheet, full line-slider out of sheet motion of the slider out of the sheet. Comparing the diagrams in Fig. 5.3, it can be concluded: 1. Cutting lasts more longer with the simple and eccentric slider-crank mechanism than with the two joined slider-crank mechanism. 2. The interval in which the slider (cutting tool) is above the cutting object is much longer for the two joined slider-crankmechanism than for the simple and eccentric one"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003076_tmag.2019.2955884-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003076_tmag.2019.2955884-Figure2-1.png",
        "caption": "Fig. 2. Predicted flux flow patterns of the exterior-rotor PM-SRM.",
        "texts": [
            " 1 depicts the configuration of the proposed exteriorrotor PM-SRM with multiple teeth structures. The motor is composed of three phases, each of which has four concentrated windings. Each stator pole consists of four small teeth and the rotor comprises 50 teeth, so the motor has a 48/50-tooth configuration. Six PMs are embedded inside the gap between the end teeth of the neighboring stator poles, all of which have the same magnetization direction. Table I lists the main dimensions and parameters of the proposed PM-SRM, PMless SRM, and a classical external rotor 12/10-pole SRM. Fig. 2 illustrates the flux flow patterns of the proposed PM-SRM. Under zero excitation current, the flux of the PMs 0018-9464 \u00a9 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. does not cross the air gaps and travels through the stator core. Once a phase is excited, the flux generated by the windings enters the air gaps and forces the PMs flux to enter the air gaps and close through the rotor back iron"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001859_1.4864957-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001859_1.4864957-Figure6-1.png",
        "caption": "FIGURE 6: Design for incorporation of ultrasonic porosity sensor into DMLS machine.",
        "texts": [
            "5%) in total porosity, and should be sensitive enough to detect process changes that cause such a change in the material porosity. One clear conclusion taken from both the XRCT images as well as the measurements of the individual cylinders cut from each disk is that the porosity in these samples is not uniformly distributed; the samples have clear local variations in porosity, both in the build direction and in the plane of each build. We next plan to integrate an ultrasonic transducer into a DMLS machine. This will be done by adding two smaller build plates on top of the standard metal DMLS build plate, as shown in Figure 6. The middle plate will hold the ultrasonic transducer and wire. A sacrificial part, with a geometry amenable for ultrasonic wavespeed measurements, will be built on the top plate, along with whatever parts are being fabricated. The ultrasonic wavespeed in this part will be measured after each layer is melted, as a means of process monitoring. 1203 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 202"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003363_s12540-019-00563-1-Figure12-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003363_s12540-019-00563-1-Figure12-1.png",
        "caption": "Fig. 12 Schematic of the microstructure formation mechanism of wire-arc additively manufactured Ti\u20136Al\u20134V alloy as a function of the cooling rate",
        "texts": [
            " The dislocations function as nucleation sites for fine \u03b1 grains along the prior \u03b2 grain boundary during the subsequent welding processes. The cooled specimen has a smaller grain size (due to the rapid cooling rate) than the origin specimen. As a result, the cooled specimen has a higher Vickers hardness and tensile strength than the origin specimen. This difference in mechanical properties is due to the difference in the microstructure formation behavior of grain boundary \u03b1 and Widmanst\u00e4tten structure at different cooling rates. Figure\u00a012 illustrates the microstructure formation mechanism of wirearc additively manufactured Ti\u20136Al\u20134V alloy as a function of cooling rate. After the WAAM process, prior \u03b2 grains are formed during the solidification process. Grain boundary \u03b1 is formed along the prior \u03b2 grain boundary during subsequent cooling. At grain boundary \u03b1, fine \u03b1 grains nucleate and grow into prior \u03b2 grain inside the region. At the same time, \u03b1 and \u03b1\u2032 grains nucleate and grow rapidly inside the prior \u03b2 grains. The microstructure varies depending on the 1 3 cooling rate"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003091_j.mechmachtheory.2020.103989-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003091_j.mechmachtheory.2020.103989-Figure1-1.png",
        "caption": "Fig. 1. Equivalent lubrication model for the spur gear pair.",
        "texts": [
            " When the non-Newtonian characteristics and the squeeze effect of lubricating oil are considered, the EHL problem of the line contact is governed by the one-dimensional transient Reynolds equation [28] : \u2202 \u2202x [( \u03c1 \u03b7 ) e h ( x, t ) 3 \u2202 p ( x, t ) \u2202x ] = 12 u r ( t ) \u2202 ( \u03c1\u2217h ( x, t ) ) \u2202x + 12 \u2202 ( \u03c1e h ( x, t ) ) \u2202t (4) where ( \u03c1/\u03b7) e = 12( \u03b7e \u03c1\u2032 e /\u03b7 \u2032 e \u2212 \u03c1 \u2032\u2032 e ) , \u03c1 \u2217 = [ \u03c1\u2032 e \u03b70 ( u g \u2212 u p ) + \u03c1e u p ] / u r , \u03c1e = 1 h \u222b h 0 \u03c1dz, \u03c1 \u2032 e = 1 h 2 \u222b h 0 \u03c1 \u222b z 0 dz \u2032 \u03b7\u2217 dz, \u03c1 \u2032\u2032 e = 1 h 3 \u222b h 0 \u03c1 \u222b z 0 z \u2032 dz \u2032 \u03b7\u2217 dz, 1 \u03b7e = 1 h \u222b h 0 dz \u03b7\u2217 , 1 \u03b7 \u2032 e = 1 h 2 \u222b h 0 zdz \u03b7\u2217 . where p and h are contact pressure and film thickness within the contact area, respectively; ( \u03c1/ \u03b7) e , \u03c1\u2217 and \u03c1e are used to characterize the variation of viscosity and density along z-direction; x is the direction of the fluid movement; and t stands for time. For one-dimensional line contact, the oil film thickness is composed of three parts, namely the rigid body displacement, the geometric gap and the elastic deformation, as illustrated in Fig. 1 . The equation for oil film thickness h is described by h ( x, t ) = \u2212h 0 ( t ) + x 2 2 R ( t ) + \u03b4( x, t ) (5) where h 0 ( t ) is the rigid body displacement. The normal pressure distributed by any arbitrary manner is shown in Fig. 2 . According to elastic half-space theory, the elastic deformation \u03b4 of the two contact bodies loaded by the normal pressure can be calculated by \u03b4( x, t ) = \u2212 4 \u03c0E \u2032 \u222b x out x in ln \u2223\u2223\u2223\u2223x \u2212 x \u2032 x 0 \u2223\u2223\u2223\u2223p ( x \u2032 , t ) dx \u2032 (6) where E \u2032 = 2 / ( ( 1 \u2212 v 2 p ) / E p + ( 1 \u2212 v 2 g ) / E g ) is the equivalent modulus of elasticity; p ( x \u2032 , t ) is the normal pressure at the location x \u2032 and time t; x in and x out are the inlet and outlet positions of the contact zone, respectively; x 0 is the reference distance where the elastic deformation is zero"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001968_978-94-007-6101-8-Figure5.5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001968_978-94-007-6101-8-Figure5.5-1.png",
        "caption": "Fig. 5.5 Two poses of the second and third segment: \u201celbow up\u201d and \u201celbow down\u201d",
        "texts": [
            " The ratio of the segment lengths 1 : 1 at selected constant collective length of both segments, results in maximal volume of the robot workspace [1]. Equation (5.24) is rewritten as: 5.2 Inverse Model 79 r2 = 2a2 2 \u2212 2a2 2 cos\u03b1 (5.25) From where the angle \u03b1 is expressed: \u03b1 = arccos ( 1 \u2212 1 2 ( r a2 )2 ) (5.26) The center of the wrist Q can be positioned into a selected point of a workspace in two different ways, which are called \u201celbow up\u201d and \u201celbow down\u201d. Both poses of the second and the third segment are together with the corresponding angles shown in Fig. 5.5. From Fig. 5.5 we can read the \u201celbow up\u201d angle \u03d13 = \u03b1 + \u03c0/2 and for the \u201celbow down\u201d \u03d13 = \u03c0/2 \u2212 \u03b1. As the triangle from the right Fig. 5.4 is because of equal segment lengths a2 = d4 isosceles, we can write: \u03b3 = (\u03c0 \u2212 \u03b1)/2 From the right Fig. 5.4 we can also read: \u03b4 = arctan2 qz \u2212 d1\u221a q2 x + q2 y (5.27) For the pose \u201celbow up\u201d the angle in the second joint is equal to \u03d12 = \u03b4 + \u03b3 , while for \u201celbow down\u201d we have \u03d12 = \u03b4\u2212 \u03b3 . From the left Fig. 5.4 we read also the angle in the first joint: \u03d11 = arctan2 qy qx (5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003759_j.ymssp.2019.02.044-Figure15-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003759_j.ymssp.2019.02.044-Figure15-1.png",
        "caption": "Fig. 15. Variable transmission path.",
        "texts": [
            " 12 and 13 are approximated as a square wave form depending on the calculated gear mesh frequency. The maximum and the minimum values of those functions are defined using the potential energy method as reported in Section 4 considering only the mean values of extremums. 5.3. Influence analysis of the rotational motion of planets: amplitude modulation phenomenon Fig. 14 shows the vertical acceleration signal of the sun and the ring gear within one carrier period rotation simulated at the sensor location as shown in Fig. 15. It can be noticed that the vibration components induced by the ring gear are under amplitude modulation. There are totally four fluctuations since the planetary gear-set possesses four planets. It is explained by the alternation of coming closer and going further of planets from the sensor location: when one planet approaches to the sensor, the amplitude of vibration signals increases, and vice versa, when the planet goes away, the amplitude of vibration signals decreases. The same behavior is presented by the sun gear. There are four fluctuations. Its origin is the variable transmission path of vibrations from the sun to the sensor location as shown in Fig. 15. When the planet is at the closest position of the transducer, the path is minimum. Hence, vibrations induced by the sun will go through the planet gear directly to the sensor. Thus, vibration signal is at their maximum values. When the planet leaves, the path will be divided into two paths: first one through the planet and the other one through the ring gear. So, vibrations will be damped and therefore the energy of vibration signals decreases. Those results are similar to the results conducted by Liu et al. [22]. 5.4. Influence analysis of the size of planets: overlap phenomenon It is easy to observe in Fig. 14 that the four fluctuations are overlapping one by one. The origin of the overlap phenomenon comes from the fact that the transducer perceived signals from the hole planetary gear-box. As shown in Fig. 15, when planetN leaves the sensor location, planetN\u00fe1 becomes closer. Hence, signal induced for instance by the ring gear and modulated with planetN will decrease. At the same time, the level of energy of the next portion of signal induced by the ring gear which is modulated by planetN\u00fe1 will increase. Moreover, the size of the overlap depends only on the radius of the planet. Hence, an investigation of the impact of this constraint is developed in the following. To do this, the radius of the ring is kept constant and an increasing of the radius of the carrier is done"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002050_j.surfcoat.2017.10.080-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002050_j.surfcoat.2017.10.080-Figure2-1.png",
        "caption": "Fig. 2. Schematic representation of the design of tensile dog-bone specimens for AISI 420 SS clad layer on 300M substrate: (a) grind-out profile (b) as-deposited AISI 420 SS powder (c) Wire-cut and post-clad CNC machining of the dog-bone specimens.",
        "texts": [
            " A continuous raster scan path, denoted by as-clad (\u0394ttrack = 0 s), schematically shown in Fig. 1a. A second variable, denoted by as-clad (\u0394ttrack = 80s), involving of a 80 s idle time between each clad track. This idle time was selected to allow the previous clad track to cool close to room temperature before the commencement of the subsequent clad track, schematically shown in Fig. 1b. For a comparison, the mechanical properties of the 300M steel baseline substrate were also tested. A representative in-service grind-out was applied on each 300M substrate, as shown schematically in Fig. 2a. The grind-out depth was 0.4 mm \u00b1 0.05 mm (10% of the total thickness of the tensile specimens) with a width of 13.0 mm. To ensure a smooth blended profile, a 45\u00b0 angle is incorporated on the edge of the grind-out using a radius of approximately 6.0 mm. Laser cladding was performed to restore the geometry in and around the grind-out region. The length of each deposited clad layer was approximately 20 mm and the total axial length was 10 mm. The distance between each clad layer was 5.0 mm. For each variable, a total of 5 clad layers were deposited, as shown schematically in Fig. 2b. To achieve flat tensile specimens, the excess clad material was machined off using a CNC mill. The final clad thickness after post-clad machining was approximately 0.4 mm. Finally, five dog- bone specimens were machined from each plate, as schematically shown in Fig. 2c. Axial tension testing was performed using a 50 kN Instron testing machine using a strain rate of 1.0 mm/min, in accordance with ASTM procedure 8 M. The thickness of each dog-bone specimen was 4 mm with a gauge length and width of 20 mm and 5 mm, respectively. The strain was measured using an Epsilon 10 mm extensometer. The fracture surface was analysed using a Verios 460L Scanning Electron Microscope (SEM). A 15 kV electron beam and 25 pA current was used. The clad layer of each tensile sample were cross-sectioned, mounted, and polished to a 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000230_j.talanta.2007.10.023-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000230_j.talanta.2007.10.023-Figure2-1.png",
        "caption": "Fig. 2. Schematic diagram of a subcutaneously implanted needle-type sensor: ( r (",
        "texts": [
            " The sensor must be of a shape and small size that allows conenient implantation and results in minimal discomfort. Sensors ith outer diameter smaller than 450 m (i.e., needles smaller han 26-gauge) are essential to meet these demands. Such miniaurization of in vivo sensors is not trivial. The fabrication f subcutaneously implanted needle-type sensors commonly nvolve controlled deposition of an inner permselective coating, ollowed by the enzyme layer, and an outer layer that renders biocompatible interface and mass transport control (Fig. 2). uch placement of the sensor on the needle shaft (rather than at he tip) facilitates the membrane coating. .2.1. Inflammatory and biofouling processes Implanted glucose sensors are subject to undesirable interctions between the sensor surface and biological medium that ause deterioration of the sensor performance, and proved to be he major barriers to the development of reliable implantable [ m E a a) Teflon-coated Pt\u2013Ir wire; (b) Teflon tip; (c) sensing cavity; (d) Ag/AgCl eference electrode; (e) heat-shrinkable tubing; (f) reference electrode terminal; g) working electrode terminal (from Ref"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001115_j.wear.2015.01.047-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001115_j.wear.2015.01.047-Figure1-1.png",
        "caption": "Fig. 1. PRS main components.",
        "texts": [
            " The experiments reveal a quick adhesive wear in dry or bad lubricated conditions, while a low friction coefficient remains if the contact is well lubricated. The influence of the input parameters concurs with the theoretical calculation. The evolution of grease lubrication during duty lifetime and the influence of the tribo-chemical films on this lifetime are also studied. & 2015 Elsevier B.V. All rights reserved. The planetary roller screw (PRS) is a device that converts rotation to translation motion or vice versa. This mechanism includes rollers between the screw and the nut to limit friction (Fig. 1). The basic principle is similar to the ball screw mechanism, but it is designed for high speed and long life applications. Especially, the rollers threads increase the contact surface and then allow carrying heavier loads for a relatively small external diameter. These features make the PRS attractive for aeronautics electromechanical actuators that must be small sized and highly stressed. The lifetime calculation of this component is based on fatigue failure like most bearing mechanisms. However, it is known that bearing parts made of stainless steel often fail long before the calculated time, because of other failure modes such as adhesive wear [1]",
            " Second, a calculation method has been implemented to calculate the contact features such as slide/roll ratios, stresses and stick/slip zones distribution, in order to evaluate its susceptibility to smearing. Then, a specific tribometer that reproduces the RPS contact is presented. Rolling\u2013sliding wear tests were performed with different working conditions such as speed, creep ratio, and lubrication. Wear tracks and forces measurement data are analyzed. The PRS consists of a screw and a threaded nut of the same pitch (Fig. 1), with rollers in between. The thread profile of the screw and the nut is straight and usually cut to 901 for best efficiency. Threaded rollers are set between the two components, and their profile is curved to further reduce friction. The axial load is transmitted through multiple contacts between the threaded components. Then, these contacts can be described as ellipsoidon-flat contacts (Fig. 2) that are characterized by three radii: the pitch radius of the screw (or the nut) and the roller, and the roller's radius of curvature"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000411_s10008-010-1025-9-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000411_s10008-010-1025-9-Figure5-1.png",
        "caption": "Fig. 5 Peak currents of 15 \u03bcM DA, AA, UA at Au electrode, MIP electrode and NIP electrode, respectively",
        "texts": [
            " Interference study A molecularly imprinted sensor should show a minimum of affinity towards molecules having structures Table 1 Comparison of the MIP electrode with other modified electrodes Modified electrode Detection range (mol/L) Detection limit (mol/L) Reference Fc-SWNTs 5.0\u00d710\u22126-3.0\u00d710-5 5.0\u00d710\u22128 [9] Poly (caffeic acid) 1.0\u00d710\u22126-3.5\u00d710\u22125 2.0\u00d710\u22127 [25] Poly(4-(2-Pyridylazo)-Resorcinol) 5.0\u00d710\u22126-3.0\u00d710\u22125 2.0\u00d710\u22127 [30] PtAu hybrid film 2.4\u00d710\u22125-3.8\u00d710\u22124 2.4\u00d710\u22125 [31] MIP 5.0\u00d710\u22127-4.0\u00d710\u22125 1.3\u00d710\u22127 Proposed method closely related to the imprinted molecules. We compared the electrochemical response of Au electrode, MIP electrode, and NIP electrode to the same concentration of DA, AA, and UA (15 \u03bcM). As shown in Fig. 5, the peak currents of the three analytes on the Au electrode were almost as high as each other, while on the MIP electrode, the current of DA was apparently higher than the current of AA and UA, which showed an excellent selectivity of the MIP electrode. In order to further examine the selectivity of the designed MIP electrode, the response of the modified electrode was tested in a solution containing 10 \u03bcM DA and 100-fold amounts of potential interfering substances such as AA and UA. The response-selectivity coefficient kpc= ip/ic [20] was calculated to demonstrated the selectivity of the MIP sensor, where ip is the peak intensity response of the sensor to 10 \u03bcM DA and ic is the peak intensity response caused by 1,000 \u03bcM interferents"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002283_j.rcim.2017.10.003-Figure18-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002283_j.rcim.2017.10.003-Figure18-1.png",
        "caption": "Fig. 18. Pinion FEM model after machine setting modification.",
        "texts": [
            " [13] written by Artoni, the most desirable ne among the optimal results on the residual ease-off is that the mean bsolute value by nonlinear least square procedure is 1.3 \u03bcm, while the aximum is 4.2 \u03bcm. As mentioned in the proposed modification, if the btained geometric performance can not meet the requirement, there re two improved methods. Here, its improved modification is omitted or brevity and the details can be referred to the literature [15,24,43,48] . The LTCA based on FEM software is performed to evaluate the meshng impact properties and dynamic contact strength [13,24,48] . Fig. 18 hows a FEM pinion mode. It is a member of hypoid gear drive in the ear meshing position. In establishment of an accurate model for LTCA, t is required to be divided into much more mesh to ensure that the nite units are many enough in the tooth contact position. For example, ig. 19 represents the analysis and comparison of different contact eleents for the evaluation items on the maximum contact stress, considerng the calculation result, the error proportion and computational time. here, there are some same conditions to be set for LTCA or DTCA"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000560_j.jsv.2009.03.013-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000560_j.jsv.2009.03.013-Figure6-1.png",
        "caption": "Fig. 6. Lubricant thickness between the roller and the cage.",
        "texts": [
            " Two geometric relations must be added to describe the relative displacement between the inner and the outer ring centers (Fig. 5) and the lubricant film thickness between the roller and the cage pocket. The first relation includes the elastohydrodynamic lubrication (EHL) film thickness at the roller/race contacts h, the ARTICLE IN PRESS A. Leblanc et al. / Journal of Sound and Vibration 325 (2009) 145\u2013160 151 contact deformations d, the radial clearance Jd and the structural deformations u: Jd 2 \u00fe dij \u00fe doj hij hoj \u00fe uij \u00fe uoj \u00bc Y i cosCj X i sinCj (19) The lubricant film between the roller and the cage (Fig. 6) is given by H1j \u00bc dm 2 Ccj arctan 2Rr dm arctan X c EX cosCcj \u00fe Y c EX sinCcj Rc EX X c EX sinCcj Y c EX cosCcj Cj 0 BB@ 1 CCA 0 BB@ 1 CCA (20) where Ccj \u00bc Cc \u00fe 2p\u00f0j 1\u00de=N. The basic testing of the present code has been performed with ADOREr [3] and with the research model used by Ghaisas et al. [23]. Fig. 7 shows the correlation coefficients for the radial displacements predicted by Gupta\u2019s software and our model applied on a perfect roller bearing with radial loading [3, Table 8-3]. High rate of agreement is achieved for the inner ring trajectories and for the speed range investigated"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003887_j.etran.2020.100080-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003887_j.etran.2020.100080-Figure3-1.png",
        "caption": "Fig. 3. Design consideration with more PM material, thinner stator yoke and larger size [20].",
        "texts": [
            " [33] that SPM machines with lower energy PMs can still be competitive with machines adopting higher energy PMs if the machine designs were optimized specially for each PM material, with the advantage of low price. In spite of larger amount of ferrite used in SPM machines, the airgap flux density still could not achieve that of rare-earth ones [30]. Thus, the stator yoke thickness could be reduced in order to increase the slot area for installation of more armature conductors to increase the electric load and power output [20], as shown in Fig. 3. In this case, under the same current density, the copper loss would increase and the overall efficiency would drop. In H.R. Bolton\u2019s study, over 10% of efficiency difference was found between rare-earth and ferrite SPMs [20]. In Ref. [34], copper loss of the ferrite generator was almost 3 times that of NdFeB with the same outer diameter, and thus the ferrite machine suffered 7% lower efficiency. Andwith 30% larger diameter, the efficiency of the ferrite motor was still 1% lower compared to the NdFeB motor in Ref"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001968_978-94-007-6101-8-Figure2.8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001968_978-94-007-6101-8-Figure2.8-1.png",
        "caption": "Fig. 2.8 Orientation of robot gripper",
        "texts": [
            "29) In a similar way we find also the angle \u03c8 : r1yr3x = s\u03d5c\u03c8 (s\u03d5s\u03c8 + c\u03d5s\u03d1c\u03c8) r1x r3y = c\u03d5c\u03d1 (\u2212c\u03d5s\u03c8 + s\u03d5s\u03d1c\u03c8) r1yr3x \u2212 r1x r3y = c\u03d1s\u03c8 r1x r2y = c\u03d5c\u03d1 (c\u03d5c\u03c8 + s\u03d5s\u03d1s\u03c8) r1yr2x = s\u03d5c\u03d1 (\u2212s\u03d5c\u03c8 + c\u03d5s\u03d1s\u03c8) r1x r2y \u2212 r1yr2x = c\u03d1c\u03c8 \u03c8 = arctan r1yr3x \u2212 r1x r3y r1x r2y \u2212 r1yr2x (2.30) Let us go back to the numerical example where the matrix (2.27) represents the orientation of the gripper. When calculating the value of the angle \u03d1 , we can notice, that the numerator (r1z) equals zero, while the denominator is non-zero, therefore \u03d1 = 0. The same is valid for the angle \u03d5 = 0, while the angle \u03c8 = \u221260\u25e6. The orientation of the gripper with respect to the reference frame is shown in Fig. 2.8. 2.2 Orientation 25 The gripper lays in the y0, z0 plane. From the figure we can read the angles between the axes of the reference and gripper coordinate frame: nx = cos 0\u25e6, sx = cos 90\u25e6, ax = cos 90\u25e6 ny = cos 90\u25e6, sy = cos 60\u25e6, ay = cos 30\u25e6 nz = cos 90\u25e6, sz = cos 150\u25e6, az = cos 60\u25e6 We can see that this is the original matrix (2.27). The orientation can be described also by the help of the Euler angles, where we first perform the rotation \u03d5 about the z axis, afterwards the rotation \u03d1 about the new y axis and finally the rotation \u03c8 about the momentary z axis (Fig",
            " The following quaternion is obtained: q = 1 2 + 1 2 i+ 1 2 j+ 1 2 k We will insert: r1 = 0+ i into Eq. (2.37) describing the rotation. The following multiplication must be performed: 2.3 Quaternions 35 r2 = 1 2 (1+ i+ j+ k)(i) 1 2 (1\u2212 i\u2212 j\u2212 k) = 1 4 (i\u2212 1\u2212 k + j)(1\u2212 i\u2212 j\u2212 k) = 1 4 (i\u2212 1\u2212 k + j+ 1+ i+ j+ k \u2212 k + j\u2212 i+ 1+ j+ k \u2212 1\u2212 i) = j We obtained the same result as when using the Rodrigues\u2019s formula. Let us finally study, how to describe by the use of quaternions the orientation of the gripper shown in Fig. 2.8 from the Sect. 2.2. The orientation of the gripper is obtained as result of the geometric model of the robot in the form of rotation matrix (2.27). We calculate the corresponding quaternion by the use of Eq. (2.43): q0 = 0.866 q1 = \u22120.5 q2 = 0 q3 = 0 In previous chapter we have found out that the rotation matrix (2.27) belongs to the following RPY angles: \u03d5 = 0, \u03d1 = 0, and \u03c8 = \u221260\u25e6. The orientation quaternion can be obtained also from the RPY angles. Rotation R is described by the quaternion: qz\u03d5 = cos \u03d5 2 + sin \u03d5 2 k (2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000083_j.mechmachtheory.2009.01.010-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000083_j.mechmachtheory.2009.01.010-Figure3-1.png",
        "caption": "Fig. 3. Line of action of a skew conical gear drive.",
        "texts": [
            " The distance shifted Dbi,o can be obtained by Dbi;o \u00bc \u00f0bi;o be\u00de\u00bdtan\u00f0h Dh\u00de tan h tan\u00f0h Dh\u00de : \u00f08\u00de The position of the section on toe bi or on heel bo in Eq. (8) is positive if the section is located on the positive z-coordinate of S1 and vice versa. The meshing relations are based on the geometrical characteristics of involute cylindrical gearing: the points of contact between two engaged teeth always lie on a line, i.e. the line of action. Because the line of action is also commonly normal to the tooth profiles of the gears, it must be also tangential to the base cylinders and the base helices. Fig. 3 shows the base cylinders of a skew conical gear pair with its corresponding line of action T1T2. Coordinate system Sf is employed for spatial analysis of the gear meshing, in which the xf-axis is arranged as the common perpendicular of the two skew gear axes, and the zf-axis is the axis of gear 1. In order to solve the spatial relation, the \u2018\u2018line coordinate\u201d, or the so-called \u2018\u2018dual-number\u201d method [23], is used in this study to determine the line of action. The shaft angle R and the offset a between the axes of the gears define the dual angle R\u0302, i",
            ", R\u0302 \u00bc R ea: \u00f09\u00de According to the dual vector definition, the axes of the two gears can be expressed as A\u03021 \u00bc 0 0 1 2 64 3 75; \u00f010\u00de A\u03022 \u00bc 0 sin R\u0302 cos R\u0302 2 64 3 75 \u00bc 0 sin R ea cos R cos R\u00fe ea sin R 2 64 3 75; \u00f011\u00de for gears 1 and 2, respectively. Based on the condition of tangency to the base cylinder and the base helices, the line of action n\u0302 can be represented as a dual vector with the base helix angle bCb1 and the base radius rCb1 of the base cylinder of gear 1, as well as the unknown parameters w and bL for locating the point of tangency T1; see Fig. 3 n\u0302 \u00bc n\u00fe e n rG; \u00f012\u00de with n \u00bc cos bCb1 sin w cos bCb1 cos w sin bCb1 2 64 3 75; \u00f013\u00de rG \u00bc rCb1 cos w rCb1 sin w bL 2 64 3 75: \u00f014\u00de In the above expression, n represents the direction of the line of action, and rG is the position vector for the point of tangency T1. The upper sign in the expression of the normal n denotes the left-hand flank in engagement and the lower sign denotes the right-hand flank. The meshing condition is such that the line of action n\u0302 is tangential to the base cylinder and the base helix of gear 1; see Eqs",
            " Because conical gears can be regarded as cylindrical gears, with variable profile-shifting along the face width, a change in the contact position also means a change in the meshing characteristics. The relations between the working parameters, the gearing parameters and the detailed design approach can be found in a previous paper [15]. The position of the contact points in a skew conical gear drive with profile-shifted transmission can be determined with the aid of the meshing model shown in Fig. 3 and the frequently adopted working pitch cones model [25] in Fig. 4. The geometrical relation between the working pitch cones of a conical gear drive and the corresponding coordinate systems are illustrated graphically in Fig. 4. The location of the two working pitch cones, with working cone angles hw1 and hw2, is determined based on the assembly parameters: shaft angle R, offset a and working mounting distances Dw1,2. The parameters bC1,2 indicate the distance between the working pitch circle with radius rCw1,2 and the reference pitch circle with radius rC1,2 across the face-width",
            " 6, where a common tangential plane (the plane of action), and the base cylinders of the skew gear drive, are tangential to each other [5,13]. Another design condition is the consideration of edge contact. Edge contact occurs when the line of action is shifted outside of the face-width from the theoretical position caused either by the assembly errors or by the manufacturing errors. The shift of the line of action along the gear axis can be served as an evaluation criterion for edge contact. As the definition in Fig. 3, the shift of line of action DbL can be regarded as the displacement from the theoretical position bL0 to the actual position bL * due to the errors, i.e., DbL \u00bc b L bL0: The actual position bL * for locating the line of action due to an error is obtained from Eqs. (16) and (17) with substitution of the corresponding deviated parameter. In general the shift DbL must be at least smaller than one half of the active face-width. Further information about conical gear drives in approximate line contact can be found in the paper [14]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002759_tpel.2019.2918683-Figure15-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002759_tpel.2019.2918683-Figure15-1.png",
        "caption": "Fig. 15. Experiment platform.",
        "texts": [
            " Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. to 3 N.m at the instant t=1 s. It can be seen that, during the transient process, the copper loss of the PMSM drive system controlled by the proposed control method is still smaller than that of the PMSM drive system controlled by the traditional vector control method, besides the steady state. To further validate the proposed method, the experimental platform is setup, as shown in Fig. 15. Two PMSMs are directly connected through one coupling, where one is used as test machine, and the other one is used as load machine. The load torque of the test PMSM is imposed by a load PMSM. The load PMSM is controlled by the id=0 control method, and the load torque is adjusted by the control system of the load PMSM. All the switching commands are generated by the dSPACE DS1103 controller. The parameters of the PMSMs used for the experimental verification are the same as those listed in Table I"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002710_9783527803293-Figure7.6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002710_9783527803293-Figure7.6-1.png",
        "caption": "Figure 7.6 Hydroxylation of coniferyl alcohol derivatives (a) by ferulic acid 5-hydroxylase (F5H) to synthesize hydroxylated products (b) that can be used as precursors for sinapic acid synthesis (c).",
        "texts": [
            " These trihydroxyphenolic acid products (THCA, THPA, and gallic acid) have higher antioxidant, anticancer, anti-inflammatory, and antimicrobial activities than the original phenolic acid substrates [33, 45, 70]. Ferulic acid can be hydroxylated by ferulic acid 5-hydroxylase (F5H), a P450dependent monooxygenase, to synthesize 5-hydroxyferulic acid, a compound that can be used as a precursor to synthesize sinapic acid. The same enzyme can also use coniferyl alcohol and coniferyl aldehyde to form 5-hydroxyconiferyl alcohol and 5-hydroxyconiferyl aldehyde. Both compounds can be also used as precursors in sinapic acid synthesis (Figure 7.6) [71\u201374]. 7.3.2.2 Methylation A phenolic group of caffeyl alcohol/aldehyde and caffeic acid can be methylated by S-adenosylmethionine (SAM)-dependent caffeate O-methyltransferase (COMT) to produce coniferyl alcohol/aldehyde and ferulic acid, respectively. The 5-hydroxyl moiety of 5-hydroxyconiferyl alcohol/aldehyde and 5-hydroxycaffeic acid can be further methylated by COMT to synthesize sinapyl alcohol/aldehyde and sinapic acid, respectively (Figure 7.7) [73\u201375]. 7.3.2.3 Demethylation The 3-methoxy group of vanillic acid, one of the major lignin-derived phenolic acids, can be demethylated by H4folate-dependent O-demethylase (LigM) in Sphingomonas paucimobilis SYK-6 [24, 76] or a nonheme irondependent demethylase in Pseudomonas sp"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000648_978-3-642-17531-2-Figure4.7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000648_978-3-642-17531-2-Figure4.7-1.png",
        "caption": "Fig. 4.7. Planar elbow manipulator with elastic joints (absolute angles, joint elasticity modeled as torsion springs 1 2",
        "texts": [
            " If additionally G = 0 , the system is termed a non-gyroscopic conservative multibody system or a multibody system with simple multibody structure (Pfeiffer 2008): M y K y 0 . (4.31) 234 4 Functional Realization: Multibody Dynamics The form of model in Eq. (4.31) is of great significance as the MBS eigenvalue problem can be directly formulated using it. The inherent energy conservation represented in the model can additionally be advantageously drawn upon for the verification of linear and nonlinear MBS models. Example 4.2 Planar elbow manipulator with elastic joints. Fig. 4.7 shows a rigid elbow manipulator ( 1 10 2 20 , , ,m I m I ) with massless, frictionless, yet elastic joints ( 1 2 ,k k ). In the joints, massless actuators apply torques ( 1 2 , ) relative to the inertial frame {I} (e.g. a chain drive with shared base). The joint angles are available in the form of absolute angles ( 1 2 ,q q ) relative to {I} 14. ,k k ) 14 Note the difference from a manipulator with integrated motors in the joints. In that case, the torques act as inner torques (action/reaction), relative angles are measured at the joints, and motor masses in the joints must be taken into account, so that a different mathematical model results"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002010_j.optlastec.2016.01.002-Figure10-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002010_j.optlastec.2016.01.002-Figure10-1.png",
        "caption": "Fig. 10. Sampling method of tensile samples.",
        "texts": [
            " The tensile strengths of the specimens made by DLF are higher than that of forgings, regardless of how the oblique angle changes. However, the elongation is only about 33% of the homogenous forgings (40%). In order to study the effect of angle (\u03b2) between tensile loading direction and horizontal direction on tensile properties of oblique thin-walled part, samples with angle \u03b2 of 0\u00b0, 45\u00b0, 90\u00b0, 160\u00b0 were produced to perform tensile test during the oblique angle \u03b8 is 20\u00b0. The sampling methods are shown in Fig. 10. The results in Table 4 show that there is obvious difference among the three samples with the angle \u03b2\u00bc0\u00b0. It is due to heights of the specimen position are apparent different. For example the sample 1 is near the surface, while sample 3 is near the substrate. Tabernero et al. also observed the similar phenomenon [19]. When 0o\u03b2o180\u00b0, the UTS and elongation increase firstly and then decrease with the increase of the angle between tensile loading direction and horizontal direction. The maximum of average UTS appears at \u03b2\u00bc45\u00b0 is 744"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001022_1.4005336-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001022_1.4005336-Figure9-1.png",
        "caption": "Fig. 9 An actuation singularity: all actuation forces are coplanar, condition (3d) of GG",
        "texts": [
            " Consequently, such a configuration corresponds to a singular complex, i.e., condition (5b) of GG; Journal of Mechanisms and Robotics FEBRUARY 2012, Vol. 4 / 011011-9 Downloaded From: http://mechanismsrobotics.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jmroa6/28019/ on 02/13/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use (2) The four actuation forces are coplanar. In that case, the screw subspace F becomes of dimension 3, which corresponds to condition (3d) of GG, all lines in a plane. Such a configuration is illustrated in Fig. 9. (e) (fi fj) k \u00f0ukl ij z\u00de k (fk fl). As mentioned previously, this condition amounts to \u00f0fh\u00de: \u00f0uj\u00de : \u00f0db\u00de. In that case, points f, h, u, j, d, and b are aligned, as shown in Fig. 10(e). Therefore, such a configuration corresponds to a singular complex, i.e., condition (5b) of GG. (f) ((fi fj) (fk fl))\\ \u00f0ukl ij z\u00de. This is the general case of Eq. (20). Without loss of generality, let us consider that ((f1 f2) (f3 f4))\\ \u00f0u34 12 z\u00de. As mentioned previously, in that case, F1 and F2 lie in a plane containing T 12 and, in turn, F3 and F4 lie in a plane containing T 34, as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002988_j.jmbbm.2017.11.009-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002988_j.jmbbm.2017.11.009-Figure1-1.png",
        "caption": "Fig. 1. (a) Design of the clasp specimen, consisting of a clasp arm, loading sphere, and plate for fixing to the fatigue-testing machine. In one group, the support structure was designed for clasp arm (supported specimens) and in the other group, it was omitted (unsupported specimens). Kajima et al. (2016) (b) Schematic of specimen orientations on the base plate.",
        "texts": [
            " Commercially available Co\u2013Cr\u2013Mo alloy powders (MP1, EOS, Krailling, Germany) were used in this study. The chemical compositions of the powders as given by the manufacturer are shown in Table 1. Clasp-shaped specimens were prepared using an SLM machine equipped with a fiber laser (EOSINT M280, EOS, Krailling, Germany). The SLM machine was operated using the standard deposition parameters for MP1 under a nitrogen atmosphere. The shape of the specimens, designed according to a previous study (Kajima et al., 2016; Mahmoud et al., 2005), is shown in Fig. 1. The specimen consists of a clasp arm and plate, with the plate serving as an attachment for fixing the clasp to the fatigue-testing machine (MMT-250N, Shimadzu Corp, Kyoto, Japan). The clasp arm originated from the plate with a radius of curvature of 5 mm and a central angle of 137.5\u00b0. The width and thickness at the tip of the clasp arm pattern were 0.82 mm and 0.656 mm, respectively, while those at the joint linking the arm and the plate were 1.3 mm and 1.04 mm, respectively. A sphere (0.6 mm diameter) was designed at the tip to provide a point at which to apply a force (Kajima et al., 2016). In order to investigate the effect of the presence of a support structure on the fatigue strength, one group consisted of specimens with a support structure for overhanging parts of clasp arm (denoted by \u201csupported specimens\u201d) and the other group consisted of unsupported specimens (denoted by \u201cunsupported specimens\u201d) (n = 6 for each group) (Fig. 1a). The support structures were designed as blocks that could easily be removed from the specimens without damage. All specimens were prepared with the longitudinal axes inclined from the horizontal plane by 45\u00b0, as shown in Fig. 1b, because clasps with this angle can generally be manufactured to be selfsupporting (Calignano, 2014; Hussein et al., 2013a; Thomas and Bibb, 2008). Prior to fatigue testing, the surface roughness and microstructure were analyzed. The surface roughness (Ra) of the inner surface of all clasp arms was analyzed using a 3D laser measuring microscope (OLS4000, OLYMPUS, Tokyo, Japan). Each sample was measured three times, and the mean value for Ra was calculated. Next, a sample was randomly selected from each group in order to analyze the microstructure"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001218_j.talanta.2011.03.006-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001218_j.talanta.2011.03.006-Figure1-1.png",
        "caption": "Fig. 1. (A) The AgLAF\u2013AgSAE \u2013 ready-for-measurement configuration: (1) silver solid amalgam annular band electrode (AgSAE); (2 and 3) O-rings; (4) 1 wt.% silver",
        "texts": [
            " These were: vitamin C tablets excipients: lactose monohydrate, polyvidone (PVP), talc, magneium stearate, starch), product of Pharmaceuticals Poland; vitamin 2 tablets (excipients: sucrose, lactose, starch, gum arabic, talc, tearic acid, amylum tritici), product of PLIVA, Poland and vitamin 1 tablets (excipients: lactose monohydrate, starch, polyvidone PVP), magnesium stearate), product of Polfarmex S.A., Poland. ccording to the manufacturer, they contained respectively 100 mg C, 25 mg VB1 and 3 mg VB2. .3. Preparation of the AgLAF\u2013AgSAE The structure of the applied electrode, which allows the silver iquid amalgam film to be refreshed before each measurement and s essential for its performance, is presented in Fig. 1. Fig. 1A shows liquid amalgam (AgLA); (5) PTFE centering element; (6) electrode body; (7) solenoid; (8) electric contact pin; (9) spring. (B) Construction of the AgSAE: (a) silver tube; (b) stainless steel wire; (c and d) resin. (C) The AgLAF\u2013AgSAE in the position of the AgLAF film refreshing. the structure of the automatically controlled AgLAF\u2013AgSAE: silver solid amalgam annular band electrode \u2013 AgSAE (1); O-rings (2 and 3); 1 wt.% silver liquid amalgam (AgLA) drop, ca. 50 L, (4); PTFE fastening element (5), fastened together in the polypropylene electrode body (6); linear actuator (solenoid) (7); electric contact pin (8); spring (9). Fig. 1B shows the preparation of the AgSAE. The polycrystalline silver tube (a) was slid over and mechanically tightened on the stainless steel wire (b). The steel wire below and above the silver tube was covered by resin (c). The excess resin was then mechanically removed (d). After mounting, the electrode surface (resins and silver) was ground by emery papers of decreasing roughness and was finally polished with 0.3 m Al2O3 powder. After thorough rinsing, the electrode was placed for about 2\u20133 s in 5% HNO3 solution and afterwards for 1 h in 1 wt.% silver liquid amalgam. The procedure of refreshing of silver liquid amalgam film (AgLAF) consists of pulling up the AgSAE inside, across the liquid amalgam chamber (Fig. 1C) and then pushing it back outside the electrode body (Fig. 1A). During these movements, the AgSAE makes in contact with the liquid amalgam twice. During the insertion of the AgSAE through the O-rings, the solid and gas contaminants are removed from its surface. 3. Results and discussion 3.1. Characteristic features of the AgLAF\u2013AgSAE The AgLAF\u2013AgSAE electrode demonstrates many features specific for DME and the time period of the contact of the electrode with the sample solution after film refreshment may be completely controlled. Therefore, AgLAF\u2013AgSAE may be used in the routine electroanalysis of vitamins instead of dropping mercury electrode (DME) [25,26]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001441_iet-cta.2010.0621-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001441_iet-cta.2010.0621-Figure2-1.png",
        "caption": "Fig. 2 Variable-length pendulum",
        "texts": [
            " Then, one obtains V\u0307 \u2264 \u2212as|s| \u2212 ar|r\u0302 \u2212 r\u2217| = \u2212 2 \u221a as \u00b7 |s| 2 \u221a \u2212 ar 2l \u221a \u00b7 |r\u0302 \u2212 r\u2217| 2l \u221a \u2264 \u2212min 2 \u221a as, ar 2l \u221a{ } |s| 2 \u221a + |r\u0302 \u2212 r\u2217| 2l \u221a ( ) (42) With the help of Lemma 3, it yields V\u0307 \u2264 \u2212min 2 \u221a as, ar 2g \u221a{ } |s| 2 \u221a ( )2 + |r\u0302 \u2212 r\u2217| 2l \u221a ( )2 ( )(1/2) = \u2212min 2 \u221a as, ar 2l \u221a{ } \u00b7 V (1/2) (43) By using Lemma 2, it is concluded that the sliding mode s \u00bc 0 is established in finite time. This completes the proof. A Remark 2: The missing derivatives of s\u0307 can be estimated online by means of the robust exact finite-time convergent differentiator [28]. Using the results of the Theorems 1 and 4, second-order sliding mode is guaranteed by the proposed control algorithm. The schematic block diagram of the proposed second-order SMC scheme is shown in Fig. 1. Consider a variable-length pendulum control problem [8] (Fig. 2). All motions are restricted to the vertical plane. A load of a known mass m moves without friction along the pendulum rod. Its distance from O equals R(t) and is not 309 & The Institution of Engineering and Technology 2011 measured. An engine is connected to the rod and transmits a torque w to it. Torque w is considered as control. The task is to track some function xc given in real time by the angular coordinate x of the rod. The system is described by the equation x\u0308 = \u22122 R\u0307(t) R(t) x\u0307 \u2212 g R(t) sin x + 1 mR(t)2 w (44) where m \u00bc 1 kg and g \u00bc 9"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001885_j.matpr.2015.10.028-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001885_j.matpr.2015.10.028-Figure8-1.png",
        "caption": "Fig. 8. a) Layered die cap, b) geometry of the cooling channel (negative) [12], c) plastic deformation of the die in extrusion direction [8] (optical geometry measurement, GOM-Atos)",
        "texts": [
            " For the manufacturing of an extrusion die with integrated cooling channels placed close to the forming zone the Layer Laminated Manufacturing Method was chosen. Single steel sheet layers were cut in a CNC laser cutting center (Trumpf TL 1005) according to the die cap geometry and assembled. The lamellas of the die were cut out sheets of the hot working steel 1.2343/H11 (heat treated to 54 HRC) with a thickness of 1 mm (welding chamber, cooling channel lamellas) and 2 mm (die bearing lamella). The stacked lamellas are supported by a 19 mm thick backer platen made also of the hot working steel 1.2343/H11 (Fig. 8 a)). The cooling channels were aligned around the circumference of the square die opening directly behind the die bearing lamella. To keep each lamella as one single unit, the cooling channels are splitted into two lamellas (Fig. 8 b)). Layered dies have a lower stiffness than solid dies. For this reason the right material and layer thickness have to be chosen. With the former described set-up hollow profiles could be manufactured successfully. After etching the die in caustic soda, by optical measurement (GOM-Atos) of the die bearing lamella it could be seen, that no plastic deformation of the die occurred (Fig. 8 c)). Also the cooling channels were covered sufficiently by the bearing lamella (Fig. 8 c)). This set-up was used for the following experiments carried out. 4. Comparison mandrel cooling vs. die cap cooling The new extrusion dies were tested on a 2.5 MN direct extrusion press (Collin PLA 250). Fig. 9 shows the comparison of the results of cooling the mandrel or the die cap. The average profile\u2019s exit temperatures (average value in a quasi-steady state after starting the cooling since 1/3 billet length was extruded) for different profile\u2019s exit speeds without and with applying cooling with compressed air as coolant are shown (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002828_aa543e-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002828_aa543e-Figure1-1.png",
        "caption": "Figure 1. Planetary gearbox structure.",
        "texts": [
            " In recent years, many researchers have proposed fault diagnostics methods for planetary gearboxes that work through vibration signals [2\u20134]. These studies have made important contributions to our understanding of the fault behaviors of planetary gearboxes under stationary operational conditions. However, it has been observed that the structure of a planetary gear system is very different from that of a fixed axis gear transmission system, in that several rotating parts rotate simultaneously, i.e. the sun gear, the planet gears, the planet carrier and sometimes even the ring gear, as shown in figure\u00a01. Therefore, the vibration analysis of planetary gearboxes through traditional vibration-based diagnostic methods, Keywords: planetary gearbox, fault diagnosis, computed order tracking (COT), Vold\u2013Kalman filter order tracking (VKF-OT) (Some figures\u00a0may appear in colour only in the online journal) MST 10.1088/1361-6501/aa543e Paper 3 1361-6501 1361-6501/17/035003+10$33.00 K Feng et\u00a0al i.e. time or frequency domain analysis, is much more complicated than for fixed axis gear systems. Researchers [5] have mentioned that fixed axis gearbox diagnostic tools are not always workable for planetary gear systems because of their unique dynamic motions, and methodologies to deal with the complicated vibrations of planetary gear systems are of great importance for condition monitoring"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001940_j.jsv.2018.02.033-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001940_j.jsv.2018.02.033-Figure1-1.png",
        "caption": "Fig. 1. Geometric definition of (a) a flux tube and (b) a magnetic equivalent circuit.",
        "texts": [
            " The dynamic characteristics including spectra of stator and rotor currents, varying rotor rotational speed, electromagnetic torque, dynamic mesh forces and accelerations of the ring gear are obtained. The rest of the study is structured as follows: Section 2 presents the PNMmotormodel. Section 3 presents dynamicmodels of the planetary geared rotor system and the induction machine. Section 4 presents dynamic characteristics simulation and analysis for the electromechanical system with or without load and unsymmetrical voltage sags separately. Finally, several conclusions are presented. The PNM method is based on the decomposition of an electromagnetic system into flux tubes as shown in Fig. 1a. With magnetic flux and magnetomotive force (MMF) being the variables, each tube is characterized by its permeances, and all the permeances are linked together to give a permeance network model. Once the PNM is developed, the Kirchhoff's current law is used to establish a nodal-based solution for the magnetic circuit [12]. Elements that appear in a magnetic equivalent circuit can be divided into two groups: active (MMF) and passive (permeances) as shown in Fig. 1b. A permeance is used here instead of an inverse of reluctance Rm, which is defined as follows [12]: P \u00bc mA\u00f0x\u00de l (1) where P, m, A(x), and l are permeance, permeability, crosssection area, and length of an element, respectively. The MMF sources can be calculated by multiplying the current in each phase by the number of the turns in the corresponding slot for the stator or the rotor loop currents for the rotor whichmay be represented as being either in the yoke or the tooth. The PNM equations of an electrical machine can be formulated in terms of the magnetic scalar potential u after the permeances and MMF sources are calculated"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000083_j.mechmachtheory.2009.01.010-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000083_j.mechmachtheory.2009.01.010-Figure2-1.png",
        "caption": "Fig. 2. (a) Definition of end relief and (b) coordinate system for an end-relieved tooth flank.",
        "texts": [
            " The equation of meshing (2) can be determined from the following equation expressed in line coordinates [13]: Du\u00bdn\u0302b $\u03021C \u00bc 0; \u00f03\u00de where n\u0302b is the dual unit vector for the normal to the rack cutter surface RC; and $\u03021C is the relative screw between the rackcutter and the gear. After the elimination of one parameter with Eq. (2), the surface of the conical gear can now be described with two parameters, l and u. The complete expressions of the mathematical model can be found in Appendix A, or in Refs. [7,13]. In order to avoid the concentration of contact stress on the end of the face-width, teeth are usually manufactured to have end-relief. Fig. 2a shows a representation of end relief which can be regarded as straight line modification. In practical applications, the amount ce and the length be of the tooth of a conical gear are used to determine the end relief. The following rule of thumb can be applied: [22] be \u00bc \u00f00:1 to 0:2\u00de b; \u00f04\u00de ce \u00bc \u00f02 to 3\u00de dbth; \u00f05\u00de where dbth is the combined deflection of mated teeth, assuming an even load distribution over the face-width. Given the length be and the amount ce, the motion trace of the center of the hob or the grinding wheel is shown in Fig. 2b. The end-relieved tooth surface near the toe can be regarded as a conical gear with a larger cone angle (h + Dh), while the relieved surface near the heel as the gear has a smaller cone angle (h Dh). The parameter Dh is determined from the length be and the amount ce Dh \u00bc arctan ce be : \u00f06\u00de The approach mentioned in Section 2.1 can be used to generate the end-relieved tooth surfaces with different cone angles (h \u00b1 Dh). However, the reference plane of the tooth surface for end-relief at the toe or the heel is shifted by a distance Dbi or Dbo, respectively, with respect to the reference plane of the active tooth flank along the gear axis; see Fig. 2b. The corresponding coordinate z1i,o of the end-relieved flanks at the toe and the heel of the conical gear (in coordinate system S1) should be modified by a distance Dbi,o, i.e., z1i;o \u00bc zEi;o \u00fe Dbi;o; \u00f07\u00de where zEi,o is the z-coordinate determined by the afore-mentioned generating approach. The distance shifted Dbi,o can be obtained by Dbi;o \u00bc \u00f0bi;o be\u00de\u00bdtan\u00f0h Dh\u00de tan h tan\u00f0h Dh\u00de : \u00f08\u00de The position of the section on toe bi or on heel bo in Eq. (8) is positive if the section is located on the positive z-coordinate of S1 and vice versa"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002120_j.mechmachtheory.2015.09.010-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002120_j.mechmachtheory.2015.09.010-Figure1-1.png",
        "caption": "Fig. 1. Geometric relationships of tooth-profile generating.",
        "texts": [
            " c) A series of problems closely related to the process was discussed, including the feeding strategy, cutter-retracting approach, cutter preset method, and the design method of stock and fixture. d) A pair of non-circular gears with a 3-order sinusoidal gear ratio was then used as an example; the stock and corresponding fixture were designed, the processing parameters were set, the cutting process was simulated in the form of a computer graphic, and finally, the process was implemented with a 3-linkage CNC gear-shaping machine. Fig. 1 shows the geometric relationship of tooth-profile generating with a shape cutter. Its principle was to ensure the pure rotation between the pitch curve of a non-circular gear and the pitch circle of the shape cutter. Supposing that the shaped non-circular gear is fixed on the ground, the coordinate system S0(O0 \u2212 x0y0) is rigidly connected to the gear. Its pitch curve is then defined as r(\u03c6). P represents the contact point between the pitch curve and pitch circle with a polar angle \u03c6, thus: xp \u00bc r \u03c6\u00f0 \u00de cos \u03c6\u00f0 \u00de yp \u00bc r \u03c6\u00f0 \u00de sin \u03c6\u00f0 \u00de : \u00f01\u00de Assuming that t is the unit tangent vector of the pitch curve, and according to the basic knowledge of the planar curve [19], the tangent vector at P can be found by: t0 \u00bc d r \u03c6\u00f0 \u00de cos \u03c6\u00f0 \u00de\u00f0 \u00de d\u03c6 d r \u03c6\u00f0 \u00de sin \u03c6\u00f0 \u00de\u00f0 \u00de d\u03c6 2 664 3 775 \u00bc r0 \u03c6\u00f0 \u00de cos \u03c6\u00f0 \u00de\u2212r \u03c6\u00f0 \u00de sin \u03c6\u00f0 \u00de r0 \u03c6\u00f0 \u00de sin \u03c6\u00f0 \u00de \u00fe r \u03c6\u00f0 \u00de cos \u03c6\u00f0 \u00de \u00f02\u00de where r0\u00f0\u03c6\u00de \u00bc dr\u00f0\u03c6\u00de d\u03c6 The module of the tangent vector is: jt0j \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r0 \u03c6\u00f0 \u00de cos \u03c6\u00f0 \u00de\u2212r \u03c6\u00f0 \u00de sin \u03c6\u00f0 \u00de\u00bd 2 \u00fe r0 \u03c6\u00f0 \u00de sin \u03c6\u00f0 \u00de \u00fe r \u03c6\u00f0 \u00de cos \u03c6\u00f0 \u00de\u00bd 2 q \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r0 \u03c6\u00f0 \u00de\u00bd 2 \u00fe r \u03c6\u00f0 \u00de2 q : \u00f03\u00de Thus, the unit tangent vector is: t \u00bc t0 t0j j \u00bc r0 \u03c60\u00f0 \u00de cos \u03c6\u00f0 \u00de\u2212r \u03c6\u00f0 \u00de sin \u03c6\u00f0 \u00deffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r0 \u03c6\u00f0 \u00de\u00bd 2 \u00fe r \u03c6\u00f0 \u00de2 q r0 \u03c6\u00f0 \u00de sin \u03c6\u00f0 \u00de \u00fe r \u03c6\u00f0 \u00de cos \u03c6\u00f0 \u00deffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r0 \u03c6\u00f0 \u00de\u00bd 2 \u00fe r \u03c6\u00f0 \u00de2 q 2 666664 3 777775 \u00bc tx ty : \u00f04\u00de Assuming that the unit normal vector of a pitch curve is n at point P, as it is perpendicular to the unit tangent vector [20] then the following is true: n \u00bc ty \u2212tx \u00bc r0 \u03c6\u00f0 \u00de sin \u03c6\u00f0 \u00de \u00fe r \u03c6\u00f0 \u00de cos \u03c6\u00f0 \u00deffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r0 \u03c6\u00f0 \u00de\u00bd 2 \u00fe r \u03c6\u00f0 \u00de2 q \u2212r0 \u03c6\u00f0 \u00de cos \u03c6\u00f0 \u00de \u00fe r \u03c6\u00f0 \u00de sin \u03c6\u00f0 \u00deffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r0 \u03c6\u00f0 \u00de\u00bd 2 \u00fe r \u03c6\u00f0 \u00de2 q 2 666664 3 777775: \u00f05\u00de As shown in Fig. 1, a mobile coordinate system S1(O1 \u2212 x1y1) was set at the center of the shape cutter, its x1-axis and y1-axis parallel to the unit normal vector n and the unit tangent vector t, respectively; the distance between O1 and point P is the radius of the cutter's pitch circle, namely O1P = ro. The reference frame S2(O2 \u2212 x2y2) is fixed on the shape cutter, and its angle relative to S1 is \u03b8 (the rotation angle of the shape cutter). The arc length of the pitch curve at point P is S \u03c6\u00f0 \u00de \u00bc Z\u03c6 0 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r0 \u03c6\u00f0 \u00de\u00bd 2 \u00fe r \u03c6\u00f0 \u00de2 q d\u03c6: \u00f06\u00de With the pure rolling relationship [21], the rotating angle of the shape cutter can be represented as: \u03b8 \u00bc S \u03c6\u00f0 \u00de ro \u00bc Z\u03c6 0 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r0 \u03c6\u00f0 \u00de\u00bd 2 \u00fe r \u03c6\u00f0 \u00de2 q d\u03c6 ro : \u00f07\u00de The center of the shape cutter O2 is on a normal equidistant line of the pitch curve [22], namely: xo2 \u00bc r \u03c6\u00f0 \u00de cos \u03c6\u00f0 \u00de\u2212roty yo2 \u00bc r \u03c6\u00f0 \u00de sin \u03c6\u00f0 \u00de \u00fe rotx : \u00f08\u00de Thus, the center distance between the cutter and non-circular gear can be found by: E \u00bc jO2O0 \u21c0j \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi xo2 2 \u00fe yo2 2 q \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r \u03c6\u00f0 \u00de2 \u00fe ro 2 \u00fe 2ror \u03c6\u00f0 \u00deffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r0 \u03c6\u00f0 \u00de\u00bd 2 \u00fe r \u03c6\u00f0 \u00de2 q vuut : \u00f09\u00de The polar angle of the cutter at point O2 is: \u03b3 \u00bc a tan yo2 xo2 \u00bc a tan r \u03c6\u00f0 \u00de sin\u03c6\u00fe rotx r \u03c6\u00f0 \u00de cos\u03c6\u2212roty \" # \u00bc a tan ro \u2212r \u03c6\u00f0 \u00de sin\u03c6\u00fe r0 \u03c6\u00f0 \u00de cos\u03c6 \u00fe r \u03c6\u00f0 \u00de sin\u03c6 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r0 \u03c6\u00f0 \u00de\u00bd 2 \u00fe r \u03c6\u00f0 \u00de2 q ro \u2212r \u03c6\u00f0 \u00de cos\u03c6\u2212r0 \u03c6\u00f0 \u00de sin\u03c6\u00bd \u00fe r \u03c6\u00f0 \u00de cos\u03c6 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r0 \u03c6\u00f0 \u00de\u00bd 2 \u00fe r \u03c6\u00f0 \u00de2 q 8>< >: 9>= >;: \u00f010\u00de The angle between O0O2 and PO2 is: \u03b1 \u00bc a cos PO2 \u21c0 O0O2 \u21c0 PO2 \u21c0 O0O2 \u21c0 0 B@ 1 CA \u00bc a cos xo2\u2212xp; yo2\u2212yp xo2; yo2\u00f0 \u00de Ero 2 4 3 5 \u00bc a cos ro \u00fe r \u03c6\u00f0 \u00de2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r0 \u03c6\u00f0 \u00de\u00bd 2 \u00fe r \u03c6\u00f0 \u00de2 q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r \u03c6\u00f0 \u00de2 \u00fe ro 2 \u00fe 2ror \u03c6\u00f0 \u00deffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r0 \u03c6\u00f0 \u00de\u00bd 2 \u00fe r \u03c6\u00f0 \u00de2 q vuut : \u00f011\u00de Based on the geometric relations above, the coordinate transformation matrix between reference frames [23] S2 and S1 is: M12 \u00bc cos\u03b8 sin\u03b8 0 \u2212 sin\u03b8 cos\u03b8 0 0 0 1 2 4 3 5: \u00f012\u00de The coordinate transformation matrix between reference frames S0 and S1 is easily obtainable through the use of the vector, and the coordinate basis vector of S0 is thus: i0 \u00bc 1 0 j0 \u00bc 0 1 8>< >: : \u00f013\u00de Similarly, the coordinate basis vector of S1 is: i1 \u00bc n j1 \u00bc t : \u00f014\u00de Thus, the transformation matrix between reference frame S0 and S1 is: M01 \u00bc i0 i1 i0 j1 xo2 j0 i1 j0 j1 yo2 0 0 1 2 4 3 5 \u00bc ty tx xo2 \u2212tx ty yo2 0 0 1 2 4 3 5: \u00f015\u00de The tooth profiles of the shape cutter are the same as those of spur gears, which are generated from rack cutters and can be defined as r2\u00f0t\u00de \u00bc \u00bd x2\u00f0t\u00de y2\u00f0t\u00de 1 T in reference to Ref",
            " When shaping a gear, the feed of the cutter should perform motions in two directions instead of a single conjugate meshing of the gear. Similar to the process of a cylindrical gear, several process cycles are set in advance, the number of which is codetermined by the cutter parameters and the processing capability of the machine tool. An exceedingly small number of cycles will do harm to the cutter and the machine tool, while too many cycles will reduce process efficiency. Fig. 3 shows the geometric relationship in shaping a non-circular gear involving feed; and different from that shown in Fig. 1, the cutter pitch circle and gear's pitch curve are no longer in line with each other, namely O0 2P \u2260 ro. Supposing that O0 2P 0 \u00bc ho, in terms of Eq. (8), the position of O2 ' can be obtained with the following equation: x0o2 \u00bc r \u03c6\u00f0 \u00de cos\u03c6\u2212hoty y0o2 \u00bc r \u03c6\u00f0 \u00de sin\u03c6\u00fe hotx ( : \u00f027\u00de Thus, the center distance is: E0 \u00bc jO0 2O0 \u21c0j \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r \u03c6\u00f0 \u00de2 \u00fe ho 2 \u00fe 2hor \u03c6\u00f0 \u00deffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r \u03c6\u00f0 \u00de2 \u00fe r0 \u03c6\u00f0 \u00de\u00bd 2 q vuut : \u00f028\u00de is in the tangential direction (\u03c6 increase while ho stays constant)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002004_1.4028532-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002004_1.4028532-Figure2-1.png",
        "caption": "Fig. 2 CC surfaces from developable surface inversion. (a) Cylindrical inversion and (b) conical inversion.",
        "texts": [
            " Journal of Mechanical Design DECEMBER 2014, Vol. 136 / 121404-1Copyright VC 2014 by ASME Downloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use with complete definitions available in Ref. [21]. Parameter equations in Ref. [21] are referred to directly where appropriate. A common method for creating CC origami geometry is to invert sections of known developable surface [2], such as a cylinder or cone, shown in Fig. 2. This is a relatively inefficient way to generate CC geometry, as it requires defining a developable surface and an intersecting cutting plane, and then calculating the elliptical curve that occurs at the intersection of the two. By reversing this process, that is to say by first defining an elliptical surface and then projecting this ellipse along reflected axes, a much simpler method to generate CC geometry is obtained. Furthermore, by fitting this ellipse through a known rigid origami pattern, specifically a Miura-derivative pattern, geometric solutions for projected axes direction, unit volume, and pattern closure can be reused",
            " 136 / 121404-5 Downloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/28/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use creation and rigid subdivision stages to a prismatic Tapered Miura-base pattern. Whereas the CC-Miura pattern can be conceptually thought of as the developable surface created from the inversion of a cylindrical surface, the CC-tapered Miura pattern can be thought of as a developable surface created from the inversion of a conical surface, shown in Fig. 2(b). 4.1.1 Ellipse Creation. Ellipses fitted through zigzag creases on a prismatic Tapered Miura-base are shown in Fig. 9(a). It can be seen that unlike the CC-Miura pattern, sequential ellipses expand on the base geometry to form an inverted conical surface. From Eq. (50) in Ref. [21], bj \u00bc b1 \u00fe \u00f0j 1\u00deac sin q= sin /f , it is known that the side length of sequential zigzags bj scales linearly for each jth zigzag crease line. Therefore, in the simplest embodiment, each ellipse is assumed to have the same gradient parameter u, shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001880_j.applthermaleng.2014.02.008-Figure13-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001880_j.applthermaleng.2014.02.008-Figure13-1.png",
        "caption": "Fig. 13. The heat flux distribution of the rotor (unit: W/m2).",
        "texts": [
            " Firstly, the downward gradient of the temperature-rise on stator yoke in L2 is a little steeper than L1, and this is because the bad heat transfers capability of the connecting box. Secondly, based on the same reason, the temperature-rise in stator area of L1 is higher than that L2. Fig. 12(c) and (d) show the fan effect on the path L3 and L4. In the stator area, the highest temperature moves to load side. The fan effect on the rotor can be neglected, and the highest temperature area is still located in the axial center. The heat flux distribution of the rotor under the healthy and faulty condition is shown in Fig. 13. From it, we can clearly know that the heat flux distribution of the rotor in all directions is uneven, and the heat flux value of the joint of the bars and the end rings is relatively high, where the broken bar fault always appears. When broken bar fault happens, the heat flux of the joint adjacent to broken bar increases very obviously. The main aim of the study is to develop and verify the thermal model for analyzing and predicting thermal behavior of TEFC induction motor with healthy cage or with broken bar"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003375_j.actaastro.2020.04.016-Figure12-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003375_j.actaastro.2020.04.016-Figure12-1.png",
        "caption": "Fig. 12. Stereo camera unit hardware.",
        "texts": [],
        "surrounding_texts": [
            "In order to accomplish the three missions, satellite and ground station systems were designed. Table 1 shows basic specifications of the CubeSat. Fig. 2 shows the on-board components and Fig. 3 shows the system diagram of OrigamiSat-1. The system consists of four major subsystems: (i) membrane deployment unit, (ii) stereo camera unit, (iii) bus, and (iv) ground station. For the bus, most components are composed of purchased CubeSat components, which are made of commercial off-theshelf (COTS) components. Three circuit boards are developed in-house. This design aims at facilitating future space technology demonstrations in various sectors. Finally, Fig. 4 shows the mission sequence. (1) the CubeSat is released from a rocket, (2) the deployable antennas are deployed, (3) the extendable mast is extended to enable taking pictures/movies of the deployable membrane, and finally (4) the multifunctional membrane is deployed. In the following subsection, each of the satellite subsystems is described."
        ]
    },
    {
        "image_filename": "designv10_5_0000487_1077546309352826-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000487_1077546309352826-Figure2-1.png",
        "caption": "Figure 2. Inverted pendulum system",
        "texts": [],
        "surrounding_texts": [
            "_Vi \u00bc giSi \u00bd Xp\nj\u00bc1\ngij x\u00f0 \u00de ej 1\nri\ngiS 2 i \u00fe\n1 2 gie T im\n\u00f0LT i Ki \u00fe KiLi\u00deeim \u00fe gi\u00bd\nXp\nj\u00bc1\ngij x\u00f0 \u00de ej 1\nri\nSi\nbT i Kieim \u00bc giSi oi\n1 ri giS 2 i \u00fe 1 2 gie T im\n\u00f0LT i Ki \u00fe KiLi\u00deeim \u00fe gioi bT i Kieim\n1 ri giSi bT i Kieim:\n\u00f039\u00de\nThus, (39) can be rewritten as\n_Vi \u00bc gioi \u00f0Si \u00fe bT i Kieim\u00de\n1 ri giS 2 i \u00fe 1 2 gie T im\n\u00f0LT i Ki \u00fe KiLi\u00deeim\n1 ri giSi bT i Kieim\n\u00bc gi\u00bd 1ffiffiffi 2 p ffiffiffiffi ri p oi 1ffiffiffiffiffiffi 2ri p \u00f0Si \u00fe bT i Kieim\u00de 2 \u00fe 1\n2 girio 2 i \u00fe\n1\n2ri\ngi\u00f0Si \u00fe bT i Kieim\u00de2\n1 r giS 2 i\n\u00fe 1\n2 gie T im\u00f0L T i Ki \u00fe KiLi\u00deeim\n1 ri giSi bT i Kieim\n\u00bc gi\u00bd 1ffiffiffi 2 p ffiffiffiffi ri p oi 1ffiffiffiffiffiffi 2ri p \u00f0Si \u00fe bT i Kieim\u00de 2 \u00fe 1 2 girio 2 i \u00fe 1\n2ri\ngi\u00f0S2 i \u00fe 2Sib T i Kieim \u00fe eT imKibib T i Kieim\u00de\n1 ri giS 2 i\n\u00fe 1\n2 gie T im\u00f0L T i Ki \u00fe KiLi\u00deeim\n1 ri giSi bT i Kieim\n1 2 gie T im\u00f0L T i Ki \u00fe KiLi \u00fe 1\nri\nKibib T i Ki\u00deeim\n1\n2ri\ngiS 2 i\n\u00fe 1\n2 girio 2 i\n\u00bc 1\n2 gie T im\u00f0L T i Ki \u00fe KiLi \u00fe\n1 ri Kibib T i Ki\n1 ri cic T i \u00deeim \u00fe 1 2 girio 2 i\n\u00f040\u00de\nFrom (33),\n_Vi 1\n2ri\ngie T imQieim \u00fe\n1 2 girio 2 i : \u00f041\u00de\nIntegrating both sides of (41) yields\nVi\u00f0tf \u00de Vi\u00f00\u00de 1\n2ri\ngi\n\u00f0tf\n0\neT imQieimdt \u00fe rigi\n2\n\u00f0tf\n0\no2 i dt:\n\u00f042\u00de\nThus,\n\u00f0tf\n0\neT imQieimdt 2ri\ngi\nVi\u00f00\u00de 2ri\ngi\nVi\u00f0tf \u00de \u00fe r2 i\n\u00f0tf\n0\no2 i dt:\nSince 0 and Vi 0, (31) can be rewritten as\n\u00f0tf\n0\neT imQieimdt 2\ngi\nVi\u00f00\u00de \u00fe r2 i\n\u00f0tf\n0\no2 i dt:\nWith (37), the following result can be obtained:\n\u00f0tf\n0\neT imQieimdt eT im\u00f00\u00dePieim\u00f00\u00de \u00fe 1\ngi\n~yT \u00f00\u00deHi ~y\u00f00\u00de\n\u00fe r2 i\n\u00f0tf\n0\no2 i dt:\n\u00f043\u00de\nThus, the H1 tracking performance in (28) is achieved\nand the nonlinear system (6) can be controlled.\nIn order to solve the control problem more efficiently, the control objective can be formulated as a minimization problem, so that the attenuation level ri in the H1 tracking performance of (30) is reduced in order to be sufficiently small.\nNote that the matrix inequalities in (33) can be transformed into a certain form of LMI. That is, with the Schur complements (Boyd et al., 1994), (33) is equivalent to\nLT i Ki \u00fe KiLi 1\nri cic\nT i Kibi Q 1=2 i\nbT i Ki ri 01 n\n\u00f0Q1=2 i \u00de T 0n 1 ri In n\n2 64\n3 75 0; \u00f044\u00de\nwhere \u00f0Q1=2 i \u00de T Q 1=2 i \u00bc Qi. Therefore, the minimization problem can be formulated into an EVP:\nsubject to Ki \u00bc KT i > 0 and (44).\nBased on the above analysis, the design procedure of the\nGA-based H1-AFSMC can be summarized as follows:\n[step 1] Construct the fuzzy models (21) based on a genetic algorithm and specify each suitable sliding surface as Si \u00bc cT i eim.\n[step 2] Specify Qi and a prescribed attenuation level ri. Next, solve the LMI of (33) or the EVP of (44) to obtain Ki and letPi \u00bc cic T i \u00fe Ki.\n[step 3] Apply the controller, as given by (16) and (24), to control the nonlinear system (35) and adjust y\u0302j by the adaptive law, as given by (34).\nat UNIV OF SOUTHERN CALIFORNIA on April 4, 2014jvc.sagepub.comDownloaded from",
            "Remark: Conventionally, in the design of the AFSMC, Si is defined as Si \u00bc cT i eim. This implies that the order of the motion equation in the sliding motion is equal to n 1. Thus, conventional AFSMC only considers the information from x1; x2; ; xn 1, and can achieve the following H1 tracking performance criterion:\u00f0tf\n0\nxT Q x dt S2\u00f00\u00de \u00fe xT \u00f00\u00de P x\u00f00\u00de \u00fe ~yT \u00f00\u00de\nG 1~y\u00f00\u00de \u00fe r2\n\u00f0tf\n0\no2dt;\n\u00f045\u00de\nwhere x \u00bc \u00bdx1; x2; ; xn 1 T , P and Q are symmetric positive definite weighting matrices and G > 0 is an adaptive gain matrix.\nHowever, as discussed above, the proposed control strategy considers that all the information of x1; x2; ; xn 1 can achieve the following H1 tracking performance criterion:\u00f0tf\n0\neT imQieimdt eT im\u00f00\u00dePieim\u00f00\u00de \u00fe 1\ngi\n~yT \u00f00\u00deHi ~y\u00f00\u00de\n\u00fe r2 i\n\u00f0tf\n0\no2 i dt:\nNumerical Simulation\nIn this Section, the proposed GA-based H1 AFSMC is demonstrated with an example of the control methodology.\nConsider the problem of balancing an inverted pendu-\nlum on a cart, as shown in Figure (2).\nWe assume the external disturbance d(t) \u00bc 0 in this nonlinear system. The dynamic equations of motion of the pendulum are given below (Goldberg, 1989):\n_x1 \u00bc x2 _x2 \u00bc g sin\u00f0x1\u00de amlx2 2 sin\u00f02x1\u00de=2 a cos\u00f0x1\u00de u\n4l=3 aml cos2\u00f0x1\u00de\n( ; \u00f046\u00de\nwhere x1 denotes the angle (in radian) of the pendulum from the vertical, and x2 denotes the angular vector. Thus, the gravity constant is g \u00bc 9:8m/s2, where m is the mass of the pendulum, M is the mass of the cart, l is the length of the pendulum, u is the force applied to the cart (in Newtons), and a \u00bc 1=\u00f0m\u00feM\u00de. The parameters chosen for the pendulum in this simulation are: m \u00bc 0.05kg, M \u00bc 1kg and l \u00bc 0.5m.\nThe control objective in this example is to balance the inverted pendulum with the approximate range x 2 \u00f0 p=2 ; p=2\u00de. Using the procedure discussed previously, the GA-based H1-AFSMC can be designed using the following steps:\n[Step 1] Construct fuzzy models (21) based on the genetic algorithm. The initial values of the consequent parameter vector y\u0302 can be chosen as follows:\n\u00bd 1; 0:6263; 0:4113; 0:2100; 0:0850; 0; 0:0850; 0:2100;\n0:4113; 0:6263; 1 T , with each suitable sliding sur-\nface specified as S \u00bc cT em \u00bc 5e\u00fe _e.\n[Step 2] Let Q \u00bc Qi of \u00f044\u00de \u00bc I2 2, with the attenuation level specified to be r \u00bc ri of \u00f044\u00de \u00bc 0:5. Then, use the LMI optimization toolbox in Matlab to solve the EVP of (44) in order to obtain K \u00bc Ki of \u00f044\u00de \u00bc 12:2306 2:3405\n2:3405 0:8104\nand P \u00bc Pi of \u00f030\u00de \u00bc ccT \u00fe K \u00bc 37:2306 2:6595\n2:6595 1:8104\n.\n[Step 3] Apply the controller, as given by (16) and (24),\nto control the nonlinear system (6).\nThen, let g \u00bc 0:5, and adjust y\u0302j by the adaptive law, as\ngiven by (34).\nTherefore, based on Theorem 1, the proposed GA-based AFSMC can asymptotically stabilize the inverted pendulum. The simulation results are illustrated in Figures (3) to (6). The initial conditions are x1\u00f00\u00de \u00bc 30 ; 60 and x2\u00f00\u00de \u00bc 0.\nFigures (3) and (6) show that the inverted pendulum becomes rapidly, asymptotically stable, because the system trajectories that start from any non-zero initial states rapidly and asymptotically approach the origin.\nat UNIV OF SOUTHERN CALIFORNIA on April 4, 2014jvc.sagepub.comDownloaded from",
            "at UNIV OF SOUTHERN CALIFORNIA on April 4, 2014jvc.sagepub.comDownloaded from"
        ]
    },
    {
        "image_filename": "designv10_5_0003501_j.ast.2020.106192-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003501_j.ast.2020.106192-Figure2-1.png",
        "caption": "Fig. 2. Space manipulator.",
        "texts": [
            " Using Lemma 1, (55) can be upper bounded as V\u0307 3 \u2264 \u22122(1+\u03bb2)/2\u03bbmin(K d)\u03b4c V (1+\u03bb2)/2 3 \u2212 (1 \u2212 \u03b4c) n\u2211 i=1 |z2i| ( Kdi |z2i|\u03bb2 \u2212 K pi\u03b4s ) (56) where \u03bbmin(K d) is the minimum eigenvalue of K d . From (56), it can be observed that z2 is finite-time bounded. Because s is finite-time bounded, it can be obtained from (19) that z I is finite-time bounded too. Because z I is continuously differentiable mapping with respect to time, one can concluded that z\u0307 I is finite-time bounded, which denotes that K psgn\u03bb1 (z1) \u2212 K dsgn\u03bb2 (z2) is finite-time bounded. Therefore, z1 is finite-time bounded. Numerical simulations are performed on a three-link space manipulator shown in Fig. 2 to verify the effectiveness of the proposed controller. All numerical simulations run on the software of Matlab R2017a. The space manipulator contains a spacecraft body and a robotic arm with three rigid links. The spacecraft body is defined as G0, and the j-th link is defined as G j . Each link is connected to its inboard body using a revolute joint. The spacecraft body is a free body with six degrees of freedom. A body-fixed frame O j is attached to body G j ( j = 0, 1, 2, 3) shown in Fig. 2. The dynamics of three-link space manipulator can be obtained from [25]. The generalized coordinate q of the three-link manipulator is chosen as q = [rT , \u0398 T , \u03b81, \u03b82, \u03b83]T (57) where r and \u0398 represent the position vector and the Euler angles of body G0, respectively; \u03b8 j ( j = 1, 2, 3) is the relative rotational angle of the j-th link. The inertia matrix M(q) and the nonlinear force F N (q, \u0307q) in (1) are given by M(q) = 3\u2211 M j, F N(q, q\u0307) = 3\u2211 F N j (58) j=0 j=0 Table 1 Parameters of the space manipulator"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000782_j.mechmachtheory.2012.11.006-Figure14-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000782_j.mechmachtheory.2012.11.006-Figure14-1.png",
        "caption": "Fig. 14. 3D view of the gear pair.",
        "texts": [
            " This force value can be used to calculate the axial position of the contact force resultant normalized on the active face width according to: sp \u00bc Ftn1 Ftn : \u00f025\u00de This parameter is stored in a second look-up table, calculated for the same discrete range of operating conditions used for the mesh stiffness, and interpolated during the multibody simulation. Eq. (12) is therefore modified as follows to account for shuttling: Oz \u00bc 0 0 min FW1; FW2\u00f0 \u00de\u22c5sp DTE; PMC;CD;M\u00f0 \u00de 8< : 9= ;: \u00f026\u00de Simulations for a reference helical gear pair (Fig. 14) are performed to show how the effects discussed in the previous paragraphs are captured in the multibody simulation. The gear specifications are reported in Table 1, teeth have standard size. Gears are constrained using rigid revolute joints. One gear is driven in velocity, while a resisting torque with a nominal value of 100 nm is applied to the other gear, causing a nominal normal contact force of 2726 N. Viscous damping has been added to smooth the DTE curves, equal to 105 Ns/m. Few cases were tested: 1) Gears without microgeometric modifications a"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003953_j.engfailanal.2020.104907-Figure11-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003953_j.engfailanal.2020.104907-Figure11-1.png",
        "caption": "Fig. 11. Contact patterns: (a) moment of the minimum center distance; (b) moment of the maximum center distance.",
        "texts": [
            " The fluctuation amplitude of the mesh stiffness is not affected by the initial eccentric phase difference and the fluctuation period is the product of the meshing period and the least common multiple of the tooth number of the pinion and gear. In the case of different number of teeth, the excitation effects of non-loaded transmission error under different initial eccentric phase differences are almost the same (see Fig. 10) except that there is a phase difference on the fluctuation. The contact patterns of the pinion under the maximum and minimum gear center distance are shown in Fig. 11. The contact state of the gear tooth is time-varying, which is greatly affected by the geometric eccentricity. The effective contact area of the tooth surface reaches the maximum when the gear center distance is the minimum, and the double tooth meshing area reaches the maximum. The high stress zone at the middle of the gear tooth is the single tooth contact area. The addendum and root of the tooth are excessive stress areas because of the excessively small length of the contact line. The parameters of experimental test rig are shown in Table 3"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003687_j.mechmachtheory.2019.103727-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003687_j.mechmachtheory.2019.103727-Figure1-1.png",
        "caption": "Fig. 1. Machine tool setting for pinion teeth finishing.",
        "texts": [
            " In order to improve the operating characteristics of the gear pair and to reduce the sensitivity of the gear pair to tooth errors and to the mutual position of the mating members appropriately chosen modifications are introduced into the teeth of the pinion. As a result of these modifications theoretically point contact of the meshed teeth surfaces appears instead of linear contact. The modifications are introduced by the variation in machine tool settings and in the tool geometry. The machine tool settings used for pinion tooth finishing are specified in Fig. 1: sliding base setting ( c ), basic radial ( e ), basic machine center to back increment ( f ), basic offset ( g ), tilt angle ( \u03b2), and swivel angle ( \u03b4). The other manufacture parameters are the velocity ratio in the kinematical scheme of the machine tool for the generation of the pinion tooth surface ( i g1 ), the radius of the tool ( r t1 ), and the radii of the tool profile ( r prof 1 , r prof 2 , Fig. 2 ). The tooth surface of the pinion is defined by the following system of equations: r( 1 ) 0 = M p0 \u00b7 M p4 ( i g1 ) \u00b7 M p3 ( c, f, g ) \u00b7 M p2 ( e ) \u00b7 M p1 ( \u03b2, \u03b4) \u00b7 r( T 1 ) T 1 ( r t1 , r prof 1 , r prof 2 ) (1a) v( T 1 , 1 ) 0 \u00b7 e( T 1 ) 0 = 0 (1b) where r ( T 1 ) T 1 is the radius vector of tool surface points, matrices M p0 , M p1 , M p2 , M p3 , and M p4 provide the coordinate transformations from system K T 1 (rigidly connected to the cradle and tool T 1 ) to the stationary coordinate system K 0 ",
            " A multi-objective optimization model is developed to systematically define optimal head-cutter geometry and machine tool settings simultaneously minimizing maximum tooth contact pressure, angular displacement error of the driven gear and average flash temperature and maximizing the efficiency of the gear pair. The proper manufacture variables, objective functions, and constraints are as follows. The following machine tool setting and tool geometry parameters are taken as the basis of the proposed optimization formulation (specified in Fig. 1 ): sliding base setting ( c ), basic radial ( e ), basic machine center to back increment ( f ), basic offset ( g ), tilt angle ( \u03b2), and swivel angle ( \u03b4). The other parameters are the velocity ratio in the kinematics scheme of the machine tool for the generation of the pinion tooth surface ( i g1 ), the radius of the tool ( r t1 ), and the radii of the tool profile ( r prof 1 , r prof 2 ). Therefore the vector of parameters is mp = [ c, e, f, g, \u03b2, \u03b4, i g1 , r t1 , r prof 1 , r prof 2 ] (17) The goal of the optimization is to minimize tooth contact pressure, transmission errors and fluid film average temperature and to maximize the efficiency of the gear pair while keeping the loaded contact pattern inside the physical tooth boundaries of the pinion and the gear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002730_j.synthmet.2018.08.021-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002730_j.synthmet.2018.08.021-Figure1-1.png",
        "caption": "Fig. 1. Schematic representation of the PGE, modification processes and final electrode.",
        "texts": [
            " Multi-wall carbon nanotubes (MWCNTs) with 60\u201380 nm in outer diameter and 10\u201315 \u03bcm of average length prepared by chemical vapour deposition, were purchased from Shenzhen Nanotech Port Ltd. Co. (China). An aqueous dispersion of PEDOT:PSS (1.3 wt% solid content), ascorbic acid, uric acid, dopamine, fructose, lactose, and sucrose were purchased from Sigma-Aldrich. 72,000 gmol\u22121 polyvinyl alcohol (PVA) was obtained from Merck. Also, 0.1 M sodium hydroxide solution (NaOH) was used as the supporting electrolyte. All chemical reagents were of analytical grade. All solutions were prepared using deionized water. Fig. 1 shows the schematic of PGE used as working electrode, modification processes, and the final modified electrode. For the construction of PGEs, Faber-Castell HB hardness graphite pencil leads with a 2mm diameter were employed. The graphite leads, initially 130mm long, were cut in 20mm. An electrical contact was made by soldering a high-conductivity copper wire to the pencil lead. Then, the graphite lead and solder were placed in a glass tube and a fast-drying epoxy resin (\u223c2min) was used to seal and attach the electrodes to the glass tube"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000560_j.jsv.2009.03.013-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000560_j.jsv.2009.03.013-Figure2-1.png",
        "caption": "Fig. 2. Roller/ring load distribution for a radially loaded bearing.",
        "texts": [
            " [20]: uci \u00bc rO2 4E \u00f0\u00f01 n\u00de\u00f03\u00fe n\u00de\u00f0r2i r2o\u00de \u00fe \u00f01\u00fe n\u00de\u00f03\u00fe n\u00der2o \u00f01 n2\u00der2i \u00deri (1) uco \u00bc rO2 4E \u00f0\u00f01 n\u00de\u00f03\u00fe n\u00de\u00f0r2i r2o\u00de \u00fe \u00f01\u00fe n\u00de\u00f03\u00fe n\u00der2i \u00f01 n2\u00der2o\u00dero (2) where uci and uco are the diametral growths at the inner and outer radii, ri and ro, respectively. In the present model, the centrifugal expansion is included in the diametral clearance Jd . The ring out-of-roundness u\u00f0y\u00de produced by a single line contact can be expressed through a Fourier series as follows: u\u00f0y\u00de \u00bc L X1 k\u00bc0 Kk cos\u00f0ky\u00de (3) Superposing the effect of N equidistant loads \u00f0Lj\u00de yields u\u00f0y\u00de \u00bc XN j\u00bc1 Lj X1 k\u00bc0 Kk cos\u00f0k\u00f0Cj y\u00de\u00de (4) where each contact load coincides with the roller angular position Cj (cf. Fig. 2). The stiffness coefficients Kk can be obtained from an analytical solution as the one given by Young [21]: assuming a single load is applied, the thin ring is balanced by a symmetric tangential shear stress distribution. ARTICLE IN PRESS A. Leblanc et al. / Journal of Sound and Vibration 325 (2009) 145\u2013160148 Only three stiffness coefficients are then required to obtain the ring deformations: u\u00f0y\u00de \u00bc L\u00f0K0 \u00fe K1 cos y\u00fe K2 cos 2y\u00de (5) Although this formula leads to a good approximation of the shape of the inner ring when subjected to a static load, it fails completely for a set of equally, or almost identically loaded rollers"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003848_j.jmatprotec.2020.117032-Figure11-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003848_j.jmatprotec.2020.117032-Figure11-1.png",
        "caption": "Fig. 11. Tailored blank made by orbital forming after deep drawing for R40 and R35.2.",
        "texts": [
            " In the previous sections, it is shown that manufacturing of hybrid gear components by PBF-LB and forming is possible, even though challenges exist for R35.2. The content of this section is the comparison of parts manufactured with orbital forming and hybrid parts regarding the geometry. Based on these results, the potential and characteristics of the hybrid approach are discussed. Finally, the comparison of tailored blanks with formed tooth geometry and hybrid parts is made. In a first step, the geometries of cross-sections of tailored blanks made by orbital forming of radii R40 and R35.2 (Fig. 11) and hybrid parts (Fig. 12) after deep drawing in radial direction are presented. The geometries are compared to the target tooth depth, which represents the depth of tooth cavity in the forming die. In case of orbital formed tailored blanks, the form filling after deep drawing is low. This results from insufficient material being formed. As investigations on the cross section after orbital forming show (Fig. 8), the pre-formed teeth are comparatively small. Therefore, the low form filling was expected after deep drawing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000648_978-3-642-17531-2-Figure1.5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000648_978-3-642-17531-2-Figure1.5-1.png",
        "caption": "Fig. 1.5. Piezoelectric functional materials (smart structures)",
        "texts": [
            " As a result, today, there are mechatronic system elements which enable direct measurement at physically relevant locations, \u201cthinking\u201d, and action, i.e. nearly perfect realization of functional and spatial integration. New materials: functional materials Spatial integration which creates compact, moving systems was and continues to be advanced by new materials. As the most important example, take piezoelectric materials, which now enable the construction of compact sensors and actuators, and, as a component of smart structures, the direct integration of measurement and actuation components into a mechanical structure (see Fig. 1.5) (Preumont 2002), (Srinivasan and McFarland 2001). Mechatronics: technical community At the international level, two highly respectable journals specialized in the technical area of mechatronics have established themselves: IEEE/ASME Transactions on Mechatronics (IEEE: Institute of Electri- cal and Electronics Engineers, ASME: American Society of Mechanical Engineers), IFAC Journal Mechatronics (IFAC: International Federation of Automatic Control). 5 Processor data from www.Intel.com. These journals reflect the current research into mechatronic questions"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000576_j.ins.2010.07.025-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000576_j.ins.2010.07.025-Figure7-1.png",
        "caption": "Fig. 7. Schematic of electromechanical system.",
        "texts": [
            " The parameters initial conditions are chosen as W0 a;1 \u00bc \u00bd0;0;0;0;0 T ; W0 a;2 \u00bc \u00bd0;0;0;0;0;0;0;0;0; 0;0; 0 T ; b\u03021\u00f00\u00de \u00bc b\u03022\u00f00\u00de \u00bc 0; cW a;1\u00f00\u00de \u00bc \u00bd0;0;0;0;0 T and cW a;2\u00f00\u00de \u00bc \u00bd0;0;0;0;0;0;0;0;0;0;0; 0 T . The simulation results are shown in Figs. 5 and 6. From the simulation results, it clearly shows that the method in [11] can not guarantee that all the signals of the closed-loop systems are bounded and lacks in the robustness to the unmodeled dynamics and disturbances. Example 2 [9]. Consider the electromechanical system shown by Fig. 7. The dynamics of the electromechanical system is described by the following equation. M\u20acq\u00fe B _q\u00fe N sin\u00f0q\u00de \u00bc I L_I \u00bc Ve RI KB _q ( \u00f054\u00de where M \u00bc J Ks \u00femL2 0 3Ks \u00feM0L2 0 Ks \u00fe 2M0R2 0 5Ks ; N \u00bc mL0G 2Ks \u00feM0L0G Ks ; B \u00bc B0 Ks J is the rotor inertia, m is the link mass, M0 is the load mass, L0 is the link length, R0 is the radius of the load, G is the gravity coefficient, B0 is the coefficient of viscous friction at the joint, q\u00f0t\u00de is the angular motor position (and hence the position of the load), I\u00f0t\u00de is the motor armature current, and Ks is the coefficient which characterizes the electromechanical conversion of armature current to torque"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003913_s00170-019-04908-3-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003913_s00170-019-04908-3-Figure5-1.png",
        "caption": "Fig. 5 Conical Gaussian volumetric heat source",
        "texts": [
            " qc \u00bc hc Text\u2212T\u00f0 \u00de \u00f06\u00de Above, qc is the heat dissipation, hc is the heat transfer coefficient (W/m2K), Text is the geometry temperature, and T is the ambient temperature (293 K). In addition, the radiative heat transfer from the top surface of the geometry domain was applied (Eq. (7)). The bottom surface of the geometry domain was set as the ambient temperature (293 K). qr \u00bc \u03c3sb\u03b5 Text 4\u2212T4 \u00f07\u00de Above, \u03c3sb is the Stefan-Boltzmann coefficient (W/m2K4) and \u03b5 is the emissivity coefficient. A moving heat source with a conical Gaussian shape was applied for predicting the melt pool dimensions and temperature distributions (Fig. 5). The conical Gaussian heat source is described as [11]: I x; y; z\u00f0 \u00de \u00bc q0:exp \u22122 x2 \u00fe y2 r20 \u00f08\u00de r0 z\u00f0 \u00de \u00bc re \u00fe z H re\u2212ri\u00f0 \u00de \u00f09\u00de where I(x, y, z), q0, re, and ri are the heat intensity distribution, the maximum value of heat intensity, and radius on top and bottom of the heat source profile, respectively. Based on the thermal energy conservation (Eq. (10)): \u03b1:P \u00bc \u222b0\u2212H \u222b \u221e \u2212\u221e\u222b \u221e \u2212\u221eq0:exp \u22122 x2 \u00fe y2 r20 dxdydz \u00f010\u00de where and P are the laser beam absorptivity and laser power respectively. q0 is derived from Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003199_j.mechmachtheory.2019.103576-Figure28-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003199_j.mechmachtheory.2019.103576-Figure28-1.png",
        "caption": "Fig. 28. Definition of alignment errors.",
        "texts": [
            " A point on the pinion involute flank represented in S \u2032 f is given by r ( f \u2032 ) 1 (\u03b81 , u 1 , \u03c61 ) = M f \u2032 1 (\u03c61 ) r 1 (\u03b81 , u 1 ) (68) and its corresponding normal vector is n ( f \u2032 ) 1 (\u03b81 , u 1 , \u03c61 ) = L f \u2032 1 (\u03c61 ) n 1 (\u03b81 , u 1 ) (69) The transformation matrix M f \u2032 1 takes alignment errors into account and is represented by M f \u2032 1 = \u23a1 \u23a2 \u23a2 \u23a2 \u23a2 \u23a2 \u23a2 \u23a3 cos \u03c61 \u2212 sin \u03c61 0 \u2212E \u2212 E cos (\u03b3 \u2212 \u03b3 ) sin \u03c61 cos (\u03b3 \u2212 \u03b3 ) cos \u03c61 \u2212 sin (\u03b3 \u2212 \u03b3 ) a sin ( \u03c0 2 \u2212 \u03b3 ) sin (\u03b3 \u2212 \u03b3 ) sin \u03c61 sin (\u03b3 \u2212 \u03b3 ) cos \u03c61 cos (\u03b3 \u2212 \u03b3 ) r 1 \u2212r s sin (\u03b3 \u2212 \u03b3 ) + a cos ( \u03c0 2 \u2212 \u03b3 ) 0 0 0 1 \u23a4 \u23a5 \u23a5 \u23a5 \u23a5 \u23a5 \u23a5 \u23a6 (70) where matrix L f \u2032 1 (\u03c61 ) is the upper-left 3 \u00d7 3 sub-matrix of M f \u2032 1 (\u03c61 ) . In Fig. 28 , the alignment errors a , \u03b3 and E are shown. The face-gear surface and its normal vector transformed into system S f \u2032 are given by r ( f \u2032 ) 2 (\u03b8s , \u03c6s , \u03c62 ) = M f \u2032 2 (\u03c62 ) r 2 (\u03b8s , \u03c6s ) (71) From Eqs. (74) + (75) a system of six non-linear equations is obtained. The system of equations is solved iteratively, e.g. by application of the Newton-Raphson method, while \u03c61 might be chosen as input parameter. The contact path is formed by the sum of contact points for varied pinion rotation angles \u03c6 "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000166_14644193jmbd48-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000166_14644193jmbd48-Figure6-1.png",
        "caption": "Fig. 6 Predicted contact pressure distributions at (a) \u03c6 = \u03c61, (b) \u03c6 = \u03c65, and (c) \u03c6 = \u03c610",
        "texts": [
            " With all necessary parameters at each contact point calculated by using the formulations and the contact model presented in previous sections, instantaneous efficiency of a hypoid gear pair can be calculated by applying the methodology defined in Fig. 1. A facehobbed hypoid gear pair borrowed from an automotive application will be used here as an example system to demonstrate the hypoid gear efficiency methodology. The main gear blank dimensions of this example system are listed in Table 3. The pinion member is generated and the ring gear is non-generated. The lubricant is gear oil 75W90. Figure 6 illustrates the contact pressures distribution of the hypoid ring gear in contact at three different Proc. IMechE Vol. 221 Part K: J. Multi-body Dynamics JMBD48 \u00a9 IMechE 2007 at OhioLink on October 30, 2014pik.sagepub.comDownloaded from mesh positions. As discussed earlier, contact pressures, radii of curvatures, sliding velocities, and sum of rolling velocities are four of the key geometry-related parameters used in the friction model. The distributions of these parameters along the contact lines at the same mesh angle \u03c6 = \u03c61 are shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001187_iros.2015.7354192-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001187_iros.2015.7354192-Figure1-1.png",
        "caption": "Fig. 1: (a) TSLIP model with a rigid trunk and a leg modeled as a massless prismatic spring. (b) Velocity-based leg adjustment (VBLA) during flight phase.",
        "texts": [
            " In most of the leg adjustment strategies, the foot landing position is adjusted based on the horizontal velocity [4] [20]. In this paper, VBLA (Velocity Based Leg Adjustment) presented in [21], is used as a robust method. This method can mimic human leg adjustment strategies for perturbed hopping [22] and achieve a large range of running velocities by a fixed controller [23]. Here, we use this method for walking. In VBLA, the leg direction is given by vector ~O as a weighted average of the CoM velocity vector ~V and the gravity vector ~G = [0,\u2212g]T (Fig. 1b). ~O = (1\u2212\u00b5)~V +\u00b5~G (6) where weighting constant \u00b5 accepts values between 0 and 1. 2) FMCH for hip torque control: We consider a bidirectional rotational spring between trunk and each leg. With the configuration showed in Fig. 2(a) for double support phase, the hip torques of leg i is determined by \u03c4i = ki(\u03c8i\u2212\u03c8 0 i ) (7) in which ki and \u03c80 i are the hip stiffness and rest angle for leg i, respectively, and \u03c8i is the angle between trunk and leg i as shown in Fig. 2(a). In FMCH control approach we use the leg force for modulating hip stiffness"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000083_j.mechmachtheory.2009.01.010-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000083_j.mechmachtheory.2009.01.010-Figure5-1.png",
        "caption": "Fig. 5. Coordinate system for contact points.",
        "texts": [
            ", rf1 \u00bcMf1r1; \u00f018\u00de rf2 \u00bcMf2r2: \u00f019\u00de The transformation matrix Mf1 obtained for a rotation angle /1 0 of gear 1 at the instantaneous contact point and the distance Dw1 bC1 is Mf1 \u00bc cos /01 sin /01 0 0 sin /01 cos /01 0 0 0 0 1 bC1 \u00fe Dw1 0 0 0 1 2 6664 3 7775: \u00f020\u00de On the other hand, the transformation matrix Mf2 obtained for the angle /02, the shaft angle R, the offset a, and the distance Dw2 bC2 is Mf2 \u00bc cos /02 sin /02 0 a cos R sin /02 cos R cos /02 sin R \u00f0Dw2 bC2\u00de sin R sin R sin /20 sin R cos /02 cos R \u00f0Dw2 bC2\u00de cos R 0 0 0 1 2 6664 3 7775: \u00f021\u00de For further analysis of contact stress, the coordinate system Sy is employed here to obtain the contact point and the initial separation between two engaged tooth surfaces. As shown in Fig. 5, the origin Oy of Sy coincides with the contact point, and the axis zy is selected as the line of action. The coordinate plane xy\u2013yy is attached to the common tangential plane between the two engaged tooth surfaces, while the axis xy coincides with the major axis of the contact ellipse of the engaged tooth surfaces. Consider the distance T1Oy given for positioning of the instantaneous contact point. The transformation from coordinate system Sf to Sy is expressed as ry1;2 \u00bcMyiMif rf1;2: \u00f022\u00de Matrices Mif and Myi are represented as follows: Mif \u00bc sin bCb1 sin w sin bCb1 cos w cos bCb1 Dw1 cos bCb1 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2 Cw1 r2 Cb1 q sin bCb1 cos w sin w 0 rCb1 cos bCb1 sin w cos bCb1 cos w sin bCb1 Dw1 sin bCb1 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2 Cw1 r2 Cb1 q cos bCb1 \u00fe T1C0 T1Oy 0 0 0 1 2 666664 3 777775: \u00f023\u00de Myi \u00bc cos c sin c 0 0 sin c cos c 0 0 0 0 1 0 0 0 0 1 2 6664 3 7775: \u00f024\u00de The complete expressions of position vectors ry1,2 can be found in Appendix B",
            " The total elastic deformation w1 or w2 is expressed as the sum of contact deformation wH and tooth bending deflection wB, i.e., wi \u00bc wH;i \u00fewB;i; i \u00bc 1;2: \u00f035\u00de The distribution of the contact stresses in the contact region can be calculated utilizing the method of discretization, where a set of finite numbers represent uniform contact stresses pj (j = 1,2, . . . ,n). These act at discrete segments equal in area s, as shown in Fig. 7b. The center of each segment is also the contact point with the corresponding tooth flank. The coordinates are expressed in the coordinate system Sy (xy,yy,zy) defined in Fig. 5. Assuming linear elasticity of the gear tooth, the total elastic deformation wk at point k of the corresponding opposing tooth flanks can be expressed as a linear summation of the contact deformation and the bending deflections caused by all the contact stresses pj, i.e., wk \u00bc w1k \u00few2k \u00bc Xn j\u00bc1 \u00f0fH;kj \u00fe fB;kj\u00depj: \u00f036\u00de The factors fH,kj and fB,kj in Eq. (36) represent the influence coefficients for contact deformation and tooth bending deflection at point k for a unit contact stress pj at point j namely fH;kj pj \u00bc wH1;kj \u00fewH2;kj; fB;kj pj \u00bc wB1;kj \u00fewB2;kj: In addition to the above deformation conditions, the condition for equilibrium of forces must be satisfied, namely the sum of all the contact pressures acting over each discrete segment must balance the applied force F, s Xn j\u00bc1 pj \u00bc F: \u00f037\u00de Considering all n segments, we have a system of (n + 1) independent linear equations with n unknown contact stresses pj and one unknown relative approach d for the elastic tooth contact problem from Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000620_j.triboint.2012.11.007-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000620_j.triboint.2012.11.007-Figure2-1.png",
        "caption": "Fig. 2. (a) Ball-on-disk scuffing test set-up and (b) t",
        "texts": [
            " fluid region [23] Q x,y,t\u00f0 \u00de \u00bc Zn x x,y,t\u00f0 \u00de u2 s h x,y,t\u00f0 \u00de \u00f014\u00de where the effective viscosity in the x direction Zn x \u00bc Z=cosh tm=t0 considering an Eyring fluid. For the areas where h\u00bc0, the surface shear q\u00bcmbp and Q\u00bcmbp9us9. The boundary lubrication friction coefficient mb is assumed to be 0.1 [3,23] due to the lack of the measurements of mb for the specific lubricant additive-steel combination used in this work. For the entire contact, the friction coefficient m can be found as m\u00bc RR Gqdxdy=W . For the ball-on-disk contact problem as shown in Fig. 2, the disk surface bulk temperature is controlled at the oil inlet temperature, while the ball bulk temperature is dependent on the frictional heating generated from the contact, the convective cooling provided by the ambient oil and air mixture and the operating time. The heat transfer formulation is thus only devised for the ball to estimate its surface bulk temperature. As the ball rotates against the disk, the contact produces a circumferential contact track on the ball surface. It is assumed the frictional heat is evenly distributed along this track, such that the three-dimensional heat balance problem can be reduced to a two-dimensional problem of the shaded semicircle as 0 5 15 20 25 30 225 200 175 150 125 100 75 225 200 175 150 125 100 75 225 200 175 150 125 100 75 Test duratio T 1b [\u00b0 C ] 10ru = m/s 0.25SR = \u2212 10ru = m/s 0.75SR = \u2212 10ru = m/s 1SR = \u2212 10 0 Fig. 8. Comparison of the predicted and measured Tb1 for tests in Fig. 2(b), whose heat transfer is dictated by @2T @X2 \u00fe @2T @Y2 \u00bc 1 ks @T @t \u00f015\u00de The boundary conditions along the diameter AB, the arc of the contact zone CD and the arcs of the convective cooling zones AC and BD are given as @T @X \u00bc 0, ks @T @X \u00bc ~Q 1\u00feF Tamb T\u00f0 \u00de, ks @T @X \u00bcF Tamb T\u00f0 \u00de \u00f016a c\u00de respectively. Here, ks is the solid thermal conductivity, Tamb is the ambient temperature and F is the convective heat transfer coefficient which can be estimated as [24] F Y\u00f0 \u00de \u00bc 0:0665 km r\u00f0Y\u00de Zmcm km 1=3 2o1rmr2\u00f0Y\u00de Zm 2=3 \u00f017\u00de for a circumferential surface with radius of r(Y) rotating at angular velocity o1 (Fig. 2(b)). Denoting the volume ratio of oil in the surrounding medium (air\u2013oil mixture) as w, the thermal conductivity, specific heat, viscosity and density of the air\u2013oil mixture are approximated as km \u00bc 1 w ka\u00fewkf , cm \u00bc 1 w ca\u00fewcf \u00f018a;b\u00de Zm \u00bc 1 w Za\u00fewZ0, rm \u00bc 1 w ra\u00fewr0 \u00f018c;d\u00de 700 600 500 400 300 200 100 0 700 600 500 400 300 200 100 0 700 600 500 400 300 200 100 0 n [min] W [ N ] Measured 1bT Predicted 1bT W 20ru = m/s 0.25SR = \u2212 20ru = m/s 0.75SR = \u2212 20ru = m/s 1SR = \u2212 5 15 20 25 3010 (a) I, (b) II, (c) III, (d) IV, (e) V and (f) VI defined in Table 1",
            " The evenly distributed heat flux along the circumferential contact track ~Q 1 is defined as ~Q 1 Y\u00f0 \u00de \u00bc Lx=r1 2p WQ Y\u00f0 \u00de \u00f019a\u00de where Lx is the length of the EHL computational domain in x direction and Q is the average frictional heat produced along the contact arc CD that is defined as Q Y\u00f0 \u00de \u00bc 1 Lt 1 Lx Z t dt Z x Q x,Y ,t\u00f0 \u00dedx \u00f019b\u00de with Lt denoting the length of the time period of the EHL analysis. The average heat partition coefficient W satisfies Tb1 Tb2 \u00bc havg 2kf 1 2W Q \u00f019c\u00de here, havg is the average film thickness within the Hertzian zone, and Tb1 and Tb2 are the surface bulk temperatures of the ball and disk, respectively. Instantaneous flash temperatures (Eq. (11)) are added to these temperatures to find the transient local surface temperature distributions as T1 \u00bc Tb1\u00feDT1, T2 \u00bc Tb2\u00feDT2 \u00f020a;b\u00de The scuffing tests were performed on a ball-on-disk WAM machine as shown in Fig. 2(a). During the test, the disk temperature was controlled by a thermal module located below the disk and set at the oil inlet temperature. Two disk thermocouples were used to measure and confirm the disk surface temperature. The contacting ball of diameter of 20.64 mm was held by a hollow shaft (to minimize the heat conduction through the shaft) and pushed against the disk in the normal direction of the disk surface. One thermocouple was devised to touch the ball surface near its contact track to measure its bulk temperature",
            " The rotational axis of the ball was on the vertical plane that was along the disk radial direction, such that the ball and disk surface velocities were in the same direction (perpendicular to the disk radial direction), representing the contact condition of spur and helical gears. In this experiment, a fully formulated turbine oil Mil-PRF23699 was used as the lubricant. The polyol ester formulation ) T1 and (f) T2 for test I at the last loading stage of ph\u00bc2.47 GPa. includes an anti-wear additive, tricresyl phosphate (TCP). The oil was supplied into the oil slinger and pushed through the small radial holes in the oil slinger towards the contact track by the centrifugal force as shown in Fig. 2(a). Examples of the measured three-dimensional roughness profiles of the ball and disk specimens are shown in Fig. 3. The disk surfaces were textured in the radial direction with the intention of simulating actual ground gear surface roughness (allowing the surface velocities to be perpendicular to the roughness lay direction), while the ball surfaces had a smoother, isotropic texture. The composite root\u2013mean\u2013square (RMS) roughness amplitude of the ball\u2013disk pair shown in Fig. 3 is Rq\u00bc0.53 mm. The test conditions in terms of the rolling velocity and the slideto-roll ratio SR\u00bc us=ur are listed in Table 1",
            " (1) and (3) is then solved for p over the entire contact zone. The pressure solution is checked for both the load balance convergence and pressure convergence. The converged p and h are used to find the temperature distributions of the bounding surfaces as well as the fluid. A thermal iteration loop is utilized to ensure the temperature distribution convergence. The converged solutions are then used for the initial guesses of the next time step. For the heat transfer analysis of the ball, the semicircle in Fig. 2(b) is discretized into NX\u00bc20 and NY\u00bc40 elements, which is sufficient for the estimation of the ball bulk temperature distribution. Explicit finite difference method of second order is used to solve Eq. (15). At the oil inlet temperature of Tf 0 \u00bc 121 3C , the lubricant (MilPRF-23699) has an ambient density of r0\u00bc935.2 kg/m3, viscosity of Z0\u00bc0.00273 Pa s and two-slope pressure\u2013viscosity coefficients of a1\u00bc11.3 GPa 1 and a2\u00bc5.29 GPa 1. The transition pressure for the two-slope pressure\u2013viscosity relationship of Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003076_tmag.2019.2955884-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003076_tmag.2019.2955884-Figure5-1.png",
        "caption": "Fig. 5. 3-D magnetic-flux density distributions at 8 A for (a) unaligned position and (b) aligned position.",
        "texts": [
            " (7) Comparing (5) and (6) with (7) justifies that the air-gap flux of the PM-SRM is intensified by \u03d5 g and the stator pole flux is weakened by \u03d5 sp compared to the PMless SRM. Hence, the proposed PM-SRM produces higher torque without experiencing any saturations. Fig. 4 depicts the flux lines and flux density vectors of the PM-SRM at the unaligned and aligned positions of the rotor. The obtained flux lines confirm the operating principle of the PM-SRM. Also, it is inferred that the armature field lines travel through a short path, which results in low iron losses. Fig. 5 demonstrates the flux density distributions of the proposed PM-SRM at both unaligned and aligned positions at the current of 8 A. At the unaligned position, the flux density of the stator poles is about 1.5 T. At the aligned position, the maximum flux density occurs near the stator teeth with the value of 1.9 T, which is at the knee point of the utilized steel B\u2013H curve. Hence, it is obvious that the PM-SRM is not saturated under the rated current. Fig. 6 depicts the air-gap flux density of the PM-SRM and PMless SRM at the current of 8 A as well as for the PM-SRM at zero current"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001198_j.ijsolstr.2014.06.023-Figure12-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001198_j.ijsolstr.2014.06.023-Figure12-1.png",
        "caption": "Fig. 12. Film/Sub I with clamped boundary conditions under uniaxial compression: (a) sinusoidal pattern v in the final step, (b) the final shape v3.",
        "texts": [
            " The other boundary conditions and loadings are the same as before. The same mesh as in simply supported case is carried out. Two bifurcation points have been found as shown in Fig. 10. The two instability modes correspond to modulated oscillations (see Fig. 11). The first one is similar to simply supported case except the vanishing rotations on the boundary. The second one takes a hyperbolic tangent envelope except a small localization in the middle. Then the pattern tends to be a uniform hyperbolic tangent shape when the load reaches the final step (see Fig. 12). Checkerboard modes are explored via Film/Sub II. The square film is under equi-biaxial compression both in x and y direction (see Fig. 5(b)). The deflections v3 on four edges r, s, t and u, are locked to be zero, which means the film is simply supported on the whole boundary. The displacements v1 and v2 in the film center are also set to be zero to avoid rigid body movements. The same mesh as in the sinusoidal case with totally 100,827 DOF is performed. Four bifurcations have been captured through computing bifurcation indicators (see Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002584_s00170-018-2169-5-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002584_s00170-018-2169-5-Figure4-1.png",
        "caption": "Fig. 4 Milling test sample design, virtual and real manufacturing on Aktinos-500 Kondia\u00ae",
        "texts": [
            " Turning tests samples are \u201cbar\u201d type geometry where Inconel\u00ae 718 metal powder material is added spirally around an Inconel\u00ae 718 base material bar. Design (Fig. 2) and manufacturing (Fig. 3) conditions are shown in Table 2. Spirally added material is 97.5 mm long and height is 5.2 mm being layer height 0.65 mm. Additive parameters are 650 W for laser power and 500 mm/min for feed rate. On the other hand, milling test samples are \u201cblock\u201d type geometry (Inconel\u00ae 718 metal powder) that has been added on an Inconel\u00ae 718 base material sheet. Design (Fig. 4) and manufacturing conditions are shown in Table 3. Added dimensions are 30 \u00d7 25 \u00d7 11.7 mm being layer height 0.9 mm. Additive manufacturing parameters are 500W for laser power and 300 mm/min for feed rate. Inconel\u00ae 718 can be treated by precipitation. Therefore, it is possible to manufacture the part and proceed to the heat treatment afterwards, in order to improve mechanical properties of the material that could be thermally affected by the additive process itself. In this case, precipitation hardening heat Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001006_s10846-014-0143-5-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001006_s10846-014-0143-5-Figure8-1.png",
        "caption": "Fig. 8 Helicopter longitudinal motion",
        "texts": [
            " A feedback linearization middle loop controller is used to decouple the input/output pairs. Then a PD controller is used for trajectory tracking. The final cascaded controller\u2019s matrices are able to be computed off-line, allowing for relatively simple implementation in real time. A simplified state estimator is used for real time implementation to track the yaw-rate feedback parameter. Lastly, guidance waypoints are transformed to the body frame by a direct cosine matrix. Simulated and experimental results are presented for a figure 8 trajectory with constant altitude. In [88, 89], an adaptive controller is designed on a 13 state linear model of the Yamaha R-Max with decoupled translational and attitude dynamics. A PD compensator is added to each of the loops. In [95, 96], a tracking controller using a MultiLoop PID (MLPID) is designed for a 12 state LTI model of the Berkeley Yamaha R-Max. This 3-loop architecture is similar to that in Fig. 22, consisting of an inner loop for attitude control, middle loop for linear velocity control and the outermost loop for position control"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001022_1.4005336-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001022_1.4005336-Figure5-1.png",
        "caption": "Fig. 5 Wrench graph of the 4-RUU PM in P3 Fig. 6 A constraint singular configuration of the 4-RUU PM",
        "texts": [
            " Accordingly, the four actuation forces can be expressed as F1 \u00bc ab ; F2 \u00bc cd ; F3 \u00bc ef ; F4 \u00bc gh (8) Now, let x\u00bc (x;0) and y\u00bc (y;0). Hence, line xy collects all points at infinity corresponding to directions orthogonal to z. Let j\u00bc (z;0), i\u00bc (m1;0), k\u00bc (m2;0), l\u00bc (m3;0), and m\u00bc (m4;0). Accordingly, the four constraint moments are expressed as M1 \u00bc ij ; M2 \u00bc kj ; M3 \u00bc lj ; M4 \u00bc mj (9) where i; k; l and m belong to xy. A wrench graph, representing the projective lines associated with the wrenches of the 4-RUU PM in P3, is given in Fig. 5. 6.1 Superbracket Decomposition. Due to the redundancy of constraints, a superbracket of the 4-RUU PM can be composed of the four actuation forces Fi (i\u00bc 1,...,4) in addition to two among the four constraint moments expressed in Eq. (9). Thus, one can write 4 2 \u00bc C2 4 \u00bc 6 superbrackets Sj (j\u00bc 1,...,6). However, a parallel singularity occurs when the six possible superbrackets vanish simultaneously. For example, the superbracket S1 involving the two constraint moments ij and kj takes the form S1 \u00bc \u00bdab; ef; cd; gh; ij; kj (10) From Eq",
            " Thus, j \u00bc c a and \u00bdabej \u00bc \u00bd\u00f0c j\u00debej \u00bc \u00bdcbej \u00bc \u00bdecbj . Accordingly B \u00bc \u00bdadfh \u00bdecbj \u00bdabfh \u00bdecdj \u00bc \u00bda d fh \u00bdec b j \u00bc \u00f0afh\u00de ^ \u00f0ecj\u00de ^ \u00f0db\u00de (18) where the dotted letters stand for the permuted elements as explained in Refs. [14] and [27]. From Eq. (18), term B is the meet of three geometric entities, namely, (1) \u00f0afh\u00de is a finite plane having f3 f4 as normal vector; (2) \u00f0ecj\u00de is the finite plane containing the finite points e and c and the unit vector z. Since plane \u00f0ecj\u00de contains lines T 12 and T 34 (Fig. 5), the line at infinity of plane \u00f0ecj\u00de \u00bc span\u00f0T 12; T 34\u00de can be expressed as \u00f0uj\u00de where u\u00bc (u;0) and u is the unit vector of a finite line nonparallel to z and lying in plane \u00f0ecj\u00de, i.e., crossing T 12 and T 34. Accordingly, plane \u00f0ecj\u00de has u z as normal vector. It should be noted that u and u exist unless T 12 T 34; (3) \u00f0db\u00de is the line at infinity of all parallel finite planes containing the unit vectors f1 and f2, i.e., having f1 f2 as normal vector. An actuation singularity occurs iff term B of Eq",
            " Those planes are thus all parallel and have a common line at infinity containing points j, b, d, f, and h. This line crosses all actuation forces and all constraint moments. Hence, such a configuration corresponds to a singular complex, i.e., condition (5b) of GG. Consequently, the constraint singularities of the 4-RUU PM correspond to conditions 1 and (5b) of GG. The singularity analysis of the 4-RUU PM performed in Sec. 6 leads to two singularity conditions given by Eqs. (17) and (20). These conditions were obtained from the wrench graph of the PM obtained in Fig. 5 and based on the existence of a finite line parallel to z crossing two actuation forces of two limbs of the PM. Since this is true in a general configuration for all architectures of Fig. 1, a similar wrench graph can be obtained for each architecture. As a consequence, the two singularity conditions are true for the 11 architectures shown in Fig. 1. Moreover, the actuation singularity condition obtained in Eq. (20) is valid for 3T1R PMs, whose actuation forces are four mutually skew lines. Indeed, a finite line T ij directed along z that crosses two actuation forces can be found unless one of the forces is along z or the two forces are parallel and lie in a plane that does not contain the z direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000648_978-3-642-17531-2-Figure8.3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000648_978-3-642-17531-2-Figure8.3-1.png",
        "caption": "Fig. 8.3. Magnetic field lines: a) cylindrical coil, b) ferromagnetic core (leakage field lines not shown)",
        "texts": [
            "1) describes the relationship between the exciting current and the contour integral of the magnetic field intensity, not the field intensity itself. However, Eq. (8.1) still forms the basis magnetic field calculations (Jackson 1999), (Hughes 2006). For simple, symmetric configurations, it can be straightforwardly employed to derive predictive design models. One often easily met assumption is that of a homogeneous magnetic field, i.e. the field variables H and B , or , are independent of location (constant) within a bounded domain. For example, this is the case for the interior of a cylindrical coil (Fig. 8.3a), or within a homogeneous ferromagnetic material ( 1) r (Fig. 8.3b). In the latter case, the field lines primarily flow inside the ferromagnetic material, so that magnetic flux can be easily guided through space using physical structures. 500 8 Functional Realization: Electromagnetically-Acting Transducers Magnetization curves For real flux-conducting media ( 1 r , ferromagnetic materials), the material equation (8.4) does not describe a linear relationship: it is well known that both saturation and hysteresis effects must be taken into account (Fig. 8.4a). The permeability is thus not constant, but depends on magnetic saturation (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002997_tie.2018.2807366-Figure10-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002997_tie.2018.2807366-Figure10-1.png",
        "caption": "Fig. 10. Test rig of the prototype SLIM: (a) On-site photo. (b) Diagram of the installed sensors",
        "texts": [
            "org/publications_standards/publications/rights/index.html for more information. > 7 same. Consequently, the vertical force may be the other significant reference to a. In Fig. 9(b), Fz1 and Fz2 with different primary lengths are presented, and both Fx1 and Fx2 can be obtained a higher value with a long primary, which means the larger air-gap flux due to the weaker longitudinal end effect will induce a larger slip current. For evaluating the performances of the equivalent circuit, a test rig of the SLIM, as shown in Fig. 10, is produced. The test bogie is equipped with a few pressure and tension sensors used for measuring several forces, and the major parameters of these sensors are shown in Table II. In Fig. 11, the results calculated by the equivalent circuit for LIM are compared with measurements for the thrust Fx and vertical force Fz, and these are a function of the velocity when Ip=160 A, f=5, 15, 25, 35 Hz. The experimental measurement is carried out by a test rig installed with the prototype SLIM, and it is connected with a VVVF drives"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000648_978-3-642-17531-2-Figure9.10-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000648_978-3-642-17531-2-Figure9.10-1.png",
        "caption": "Fig. 9.10. Spectrum of a band-limited signal",
        "texts": [
            " 586 9 Functional Realization: Digital Information Processing Sampling theorem, NYQUIST frequency In communications engineering and signal theory, the characteristic bounding frequency /2s of the sampling process (half the sampling frequency) is termed the NYQUIST frequency. Following the NYQUIST-SHANNON sampling theorem (Franklin et al. 1998), (Kuo 1997), signals can be completely reconstructed from the sampled series if the original signal contains no components above the NYQUIST frequency (as in Fig. 9.10). This signal reconstruction can be illustrated using Fig. 9.9 by imagining that in the sampled signal (lower-right figure, 1000N ), all harmonics\u2014 i.e. terms with 1N \u2014are eliminated with an ideal low-pass filter. In this case, only the fundamental harmonic (upper-left figure) remains. Ambiguities due to mirror frequencies Even with a band-limited input signal, the sampling process generates an infinite (periodic) mirror frequency spectrum in the output. Unfortunately, mirror frequencies can also occur within the base spectrum of the (band-limited) input signal, as when the input signal frequency contains components greater than the NYQUIST frequency /2s (see Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002452_tpwrd.2019.2891119-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002452_tpwrd.2019.2891119-Figure7-1.png",
        "caption": "Fig. 7. (a) Dual-axial TMR magnetic field measurement device (b) The TMR sensor circuit",
        "texts": [
            "01 Oe near control module and 0.034 Oe near battery. The results indicated that although the operation of UAV would introduce some harmonic component into magnetic field measurement, the distortion of the measurement result caused by UAV was small if the sensor was placed near control module, and it could be eliminated through simple filtering. This further proved that the feasibility of the proposed UAV inspection method. The dual-axial TMR magnetic field measurement device utilized in the measurement is illustrated in Fig. 7 The small cross field sensitivity of the uniaxial TMR sensor could be neglected compared with the sensitivity in the sensing axis [10], thus the sensing unit was consisted of two uniaxial TMR sensors placed perpendicularly with each other, as illustrated in Fig. 7(a). The sensitivity of each uniaxial TMR sensor was 5 mV/V/Oe, and the sensing direction was respectively 0885-8977 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. represented in the figure. The signal processing unit in which the outputs of TMR sensor were subsequently processed included the power supply, differential amplifier, and the A/D convertor",
            " In terms of the electromagnetic interference in the platform, the output signals of the measurement device needed to be processed and denoised. The wavelet denoising algorithm has the advantage of preserving important signal while removing noise, benefitting from the ability of time-frequency analysis for signals. In our experiment, the sampling rate of the measurement data was 5 MS/s, thus we chose the wavelet base as db4 and the wavelet level as 8. The measured sensing point on the sensing module is usually regarded as the central point between two sensors, which is indicated as the red point in Fig. 7. However, the position deviations, which is the difference between the actual coordinates of two uniaxial sensors and the measured sensing point in the experiment, would incur errors. We have calibrated the measurement data by adding a position bias on both coordinates of the two sensors. The expected measurement point coordinate was assumed to be (xm, ym, zm). The coordinate of the sensor measuring y axis magnetic field could be described as (xm, ym+ybias, zm+zbias), and the coordinate for z axis magnetic field could be described as (xm, ym-ybias, zm-zbias)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002365_tpel.2014.2319238-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002365_tpel.2014.2319238-Figure2-1.png",
        "caption": "Fig. 2. Magnetic flux density of a 12/8 SRM. (a). Single phase excitation. (b) Two phase excitation during phase commutation.",
        "texts": [],
        "surrounding_texts": [
            "The finite element analysis (FEA) of the studied SRM is conducted in JMAG software [38] and the non-linear inductance profile and torque profile of studied SRM is shown in Figs. 1(a) and (b), respectively. In three-phase SRM, two phases are excited during commutation. The magnetic flux density distribution of 12/8 SRM during one phase and twophase excitation are shown in Figs. 2 (a) and (b), respectively. Compared with one phase excitation mode, the two-phase excitation works at short-flux path [33] and the flux linkage of an individual phase includes both self and mutual flux linkage. Due to alternate polarities of windings of a three-phase motor, mutual flux is always additive and symmetric among individual phases. For the same current on adjacent phases, the mutual inductance profiles obtained from FEA are shown in Fig. 3(a). MA,B is the mutual inductance between phases A and B. The maximum value of mutual inductance is around 2% of the self-inductance at the same current level. The spatial relationship between self-inductance and mutual inductance of 12/8 SRM is also shown in Fig. 3. The mutual inductance profile MA,B is shifted by around 7.5\u02da compared with the self\u2013 inductance of phase A, LA. (a) 0885-8993 (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. TPEL-Reg-2014-02-0144 4"
        ]
    },
    {
        "image_filename": "designv10_5_0000031_s11044-007-9082-2-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000031_s11044-007-9082-2-Figure3-1.png",
        "caption": "Fig. 3 A 3R planar robot at its home and its unloaded (dashed) postures",
        "texts": [
            " The emergence of an asymmetric matrix is not that much related to the concept of stiffness, but rather to the concept of an elastic wrench generator. Wrench generators for various kinematic pairs were discussed in Angeles [2]. This can also be extended to conservative wrenches developed by elastic structures. Lack of space prevents us from elaborating on this concept. We illustrate here with one example how a stiffness matrix can be rendered asymmetric. To this end, let us consider the three-revolute (3R) planar robot depicted in Fig. 3 in two postures. The home posture (HP) is displayed with continuous lines, and characterized by the joint-angle values \u03b81 = 0, \u03b82 = 2\u03c0 3 , \u03b83 = 5\u03c0 3 . (46) Moreover, at the unloaded posture, displayed with dashed lines, the joint angles are all off from the above values by an angle \u03b8 = +\u03c0/100. In order to carry the robot from its unloaded posture s0 to its HP s1 we need to apply a wrench w10 to its EE, which is calculated from its Cartesian stiffness matrix KC , as given by (23). The purpose of the example is to calculate this wrench, then a wrench w21 that takes the robot to a second loaded posture s2 that we term post-loaded"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003413_j.ijfatigue.2020.106005-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003413_j.ijfatigue.2020.106005-Figure2-1.png",
        "caption": "Fig. 2. (a) Schematic diagram of LDED IN718 process. (b) The orientation and main dimensions of CT specimen.",
        "texts": [
            "5 kW; beam diameter, 5 mm; scanning speed, 10 mm/s; powder feeding rate, 25 g/min; overlap, 50%; \u0394Z, Element Fe Ni Mo Cr Nb Al Ti Co C Mn B wt.% Bal. 53.24 3.03 19.24 5.19 0.51 0.98 0.32 0.025 0.065 0.004 Note: FC, AC and WC denote furnace cooling, air cooling and water cooling, respectively. X. Yu et al. International Journal of Fatigue 143 (2021) 106005 0.6~0.8 mm. A staggered laser scanning strategy and an argon protected atmosphere (O content \u2264 50 ppm) were used to achieve favourable deposits (Fig. 2a). The CT specimens are machined from the deposits with the geometrical dimension of 62.5 \u00d7 60 \u00d7 10 mm3 according to ASTM E647 standard. Their FCG directions are set to be perpendicular to the deposition direction (Fig. 2b). FCG tests with R = 0.1 were performed using a MTS810 electrohydraulic servo fatigue testing machine at RT in air with a relative humidity of 37%. The FCG tests were run using K-control at a tensile sinusoidal form and a cyclic frequency of 15 Hz to generate data in Regions I and II. Particularly, a K-gradient of \u2212 0.1 mm\u2212 1 was applied to the decreasing K portion of the testing experiment to identify the \u0394Kth. da/dN data in Region II were generated under increasing K part of tests with a K-gradient of +0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001090_tmag.2011.2105498-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001090_tmag.2011.2105498-Figure9-1.png",
        "caption": "Fig. 9. Flux distribution in the SPSG at arbitrary rotor position due to the excitation of phase A in healthy (top), and 25% DE fault (bottom) cases.",
        "texts": [
            " Other self- and mutual-inductances of stator phases and rotor winding of the SPSG are calculated using the proposed analytic model. A Flux2D 10.2 FE package has been used to determine the stator self-inductances of the healthy and faulty SPSG [18]. To calculate self-inductance, for example the self-inductance of phase A , a dc current passes through phase A, in which the other phases and rotor winding are open circuit, and flux linkage of the same phase has been measured for a specific rotor position. is then calculated as follows: (19) Fig. 9 reveals the FE results of the magnetic flux distribution in the SPSG cross section at arbitrary rotor position in case of noneccentric and eccentric rotor caused by excitation of phase A. It indicates the symmetrical and asymmetrical flux distribution at healthy and faulty SPSG, respectively. The mentioned process has been repeated to simulate the saturated and unsaturated healthy and faulty cases for different rotor positions from 0 to 360 taking 3 steps. Results from this process in the case of saturated and unsaturated conditions, both in 25% DE, have been also shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000679_j.ymssp.2010.02.003-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000679_j.ymssp.2010.02.003-Figure6-1.png",
        "caption": "Fig. 6. Radial clearance.",
        "texts": [
            " pure-squeeze journal velocity in bearings W impedance modulus of journal bearings Wx0, Wy0 impedance of journal bearings in directions X0 and Y0, respectively (xk, yk) coordinates of the centre of gear k in reference frame OkXkYk zk number of teeth of gear k Greek symbols G eccentricity direction of the journal axis with respect to the bearing block in reference frame OkXk 0 Yk 0 ~G eccentricity direction of the gear axis with respect to the case in reference frame OkXk 0 Yk 0 DQ difference between the volumetric flow rate, coming into a control volume and coming out e eccentricity ratio in journal bearingse contact ratio y angular coordinate yi angular coordinate defining the position of the tip of tooth i (Fig. 6) yk angular displacement of gear k yp angular pitch m lubricant dynamic viscosity jkq angular position of the axis of the tooth space q for the gear k with respect to the Xk-axis o angular speed ok mean angular speed of gear k in steady-state operational conditions Subscripts i denotes isolated spaces between teeth jk applied to gear k k=1, 2 denotes gears q=1,y, zk denotes spaces between teeth development is not an easy task as it requires in a first stage a good analysis of the system in order to define the model goals",
            " (8) and (9) to the meatus on the tooth tip it is possible to calculate the volumetric flow rate in the tooth space i; both the pressure drop contribution and the \u2018drag flow rate\u2019 (due to the relative motion of the case with respect to the gear) are taken into account: Qh;i \u00bcQp;i\u00feQu;i \u00bc bkh3 i 12mlt \u00f0pi pi 1\u00de\u00fe bkokrexthi 2 \u00f011\u00de The height of the clearance hi between the tooth tip and the case depends on the position of the gear shaft (because of the eccentricity of the gear with respect to the case) and on the case wear. So, the radial clearance will be different for each tooth along the gear. This variation is depicted in Fig. 6 and it is expressed by the relationship hre;i \u00bc hrn AB \u00f012\u00de For low value of the eccentricity e [1]: ABffiAC \u00bc e cos\u00f0yi ~G\u00de \u00f013\u00de Therefore, Eq. (12) becomes hre;i \u00bc hrn e cos\u00f0yi ~G\u00de \u00f014\u00de The height of the clearance between the tooth tip and the case depends on the wear profile of the case as well. Therefore, the clearance height hi is given by hi \u00bc hw\u00f0yi\u00de\u00fehre;i \u00f015\u00de where hw(yi) is the radial height of the case wear corresponding to the tip of the tooth i. The wear profile, due to the running-in process, has been obtained by interpolating the experimental results yielded by metrological measurements",
            " 17) and angle c is commonly obtained by an approximate expression (more details are given in [12]). The impedance modulus of Eqs. (35) and (36) is W \u00bc 0:150 ~E 2 \u00fe ~G 2 1=2 \u00f01 a0\u00de3=2 1 \u00f037\u00de where the parameters ~E; ~G; a0 that depend on the eccentricity ratio are defined in [12]. It is worth noting that the eccentricity of the journal axis with respect to the bearing block (of modulus e and azimuth G, Fig. 16) is different from the eccentricity of the gear axis with respect to the case (of modulus ~e and azimuth ~G, Fig. 6), due to the relative position of the bearing blocks into the case. In fact, there is a radial backlash hb between the bearing blocks and the case as shown in Fig. 18, where the backlash is enlarged for better highlighting. Thus, the bearing blocks are floating and consequently the eccentricity of the gears with respect to the case depends not only on the relative position of the journals into the bearings but also on the relative position of the bearing blocks into the case. It is very difficult to estimate the dynamic behaviour of the floating bearing blocks; hence let us suppose that the pressure distribution around the bearing blocks is the same as around the gears"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000782_j.mechmachtheory.2012.11.006-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000782_j.mechmachtheory.2012.11.006-Figure2-1.png",
        "caption": "Fig. 2. Coordinate systems for TE calculation at initial conditions.",
        "texts": [
            " TE can be defined between two gears as a relative displacement or, equivalently, as a relative rotation; the first definition is themost convenient for our spring-damper approach and is also the one used in the LDP software. Under this definition, TE directly translates into the displacement of the spring-damper element, while the time derivative of the TE represents the velocity. During the multibody simulation, for each gear element, TE is calculated comparing in terms of position and orientation two coordinate frames connected to the gear bodieswith a reference coordinate frame. Fig. 2 shows the arrangement for the reference systems in case of external gears, the same configuration holds when gears are internal. Each gear coordinate framehas its origin at the intersection between the gear axis of rotation and the plane containing the gear face, where gear faces are chosen on the same side. Z axes lie on the axes of rotation of the gears and x axes point towards each other along the line joining the two origins. The two gears can be numbered arbitrarily and the reference frame overlapswith that of gear 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000402_1.2959106-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000402_1.2959106-Figure1-1.png",
        "caption": "Fig. 1 Dent profile",
        "texts": [
            " Dented Surfaces Dents occur on bearing surfaces due to the presence of debris particles, true brinelling, and surface spalls. Dents are much OCTOBER 2008, Vol. 130 / 041103-108 by ASME of Use: http://www.asme.org/about-asme/terms-of-use s m c p d a d a s m 0 Downloaded Fr maller than the bearing elements and thus do not change the acroscopic dimensions of the surfaces on which they are loated. Furthermore, a ball does not \u201cfall into\u201d a dent but rather asses over the top of it. Also, it should be noted that in this study ents are considered to have a sinusoidal profile, defined by dimeter d and depth h, as shown in Fig. 1. In the current DBM, ents can be located anywhere on the inner and outer races and re fixed to the races. Hence, the dent is stationary if the race is tationary or moves with the race if the race moves. In addition, ultiple dents can be placed on the raceway surfaces. 41103-2 / Vol. 130, OCTOBER 2008 om: http://tribology.asmedigitalcollection.asme.org/ on 01/29/2016 Terms Dry Contact Elastic Model When two nonconformal bodies are brought together under load, the area of the contact and the pressure distribution generated between the bodies is well modeled by the Hertzian contact theory",
            " In this investigation, the bearing dynamic simulation starts with having the inner race at rest and exponentially increasing the inner race speed such that after a period of 5 ms the inner race achieves the desired steadystate speed. In order to explicitly describe the effects of dents, the results are divided into different sections dealing with effects of dent size, inner race speed, dent location, and dent cluster. Dent Model The effect of a dent in the dynamic bearing model is demonstrated by simulating a ball bearing containing ten balls with a dent located on the outer race. The dent is positioned to have its axis Fig. 1 on the Y-Z plane at 30 deg from the Y-axis Fig. 9 . In order to clearly demonstrate the effect of a dent on bearing operation, a case of a bearing with 5 m interference was considered i.e., the radius of the inner race plus the ball diameter is 5 m larger than the outer race radius . In this configuration the balls experience the same contact loading condition, as shown in Fig. 10 a . However, in the presence of a dent on the outer race, the contact force exhibits fluctuations indicating vibrations excited due to the dent Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002469_tii.2019.2929748-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002469_tii.2019.2929748-Figure1-1.png",
        "caption": "Fig. 1. The single-link robotic manipulator",
        "texts": [],
        "surrounding_texts": [
            "In this section, a case study of the single-link robotic manipulator with the inclusion of DC motor dynamics is presented to verify the effectiveness of the proposed adaptive ETC, and its system model dynamics is described by Mq\u0308 +Dq\u0307 +mgL sin q =kII km1 I\u0307 + km2 I + km3 q\u0307 =V + Vd (42) where q denotes the manipulator joint angle, I denotes the motor current, M denotes the inertia, D denotes the damping coefficient, m denotes the mass, g denotes the acceleration of gravity, L denotes the half length of the link, kmj , j = 1, 2, 3, kI denote positive constants in the electrical subsystem, V denotes the input voltage, and Vd denotes the disturbance in the input voltage. In fact, the manipulator angle, angle velocity, and the motor current of this system are constrained. By the following variable substitution x1 = q, x2 = q\u0307, and x3 = I , (42) can be transformed into the form as x\u03071 =x2 x\u03072 =\u03b8T2 f2(x\u03042) + g2x3 x\u03073 =\u03b8T3 f3(x\u03043) + g3u+ \u2206 where \u03b82 = [\u2212mgL/M,\u2212D/M ]T , g2 = kI/M , \u03b83 = [\u2212km3 /km1 ,\u2212km2 /km1 ]T , g3 = 1/km1 , and \u2206 = Vd/km1 are all unknown nonlinearities, f2 = [sin(x1), x2]T , f3 = [x2, x3]T , and u = V/km1 . The objective of the adaptive ETC control problem is to drive the output x1 follow the reference trajectory yd(t) = 0.7 sin(2.5t) with reducing the communication burden, and guaranteeing the state constraints as follows: |x1(t)| < \u03c0 2 , |x2(t)| < \u03c0, |x3(t)| < 20 The following three methods are made comparisons respectively. \u2022 C1: The classical adaptive control law (24). \u2022 C2: The fixed threshold adaptive ETC (28). \u2022 C3: The relative threshold adaptive ETC (30). The parameters of the system are m = 1kg, L = 0.15m, M = 1kg\u00b7m2, D = 1, kI = 1, km1 = 1, km2 = 1, Vd = sin(t), and km3 = 0.2. The initial states are set to be [x1(0), x2(0), x3(0)]T = [0.2, 0.8, 0]T . The design parameters are chosen as k1 = 2, k2 = 2 and k3 = 2. Note that the adaptive control law in equation (24) is continuous-time. However, it is practical to use discrete-time controller with sufficient small sample intervals to replace the continuous one. Thus, the sampling interval when applying the period controller is 1 ms. 1551-3203 (c) 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. The tracking performance of the proposed adaptive ETC approaches applying to the single-link manipulator is provided by Fig. 2, which illustrates that the presented two threshold strategies can effectively drive the output signal to follow the reference trajectory. In the first 4s, it can find out that the tracking error for C2 and C3 is smaller than C1. In other times, the tracking error of the three cases is almost the same. Fig. 3 shows the phase portrait of the system trajectories. This figure clearly illustrates that all of the system states are within the predetermined constraint space. 0 1 2 3 4 5 6 7 8 9 10 Time (s) C3 C2 Triggering event C2 C3 Fig. 5. The triggering event The control inputs are shown in Fig. 4, and the corresponding triggering times are illustrated in Fig. 5. As indicated in this figure, it is calculated that there are only 109 and 80 control samples in 10s required to update the C2 and C3, respectively. Under the same condition, C1 needs 10,000 control updates to apply the classical period controller. Thus, the proposed adaptive ETC strategies can obviously decrease the control updates, namely, the communication burden can be considerably reduced. The time interval of triggering event is displayed in Fig. 6, from which one can find that the Zeno behavior does not happen. In addition, it is observed that C3 can guarantee a longer event inter-execution interval. But a large control measurement error will also lead to the larger output tracking error as shown in Fig. 2. In contrast, C2 can achieve a smaller tracking error by exploiting the small inter-execution interval."
        ]
    },
    {
        "image_filename": "designv10_5_0002004_1.4028532-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002004_1.4028532-Figure7-1.png",
        "caption": "Fig. 7 Comparison of folding motion of simulated (left) and aluminum prototype (right) CC-Miura pattern",
        "texts": [
            " [21], \u00f01\u00fe cos gZ\u00de\u00f01 cos gA\u00de \u00bc 4 cos2 /, this occurs at cos gK A;min \u00bc sin2 /1 cos2 /1 (23) It is believed that this is the first analytical prediction for the maximum compressibility of CC origami patterns [23]. A comparison between the unfolded rigid strip assembly and the unrolled projected ellipse (u03; v 0 3) given by Eqs. (14) to (15) is shown in Fig. 6(b), with good agreement seen. A comparison between the folding motion of the simulated geometry and the aluminum prototype, set at dimensions a\u00bc 60 mm, b\u00bc 60 mm, / \u00bc p=3; gZ \u00bc p=2, m\u00bc 3, n\u00bc 3, and u \u00bc umin, also shows good agreement, shown in Fig. 7. 3.3 Tessellations. As a final comment on the creation of the CC-Miura pattern, it should be noted that many different curves can be defined through three nodes on a prismatic base pattern, beyond the simple elliptical curve discussed above. More complex conic curves can be derived by fitting partial elliptical curves through half-units of the base prismatic geometry, and can still be completely defined with the single gradient parameter u. Different curves defined with the same gradient on the same prismatic base are termed tessellations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002896_j.jmapro.2019.04.018-Figure12-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002896_j.jmapro.2019.04.018-Figure12-1.png",
        "caption": "Fig. 12. Control strategy demonstrator. (a) CAD model; (b) Deviations of the finished geometry relative to CAD.",
        "texts": [
            " With the exception of the case in which geometrical control was applied (Fig. 11d), the process became unstable after depositing several layers. When the distance between the nozzle and the part increased, the wire melted before it reached the surface and produced a nonbonding of the material to the part (Fig. 11b and c). On the other hand, when the distance between the head and the piece decreased, wire adherences could be found on part if not properly melted (Fig. 11a). The demonstrator shown in Fig. 12a was constructed with LMD and powder to test the effectiveness of height control on medium to large sized parts. Fig. 12b shows geometric deviations relative to CAD. Although the part was successfully constructed, it can be noted that deviations relative to CAD increased as the part grew. This may be due to the fact that heat dissipation may become more difficult as the part grows, increasing the temperature of the part and therefore also the amount of powder that is fused. However, this work has been subjected to a purely geometric control so the thermal aspects affecting the deposition will be dealt with in future work"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000648_978-3-642-17531-2-Figure8.4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000648_978-3-642-17531-2-Figure8.4-1.png",
        "caption": "Fig. 8.4. Ferromagnetic materials: a) magnetization curve ( S B : saturation flux density, r B : remanence, c H : coercivity, 1: initial magnetization curve, 2: bounding hysteresis curve, see (Hughes 2006)); b) saturation-dependent permeability curve",
        "texts": [
            "3a), or within a homogeneous ferromagnetic material ( 1) r (Fig. 8.3b). In the latter case, the field lines primarily flow inside the ferromagnetic material, so that magnetic flux can be easily guided through space using physical structures. 500 8 Functional Realization: Electromagnetically-Acting Transducers Magnetization curves For real flux-conducting media ( 1 r , ferromagnetic materials), the material equation (8.4) does not describe a linear relationship: it is well known that both saturation and hysteresis effects must be taken into account (Fig. 8.4a). The permeability is thus not constant, but depends on magnetic saturation (Fig. 8.4b) (Hughes 2006). The saturation effect\u2014characterized by the saturation flux density S B \u2014 materially limits the maximum achievable flux density, and thus the maximum possible transducer force (typical values are 1.2 1.7 T S B , (Kallenbach et al. 2008)). 8.2 Physical Foundations 501 Traversing the hysteresis curve during dynamic operations (with varying flux) results in a dissipation of energy (a transformation into heat). If present, such effects must be accounted for as losses in a transducer\u2019s dynamic model (Schweitzer and Maslen 2009)",
            " The inductance concisely describes the electromagnetic properties of an electromechanical system. The mechanical component is reflected in the dependence of the inductance on the configuration geometry. Given a variable geometry, the inductance can thus be made to depend on motion variables (defining the electromechanical energy transfer). The electrical back effects of the magnetic field are expressed via the appropriate material properties (the permeability ). As a rule, nonlinear properties are accounted for via current-dependent saturation effects, i.e. ( )L L i , see Fig. 8.7 (cf. Fig. 8.4). There is then a distinction between the operating-point-dependent static inductance st L 8.2 Physical Foundations 505 and the differential inductance d L (see Fig. 8.7). The dynamics in the linear portion of the i curve are termed electrically linear, i.e. 0 L i (in this regime, energy = co-energy). For the electromechanical transducers considered here, inductance generally depends both on an electrical coordinate (the current i ) and a mechanical coordinate (the displacement x ). Formally expressed, ( , )L L x i ",
            " Specific pole force: the pole area condition According to Eq. (8.32), the pole force of an electromagnet is proportional to the square of the flux density and directly proportional to the pole area pol A . For purposes of de- sign, the specific pole force 2 , 0 2 em em pol pol F B f A or 2 2[N/cm ] [T] , 40 em pol f B (8.41) gives a concrete measure for the magnetically achievable pole force given elementary geometric boundary conditions. Given an assumed flux density B (less than the saturation flux density S B , where typically 1.2 1.7 T S B , cf. Fig. 8.4), Eq. (8.41) de- fines the required pole surface pol A . For 1 TB , a specific load capacity of 2 , 40 N/cm em pol f is thus typical. em F x curve, b) piecewise displacement-independent ( ) em F x curve (constant force), from (Kallenbach et al. 2008) 8.3 Generic EM Transducer: Variable Reluctance 523 Magnetomotive force condition, field coil The magnetomotive force required to produce a certain reluctance force can easily be estimated from the elementary magnetic circuit equation (8.12). Neglecting the reluctance ,m Fe R in the iron core relative to the air gap reluctance R , it follows from Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000807_j.mechmachtheory.2013.06.013-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000807_j.mechmachtheory.2013.06.013-Figure3-1.png",
        "caption": "Fig. 3. Generation surface of shaper.",
        "texts": [
            " (1) in the coordinate system Sr as: rr ur; \u03b8r\u00f0 \u00de \u00bc ur\u2212f d\u00f0 \u00de sin\u03b1d\u2212ld cos\u03b1d\u2212aru 2 r cos\u03b1d ur\u2212f d\u00f0 \u00de cos\u03b1d \u00fe ld cos\u03b1d \u00fe aru 2 r sin\u03b1d \u03b8r 1 2 664 3 775 \u00f01\u00de \u03b8r is measured along Zr axis. where The normal to the surface of the parabolic rack cutter As is determined as: Nr ur\u00f0 \u00de \u00bc cos\u03b1d \u00fe 2arur sin\u03b1d \u2212 sin\u03b1d \u00fe 2arur cos\u03b1d 0 2 4 3 5: \u00f02\u00de Similarly we may represent vector function rc(uc,\u03b8c) of pinion rack-cutter A1 and normal Nc(uc). The shaper surface \u2211s is calculated as the envelope to the family of the rack cutter surface As, as Fig. 3 shows. The circle and coordinate axis xr in Fig. 3 coincide with the pitch circle of the shaper and the pitch line of the rack cutter respectively. The relative movement between coordinate systems Sr and Ss simulates the generation process of the shaper. Coordinate systems Sn, Ss and Sr are rigidly connected to the frame of the cutting machine, the shaper and the rack cutter respectively. rps is the pitch radius of the shaper, \u03c8r is the generalized parameter of motion and \u03c8r \u22c5 rps expresses the displacement of the rack cutter. The position vectors rs of the shaper surface are expressed by Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003887_j.etran.2020.100080-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003887_j.etran.2020.100080-Figure4-1.png",
        "caption": "Fig. 4. The rotor design with combined circumferentially and radially magnetized PMs [42].",
        "texts": [
            " [40] concentrated on themagnet pole shape optimization to increase airgap flux density and reduce the cogging torque. Y. Im in Refs. [41] focused on the rotor rib shape optimization using response surface methodology to improve performance of ferrite IPM. However, the improvements are still far from the requirements of high torque density applications. B.N. Chaudhari et al. in Ref. [42,43] presented an IPM design using combined circumferentially and radially magnetized PMs to increase the flux density and rotor saliency, as shown in Fig. 4. However, since the magnet poles were not sinusoidal distributed in the rotor, there would be a high content of harmonics in the airgap flux density, which would affect the overall performance of the machine. Although in small-scale low power density applications, by using much larger amount of PM material, ferrite machines can achieve similar torque output at the expense of lower efficiency compared to their rare-earth counterparts [44,45], it is almost impossible to accomplish the design goal for high power rangewith sizing constraint [46]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000414_s026357470999083x-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000414_s026357470999083x-Figure2-1.png",
        "caption": "Fig. 2. Modeling of a small section dx of a tendon and sheath.",
        "texts": [
            " As such, a novel means of predicting force and elongation of the tendon sheath system at the end effector of an instrument is proposed. The studies made on tendon sheath actuation and the theory behind its application is presented. An experimental approach is described and the result for a typical trial is presented. The limitations and possible means to reduce errors are presented in the discussion followed by the conclusion at the end of the paper. In the following, the sheath is assumed to be bent with a constant radius of curvature as seen in Fig. 2. In our model \u03bc is the friction coefficient between the sheath and the tendon, N is the normal force the sheath is exerting on the tendon in this unit length, T is the tension of the tendon, C is the compression force experienced by the sheath, Tin is the tension at one end of the sheath, R is the bending radius of the tendon, x is the longitudinal coordinate from the housing end of the sheath to the present location, F is the friction between the tendon and the sheath in this unit length. To simplify our model, \u03bc can be assumed as the dynamic friction when the tendon is moving within the sheaths and it is a constant"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002221_s11071-015-1892-9-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002221_s11071-015-1892-9-Figure1-1.png",
        "caption": "Fig. 1 Planar presentation of RIP system",
        "texts": [
            " In Example A, we apply the proposed tracking method to a rotary inverted pendulum (RIP) system with uncertainty and time-varying delays due to non-symmetrical backlash and various frictions. In Example B, the vibration control of an uncertain time-delay system which is proposed in [1] is presented. In Example C, for the sake of comparison, we apply the proposed method to an uncertain system with multiple time-varying delays provided in [1,34], and we compare the performance of the three controllers. 5.1 Example A: RIP system The RIP system is a well-known test platform for evaluating control methods. Figure 1 shows the schematic diagram of an RIP system [40,47]. Let \u03b1p be the pendulum angle and \u03b8a be the arm angle. Also, let \u03c4a, u, lp, mp, ra and Jb be the motor torque, control input, pendulum length, pendulum mass, arm length and moment of inertia of the effective mass, respectively. The dynamic equations of this system considering time-varying delays, backlash and friction effects are [40]: (Ap + Bp sin2 \u03b1p)\u03b8\u0308a + (Cp cos\u03b1p)\u03b1\u0308p \u2212 (Cp sin \u03b1p)\u03b1\u0307 2 p + (Bp sin 2\u03b1p)\u03b1\u0307p\u03b8\u0307a + Fp\u03b8\u0307a + Gpsgn(\u03b8\u0307a)+ Hp\u03b8a = Ipu + Ap Bp \u2212 C2 p Bp 2\u2211 i=1 Adi(v(t)) \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a3 \u03b1p(t \u2212 \u03c4i ) \u03b1\u0307p(t \u2212 \u03c4i ) \u03b8a(t \u2212 \u03c4i ) \u03b8\u0307a(t \u2212 \u03c4i ) \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a6 , (61) Bp\u03b1\u0308p + (Cp cos\u03b1p)\u03b8\u0308a \u2212 (Bp sin \u03b1p cos\u03b1p)\u03b8\u0307 2 a \u2212 Dp sin \u03b1p + Ep\u03b1\u0307p = 0, (62) where Ep, Fp, Ip, Gp and Hp are the pendulum damping constant, arm damping constant, control input coefficient, arm Coulomb friction and elasticity coefficients, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003720_j.addma.2020.101491-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003720_j.addma.2020.101491-Figure2-1.png",
        "caption": "Fig. 2. Computed deposit profiles with increments of individual layers during ten-layer and single-track laser DED for various laser powers, scanning speeds, and mass feed rates: (a) laser power 1800W, scanning speed 5mm/s, mass feed rate 10 g/min, bidirectional scanning, (b) laser power 1800W, scanning speed 5mm/s, mass feed rate 20 g/min, bidirectional scanning, (c) laser power 1500W, scanning speed 5mm/s, mass feed rate 20 g/min, bidirectional scanning, (d) laser power 1500W, scanning speed 8mm/s, mass feed rate 20 g/min, bidirectional scanning, (e) laser power 1500W, scanning speed 8mm/s, mass feed rate 20 g/min, unidirectional scanning.",
        "texts": [
            " In this section, results on multiple scales including the build in 3D, the layer in 2D or 1D considering the single-track per layer feature of the thin wall structure, and the molten pool as the basis for 3D printing will be interpreted. In this subsection, various features of individual layers during tenlayer laser DED will be explored. The progressive layer wise increments will be demonstrated in both longitudinal and transverse sections. Moreover, the statistical data of the layer dimensions will be discussed. 3.1.1. Profiles of individual layers Fig. 2 shows the profiles of both the full height build and the interior layers in the transverse sections for various process conditions. It can be observed that all layers possess convex top boundaries, although with different curvatures. Taking Fig. 2(d) for example, the 1st layer is deposited on the substrate with a flat top surface. Subsequently, the 2nd layer is deposited on top of the convex 1st layer. Therefore, the net increment of the build with the printing of the 2nd layer can be demonstrated by the green zone which has both convex top and bottom boundaries. Similarly, a thin curved incremental zone is generated upon the printing for each of the subsequent layers. In other words, the colorcoded thin curved zones in Fig. 2 demonstrate the layer wise growth of the build on the top with variable shapes and sizes. Comparing the five cases shown in Fig. 2, the coverage of the top layer over previous layers varies significantly depending on the process conditions. For the high heat input condition, as shown in Fig. 2(a), the 10th layer completely covers all other layers so that the progressive Table 2 Material properties of substrate and metal powder [41] Name Ti-6Al-4V Ti Density (kg m-3) 4000 - Solidus temperature (K) 1878 - Liquidus temperature (K) 1928 - Latent heat of fusion (m2 s-2) 2.85\u00d7105 - Thermal conductivity of solid (W m- 1 K-1) 1.57+ 2.9\u00d7 10-2T - 7\u00d7 10-6T2 25 Thermal conductivity of liquid (W m- 1 K-1) 33 31 Specific heat of solid (J kg-1 K-1) 512.4+ 0.15 T - 1\u00d710-6T2 760 Specific heat of liquid (J kg-1 K-1) 825 783 Viscosity (kg m-1 s-1) 4\u00d710-3 4\u00d710-3 d\u03c3/dT (N m-1 K-1) \u22120.26\u00d710-3 - growth of the layers appears in an onion-like structure. In contrast, for low heat input and high mass input conditions, as shown in Fig. 2(c) and (d), the top layer only covers several layers below. Fig. 2(b) shows intermediate incremental thicknesses due to its higher powder feed rate than Fig. 2(a) and higher laser power than Fig. 2 (c) and (d). In brief, the comparative results shown in Fig. 2 imply that the net increment of the build volume increases in curved fashions upon the layer by layer deposition process, with progressive growth profiles depending on specific conditions of energy, momentum, and mass transfer. Fig. 2(e) shows significantly different deposit profiles compared with those generated with bidirectional scanning strategy. A prominent bump can be observed at the beginning part of the build, followed by a lower build top along the scanning direction. Details on the formation mechanisms for such a special profile will be interpreted in subsequent sections. Note that the layer wise increments of the build shown in Fig. 2 cannot be observed by post-process characterizations of the samples. This is because that the top part of each layer has been remelted and thus reformed during the printing of subsequent layers, which has also been reported for modeling results using finite element analysis [42]. Remarkably, the multiple layer profiles shown in Fig. 2 are results recorded from various temporal steps, which are displayed on an identical 3D space owing to the advanced capability of the phenomenological model. The curvatures of the layer wise increments largely depend on the extent of the lateral growth. The onion-like feature of the layer structure would be reduced with smaller dimensional differences between adjacent layers. Another intriguing point is that the color-coded increment zones are fresh domains produced by the current layer over previous layers"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003337_j.physa.2019.122435-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003337_j.physa.2019.122435-Figure1-1.png",
        "caption": "Fig. 1. Bacterial gliding on an inclined solid substrate.",
        "texts": [
            " The modeling of gliding problem under lubrication assumption is explained in Section 3. Section 4 consist of formulas for forces and energy dissipation. Section 5 comprises of solution methodology. The mechanical effects of slime rheology and inclination effects are shown and explained through graphs in Section 6. The key findings are given in Section 7. Let U and V denote the components of flow fluid (slime velocity) in X- and Y -direction due to gliding motion of the organism. The flow is inherently unsteady and two-dimensional i.e. U = U (X, Y , t), V = V (X, Y , t). Fig. 1 illustrates the geometry of the hydrodynamical model of bacterial gliding. The organism is modeled as an inextensible sheet on whose surface transverse waves are propagating with velocity c in the positive X-direction. As a result of these traveling waves bacteria manages to push the slime (Bingham fluid or Carreau fluid) backward and self-propel itself with the velocity Vg . In lab frame, the wave speed is (c \u2212 Vg ). The shape of the glider is as follows [13\u201318]: h (X, t) = h0 + a Sin [( 2\u03c0 \u03bb ) ( X \u2212 (c \u2212 Vg )t )] , (1) Here h0 is the mean distance of the micro glider from the inclined sold boundary, t is the time, a is the wave amplitude and \u03bb is the wavelength"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003709_j.jmps.2020.104022-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003709_j.jmps.2020.104022-Figure2-1.png",
        "caption": "Fig. 2. Generation of curvature and torsion by incremental axial growth in a cylindrical rod. In (a), a linear growth gradient \u03b3 in the e X direction generates a rod with intrinsic curvature \u03b3 . In (b), the linear growth gradient \u03b3 twists along the Z axis at rate \u03c9, thus generating both intrinsic curvature \u03b3 and intrinsic torsion \u03c9.",
        "texts": [
            " (37) Here we have used \u03be = (\u03b6 \u2212 1) /R and the standard conversion between Lam\u00e9 parameters and the Young\u2019s modulus E and Poisson ratio \u03bd: \u03bb = \u03bdE (1 + \u03bd)(1 \u2212 2 \u03bd) , \u03bc = E 2(\u03bd + 1) . (38) By direct comparison with the energy of an extensible elastic rod (see Appendix A for detail), E rod = 1 2 \u222b L 0 ( EA (\u03b6 \u2212 1) 2 + EI 1 ( u 1 \u2212 \u02c6 u1 ) 2 + EI 2 ( u 2 \u2212 \u02c6 u2 ) 2 + \u03bcJ( u 3 \u2212 \u02c6 u3 ) 2 ) d S, (39) we conclude that the morphoelastic rod has acquired through a growth gradient along the X direction an intrinsic curvature \u02c6 u2 = \u2212\u03b3 , as shown in Fig. 2 (a). We also see that the stiffnesses of the grown rod are identical to the stiffness of the original rod since for a circular cross-section we have A = \u03c0R 2 , I 1 = I 2 = \u03c0R 4 4 , J = 2 I 1 = \u03c0R 4 2 , (40) and these dimensions have not changed in the grown rod. Next, we generalize the previous case by considering an axial incremental growth function for a rod with section S and made out of an isotropic material. The computations in this case are very close to the previous case and we merely outline the main results",
            " The latter can be characterised by a function \u03d5( S ) that describes the angle between the normal vector to the centerline and the vector d 1 . In general, curvature \u03ba , twist \u03d5, and torsion \u03c4 are related to the curvature vector by u = (\u03ba sin \u03d5 , \u03ba cos \u03d5 , \u03c4 + \u2202\u03d5 \u2202S ) . (66) In the case of the curvatures (65) generated by (64) , we have \u02c6 u3 = 0 , hence \u02c6 \u03ba = \u221a \u02c6 u 2 1 + \u0302 u 2 2 = \u03b3 , \u02c6 \u03c4 = \u2212\u2202 \u02c6 \u03d5 \u2202S = \u2212\u2202 S ( arctan ( \u0302 u1 / \u0302 u2 ) ) = \u03c9. (67) That is, a linearly rotating growth gradient produces a helix as illustrated in Fig. 2 (b). There are other possible mechanisms to generate torsion. One is to have a growth field creating residual shear in the section. This is obtained by having a growth tensor with non-diagonal components coupling the axial direction with any direction in the section. The shear created is partially removed by twisting the rod around its axis. By itself, this is not enough to generate torsion, But, in the presence of curvature, such twisting creates torsion. Another possible mechanism is to have an anisotropic material"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001769_j.jmsy.2016.08.004-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001769_j.jmsy.2016.08.004-Figure1-1.png",
        "caption": "Fig. 1. UGM based on universal machine settings.",
        "texts": [
            " The mathematical model of the ooth flank is obtained by formulating the theory of gearing based n the actual generation process. Recently, a so-called universal generation model (UGM) based on universal machine settings has been developed by Gleason Works and applied to the geometric description of the tooth flank for both face-milled and face-hobbed spiral bevel gears [12]. Whether for a mechanical machine tool or the Six-axis CNC free-form one, and whether for a Gleason\u2019s machine or a Klingelnberg\u2019s one, the generation motion can be executed by universal machine settings [19]. Fig. 1 is a schematic representation of the UGM based on a virtual cradle-type universal generator (e.g., the well known Gleason\u2019s cradle-style machine tool is a typical one, as shown in Fig. 1(a)). Traditional vertical motion, helical motion, and modified roll motion are actually its specific cases. EM = EM0 + V1q + 1 2 V2q2 + 1 3 V3q3 + \u00b7 \u00b7 \u00b7 + 1 n Vnqn. (1) XB = XB0 + H1q + 1 2 H2q2 + 1 3 H3q3 + \u00b7 \u00b7 \u00b7 + 1 n Hnqn. (2) \u03d5 = m0 ( q \u2212 Cq2 \u2212 Dq3 \u2212 Eq4 \u2212 Fq5 ) . (3) Generally, there are 8 basic motion settings in the UMC framework, besides the above two settings EM and XB. There are also other machine settings, namely, ratio of generating roll Ra, Sr, XD, m, and , which can vary during generation as there are the higherorder polynomial functions of q. In addition, the ratio of roll m0 is the coefficient of the linear term of the modified \u03d5, where C, D, E, F are the second, third, fourth and fifth order modified coefficients about the rotation angle q [9,11,13]. Each machine setting is analytically described as a motion element associated with a coordinate system. The blank and the cutter head are rigidly fixed and their related motion is executed (Fig. 1) after the main coordinate systems are established. To this end, some calculating transformation matrices from the cutter to the blank are needed, and the mathematical model of the gear tooth flank can be obtained as follows:\u23a7 \u23a9 nb( , , q) \u00b7 v( , , q) = 0 where rb and nb are the vector and normal vector of the tooth flank; Mbc is the transformation matrix during acturi t e M w p w p r c e b w i a c e E{ w fl degree for a target flank, it is necessary to define the residual easeoff as the vector h = (h1, "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002371_humanoids.2015.7363442-Figure11-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002371_humanoids.2015.7363442-Figure11-1.png",
        "caption": "Fig. 11: Constraints on the door handle turning motion plan.",
        "texts": [
            " 10), which are computed based on the handle configuration detected by the robot vision system. 2) Turning Handle: During the handle turning motion, the handle hinge does not translate. There is only the rotation movement of the hinge. Two Cartesian posture constraints are applied to the trajectory. First is the final step constraint. The offset transform T 1 2 is from grasper frame C1 to the current handle hinge frame C2, while the target frame C3 is the current handle hinge frame rotating around 80o.(see Fig. 11) The second one is a posture constraint for all trajectory steps, which limits the movement of the current handle hinge frame and only allows it to move along the hinge axis through setting the coefficients of the posture constraints diag(c1,c2, ...,c6) as diag(1,1,1,1,0,1). When the handle is held in the hand, the transform T 1 2 can be obtained by adding a minor offset to the current gripper frame configuration, calculated by forward kinematics. 3) Pulling Door Open: Similar to the handle turning motion, opening the door also has a rotation-only point which is on the door hinge"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001532_s00170-017-1413-8-Figure13-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001532_s00170-017-1413-8-Figure13-1.png",
        "caption": "Fig. 13 Slices of the nominal model and damaged model",
        "texts": [
            " 12 that there is a missing volume on the damaged model and it is required to extract the points from the defective region. These extracted points can be used to reconstruct the model of the missing volume to provide build-up tool path and machining tool path. Then the laser can follow the build-up path to deposit material in this region. CNC machining tool path can be used to remove the extra deposited material to regain the designed dimensions. Once the damaged model was best fitted with the nominal model, both models were sliced to a number of layers with a layer thickness of 0.5 mm as shown in Fig. 13. Then the area of each layer from both models was calculated and compared. Area comparison method was adopted to detect the defective region on the damaged model as shown in Fig. 14. For each layer, the area of the polygon of the nominal model was obtained as \u03b1 and the area of the corresponding layer of the damaged model was obtained as \u03b2. A tolerance \u03c4 was set to deal with the unavoidable error in the model reconstruction process using 3D scanner. If the difference\u0394 =\u03b1 \u2212 \u03b2 was larger than the pre-defined tolerance \u03c4, this layer on the damaged model was defined as a defective layer"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002749_j.addma.2019.01.011-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002749_j.addma.2019.01.011-Figure6-1.png",
        "caption": "Fig. 6. Simplified representation of the measuring principle. The two-camera system is installed inside the LBM building chamber. The viewing areas of the cameras overlap on both the building board and the substrate plate. Coordinates will be calculated with common intersection points on the object of both cameras. The projection system is mounted outside the chamber. The projection of the structured light takes place through a window, which is installed by the original equipment manufacturer for observational purposes.",
        "texts": [
            " The key to accurate reconstruction of the 3D shape is proper calibration of each element used in the structured light system. Calibration is necessary to be able to transform measured values (in this case phase values of the fringe pattern) into physical quantities. For this purpose, the geometrical parameters of the overall system are recorded in a way that the optical rays to be intersected can be correctly determined in a common coordinate system and lead to reliable 3D coordinates. To guarantee precise and at the same time robust measurements, we use a two-camera system in our setup, see Fig. 6. The advantage of this arrangement is that only corresponding visual rays between the cameras must be determined. The position of the projector is irrelevant for calculating measured values. Fig. 6 shows an example of a visual ray intersection using the two rays highlighted in blue. Both viewing areas of the cameras have a complete overlap on the building plate inside the LBM chamber. We use commercial 6-megapixel CCD camera types, which means, in best arrangement (adaption to size of building plate 280\u00d7 280 mm2) we receive 6 million intersection points of vision rays. These can be transformed in the same number to (x, y, z) coordinates. A special feature of the set-up is the BIAS vision ray calibration with flexible patterns for the quantitative geometric camera description [18]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003618_s00170-020-05980-w-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003618_s00170-020-05980-w-Figure1-1.png",
        "caption": "Fig. 1 Tensile sample dimensions and locations for cutting",
        "texts": [
            " The outcome of this study may be used to build a complete heat-treating guideline for Inconel 625 fabricated using the CMT-WAAM system. The square wall fabricated during part 1 of this study is used here for further study of the strength of this material [19]. In the previous study, the separated three of the square walls were heat-treated at 980 \u00b0C with varying time (i.e., 30 min, 1 h, and 2 h), followed by water quenching [19]. The asdeposited one wall and the three heat-treated walls are then machined down to separate four tensile samples using wire electrical discharge machining from each of the walls as shown in Fig. 1a. ASTM E8 standard for subsidized sample dimension is followed during machining (Fig. 1b). To remove stress concentration due to electrical discharge machining (EDM) cut, the tensile samples are polished with 100 grit polishing cloth afterward. The tensile test was conducted at room temperature in an MTS servo-hydraulic machine with a 3-mm/min strain rate. The images of the fractured surface were taken with Hitachi SU8020 and Quanta FEI 200 scanning electron microscopes (SEM). The energy dispersive spectroscopy (EDS) was performed with the energy-dispersive X-ray spectroscopy (EDAx) equipped with the SEM"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000233_j.matdes.2008.03.030-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000233_j.matdes.2008.03.030-Figure3-1.png",
        "caption": "Fig. 3. Wire height position",
        "texts": [
            " The wire position relative to the substrate considers both the angle of attack and the distance between the wire tip and the substrate. These control the metal transfer mode and the pressure exerted by the wire tip on the molten pool. By keeping this angle low splashing of molten material is prevented and rippled texture after solidification of the component is avoided. The distance between relative to substrate. the wire tip and the substrate controls the detaching mode of the droplets from the wire tip and the way they travel to the substrate. The droplets detach from the wire by gravity and surface tension forces (Fig. 3). If the droplet touches the substrate before detaching from the wire tip, the effect of surface tension forces is predominant and the molten pool formed is continuous and smooth in height and shape. If this distance increases the gravity force is more significant and the droplets are detached in a globular like mechanism. These drops rapidly solidify on the substrate creating surface irregularities and poor continuity between layers. The component produced is irregular, rough and more prone to oxidation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003793_j.mechmachtheory.2019.103764-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003793_j.mechmachtheory.2019.103764-Figure8-1.png",
        "caption": "Fig. 8. Shaft orbits of GTF star gearing system.",
        "texts": [
            " 7 (d), in which the vibration amplitude of carrier is much smaller than that of star gear since vibration displacements between star gears offset each other. In addition, the center of carrier orbit is deviated from the center of the origin, which is led by the varying vibration range of star gears. Input shaft and output shaft are supported by two bearings each, assume the two bearings are contacted and located in the middle length of each rotors. The floating orbits of bearing centers are obtained as shown in Fig. 8 , in which the black trajectories show the central orbits of bearings that far from the gearbox, the blue trajectories show the central orbits of bearings that close to the gear plane of the star gearing system, it can be obviously concluded that the vibration amplitudes of remote bearings are bigger than that of the proximal bearings. In addition, the orbit centers of those bearings are deviated from the origin to different degrees due to the gravitational effects and eccentric error of central floating components (sun gear and ring gear)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003199_j.mechmachtheory.2019.103576-Figure35-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003199_j.mechmachtheory.2019.103576-Figure35-1.png",
        "caption": "Fig. 35. Contact patterns for different quantities of face-gear crowning and pinion profile modifications according to Table 8 : (left) Base geometry; (middle) Optimized gear drive 1; (right) Optimized gear drive 2; (above) Positive alignment errors; (middle) No alignment errors; (below) Negative alignment errors.",
        "texts": [
            " For the base geometries, the pinion is not modified and the initial face-gear crowning is realized by a shaper which has one tooth more than the pinion. The shift of the shaper a ( c ) has been set to reach a working transverse pressure angle of \u03b1w = 30 \u25e6. This is an appropriate value that shifts the contact path in an area that provides space for changes in the path that occur due to alignment errors. Fig. 34 shows the resulting contact paths for all geometry versions for the following three cases: none, positive, or negative alignment errors. The corresponding contact patterns are shown in Fig. 35 . The contact pattern for the base geometries indicates edge contact at the tooth tips; the contact paths for positive and negative alignment errors indicate edge contact on the inner and outer diameter of the face-gear. Therefore, pinion profile modifications and an increase of the face-gear crowning are required. With respect to the method for face-gear crowning, two optimizations are performed. In the first optimization, face-gear crowning is generated only due to the different number of teeth of pinion and shaper",
            " The further increase in the number of teeth of the shaper realized by the first optimization, completely avoids edge contact on the inner and outer diameter of the face-gear. However, the usable flank is not used optimally. With maximum positive or negative misalignment there is still a distance from the contact pattern to the inner or outer diameter. For the second optimization variant, instead of increasing the number of teeth of the shaper, the additional crowning to avoid edge contact is produced by plunging the tool. In Fig. 35 , the contact patterns for both optimized geometries are shown. Most of the contact ellipses for the second optimization variant are enlarged in its width compared to the first optimization in case of no alignment errors; hence, the resulting contact pressure is slightly less. With positive or negative alignment errors, there is an increase in contact pressure in some areas. However, the increase of contact pressure is not too significant. The contact pressure for the both optimized face-gear drives are shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003394_j.compstruct.2020.112698-Figure12-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003394_j.compstruct.2020.112698-Figure12-1.png",
        "caption": "Fig. 12. Maximum Principal Stress (MPS) in CFRP roll cage: overview and details of the most significant areas.",
        "texts": [
            " The total and directional deformation of the safety cage are presented in Fig. 11, where it is confirmed that the structure meets the safety criteria set by the regulations, which state that lowering of the roof must not exceed 25 mm. Maximum deformation in this direction (equivalent to the Z axis) is 24.9 mm, with this value obtained in sections near the doors where deformation does not interfere with the space occupied by the passengers. The simulation instead predicts that the central part of the roof lowers by <20 mm. Fig. 12 provides an initial overview of the stress state, expressed in terms of the Maximum Principal Stress (MPS) averaged across all layers. This figure allows quick identification of the most critical zones, including the contact area between the plate and top rail rmation of the CFRP roll cage. (Fig. 12a) and the two intersections between the central pillar, top rail and roof rail on both the driver (Fig. 12b) and passenger (Fig. 12c) sides of the vehicle. It must be noted that despite symmetry of the structure and constraints with respect to a vertical Y\u2010Z plane, the presence of an X\u2010component (~22% of the total) of the external force leads to an asymmetrical stress state and deformation. Consequently, the left intersection is mostly subject to compressive stresses in the y\u2010direction and the right to tensile stresses in the x\u2010 direction. The latter are less severe (~850 compared to ~1000 MPa) but also less critical in relation to material strength, which is higher under tensile loading than under compressive loading for CFRP (2231 compared to 1082 MPa for T1000). For the same reason, the zone with highest stress on the top rail is on the right (~380 compared to ~240 MPa) and shifted ~50 mm to the right with respect to the plane of symmetry (Fig. 12a). Fig. 13 shows a distribution map of the MPS for each separate section for the most stressed layer. The highest value of MPS for each layer is reported in Table 4. The seats are not shown since they are subject to negligible stress under these test conditions. Considering these values, the material stress limits for T800 or T1000 are not exceeded at any point. Principal stresses are useful for comparing metal and composite cages in the case of a rollover. In Fig. 14, the structural response of these structures in the above\u2010mentioned conditions is represented in terms of von Mises equivalent stress for Ti\u2010alloy and Maximum Principal stress for CFRP",
            " All other parts of the safety cage do not exhibit criticalities (IRF < 0.750). Fig. 19 presents the related IRF map for the left intersection, reporting the critical layer and corresponding criterion for each FE. Fig. 20 provides details distinguishing the criteria in question. Without entering into detail, the failure criteria generally confirm that the structure is safe in all areas even if, under the defined loading conditions, failure could take place in one of the two intersections already identified (Fig. 12b and c). Although the stress states in these areas are generally oriented in such a way as to cause matrix failure, further reinforcement was nonetheless deemed appropriate. Given the need to contrast stresses in different directions to the principal ones, already supported by unidirectional fibers subject to stress well below their limit, reinforcement was performed using bidirectional layers (T800) and doubling T800 layers already present for approximately 200 mm in all directions. For instance, the roof rail layout (detailed in Table 3) was modified locally by adding 4 layers of T800"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001027_ijpt.2011.041907-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001027_ijpt.2011.041907-Figure2-1.png",
        "caption": "Figure 2 Basic geometric parameters of a spur gear mesh",
        "texts": [
            " With the positive directions of the alternating rotational displacements \u03b81 and \u03b82 and the applied torque T1 and T2 defined in Figure 1(a), the equations of motion of the spur gear pair can be written as 1 1 1 1 1 1 1 ( ) ( ) ( ) , N n n n J t r k t t T F R\u03b8 \u03b4 = + = +\u2211 (1a) 2 2 2 2 2 2 1 ( ) ( ) ( ) , N n n n J t r k t t T F R\u03b8 \u03b4 = \u2212 = \u2212 \u2212\u2211 (1b) where the additional subscript n denotes the nth loaded tooth pair such that F1n and F2n represent the pinion and gear traction forces of the nth tooth pair in contact, and R1n and R2n are the corresponding contact radii as shown in Figure 2 for a tooth pair contacting at point C (The subscript n is omitted in the figure for simplicity purposes). Here, N denotes the number of tooth pairs in contact at a certain mesh position. For most spur gear pairs, the maximum N is 2, such that the contact ratio of the gear pair is between 1 and 2. A gear load distribution model similar to that of Conry and Seireg (1973) is used to determine the static transmission error under unloaded (e(t)) and loaded ( ( ))e t conditions. The difference between e(t) and ( )e t is used to estimate the mesh stiffness as 1 1( ) ( ) [ ( ) ( )]k t T r e t e t= \u2212 (Tamminana et al",
            " The tooth surface velocities consist of a kinematic component due to the nominal rotation of the gears and an alternating (dynamic) component due to the vibratory motions of \u03b81 and \u03b82. For any arbitrary contacting tooth pair, the instantaneous tangential surface velocities of the pinion and gear are 1 1 1 1 2 2 2 22( ) ( ) ( ), ( ) ( ) ( )u t u R t t u t u R t t\u03b8 \u03b8= + = + (3a,b) where 1 1 1( )u R t \u03c9= and 2 2 2( )u R t \u03c9= are the kinematic surface velocities of the pinion and the gear that are rotating at the speeds of \u03c91 and 2 1 2 1( )Z Z\u03c9 \u03c9= (Z1 and Z2 are the numbers of teeth of the pinion and the gear) as shown in Figure 2. The movement of the surfaces of the tooth pair in contact entrains the lubricant into the contact zone, establishing a hydrodynamic fluid film that separates the contacting surfaces. The viscous shear that the lubricant film endures transforms certain amount of kinetic energy into frictional heat, dissipating the power to constrain the motion amplitudes, which is also referred as viscous damping effect. As illustrated in Figure 3, the shear stress within the lubricant varies linearly along the film thickness direction z",
            " The coefficients c0, c1, c2 and c3 are determined in such a way that both \u03b7 and d\u03b7/dp are continuous at the transition points. It is also noted here that any measured pressure-viscosity function can be used in place of equation (5). From equation (4), 1( ) ( ,0)x x\u03c4 \u03c4= and 2 ( ) ( , )x x h\u03c4 \u03c4= are obtained as the viscous shear stresses acting on the pinion and gear tooth surfaces at z= 0 and z = h, respectively. For the computation of \u03c41(x) and \u03c42(x) as the contact point C moves along the line of action B1B2 as sown in Figure 2, the continuous gear EHL formulation of Li and Kahraman (2010a) is employed. Instead of treating the contact at each mesh position as an independent steady-state EHL event with constant contact parameters, this model follows the tooth contact from the Start of Active Profile (SAP) all the way to the tip of the tooth, in the process including the variations of the contact radii, surface velocities and the normal tooth force along the mesh position. The squeezing and pumping effects caused primarily by the sudden tooth load changes due to the fluctuation of the number of tooth pairs in contact are also captured in this model (Li and Kahraman, 2010a)",
            " However, the use of the proposed formulation requires one to couple a transient EHL model with a gear dynamics model, involving a certain level of complexity especially when applied to larger, multi-mesh gear systems. Therefore, a simplified formulation of an equivalent damper along the line of action direction has certain practical value. One such formulation is possible when the variations of the tooth contact radii of curvature along the mesh cycle are ignored. Considering the radii of curvature when the contact point C is at the pitch point as the representative radii of curvature, 1 1 tanR r \u03c6= and 2 2 tanR r \u03c6= as shown in Figure 2 where \u03c6 is the pressure angle. Substituting these radii into equation (10), one obtains 2 2 2 1 1 1 1 1 2 2 1 1 1 1 1 1 ( ) tan ( ) tan ( ) ( ) ( ) tan ( ), N N n n n n N sn rn n J t r D t r r D t r k t t T r F F \u03b8 \u03c6 \u03b8 \u03c6 \u03b8 \u03b4 \u03c6 = = =    + \u2212 +        = + \u2212 \u2211 \u2211 \u2211 2 2 2 2 2 1 2 1 2 2 2 1 1 2 2 1 ( ) tan ( ) tan ( ) ( ) ( ) tan ( ) N N n n n n N sn rn n J t r r D t r D t r k t t T r F F \u03b8 \u03c6 \u03b8 \u03c6 \u03b8 \u03b4 \u03c6 = = =    \u2212 + \u2212        = \u2212 \u2212 + \u2211 \u2211 \u2211 (11a,b) which reduces the damping matrix of equation (10c) to 2 2 1 1 2 mesh 2 1 1 2 2 tan "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000747_s12283-013-0117-z-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000747_s12283-013-0117-z-Figure1-1.png",
        "caption": "Fig. 1 Free-body diagram showing forces (not necessarily to scale) acting on a spherical projectile with backspin. Note that the direction of x is out of the page",
        "texts": [
            " This is done by defining a new dimensionless lift coefficient as C0L \u00bc CL SP ; \u00f04\u00de where the dimensionless spin parameter is given by SP \u00bc rx v ; \u00f05\u00de which is the ratio of the ball\u2019s tangential equatorial speed to its center-of-mass speed. Here, r is the ball\u2019s radius. The alternate lift equation then becomes FL \u00bc 1 2 C0LqrxAv: \u00f06\u00de Equation 6 has a slight advantage over Eq. 3 due to spin rate being explicitly given in Eq. 6, but either equation is fine to use. The free-body diagram for a spherical projectile moving through air is shown in Fig. 1. The direction of the lift force is usually in the direction of x v; though it may point opposite that in the case of the reverse Magnus effect (more on that in Sects. 4.5 and 4.15). The magnitude of the buoyant force, FB, is usually small, but easy to include in a numerical determination of a ball\u2019s trajectory. For a baseball, FB is only 1.5 % of the ball\u2019s weight, which is mg = 5.125 oz = 1.425 N. Keep in mind that the force the air exerts on a projectile is, however complicated, a force that points in a single direction. Splitting that force into the components seen in Fig. 1 is a matter of convention, albeit a popular convention. Putting the x direction along the horizontal and the y direction along the vertical, the baseball\u2019s trajectory lies in the x-y plane. If the ball had spin that was not pure backspin or topspin it would move out of that plane (we ignore asymmetric wake deflection due to asymmetric surface orientations, which average out due to the high spin rate). Newton\u2019s 2nd law gives [12] \u20acx \u00bc bv CD _x\u00fe CL _y\u00f0 \u00de \u00f07\u00de and \u20acy \u00bc bv CD _y\u00fe CL _x\u00f0 \u00de \u00fe 4pr3q 3m 1 g; \u00f08\u00de where b \u00bc qA=2m; v \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffi _x2 \u00fe _y2 p ; and a dot signifies one total time derivative"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001452_1.4005655-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001452_1.4005655-Figure2-1.png",
        "caption": "Fig. 2 Basic geometric parameters of an involute spur gear pair",
        "texts": [
            " Characterizing a spur gear contact as a line contact problem, the one-dimensional transient Reynolds equation governs the lubrication characteristics of the contact areas where hydrodynamic fluid film separates the surfaces @ @x f @p\u00f0x; t\u00de @x \u00bc @ ur\u00f0t\u00deq\u00f0x; t\u00deh\u00f0x; t\u00de\u00bd @x \u00fe @ q\u00f0x; t\u00deh\u00f0x; t\u00de\u00bd @t (1a) In the areas where the asperities interact (i.e., metal-to-metal contacts with no fluid film in between), the reduced form of Eq. (1a) is employed [1,15,22\u201324] @ ur\u00f0t\u00deh\u00f0x; t\u00de\u00bd @x \u00fe @h\u00f0x; t\u00de @t \u00bc 0 (1b) In these equations, x is the coordinate along the rolling (tooth profile) direction and travels with the contact along the line of action (Fig. 2), t is the time, and p\u00f0x; t\u00de, h\u00f0x; t\u00de, and q\u00f0x; t\u00de denote the instantaneous pressure, film thickness, and density distributions of the fluid across the contact. The rolling velocity ur\u00f0t\u00de \u00bc \u00bdu1\u00f0t\u00de \u00feu2\u00f0t\u00de =2 is the instantaneous average of the time varying pinion and gear surface velocities u1\u00f0t\u00de and u2\u00f0t\u00de. Referring to Fig. 2, u1\u00f0t\u00de \u00bc x1r1\u00f0t\u00de and u2\u00f0t\u00de \u00bc x2r2\u00f0t\u00de, where x1 and x2 are the nominal angular velocities of the gears, and r1\u00f0t\u00de \u00bc B1C \u00bc rb1h1\u00f0t\u00de and r2\u00f0t\u00de \u00bc B2C \u00bc rb2h2\u00f0t\u00de are the time-varying radii of curvature (rb1 and rb2 are the base circle radii). Assuming an Eyring fluid, the non-Newtonian effects are incorporated in the flow coefficient as [1,15] f \u00bc qh3 12g cosh sm s0 (1c) where g is the lubricant viscosity, s0 is the pressure dependent Eyring stress [22], and sm is the mean viscous shear stress determined by sm=s0 \u00bc sinh 1\u00bdgus\u00f0t\u00de=\u00f0s0h\u00de . Here, the instantaneous sliding velocity us\u00f0t\u00de \u00bc u1\u00f0t\u00de u2\u00f0t\u00de is also time dependent. Designating gear 1 as the driving gear, the kinematics of involute gearing states that u1\u00f0t\u00de < u2\u00f0t\u00de when the contact is below the pitch line along the line segment B1C in Fig. 2, u1\u00f0t\u00de \u00bc u2\u00f0t\u00de (no sliding, pure rolling) when the contact is at the pitch point C, and u1\u00f0t\u00de > u2\u00f0t\u00de when the contact is at the addendum region (along the line segment B2C in Fig. 2) of the driving gear. The local film thickness at the position x and time t is defined as h\u00f0x; t\u00de \u00bc h0\u00f0t\u00de \u00fe g0\u00f0x; t\u00de \u00fe V\u00f0x; t\u00de R1\u00f0x; t\u00de R2\u00f0x; t\u00de (2)Fig. 1 Flowchart of the gear contact fatigue methodology 041007-2 / Vol. 134, APRIL 2012 Transactions of the ASME Downloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/27/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use where h0\u00f0t\u00de is the reference film thickness, and R1\u00f0x; t\u00de and R2\u00f0x; t\u00de are the roughness heights of the two tooth surfaces moving at u1\u00f0t\u00de and u2\u00f0t\u00de, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001652_s00170-017-0760-9-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001652_s00170-017-0760-9-Figure5-1.png",
        "caption": "Fig. 5 a 3D conical Gaussian model of the heat source (adapted from [31]). b Heat source located on the cladding path, and the travel path",
        "texts": [
            " A 3D conical Gaussian is a heat source model that is capable of modeling the high energy produced by the laser beam. This model is defined by means of the heat source power, radius of the affected surface, and by the penetration depth. The 3D conical Gaussian heat source is described by Eqs. (5) and (6). Equation (5) expresses the heat flow density into the material depending on the spatial coordinate data. Equation (6) provides the Eq. (5) radius change in the conical shape heat source model [9, 14]. Figure 5 shows a schematic view of the needed parameters to define this heat source model: q x; y; z\u00f0 \u00de \u00bc q0exp \u2212 x2 \u00fe y2 r20 z\u00f0 \u00de \u00f05\u00de r20 z\u00f0 \u00de \u00bc re \u00fe ri\u2212re zi\u2212ze z\u2212ze\u00f0 \u00de \u00f06\u00de where q0 is the heat flow density (W/m3), re and ri are the determinate 3D Gaussian radii (m), ze and zi are the determinate length of 3D Gaussian (m), and x, y, and z are the point coordinates (m). In metallurgical terms, a material is defined by proportions Zi of the various phases (ferrite, bainite, martensite, austenite, etc.). The phase transformation which takes place in the HAZ was considered using the Leblond model [21] for the heating and the Ko\u00efstinen-Marb\u00fcrger model [20] for the cooling path"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001786_s00170-017-0546-0-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001786_s00170-017-0546-0-Figure2-1.png",
        "caption": "Fig. 2 Cathode and anode arrangements (bottom view): a C1-A1, b C1-A2, c C2-A3 (cathode-to-anode distance in mm)",
        "texts": [
            " The results of this work should therefore assist in establishing the EP allowances for L-PBF built IN625 components, and, therefore, confer the desired geometry to the part, while providing the necessary surface finish characteristics. This work is structured as follows. First, the experimental setup is presented in Sect. 2. The developed experimental methodology is given in Sect. 3. Sections 4, 5, and 6 contain results, discussions, and conclusions of this study, respectively. Three cathode-anode arrangements were designed for this study (Fig. 2). The first arrangement, C1-A1 (a), was used for the current density (J) versus applied potential (Va) characterization of the L-PBF built IN625 specimens. The second, C1-A2 (b), was designed to study the impact of the EP parameters on the roughness, mass, and thickness reduction of specimens containing surfaces with different build orientations, as well as for processing optimization. The third arrangement, C2-A3 (c), was designed to simulate the polishing of an internal surface of a tube. This last arrangement (barrel) was composed of 7 staves, with each stave being produced at a given build orientation",
            " For the V1000 progr test, the potential was progressively increased at a rate of 1 V/s until the target value of 9 V was reached, and then maintained constant for the remainder of the test. In the case of an instantaneous potential application, two exposure intervals were compared\u20141000 (V1000 inst ) and 5000 (V5000 inst ) mA cm\u22122 min. The opt imum EP control s t ra tegy, which was established using the V-shaped anodes, was then used for the EP tube simulation experiments. The barrel- and startype anodes were mounted as shown in Fig. 2c and dipped into the electrolyte by 20 mm of their height, which offered a 16.8 cm2 working wet surface. During the EP process, the exterior surface of the barrel (staves) was covered with electric tape to prevent its polishing, thus allowing an adequate measurement of the thickness reduction and mass loss on each individual stave. The barrel was mounted, polished, and then dismounted to allow surface roughness measurements. Additionally, the surface finish of each separate stave was measured after each period of EP"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001181_j.apenergy.2013.01.073-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001181_j.apenergy.2013.01.073-Figure1-1.png",
        "caption": "Fig. 1. Photograph (a) and schematic structure (b) of the one-compartment direct glucose alkaline fuel cell.",
        "texts": [
            " The carbon cloth was air-dried, sintered and cooled. Repeated steps above were taken for more than three times to obtain a total amount of 4 PTFE coatings. The catalyst ink was prepared by mixing Pt/C catalyst with a loading of 0.5 mg Pt/cm2, iso-propanol as the solvent and 5 wt% Nafion as the binder. Well dispersed catalyst ink was brushed on the side opposite the diffusion layer coatings. The homemade cathode was air-dried for 24 h before use. The one-chamber fuel cell is made from polymethyl meth acrylate (PMMA). As can be seen in Fig. 1, the fuel cell was composed of an anode, an air-breathing carbon cloth cathode and a 30 mm diameter cylindrical internal chamber. A teflon-coated stir bar anchored on a wire was used to stir the chamber solution when necessary. The anode substrate was nickel foam (purity: 99.9%, number of pores per inch: 110, density: 380 g/m 2, average pore size:590 lm, thickness: 1.7 mm) from HANBO (Shenzhen) Co. Ltd. Nickel wire was used for electrode connection because it is corrosion-resistant and inexpensive"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000648_978-3-642-17531-2-Figure2.33-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000648_978-3-642-17531-2-Figure2.33-1.png",
        "caption": "Fig. 2.33. Elementary mechatronic transformer transducers (ideal, lossless): a) electrical transformer, b) mechanical transmission, c) rack and pinion",
        "texts": [
            " In the case of a transformer, the transducer constant n determines the relation between pairs of the same power variables 1 2,e e or 1 2,f f of the two ports. In the case of a gyrator, the transducer constant r is used to relate pairs of differing power variables 1 2,e f or 2 1,e f of the two ports. 14 Using so-called multi-ports, the simultaneous interactions between more than two domains can be described in an expanded form. The physical units of the transducer constants n, r are determined by the domain-specific power variables. Fig. 2.33 shows physical examples of transformer type transducers and Fig. 2.34 shows a physical example of a gyrator type transducer. In the matrix form shown, the transfer matrix represents the so-called chain matrix of two-port network theory. Mechanical transducers: variable definitions Recall that, due to the arbitrary assignment of domain-specific power variables, the description of physical transducer implementations is not unique. Particular attention is due in the case of mechanical transducers. Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000324_j.ijengsci.2008.01.007-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000324_j.ijengsci.2008.01.007-Figure2-1.png",
        "caption": "Fig. 2. Transversely isotropic half-space under an arbitrary finite time-harmonic buried load.",
        "texts": [
            " For the case of an isotropic solid these branch points reduce to nk1 \u00bc kp x ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi q=\u00f0k\u00fe 2l\u00de p , and nk2 \u00bc nk3 \u00bc ks x ffiffiffiffiffiffiffiffi q=l p , where k and l = Lame constants; kp and ks = compressional and shear wave numbers, respectively (e.g. [4,5]). 3. Statement of the problem In this paper, the physical domain of interest is taken to be a homogeneous, transversely isotropic, elastic half-space bounded by a horizontal surface. A cylindrical coordinate system is set at the surface in such a way that z-axis is normal to the horizontal surface and it is the axis of symmetry of the medium (see Fig. 2). An arbitrary time-harmonic body force field is assumed to be distributed on a finite region Ps which is located at the depth z \u00bc s. Although the formulation in the last section does not allow for body forces explicitly, the action of an arbitrarily distributed source on the plane z \u00bc s can be represented as a set of prescribed stress discontinuities across the corresponding planar region [4,5], i.e. szr\u00f0r; h; s \u00de szr\u00f0r; h; s\u00fe\u00de \u00bc P\u00f0r; h\u00de; \u00f0r; h\u00de 2 Ps 0; \u00f0r; h\u00de 62 Ps ( ; szh\u00f0r; h; s \u00de szh\u00f0r; h; s\u00fe\u00de \u00bc Q\u00f0r; h\u00de; \u00f0r; h\u00de 2 Ps 0; \u00f0r; h\u00de 62 Ps ( ; szz\u00f0r; h; s \u00de szz\u00f0r; h; s\u00fe\u00de \u00bc R\u00f0r; h\u00de; \u00f0r; h\u00de 2 Ps 0; \u00f0r; h\u00de 62 Ps ; ( \u00f019\u00de where P\u00f0r; h\u00de, Q\u00f0r; h\u00de and R\u00f0r; h\u00de are the specified body-force distributions in radial, angular and axial directions, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002004_1.4028532-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002004_1.4028532-Figure9-1.png",
        "caption": "Fig. 9 Curved crease tapered Miura geometry creation. (a) Three point ellipse, (b) projected surface, (c) divisor lines and exploded rigid strips, and (d) crease pattern.",
        "texts": [
            "org/about-asme/terms-of-use creation and rigid subdivision stages to a prismatic Tapered Miura-base pattern. Whereas the CC-Miura pattern can be conceptually thought of as the developable surface created from the inversion of a cylindrical surface, the CC-tapered Miura pattern can be thought of as a developable surface created from the inversion of a conical surface, shown in Fig. 2(b). 4.1.1 Ellipse Creation. Ellipses fitted through zigzag creases on a prismatic Tapered Miura-base are shown in Fig. 9(a). It can be seen that unlike the CC-Miura pattern, sequential ellipses expand on the base geometry to form an inverted conical surface. From Eq. (50) in Ref. [21], bj \u00bc b1 \u00fe \u00f0j 1\u00deac sin q= sin /f , it is known that the side length of sequential zigzags bj scales linearly for each jth zigzag crease line. Therefore, in the simplest embodiment, each ellipse is assumed to have the same gradient parameter u, shown in Fig. 9(b), and elliptical coefficients for the jth ellipse, shown in Fig. 9(a), are obtained by substituting the bj for b and gfZ for gZ in Eqs. (2)\u2013(6). The coefficients are given superscripts kj, bj, dj, and cj and substituted into Eqs. (9) and (10) to give the jth elliptical curve (uj,vj) as a function of t uj \u00bc gj \u00fe cj cos t (26) vj \u00bc hj \u00fe dj sin t (27) where tlim t tlim. As the straight-crease lines in the CCtapered Miura pattern are not parallel, the limits for the gradient parameter u differ to that for the CC-Miura pattern. The lower bound umin remains unchanged from Eq. (7), but the upper bound is changed to umax \u00bc p=2\u00fe q, where q is the angular rotation of the folded prismatic base geometry given by Eq. (57) in Ref. [21], q \u00bc \u00f0gcZ gfZ\u00de=2. Note that this is for the case where an ellipse is defined through the three nodes of the zigzag crease in a close\u2013 far\u2013close vertices sequence, as is shown in Fig. 9. It is also possible to define an ellipse in a far\u2013close\u2013far vertices sequence. In this instance, the upper limit of the gradient parameter is umax \u00bc p=2 q. 4.1.2 Rigid Subdivision. The CC-tapered Miura can subdivided into rigid strips in the same manner as the CC-Miura pattern, except with radial rather than parallel divisor lines. Vertices Wk,j are calculated at the intersection of the kth radial crease and the jth zigzag crease (k\u00bc 1, 2,\u2026, s, j\u00bc 1, 2,\u2026, n). If a 3D Cartesian coordinate system with origin and orientation shown in Fig. 9(a) is used, the coordinate vector (xk,j, yk,j, zk,j) of Wk,j can be given as xk;j \u00bc Rc;j cos h\u00fe uk;j\u00f0tk\u00de (28) yk;j \u00bc Rc;j sin h\u00fe vk;j\u00f0tk\u00de (29) zk;j \u00bc 0 for odd j ac cos\u00f0gcA=2\u00de for even j (30) where h \u00bc \u00f0k k 1\u00de qset=S and Rc,j is given by Eq. (58) in Ref. [21] as Rc;j \u00bc bj sin\u00f0gfZ=2\u00de= sin q. Rotated elliptical coordinates (uk,j, vk,j) are obtained by rotating the (uj, vj) ellipse to match the orientation of the corresponding three-node zigzag on the base pattern uk;j\u00f0tk\u00de vk;j\u00f0tk\u00de \u00bc cos\u00f0h\u00fe qset\u00de sin\u00f0h\u00fe qset\u00de sin\u00f0h\u00fe qset\u00de cos\u00f0h\u00fe qset\u00de uj\u00f0tk\u00de vj\u00f0tk\u00de (31) As before, tk\u00bc tlim(k*/S \u2013 1) and k*\u00bcmod(k \u2013 1, 2S)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003848_j.jmatprotec.2020.117032-Figure13-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003848_j.jmatprotec.2020.117032-Figure13-1.png",
        "caption": "Fig. 13. Tailored blanks made by orbital forming after upsetting for R40 and R35.2.",
        "texts": [
            "2 the tooth height, represented by the length of the tooth along the cup side wall, is much longer than for layout R40. As identified in Section 3.4 the area at the cup radius is crucial for formability. However, in both cases the parts can be formed without failure. The next forming step is upsetting, where the upsetting force is set to FU = 600 kN. This operation is used to form the tooth geometry and calibrate the shape of the cup. A comparison of geometries is done for tailored blanks made by orbital forming (Fig. 13) and hybrid parts (Fig. 14). For tailored blanks severe buckling and folding of the sheet metal can be identified at the cup side wall and at the inner radius of the cup. The deformation is much smaller for R35.2 mm, because of increased stiffness of the component due to the longer teeth along the cup wall. This indicates compression stresses in vertical direction leading to buckling of the sheet metal. For both layouts the target geometry is not reached, since the teeth are not formed sufficiently"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002023_s11012-016-0502-3-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002023_s11012-016-0502-3-Figure6-1.png",
        "caption": "Fig. 6 FE model of spur gear pair with gear tip-fillet: a FE model, b enlarged view",
        "texts": [
            " TVMS calculation schematic considering the effects of the gear tip-fillet and friction is shown in Fig. 5, and the effects of ETC, filletfoundation deformation, manufacturing errors, assembly errors, friction and the tip-fillet can be considered conveniently to calculate TVMS and LTE. In this section, a 2D FE model with contact elements considering the effects of gear tip-fillets and ETC is established to verify IAM. Furthermore, the effects of different radii of the tip-fillet on TVMS are also discussed. The schematic of the 2D FE model with contact elements is shown in Fig. 6. In the figure, the inner ring nodes of the driving gear are coupled with the master nodes, and the master node of the driving gear is free to rotate, and the driven gear is constrained. The torque is equivalent to the tangential forces which are applied to the inner ring nodes of the driving gear. Parameters of the spur gear pair are listed in Table 1, and the parameters of the driven gear are the same with the driving gear. Based on the IAM and FE method, TVMS of healthy spur gear pairs under different radii of tip-fillet (rc = 0m, 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002944_iet-rpg.2016.0236-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002944_iet-rpg.2016.0236-Figure2-1.png",
        "caption": "Fig. 2 Meshing force diagram of the planetary gear train",
        "texts": [
            " Since the component of gear meshing force is a periodic function related to the meshing frequency [8], the dynamic meshing force of the planet\u2013ring gear pair Fr and that of the planet\u2013sun one, Fs, can be expressed using Fourier series and their exponential form, respectively Fr(t) = \u2211 m = 1 M Frmcos(2\u03c0m f zt + \u03b8rm) = \u2211 m = \u2212 M M F\u0304rm ej2\u03c0m f zt (2) Fs(t) = \u2211 m = 1 M Fsmcos(2\u03c0m f zt + \u03b8sm) = \u2211 m = \u2212 M M F\u0304sm ej2\u03c0m f zt (3) where Frm and \u03b8rm are the mth amplitude and phase of the meshing force of the planet\u2013ring gear pair, and F\u0304rm is its Fourier complex coefficient. Similarly, Fsm and \u03b8sm are the mth amplitude and phase of the meshing force of the planet\u2013sun gear pair, and F\u0304rm is its Fourier complex coefficient. Assuming that sensor coordinate is X \u2032O\u2032Y\u2032, as shown in Fig. 2, the projection vr of the dynamic meshing force Fr on the positive Y\u2032 and the vs of Fs are periodic functions of the planet carrier rotational frequency fc, which can be expressed as vr(t) = sin(2\u03c0 f ct + \u03b1r) = \u2211 n = \u2212 1 1 Vn ej2\u03c0n f ct (4) 426 IET Renew. Power Gener., 2017, Vol. 11 Iss. 4, pp. 425-432 \u00a9 The Institution of Engineering and Technology 2016 vs(t) = \u2212 sin(2\u03c0 f ct + \u03b1s) = \u2211 n = \u2212 1 1 Vn ej\u03c0 ej2\u03c0n f ct (5) where \u03b1r and \u03b1s are the pressure angles on the reference circle when the planet gear meshes with the ring gear and sun gear, respectively; Vn is the Fourier complex coefficient with n \u2260 0",
            " When the order of the meshing frequency extends to m, the frequency components of the response x0(t) can be expressed as f mkn = (mzr + k + n) f c (10) where m = 1, 2, \u2026M; k = 0, \u00b1 1,\u2026, \u00b1 K; n = \u00b1 1. 1. At the initial time t = 0, the angle \u03c8 between the centreline of planet\u2013sun gear pair and the axis Y equals to \u03c8i, \u03c8i \u2260 0 Compared with the situation \u03c8i = 0, the existence of \u03c8i leads to a time shift of dynamic meshing force, direction projection function and transmission path function. Taking the rotation of planet carrier as an input and that of the sun gear as an output (as shown in Fig. 2), and let the clockwise rotation to be positive. According to the motion relationship between these machine parts, the time shift of dynamic planet\u2013ring meshing force is tri in advance, whereas that of dynamic planet\u2013sun meshing force is tsi behind, and those of transmission path function and direction projection function are both tci in advance tri = \u2212 \u03c8 i ( f r + f c) = \u2212 \u03c8 i 2\u03c0 f c (11) tsi = \u03c8 i 2\u03c0( f s \u2212 f c) (12) tci = \u2212 \u03c8 i (2\u03c0 f c) (13) According to the time-shift characteristics of Fourier transform, we could deduce the expression of the vibration response xri(t) and xsi(t) in the positive Y direction of the coordinate XOY, and the IET Renew"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000218_1.3063817-Figure21-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000218_1.3063817-Figure21-1.png",
        "caption": "Fig. 21 Conceptual illustration of force-field acting on pockets of the flexible cage",
        "texts": [
            " The results displayed are for two full revolutions of the all around the outer race. The ball-pocket force slows the cage otation as the ball\u2019s position in the outer race moves from 90 eg to 0 deg, but it advances the cage rotation from roughly 75 eg to 210 deg 150 deg . At every other location in the outer ace, the balls are in transition, causing the cage to tilt. This patern of advancing and hindering forces on the cage pocket is contant during steady-state operation. Moreover, it is the same for very ball-pocket pair. Figure 21 illustrates the ball impact forces pplied to the cage pockets as they make a full revolution around he outer race. The arrow in the center depicts the sense of the age rotation. The lengths of the arrows indicate the relative magitudes of the forces. Because this pattern is unchanging and idenical for every ball-pocket pair during steady-state bearing operaion, it acts as a force field on the cage pockets. The majority of he force field directs the cage to move down and to the left, hich explains why the cage has shifted down and to the left in ig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000198_j.jelechem.2010.11.028-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000198_j.jelechem.2010.11.028-Figure3-1.png",
        "caption": "Fig. 3. Cyclic voltammograms of 1.0 mM (a) 2AP, (b) 3AP and (c) 4AP in pH 7.0 buffer solution at SPCE before (dashed line) and after (solid line) electrochemical pretreatments. Scan rate = 0.1 V s 1.",
        "texts": [
            " The surface morphology becomes a rough configuration of large pores, multilayers and a sponge-like network honeycombed by nano-size cavities as the positive potential was greater than 1.6 V (Fig. 2E and F). The surface morphology changes imply the alteration of electrode characteristics, and thus the usage as an electrochemical sensor. Experimentally, the pretreated electrodes obtained with excessively high positive potentials show poor reproducibility in the detection of aminophenol isomers by cyclic voltammetry (see below). Fig. 3 shows the cyclic voltammograms for individual 2-aminophenol (2AP), 3-aminophenol (3AP) and 4-aminophenol (4AP) in pH 7 buffer solution at SPCE before and after electrochemical pretreatment. It was observed that the response of each analyte was specific, exhibiting different electron transfer activities at both the untreated and pretreated electrodes. Analytical data obtained from these voltammograms are shown in Table 2. As to 2AP (Fig. 3a), compared to that at a bare SPCE, an enhanced oxidation reaction at the SPCE was observed with a negative shift of 200 mV accompanied with an increase in peak current. The oxidation of 3AP (Fig. 3b) showed a similar trend, except a less shift in peak potentials. For 4AP, improved redox properties were observed at SPCE as compared to SPCE (Fig. 3c). The anodic to cathodic peak current ratio (Ipa/Ipc) was 0.921 and the peak-to-peak potential separation (DEp) was 0.064 V, suggesting that electro- chemical oxidation of 4AP at SPCE is a quasi-reversible redox reaction. Generally speaking, the increase in the oxidation peak currents and the lowering of oxidation peak potentials are clear evidence of the catalytic effect of the SPCE on each analyte. This is in agreement with previous studies showing that increased electrochemical activity was achieved at electrochemically pretreated electrodes for a wide range of reversible and irreversible redox processes [15\u201321]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001968_978-94-007-6101-8-Figure5.6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001968_978-94-007-6101-8-Figure5.6-1.png",
        "caption": "Fig. 5.6 Robot wrist",
        "texts": [
            " It is defined as a function of a fraction a/b while taking into consideration the sign of the numerator a and the denominator b. The function is given in the table: a > 0 and b > 0 arctan2 a/b = arctan a/b a > 0 and b < 0 arctan2 a/b = \u03c0 + arctan a/b a < 0 and b > 0 arctan2 a/b = arctan a/b a < 0 and b < 0 arctan2 a/b = arctan a/b \u2212 \u03c0 When the three axes of the wrist intersect in the same point, we can separately consider the displacements of the robot arm (\u03d11, \u03d12, \u03d13) and the displacements of the robot wrist (\u03d14, \u03d15, \u03d16). Figure 5.6 shows the robot wrist, while the robot arm is placed into the initial pose. Now, the unit vector of the robot end-segment a can be decomposed into components along the base coordinate frame ax0, ay0, and az0. The angle in the fourth joint is obtained by the Eq. (5.29): \u03d14 = arctan2 ay0 ax0 (5.29) The relation between an arbitrary orientation of vector a and the orientation of vector a0, when the first three joints are in the initial pose, is given by the following equation: a0 = 0RT 3 a (5.30) The rotational part of the matrix (5.7) is first transposed and afterwards multiplied by the vector [ax ,ay,az]T, yielding: ax0 = ax c1c23 + ays1c23 + azs23 (5.31) ay0 = ayc1 \u2212 ax s1 (5.32) az0 = \u2212ax c1s23 \u2212 ays1s23 + azc23 (5.33) The joint variable \u03d15 is defined as the angle between the axes x4 and x5, as evident from Fig. 5.6. When replaced by an equivalent angle between the segments d4 and d6, the following relation is obtained: \u03d15 = arctan2 \u221a a2 x0 + a2 y0 az0 (5.34) There remains only the angle \u03d16. We express s6 from Eq. (5.13) and input it into (5.16), while expressing c6: c6 = ( nz s4 ( c4c5 + c23 s23 s5 ) \u2212 sz ) s23s4 (c4c5s23 + c23s5)2 + s232s42 (5.35) The function arccos yields the values between 0 and \u03c0 . We therefore use + arccos c6 in the first half of rotation about the vector a, and \u2212 arccos c6 in the second half"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000857_j.cma.2013.12.017-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000857_j.cma.2013.12.017-Figure9-1.png",
        "caption": "Fig. 9. Coordinate systems applied for simulation of meshing and contact.",
        "texts": [
            " Relative positioning of the wheel with respect to the pinion is considered in order to investigate the sensitivity of the contact patterns and function of transmission errors when errors of alignment occur. The errors of alignment considered are: (i) DA2 as the axial displacement of the wheel with respect to the pinion (Fig. 8(a)), (ii) DC as the center distance error (Fig. 8(b)), (iii) DV as the intersecting shaft angle error (Fig. 8(c)), and (iv) DH as the crossing shaft angle error (Fig. 8(d)). Fig. 9 represents the applied coordinate systems for tooth contact analysis (TCA) and simulation of transmission errors. The following auxiliary coordinate systems have been defined: Parameter PINION WHEEL Number of teeth, N 24 34 Module, m [mm] 2 Face width, FW [mm] 20 Young\u2019s Modulus, E [GPa] 210 Poisson\u2019s ratio, m 0.3 Nominal torque applied, T [Nm] 150 \u2013 Angles /1 and /2 are the angles of rotation of the pinion and wheel, respectively. The common basic geometric design data for all examples of design investigated are shown in Table 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000560_j.jsv.2009.03.013-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000560_j.jsv.2009.03.013-Figure4-1.png",
        "caption": "Fig. 4. Loads acting on the cage.",
        "texts": [
            " A resisting torque (CP) due to an asymmetric hydrodynamic pressure field and the oleodynamic drag force (FOL) are considered. Due to small internal clearances needed for high-speed operation, friction effects at the roller end/cage pocket (friction torque CC) and roller end/guiding flange (traction force FE and friction torque CE) are also considered. In addition to the roller/cage interactions, the contact between the cage and the guiding ring surfaces introduces a normal load (QC) and a friction torque (CC) linked to the cage attitude angle (f) and eccentricity (EX), through a short journal bearing model (see Fig. 4). Finally, the roller/ring reaction forces balance the inner ring. See Cavallaro paper [19] for details on force models used. For the roller j, the application of the Newton\u2019s second law yields mr dm 2 doj dt \u00bc QC2j QC1j FOL\u00fe Fij Foj \u00fe FEj (8) Jr doj dt \u00fe doRj dt \u00bc RR\u00f0FC1j \u00fe FC2j Fij F oj\u00de \u00fe CEj \u00fe CCj \u00fe CPij \u00fe CPoj (9) ARTICLE IN PRESS A. Leblanc et al. / Journal of Sound and Vibration 325 (2009) 145\u2013160 149 with dCj dt \u00bc oj (10) Similarly, for the cage: mc dVX c dt \u00bc XN j\u00bc1 \u00f0\u00f0QC2j QC1j\u00de cosCj \u00fe \u00f0FC2j \u00fe FC1j\u00de sinCj\u00de \u00fe \u00f0QCi \u00feQCo\u00de sin w (11) mc dVY c dt \u00bc XN j\u00bc1 \u00f0\u00f0QC2j QC1j\u00de sinCj \u00fe \u00f0FC2j FC1j\u00de cosCj\u00de \u00f0QCi \u00feQCo\u00de cos w (12) Jc doc dt \u00bc XN j\u00bc1 \u00f0QC2j QC1j\u00de dm 2 \u00f0FC2j \u00fe FC1j\u00deRR CCj \u00fe CCi CCo EX QCi sin w (13) ARTICLE IN PRESS A"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002004_1.4028532-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002004_1.4028532-Figure6-1.png",
        "caption": "Fig. 6 Maximum and minimum limits of CC foldability. (a) Isometric view and (b) top view.",
        "texts": [
            " [21], where it was shown that any single input variable can be used with the above five constant parameters to simulate the singleDOF folding motion of a piecewise Miura-derivative pattern. In this instance, it is most convenient to define pattern variable gK A between upper and lower bounds gK A;max and gK A;min. The upper bound simply occurs when the pattern is completely flat, gK A;max \u00bc p. The lower bound corresponds to the maximum compressible configuration of the CC model, which is calculated by assuming that this state occurs when the outermost rigid strip is folded completely flat, which is to say when g1 Z \u00bc 0, shown in Fig. 6. From Eq. (1) in Ref. [21], \u00f01\u00fe cos gZ\u00de\u00f01 cos gA\u00de \u00bc 4 cos2 /, this occurs at cos gK A;min \u00bc sin2 /1 cos2 /1 (23) It is believed that this is the first analytical prediction for the maximum compressibility of CC origami patterns [23]. A comparison between the unfolded rigid strip assembly and the unrolled projected ellipse (u03; v 0 3) given by Eqs. (14) to (15) is shown in Fig. 6(b), with good agreement seen. A comparison between the folding motion of the simulated geometry and the aluminum prototype, set at dimensions a\u00bc 60 mm, b\u00bc 60 mm, / \u00bc p=3; gZ \u00bc p=2, m\u00bc 3, n\u00bc 3, and u \u00bc umin, also shows good agreement, shown in Fig. 7. 3.3 Tessellations. As a final comment on the creation of the CC-Miura pattern, it should be noted that many different curves can be defined through three nodes on a prismatic base pattern, beyond the simple elliptical curve discussed above. More complex conic curves can be derived by fitting partial elliptical curves through half-units of the base prismatic geometry, and can still be completely defined with the single gradient parameter u"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001090_tmag.2011.2105498-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001090_tmag.2011.2105498-Figure4-1.png",
        "caption": "Fig. 4. Sketch of position of a point on the tip of the rotor pole shoe illustrating DE fault condition.",
        "texts": [
            " In this case, only second, fourth, sixth, and eighth harmonics have been considered to evaluate . III. INVERSE AIR-GAP FUNCTION OF SATURATED SPSG UNDER DYNAMIC ECCENTRICITY FAULT In this stage of modeling process, attempt is made to incorporate the DE effect to the function. First, the DE degree (DED) in SPSG defined as follows: (8) where and are the centerlines of the stator and rotor, respectively; and is the DE vector. This vector rotates around the stator centerline with velocity equal to the mechanical velocity of the rotor. Fig. 4 shows the position of point P on the top of rotor pole shoe in the case of DE fault. The projection of vector over the vector can be written as follows: (9) where is angular position of DE vector. As illustrated in Fig. 4, , where the is the initial angle of DE vector. is fixed due to the same velocity of and vectors. Therefore, follows the variation of the rotor position angle. Also, can be determined as follows: (10) Term is much smaller than the rotor radius , therefore, may be approximated by . Distance of point from the stator center is obtained as follows: (11) Consequently, the air-gap length between the stator and point P in the presence of DE fault can be calculated as (12) where is the inner radius of stator"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001496_tcst.2015.2454445-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001496_tcst.2015.2454445-Figure5-1.png",
        "caption": "Fig. 5. Sketch of a complete quadrotor landing maneuver.",
        "texts": [
            " The last one, the q1 \u2192 q2 transition maneuver in [t0, t1), is obtained as a combination of an \u03b5-robust q1 \u2192 q2 approach maneuver and a set of \u03b5-robust q2-single maneuvers. We now present multiple straightforward robust approach trajectories whose practical tracking leads the quadrotor from FF to a final landed position in a controlled manner. The maneuvers are parameterized by their starting conditions and are combined to generate the robust transition maneuvers. The proposed complete landing maneuver is shown in Fig. 5. The landing procedure starts in FF, where a horizontal landing path is tracked. This eventually leads to a collision with the sloped ground, at which instant the supervisor selects the TLs controller and starts tracking a reference maneuver that leads the quadrotor to the TL state. The quadrotor then slides up the slope, tracking a TLs to TL trajectory, until it comes to a halt at a desired location. Upon coming to a halt, the quadrotor transitions to the TL operating mode and the supervisor uses the TL low-level controller to track a TL to LL trajectory that finally levels the quadrotor with the ground, without starting to slide again",
            " The positive velocity corresponds to a landing maneuver where the quadrotor lands from the lower side of the slope. If tracked with an error smaller than \u03b5, this maneuver ensures that only one of the quadrotor\u2019s landing gears hits the slope and that the quadrotor starts to slide on the ground, forcing a transition to the TLs mode. The time instant at which the transition occurs depends on the location of the slope, the quadrotor initial position (x0, z0), and the lateral approach velocity vx . 2) TLs \u2192 TL Robust Transition Maneuver: Following Fig. 5, in the TLs operating mode, the quadrotor tracks a straight line along the slope and decreases its velocity, until it comes to a halt. We define a reference maneuver with constant acceleration for the contact point and a fixed tilt angle as follows: \u03be (t) = \u03be0 + v\u03be (t \u2212 t0) \u2212 a\u03be (t \u2212 t0) 2 \u03b8 (t) = \u03b80 for the initial conditions \u03be0 \u2208 R and positive parameters v\u03be , a\u03be , and \u03b80. The corresponding reference inputs F 1 (t) and F 2 (t) are obtained by dynamic inversion of vehicle model. A set of maneuvers with different initial condition parameters at the initial time instant t0 is considered so as to cover the whole region of possible initial conditions that arises when the tracking of the preceding maneuver is not perfect"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002620_j.msea.2019.138481-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002620_j.msea.2019.138481-Figure1-1.png",
        "caption": "Fig. 1. (a) Specimen orientations during processing; (b) tensile specimens machined from prismatic rectangular blanks (dimensions in mm).",
        "texts": [
            " Certainly, the prediction of the strength and ductility of an alloy cannot be established on the basis of its chemical composition alone since these characteristics will evidently depend on the processing and post-processing history of the material. In this work, an EOSINT M280 (EOS GmbH, Munich Germany) laser powder bed fusion system equipped with a 400 W ytterbium fiber laser and EOS IN625_Surface 1.0 Parameter Set (laser power ~300 W, scanning speed ~1000 mm/s, hatching space ~0.1 mm, and layer thickness ~40 \u03bcm) were employed to fabricate vertically-oriented 85 \ufffd 18 \ufffd 3 mm3 blanks and 10 \ufffd 10 \ufffd 10 mm3 cubic specimens (Fig. 1a). The degree of porosity measured in our previous studies [26, 27] was lower than 0.1%. The vertical orientation of specimens was chosen according to our previous studies [21] as specimens having maximum elongation compared to their horizontal and 45\ufffd-oriented counterparts. Directly after LPBF, the specimens with the building platform were subjected to the EOS- recommended stress relief annealing (SR) at 870 \ufffdC for 1 h, followed by forced air cooling; it is at a scale of dislocation rearrangements that the internal stresses are relieved [28,29]. The stress relief annealing was performed using a Nabertherm H41/N K. Inaekyan et al. Materials Science & Engineering A 768 (2019) 138481 furnace under argon continuous flow (~15 l/min). Next, all specimens were cut from the platform, and the blanks machined by EDM (electrical discharge machining) to obtain the dumbbell-shaped tensile testing specimens shown in Fig. 1b with the same surface finish (Ra \u00bc 0.76 \ufffd 0.02 \u03bcm; Rz \u00bc 4 \ufffd 0.2 \u03bcm). Some SR specimens were reserved for future study, while the others were subjected to either intermediate-temperature annealing (ITA) at 980 \ufffdC (1 h) (ASTM B443, Grade 1) or high-temperature solution treatment (ST) at 1120 \ufffdC (1 h) (ASTM B443, Grade 2) in an open-air furnace (Pyradia, USA), followed by air cooling. Some of the ST and wrought annealed alloy specimens were also subjected to aging at 760 and 980 \ufffdC for 100 h (see Fig",
            " Similarly, aging at 980 \ufffdC for 100 h (AG980) was designed to promote carbides formation in the solution-treated (ST) alloy, and to assess the impact of these carbides on the alloy mechanical properties [23]. However, note that the TTT diagram for LPBF IN625 can differ from that for the wrought alloy as shown in Fig. 2b,c in terms of the \u03b4 phase formation, for example. Following the post-processing treatments, the alloy microstructure was characterized using a Hitachi SU8230 scanning electron microscope (SEM), equipped with an electron backscatter diffraction (EBSD) unit. The microstructural analysis was performed on the horizontal (XY) and vertical reference (ZX) faces of cubic specimens (Fig. 1a), as well as on coupons cut from tensile samples. All the specimens were polished manually (1 \u03bcm grit size), and then using a vibrometer and colloidal silica (0.05 \u03bcm grit size). For EBSD analysis, samples were tilted at 70\ufffd and scanned at 20 kV, with a step of 1\u20132 \u03bcm. The SEM observations of precipitates were performed using the secondary (SE) and backscattered (BSE) electron imaging modes and EDX analysis. The transmission electron microscope (TEM) observations of precipitates in selected specimens were performed using a JEOL JEM-2100 F TEM at an acceleration voltage of 200 kV"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001331_tmag.2014.2310179-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001331_tmag.2014.2310179-Figure1-1.png",
        "caption": "Fig. 1. Cross sections. (a) and (b) Modular and UNET machines with tooth tips. (c) and (d) Modular and UNET machines without tooth tips. Ri is the stator inner radius. For UNET machines shown here, the windings are only wound on the narrower teeth, while on the wider teeth is also applicable for increasing winding factor.",
        "texts": [
            " However, if the same PM volume is used for modular SFPM machines, the output power density can be higher than that of their nonmodular counterparts [11]. Manuscript received November 17, 2013; revised January 24, 2014; accepted March 3, 2014. Date of publication March 11, 2014; date of current version July 7, 2014. Corresponding author: G. J. Li (e-mail: g.li@sheffield.ac.uk). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMAG.2014.2310179 Similar structures have been proposed in [13]. Similar to Fig. 1(c), a simple and effective method has been employed by inserting flux gaps into alternate stator teeth of a 12-slot/14-pole interior permanent magnet machine. The objective is to mitigate the space harmonics in the air-gap flux density because of armature currents, and to increase winding factor. As a result, the rotor power losses, particularly the PM eddy current losses, can be significantly mitigated. Additionally, the average torque can be increased. The flux gaps can also be located in the stator yoke to decrease space harmonics which generate iron losses [3], [14]",
            " In addition to the previously mentioned modular machine topologies, structures with unequal tooth (UNET) widths can also be employed to increase machine winding factor and power density [15]\u2013[18]. By using unequal tooth widths, a winding factor 1 can be achieved [15], [16]. However, the influences of flux gaps and UNET widths on air-gap flux density owing to PMs are different. Similar phenomena can be observed for flux paths in the stator iron core. As a result, their influences on machine performance are also different. To analyze these influences, modular [Fig. 1(a) and (c)] and UNET machines [Fig. 1(b) and (d)] either with or without tooth tips, will be comprehensively investigated in this paper. Moreover, several general rules covering different machine topologies with different slot/pole number combinations will be established. In this paper, the machine topologies and their features are presented in Section II. The influences of flux gap and UNET widths on winding factor, the air-gap flux density because of PMs, etc., are investigated in Section III. The experimental validation is given in Section IV. 0018-9464 \u00a9 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. The cross sections of the investigated machines are shown in Fig. 1, in which only the stators are shown. In each case, the rotors are surface-mounted permanent magnet (SPM) topologies, having full pole arc magnets (Fig. 15). To obtain a modular structure, flux gaps are inserted into the middle of alternate stator teeth [Fig. 1(a) and (c)]. However, when flux gap width (\u03b20) changes, to limit the magnetic saturation in tooth bodies, the total iron width (2t0) remains unchanged. The tooth tip width (tw) is also constant to keep the slot opening unchanged. Conversely, the UNET machines [Fig. 1(b) and (d)] are obtained by filling the flux gaps of the relevant modular machines with iron. This material is the same as that of the stator iron core. Therefore, both the modular and UNET machines have the same dimensions. For comparison purposes, throughout this paper, the UNET width (UNET machines) will be equal to the flux gap width (\u03b20, modular machines). For all investigated machines, the calculations will be based on the machine parameters given in Table I. The windings of all the machines are single-layer concentrated windings, and wound on the teeth without flux gaps for the modular machines",
            " For nonmodular and equal teeth machines, without considering higher order harmonics, the distribution factor (kd), the pitch factor (kp), and the winding factor (kw) can be calculated by kd = sin(q\u03c3/2) q sin (\u03c3/2) (1) k p = sin ( \u03c4s \u03c4p \u03c0 2 ) = sin ( p\u03c0 Ns ) (2) kw = k p \u00b7 kd (3) where q is the number of coils per phase, \u03c3 is the angular phase between two adjacent coils of one phase (in electrical degrees), \u03c4p = 2\u03c0/(2 p) is the pole pitch, \u03c4s = 2\u03c0/Ns is slot pitch, Ns is the slot number, while p is rotor pole pair number. For single-layer concentrated winding machines (Fig. 1), to minimize the unbalanced magnetic force, an even number of coils per phase has to be employed. Therefore, the stator slot numbers must be multiples of 12. Using the method developed in [24], the winding factors of nonmodular and equal teeth machines with different slot/pole number combinations have been calculated. It has been found that for machines with different slot numbers, they have the same maximum Kd , that is, 1 and the same maximum Kw , that is, 0.966. Moreover, all the machines having the maximum Kd and the maximum Kw are either multiples of 12-slot/10-pole or multiples of 12-slot/14-pole ones. Therefore, only the 12-slot/10-pole and 12-slot/14-pole machines will be chosen as examples to investigate the influence of flux gaps and UNET widths on machine performance. As the slot opening is constant for machines with tooth tips, (2) is still applicable to calculate K p of the UNET machines with tooth tips. This is because their slot pitches are unchanged for different \u03b20 [Fig. 1(b)]. Therefore, the winding factors of the UNET machines with tooth tips are independent of \u03b20. However, this is not the case for the modular machines either with or without tooth tips [Fig. 1(a) and (c)] and the UNET machines without tooth tips [Fig. 1(d)]. Thus, certain modifications should be performed to take account of the influences of flux gaps and UNET for calculating the pitch factors k p = sin ( (\u03c4s \u2212 ) \u03c4p \u03c0 2 ) for modular machines (4a) k p = sin ( (\u03c4s + ) \u03c4p \u03c0 2 ) for UNET machines with Ns > 2 p (4b) = asin ( \u03b20 2\u00d7Ri ) . (5) Using (4a) and (5), the pitch factors and hence the winding factors for the investigated machines have been calculated (Fig. 2). It is found that for the modular machines having higher slot number than pole number, that is, 12-slot/10-pole, the winding factor decreases with the increase in \u03b20"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003759_j.ymssp.2019.02.044-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003759_j.ymssp.2019.02.044-Figure8-1.png",
        "caption": "Fig. 8. Overall links of one planet.",
        "texts": [
            " Xcg \u00fe XN 1 kpnTc2Xng \u00bc Fc \u00fe Fc ind \u00f034\u00de The developed expressions of Mc; \u20acXcg ; Tc1;Kc;Xcg ; Tc2;Xng ; Fc and Fc ind can be found in C. 3.4. Equation of motion of one planet It was shown previously that local displacements (Ui 8i 2 sun; planet; carrier; ring) are expressed as global displacements (Uig) with respect to the fixed frame tied to the carrier in Eqs. (3), (4), (14) and (24). The displacements along different lines of action (d g sn; d g nr) and the radial and tangential deflections of planet bearing (d g nrd; d g ntg) are also developed as global displace- ments in Eqs. (6), (16), (27) and (28) (Fig. 8). The position of the planet is given by Rn ! \u00bc Ung i !\u00fe Vng j ! \u00f035\u00de The velocity of the planet is given by _Rn ! \u00bc _Ung i !\u00fe _Vng j ! \u00f036\u00de The potential energy of the planet is Epn \u00bc 1 2 kpn d g nrg 2 \u00fe d g ntg 2 \u00fe 1 2 ksn t\u00f0 \u00ded g sn 2 \u00fe 1 2 knr t\u00f0 \u00ded g nr 2 \u00f037\u00de The kinetic energy of the carrier is Ecn \u00bc 1 2 mn _U2 ng \u00fe _V2 ng \u00fe 1 2 In r2bn _W2 ng \u00f038\u00de By applying LAGRANGE formulation given by Eq. (39), Eq. (40) is concluded @Epn @Ung \u00fe d dt @Ecn @ _Ung ! @Ecn @Ung \u00bc 0 @Epn @Vng \u00fe d dt @Ecn @ _Vng "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003365_j.oceaneng.2020.106949-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003365_j.oceaneng.2020.106949-Figure1-1.png",
        "caption": "Fig. 1. Layout comparison of the Cross-rudder and X-rudder. (a) Cross-rudder; (b) X-rudder.",
        "texts": [
            " Section 2 presents the X-rudder AUV models, trajectory tracking mission, and control problem formulation. Section 3 proposes the optimal robust trajectory tracking control scheme, and presents the detailed deriving process of kinematics and dynamics controller. Section 4 validates the previous analysis and design through simulation cases and discussions. Section 5 demonstrates the conclusions of this work. In this paper, a X-rudder AUV will be studied, which has a special control surface layout, as shown in Fig. 1. Compared with traditional Cross-rudder AUV, X-rudder AUV has following advantages: 1) Higher safety: The X-rudder can be arranged within the vehicle\u2019s baseline, thus avoiding unexpected collisions between the rudders and underwater obstacles; 2) Better maneuverability: The X-rudder AUV has better hydrodynamic performance and stability in both horizontal and vertical planes, and the rolling motion can be controlled; 3) Better rudder efficiency: The X rudder adopts a diagonal arrangement to obtain the maximum extension length, which helps achieving large aspect ratio and high rudder efficiency; 4) Stronger anti-sinking ability: Due to the independent control property and diagonal arrangement, the X-rudder AUV has better ability to resist the rudder stuck, and also reduces the serious damage caused by rudder stuck; 5) Lower noise: The layout of X rudder helps reduce interference between the rudder and propeller, thus reducing the noise"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003793_j.mechmachtheory.2019.103764-Figure10-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003793_j.mechmachtheory.2019.103764-Figure10-1.png",
        "caption": "Fig. 10. Support range of bearings on input and output shaft.",
        "texts": [
            " Vibration characteristics of star gearing system under various support mode of rotors According to Eq. (3) , the distance between the bearing and gear plane of star gearing system could results in the difference of vibration characteristics and the floating amounts of those components in the system. Therefore, the location of bearings on the rotors can be rearranged to control the vibration amplitude in order to achieve better load sharing performance and reduce the floating amount of those components. The range of length that bearings can placed in the rotors are shown in Fig. 10 , it can be easily seen that the bearings can only be placed in certain range of length among the whole rotors. The arrangement and permutations of bearings are shown in Fig. 11 , in which b i represent the position of bearings, the number of i becomes bigger as the distance between bearing and the gear plane of star gearing system closer. In general, the valid length of input shaft is nine times the thickness of bearings that match the input shaft, while the valid length of output shaft is six times the thickness of bearings that match the output shaft"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001357_iros.2013.6696696-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001357_iros.2013.6696696-Figure5-1.png",
        "caption": "Fig. 5. Flybox UAV in the hexacopter configuration.",
        "texts": [
            " (18), we can now compute the augmented thrust vector magnitude T\u0304 that compensates for the drag by T\u0304 = T (1\u2212 (ca + cd)v3) (20) Equivalently, the external acceleration \u03b3e is now \u03b3e = ge3 \u2212 g(ca + cd)\u03be\u0307. (21) The drag-compensated external acceleration can now be incorporated in the position controller Eq. (17). The magnitude of the thrust vector is then computed using Eq. (14) and subsequently drag compensated using Eq. (20). The presented control scheme is implemented and evaluated on the Flybox hexacopter UAV designed and built by Skybotix AG. The UAV is depicted in Fig. 5. The mechanical, electrical and software setup of the platform are described in detail in [5], the general description of the control setup, as used for these experiments is found in [3]. Table I depicts the specifications of the Flybox UAV that are also used in simulation. B. Identification Drag Coefficient In order to compensate for the blade flapping and induced drag in the control scheme, we first identify the lumped drag coefficient (ca + cd) in a batch-estimation offline scheme. We can show that the accelerometer output and the vehicle\u2019s velocity can be directly related to the drag coefficient"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001471_j.mechmachtheory.2014.07.013-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001471_j.mechmachtheory.2014.07.013-Figure8-1.png",
        "caption": "Fig. 8. Eccentricity default of bevel gear (12).",
        "texts": [
            " These defects may be related to themanufacture, installation and operation of the gearbox. Eccentricity defect, profile error and tooth crack are the defects which are included in our model. 7.1. Eccentricity defect The eccentricity is the result of the non-concentricity between the axis of the pitch cylinder of the gear and the axis of rotation of the shaft to which the gear is bonded. The eccentricities of the gears and shafts can lead to mounting errors which create much noise. An eccentric wheel is characterized by two parameters eij and \u03bbij (Fig. 8.): - eij : the distance between the axis of rotation and the axis of inertia of the wheel and expressed by: e12 t\u00f0 \u00de \u00bc e12 sin \u03a91t\u2212\u03bb12\u2212\u03b11\u00f0 \u00de: \u00f038\u00de - \u03bbij is a phase relative to a fixed reference. We supposed this eccentricity is located on the bevel gear (12). The eccentricity defect affects the tooth deflections. So, there is a potential energy which will give additional force {Fex(t)}. Fex t\u00f0 \u00def g \u00bc K1 t\u00f0 \u00dee12 t\u00f0 \u00de c1 c2 c3 c4 c5 c6 0 0 0 c7 c8 c11 c10 0 0 0 c9 c12 0 0 0f gT \u00f039\u00de The spectral representation (Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001257_tim.2013.2283548-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001257_tim.2013.2283548-Figure1-1.png",
        "caption": "Fig. 1. System overview.",
        "texts": [
            " Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. In Section VII, we analyze how the sensor noise, sensor saturation, and shock during the impact affect the position estimation. Finally, the concluding remarks are given in Section VIII. The proposed system estimates the attitude and position of a golf club during a swing motion. It consists of a unit attached to the golf club and a camera system (see Fig. 1). The inertial sensors and infrared light emitting diodes (LEDs) are attached to the golf club. As inertial sensors, an XSens MTi unit (three-axis accelerometers and three-axis gyroscopes) is used. Three-axis magnetic sensors are also included in XSens MTi; however, these sensors are not used in this case. Eight infrared LEDs are mounted on a \u201cT\u201d-shaped marker. These infrared LEDs are captured by a camera system. The camera system consists of two USB cameras (Pointgrey Firefly FMVU-03MTC), which are fixed on a rigid aluminum bar",
            " The sensor unit (the infrared LEDs and the inertial sensor unit) is rather bulky and it may affect the golf club motion during measurement. No conscious effort has been made to miniaturize the sensor unit as in [13]. The main aim of this paper is to show the feasibility of golf swing motion tracking through sensor fusion. Three coordinate systems are used in this paper: the left camera coordinate system, the right camera coordinate system, and the body coordinate system. The origin of the left (right) camera coordinate system coincides with the pinhole of the left (right) camera (see Fig. 1) assuming perspective projection. The left camera coordinate system is the reference coordinate system. If \u201ccamera coordinate system\u201d is used without \u201cright\u201d and \u201cleft\u201d adjectives, it refers to the left camera coordinate system. It is assumed that the y-axis of the camera coordinate system is parallel to the local gravitational acceleration direction. If this is not the case (e.g., the camera holding the aluminum bar is located on a slope), we need to compensate the slope angle. The three axes of the body coordinate system coincide with three axes of the inertial sensors",
            " 2, whose trajectory is given in Fig. 4. During the zero-velocity interval, change of the accelerometer value is small and the gyroscope value is also small. As illustrated in [15], zero-velocity intervals can be detected using accelerometers or gyroscopes or both of them. We found that the gyroscope value is a more reliable indicator of the zero-velocity intervals. This is presumably due to the fact that a golf swing is mainly a rotational movement. Since the main rotation axis is the z-axis (see Fig. 1), yg,k,z is used to detect the zero-velocity interval. The discrete time k is assumed to belong to the zero-velocity interval if the following conditions are satisfied: |yg,k,z| < 0.08 rad/s, before the impact |yg,i,z | < 0.08 rad/s, k \u2264 i \u2264 k + 5 after the impact. (2) When there is no impact (e.g., in the case of a practice swing), the first condition is applied in the first half time interval and the second condition is applied in the second half time interval. The first condition in (2) detects the address and top-ofswing phases",
            " The camera images during the address and impact phases are given in Fig. 3. Note that there is almost no motion blurring since the shutter speed (200 \u03bc/s) is fast. The estimated golf club swing trajectory (blue circle) is given in Fig. 4. In the graph, the initial position is set to zero: i.e., ([r ]c\u2212initial position) is plotted. The trajectory and swing speed are from r\u0302s,k and v\u0302s,k . The arrows in Fig. 4 denote the speed and the club face direction (recall that the club face direction is the \u2212Yb-axis in Fig. 1). The length of the arrow is proportional to the club speed (\u2016v\u0302s\u2016). Note that v\u0302s is not the golf club head speed (v\u0302head) but the speed of the inertial sensor unit (see Fig. 1). Since the club head is located farther from the swing rotation axis (near the hand grip), the club head speed should slightly larger than v\u0302s . The club face direction is computed by the following: Cc b \u23a1 \u23a3 0 \u22121 0 \u23a4 \u23a6 b . In Fig. 4, the club speed and club face angle are given for a few selected points. The club face angles at the address and impact phases are computed using the Euler angles of q\u0302s,k . In Fig. 5, the estimated quaternion q\u0302s,k is transformed into the Euler angles, where the aerospace sequence (\u03c8 , \u03b8 , \u03c6 angle rotation around z, y, x axes) is used (see [22, Ch"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000642_tpel.2011.2168240-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000642_tpel.2011.2168240-Figure4-1.png",
        "caption": "Fig. 4. Phasor diagrams at particular flux position for (a) low-speed operation and (b) high-speed operation.",
        "texts": [
            ", 150\u2013200% of rated current machine) are used to obtain the maximum torque capability. The maximum output torque can be retained as long as the operation of rotor speed does not exceed its base speed. According to (6), the angle \u03b4sr plays a vital role in controlling the output torque. Since the angle \u03b4sr mainly depends on the slip angular frequency (\u03c9s \u2212 \u03c9r ), to maintain the output torque to its maximum value, the slip angular frequency (\u03c9s \u2212 \u03c9r ) must always be kept at its maximum value. This is typically established for speeds below the base speed. Fig. 4 shows the phasor diagrams of (2) under steady-state conditions for operations below base speed [see Fig. 4(a)] and at base speed [see Fig. 4(b)]. For each case, the same magnitude of stator flux vector is used and the vectors are drawn in stator flux d\u2013q reference frame. In the case of low-speed operation, the back-emf, j\u03c9s\u03a8s is small enough such that sufficient stator voltage can be generated to control both stator flux and torque, simultaneously. At base speed [see Fig. 4(b)], the stator voltage vector touches the hexagonal stator voltage boundary limit. Hence, there are two options to further increase the speed beyond the base and at the same time maintain the maximum torque capability. 1) Weaken the flux (in normal practice to be inversely proportional with speed), so that the magnitude of the vector j\u03c9s\u03a8s is retained as the frequency increases. However, the d component of the stator current will be reduced. Under this condition, the average stator voltage will stay on the hexagonal boundary and the stator flux is regulated using two active voltage vectors"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000415_j.automatica.2011.02.013-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000415_j.automatica.2011.02.013-Figure1-1.png",
        "caption": "Fig. 1. Convergence of the system trajectory into the invariant ellipsoid.",
        "texts": [
            " Consider the following benchmark example: A =  1 2 0.4 \u22121.5 0.7 2 0.5 \u22120.6 1  , B = 0.3 0 1.2  , D = 1 0 1 \u22121 0 1  . The disturbances f =  0.0028 cos(0.4t) \u2212 0.0879 sin(0.4t) 0.0499 cos(0.4t) + 0.0049 sin(0.4t)  satisfy the inequality f T  130 15 15 400  f < 1 and u(t) is the scalar sliding mode controller has the form u(t) = \u2212(C\u0303B)\u22121C\u0303Ax \u2212 0.5 sign[C\u0303x], C\u0303 \u2208 R1\u00d73. The numerical procedure described above gives \u03c4 = 1.5265, \u03b4 = 28.08 and Z =  0.0053 \u22120.0073 0.0089 \u22120.0073 0.0103 \u22120.0148 0.0089 \u22120.0148 0.0488  C\u0303 = (2.6974, 2.1442, 0.1590). The Fig. 1 shows the corresponded \u2018\u2018quasi-minimal\u2019\u2019 invariant ellipsoid \u03b5(Z\u22121) and presents the convergence process of the system trajectory into this ellipsoid. Evolution of the control law is presented in Fig. 2. All simulation results were implemented using Matlab with the ode23 solver, and a relative tolerance of 10\u22123. To avoid the chattering effect (Utkin et al., 1999) the sign functionwas replaced by a saturation function sat(\u03c1) := 1 if \u03c1 > 0.04 25\u03c1 if \u2212 0.04 \u2264 \u03c1 \u2264 0.04 \u22121 if \u03c1 < \u22120.04. In this paper a new sliding mode control designing algorithm is presented"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000135_j.cclet.2010.06.020-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000135_j.cclet.2010.06.020-Figure1-1.png",
        "caption": "Fig. 1. Cyclic voltammograms of FMCAMCNTPE in 0.1 mol L 1 PBS (pH 7.0) at a scan rate of 10 mV s 1 in the absence (a) and in the presence of 400.0 mmol L 1 CA (c). (b) as (c) for an FMCAMCPE. (d) as (c) and (e) as (b) for the unmodified electrode.",
        "texts": [
            " It is interesting to note that the results obtained show that amount of captopril in ill people had heart problem and used captopril is lower than of who is safe and used captopril. However, amount of captopril in illness urine at different times was determined and maximum of captopril was found in 2.5 h after the consumption of this tablet. This time is agreed with previous reported result in scientific source. The voltammetric behavior of ferrocenemonocarboxylic acid modified carbon nanotubes paste electrode (FMCAMCNTPE) in the buffer solution (pH 7.0) is shown in Fig. 1. The cyclic voltammetric responses for the electrochemical oxidation of 400 mmol L 1 of CA at FMCAMCNTPE are shown in curve c (Fig. 1) and at the ferrocenemonocarboxylic acid modified carbon paste electrode (FMCAMCPE) in curve b (Fig. 1). Curves d and e (Fig. 1) are the same as curves c and b (Fig. 1), respectively, but only without mediator. As can be seen, the anodic peak potentials for the oxidation of CA at FMCAMCNTPE (curve c) are about 470 mV, whereas this potential is 480 mV when using FMCAMCNTPE (curve b). On the other hand, CA oxidation (without mediator) does not take place at the surface of electrode up to +1.0 V. Similarly, when we compared the oxidation of CA at the surface of FMCAMCNTPE (Fig. 1c) and the FMCAMCPE (Fig. 1b), an enhancement of the anodic peak current was found to occur at FMCAMCNTPE versus AgjAgCljKClsat. In other words, the data obtained clearly show that the combination of multiwall carbon nanotubes and the mediator (ferrocenemonocarboxylic acid) definitely improve the characteristics of the electrode for the oxidation of CA. Therefore, results show a good catalytic activity for this mediator in the determination of CA using EC mechanism (see Fig. 2). In order to obtain information on the rate-determining step, a Tafel slope, b, was determined using the following equation for a totally irreversible diffusion controlled process [11] (Figs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000922_j.mechmachtheory.2013.11.001-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000922_j.mechmachtheory.2013.11.001-Figure1-1.png",
        "caption": "Fig. 1. (a) Constructive solution of an 8-link planetary gear train, and (b) its representation in the form of a graph.",
        "texts": [
            " Each planet is linked to its respective arm by a turning pair and to other members by gear pairs. The arms have a rotational movement around the PGT's principal axis, and are characterized by having at least one turning pair with a planet; they may also have gear pairs with other members. Finally, the suns are links that only have gear pairs with other links and also have a rotational movement around the PGT's principal axis. Suns and arms are central links since they rotate around the central axis of the PGT, whereas the planets are non-central links since they have a planetary motion. Fig. 1(a) shows a scheme of an 8-link PGT. Links 1, 2, and 3 are the suns; links 4 and 5 are the arms; and links 6, 7, and 8 are the planets of the PGT. Finally, the structure of a PGT is completely defined by its list of circuits. Each circuit is the set of three links that it is involved in each gear pair. These three links are the sun and the planet that are linked by the gear pair, and the arm that makes it possible that kinematic link. Therefore, the number of circuits is equal to the number of gear pairs. For example, the circuits of the PGT shown in Fig. 1(a) are (1, 6, 4), (1, 7, 4), (2, 6, 4), (2, 8, 5), (3, 7, 4) and (3, 8, 5), where the order of the links in each circuit is sun, planet and arm. A PGT can also be represented as a graph in which each vertex corresponds to a link of the train, and each edge corresponds to a kinematic pair between the links corresponding to the vertices at the ends of the edge. In this paper, we shall use the graph representation introduced in [1] in which the vertices of the graph are drawn in three rows. The top row corresponds to the arms, the central row to the planets, and the bottom row to the suns. The kinematic pairs are represented by solid edges for the turning pairs and dashed edges for the gear pairs. For the sake of simplicity only those turning pairs linking the planets with the suns and/or arms are included in the graph representation proposed in [1]. Fig. 1b shows the graph representing the train of Fig. 1(a). There can be a great diversity in the constructional solutions adopted for a given PGT, i.e., different constructional solutions based on the same underlying structure (given by its graph) and the same inversion. The inversion is the triplet: input link, output link, and ground link. The notation used for the inversions will be (X,Y-Z) where X is the input link, Y the output link, and Z the ground link. The structure of a PGT is defined by the set of links of the train and by the relationship of the pairs that link each of these members to the others",
            " The number of the different constructional solutions depends on how the links are designed. In the present work, a constructional solution of a PGT will be understood to be the set of types of gear pairs used \u2013 external or internal \u2013 and the specific form in which each link is constructed. In particular, in this work we shall focus on the constructive solution adopted for each planet. Therefore, the expression \u201csimple planet\u201dwill be used for a planet constructed with a single gear and \u201cdouble planet\u201d for one constructed with two gears. Fig. 1(a) shows a particular constructive solution of the PGT whose graph is shown in Fig. 1(b). This solution results from choosing the inversion 1,5\u20132 of the graph, so that the input link is the sun 1, the output link is the arm 5, and the ground link is the sun 2. Additionally, this constructive solution is characterized by having two simple planets (planets 6 and 8) and a double planet (planet 7), and for having chosen external gears for the gear pairs between the links 1\u20136, 1\u20137, 3\u20137, and 3\u20138, and internal gears for the 2\u20136 and 2\u20138 pairs. All the possible combinations of external and internal gears and of the constructive form adopted for each planet give rise to the set of constructive solutions of a PGT",
            " In graphs with only one arm link, this cannot be selected for the PGT's ground link since otherwise the train would be a conventional, not planetary, type. Thus, only when there are 2 or more arms may one of them be chosen as ground link. The possible inversions satisfying the above constraints can be enumerated from the circuits of a graph by means of the following steps: 1. Obtain the set S1 of Nc elements formed by the indices of the central members of the graph (suns and arms). For the graph of Fig. 1 one would have: S1 = {1, 2, 3, 4, 5} and Nc = 5. 2. Obtain the set S2 of Ns1 elements formed by the indices of the suns that are only connected by one gear pair to the other members, and which therefore must be part of the inversion. Therefore, for 1-dof PGTs, one must have that Ns1 \u2264 3. In the case of Fig. 1, the suns are the links 1, 2, and 3, and they each have two gear pairs, as one sees in the graph of the train. Hence Ns1 = 0, and S2 is the empty set. 3. Obtain the set S3 = S1 \u2212 S2 of N3 = Nc \u2212 Ns1 elements. This is the set of central members excluding the suns with only one gear pair. 4. The determination of the possible inversions and of the combinatorial operations this involves depends on the value of Ns1. Table 1 indicates which are those operations as a function of Ns1, which, as noted above, can be at most 3",
            " Similarly, we use the notation Pa(S) for the permutations of a elements, and \u222aPa(S\u2297C) for the union of the permutations of a elements of all the sets resulting from the Cartesian product of the sets S and C. The number of inversions listed in the rightmost column of Table 1 is simple to calculate. For the case Ns1 = 0, the number of inversions is equal to the number of possible ways of combining the elements of the set S1 three by three, considering the order of those elements, since the order coincides with the assignment as input, output, or ground link. For example, the eight-link graph of Fig. 1(b) has no sun with a single gear pair, so that Ns1 = 0 and N3 = Nc = 5. The number of inversions of this graph is 60 = 5 \u00d7 4 \u00d7 3. These are the 60 possible ways of combining the elements of the set S1 = {1, 2, 3, 4, 5} three by three. For Ns1 = 1, the only sun with one gear pair must be an input, output, or ground link. The other two links of the inversion are therefore taken from the possible ways to combine the elements of S3 two by two, regardless of their order. This number is N3(N3 \u2212 1)/2, and is the number of sets that constitute the Cartesian product S2\u2297C N3 ;2\u00f0 \u00de ",
            " This range depends on the values of the gear ratios Zij for each gear pair i\u2013j. In this section, we shall take positive values for Zij when both sets of teeth are external, and negative when one is internal. This was the choice adopted in [9], and is also followed in the present work because the method used to obtain the efficiency will be that proposed in [9]. In particular, this facilitates the use of the expressions of that method with which to calculate the efficiency. For example, for the train of Fig. 1 one would have Z26 b 0 and Z16 N 0. Finally: Zij \u00bc Zi Z j \u00bc no : of teeth of gear i no : of teeth of gear j \u00f01\u00de the sign will be positive for external gearing, and negative for internal gearing, as noted above. where Another important consideration for fixing the constraints on the gear ratios is the number of gears comprising each planet. Typically, the planet consists of 2, 3, or 4 gears, physically limiting the available space and therefore the diameter of the gear, and hence the number of teeth. In this work, the planet link is considered to consist of 3 gears at 120\u00b0 from each other. Fig. 3 shows the limiting arrangement of the three planet gears when they make tangential contact. Finally, if a given planet consists of two gears, such as planet 7 of Fig. 1, the diameter ratio of the two gears will not be able to exceed certain values, in this case conditioned by considerations of sufficient ruggedness. 3.1. Constraints for the simple planet configuration In the case where the gearing is by external contact (Zij N 0), the allowable range envisaged in the present work is: 1 5 \u2264 Zij \u2264 5: \u00f02\u00de This implies that the number of teeth of the larger gear will be at most five times the number of teeth of the smaller gear. Note that in this work the designation simple planet is used when the planet link is constituted by a single gear, as is the case of planets 6 and 8 of Fig. 1. It is necessary to verify that the range allowed by Eq. (2) is compatible with the situation of tangency limit shown in Fig. 3. This figure shows the pitch circles of the sun (central circle) and the three planet gears (outer circles). The radius of the sun is RS, and that of each planet gear is Rp. The figure represents the extreme situation, i.e., when the gear ratio causes the gears to be tangent to each other and thereby impedes their rotation. In this situation, it follows straightforwardly that: Rp \u00bc Rs \u00fe Rp sin \u03c0 3 \u00bc Rs \u00fe Rp ffiffiffi 3 p 2 : \u00f03\u00de r of graphs and possible different gear trains having up to nine links"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001813_j.ijheatmasstransfer.2018.04.164-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001813_j.ijheatmasstransfer.2018.04.164-Figure9-1.png",
        "caption": "Fig. 9. Calculated temperature profile and flow pattern in the molten pool for Case 1: (a) longitudinal cross section; and (b) streamlines of the fluid flow.",
        "texts": [
            " Furthermore, the predicted molten pool geometry (half width and depth) and the maximum bulge height were measured for Case 1 and Case 2, and the results were compared with the experimental values, as shown in Table 4. Indeed, there is good agreement between the experimental and simulation results for the two sets of laser conduction welding process parameters. The molten pool size and bulge height increase with an increase in the laser power. The half width and depth of the molten pool are larger for Case 1 compared with those for Case 2, as a result of the higher power density in Case 1. Fig. 9 shows the temperature distribution and fluid flow pattern of the molten pool for Case 1. It is found that the predicted maximum temperature values of the molten pool are 2150 and 2011 K for Case 1 and Case 2, respectively. It can be observed from Fig. 9(a) that a distinct molten pool forms in the laser affected zone. The laser beam traverse causes the molten pool to be compressed at the front and stretched behind the laser beam. Two counterrotating flow patterns are observed in the molten pool, where there is outward flow at the pool surface and inward flow at the bottom of the pool. The fluid velocity is maximum at the pool surface and therefore, the outward surface flow is much faster than the inward return flow. The melting material is pushed from the center to the periphery of the molten pool. In order to further investigate the flow pattern of the melting material, the streamlines of the fluid flow in the molten pool were plotted, as shown in Fig. 9(b). With the Marangoni outward flow, the heat from the laser beam source is transported to the periphery of the molten pool, which leads to a more uniform temperature distribution een experiments and simulations. and lower maximum temperature. The laser conduction welding process results in a wide, shallow molten pool. As an austenitic steel, the 304 stainless steel substrate does not undergo phase transition during the laser conduction welding process. The evolution of the free surface shape and weld bead formation of 304 stainless steel are mainly governed by the fluid flow of the molten pool, which is a combined effect of the material density change and temperature coefficient of surface tension during laser heating. The density of 304 stainless steel decreases as its temperature increases, resulting in volumetric expansion of the material. The material expansion caused by the melting metal contributes to the bulge formation of free liquid/gas interface, as shown in Fig. 8(a). In addition, the melting material is pushed from the central region toward the periphery of the molten pool due to the Marangoni outward flow. This results in an obvious bulge formation in the trail of the molten pool, as shown in Fig. 9(a). The geometry of the clad layer and penetration depth of a single track deposited onto the substrate determined from experiments were used to validate the laser hot-wire deposition numerical model. Fig. 10(a) shows the comparison of the cross-sectional profile of the deposited track between simulations and experiments. The left-hand side of Fig. 10(a) shows a typical microstructure obtained from the single-track cladding experiments. It can be observed that there is good metallurgical bonding at the clad layer/substrate interface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002216_00207179.2014.974675-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002216_00207179.2014.974675-Figure2-1.png",
        "caption": "Figure 2. Two Link Planar Manipulator",
        "texts": [
            " It is assumed that the only nonconservative generalized forces are the control inputs Fx = fc(t), (7) F\u03b8 = \u03c4c(t). (8) Under this assumption, the dynamics model is given by equations (3)-(4) with: M(q) = [ mc + mp mpd cos \u03b8 mpd cos \u03b8 I + mpd 2 ] , C(q, v) = [ 0 \u2212mpd\u03b8\u0307 sin \u03b8 0 0 ] G(q) = [ 0 \u2212mpgd sin \u03b8 ] , Fc = [ fc(t) \u03c4c(t) ] , FNC (q, v) = [ 0 0 ] . D ow nl oa de d by [ U ni ve rs ity o f N eb ra sk a, L in co ln ] at 0 6: 29 0 7 N ov em be r 20 14 Acc ep ted M an us cri pt 2.2 Two-Link Planar Manipulator The second example considered is a two link planar manipulator, a schematic of which is shown in Fig. 2. The model of a two-link planar nonlinear robotic system with the assumption of lumped masses at the joints can be found in (Lin & Wang, 2010). This model is presented and used here. The generalized coordinates are the rotation angles of the arms q = [\u03b81 \u03b82] T . The dynamics model is of the form given by equations (3)-(4), with: M(q) = [ (m1 + m2)d 2 1 + m2d 2 2 + 2m2d1d2 cos \u03b82 m2(d 2 2 + d1d2 cos \u03b82) m2(d 2 2 + d1d2 cos \u03b82) m2d 2 2 ] , C(q, v) = \u2212m2d1d2 \u03b8\u03072 sin \u03b82 [ 2 1 1 0 ] , Fc = [ \u03c41(t) \u03c42(t) ] , FNC = [ 0 0 ] , G(q) = g [ (m1 + m2)d1 cos \u03b81 + m2d2 cos(\u03b81 + \u03b82) m2d2 cos(\u03b81 + \u03b82) ] ",
            " The FTS scheme is seen to use less control effort while stabilizing the system D ow nl oa de d by [ U ni ve rs ity o f N eb ra sk a, L in co ln ] at 0 6: 29 0 7 N ov em be r 20 14 Acc ep ted M an us cri pt faster than the AS scheme. Furthermore it is seen that the FTS scheme is more robust than the AS scheme to the unknown disturbance inputs due to friction. 4.2 Two-Link Planar Manipulator System For this simulation, the parameter values chosen are the link masses m1 = 3 kg and m2 = 10 kg, the link lengths d1 = 1 m and d2 = 1 m; it is assumed that there is no friction at the joints. These parameters are as defined in Fig. 2. The scalar control gains are k = 0.6, \u03b3 = 1, and \u03b1 = 21/29. We chose the initial values (\u03b81)0 = 4.5 rad, (\u03b82)0 = 3 rad, (\u03b8\u03071)0 = 0 rad/s, and (\u03b8\u03072)0 = 0 rad/s. The objective is to stabilize the two link planar manipulator to the equilibrium configuration [\u03b81 \u03b82] T = [\u03c0/2 0]T . This simulation also compares the finite time stabilization (FTS) control law of (19) with an asymptotically stabilizing (AS) control law obtained by setting \u03b1 = 1 in this control law, while the parameters k and \u03b3 remain the same"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002213_j.mechmachtheory.2014.06.006-Figure12-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002213_j.mechmachtheory.2014.06.006-Figure12-1.png",
        "caption": "Fig. 12. State 8 of the derivative queer-square mechanism (\u03b11 N 0, \u03b12 b 0, \u03b211 \u2260 \u03b212, \u03b221 = \u03b222).",
        "texts": [
            " According to the positive or negative angles \u03b11 and \u03b12, category 3 is further separated to four states: state 7 where limb1s and limb2s have a relatively higher position compared to the base (\u03b11 N 0, \u03b12 N 0), state 8 where limb1s has a higher and limb2s has a relatively lower position compared to the base (\u03b11 N 0, \u03b12 b 0), state 9 where limb1s is lower and limb2s is relatively higher than the base (\u03b11 b 0, \u03b12 N 0), state 10 where limb1s and limb2s both have a relatively lower position compared to the base (\u03b11 b 0, \u03b12 b 0). The derivative queer-squaremechanism in state 5 is demonstrated in Fig. 11 and the angle ranges of state 5 are expressed as \u03b11N0;\u03b211N0;\u03b212N0 \u03b12N0;\u03b221b0;\u03b222b0 : \u00f034\u00de It is obvious to notice that limb1s and limb2s are higher than the base OA1A2 and the platform E1F1E2F2 is higher than limb1ap and limb2p in state 7. Fig. 12 offers an observation of the derivative queer-square mechanism in state 8. The geometrical ranges of the revolute angles of the derivative queer-square mechanism in state 8 are illustrated as \u03b11N0;\u03b211b0;\u03b212b0 \u03b12b0;\u03b221b0;\u03b222b0 : \u00f035\u00de In state 8, limb1s is located in the higher position and limb2s is located in the lower positionwith respect to the baseOA1A2, and the platform E1F1E2F2 is located relatively lower than limb1ap and higher than limb2p. The observation of the derivative queer-square mechanism in state 9 is presented in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000004_iros.2010.5650416-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000004_iros.2010.5650416-Figure5-1.png",
        "caption": "Fig. 5: By expressing foot GRF with respect to the local frame of the foot located at the ankle, we can factor out the moments \u03c4r , \u03c4l applied to the ankle by the foot GRFs fr and fl. rr and rl denote the ankle locations.",
        "texts": [
            " For example, [19] used 16 variables to model a GRF and CoP of one foot, which is 10 more than the dimension of the unknowns. Instead of increasing the search space to make the optimization problem easier, our method is to approximate the nonlinear optimization problem by sequentially solving two smaller-sized constrained linear least-squares problems, first one for determining the foot GRFs, and the next for determining the foot CoPs. To this end, let us first rewrite (1) and (2) for the double support. Following [2], we will express the GRF at each foot with respect to the ankle (Fig. 5). The benefit of this representation is that we can explicitly express the torques applied to the ankles. l\u0307 = mg + fr + f l (5) k\u0307 = k\u0307f + k\u0307m (6) k\u0307f = (rr \u2212 rG) \u00d7 fr + (rl \u2212 rG) \u00d7 f l (7) k\u0307m = \u03c4 r + \u03c4 l (8) where fr and f l are the right and left foot GRFs, rr, rl are the ankle locations, and \u03c4 r, \u03c4 l are the ankle torques. In (6), we divide k\u0307 into two parts, k\u0307f , due to the ankle force, and k\u0307m, due to ankle torques. The idea of our method is simple and intuitive. In order to minimize the ankle torques (k\u0307m \u2192 0), foot GRFs fr, f l should create k\u0307f as close to the desired rate of change of angular momentum (k\u0307f \u2192 k\u0307d) as possible while satisfying l\u0307d"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003900_tro.2020.3031236-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003900_tro.2020.3031236-Figure5-1.png",
        "caption": "Fig. 5. Grasper design along with NC and Gr frames. All measurements are in mm.",
        "texts": [
            " GrTNC can be calculated with the following: CTGr GrTNC = CTNC (8) Using needle tip, needle geometry, computer-aided design (CAD) model of the grasper, and measured grasper frame, CTNC is fully defined as follows: CTNC = [ CrxNC CryNC CrzNC CpNC 0 0 0 1 ] (9) where CrxNC, CryNC, and CrzNC refer to the x, y, and z vector components of the rotation matrix and CpNC is the position vector, defining the needle center frame in the camera frame. Each of these components is obtained using the following equations:[ CpNC 1 ] = CTGr [ GrpNC 1 ] GrpNC = \u23a1 \u23a2\u23a3 dx 0 \u2212dz \u23a4 \u23a5\u23a6 (10a) CrxNC = CpNT \u2212 CpNC \u2016CpNT \u2212 CpNC\u20162 (10b) CrzNC = CrzGr (10c) CryNC = CrzNC \u00d7 CrxNC. (10d) In (10a), dx, and dz are the position offsets (in the x and z directions, respectively) between the needle center frame and the grasper frame (see Fig. 5). These offsets are obtained using the grasper\u2019s CAD model. In (10b), CpNT is the measurement of the needle tip using the computer vision. Equation (10c) states that the z coordinates of the needle center frame and the grasper frame are identical. Once CTNC is fully obtained as explained above, GrTNC is then acquired using (8) with the same steps described to obtain CTB. 2) Controller: The robot controller is implemented with realtime state estimation using encoders and stereo vision feedback, the registered frames, and the robot differential kinematics",
            "2) measures the wrist joint angles only. This information is fused via a Kalman filter to estimate joint angles at 1 kHz (high frequency and high accuracy). Authorized licensed use limited to: Western Sydney University. Downloaded on June 15,2021 at 01:31:14 UTC from IEEE Xplore. Restrictions apply. 1) Needle Grasper: In order to improve needle grasp (e.g., no needle slip) and enable accurate needle pose estimation both inside and outside the tissue, a customized color-coded 3D-printed needle grasper was designed and used (see Fig. 5). The grasper is attached to the end-effector of a large needle driver (Intuitive Surgical, Inc., Sunnyvale, CA, USA) prior to the suturing operation and permits secure grasp and release of a CTX suturing needle (Ethicon, Inc., Somerville, NJ, USA). Imperfect manual installation of the grasper may introduce small errors in ETGr obtained from the CAD model. Since ETGr is included in both the needle path planner and the estimator and the vision feedback is used in the controller, it is expected that such small errors do not affect the overall performance of the controller",
            " It should be noted that the use of similar graspers for autonomous suturing has been explored by other studies, such as [18] and [32]. However, an important distinction of our design is the additional endstop that mechanically blocks the motion of the needle during the insertion phase. The needle grasper has dimensions of 9.9\u00d710.0\u00d77.0 mm3 for the extracting arm (without endstop) and 12.9\u00d710.0\u00d77.0 mm3 for the inserting arm (with endstop). Four distinctively colored (two green, two blue) 4-mm2 square markers are attached to the grasper at known locations, as shown in Fig. 5. These markers are detected via a vision algorithm and used to identify pose of the needle grasper. Once the needle is in contact with the endstop, it is reasonable to assume that no slip occurs. Hence, the kinematic relation between the needle center and grasper is fixed during suturing. This enables calculation of the needle center pose using the configuration of the needle grasper, even when the needle is obscured. 2) Enhanced Instrument With Additional Encoders: As the wrist joints of surgical instruments are the farthest operation points from the robot base, they have higher kinematic inaccuracy in a cable-driven surgical robot",
            " The other method involves indirect estimation of the needle pose via measurement of external features and known kinematic relationship [24], [26]. Our approach consists of a combination of the two methods in order to exploit the advantages of both. Estimation of five DOFs of the needle pose is obtained by indirect measurement using the customized grasper. The last DOF, which is dependent on where the grasper holds the needle, is obtained by direct measurement of the needle tip and is used to register the needle center to the grasper. The estimation of this last DOF (the xaxis of NC shown in Fig. 5) is only performed when the robot grasps/regrasps the needle. Since the needle tip measurement is essential for estimation of needle pose, the desired grasp point on the needle for the extracting arm is selected such that the grasper does not occlude the needle tip. Of note, this is possible due to the fact that the needle tip position from vision and the needle tip orientation from the grasper are known. This hybrid estimation method provides two main advantages over the approaches in the literature",
            " To do so, we first set d = 1 and solve the linear least square Mz\u0302 = 14\u00d71 that has the solution of z\u0302 = (M\u1d40M)\u22121M\u1d4014\u00d71. Once we get z\u0302, the solutions for z and d of the original problem are z\u0302/\u2016z\u0302\u20162 and 1/\u2016z\u0302\u20162, respectively. If the third element of z is positive (i.e., the normal vector is not pointing toward the camera), we negate both z and d. A ten-sample moving average filter was used to reduce the noise. The x-coordinate of the grasper frame (Gr) lies along the vector passing through the green markers. The origin of Gr is located on one of the green markers as shown in Fig. 5. The grasper plane and frame are depicted in Fig. 5. Needle Center Frame (NC). As depicted in Fig. 5, the needle plane is defined as the plane passing through the NC parallel to the grasper plane. The needle center position is obtained from the measured Gr and the grasper CAD model. The z-coordinate of NC is set to be parallel to that of Gr. The x-coordinate is the vector from the needle center position to the needle tip position. A Kalman filter is exploited to smooth the positions of the needle center and grasper origins as follows: \u03bdk+1 = \u23a1 \u23a2\u23a2\u23a2\u23a3 I3 \u0394t\u00d7 I3 03\u00d73 03\u00d73 03\u00d73 I3 03\u00d73 03\u00d73 03\u00d73 03\u00d73 I3 \u0394t\u00d7 I3 03\u00d73 03\u00d73 03\u00d73 I3 \u23a4 \u23a5\u23a5\u23a5\u23a6 \u03bdk +wk yk = [ I3 03\u00d73 03\u00d76 03\u00d76 I3 03\u00d73 ] \u03bdk + vk (15) where k is the time instance, \u03bd \u2208 R12 is a state vector consisting of positions and velocities of the needle center and grasper origins, and y \u2208 R6 is a measurement vector of the positions of the origins"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001890_tia.2014.2309717-Figure11-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001890_tia.2014.2309717-Figure11-1.png",
        "caption": "Fig. 11. Deformations caused by magnetic forces at no-load in prototype machine.",
        "texts": [
            " Since the peak-peak value is reduced by 24% in the case of magnetic wedge 1 compared to the case of open slots, it is natural to have smaller deformations in the stator bore and consequently have a lower vibration level when the magnetic wedges are inserted in the slots. Results of the structural analysis verify that the stator bore experiences smaller deformations in the case of the magnetic wedge 1 (\u03bcr = 5). In this case the magnitude of the deformations is reduced by 22% compared to the case of open slots. Fig. 11 shows the deformations in the prototype machine with open slots. The 4th spatial mode can be observed in the deformation pattern in the figure. According to Section III-B, the magnitude of the 4th spatial harmonic is lowest in the case of semi-closed slots meaning that the vibration level is also expected to be lowest. Rotor losses at no-load is also smallest when using semi-closed slots due to the reduced slot harmonic effect. However, according to Section III-C, the electromagnetic torque is reduced in this case Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000083_j.mechmachtheory.2009.01.010-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000083_j.mechmachtheory.2009.01.010-Figure1-1.png",
        "caption": "Fig. 1. (a) Method for generating a conical gear and (b) coordinate system S1 for the generated conical gear.",
        "texts": [
            " The parameters for end relief are therefore also included in the mathematical modeling of the tooth surface. The finite element method (FEM) is also applied to verify the calculated results. The tooth surface of a conical gear can be modeled analytically with the aid of a gear cutting simulation based on the theory of gearing [16,17]. The method for generating conical gears is similar to that for cylindrical gears, but the pitch plane of the rack-type cutter is inclined to the axis of the gear at a cone angle h; see Fig. 1a. Three coordinate systems are set up for determination of the surface of the conical gear. S1(x1,y1,z1) and SC(xC,yC,zC) are rigidly connected to gear 1 and the rack-cutter, respectively, while Sb(xb,yb,zb) is rigidly connected to the frame. The coordinate plane x1\u2013y1 of S1 is attached to the reference plane of a conical gear, with the positive direction of the axis z1 pointing toward the heel of the conical gear along the axis of the gear; see Fig. 1b. Similarly, the coordinate plane xC\u2013yC of SC is also coplanar with the reference plane of the conical gear, and the axis zC is parallel to the gear axis. The generating surface of the rack-cutter rC is a plane, and given in parametric form with the parameters l and u. Based on the theory of gearing, the generated surface of the conical gear P1 is determined from the family of the rack-cutter surface r1(l,u,/1) in the S1 coordinate system associated with the equation of meshing, namely r1\u00f0l; u;/1\u00de \u00bcM1CrC\u00f0l; u\u00de; \u00f01\u00de f \u00f0l;u;/1\u00de \u00bc 0: \u00f02\u00de The coordinate transformation matrix M1C is utilized to perform the kinematical relation between the rack-cutter and the generated gear with the parameter /1 of rotation of the gear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003900_tro.2020.3031236-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003900_tro.2020.3031236-Figure8-1.png",
        "caption": "Fig. 8. Illustration of needle pose estimation evaluation results. Each figure shows (a) SNE and (b) representative configuration as well as the needle pose estimation from the needle grasper.",
        "texts": [
            " A Contoured Tissue Tray (CTT-10) was used to immobilize each tissue phantom. 1) Needle Pose Evaluation (NPE): Since the needle pose estimation is obtained from the needle grasper measurements and affects the overall performance of the system, it is crucial to evaluate the accuracy of our estimation algorithm. Obtaining an accurate ground truth of the needle center pose is rather abstract and challenging as it is not physically accessible and/or visible [18]. Hence, a structure for needle estimation (SNE), which encloses the needle, was designed and 3-D printed (see Fig. 8). Three red markers are placed on the SNE to uniquely define the needle pose using computer vision. It is expected that the SNE provides higher accuracy pose estimation than the needle grasper. This is because in the SNE, the marker 2 is colocated with the needle center (see Fig. 8(a)) and smaller markers are used, which reduce the errors from pixel correspondence. Therefore, needle pose estimation from the SNE is used for ground truth. This NPE method can capture errors in estimating the relationship between the needle center and the grasper pose (GrTNC). A possible source for these errors could be misalignment of the needle inside the grasper. Note that using this method, however, we cannot assess the errors from the intrinsic/extrinsic calibration of the stereo camera system as we deploy the same vision system for obtaining the ground truth",
            " Such adjustment motions of the needle might introduce undesirable stress on the tissue when the extracting arm is grasping the needle. The adjustment motions, however, are small due to a good control accuracy of our framework shown in the results. 1) Structure for Needle Estimation (SNE): To quantify the accuracy of the 6-DoF needle pose estimation, the needle center pose is measured with the grasper (actual) and compared against the one from SNE (ground truth). The actual pose was expressed in the ground truth frame (see Fig. 8) and error positions and Euler angles are acquired. 2) Autonomous Suturing Evaluation (ASE): Accurate motion control of the needle inside the tissue is important for a successful suturing. We evaluate the efficacy of the proposed automated suturing from two perspectives: robot control in an unknown tissue environment; and medical suturing requirements. From the control perspective, the root-mean-square error (RMSE) of the needle trajectory during stitching and extraction is presented. From the clinical perspective, the suture parameters of the needle path planning are used to evaluate the system performance and suture quality. The needle was placed at ten random configurations within the required workspace to evaluate the pose estimation. Fig. 8(b) depicts one such configuration. At each configuration, 500 data samples were collected at 30 Hz. The mean and standard deviation of the estimation errors are reported in Table II. As can A total of 16 (2 tissue phantoms \u00d7 2 reference needle trajectories \u00d7 4 repetitions) trials were performed for ASE. Six snapshots of automated suturing for each permutation of tissue phantom and reference needle trajectory are illustrated in Fig. 9. A sample of 2-D and 3-D needle tip and center trajectories are shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000648_978-3-642-17531-2-Figure6.11-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000648_978-3-642-17531-2-Figure6.11-1.png",
        "caption": "Fig. 6.11. Voltage-drive plate transducer: a) electrode separation of : electrode travel 0 /3x , b) increased electrode separation of 3 : increased electrode travel 0 x , c) smaller electrode separation of with serial capacitance",
        "texts": [
            "10 shows the ELM coupling factor as a function of the stable rest displacement R x for 0 0F . For an increasing rest displacement, the ap- plied mechanical power clearly climbs as well. However, in this case, electrostatic softening also renders the transducer increasingly unstable. Thus, in order to prevent pull-in, large coupling factors are only possible with strict limits on the range of motion. Geometric motion restrictions Pull-in appreciably reduces the range of motion of a voltage-drive transducer. The transducer in Fig. 6.11a can be stably operated only up to 3 pi x . If an armature travel of max x were desired, the uncharged electrode separation would have to be physically increased to 3 (Fig. 6.11b). However, according to Eq. (6.26), the tripling of the air gap implies that this range of motion requires a 33 5 -fold increase in the control voltage relative to the original design in Fig. 6.11a. The increased gap results in a smaller total capacitance, which can be thought of as a serial connection of the original plate arrangement and the extended version in Fig. 6.11c. 412 6 Functional Realization: Electrostatic Transducers serial C : increased electrode travel 0 x Serial capacitance One practical option for increasing the stable range of motion while maintaining the same electrode geometry is the use of a serial capacitor as shown in Fig. 6.11c (Seeger and Crary 1997), (Chan and Dutton 2000). This allows the entire available electrode travel of the original transducer to be exploited. The total capacitance of the arrangement in Fig. 6.11c is ( ) T serial T serial serial C C C x C C x x C . (6.34) From Eq. (6.34), a fictitious increase in the electrode separation of the uncharged transducer to can be seen. Without affecting the system behavior, the pull-in limits can now be computed relative to . Thus, to achieve the electrostatic armature travel shown in Fig. 6.11a, a serial capacitance 0 1 1 2 2serial C C should be chosen. 6.4 Transducer with Variable Electrode Separation and Voltage Drive 413 Mechanism The mechanism through which the serial capacitance acts is providing a voltage divider on the drive voltage according to serial T S S T serial serial C x u u u C C x C . Thus, for an increasing source voltage S u , and resulting increasing displacement x and transducer capacitance T C , the polarization voltage T u at the transducer is automatically reduced (through electrical feedback)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002225_j.mechmachtheory.2014.02.016-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002225_j.mechmachtheory.2014.02.016-Figure3-1.png",
        "caption": "Fig. 3. Simply supported transmission shaft.",
        "texts": [
            " Similarly, on the driven gear, one has Fhx2 \u00bc \u2212Fhs \u00bc khet t\u00f0 \u00des\u00fe kh s2 sc 0 0 r1s \u2212s2 \u2212sc 0 0 r2s h i q \u00fe ch e\u0307t t\u00f0 \u00des\u00fe ch s2 sc 0 0 r1s \u2212s2 \u2212sc 0 0 r2s h i q\u0307 Fhz2 \u00bc \u2212Fhc \u00bc khet t\u00f0 \u00dec\u00fe kh sc c2 0 0 r1c \u2212sc \u2212c2 0 0 r2c h i q \u00fe ch e\u0307 t t\u00f0 \u00dec\u00fe ch sc c2 0 0 r1c \u2212sc \u2212c2 0 0 r2c h i q\u0307 Th2 \u00bc r2 Fh \u00bc \u2212 r2khet t\u00f0 \u00de \u00fe r2kh \u2212s \u2212c 0 0 \u2212r1 s c 0 0 \u2212r2\u00bd q \u2212 r2ch e\u0307t t\u00f0 \u00de \u00fe r2ch \u2212s \u2212c 0 0 \u2212r1 s c 0 0 \u2212r2\u00bd q\u0307: \u00f019\u00de where where respec shaft, fs \u00bc 2 66664 us, the stiffness and damping matrices khsh, and chsh and error excitation vector rh due to gear meshing are written as s Th follow sh \u00bc s2 sc c2 0 0 0 Sym: 0 0 0 0 r1s r1c 0 0 r21 \u2212s2 \u2212sc 0 0 \u2212r1s s2 \u2212sc \u2212c2 0 0 \u2212r1c sc \u2212c2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 r2s r2c 0 0 r1r2 \u2212r2s \u2212r2c 0 0 r22 2 6666666666666664 3 7777777777777775 \u00f020\u00de rTh \u00bc \u2212s \u2212c 0 0 \u2212r1 s c 0 0 \u2212r2\u00bd khe tsin \u03a9mt\u00f0 \u00de \u00fe \u2212s \u2212c 0 0 \u2212r1 s c 0 0 \u2212r2\u00bd che t\u03a9tcos \u03a9mt\u00f0 \u00de: \u00f021\u00de The transmission shaft is modeled as mass-less and a simply supported Timoshenko beam, as shown in Fig. 3. The gears are mounted at the mid-span, so that the shaft loads, including shear forces P1, and P2, bending moments P3, and P4 and torsional moment P5, are located at the L/2. The flexibility matrix of the transmission shaft is derived. According to the Castigliano theorem, the flexibility coefficients of the shaft corresponding to the shear forces, bending moments, torsional moment and the combinations of both are expressed as f ij \u00bc \u2202Uo \u2202Pi\u2202P j i; j \u00bc 1;2; \u22ef5\u00f0 \u00de \u00f022\u00de Uo is the strain energy of the shaft, and could be written as Uo \u00bc 1 2 P2 1L 4\u03baGAs \u00fe P2 1L 3 48EIs \u00fe P2 2L 4\u03baGAs \u00fe P2 2L 3 48EIs \u00fe P2 3L 12EIs \u00fe P2 4L 12EIs \u00fe P2 5L 2GJs "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002645_j.mechmachtheory.2015.02.006-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002645_j.mechmachtheory.2015.02.006-Figure6-1.png",
        "caption": "Fig. 6. Relations between path of contact and transmission error curve.",
        "texts": [
            " Four cases of tooth geometry modifications by roll motion (or additional translational displacement of the rack cutting) of pinion meshing with the standard involute gear tooth surface are applied for the spur and helical gear drive with 0-TE (the pinion is a standard involute tooth surface), 2-TE, 4-TE and H-TE in the numerical example respectively. Before discussing numerical example, we should illustrate some definitions of effective contact ratio \u03b5e and geometrical total contact ratio \u03b5t as follows: \u03b5e \u00bc \u03c6r=\u03c6p \u03b5t \u00bc \u03c6t=\u03c6p: \u00f026\u00de Here, as shown in Fig. 6,\u03c6r is the rotational angle of the driven gear duringwhich a tooth pair is actually in contactwith each other. \u03c6t is the rotational angle of the driven gear from p1 to pn.\u03c6p is the angular pitch. \u03b5t is geometrically determined by gear dimensions. \u03b5e is determined by themodified tooth surfaces and loads based on the path of contact. Therefore, we distinguish the actual contact ratio \u03b5e from the geometrical total contact ratio \u03b5t. 4.1. Optimal coefficient of H-TE function for spur gears and helical gears The optimal coefficients of H-TE for spur gears and helical gears are shown in Table 2"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003953_j.engfailanal.2020.104907-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003953_j.engfailanal.2020.104907-Figure3-1.png",
        "caption": "Fig. 3. Dynamic model of the gear pair.",
        "texts": [
            " Finally, the mesh stiffness, load distribution and contact patterns are calculated according to the deformation compatibility equation, which is expressed as: where Fn is the load distribution vector; \u03b5 is the clearance vector, which contains various kinds of profile error. The tooth modification and the separation distances between two engaged tooth flanks (Sa and Sr in Ref. [38]) are all categorized as profile error. T and rb1 mean the transmitted torque and the radius of the base circle of the pinion. The mesh stiffness can be solved through an iterative algorithm based on deformation compatibility [16]: =k T r ste min / ( ) b1 (9) The dynamic model of the gear pair is shown in Fig. 3. The angle between the plane of action and the y-axis is: = + t t counterclockwise t t clockwise ( ) ( ) : ( ( ) ( )) : t t 12 12 1 12 1 (10) The displacement relation between the center of mass and center of rotation is derived as follows: = + + = + + = + = + + x x y y x x y y \u00b7cos( sgn\u00b7 t) \u00b7sin( sgn\u00b7 t) \u00b7cos( sgn\u00b7 t) \u00b7sin( sgn\u00b7 t) t t t t 1 1 1 1s 1 1 1 1 1s 1 2 2 2 2s 2 2 2 2 2s 2 (11) where x1t, x2t, y1t and y2t are the horizontal and vertical displacement of the centers of mass of the pinion and gear"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000559_icar.2011.6088631-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000559_icar.2011.6088631-Figure2-1.png",
        "caption": "Fig. 2. UPAT Tilt-Rotor prototype",
        "texts": [
            "), can greatly aid in saving lives in emergency situations. Towards this goal, a special UAV design, enabling the vehicle to execute flight mode conversion manoeuvres, from rotorcraft hovering mode to fixed-wing longitudinal flight mode and conversely as shown in Figure 1, has been selected to be the candidate of our experimental procedure. The vehicle has the ability to modify the angle of its rotors relative to its airframe by rotating them perpendicular to the wing axis. This small-scale Tilt-Rotor (TR) prototype shown in Figure 2, assembled in our laboratory, has been designed with special attention given to its ability to perform full cyclic tilting of the rotors. In this article, the problem of attitude control of the aforementioned vehicle in Bi-Rotor Hovering flight mode is addressed through an experimental procedure. The goal 978-1-4577-1159-6/11/$26.00 \u00a92011 IEEE 465 is the ultimate implementation of a control system able to perform adequately in stabilizing the TR in an actual testing environment. In our experimental setup, an integrated sensor system, and a microcontroller were utilized in the control system implementation and data acquisition combined with a wireless communication system which was used to acquire the data at the ground station"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000004_iros.2010.5650416-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000004_iros.2010.5650416-Figure1-1.png",
        "caption": "Fig. 1: External Forces",
        "texts": [
            " However, rotational dynamics of a robot also plays a significant role in balance [10]. In fact, complete control of CoP, which is one of the most important indicators for balance, is impossible without also controlling the angular momentum. This will be evident from the following discussion. The rate of change of linear momentum l\u0307 and the angular momentum k\u0307 about the robot CoM (hence dubbed centroidal angular momentum in this paper) of a humanoid robot are related to the GRF f and CoP location p as follows (Fig. 1): l\u0307 = mg + f (1) k\u0307 = (p \u2212 rG) \u00d7 f + \u03c4n (2) S.-H. Lee is with the School of Information and Communications, Gwangju Institute of Science and Technology, South Korea shl@gist.ac.kr. This work was done while SHL was at Honda Research Institute. A. Goswami is with Honda Research Institute, Mountain View, CA, USA agoswami@honda-ri.com where m is the total mass, rG is CoM location, and \u03c4n is the normal ground reaction torque at the CoP. Together l and k is called the spatial centroidal momentum, or in this paper, simply spatial momentum h = (k, l) of the robot"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003881_j.mechmachtheory.2020.104047-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003881_j.mechmachtheory.2020.104047-Figure6-1.png",
        "caption": "Fig. 6. Forces applied on the rolling element.",
        "texts": [
            " \u03c9 c = N b \u2211 k =1 F ck d m 2 \u2212 f ck D 2 (17) where m c and I c are the mass and moment of inertia of cage respectively; d m is the pitch diameter; \u03c9 rk = . \u03b8k and \u03c6k = \u03b8k + 2 \u03c0(k \u2212 1) / Z b , \u03c9 rk is the orbital speed of the k th rolling element around the z -axis; Z b is the number of the ball. For a high-speed bearing, its dynamic response is affected by the gyroscopic moment and centrifugal force. In the multiple-degree-of-freedom (11 DOFs) model of rolling bearing, the force analysis of a rolling element is illustrated in Fig. 6 . The differential equations for controlling the rotational motion of the ball are given by \u23a7 \u23a8 \u23a9 I r . \u03c9 rk = F ck d m 2 I b . \u03c9 bk = f ck D 2 (18) where I b = m b D 2 10 is the rotational inertia of the ball, and I r = m b D 2 10 + m b ( d m 2 ) 2 is the inertia moment of the element about z -axis in the bearing coordinate system. m b is the mass of the rolling element. In order to fully consider the effect of the localized defect on the acceleration of the rolling element, the motion of the ball along y and z directions are defined by two differential equations instead of equilibrium equations"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002010_j.optlastec.2016.01.002-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002010_j.optlastec.2016.01.002-Figure4-1.png",
        "caption": "Fig. 4. Ideal forming process (a) and thermal history of deposition layers (b) during DLF.",
        "texts": [
            " The microstructures were determined by optical microscope (Nikon model MA100). The hardness of the specimens was measured by a Vickers microhardness tester (MVC-1000B). A non-standard tensile sample was adopted as showed in Fig. 3. Three samples for different sampling position were produced and subjected to the tensile testing, and the average tensile strength and elongation were taken. During the DLF process, the surface of the former layer would be remelted and resolidified with the latter layer. In the ideal forming process model as shown in Fig. 4a, because of the hemisphere surface of the former layer, the liquid metal of the remelting region (SABC) would be filled into the area (SADE and SCFG) to form a smooth face for the latter deposition layer. That is to say, there is a fundamental quotation, SABC\u00bc SADE\u00feSCFG. In the deposition process, heat is extracted very few through air and mainly through previous deposition layers which makes grains to grow following the direction of maximum heat flow and results in the different distribution of residual stress [17]. Heat conduction through previous deposition layers significantly affects the properties of DLF parts. The detail thermal history of deposition layers during DLF are shown in Fig. 4b. The latter deposition process makes the former layer generate three regions: remelting region, double quenched region and tempered region. Remelting region of the former layer forms integrity with the latter layer accompanied by rapid remelting and resolidified. During the deposition of latter layer, quenched region of the former layer would undergo a quenching process again because of the high conducted heat from latter deposition process. As for the bottom region of the former layer, it is far from the remelting region, and its reheating temperature is low, as well as the re-cooling rate",
            " The low solidification rate restrains the growth of columnar crystal and contributes to the formation of more equiaxial crystal, as shown in Fig. 7c. The effect of oblique angle on hardness of oblique thin-walled part in the high side and the testing position are shown in Fig. 8. It is found that the average hardness of the high side decreases with the increase of oblique angle. The inputted heat from the laser beam tempers the previous deposition layers through the heat conduction as the analysis about Fig. 4 and hence results in the decrease of the hardness. Bigger oblique angle equals to higher deposition and more tempering time. Thus there is a decrease of hardness with the increase of oblique angle because of more obvious tempering effect. During the oblique angle is kept constant, the hardness of the high side increases until the distance to the substrate is about 25 mm, and then decreases with the increase of the deposition height. Due to the high cooling rate produced by the substrate in the fewer initial deposition layers, the inputted heat is insufficient to warm the previous layers"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003091_j.mechmachtheory.2020.103989-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003091_j.mechmachtheory.2020.103989-Figure3-1.png",
        "caption": "Fig. 3. A discrete dynamic model of a spur gear pair.",
        "texts": [
            " The load distribution coefficient for the tooth pair 1 and tooth pair 2 can be written as \u03b31 = F 1 / ( F 1 + F 2 ) , \u03b32 = F 2 / ( F 1 + F 2 ) (21) In the single tooth contact zone, the \u03b31 = 1 . For a spur gear pair with the contact ratio 1 < \u025b < 2, the combined mesh stiffness of a gear pair is computed by k ls ( t ) = n t \u2211 j=1 k j e ( F j ) , ( n t = 1 , 2 ) (22) where n t is the number of meshing tooth pairs at the same time, either 1 or 2. The dynamic transmission system in this work consists of a pinion and a gear, installed on well assembled shafts, as illustrated in Fig. 3 . Each gear body i ( i = p, g ) is described by a rigid body that includes the base radius r ib and mass moment of inertia J i . The torsional degree-of-freedom (DOF) \u03b8 i is denoted about the nominal rotation of the gear. The gear mesh is described by the load-dependent mesh stiffness, damping, backlash elements in the LOA direction. The coupled tribo-dynamic model of a gear pair with two-DOFs is established, in which the combined mesh stiffness under the DMF and the nonlinear backlash with the effect of the upper limit of the center oil film thickness are considered"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003127_tasc.2016.2542192-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003127_tasc.2016.2542192-Figure8-1.png",
        "caption": "Fig. 8. Temperature contour after heat transfer optimization.",
        "texts": [
            " The diameter of the heat-absorption part is 8 mm, and the length is 100 mm. The outer diameter of the cooling section is 16 mm, and the length is 150 mm. When the temperature difference of the cold side and the hot side reaches to 50 \u25e6C, the heat-transfer power of one heat pipe is 10 W (The date is provided by the manufacturer). According to the principle of identical heat dissipation, the equivalent coefficient of convective heat transfer is about 19000 W/(m2 \u00b7 K). After optimization, the temperature of winding declined to 136 \u25e6C (as is shown in Fig. 8), which is about 180 \u25e6C lower than before. The temperature of the magnets is about 91 \u25e6C, while the magnets (38EH) can endure 180 \u25e6C high temperature. So the heat pipe has great influence on the heat dissipation, and the motor will work in safety temperature grade. If there is no weight limitation, we could use more heat pipes and electromagnetic material to further reduce the motor temperature rise. In order to prove the validity of calculations, a motor prototype has been made to test the output power, the efficiency and the winding temperature"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003226_j.cirpj.2020.01.002-Figure12-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003226_j.cirpj.2020.01.002-Figure12-1.png",
        "caption": "Fig. 12. Predicted and simulated total strain using (a) analytical modeling and (b) FEM for the laser power of 220 W, scan speed of 30 mm/s, and absorptivity of 80%.",
        "texts": [
            " For the fourth case study with the laser power of 660 W and 50 mm/s the predicted stress is around 450 MPa, and the simulated stress is 405.95 MPa, as depicted in Fig. 10(a and b). The obtained error between predicted and simulated stress is 9.7%. For the last case study with the laser power of 660 W and a scan speed of 30 mm/s, as shown in Fig. 11(a and b), the predicted stress is 500 MPa, and the simulated stress is 460.18. The obtained error for this case is 8.6%. Good agreement has been achieved between the proposed elastoplastic thermal stress analysis and the simulated thermomechanical model. Fig. 12(a and b) illustrate the obtained total strain from elastoplastic analytical model and FEM for the laser power of 220 W and a scan speed of 30 mm/s. The predicted total strain from the analytical model is 0.018 mm/mm and the obtained strain from FEM is 0.018 mm/mm. The accuracy of the proposed elastoplastic analytical model is verified through obtaining same performance as FEM. or the laser power of 440 W, scan speed of 30 mm/s, and absorptivity of 80%. Fig. 10. Predicted and simulated stress using (a) analytical modeling and (b) FEM for the laser power of 660 W, scan speed of 50 mm/s, and absorptivity of 80%"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003686_tie.2019.2959504-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003686_tie.2019.2959504-Figure6-1.png",
        "caption": "Fig. 6. Open-circuit flux distribution of 12-stator-pole/10-rotor-tooth DF-FSPM machine and definition of dq-axes of rotor armature machine part. (a) Open-circuit flux distribution, rotor position = 15 mech. deg. (b) Dq-axes of rotor armature machine part.",
        "texts": [
            " 5(a), positive maximum stator flux linkage is obtained when the angle between the midline of rotor tooth (red arrow) and stator coil axis (blue arrow) is 9 mech. deg. Hence, the d-axis of the stator-armature machine part is 9 mech. deg. shifted from the midline of rotor tooth, as shown in Fig. 5(b). The q-axis leads the d-axis by 90 elec. deg. (viz. 9 mech. deg.), which coincides with the midline of rotor tooth. The d- and q-axes of the rotor-armature machine part can be defined in a similar way. As shown in Fig. 6(a), positive maximum rotor flux linkages are obtained when the rotor coil axis (red arrow) aligns to the midline of stator slot (blue arrow). Therefore, the midline of stator slot is defined as the d-axis of the rotor-armature machine part, as shown in Fig. 6(b). The q-axis leads the d-axis by 90 elec. deg. (viz. 15 mech. deg.), which is the midline of PM. Zero d-axis control strategy is employed in this paper since both the stator- and rotor-armature machine parts exhibit negligible reluctance torque, as will be shown later. 0278-0046 (c) 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. IV. ELECTROMAGNETIC PERFORMANCE By way of examples, the electromagnetic performance of the proposed DF-FSPM and conventional FSPM machines with 12-stator-pole/10-rotor-tooth is compared in this section"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002000_s11663-014-0183-z-Figure10-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002000_s11663-014-0183-z-Figure10-1.png",
        "caption": "Fig. 10\u2014Representative contour of the CET criterion on the trailing edge of the melt pool.",
        "texts": [
            " Since the temperature gradient is much higher in the leading edge region of the melt pool and the leading edge will not have any role in solidification, only the trailing edge of the melt pool should be considered for solidification analysis. Thus, time tracking of solidification history is developed in Part I to address the solidification conditions based on thermal conditions exclusively at the melt pool trailing edge. A representative contour of the melt pool trailing edge with G3:4 001 V001 plotted over it is shown in Figure 10. As shown, at the trailing edge, the CET criterion displays a minimum value of 3.695 9 1016 near the top and a maximum value of 1.559x1023 at the bottom of the melt pool. The plots of the CET criterion value with time for three different samples are shown in Figure 11 with the standard error bar value set equal to standard error for the population. Previous literature suggests an optimal value of 2.7 9 1024 (SI units).[12,13,19] In contrast, the maximum value found in the present study is close to 5 9 1018, which is considerably lower"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003503_tmech.2020.3026994-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003503_tmech.2020.3026994-Figure3-1.png",
        "caption": "Fig. 3: Calculating the estimated real robot\u2019s TCP position vectors for the real circular path",
        "texts": [
            " We must therefore take into account the error measured by the ballbar sensor, ebn in polar coordinates, then measure the robot\u2019s TCP real coordinates in yz-plane yrn and zrn as follows: yrn = (r + ebn) sin \u03b8n (10) zrn = (r + ebn) cos \u03b8n + 172, (11) Accordingly and because we are only able to measure the rotation error by the ballbar in real-time, we can only estimate the real position and velocity vectors based on this measured error, by replacing the desired coordinates in yz-plane ydn and zdn in Eqs. (7), (8) and (9) by the real ones yrn and zrn . Therefore, the robot\u2019s TCP real position and velocity vectors can be estimated as follows: vprn = [ yrn+1 \u2212 yrn zrn+1 \u2212 zrn ] , (12) v\u0302prn = vprn /\u2016vprn \u2016, (13) vvrn = \u03c5rv\u0302prn . (14) The aforementioned real robot\u2019s TCP position and velocity vectors have been presented only to emphasize how the real vectors are affected by the error measured by the ballbar compared to the desired ones. Fig. 3 highlights and justifies the error in the robot\u2019s TCP coordinates, radius variation and position vectors. Many advanced and high performance control techniques exist in the literature as described in Section I-B. For industrial robots however, there is a theory-practice gap: control methods developed in academia are seldom used in this industry where the choice is usually to sacrifice the robot performance for the sake of design simplicity [37]. Many robot applications in the literature use advanced control algorithms (adaptive, non linear, etc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001880_j.applthermaleng.2014.02.008-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001880_j.applthermaleng.2014.02.008-Figure6-1.png",
        "caption": "Fig. 6. The current density distribution of th",
        "texts": [
            " From it, we can know that thedistribution ofmagneticfield for the case of nobroken bars is symmetrical, while the symmetry of magnetic field distribution is distorted in the case of broken bars and a higher degree of magnetic saturation can be observed around the broken bars. In the rotor bar, complex vector magnetic potential _Az should satisfy [21]. v2 _Az vx2 \u00fe v2 _Az vy2 \u00bc jum0s _Az m0 _Jsz (12) where, s is the conductivity of the bars, m0 is the permeability, _Az is magnetic vector potential, _Jsz \u00bc _Im=Sb, _Im is the current passing through bar, and Sb is the cross-sectional area of bar, and the current density distribution, including the healthy rotor and faulty rotor is showed in the following Fig. 6. From it we can know that the current of the rotor bar adjacent to broken bars is amplified, and the loss will increase. The average current density _Jze\u00f0av\u00de in every element is _Jze\u00f0av\u00de \u00bc _Jsz jus _Aze\u00f0av\u00de (13) where, _Aze\u00f0av\u00de is the average magnetic vector potential of the node in every element. Rotor losses are P \u00bc XNe i\u00bc1 Jze\u00f0av\u00de 2 Delef s (14) where, Ne is the total element number of rotor bars, and De is the element area. Iron losses are highly dependent on frequency and magnetic fluxes. The core losses in this paper are calculated based on the following formula [22]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001528_j.addma.2017.08.012-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001528_j.addma.2017.08.012-Figure2-1.png",
        "caption": "Fig. 2. General schematic of a pro",
        "texts": [
            " Experiment procedures Process calorimetry experiments may be used to measure the mount of total energy absorbed during the deposition process. description of process calorimetry has been discussed previusly by Martukanitz et al. [7]. For these experiments the process alorimeter utilized tubing representing the substrate material ith a known water flow rate to measure the amount of energy bsorbed by the change in water temperature between the inlet nd outlet. A general schematic of the process calorimeter is shown n Fig. 2. During processing with the calorimeter, specific process arameters that are of interest may be employed. Based on the total nergy leaving the laser processing head, which is also measured o account for losses in the optical delivery system, and the amount f energy that is absorbed by process calorimetry, defined by the bsorption coefficient, , may be determined using Eq. (2). Calorimetry experiments were conducted to determine the mount of energy that was absorbed by the substrate during laserased directed energy deposition for two material representing Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000454_0076-6879(78)57040-7-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000454_0076-6879(78)57040-7-Figure2-1.png",
        "caption": "FIG. 2. Chemiluminescence (CL) intensity from luminol vs pH using ferricyanide as cooxidant/catalyst [D. T. Bostick and D. M. Hercules, Anal. Chem. 47, 447 (1975); J. P. Auses, S. L. Cook, and J. T. Maloy, Anal. Chem. 47, 244 (1975)].",
        "texts": [
            " The analytical system must be designed so that ferricyanide and luminol come in contact either when the CL reaction is initiated or in some controlled manner just before the reaction is started. Peroxidase catalysis is promising over the pH range from 7 to 9, since it gives greater CL intensity than other catalysts/cooxidants under these conditions. Peroxidase-catalyzed luminol CL has been studied in detail, although not from an analytical point of view. 11 While peroxidase is suitable for low pH, it has very low activity above pH 9 where luminol CL is most efficient. pI-I The luminol reaction is most efficient at high pH. Figure 2 shows intensity vs pH, using ferricyanide catalysis. Maximum CL is observed in the pH range from 10.4 to 10.8. The decrease as one goes to lower pH values is quite rapid. Since background CL behaves similarly with pH, however, the signal-to-background ratio does not decrease nearly as rapidly as the absolute response. The pH range from 10.4 to 10.8 should give best precision, since in this range small variations in pH will not significantly affect CL intensity. Other catalysts/cooxidants show similar but not identical CL intensity vs pH behavior"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000642_tpel.2011.2168240-Figure14-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000642_tpel.2011.2168240-Figure14-1.png",
        "caption": "Fig. 14. Comparison of stator flux locus obtained in (a) DTC1, (b) DTC2, and (c) DTC3.",
        "texts": [
            " From this figure, it can be seen that the regulation of output torque in DTC2 is poor when the stator flux locus returns to the circular shape because of the excessive flux reference. For this reason, the step reduction of the flux amplitude as introduced in (8) is applied in DTC3 at the instant the stator flux returns to the circular locus when the reference speed is reached. By doing so, the DTC3 provides better output torque control and higher capability of torque as depicted in Fig. 13. The operation of stator flux locus for DTC1, DTC2, and DTC3 corresponding to the results obtained in Fig. 11 are depicted in Fig. 14. It is apparent that the step reduction of flux magnitude proposed in DTC3 fits into the hexagonal flux locus as the motor speed reaches its reference. On the other hand, the magnitude of circular flux locus in DTC2, which is identical to the magnitude of hexagonal flux locus, gives a flux reference which is too high and hence causes poor performance of torque control at very high speed operation as shown in Figs. 11(b) and 13(b). From Fig. 14, it also can be noticed that the magnitude of the stator flux in DTC1 and DTC3 are the same as the motor speed reaches its reference. Fig. 15 depicts the experimental results of motor torque, stator flux, motor speed, and stator current when the step change of reference speed is applied in DTC3, DSC, and DTC-CSF2. From Fig. 15, it can be observed that the capabilities of torque obtained in these schemes, during motor accelerations, are comparable to the flux locus that forms into the hexagonal shape"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002436_j.ymssp.2018.06.034-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002436_j.ymssp.2018.06.034-Figure6-1.png",
        "caption": "Fig. 6. Schematic view of test bearing housing and sensor used to measure cage whirling amplitude.",
        "texts": [
            " To measure the temperature of the test ball bearing, a T-type thermocouple is placed in point contact with the outer ring of the bearing, and the thermocouple is surrounded by a flexible pipe filled with a low-thermal-conductivity material to minimize the effects of cryogenic fluids. The radial rod arm equipped with a ball bearing not only adds loads but also measures the rotational force of the hous- ing through a load cell. In addition, various torques were applied to the housing through a digital torque wrench before the test, and the value of the load cell was measured to confirm the reliability of the torque value. Fig. 6 depicts the test bearing housing and the fiber-optic displacement sensors used to measure the cage whirling amplitude. The cryogenic fluid introduced through the axial rod arm machined into the hollow shaft passes through the shoulder clearance of the test ball bearing and fills the chamber. Further, the cryogenic fluid is discharged to the outside through the top cover of the chamber. The signals measured through the optical displacement sensor and the eddy current sensor are collected through a real-time FFT analyzer"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000329_j.jmps.2008.09.011-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000329_j.jmps.2008.09.011-Figure2-1.png",
        "caption": "Fig. 2. Residual stress of the film represented by stress elements in different orientations: (a) in the x\u2013y coordinates, (b) in the principal directions, and (c) in an arbitrarily rotated direction.",
        "texts": [
            " The interface between the layers is assumed to remain bonded. To be specific, we consider a cubic crystal film with the surface normal in the [0 0 1] crystal direction. For convenience, a Cartesian coordinate system is set up in the reference state such that the x\u2013y plane is parallel to the film surface and the inplane axes align with the [10 0] and [0 10] directions of the crystal (see Fig. 1a). In general, the residual stress in the film has three in-plane components, sR xx, sR yy, and sR xy, as illustrated in Fig. 2a. The stress state can also be represented by two principal stresses (s1 and s2) and the corresponding principal angle (yp), as illustrated in Fig. 2b. The tensor property of the stress gives the principal stresses and the principal angle in terms of the original stress components, namely s1;2 \u00bc sR xx \u00fe sR yy 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sR xx sR yy 2 !2 \u00fe \u00f0sR xy\u00de 2 vuut , (1) tan 2yp \u00bc 2sR xy sR xx sR yy . (2) As a necessary condition for the film to wrinkle, at least one of the two principal stresses must be negative (compressive)",
            " (17) leads to A\u00f0t\u00de \u00bc A0 exp sy t t , (19) where A0 is a constant for the initial amplitude, t \u00bc Z/C11 is a characteristic time scale, and sy \u00bc (ay mR)/C11 is the dimensionless growth rate of the perturbation amplitude. The result from the linear analysis is identical to that for an isotropic elastic film (Im and Huang, 2005) except for the dependence of the growth rate on the angle y through E\u0304y and sy. As defined in Eq. (16), the stress sy is simply the normal component of the residual stress acting on a section rotated with the angle y, as illustrated in Fig. 2c. When the residual stress in the reference state is equi-biaxial, i.e., sR xx \u00bc sR yy \u00bc s1 and sR xy \u00bc 0, we have sy \u00bc s1, independent of the angle y. Thus, an equi-biaxial stress is isotropic. Otherwise, the stress state is anisotropic. In terms of the principal stresses, we rewrite sy in the form sy \u00bc s1 1 1 s2 s1 sin2 \u00f0y yp\u00de . (20) Hence the ratio between the two principal stresses determines the angle dependence of sy and represents the stress anisotropy. The modulus E\u0304y defined in Eq. (15) is essentially the plane-strain modulus in the direction of the wrinkle wave vector"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003670_j.isatra.2019.08.026-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003670_j.isatra.2019.08.026-Figure1-1.png",
        "caption": "Fig. 1. The body frame and inertial frame for the spacecraft.",
        "texts": [
            " Firstly, based on the backstepping method and the feedback domination method, in the presence of parametric uncertainties, a fixed-time attitude stabilization controller is explicitly constructed step by step. At the second step, by taking the external disturbances into account, by combining with variable structure control theory, a novel fixed-time attitude stabilization controller is developed . 2. Mathematical model and problem description 2.1. Spacecraft attitude system Since the modeling of spacecraft involves the transformation of coordinate system, the inertial and the body reference frames are shown in Fig. 1. \u03c7n = {xn, yn, zn} represents the inertia frame. \u03c7b = {xb, yb, zb} denotes the body frame. The origin of the body fixed frame is the center of mass of the spacecraft whose axes are aligned with the head of spacecraft. Usually, there are kinematics and dynamics equations for the mathematical model of spacecraft attitude system. As that in [22, 37], the attitude (i.e., orientation) of spacecraft is given by using Modified Rodriguez Parameters (MRPs). The MRPs for the spacecraft is given as \u03c3 = \u03c2 tan(\u03d6/4) \u2208 R3, \u22122\u03c0 < \u03d6 < 2\u03c0, (1) where \u03d6 is the Euler angle and \u03c2 is the Euler axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000176_1.4001485-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000176_1.4001485-Figure2-1.png",
        "caption": "Fig. 2 Schematic layout of the cradle-style machine",
        "texts": [
            " It consists of three portions: art I is a straight line while parts II and III are portions of two ircles with radii f edge radius and R1 spherical radius . Rp is he point radius and p is the blade angle. The position vector of he points belonging to the generating tool surface is indicated as e , . The parameters and are the arc length on the blade rofile and the rotation angle about the tool axis, respectively. The proposed mathematical model of the machine kinematics eproduces the universal generation model UGM developed by he Gleason Works 11 , and it is based on the virtual cradle-style achine, Fig. 2. 41010-2 / Vol. 132, APRIL 2010 om: http://mechanicaldesign.asmedigitalcollection.asme.org/pdfaccess.ash Since UGM incorporates the universal motion concept UMC , the basic machine settings are defined in a dynamic manner as polynomial functions of the cradle rotation angle which acts as the motion parameter 12,13 . For instance, the basic blank offset EM0 is just the constant term of the vertical motion UMC polynomial EM = EM0 + k=1 n 1 k Vk k 1 where, usually, n=4. The same is true for all the 8 virtual axes of the generator"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000382_j.snb.2008.03.024-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000382_j.snb.2008.03.024-Figure1-1.png",
        "caption": "Fig. 1. (a) Schematic configuration of screen-printed electrodes. (b) Scanning electron micrograph of the surface of the screen-printed electrode.",
        "texts": [
            " Next, aliquots of the silica sol\u2013gel (25 L) and 5% PVA solution (100 L) were mixed thoroughly by ultrasonication. PVA serves as a polymer to prevent sol\u2013gel films from fracture. The solution mixture was freshly prepared prior to the fabrication of every biosensor. A TORCH T3244 manual screen-printing machine (Beijing Torch Co., Ltd., China) was used to fabricate the carbon screen-printed electrodes by depositing several layers of inks on a PVC substrate. The steps used in electrodes preparation are shown in Fig. 1a. The silver ink (BY2100, Shanghai Baoyin Electronic Materials Co., Ltd., China) acting as conductive medium was printed as the first layer and cured at 100 \u25e6C for 40 min, then the second layer was printed with the carbon ink (Jelcon CH-10, Jujo Chemical Co., Ltd., Japan) to obtain the working electrode, followed by heat treat at 100 \u25e6C for 40 min. The insulating ink (Jelcon AC-3G, Jujo Chemical Co., Ltd., Japan) was used finally to provide the insulation layer defining the working electrode surface area (diameter: 4 mm) and dried at 80 \u25e6C for 10 min",
            "460 V which is the same as the standard electrode potential for FAD/FADH2 at pH 7.0 (25 \u25e6C) [22], indicating that the direct electrochemistry behaviors of these GOx are allowed. The favorable results could be mainly attributed to two factors. Firstly, silica sol\u2013gel/PVA hybrid material, endowed with a great amount of OH groups, provides a biocompatible microenvironment for encapsulation of GOx. So the loss of biological activity of GOx can be avoided efficiently. Secondly, as the SEM image shows (Fig. 1b), the screen-printed carbon layer possesses a type of porous and fractured structure, allowing a larger amount of enzymes to be immobilized closely on the electrode surface, where direct electron communication between enzymes and electrodes is permitted. In addition, existence of silica sol\u2013gel is considered to improve the structural rigidity of the film, and make the film more stable and compact. Compared to GOx molecules in only PVA, those embedded in silica sol\u2013gel/PVA hybrid film occupy more favorable position for electron communication with the underlying electrode"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000648_978-3-642-17531-2-Figure8.5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000648_978-3-642-17531-2-Figure8.5-1.png",
        "caption": "Fig. 8.5. Magnetic circuit, representative configuration: a) physical configuration, b) magnetic network with lumped parameters",
        "texts": [
            "8) In a homogeneous magnetic field (with field line length l and crosssection A ), m R is then a constant, where ,12m m u Hl l R HA A . (8.9) It can be seen from Eq. (8.9) that the reluctance depends only on geometric parameters and the magnetic properties of the material in which the magnetic flow occurs. Magnetic circuit, magnetic network For spatially distributed configurations with a piecewise-homogeneous field, using the reluctance allows a magnetic network model or magnetic circuit to be set up analogously to an electrical network (Fig. 8.5). For each spatially homogeneous section, a reluctance can be defined as a lumped network element. The following two identical relations result from AMP\u00c8RE\u2019s law (8.1) for the configuration in Fig. 8.5a: 1 2 , , 2 1 P P Fe m Fe m P P H ds H ds u u NiF , (8.10) 0 Fe Fe Fe Fe Fe Fe Fe Fe l H l H R R A A F . (8.11) 502 8 Functional Realization: Electromagnetically-Acting Transducers Analogously to electrical networks, the formulation in Eq. (8.10) can be interpreted as KIRCHHOFF\u2019s mesh rule for a magnetic circuit (with magnetic potential differences m u , and the MMF F as a magnetic potential source, see also Fig. 8.6a). From the formulation in Eq. (8.11), the equivalence of magnetic flux to electric current in an electrical network can be seen. KIRCHHOFF\u2019s node rule for a magnetic circuit is depicted in Fig. 8.6b. Relative to the excitation terminals , S S F , the magnetic behavior of the entire system can be compactly described by the reluctance m R at the terminals. This property ultimately offers the basis for a concise formulation of the generic transducer equations. 8.2 Physical Foundations 503 Magnetic circuit with air gap For the example configuration in Fig. 8.5a, neglecting leakage flux (i.e. Fe S ), , , , ,S Fe m Fe m S m Fe m R R R RF , (8.12) and, considering customary material properties 0Fe , , , 0 0 Fe m m Fe m Fe Fe l R R R A A A . (8.13) In a magnetic circuit with an air gap, the reluctance is thus primarily determined by the air gap. The highly permeable iron core offers negligible resistance to the magnetic flux, and simply guides the magnetic field lines along desired spatial paths. If several air gaps are present, their reluctances should be added corresponding to the flow topology (in series or parallel)",
            " 506 8 Functional Realization: Electromagnetically-Acting Transducers Thus, given a known reluctance m R for the total configuration, it follows that the inductance is 2 m N L R . (8.20) If the assumptions listed above are valid, the inductance of any configuration can thus be determined as a function of the reluctance in a relatively simple manner. Inductance for magnetic circuits with air gaps: reluctance transducers For a magnetic circuit with an air gap (corresponding to the configuration in Fig. 8.5a), the inductance at the electric terminals is 2 0 A L N . (8.21) Eq. (8.21) illustrates the typical dependence of inductance on structural geometric parameters in electromagnetic (EM) transducers. By varying the geometry of the air gap (varying or A using a movable armature), the reluctance of the magnetic circuit\u2014and thus the inductance of the system\u2014can be varied, resulting in a dependence ( , )L A and variable electromagnetic properties. This also gives rise to the alternate term for electromagnetic (EM) transducers: reluctance transducers"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003841_1.j059216-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003841_1.j059216-Figure5-1.png",
        "caption": "Fig. 5 Stanchion in the experiment (a) and in the FE model (b); detail of a bolted connection (c).",
        "texts": [],
        "surrounding_texts": [
            "Concerning the seats, having a total mass of 34 kg [43,44], Quad4 and Tria3 shell element types have been used to model the seats\u2019 support system (entirely made of 70xx aluminum alloys), whereas Tetra4 3D element type has been used to model the polyurethane foam cushions [39], for a total of 53,932 nodes and 64,752 elements (Fig. 6a). Rigid connections have been used to link seats and rails. As aforementioned, a 50% Hybrid II and a 50% FAA Hybrid III male ATDs were used in the experiment. Features that distinguish a standard Hybrid III from a Hybrid II include a slouched spine sitting posture, a curved lumbar spine, and themass [54]. The slouched spine adapter in the standard Hybrid III resulted in a lower measured lumbar load than the Hybrid II. Generally, FAA Hybrid III results are more accurate and with lower variability in the measurements when compared with Hybrid II [55]. In particular, the FAA Hybrid III dummy used during the test was instrumented with a triaxle lumbar load cell model 1892 made by Robert A. Denton Inc. and with an Entran piezo-resistive accelerometer of 500 g installed in the head. TheHybrid II exemplar employed in the test was not instrumented and used just to balance the fuselage section during the suspension phase and to load properly the seat during crash. Nevertheless, all the Hybrid II body parts and joints worked, allowing performing the comparison between recorded data and numerical dummy ones. The Hybrid III numerical dummy model has been found to be the most suitable for the current work purposes as it includes all human body parts that are useful, in the postprocess phase, for calculating the indices to assess the injury criteria provided by the reference standards. The LSTC/NCAC Hybrid III 50th percentile male dummy model [56,57], illustrated in Fig. 6b, has been used. This FE model consists of 276,008 nodes, 452,598 elements, solids, and shells. Both the experimental dummies have been modeled using the Hybrid III numerical dummy, and they have been correctly positioned following the AC25.562-1B (FAA (2006)) [46]. Moreover, it is imperative that, during an emergency landing, all passengers wear safety belts to ensure that they are not violently projected toward fuselage parts or other passengers, with fatal consequences. Aircraft safety belts\u2019 performance criteria are similar to those specified by the Federal Motor Vehicle Safety Standards for automobiles but also include a limit on pelvic force to prevent spinal injuries thatmay be caused by thevertical component of impact force. Therefore, the ATDs have been restrained on the seats by a torso belt oriented almost horizontally, thus avoiding any kind of dangerous movement. The modeled safety belt, Fig. 6c, consists of 305 nodes and 480 2D shell elements. The belts\u2019 material and properties are those supplied with the manikin model, which are valid for safety belts normally used in the automotive industry."
        ]
    },
    {
        "image_filename": "designv10_5_0003796_j.mechmachtheory.2020.103799-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003796_j.mechmachtheory.2020.103799-Figure1-1.png",
        "caption": "Fig. 1. The waviness model of an ACB.",
        "texts": [
            " They proposed some methods to control the fluctuation of friction moments. Deng et al. [29] used the law of conservation of energy to discuss the effects of waviness on the friction moment fluctuation of an ACB. Although the above works studied the friction moment of bearings with the waviness, the friction moment calculation methods are the time-invariant ones. However, the waviness and the contact forces among the contact parts with and without the waviness are time-varying ones as shown in Fig. 1 . This work can calculate the whole time-varying friction moment during the bearing operational processing, which is not the fixed friction moment calculation method as given in most listed studies. Although Ref. [29] considered the time-varying friction moment, they only formulated the axial load and ignored the centrifugal forces of balls. However, the radial load and centrifugal forces of balls can greatly affect the friction moments as given in Ref. [30] . Thus, this work will be focused on this issue",
            " Moreover, the friction moments will fluctuate strongly during the bearing actual operational processing as given in this work, which cannot described by the fixed friction moment calculation method. Thus, this work can provide a more reasonable friction moment calculation method for understanding the power loss and wear of the ACBs. In the actual rotating process of an ACB, the contact forces among the contact parts are time-varying ones, whose directions and amplitudes are different for each angular contact position as shown in Fig. 1 . Especially, when the sinusoidal waviness is considered, the contact forces caused by the waviness are also time-varying ones, which should be very different with those in a healthy ACB as given by Ref. [32] . Thus, the friction moments in the ACB are time-varying ones during the rotating process of the ACB since the friction moments are determined by the contact forces. The time-invariant friction moment calculation method is not correspondent with the listed practice cases. However, the previous works in the listed references only proposed the time-invariant friction moment calculation methods",
            " In practice, the profiles of waviness and roundness errors are similar. However, the frequency response range of roundness error is from 2 upr (undulation per revolution) to 15 upr, and that of waviness error is from 15 upr to 250 upr [30] . Since the frequency response of the waviness error is different with that of the roundness error, the effect of the waviness error on the friction moments of ACB will be different with that of the roundness error. The waviness on the inner raceway, outer raceway, and balls are formulated in this work as shown in Fig. 1 . The waviness on the outer raceway is determined by [33] p o j = q \u2211 l=1 A o l cos [ \u2212l ( \u03c9 o \u2212 \u03c9 m ) t + 2 \u03c0( j \u2212 1) Z + \u03b1o l ] (1) where l is the waviness number, q is the total waviness number, j is the number of ball, A o l is the waviness amplitude, \u03c9 o is the angular velocity of outer raceway, \u03b1o l is the initial phase angle, and \u03c9 m is the angular velocity of cage, which is defined as [31] \u03c9 m = \u03c9 s 2 \u00b7 ( 1 \u2212 D w cos \u03b1 d m ) (2) where \u03c9 s is the angular velocity of shaft, which is derived by [31] \u03c9 s = 2 \u03c0n 60 (3) The pitch diameter d m is calculated by [31] d m = (d + D ) (4) 2 where D and d represent the diameters of the outer and inner raceways, respectively",
            " (16) is calculated by [31] \u2211 \u03c1o / i = 1 D w ( 4 \u2212 1 f o / i \u2213 2 \u03b3 1 + \u03b3 ) (18) The above symbol is used for the inner raceway, and the below symbol is used for the outer raceway. The main curvature function of outer raceway is calculated by [31] F (\u03c1) o / i = 1 f o / i \u2213 2 \u03b3 1 \u00b1\u03b3 4 \u2212 1 f o / i \u2213 2 \u03b3 1 \u00b1\u03b3 (19) The above symbol is used for the inner raceway, and the below symbol is used for the outer raceway. where f o = r o / D w , in which r o is the curvature radius of outer raceway; f i = r i / D w , in which r i is the curvature radius of inner raceway. When the waviness is considered, as is demonstrated in Fig. 1 , the contact force Q will produce an increment value Q , the contact deformation \u03b4 can also generate a variation \u03b4. When \u03b4 is a small one, according to Taylor series expansion, Eq. (15) is given as [29] Q + Q = K p \u03b4 3 2 + 3 K p \u03b4 1 2 2 \u03b4 + 3 K p \u03b4\u2212 1 2 8 ( \u03b4) 2 (20) Since the value of higher order is small, they can be ignored. Thus, Eq. (20) is given by [29] Q + Q = K p \u03b4 3 2 + 3 K p \u03b4 1 2 2 \u03b4 (21) The variation of contact deformation caused by the outer raceway waviness is given by [29] \u03b4o j (t) = \u2212 p o j cos \u03b1 (22) The relative pitch diameter is calculated by d \u2032 om = D + d 2 + \u03b4o j (23) The variation of contact force is given by Q oj = 3 K \u2032 po \u03b4o 1 2 2 \u03b4oj (24) where \u03b4o is the contact deformation between the ball and outer raceway, which is obtained as \u03b4o = n \u03b4o ( 9 32 \u03b72 Q o 2 \u2211 \u03c1 \u2032 o )1 / 3 (25) On the basis of the static calculation method in Refs",
            "005 \u00b0; the inner groove curvature radius is 2.06 mm; the outer groove curvature radius is 2.10 mm; the bearing clearance is 10 \u03bcm; the lubrication oil density is 0.93 g/cm 3 ; the viscosity is 14 cst. The timedomain friction moment of healthy ACB is shown in Fig. 3 . In Fig. 3 , the friction moment is not a constant value, which is a time-varying one with a periodic fluctuation. The reason is that the contact forces among the contact parts are periodic ones during the rotating process as analyzed in Fig. 1 . However, as shown in Fig. 3 , the previous time-invariant method [30] cannot formulate the time-varying fluctuation. In addition, the friction moment is fluctuating nearby a constant value; and the constant value is same as that calculated by the previous time-invariant method. It corresponds with the fact and proves the correctness of the proposed method. Fig. 4 illustrates the effect of the outer raceway waviness amplitude on the time-domain friction moment. In Fig. 4 , the radial force and shaft velocity are 20 0 0 N and 20 0 0 r/min, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003887_j.etran.2020.100080-Figure13-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003887_j.etran.2020.100080-Figure13-1.png",
        "caption": "Fig. 13. Examples of dual-",
        "texts": [
            " There are many other works proposing ferrite PM machines for various applications with different motor configuration, such as flux switching, claw-pole, Vernier-type and axial flux machines, to name but a few. Below we attempt to describe the key ones that attract more interests among researchers. Due to the low residual flux density of ferrite PMs, researchers intend to expand the active space to placemore PMs to enhance the ype machine with 3D trench airgap [85]. airgap flux density. A novel rotor structure consisting of upper and lower cores with an axially-magnetized ferrite pole was developed in Ref. [93,94] to reduce the use of rare-earth material, as demonstrated in Fig. 13(a). However, a key issue with this structure was that at the same circular position, the electrical phases of magnetic field from the upper and lower part were different. Thus two sets of armaturewindings would be needed to adapt the rotor structure. A. Gazdac in Refs. [95] presented a PM induction machine (PMIM) combining squirrel-cage IM and PM rotors, as depicted in Fig. 13(b). However, the IM rotor would have a slip from synchronous speed, and the two rotors rotated at different speeds. Hence, two set of bearings and connections were required for the two rotors. R. Qu et al. in Ref. [96] proposed a dual-PM-rotor toroidally-wound PM (RFTPM) machine to improve torque density and efficiency, as shown in Fig. 13(c). Inner rotor fully utilised the inner space and toroidal armature reduced end-winding lengths. Yet, ferrite SPM structure cannot generate enough airgap flux distribution, and the torque density (4.32 Nm/L claimed) was still too low for traction applications. By using dual-rotor configurations, the flux density could be improved to some extent, but the mechanical structure tends to be more complicated, which would increase the manufacturing cost. Flux switching PM (FSPM) machines with both ferrite magnet and field windings in the stator were presented in Ref"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001742_0954406214531943-Figure16-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001742_0954406214531943-Figure16-1.png",
        "caption": "Figure 16. The contact force of rolling ball under different loads for the guideway with low preload. (a) P\u00bc 0; (b) P\u00bc 1000 N; (c) P\u00bc 1500 N; (d) P\u00bc 2000 N; (e) P\u00bc 2500 N; (f) P\u00bc 3000 N.",
        "texts": [],
        "surrounding_texts": [
            "The statics modeling with FEM may not have to be based on the assumptions made in analytical modeling. So, using the modeling method can directly achieve the accurate statics model. In this section, the same linear guideway is taken as study object, and the statics characteristics are calculated and analyzed with the FEM. To improve the efficiency of analysis, a component finite element modeling method is proposed, which can attain the same calculation accuracy as the full finite element model. Finite element modeling of the single ball bearing To obtain the statics characteristics of whole guideway by FEM, the single ball bearing should be analyzed first. Here, two mass blocks are chosen to simulate the contact between rolling ball and rail or carriage, and the created finite element model of single ball bearing is shown in Figure 9. In the model, the rolling ball and two mass blocks are modeled with Solid45 element, and the contacts between rolling ball and grooves are modeled with Conta174 contact element and Targe170 target element, respectively. As a whole, the model consists of 29,972 elements and 29,163 nodes. To exclude the impact of mesh density on the results, the contact areas are refined, where the amounts of contact elements and target elements are 1944 and 480, respectively. The uniform load PA \u00bc F=A is applied on the surface of upper mass block, where A is the area of active surface. The total deformation h of single ball bearing can be solved by contact analysis module of ANSYS, which contain the deformation between the ball and lower block h1 and the deformation between the ball and upper block h2. It is assumed that the contact areas of rolling ball with the upper and lower block are same, and so the produced deformation is h1\u00bc h2. From the contact deformation, the contact stiffness between rolling ball and grooves can be determined as kn1 \u00bc kn2 \u00bc F h1 \u00f024\u00de where kn1 represents the contact stiffness between rolling ball and groove of rail and kn2 represents the contact stiffness between rolling ball and groove of carriage. Using the FEM, the analysis results of single ball bearing are also shown in Figure 6. It can be seen that the contact deformation and stiffness obtained with FEM are slightly different than the analytical results, but the tendencies of variation are consistent. at UNIV OF CONNECTICUT on June 15, 2015pic.sagepub.comDownloaded from Modeling of the full finite element model of guideway To create the full finite element model of the linear guideway, each ball bearing in the grooves should be molded using contact elements introduced in the above section, and the created model is shown in Figure 10. There are 1,380,934 elements and 1,380,934 nodes in the model, during which there are 93,312 contact elements and 13,392 target elements. The load interval is chosen from 0 to 20 kN, the relative deformation H and vertical stiffness KF are calculated using the full finite element model, and the results are shown in Figure 11. The expression of vertical stiffness of guideway is KF P H \u00f025\u00de It can be seen from Figure 11 that the calculation results are consistent with the statics experiment. However, due to the huge number of contact elements in the model, the calculations need to consume a lot of time. In this study, it takes 59 h to complete the calculation by using DELL workstation. This computational efficiency is unacceptable. Therefore, a new finite element modeling method should be developed, which can both achieve high-calculation accuracy and complete the calculation efficiently. Modeling of the component finite element model of guideway To improve the calculation efficiency, the component finite element model is proposed in this section. The idea of creating the component finite element model is shown in Figure 12. The guideway is considered as consisting of several components, and each component contains rail slice, carriage slice, and some rolling balls. Because only the statics characteristics of vertical direction of guideway are studied in this work, the component finite element model can simulate the statics characteristics of whole guideway. When the load P is applied on the upper surface of carriage, the force of applying on the component finite element model is P/n. Under the load of P/n, the relative deformation H0 can be obtained by using the component finite element model. Then the vertical stiffness K0F of guideway is computed according to K0F P H0 \u00f026\u00de Compared with the full finite element model, the number of element and node of component finite element model is very small. In the model of Figure 12(b), there are 120,474 elements and 117,697 nodes, and during which, there are 7776 contact elements and 1152 target elements. Using the component finite element model and the same DELL workstation, the statics of guideway is recalculated, and the calculation results are also listed in Figure 11. As shown in Figure 11, the results obtained by the component finite element at UNIV OF CONNECTICUT on June 15, 2015pic.sagepub.comDownloaded from model are also consistent with the experiment. So, the correctness of the proposed method is proved. The calculation using the component finite element model has very high efficiency. The calculation only consumes 2 h. Therefore, it is very meaningful for engineering calculation. Effects of load and preload on the static characteristics of guideway In order to exhibit effects of load and preload on the statics characteristics, the linear guideways SHS-35R with low and high preloads were taken as examples, and the relative deformation and vertical stiffness were calculated and analyzed by using the analytical model and component finite element model proposed in this paper. Calculation of the static characteristics of guideway in low and high preloads From Table 1, corresponding to different preload status, the preload of single ball bearing can be obtained, and the value is determined as 51.92N for the low preload and 363.42N for the high preload. Then, using equation (17), the critical loads PC for the two preloads status can be obtained, and the values are 2.5 and 17.5 kN, respectively. First, when the load verifies from 0 to 20 kN, the statics characteristics of guideway are calculated using the corrected analytical model, and the results are shown in Figures 13 and 14, respectively. Next, the component finite element model is used to calculate the same question. For the low and high preloads, the initial deformations of the ball bearing are 1.4841 and 5.6176 mm, and the initial contact stiffness is 34.97 and 64.69N/mm, respectively. The calculation results are also shown in Figures 13 and 14. It can be seen that the results obtained by corrected analytical model and component finite element model are almost consistent. In addition, for the two preload statuses, the contact forces of rolling ball in upper and lower grooves are also calculated under difference loads. Figure 15 shows the results obtained by analytical model, and Figures 16 and 17 show the results obtained by FEM. at UNIV OF CONNECTICUT on June 15, 2015pic.sagepub.comDownloaded from at UNIV OF CONNECTICUT on June 15, 2015pic.sagepub.comDownloaded from Load and preload effects of guideway It can be seen in Figures 13 and 14 that, no matter the guideway is in low or high preload, the relative deformation increases with the increment of load. But the curvatures of increment are different because of the difference of the critical load PC for the low and high-preloaded guideway. In the considered load range, the relation curves between vertical stiffness and load are significantly different. For the low-preloaded guideway shown in Figure 13(b), the vertical stiffness reduces to a minimum value with the increment of load first and then increases with the increment of load. But for the high-preloaded guideway shown in Figure 14(b), the vertical stiffness always decreases with the increment of load. The reason of this phenomenon is also the difference of the critical load PC for the two preload statuses. When the change of loads is small, the vertical stiffness can be approximated as a constant. For example, when the load P verifies from 0 to critical load PC, the vertical stiffness is obtained from Figures 13 and 14 and is listed in Table 3. It can be seen from Table 3 that, during the considered load range, the vertical stiffness changes slightly, so the vertical stiffness of guideway can be treated as a constant in some approximate calculations. The preloads also have a significant impact on the statics characteristics of guideway. Comparing the relative deformation-load relation curves, which are shown in Figures 11, 13 and 14, it can be found that the relative deformation decreases with the increment of preload. This phenomenon shows that the increased preload can significantly increase the vertical stiffness of guideway. To further explain the load and preload effects of guideway, the change of contact force of rolling ball is also discussed. It can be seen in Figure 15 that when P<PC, the contact force PU in upper groove increases with the increment of load, and the contact force PL in lower groove decreases with the increment of load instead. When P\u00bcPC, the contact force PL in lower groove is zero. When P>PC, the rolling ball in lower groove loses the supporting capability, and the contact force PU in upper groove increases rapidly with the increment of load. The results obtained by FEM, which are shown in Figures 16 and 17, also show the same rule. Comparing the contact forces of rolling balls of low and high-preloaded guideway, it can be found that the greater preload will make the rolling balls bear larger contact forces, which will lead to the increment of the friction force and traction force of guideway. Therefore, the suitable preload should be chosen according to the work conditions of guideway."
        ]
    },
    {
        "image_filename": "designv10_5_0001580_j.phpro.2012.10.061-Figure13-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001580_j.phpro.2012.10.061-Figure13-1.png",
        "caption": "Fig. 13. LDMD parts: (a) A tibial prosthesis (on the right) achieved from CAD file (on the left); (b) an airduct (made on MultiCLAD machine at IRCCYN lab-ECN Nantes)",
        "texts": [
            " Indeed, the progressive clogging of the nozzle during the process leads to an irregular flow rate. This can be noticed by various rate measurements of the powder feed at the nozzle output. The powder flow remains stable during a certain period of time. Though, when the powder packet is removed we can observed defects in the manufactured part. These parts showing various shapes have been built without process control/monitoring, using different strategies of construction with the optimized operating parameters. Fig. 13 illustrates some applications of the LDMD process. The influence of the powder characteristics having an impact on the piece properties can be observed at different levels. Within the framework of this study, three batches of stainless steel A.316L powder have been acquired, analyzed and tested. From a chemical point of view, the batch T does not meet the requirements of the requested powder, due to excessive carbon and oxygen ratios. However, this powder has not been rejected as it remained interesting to see the influence of these defects on the process"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003753_s12206-019-0140-5-FigureA.2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003753_s12206-019-0140-5-FigureA.2-1.png",
        "caption": "Fig. A.2. Position of ball center, inner and outer race curvature center before and after loading.",
        "texts": [
            "9) The ball orbital speed and spinning speed can be calculated by ( )( ) ( )( ) 1 1 cos cos tan sin 1 1 cos cos tan sin e i i m i e e g a a b a w w g a a b a - \u00e6 \u00f6+ + = +\u00e7 \u00f7\u00e7 \u00f7- +\u00e8 \u00f8 (A.10) 1 cos tan sin cos tan sin cos 1 cos 1 cos e e i i R e i w a b a a b aw g b g a g a - \u00e6 \u00f6- + + = +\u00e7 \u00f7\u00e7 \u00f7+ -\u00e8 \u00f8 (A.11) where .a m D d =g (A.12) The ball contact forces are calculated by the Hertzian theory 3/2 i i iQ K d= (A.13) 3/2 e e eQ K d= (A.14) where Ki and Ke are the contact constants depending on the material and geometry at the contact [1]. The contact deformation can be calculated from the geometric relationships shown in Fig. A.2 as follows: 0i i il ld = - (A.15) 0e e el ld = - (A.16) 1 0 0 0 0 sintan cos i z z i i x x l v u l v u aa a - - + = - + (A.17) 1 0 0 0 0 sintan cos e z e e x l v l v aa a - + = + (A.18) 0 0sin sin i z z i i l v ul a a - + = (A.19) 0 0sin sin e z e e l vl a a + = (A.20) where the subscripts e and i denote the outer and inner race, respectively, and the subscript 0 indicates the initial value. The contact load of the inner race is given by { } cos / sin sin / cos . 0.5 / i i g i i i g i g Q M D Q Q M D M D \u00ec \u00fc- + \u00ef \u00ef = - -\u00ed \u00fd \u00ef \u00ef \u00ee \u00fe a a a a (A"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000176_1.4001485-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000176_1.4001485-Figure3-1.png",
        "caption": "Fig. 3 System setup and misalignments definition",
        "texts": [
            " In practice, these are egistered when the gear and the pinion are rolled together at very ight load. Mathematically, this condition is modeled by solving he following system of equations several variants exist s f1 u1,v1; 1 = s f2 u2,v2; 2 n f1 u1,v1; 1 = n f2 u2,v2; 2 5 here s f1 and s f2 are the B-spline pinion and gear position vecors, respectively, both expressed with respect to a fixed reference oint Of. It is worth remarking here that the expressions for vecors s f1 and s f2 include the unified misalignments E , P ,G , elsehere denoted as assembly errors, compare Ref. 6 , see Fig. 3 . For a given set of misalignments E\u0304 , P\u0304 , G\u0304 , \u0304 , system 5 con- ists of five scalar equations in six unknowns u1 ,v1 , 1 ,u2 , 2 , 2 . If the pinion rotation angle 1 is taken as an input paramter, the solution u1 1 ,v1 1 ,u2 1 ,v2 1 , 2 1 6 rovides information about the point of contact on the mating urfaces and the gear angular position 2. Solution 6 is obtained umerically for a certain number of pinion angular positions hroughout one mesh cycle. The transmission error function is then calculated as 2 1 = 2 1 \u2212 N1 N2 1 7 here N1 and N2 are the numbers of teeth of the pinion and the ear, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003890_j.ymssp.2020.107280-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003890_j.ymssp.2020.107280-Figure8-1.png",
        "caption": "Fig. 8. The interior view of experimental gear system: (1) the pinion, (2) gear case, (3) angular contact ball bearing of the pinion, (4) angular contact ball bearing of the gear, (5) the gear, (6) shaft of the gear.",
        "texts": [
            " The brief working procedure is that the servo driver controls the serve motor, providing driving force for the experimental gear system and outputting the required operating speed. Then the control unit of the magnetic powder brake controls the magnetic powder brake, providing load torque for the experimental gear system. The signal acquisition and processing system completes the data acquisition and processing of the experimental signals. The interior view of the experimental gear system is given in Fig. 8. The system consists of the pinion shaft, the gear, the gear shaft, the angular contact ball bearing and the case. This system adopts a single-stage involute spur gear transmission system, and the support bearing adopts angular contact ball bearings (7206 series and 7207 series). Due to the difference of the transmission path for vibration signal, the selection of the sensor location will lead to different features of the vibration signal. Therefore, a good test position is very important for the data acquisition and processing"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001758_jrproc.1956.275102-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001758_jrproc.1956.275102-Figure1-1.png",
        "caption": "Fig. 1-Principle of transfluxor.",
        "texts": [
            " In the present paper, after a short review of the principle of the new device, its operation is illustrated in detail by the characteristics of a typical two-apertured transfluxor and some of its applications. Several examples of logical functions attainable with multi-apertured transfluxors are also included. Consider a core made of magnetic material such as a molded ceramic \"ferrite\" which has a nearly rectangular hysteresis loop and consequently a remanent induction Br substantially equal to the saturated induction B,. Let there be two circular apertures of unequal diameter which form three distinct legs, 1, 2, and 3 in the magnetic circuit, as illustrated in Fig. 1. The areas of the cross sections of the legs 2 and 3 are equal and the cross section of leg 1 is equal to, or greater than, the sum of those of legs 2 and 3. The operation of the device previously explained' is reviewed here for convenience. Assume that at first an intense current pulse is sent through winding WI on leg 1 in a direction to produce a clockwise flux flow which 1956 321 PROCEEDINGS OF THE IRE saturates legs 2 and 3. This is possible since the larger leg 1 provides the necessary return path. These legs will remain saturated after the termination of the pulse since remanent and saturated inductions are almost equal. Consider now the effect of an energizing alternating current in winding W3 linking leg 3, producing an alternating magnetomotive force along a path surroundinig the smaller aperture, but of insufficient amplitude to produce significant flux change around both apertures, as shown by the shaded area in Fig. 1. When this rnagnetomotive force has a clockwise sense, it tends to produce an increase in flux in leg 3 and a decrease in leg 2. But no increase of flux is possible in leg 3 because it is saturated. Consequently, there can be no flux flow at all, since magnetic flux flow is necessarily in closed paths. Similarly, during the opposite phase of the ac, the magnetomotive force is in a counter-clockwise sense and tends to produce an increase in flux in leg 2, which is again impossible since that leg is saturated",
            " The transfluxor is in its \"blocked\" state and no voltage is induced in an output winding Wo linking leg 3. Consider now the effect of a current pulse through winding WI in a direction producing a counter-clockwise m.agnetomotive force. Let this pulse be intense enough to produce a magnetizing force in the closer leg 2 larger than the coercive force Hc, but not large enough to allow the magnetizing force in the more distant leg 3 to exceed the critical value. This pulse, called hereafter the \"setting pulse,\" will cause the saturation of leg 2 to reverse and become directed upwards (Fig. 1), but will In this condition, the alternating magnetomotive force around the small aperture resulting from the alternating current in winding W3 will produce a corresponding flux flow around the small aperture. The first counter- clockwise phase of the ac will reverse the flux, the next clockwise phase will reverse it again, and so on indefinitely. This flow may be thought of as a back-and-forth \"transfer\" of flux between legs 2 and 3. The alternating flux flow will induce a voltage in the output winding Wo",
            " The relations which exist between the primary and secondary circuits of a pulse transformer apply equally well to the output circuit of the transfluxor provided account is taken of the definite \"set\" cross-sectional area of the equivalent core and the properties of the material of the core. These include the shape of the hysteresis loops and the intrinsic possible rates of flux reversal. The salient properties of the output circuit can be illustrated by the cases of very high and very low-impedance loading. 0 1- -J 0 1->to Z) 0 I- 01 I- 1-0 AMF LL__ L7 a5 TIME- MICROSECONDS ttx) PM ~44+ TIME- MICROSECIND(b) 4 SET 2(MMF -1.5:Z Fig. 1 1-Voltage output wave forms for open circuit. (a) Large drive. (b) Small drive. Output voltage wave forms are shown in the oscilloscope trace photographs of Figs. 1lia and 1llb for the case of an open-circuited output winding; i.e., a very high impedance load. The traces are for the various values of setting, as indicated. For the relatively large (5 AT) and fast rising (3.3 AT/pusec) drive of Fig. lla and for the relatively small (1 AT) and slow rising (.7 AT/pisec) drive of Fig. hib, the voltage peaks vary linearly with the current settings"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002491_s11581-015-1486-z-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002491_s11581-015-1486-z-Figure5-1.png",
        "caption": "Fig. 5 CVs of 5.0 \u00d7 10\u22124 mol L\u22121 L-dopa on the PG/ZnO/CNTs/ CPE at different scan rates (20 to 250 mVs\u22121) in PBS (pH 7.0)",
        "texts": [
            " Furthermore, simultaneous presence of the modifiers has more enhancing effect on L-dopa oxidation anodic peak current. The differential pulse voltammograms recorded for L-dopa and AA (containing 2.0 \u00d7 10\u22124 mol L\u22121 L-dopa and 1.0 \u00d7 10\u22123 mol L\u22121 AA) at the CNTs/CPE, ZnO/ CNT/CPE, and PG/ZnO/CNTs/CPE are shown in Fig. 4. As shown in Fig. 4, the amounts of the anodic peak currents of both investigated compounds at the ZnO/CNTs/CPE and PG/ZnO/CNTs/CPE and oxidation potential separation are higher than that of at the CNTs/CPE. In Fig. 5, the effect of scan rate on the anodic peak current of L-dopa was studied at the PG/ZnO/CNTs-modified CPE by cyclic voltammetry in the range 20\u2013250 mVs\u22121. The results showed that the peak current of L-dopa vary linearly with scan rate (inset and equations in Fig. 5), which confirm the adsorption-control process for electro-oxidation of L-dopa on the surface of investigated electrode in the studied range of potential sweep rates. As the protons took part in the electrode reaction process of Ldopa, pH of the working buffer is very important for L-dopa detection. Therefore, the current responses and oxidation potentials of L-dopa at PG/ZnO/CNTs/CPE were investigated in the pH range from 3.0 to 7.0 of PBS by DPV. As shown in Fig. 6a, by increasing pH, the oxidation potentials of L-dopa became more negative"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003136_j.foodchem.2016.07.124-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003136_j.foodchem.2016.07.124-Figure1-1.png",
        "caption": "Fig. 1. Schematic illustration of the fabrication for MISPE-PDMS/glass chip: (a) PDMS/glass chip was fabricated; (b) part of SPE channel in PDMS layer was cut off; (c) MISPE monolithic capillary columns were coupled with PDMS/glass chip to form the final chip.",
        "texts": [
            "3 cm) was cut off for use with the MISPE monolithic capillary columns after two holes of appropriate pore sizes were punched for input/output ports. Finally, the PDMS substrate and a glass cover plate (63 mm 63 mm) with a thickness of 3.0 mm were placed in the oxygen plasma machine for surface modification for approximately 2 min, and were sealed together using external pressure. By bonding two layers using stress, the PDMS/ glass chip was fabricated in an oven at 80 C for 12 h. Consequently, the PDMS/glass chip with 4 integrated MISPE monolithic capillary array columns was prepared, as shown in Fig. 1. Chili powders (1.0 g) supplemented with RB standard solutions were dissolved by ultrasonic extraction with 4.0 mL of water and then centrifuged for 10 min (4000 rpm). After repeating these steps, the supernatant was collected and diluted to 8.0 mL with water. The spiked sample solutions at 0.01, 0.1, 1.0 lg mL 1 were passed through chip-based MISPE monolithic array columns at a flow rate of 0.02 mL min 1 after activation with 80 lL of methanol and water. After washing with 80 lL of toluene, the effluent was obtained by eluting the array chip with 80 lL of methanol-acetic acid (90:10, v/v) at a flow rate of 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000236_j.mechmachtheory.2010.06.004-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000236_j.mechmachtheory.2010.06.004-Figure9-1.png",
        "caption": "Fig. 9. Close-up of the stress concentration zone for the ISO gear.",
        "texts": [
            " 8 a plot with iso-lines and gray scale of the largest principal stress is shown. The plot only shows the stress at points where the numerical largest principal stress is positive, i.e., where there is predominating tension. If the numerical largest principal stress is negative, i.e., there is predominating compression, the color is white. In Fig. 8 the external loading on the tooth is also shown together with the reaction forces at the clamped boundaries. The load is scaled such that themaximum bending stress is unity, which is illustrated, by the scale in Fig. 8. Fig. 9 shows a closeup of the stress concentration zone of the ISO tooth. Fig. 9b shows the iso-lines of the largest positive principal stress as in Fig. 8 but now without the gray scale. Fig. 9a shows the size of the largest principal stress along the part of the boundary where the stress concentration is present. The stress size is indicated by the gray area, the perpendicular thickness of the gray area corresponds to the stress level. A tensile stress is plotted under the boundary for illustrative purposes. From the stress plot in Fig. 9a it can be seen that there is a potential for improving the stress. However, the ISO tooth does have a rather nice stress distribution along the boundary, so the room for improvement through only shape optimization is limited. This was done in Ref. [1] where the best design for a gear with 17 teeth gave a stress reduction of 12.2% compared to the ISO tooth.With the asymmetric design we can also improve the stress by increasing the tooth root thickness. Fig. 10 is similar to Fig. 8. The design is optimized through a parameter study"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003076_tmag.2019.2955884-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003076_tmag.2019.2955884-Figure4-1.png",
        "caption": "Fig. 4. 2-D flux lines and flux density vectors distributions at 8 A for (a) unaligned position and (b) aligned position.",
        "texts": [
            " (4) Assuming that 3Rpm 2Rg + Rry2 + 4Rsp + 2Rsy , \u03d5g and \u03d5sp can be obtained as follows, respectively: \u03d5g \u2248 1 Rsy + 2Rsp + 2Rg + Rr y1 ||Rr y2 \u00b7 2Fc + (Rsy + 2Rsp) Rpm [Rsy + 2Rsp + 2Rg + Rr y1 ||Rr y2 ] \u00b7 Fpm \u03d5 g (5) \u03d5sp \u2248 1 Rsy + 2Rsp + 2Rg + Rr y1 ||Rr y2 .2Fc \u2212 2Rg + Rr y1 ||Rr y2 Rpm(Rsy + 2Rsp + 2Rg + Rr y1 ||Rr y2) \u00b7 Fpm \u03d5 sp . (6) In the absence of the PMs, the air gap and stator pole fluxes, \u03d5\u0302g and \u03d5\u0302sp, can be found as \u03d5\u0302g = \u03d5\u0302sp = 1 Rsy + 2Rsp + 2Rg + Rr y1 ||Rr y2 \u00b7 2Fc. (7) Comparing (5) and (6) with (7) justifies that the air-gap flux of the PM-SRM is intensified by \u03d5 g and the stator pole flux is weakened by \u03d5 sp compared to the PMless SRM. Hence, the proposed PM-SRM produces higher torque without experiencing any saturations. Fig. 4 depicts the flux lines and flux density vectors of the PM-SRM at the unaligned and aligned positions of the rotor. The obtained flux lines confirm the operating principle of the PM-SRM. Also, it is inferred that the armature field lines travel through a short path, which results in low iron losses. Fig. 5 demonstrates the flux density distributions of the proposed PM-SRM at both unaligned and aligned positions at the current of 8 A. At the unaligned position, the flux density of the stator poles is about 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003303_j.addma.2019.02.006-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003303_j.addma.2019.02.006-Figure3-1.png",
        "caption": "Fig. 3. Geometry of the simulated thin walls.",
        "texts": [
            " Instead, the energy of laser irradiation is introduced into the model by activating each layer at an elevated initial temperature as Eq. (5). = +T T \u03b7P \u03c1C h t va p s \u03b8 (5) where Ta is the ambient temperature, \u03b7 is the laser absorption efficiency, P is the laser power, \u03c1 is the material density, Cp is the specific heat capacity, hs is the hatch spacing, t\u03b8 is the layer thickness, and v is the scan speed. A more detailed overview of the numeric approach is detailed in [38]. The 5 modeled geometries are a series of thin walls (as shown in Fig. 3), 127mm in length and 63.4mm in height, with thicknesses of 0.5 mm, 2mm, 6mm, 12mm, and 24mm. The length and height of the walls are typical AM part dimensions and the range of wall thicknesses used in this study spans the expected dimensions of most features in LPBF processes. As mentioned earlier, the building process for the thin walls is simulated using two models: a powder model where the part along with actual powder elements are modeled and a convection estimation model where only the part is modeled without considering powder elements"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003300_j.cja.2018.12.015-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003300_j.cja.2018.12.015-Figure1-1.png",
        "caption": "Fig. 1 Body-fixed coordinate frame.",
        "texts": [
            " The control objective of this paper is to design an adaptive fault-tolerant attitude tracking controller for the spacecraft subject to time-varying inertia matrix, external disturbances and actuator faults so that all closed-loop signals are uniformly bounded and that the attitude tracking errors converge to a small set around the origin. To this end, the following assumption is made13,15,18: Assumption 1. The external disturbance d is bounded by k d k 6 dm, where dm > 0 is an unknown constant. Generally speaking, our system consists of a rigid spacecraft body with CM initially located at point O (the initial CM, remains fixed to the spacecraft body) and a fuel tank that is offset from point O by a distance of rf in the x-direction. As shown in Fig. 1, the body-fixed frame B remains fixed at the CM and rotates with the spacecraft. The origin Ob is located at the CM, the x-axis, xb, is directed from Ob to the fuel tank, the z-axis, zb, is the initial spin axis, and the y-axis, yb, completes the body-fixed coordinate system. In this paper, both the fuel tank and the mass-invariant part are modeled as mass points, using the solving equation for CM of a mass point system rr \u00bc P imir= P imi, where rr is the position vector of the system\u2019s CM relative to a fixedpoint; mi and ri are the mass and position vector relative to the same fixed-point of the ith mass point"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001597_jmr.2014.130-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001597_jmr.2014.130-Figure1-1.png",
        "caption": "FIG. 1. (a) Schematic of SLM process and (b) photograph of processed parts.",
        "texts": [
            " The Inconel 718 and TiC components in a weight ratio of 9:1 were homogeneously mixed in a Fritsch Pulverisette 6 planetary ball mill (Fritsch GmbH, Germany) using a ball-to-powder weight ratio of 5:1, a rotation speed of the main disc of 200 rpm, and a milling time of 4 h. The TiC/Inconel 718 parts were processed using a SLM experimental setup that mainly consisted of a continuous wave IPG Photonics Ytterbium YLR-200-SM (IPG Laser GmbH, Germany) fiber laser with a maximum output power of 200 W, an automatic powder delivery apparatus, an inert argon gas protection system, and a computer system for process control. The schematic of SLM process is plotted in Fig. 1(a). When specimens were to be prepared, all the SLM experiments were conducted in an argon environment with an outlet pressure of 30 mbar and the resultant oxygen concentration decreased below 10 ppm. Based on a series of preliminary experiments, the three main parameters involved in the shaping process including the constant laser scan speed (v) at 400 mm/min, the laser beam diameter (d) of 70 lm, and the laser power (P) varied from 80 to 130 W. An integrated parameter \u201claser energy density\u201d (g), which was defined by: g \u00bc 4P vpd2 ; \u00f01\u00de was used to estimate the laser energy input to the powder layer being processed",
            ", Vol. 29, No. 17, Sep 14, 2014 1961 http://journals.cambridge.org Downloaded: 05 Mar 2015 IP address: 134.153.184.170 study the influence of different laser parameters on processability and attendant microstructural and mechanical properties of SLM-processed composite parts. The bulk-form specimens with dimensions of 8 mm 8 mm 6 mm were successfully shaped in a layer-by-layer way. The asprepared nanocomposite parts exhibited good surface finish and sample integrity without dimensional distortion [Fig. 1(b)]. Phase identifications of SLM-processed TiC/Inconel 718 composite parts were performed by a D8 Advance x-ray diffractometer with Cu Ka radiation at 40 kV and 40 mA, using a continuous scan mode. The fabricated samples were mounted, polished, and etched in line with the standard procedures for metallographic observation. Microstructures were characterized using a scanning electron microscopy (SEM; Hitachi model S-4800, Japan) at an accelerating voltage of 3 kV, fitted with an energy dispersive x-ray spectroscopy (EDX, EDAX Inc"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003602_j.aei.2020.101135-Figure10-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003602_j.aei.2020.101135-Figure10-1.png",
        "caption": "Fig. 10. (a) Original design; (b) modified design considering the manufacturing constraint.",
        "texts": [
            " In the context of design for additive manufacturing, the service provided by the tool not only supports operations engineers to select proper process settings but also helps designers in product design. In the product design stage, the process planning tool provides a service, i.e., overhang manufacturability checks to communicate with designers about design constraints and freedom. Therefore, product designers could remove or modify the part designs that contain overhang features that are not manufacturable. As shown in Fig. 10, the original part design contains regions with overhang angles more than 40\u00b0. Based on the feedback from the manufacturability check, the designer can redesign the part by reducing the overhang angle. Once the part design has been finalized, the CAD model is passed to operations engineers in the workflow for fabrication. The operations engineers use two services, i.e., toolpath generation and adaptive process parameter estimation to obtain an adaptive process plan for fabricating the part. As shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000041_j.ijmachtools.2010.04.002-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000041_j.ijmachtools.2010.04.002-Figure1-1.png",
        "caption": "Fig. 1. The prototype of a vertic",
        "texts": [
            " This study was aimed at investigating the influence of linear guides on the dynamic characteristics of a vertical column\u2013spindle system. To this, a finite element model of the column\u2013spindle system was proposed with the integration of the modeling of linear rolling components. The dynamic characteristics of the system such as the natural vibration modes and dynamic stiffness were predicted and validated with the experimental measurements performed on a prototype. A vertical column\u2013spindle system was designed and constructed for vibration analysis, as shown in Fig. 1. The sliding carriage of the spindle head was mounted on the column with a pair of linear guides and was driven with a ball screw. The commercial linear guides (Hiwin EG series) have four ball grooves with a circular arc profile [19], and they are quantified as low preload (Z0, 0.02C) and high preload (ZB, 0.11C), where C denotes the dynamic load rating (11.38 kN). The driven ball screw has a diameter of 14 mm, and a basic dynamic load rating C of 4.07 kN. To lessen the axial backlash, the ball nut was slightly preloaded to a level of 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001658_j.jsv.2017.08.014-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001658_j.jsv.2017.08.014-Figure1-1.png",
        "caption": "Fig. 1. Geometric relation of radius of tooth profile and tooth error caused by temperature: (a) Geometric relation of radius at one point of tooth profile; (b) Tooth error caused by temperature.",
        "texts": [
            " The radius of the base circle will be changed by the thermal deformation when the standard involute gear system comes from normal state to steady-working state because of the change of the contact temperature. The theoretical parametric polar equations of the new base circle are as follows.8>< >: rct \u00bc rbt cos amt \u00bc rb \u00fe ub cos amt qmt \u00bc invamt \u00bc tan amt amt (19) Herein, the subscript t represents theoretical. qmt is theoretical polar angle and rct is theoretical polar radius. The thermal deformation occurs in two directions. One is in the tooth thickness and the other in the tooth height. The thermal deformation in the tooth height is Drc and the one in the tooth thickness is Dl as shown in Fig. 1. The actual parametric polar equations of the base circle considered the thermal deformation of the tooth profile are as follows. rca \u00bc rct \u00fe Drc qma \u00bc qmt Dqm (20) Herein, Drc and Dqm can be obtained as follows according to Fig. 1(b). Drc \u00bc D\u00f0t\u00delrb\u00f01 cos ak\u00de cos ak (21) Dl D\u00f0t\u00delrb cos ak l Dqm \u00bc 2rca \u00bc 2rca rb 2\u00f0invak inva\u00de (22) Herein, D\u00f0t\u00de is the flash temperature of the tooth surface and it is the value of the difference between the tooth contact temperature, DB\u00f0t\u00de, and the bulk temperature, DM , in steady-working state. l is the tooth thickness of the gear (m). ak is the addendum pressure angle of the gear ( ). ak \u00bc arc cos\u00f0rb=ra\u00de (23) The tooth profile deformation will occur when the tooth temperature changes. And it is the normal distance between the actual thermal deformation tooth profile and the theoretical involute profile [35]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002124_j.triboint.2015.12.046-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002124_j.triboint.2015.12.046-Figure5-1.png",
        "caption": "Fig. 5. Head modification.",
        "texts": [
            "3 \u2013 \u2013 \u2013 Density 7760 kg/m3 7190 kg/m3 15,800 kg/m3 1860 kg/m3 Heat conductivity 44 W/(m K) 90 W/(m K) 58 W/(m K) 0.566 W/(m K) Specific heat capacity 431 J/(kg K) 447 J/(kg K) 283 J/(kg K) 700 J/(kg K) A helical gear pair with positive addendum modification and defined tooth trace corrections was used as an example for the calculation. The essential geometric and operating parameters of the gear are summarized in Table 1. In the direction of height of the tooth flanks, a correction was undertaken in accordance with the head modification illustrated in Fig. 5. In the direction of width of the tooth flanks crowning was specified (cf. Fig. 6). The values for the applied corrections are also specified in Table 1. The given values for the torque and the speed provide the curves illustrated in Fig. 7 for the load and the tangential and (cf. Fig. 1). The curve when the load affecting the tooth flanks during the meshing of the gear was determined beforehand with the load distribution program RIKOR in consideration of the influence of elastic deformations of the gears [38]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001115_j.wear.2015.01.047-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001115_j.wear.2015.01.047-Figure4-1.png",
        "caption": "Fig. 4. Stick/slip distribution in the contact ellipse. (a) Stress distribution over the main ellipse axis, and (b) top view of the contact ellipse.",
        "texts": [
            " Sliding\u2013rolling contacts are also studied for railways application where the speed difference between the wheel and the rail generates traction. For complete slip of the contact area, the tangential stresses at the bodies' surfaces are easy to calculate. But, for small creep ratios, the two bodies may not be entirely slipping. Theories have been developed to take into account the materials elastic compliance. Carter [16] treated the 2D problem of the tractive rolling of elastic cylinders: the total shear stress is calculated by addition of the shear stresses for complete slip and complete stick at the leading edge of the contact (Fig. 4). For sufficiently small creep ratios, the contact area is divided into slip and stick areas. For higher speed differences, the contact is in complete slip. The different configurations of stick and slip are presented on a typical traction curve (Fig. 5), which represents the evolution of the tractive tangential force versus the creep ratio \u03c4. Later, the theory was extended to 3D contacts by Johnson [8], Haines et al., and Kalker [17] who developed algorithms based on these theories for wheel\u2013rail contact application"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000492_tie.2011.2168795-Figure37-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000492_tie.2011.2168795-Figure37-1.png",
        "caption": "Fig. 37. Amplitude of the constant field rotating synchronously with the rotor.",
        "texts": [],
        "surrounding_texts": [
            "The higher field harmonics in the rotor are superimposed on the constant field rotating synchronously with the rotor (assuming synchronous speed of rotation), as shown in Figs. 30\u201338. Fig. 38 shows the sample time waveforms of the radial and tangential flux density components for point 7 defined in Fig. 34. ACKNOWLEDGMENT The authors would like to thank J. Szulakowski from the Technical University of Lodz for his work on core loss measurements and A. Michaelides from Vector Fields Software Cobham Technical Services for the valuable help. REFERENCES [1] M. A. Saidel, M. C. E. S. Ramos, and S. S. Alves, \u201cAssessment and optimization of induction electric motors aiming energy efficiency in industrial applications,\u201d in Proc. ICEM, 2010, pp. 1\u20136. [2] E. Dlala, A. Belahcen, J. Pippuri, and A. Arkkio, \u201cInterdependence of hysteresis and eddy-current losses in laminated magnetic cores of electrical machines,\u201d IEEE Trans. Magn., vol. 46, no. 2, pp. 306\u2013309, Feb. 2010. [3] Z. Gmyrek, A. Boglietti, and A. Cavagnino, \u201cEstimation of iron losses in induction motors: Calculation method, results, and analysis,\u201d IEEE Trans. Ind. Electron., vol. 57, no. 1, pp. 161\u2013171, Jan. 2010. [4] T. D. Kefalas and A. G. Kladas, \u201cHarmonic impact on distribution transformer no-load loss,\u201d IEEE Trans. Ind. Electron., vol. 57, no. 1, pp. 193\u2013 200, Jan. 2010. [5] E. Dlala, \u201cComparison of models for estimating magnetic core losses in electrical machines using the finite-element method,\u201d IEEE Trans. Magn., vol. 45, no. 2, pp. 716\u2013725, Feb. 2009. [6] K. Yamazaki and H. Ishigami, \u201cRotor-shape optimization of interiorpermanent-magnet motors to reduce harmonic iron losses,\u201d IEEE Trans. Ind. Electron., vol. 57, no. 1, pp. 61\u201369, Jan. 2010. [7] M. Amar and R. Kaczmarek, \u201cA general formula for prediction of iron losses under nonsinusoidal voltage waveform,\u201d IEEE Trans. Magn., vol. 31, no. 5, pp. 2504\u20132509, Sep. 1995. [8] A. Belahcen and A. Arkkio, \u201cComprehensive dynamic loss model of electrical steel applied to FE simulation of electrical machines,\u201d IEEE Trans. Magn., vol. 44, no. 6, pp. 886\u2013889, Jun. 2008. [9] H. Nam, K.-H. Ha, J.-J. Lee, J.-P. Hong, and G.-H. Kang, \u201cA study on iron loss analysis method considering the harmonics of the flux density waveform using iron loss curves tested on Epstein samples,\u201d IEEE Trans. Magn., vol. 39, no. 3, pp. 1472\u20131475, May 2003. [10] S. O. Kwon, J. J. Lee, B. H. Lee, J. H. Kim, K. H. Ha, and J. P. Hong, \u201cLoss distribution of three-phase induction motor and BLDC motor according to core materials and operating,\u201d IEEE Trans. Magn., vol. 45, no. 10, pp. 4740\u20134743, Oct. 2009. [11] W. A. Roshen, \u201cA practical, accurate and very general core loss model for nonsinusoidal waveforms,\u201d IEEE Trans. Power Electron., vol. 22, no. 1, pp. 30\u201340, Jan. 2007. [12] J. Lavers and P. Biringer, \u201cPrediction of core losses for high flux densities and distorted flux waveforms,\u201d IEEE Trans. Magn., vol. MAG-12, no. 6, pp. 1053\u20131055, Nov. 1976. [13] G. Bertotti, \u201cGeneral properties of power losses in soft ferromagnetic materials,\u201d IEEE Trans. Magn., vol. 24, no. 1, pp. 621\u2013630, Jan. 1988. [14] D. Ionel, M. Popescu, C. Cossar, M. I. McGilp, A. Boglietti, and A. Cavagnino, \u201cA general model of the laminated steel losses in electric motors with PWM voltage supply,\u201d in Conf. Rec. IEEE IAS Annu. Meeting, 2008, pp. 1\u20137. [15] A. Tessarolo and F. Luise, \u201cA finite element approach to harmonic core loss prediction in VSI-fed induction motor drives,\u201d in Proc. Int. SPEEDAM, 2008, pp. 1309\u20131314. [16] Y. Han and Y.-F. Liu, \u201cA practical transformer core loss measurement scheme for high-frequency power converter,\u201d IEEE Trans. Ind. Electron., vol. 55, no. 2, pp. 941\u2013948, Feb. 2008. [17] Z. Gmyrek, A. Boglietti, and A. Cavagnino, \u201cIron loss prediction with PWM supply using low- and high-frequency measurements: Analysis and results comparison,\u201d IEEE Trans. Ind. Electron., vol. 55, no. 4, pp. 1722\u2013 1728, Apr. 2008. [18] G. Bertotti, A. Boglietti, M. Chiampi, D. Chiarabaglio, F. Fiorillo, and M. Lazzari, \u201cAn improved estimation of iron losses in rotating electrical machines,\u201d IEEE Trans. Magn., vol. 27, no. 6, pp. 5007\u20135009, Nov. 1991. [19] T. Kochmann, \u201cRelationship between rotational and alternating losses in electrical steel sheets,\u201d J. Magn. Magn. Mater., vol. 160, pp. 145\u2013146, Jul. 1996. [20] Y. Guo, J. G. Zhu, J. Zhong, H. Lu, and J. X. Jin, \u201cMeasurement and modeling of rotational core losses of soft magnetic materials used in electrical machines: A review,\u201d IEEE Trans. Magn., vol. 44, no. 2, pp. 279\u2013291, Feb. 2008. [21] L. Yujing, S. K. Kashif, and A. M. Sohail, \u201cEngineering considerations on additional iron losses,\u201d in Proc. 18th ICEM, 2008, pp. 1\u20134. [22] T. Kosaka, M. Sridharbabu, M. Yamamoto, and N. Matsui, \u201cDesign studies on hybrid excitation motor for main spindle drive in machine tools,\u201d IEEE Trans. Ind. Electron., vol. 57, no. 11, pp. 3807\u20133813, Nov. 2010. [23] O. Bottauscio, M. Chiampi, A. Manzin, and M. Zucca, \u201cAdditional losses in induction machines under synchronous no-load conditions,\u201d IEEE Trans. Magn., vol. 40, no. 5, pp. 3254\u20133261, Sep. 2004. [24] M. Centner and U. Schafer, \u201cOptimized design of high-speed induction motors in respect of the electrical steel grade,\u201d IEEE Trans. Ind. Electron., vol. 57, no. 1, pp. 288\u2013295, Jan. 2010. [25] X. Tu, L. A. Dessaint, R. Champagne, and K. Al-Haddad, \u201cTransient modeling of squirrel-cage induction machine considering air-gap flux saturation harmonics,\u201d IEEE Trans. Ind. Electron., vol. 55, no. 7, pp. 2798\u20132809, Jul. 2008. [26] P.-D. Pfister and Y. Perriard, \u201cVery-high-speed slotless permanent-magnet motors: Analytical modeling, optimization, design, and torque measurement methods,\u201d IEEE Trans. Ind. Electron., vol. 57, no. 1, pp. 296\u2013303, Jan. 2010. [27] A. Boglietti, A. Cavagnino, and M. Lazzari, \u201cComputational algorithms for induction-motor equivalent circuit parameter determination\u2014Part I: Resistances and leakage reactances,\u201d IEEE Trans. Ind. Electron., vol. 58, no. 9, pp. 3723\u20133733, Sep. 2011. [28] A. Boglietti, A. Cavagnino, and M. Lazzari, \u201cComputational algorithms for induction-motor equivalent circuit parameter determination\u2014Part II: Skin effect and magnetizing characteristics,\u201d IEEE Trans. Ind. Electron., vol. 58, no. 9, pp. 3734\u20133740, Sep. 2011. [29] G. Traxler-Samek, R. Zickermann, and A. Schwery, \u201cCooling airflow, losses, and temperatures in large air-cooled synchronous machines,\u201d IEEE Trans. Ind. Electron., vol. 57, no. 1, pp. 172\u2013180, Jan. 2010. [30] B. Piepenbreier and F. Taegen, \u201cSurface losses in cage induction motors,\u201d in Proc. Beijing Int. Conf. Elect. Mach., 1987, pp. 326\u2013329. [31] T. S\u0301liwin\u0301ski, The Methods of the Induction Motors Calculation. Warszawa, Poland: PWN, 2008, p. 324. [32] P. L. Alger, Induction Machines. Their Behavior and Uses. New York: Gordon and Breach, 1970. [33] R. Mujal-Rosas and J. Orrit-Prat, \u201cGeneral analysis of the three-phase asynchronous motor with spiral sheet rotor: Operation, parameters, and characteristic values,\u201d IEEE Trans. Ind. Electron., vol. 58, no. 5, pp. 1799\u2013 1811, May 2011. Krzysztof Komeza (M\u201911) received the Ph.D. and D.Sc. degrees from the Technical University of Lodz, Lodz, Poland, in 1983 and 1995, respectively. He is currently a Vice Director of the Institute of Mechatronics and Information Systems, Technical University of Lodz, where he has been a Professor since 1998. He has done a number of consultancy works for the electrical machines industry. He has published over 160 papers. His research interests include computational electromagnetics, efficient finite-element computations and coupled field computations, and design and optimization of electrical machines. Maria Dems (M\u201911) received the Dipl.Ing. and M.Sc. degrees in electrical engineering in 1970, the Ph.D. degree in 1978, and the D.Sc. degree in 1996, all from the Technical University of Lodz, Lodz, Poland. Since 1998, she has been a Professor with the Technical University of Lodz, where she is currently a Vice Director of the Institute of Mechatronics and Information Systems. She has done a number of consultancy works for the electrical machines industry. She is the author or coauthor of over 150 publications. She specializes in electrical engineering, particularly in modeling, design, and optimization of electrical machines, applications of modern tools, databases, and expert systems."
        ]
    },
    {
        "image_filename": "designv10_5_0003098_j.triboint.2020.106689-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003098_j.triboint.2020.106689-Figure2-1.png",
        "caption": "Fig. 2. The diagram of radial deformation.",
        "texts": [
            " For the purpose to obtain a practical analytical model and reduce ambiguity, the necessary hypotheses should be made: 1) All contact deformations are considered as elastic deformations, which only occur in the contact area and comply with the Hertz contact theory; 2) Centrifugal force and gyroscopic moment are negligible due to the low rotation speed of the screw; 3) The top roller is 1#, and the sequence number increases clockwise; 4) The separation angle of any roller i# with respect to 1# roller is \u03d5i, which could be calculated by: \u03d5i = 2\u03c0(i \u2212 1) n (i= 1, 2, ..., n) (1) where n is the total number of rollers. As shown in Fig. 2, when the PRSM is subjected to radial load, the radial contact deformation at different position angle is generated. Fig. 2 shows the solid circle denotes the initial position of the nut without radial load, and the dotted circle designates new position of the nut in radial load. According to Refs. [1,10,17], for the purpose to obtain the load distribution, the axial load of each roller is given as an input parameter, and the contact deformations and forces are solved. However, when the PRSM is subjected to both axial and radial loads, the axial load of each roller is not equal. Furthermore, it\u2019s also extremely difficult to calculate the normal contact deformations over threads in accordance with geometry relationship by ball screw method [15,16,19] or bearing method [20,21]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003426_s00170-018-3127-y-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003426_s00170-018-3127-y-Figure6-1.png",
        "caption": "Fig. 6 Model geometry and mesh, a single-track flat model, b double-track flat model, c single-track cylindrical model, and d double-track cylindrical model",
        "texts": [
            " The thermal conductivity at the temperature above the melting point was modified by multiplying a constant value to compensate for the fluid flow in the molten pool [25]. The latent heat of fusion was involved in the specific heat between the liquid and solid temperature of the materials. The modification equation is described in Eq. (6) [26]. Cm p \u00bc Lf Ts\u2212Tl \u00fe Cp T\u00f0 \u00de Ts\u2264T \u2264Tl \u00f06\u00de where Lf represent material\u2019s latent heat of fusion, Cm p is the modified specific heat, Cp(T) is the material\u2019s specific heat at temperature T, and Ts and Tl are the solid and liquid temperatures of the material, respectively, Figure 6 illustrates the geometry and mesh of the three cases. A gradient mesh was chosen in order to increase the simulation accuracy aswell as the calculation efficiency. The laser irradiation region and the HAZ were divided densely whereas the substrate away from the cladding region was meshed sparsely. In order to simulate the additive nature of the laser cladding process, the element birth and death technique in the ANSYS software was used. Before simulation, all built elements in the clad layers were deactivated",
            " First, the thermal field of the laser cladding process was analyzed. The element type solid70 was selected for the thermal analysis. Then, the mechanical analysis was performed on the samemeshmodel. For the mechanical modeling, the element type was changed to solid 185. The temperature field obtained in the first step was input as thermal loadings. The mechanical boundary conditions were applied during calculation to avoid rigid body motion. The details of mechanical boundary conditions are represented by the arrows shown in Fig. 6. A flowchart is plotted in Fig. 8 that details the simulation procedure. The accuracy of the simulated thermal results greatly influences the reliability of the calculated residual stress. Therefore, the simulated temperature distributions were first validated by the experiments. The cross-section contours of the single and double-track flat models obtained by experimentation and simulation are shown in Fig. 9. As Fig. 9a indicates, both the predicted cladding layer and the HAZ achieve a good correlation with the experimentation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003426_s00170-018-3127-y-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003426_s00170-018-3127-y-Figure9-1.png",
        "caption": "Fig. 9 Cross-section of clad, a experimental and prediction results of single-track flat model, b experimental result of doubletrack flat model, c prediction result of double-track flat model",
        "texts": [
            " The details of mechanical boundary conditions are represented by the arrows shown in Fig. 6. A flowchart is plotted in Fig. 8 that details the simulation procedure. The accuracy of the simulated thermal results greatly influences the reliability of the calculated residual stress. Therefore, the simulated temperature distributions were first validated by the experiments. The cross-section contours of the single and double-track flat models obtained by experimentation and simulation are shown in Fig. 9. As Fig. 9a indicates, both the predicted cladding layer and the HAZ achieve a good correlation with the experimentation. Figure 9b shows the cross-section of the doubletrack flatmodel obtained experimentally. In the overlapping zone, the second track is deposited along the top surface of the first track (see Fig. 9b). Therefore, the laser heat flux should be applied perpendicularly to the surface of the first track in the overlapping zone during the simulation of the double-track flat model. The simulated cross-section temperature contour of the second track is shown in Fig. 9c. It can be concluded that the predicted results coincide very well with those obtained through experimentation. Thermocouple measurements were applied to validate the simulated thermal history. Figure 10a illustrates the positons of the installed thermocouples for the single-track flat model. Figure 10b shows the numerically and experimentally obtained thermal histories for the single-track flat model. As Fig. 10b illustrates, the peak temperature of the T2 is higher than the T1. This result can be attributed to the heat accumulation during the laser cladding process"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000749_tmag.2011.2169805-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000749_tmag.2011.2169805-Figure7-1.png",
        "caption": "Fig. 7. 3-D meshed model of the 24/32-pole DSEG.",
        "texts": [
            " 5 shows the air-gap flux density distribution of the 24/32- pole DSEG with different excitation currents in the no-load condition. When the excitation current is increased to 10 A, the maximum air-gap flux density reaches almost 1.4 T. B. 3-D FEA In order to provide a more accurate calculation and verification, the 3-D FEA model of the 24/32-pole DSEG is also established. We develop the quarter FEA model by setting a master-slave boundary, as shown in Fig. 6, so the computational complexity is reduced. Fig. 7 shows the 3-D meshed model of the proposed DSEG. Fig. 8 presents the flux density vector in stator and rotor when the electrical MMF is 1000 A.T, and shows the distinct flux path and saturated condition of the magnetic core. When the DSEG is used as a direct-driven wind turbine generator, many more turns of armature windings are needed because of the low operation speed, which should cause higher inductance and resistance of phase windings, and it may negatively affect the output capability of the DSEG"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001443_ls.1271-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001443_ls.1271-Figure9-1.png",
        "caption": "Figure 9. Ball bearing-inner raceway geometry.",
        "texts": [
            " This is the viscosity required to generate a sufficiently large lambda ratio (ratio of EHD film thickness to surface roughness) and is extracted from handbook charts produced from EHD film calculations made by the bearing supplier, who assumes a representative \u03b1-value. Although bearing handbooks relieve the user from the need to calculate of EHD film thickness, it is still sometimes instructive to make this calculation, so a simple example is provided here. Consider a deep groove ball bearing having balls of radius 12.0mm and an inner groove radius 18mm. The geometry (not to scale) is shown in Figure 9. The radius of the inner groove along the axial direction is 12.5mm and is concave. The most heavily loaded ball (the one directly opposite the applied shaft load) has a loadW of 1.0 kN; (this can be evaluated from the applied bearing load usingW\u2248 5Wbearing N where N is the number of balls in the bearing). What is the minimum EHD film thickness at the inner race if this race rotates at 1000 rpm and the oil has viscosity of 0.01Pas and pressure viscosity coefficient, \u03b1* is 15GPa 1? The outer raceway is stationary"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001842_s00170-015-7647-4-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001842_s00170-015-7647-4-Figure6-1.png",
        "caption": "Fig. 6 Concept for an isolated coolant feeding up to the die bearings in the mandrel",
        "texts": [
            " For this purpose, on the one hand, channels must be considered, through which the tubes can be feeded. On the other hand, also the assembly and the connection of the partially multidirected tubes must be enabled. The isolation of the tubes requires additional amount of space, which is especially in the partially small and filigree die bridges, often not available. Furthermore, the dies will be mechanically weakened by the bigger cross sections of the channels which is mandatory necessary for an isolation. Figure 6 shows the concept for an isolated coolant feeding up to the die bearings in the mandrel. The coolant feeding is performed via tubes through the die bridges which are not directly in contact with the die. In the die, channels with a diameter bigger than the outer diameter of the tubes are inserted, so that, in between, an isolating air gap occurs. At the top of the mandrel, the tubes will be connected to the cooling channel which was inserted by selective laser melting. The attachment can be carried out by force fitting of the tube ends in a specially prepared drill hole"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001940_j.jsv.2018.02.033-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001940_j.jsv.2018.02.033-Figure6-1.png",
        "caption": "Fig. 6. The illustration of the mesh deformation of planetary gear system: (a) sun-planet gear mesh deformation (b) ring-planet gear mesh deformation.",
        "texts": [
            " The symbol cj is the damping of the gears, shaft and bearings, which can be calculated using equation cj \u00bc 0:05M \u00fe 10 5K [22,34]. In this equation, K is the stiffness,M is the equivalent mass. The rest equations of motion of the planetary gears in this paper are obtained similarly. The mesh deformations are independent of the reference frame, so the deformation and coordinate relationship for the engaged gear pairs and bearings can be obtained in the moving coordinate system oixiyi or onxnhn. From Fig. 6, the contact deformations including gear and bearing deformation can be obtained. The symbol \u03b5j (j\u00bc spi, rpi, cri cti) represents the deformation of the ith planetary gear against the sun gear or ring gear and the radial or tangential compression deformations of the ith planetary gear bearing against the carrier. For instance, the sun-planet and ring-planet gear mesh deformation equation is as follows [24]. \u03b5spi \u00bc us xs sin jspi \u00fe ys cos jspi \u00f0 ui \u00fe xi sin ai \u00fe hi cos ai\u00de (9) \u03b5rpi \u00bc ur xr sin jrpi \u00fe yr cos jrpi \u00f0ui xi sin ai \u00fe hi cos ai\u00de (10) where uj\u00bc rbj$qj (j\u00bc s, p1, p2, p3, r), xj, yj (j\u00bc s, r), xj (j\u00bc 1, 2, 3), hj (j\u00bc 1, 2, 3) denote the rotation displacement of sun, planet gears and ring gear, displacements in x and y coordinates of sun gear or ring gear and the displacements in x and h coordinates of jth planetary gear, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000842_00220345720510026301-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000842_00220345720510026301-Figure3-1.png",
        "caption": "FIG 3. Experimental setup.",
        "texts": [
            " The porcelain slurry was applied over a 2 inch length as an even thickness on one side of the strip (Fig 2). The thickness of the porcelain was controlled by a jig that could be varied to give the required total composite thickness. The strips then were suspended from a horizontal Inconel arm by placing a ceramic rod through the arm and the hole at the end of the specimen. A platinum-wound resistance furnace was then rolled horizontally into position to house the specimen. A schematic drawing of the experimental setup is shown in Figure 3. In Figure 4, the specimen is shown suspended freely inside the furnace. The end from which the photograph was taken had been fitted with a 5 inch diameter, three-eighths inch thick quartz glass. This allowed viewing of the specimen during firing. It also was possible to measure the deflection change as the temperature varied by use of a calibrated telescope. After firing to 1,850 F at a rate of approximately 57 F/minute, the power was shut off and the specimen furnace was cooled. The heating and cooling cycle is shown in Figure 5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002784_j.jmrt.2019.11.063-Figure18-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002784_j.jmrt.2019.11.063-Figure18-1.png",
        "caption": "Fig. 18 \u2013 Cracking schematic presentation of samples produced using the DMLS additive manufacturing method: F - tensile force, g - thickness of the material layer produced by the additive manufacturing method, L - elementary material layer, P \u2013 adopted contact surface of the adjacent layers, C \u2013 hypothetical cracking process of sample subjected to axial tension, Dc \u2013 sample fracture along the contact surface of adjacent layers, R1, R2 \u2013 random crack initiation and its development along the",
        "texts": [
            " Calculations of structural elements produced by the DMLS additive manufacturing method can be carried out using the properties of a titanium alloy manufactured by the traditional method. The elongation A of DMLS samples is approximately 48% lower than the results for DB samples. The damage character of DB samples is typical for elasto-plastic materials demonstrating narrowing, while DMLS samples after tensile testing have no visible narrowing. The cracking method is parallel to the sample layers surface and with the decreasing cross-sectional area of the sample, the crack develops along one of the layers. The scheme of damage method for DMLS sample is presented in Fig. 18. 3.2. Analysis of hardness test results The carried out hardness tests showed differences between the results obtained for the sample made from annealed drawn bar (Specimen DB) and the samples made using the DMLS additive manufacturing method: before (Specimen DMLS-1) and after (Specimen . 2 0 2 0;9(2):1365\u20131379 1377 D r T t D o s F p t t T s H p t D c 9 s I h T a n t a H h i t D H h e p r Z d m t t t s m m l p s H d c t p j m a t e r r e s t e c h n o l MLS-2) tensile tests. Differences in hardness also occur between the esults received for individual planes of each sample"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000782_j.mechmachtheory.2012.11.006-Figure10-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000782_j.mechmachtheory.2012.11.006-Figure10-1.png",
        "caption": "Fig. 10. POA angular misalignment calculation scheme.",
        "texts": [
            " This misalignment component is due to the relative displacement of the gears along the LOA and is already considered, scaled along the transverse direction, in Eq. (4). POA angular misalignment is calculated through the following procedure: 1) Each axis of rotation is projected on the POA in the reference frame; 2) Angles between the projected axes and the reference axis are calculated in the reference POA; 3) Misalignment is obtained by the difference of the rotations (since same rotation in the same direction implies aligned gears). The axis OLOAr defines the positive rotation for the misalignment angle \u03b1i as shown in Fig. 10. POA angular misalignment is finally expressed in terms of slope coefficient, to enter the look-up tables, as: M \u00bc tan \u03b11\u2212\u03b12\u00f0 \u00de: \u00f018\u00de POA angular misalignment causes increased separation, if negative, or extra penetration, if positive, of teeth surfaces towards one side of the active face width (Fig. 11). Since DTE and its time derivative are calculated in the reference transverse plane, which is positioned on one gear face, the other gear face remains to be considered. If extra penetration is caused on the opposite side, an additional contribution to DTE Eq"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002696_taes.2017.2691198-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002696_taes.2017.2691198-Figure1-1.png",
        "caption": "Fig. 1: Hypersonic aircraft [3] : a) 3-D shape, b) Top view, c) Side view",
        "texts": [],
        "surrounding_texts": [
            "0018-9251 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.\nmodel inversion was adopted for the design of a dynamic state feedback controller that used both elevator and canard as control surfaces, and it was extended to the system whose control surface generating aerodynamic force and moment is the elevator only in [5]. To remove a problem of \u201cexplosion of complexity\u201d generated in the backstepping control scheme [21], the concept of dynamic surface control (DSC) [22]-[24] was utilized [6]. In addition, a discrete adaptive backstepping controller with the Kriging estimator was proposed by considering stochastic boundedness [7], and a robust adaptive backstepping controller was proposed to handle control input constraints and uncertainty [8], [9]. Recently, the robust adaptive control with a combination of neural networks (NN) was proposed to handle unknown dynamics and input nonlinearity [10], and a neural discrete backstepping control method was developed in [11]. In [12], a neural adaptive control method was proposed to overcome actuator fault of the hypersonic aircraft.\nOn the other hand, the control systems based on the transformed strict feedback system have been extensively studied as well because the nonlinear hypersonic aircraft model is transformed into a pure strict feedback system by choosing appropriate outputs, (i.e, velocity and altitude) and differentiating them with respect to time [13]-[19]. In [13], the linear quadratic regulator (LQR) was chosen as a pseudo control input generated after the feedback linearization, and Ref. [14] proposed an adaptive sliding mode control method and sliding observer with a dynamic model inversion (DMI)-based controller. A concept of the NN-based adaptive control was utilized in [15], and an approximated feedback linearization method [16] was applied to the model developed by Bolender and Doman [2]. In addition, a support vector regression-based adaptive control was proposed in [17], and Ref. [18] proposed a DMI-based controller with the nonlinear disturbance observer to compensate the difference between the nominal and uncertain hypersonic aircrafts. Recently, an adaptive sliding mode controller with the grey prediction was proposed for the hypersonic aircraft with the matched uncertainties [19], and Ref. [20] reviewed flight dynamics and control approaches for the hypersonic aircraft.\nAlthough all of the above control methods have been validated by performing numerical simulations, there exist two limited points. The first one is that the unmatched uncertainties were not compensated directly when the transformed strict feedback system was utilized. Even though the recent work [18] tried to remove the unmatched uncertainties, the proposed method was to combine the nominal controller (based on the nominal system, i.e., the uncertainty-free system) with the disturbance observer, not to consider the overall uncertain dynamic system directly. On the other hand, the controller with the original hypersonic aircraft model considered the unmatched uncertainties [4]-[9]. However, it viewed the coupled effects between the thrust and elevator as the uncertainties, and compensated them by utilizing adaptive elements, thus, being able to lead an algebraic problem. That is, there exists the control input in the uncertainty. The second one is that the uncertainties related to the physical modeling (e.g., mass, moment of inertia, air density and etc.) and force/moment coefficient inaccuracies were",
            "0018-9251 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.\nnot considered simultaneously. The controller with the original hypersonic aircraft model mainly focused on the aerodynamic uncertainties, while the uncertainties related to the physical modeling inaccuracies were considered in the controller design with the transformed strict feedback system.\nTo handle all the unmatched/matched uncertainties generated by the physical modeling and force/moment coefficient inaccuracies, this study proposes the NN-based adaptive tracking controller by utilizing the transformed uncertain feedback system. In order to do so, the virtual control inputs are introduced and the DSC method is utilized. The uncertainties related to the physical modeling inaccuracy and force/moment coefficient variation of the hypersonic aircraft affect both the drift vector and control input gain matrix. Most of studies view the uncertainties in the drift vector and control input gain matrix as one lumped uncertainty vector, and ignore the control input effect in the lumped uncertainty vector. In this study, the uncertainties in the drift vector and control input gain matrix are not considered as the lumped uncertainty vector by multiplying the drift vector by the inverse of the input gain matrix [25], [26] during the controller design process. That is, this study handles the drift term with the inverse of the input gain matrix. Thus, the algebraic problem is removed when the controller is designed. Moreover, handling the inverse of the input gain matrix enables to avoid the controller singularity problem because the inverse of the input gain matrix is directly trained and adapted during the control process. In addition, the proposed controller utilizes a saturation function with a time-varying gain to remove the unmatched/matched uncertainties. The adaptive gains reduce the conservativeness of the proposed controller because it is not trivial to know the bounds of the uncertainties in advance [27]. Finally, to analyze the stability of the overall closed-loop system, this study utilizes deadzoned tracking errors, composed of",
            "0018-9251 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.\nthe tracking error and saturation function, and virtual control error between the virtual control and filtered control inputs. Thus, the uniformly ultimate boundedness (UUB) of all the error signals is directly assured, and the size of the ultimate bound of the error signals can be adjusted by the deadzone width.\nThe paper is organized as follows. The longitudinal dynamic model of the hypersonic aircraft is presented, and the matched/unmatched uncertainties generated by the physical modeling and force/moment coefficient inaccuracies are briefly introduced in Section II. In Section III, the NN-based adaptive tracking control system is designed using the virtual control input and DSC method, and the stability of the overall closed-loop system is rigorously analyzed by the Lyapunov stability theory. Numerical simulations are performed to validate the effectiveness of the proposed approach in Section IV, and conclusion is given in Section V.\nII. HYPERSONIC AIRCRAFT MODEL\nIn general, the longitudinal dynamic model of the hypersonic aircraft is described as [3],[13]\u2013[15], [28]\nV\u0307 = T cos\u03b1\u2212D m \u2212 \u00b5 sin \u03b3 r2 ,\n\u03b3\u0307 = L+ T sin\u03b1 mV \u2212 (\u00b5\u2212 V 2r) cos \u03b3 V r2 , h\u0307 = V sin \u03b3, (1)\n\u03b1\u0307 = q \u2212 \u03b3\u0307,\nq\u0307 = Myy/Iyy,\nwhere\nL = 1\n2 \u03c1V 2SCL, D =\n1 2 \u03c1V 2SCD, T = 1 2 \u03c1V 2SCT ,\nr = h+RE , Myy = 1\n2 \u03c1V 2Sc\u0304\n[ CM (\u03b1) + CM (\u03b4) + CM (q) ] ,\nCL = 0.6203\u03b1, CD = 0.6450\u03b12 + 0.0043378\u03b1+ 0.003772,\nCT =  0.02576\u03b2 if \u03b2 < 1\n0.0224 + 0.00336\u03b2 if \u03b2 > 1\n,\nCM (\u03b1) = \u22120.035\u03b12 + 0.036617\u03b1+ 5.3261\u22126,\nCM (q) = c\u0304\n2V\n( \u22126.796\u03b12 + 0.3015\u03b1\u2212 0.2289 ) q,\nand\nCM (\u03b4e) = ce(\u03b4e \u2212 \u03b1)."
        ]
    },
    {
        "image_filename": "designv10_5_0000618_j.mechmachtheory.2009.11.007-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000618_j.mechmachtheory.2009.11.007-Figure5-1.png",
        "caption": "Fig. 5. Description of one parallel module of the hybrid structure.",
        "texts": [
            " This technique has been seen as efficient for serial rigid manipulators [24\u201326] and for flexible manipulators [27,28]. . All rights reserved. fr (W. Khalil). This paper is organized as follows. Section 2 describes the dynamic modeling of one module of the system. Section 3 describes the dynamic Modeling of the hybrid structure. Finally, Section 4 presents the conclusions. The hybrid structure is made up of n parallel modules, which are serially connected to a fixed base. To facilitate the presentation of this paper we suppose that the modules are similar. The structure of a module k is described in Fig. 5, the number of degrees of freedom of the platform with respect to its base is denoted by Nk, and the number of branches is denoted mk. We define a frame Rk attached to the platform of each module k, and frame Rbk fixed to its base. Since the base of module k is fixed to the platform of module k-1, thus the transformation matrix between Rk 1 and Rbk is constant. Finally frame R0 is fixed to the base of module 1. The following kinematic models for module k will be used in the dynamic models: The kinematic model, which gives the velocity of the platform of module k as a function of the motorized joint velocities, this model is given by the relation [29]: vk \u00bc Jk _qak \u00f01\u00de where Jk \u00f06 Nk\u00de kinematic Jacobian matrix of module k"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000751_tmech.2012.2209673-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000751_tmech.2012.2209673-Figure6-1.png",
        "caption": "Fig. 6. Setup of the experiments with the ABB IRB 140.",
        "texts": [
            " In the experiments, we used a soft tissue phantom created using Ecoflex 0030, a two-part silicone rubber with Silicone Thinner (nonreactive silicone fluid), from Smooth\u2013On Inc., which was used in [32]. The silicone phantoms with three different consistencies of Silicone Thinner were used in order to cover a wide range of parameter values. ABB IRB 140, a 6-DOF robot equipped with the Gamma SI-130-10 force sensor (ATI Industrial Automation, Inc., Apex, NC) with resolution of 1/20 N was used to collect the manipulation trajectories and force sensing data. The repeatability of the robot is 0.03 mm. The setup of the experiments is shown in Fig. 6. The tissue phantoms used in the experiments were similar in shape and size to the models used in the simulation studies described in Section IV-A. Specifically, the tissue phantoms were square in shape, with dimensions of 10 cm \u00d7 10 cm \u00d7 1 cm. The tissue phantoms were placed horizontally while being grabbed and retracted by a gripper toward right. We considered two cases where the phantoms were anchored to a wall on one side (left) and two adjacent sides (left and back). The retraction actions were achieved by moving the gripper in 1\u20132 mm increments, toward right, producing about 10% elongation of the tissue phantom as shown in Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002254_s00170-016-9523-2-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002254_s00170-016-9523-2-Figure2-1.png",
        "caption": "Fig. 2 Cylindrical pressure vessel design problem",
        "texts": [
            " The maximum number of generations varied from 200 to 1200 depending on the problem. For each problem, we independently run AMDE 100 times to measure the quality of the results and the robustness of the proposed algorithm. The AMDE was implemented inMATLAB and the optimization runswere executed on a PC with a 2.2 GHz Intel Dual Core processor and 2 GB of RAM memory. This optimization problem was originally formulated by Sandgren [33]. The cylindrical vessel capped at both ends by hemispherical heads, as shown in Fig. 2, must be designed for the minimum total fabrication cost, including the material cost, forming, and welding. The problem involves fourmixeddesign variables: the thickness of the cylindrical shell (Ts), the thickness of the spherical head (Th), the inner radius (R), and the length of the cylindrical segment of the vessel (L). Ts and Th are integer multiples of 0.0625 in. The problem can be expressed as follows: Minimize : f T s; Th;R; L\u00f0 \u00de \u00bc 0:6224 TsR L \u00fe 1:7781 ThR2 \u00fe 3:1611 Ts 2L \u00fe 19:84 Ts 2R \u00f014\u00de Subject to g1 \u00bc \u2212 Ts \u00fe 0:0193 R \u2264 0 g2 \u00bc \u2212 Th \u00fe 0:00954 R \u2264 0 g3 \u00bc \u2212\u03c0R2L\u2212 4\u03c0R3 3 \u00fe 1296000\u22640 g4 \u00bc L \u2212 240 \u2264 0 \u00f015\u00de where 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003170_msec2018-6477-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003170_msec2018-6477-Figure2-1.png",
        "caption": "Figure 2: Schematic diagram of the location of flash-lamps and camera used to capture in-situ powder bed images [31].",
        "texts": [
            " A digital single-lens reflex camera (DSLR, Nikon D800E) along with multiple flash-lamps placed inside the build chamber are used to capture the layer-by-layer powder bed images. Images are captured at two instances in every layer, namely, post laser scan and post re-coat. The camera shutter is controlled by a proximity sensor that registers the location of the re-coater blade. Five images of the powder bed images are captured under bright-field and dark-field flash settings. The layout of the camera and flash-lamp location are shown in Figure 2, and the representative images under the five light schemes are shown in Figure 3. In this work, images from bright-field light scheme in Figure 3(a) are analyzed. Details of the experimental setup are available in Ref. [31]. Table 1: The combination of power (P), hatch spacing (H), scan velocity (V) process conditions used for making the titanium alloy parts. Process Condition (P, H, V) [W, mm, mm/sec] EA [J.mm-2] Andrew\u2019s number P0, H0, V0 (340, 0.12, 1250) 2.27 P -25%, H0, V0 (255, 0.12, 1250) 1"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000648_978-3-642-17531-2-Figure3.14-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000648_978-3-642-17531-2-Figure3.14-1.png",
        "caption": "Fig. 3.14. Ideal pendulum",
        "texts": [
            " Implementation in simulation tools This type of event detection is available in good simulation tools as a stand-alone function block (e.g. SIMULINK: hit crossing) or as a sub-function of discrete-event blocks (e.g. SIMULINK/STATEFLOW: edge-triggered signal inputs). In all cases, it must be possible to access the integration algorithm or its step size selection8. System configuration, problem statement As a demonstrative example of a mechanical DAE system\u2014which at first glance has very simple dynamics\u2014consider the ideal pendulum shown in Fig. 3.14. This section demonstrates the most important steps in modeling and simulating the DAE models of such systems, presenting both a signal- and equationbased approach. 8 It is once more pointed out that it always commends itself to carefully test out the proper functioning of any particular implementation. The capabilities of a simulation tool promised in the user manual are not always actually delivered, see for example the behavior of SIMULINK/STATEFLOW blocks for event detection in (Buss 2002), Sec. 6.3. 204 3 Simulation Issues For the ideal pendulum shown in Fig. 3.14, find: the equations of motion including the constraint force in the rod (a DAE system), a signal-based simulation model (block-oriented, e.g. MATLAB/SIMULINK), an equation-based simulation model (object-oriented, e.g. MODELICA). Solution 1: equations of motion as a DAE system Using the generalized coordinates ( )Tx yq and the generalized velocities ( )T x y v vq v , the resulting kinetic co-energy of the system is * 2 2/2 ( ) x y T m v v . There is a holonomic constraint of the form 2 2 2 0f x y lq ",
            " without further transformations) implemented in an equation-based simulation tool. Fig. 3.18 shows an example of such an implementation in MODELICA. In most MODELICA-based tools, consistent initial values are also automatically generated. Given an accurate implementation, these simulation results coincide with those in Fig. 3.16 and Fig. 3.17a. Bibliography for Chapter 3 209 Alternative model: system of ordinary differential equations Polar coordinates vs. Cartesian coordinates The model of the pendulum used so far is expressed in Cartesian coordinates ,x y (Fig. 3.14). The worthy reader may convince herself that an alternative model of the pendulum in polar coordinates takes the form of a system of ordinary differential equations without secondary algebraic conditions (a DAE system with index = 0) as follows: , sin . g l (3.54) The model in Eq. (3.54) can be simulated without difficulty using ordinary explicit integration algorithms. Modeling vs. simulation aspects Along with the above concluding model treatment, let it be remarked that in the context of systems design, there is always a tradeoff between modeling and simulation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002021_0959651816656951-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002021_0959651816656951-Figure1-1.png",
        "caption": "Figure 1. Reference Frames.",
        "texts": [
            " Dynamic model Quadrotor nonlinear model The equations of motion of quadrotors have been derived and analyzed by several researchers in the literature.12,13 So we only discuss the quadrotor model briefly in this paper. A quadrotor is a highly-nonlinear underactuated system with six DOF and four control inputs. In order to derive its model, two reference frames are defined; an inertial reference frame I : fOI,XI,YI,ZIg fixed to the earth and a body-fixed frame B : fOB,XB,YB,ZBg attached to the quadrotor center of mass. These two reference frames are shown in Figure 1. The rotation matrix transforming the body-fixed axes to the inertial at UNIV CALIFORNIA SAN DIEGO on July 15, 2016pii.sagepub.comDownloaded from axes is obtained using the XYZ rotation sequence and is found to be R= cucc cusc su sfsucc cfsc sfsusc + cfcc sfcu cfsucc + sfsc cfsusc sfcc cfcu 2 4 3 5 \u00f01\u00de where f, u and c are the roll, pitch and yaw angles, respectively, defining the quadrotor attitude. The terms c( ) and s( ) represent the cosine and sine functions respectively. These three Euler angles are considered to be 3DOF of the quadrotor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001973_b978-0-12-417049-0.00005-5-Figure5.15-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001973_b978-0-12-417049-0.00005-5-Figure5.15-1.png",
        "caption": "Figure 5.15 (A) Two car-like WMRs (leader follower structure). (B) Four WMRs in a typical formation (diamond structure). Source: www.robot.uji.es/lab/plone/research/pnebot/index_html2.",
        "texts": [
            " This situation is overcome if we use the transformation [16]: \u03b85 atan2\u00f0y; x\u00de for jatan2\u00f0y; x\u00de2\u03c6j, 90 \u03b85 atan2\u00f0y; x\u00de2 sgn\u00f0atan2\u00f0y; x\u00de2\u03c6\u00de3 180 for jatan2\u00f0y; x\u00de2\u03c6j. 90 \u00f05:90\u00de In this way, the distance from the origin to the WMR is equal to the error of x, and the difference angle of the WMR with the x-axis becomes the error of \u03c6. As shown in Figure 5.14D, the controller (5.88) with the above switching type transformation assures that the WMR can go to \u00f0x; y\u00de5 \u00f00; 0\u00de starting from any initial posture. Consider two car-like robots that follow a path with the first car acting as the leader and the second being a follower (Figure 5.15). For more WMRs, one following the other in front of it, this problem is known as formation control [7]. The leader follower control problem under consideration is to find a velocity control input for the follower that assures convergence of the relative distance Llf and relative bearing angle \u03b8lf of the WMRs to their desired values, under the y x v1 y x \u03b8 X Y x X y Y \u03b8 v1 (A) (B) Initial posture (C) (D) \u03c8 \u03d5 0 0 0 0 Figure 5.14 (A) For \u03c6 to converge, jxj must be increased. (B) Case jatan2\u00f0x; y\u00de2\u03c6j, 90 . (C) Case jatan2\u00f0x; y\u00de2\u03c6j. 90 . (D) Convergence to the origin \u00f0x; y\u00de5 \u00f00; 0\u00de using Eq. (5.90). assumption that the leader motion is known and is the result of an independent control law [7]. To solve the problem, we will apply the Lyapunov-based control design method using the kinematic and dynamic equations of the bicycle equivalent presented in Section 3.4 (see Eqs. (3.56), (3.57), (3.60a) (3.60d)). In Figure 5.15, vl, \u03c6l, and \u03c8l are the linear velocity, orientation angle, and steering angle of the leader, and vf , \u03c6f , \u03c8f are the respective variables of the follower. The coordinates of points Gl and Gf are denoted by \u00f0xl; yl\u00de and \u00f0xf ; yf\u00de. We first derive the dynamic equations for the errors: \u03b51 5 xfd 2 xf ; \u03b52 5 yfd 2 yf ; \u03b53 5\u03c6fd 2\u03c6f \u00f05:91\u00de where xfd, yfd, and \u03c6fd represent the desired trajectory of the follower in world coordinates, which are transformed to \u03b5f1, \u03b5f2, and \u03b5f3 in the local coordinate frame of the follower. From Figure 5.15 we get: L2lf 5 L2lf;x 1 L2lf;y \u00f05:92a\u00de Llf;x 5 xl 2 xf 2 d\u00f0cos \u03c6l 1 cos \u03c6f\u00de \u00f05:92b\u00de Llf;y 5 yl 2 yf 2 d\u00f0sin \u03c6l 1 sin \u03c6f\u00de \u00f05:92c\u00de tg\u00f0\u03b8lf 1\u03c6l 2\u03c0\u00de5 Llf;y=Llf;x \u00f05:92d\u00de Differentiating Eqs. (5.92b) and (5.92c) gives: _Llf;x 5 _xl 2 _xf 1 d\u00f0 _\u03c6l sin \u03c6l 1 _\u03c6f sin \u03c6f\u00de \u00f05:93a\u00de _Llf;y 5 _yl 2 _yf 2 d\u00f0 _\u03c6l cos \u03c6l 1 _\u03c6f cos \u03c6f\u00de \u00f05:93b\u00de with (see Eqs. (3.56) and (3.57)): _ygl 5 \u00f0d=D\u00de _xgltg\u03c8l; _ygf 5 \u00f0d=D\u00de _xgf tg\u03c8f \u00f05:93c\u00de where D5 2d. Using Eqs. (3.56) and (5.93c) in Eqs. (5.93a) and (5.93b), we obtain: _Llf;x 5 _xgl cos \u03c6l 2 _xgf cos \u03c6f 1 _xgf\u00f0tg \u03c8f\u00desin \u03c6f \u00f05:94a\u00de _Llf;y 5 _xgl sin \u03c6l 2 _xgf sin \u03c6l 2 _xgf\u00f0tg \u03c8f\u00decos \u03c6f \u00f05:94b\u00de while from Figure 5.13 we have: Llf;x Llf 5 cos\u00f0\u03b8lf 1\u03c6l 2\u03c0\u00de; Llf;y Llf 5 sin\u00f0\u03b8lf 1\u03c6l 2\u03c0\u00de \u00f05:95\u00de Then, differentiating Eqs. (5.92a) and (5.92d), introducing Eqs. (5.94a) and (5.94b), and using the auxiliary variable: \u03b6 f 5 \u03b8lf 1\u03c6l 2\u03c6f we get, after some algebraic manipulation: _Llf 52 _xgl cos\u00f0\u03b8lf\u00de1 _xgf tg\u00f0\u03c8f\u00desin \u03b6f 1 _xgf cos \u03b6 f \u00f05:96a\u00de _\u03b8 lf5 \u00f01=Llf\u00de\u00bd\u00f0 _xgl sin \u03b8lf2 _xgf sin \u03b6 f\u00de1 _xgf tg\u03c8f cos \u03b6f 2\u00f01=D\u00de _xgltg\u03c8l \u00f05:96b\u00de Using Figure 5.15, the actual and desired coordinates of the follower\u2019s point A can be expressed in terms of the coordinates of the leader\u2019s point B. Therefore, we use the variables fLlf ; \u03b8lfg and fLlfd; \u03b8lfdg and get the error equations (in the world coordinate frame): \u03b5f1 5 Llfd cos\u00f0\u03b8lfd 1 \u03b5f3\u00de2 Llf cos\u00f0\u03b8lf 1 \u03b5f3\u00de2 d cos\u00f0\u03b5f3\u00de1 d \u00f05:97a\u00de \u03b5f2 5 Llfd sin\u00f0\u03b8lfd 1 \u03b5f3\u00de2 Llf sin\u00f0\u03b8lf 1 \u03b5f3\u00de2 d sin\u00f0\u03b5f3\u00de \u00f05:97b\u00de \u03b5f3 5\u03c6l 2\u03c6f \u00f05:97c\u00de Finally, differentiating Eqs. (5.97a) (5.97c), we obtain the dynamic equations for \u03b5f1, \u03b5f2, and \u03b5f3: _\u03b5f1 5 _xgl cos\u00f0\u03b5f3\u00de2 _xgf 1 _ygl\u00bd2Llf sin \u03b6f 2 \u03b5f2 1 _ygf\u03b5f2 \u00f05:98a\u00de _\u03b5f2 5 _xgl sin\u00f0\u03b5f3\u00de2D _ygf 1 _ygl\u00f0\u03b5f1 2 d\u00de2 _ygf\u00f0\u03b5f1 2 d\u00de1 _yglLlf cos \u03b6f \u00f05:98b\u00de _\u03b5f3 5 \u00f01=D\u00de\u00bd _xgl tg \u03c8l 2 _xgf tg \u03c8f \u00f05:98c\u00de We are now ready to apply the usual two-stage (kinematic, dynamic) backstep controller design"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002200_admt.201800486-Figure11-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002200_admt.201800486-Figure11-1.png",
        "caption": "Figure 11. a) Schematic illustration of the fabrication process of a carbon nanoscroll. The graphite flakes were rapidly heated by microwave irradiation and then cooled by liquid nitrogen. Reproduced with permission.[174] Copyright 2011, Wiley-VCH. b) Production of rolled-up tubes of InGaAs/Cr/graphene and SEM images of the tube. Adapted with permission.[186] Copyright 2014, American Chemical Society. c) Schematic of rolling TMD monolayer flakes and TEM images of MoS2 nanoscrolls (scale bars: 20 nm; inset = 2 nm). Adapted with permission.[190] Copyright 2018, Springer Nature.",
        "texts": [
            "[41,51] Since the discovery of graphene, 2D materials have sparked intense research interest due to its extraordinary characteristics. Theoretical research has predicted that rolling 2D materials can yield exceptional electronic and photonic properties.[166\u2013173] However, owing to the weak mechanical strength and high chemical reactivity, rolled-up 2D materials were limited to Adv. Mater. Technol. 2019, 4, 1800486 www.advancedsciencenews.com \u00a9 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim1800486 (12 of 26) www.advmattechnol.de multilayer carbon,[174\u2013177] graphene oxide,[111,178\u2013181] and boron nitride (Figure 11a).[182] These nanoscrolls were formed either by internal stress such as synthesis conditions,[104,107,183] or external stress such as van der Waals force[111,178,184] and magnetic field.[185] To resolve this limitation, researchers transferred monolayer graphene on strain-engineered epitaxial layers, as displayed in Figure 11b.[186,187] The strained heteroepitaxial layers not only provided sufficient internal strain, but also enhanced the strength of the materials system. Therefore, the graphene sheet adhered to the wall of heterostructures during selective etching, producing tubes with well-defined diameters. Recent advances in the synthesis of 2D materials have enabled experimental realization of rolling high-quality monolayer 2D materials alone. Utilizing surface tension of solution, Xie et al.[97] developed a simple method to effectively roll monolayer graphene containing few impurities, as exhibited in Figure 11c. With isopropyl alcohol solution treatment, mechanical exfoliated graphene on SiO2 substrates turned to a nanoscroll. Later on, Patra et al.[188] predicted that water nanodroplets could also guide the folding and rolling of planar graphene sheets, where the scrolling results from the interaction between capillarity and elasticity,[98] and this prediction was then experimentally confirmed.[189] More recently, Cui et al.[190] reported the rolling of transition metal dichalcogenides (TMDs) with the assistance of aqueous solutions such as ethanol"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000783_s12206-010-0309-4-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000783_s12206-010-0309-4-Figure4-1.png",
        "caption": "Fig. 4. Cavity formation in laser welding on the board without (a) and with (b) filler wire.",
        "texts": [
            " This indicates that factors that improve keyhole stability can reduce the quantity of gas cavities in the laser welding for 5A06 aluminum alloy. In general, the bottom diameter of the keyhole gradually decreased because of the reflection of the irradiation laser in the wall of the keyhole, and not because of the direct irradiation of the laser beam. The tip of the keyhole was bent away from the welding direction due to the drag force in the liquid metal. Since the tip of the keyhole is so tiny, it can be easily closed by the flow of molten metal. Fig 4a shows that it became a bubble in the molten pool with the sweep of the keyhole. A bubble usually becomes a gas cavity in the weld bead because it is often difficult for bubbles to escape from the molten pool at high crystallization rates of laser welding. In laser welding with filler wire, when the keyhole could not penetrate the test plate, the depth of penetration was reduced from 3.12 mm (without filler wire) (see No. 1 in Fig. 2) to 2.78mm (with filler wire) (see No. 2 in Fig. 2). This is because a part of the laser beam was used to melt the filler wire; thus, the laser energy used to produce a keyhole was lower than laser autogenous welding",
            " First, the wire feeding system might not have been absolutely stable; hence, fluctuations of the filler wire in terms of speed and/or feed-in position resulted in a fluctuating laser energy used to generate the keyhole. The penetration depth of the keyhole might have caused extra fluctuation by the laser welding with filler wire. Second, the filling wire was heated and melted using a laser beam to form a globular droplet periodically, and the droplet was periodically transferred to the weld pool. These periodical processes might have resulted in the disturbance of laser transfer and instability of the keyhole and molten pool. Fig. 4 shows the role of the filler wire in increasing the probability of the formation of the cavity. In welding a butt joint with a 4.0 mm test plate and a zeromm welding gap, the test panel was critically penetrated with a 3.5 kW laser power. The depth of penetration fluctuated at larger scopes, and numerous larger gas cavities were found in the vertical section of the weld (see No. 3 in Fig. 2). When the laser power was increased to 3.8 kW, fluctuations in the depth of penetration became smaller, and the test panel was completely penetrated"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000862_iecon.2011.6119449-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000862_iecon.2011.6119449-Figure3-1.png",
        "caption": "Fig. 3. Voltage pulse injection upon aligned stator and rotor reference frame at stand still",
        "texts": [
            " For a given load line the slope defines how strong the magnetization will vary upon temperature (Fig. 1). For the motor under test the load line is not known. In order to quantify a variation of the magnetization upon temperature, the stator flux linkage is measured at no-load as a function of the permanent magnets temperature. The obtained results are shown in Fig. 2. In the following, an experimental setup is described that is carried out to visualize the basic relationships of the proposed method. As it is illustrated in Fig. 3, the d-axis of the rotor is aligned with the \u03b1-axis of the stator winding. This can be achieved by simply applying a stationary, not rotating, voltage space vector with zero degree angle and amplitude to produce as much as enough a current space vector to align the magnets with the motor phase a. Thus, it is assured that the magnetic axis of stator phase winding a is maximum magnetized by the rotor flux. At this position of the rotor, a voltage pulse with magnitude of 2/3 the dc bus voltage Vdc is applied in the pure d-direction of the machine by an inverter switching scheme depicted in Fig. 3. It should be noted here that by a corresponding rotor position, d-voltage pulse can be achieved by any of the 6 basic space vector switching patterns. The duration of the voltage pulse is selected for this experiment as much as 240\u00b5s for the sake of better visualization of the effects. The time trace of the resulting dcurrent id is measured at various temperatures of the permanent magnets as shown in Fig. 4. The obtained curves demonstrate two basic phenomena:  The gradient of the current curve increases due to an increase in the level of saturation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001968_978-94-007-6101-8-Figure4.9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001968_978-94-007-6101-8-Figure4.9-1.png",
        "caption": "Fig. 4.9 Spherical robot manipulator with appertaining coordinate frames",
        "texts": [
            " First we shall determine the direction of the x1 axis. The axes of the two rotational joints intersect, the origin of the next coordinate frame is to be placed into the intersection of both axes. The z1 axis runs along the rotational axis of the second joint. Its direction makes no difference. The x1 axis is perpendicular to the plane defined by the axes z0 and z1. Also this axis can be drawn in one or another direction. The x0 axis has the same direction as x1 axis. The selected directions of the axes are drawn in Fig. 4.9. The frame belonging to the translational joint is placed to the start of displacement, which is in our case 4.2 Examples of Geometric Robot Models 69 the center of the second joint. Also the axes z1 and z2 intersect, so that the x2 axis is perpendicular to them as shown in Fig. 4.9. It is most appropriate to make the robot end-point frame x3, y3, z3 parallel to precedent frame x2, y2, z2. Let us compose the table of DH parameters. First we insert into the last columns the joint variables \u03d11, \u03d12, and d3. The column ai represents the distance between the origins of two neighboring frames along the xi axis. In our case all four z axes intersect in the same point, so that three zeros are to be written into the ai column. The z1 axis is perpendicular to z0 axis. When looking at the plane z0, z1 from the positive x1 axis, then the rotation from z0 to z1 is counter clockwise",
            "3), while obtaining the following relations between the neighboring frames: 70 4 Geometric Robot Model 0A1 = \u23a1 \u23a2\u23a2\u23a3 c1 0 s1 0 s1 0 \u2212c1 0 0 1 0 l1 0 0 0 1 \u23a4 \u23a5\u23a5\u23a6 1A2 = \u23a1 \u23a2\u23a2\u23a3 c2 0 s2 0 s2 0 \u2212c2 0 0 1 0 0 0 0 0 1 \u23a4 \u23a5\u23a5\u23a6 2A3 = \u23a1 \u23a2\u23a2\u23a3 1 0 0 0 0 1 0 0 0 0 1 d3 0 0 0 1 \u23a4 \u23a5\u23a5\u23a6 The geometric model of a spherical robot mechanism with three degrees of freedom has the following form: 0A3 = 0A1 1A2 2A3 = \u23a1 \u23a2\u23a2\u23a3 c1c2 s1 c1s2 d3c1s2 s1c2 \u2212c1 s1s2 d3s1s2 s2 0 \u2212c2 l1 \u2212 d3c2 0 0 0 1 \u23a4 \u23a5\u23a5\u23a6 Let us for a while consider the initial pose of the robot mechanism. This is the pose where the joint variables \u03d1i and di equal zero. After drawing the coordinate frames into the robot mechanism, we left the mechanism in an arbitrary pose. Let us see 4.2 Examples of Geometric Robot Models 71 what is the initial pose of our simple spherical mechanism by considering the second joint. The angle \u03d12 is defined as the angle between the axes x2 and x1 about the z1 axis. From Fig. 4.9 we can see that zero angle occurs when the axes x2 and x1 are superimposed. This is the initial pose of the spherical robot which is shown in the left side of Fig. 4.10. Such initial pose cannot be reached by real industrial robots because of the limitations in joint movements. The producers of robots select such initial poses of robot mechanisms that the robot end-point is above the working area where the robot is supposed to execute its task. In our example of spherical robot such pose can be e"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001415_17452759.2017.1310439-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001415_17452759.2017.1310439-Figure1-1.png",
        "caption": "Figure 1. Temperature gradient mechanism in laser-based additive manufacturing systems during (a) heating and (b) cooling, Mercelis and Kruth (2006).",
        "texts": [
            "it surrounding material can be assimilated to a structural unbalance that effectively restrains the movement of the heated metallic material when the latter changes in state. During the cooling, a complex contraction of the irradiated region takes place, that is a tension state, while the material that surrounds the irradiated zone undergoes an expansion that results in a compression state. The volumetric shrinking of the material melted during the cooling induces compression stresses in the surrounding material, which is under the influence of the temperature gradient, as illustrated in Figure 1 (Kruth et al. 2003). Gusarov et al. (2011) proposed a thermos-elastic model, which showed that longitudinal tensile stresses are on average two times greater than transversal ones. The model explains the formation of two longitudinal and transversal crack systems that were observed during experiments. The island scanning strategy of some SLM machines can reduce residual stresses by shortening the scan tracks (Kruth et al. 2012); the rotation of the scan pattern between layers is another adopted solution that is able to create a more uniform stress distribution by compensating for directional anisotropy"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001027_ijpt.2011.041907-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001027_ijpt.2011.041907-Figure1-1.png",
        "caption": "Figure 1 Discrete dynamic model of a spur gear pair",
        "texts": [
            " A full film lubrication version of the gear EHL model (Li and Kahraman, 2010a) is incorporated with a purely torsional spur gear dynamics model to obtain an approximate equivalent damper in the direction of line of action. The variation of the damping value with the gear mesh position (gear rotation) is investigated and the influences of various contact conditions including speed, torque and lubricant temperature on the resultant gear mesh damping value are demonstrated. A conventional single DOF NTV dynamic model for spur gear pairs, which was shown to correlate well with various spur gear dynamics experiments (Tamminana et al., 2007), is used here to investigate the gear mesh damping mechanism. As shown in Figure 1(a), the mating gear pair with base radii of r1 and r2 is represented by two rigid wheels of polar mass moments of inertia J1 and J2, connected via a time-varying mesh spring element k(t) subject to a backlash of 2b and a viscous damper c, both applied along the line of action of the gears. As stated earlier, any manufacturing errors as well as any intentional tooth profile modifications are also considered and modelled as the external displacement excitation e(t). In the attempt to capture the actual gear mesh damping mechanism instead of assuming any constant damper, the power dissipation at the interface of the mating tooth pair (Figure 1(b)) is used to model the gear mesh damping in place of the constant c. It is noted in this figure that both the traction forces exerted on the pinion and gear tooth surfaces by the lubricant film, F1 and F2, and the tangential dynamic tooth surface velocities, u1 and u2, are in the off line of action direction of the gears. With the positive directions of the alternating rotational displacements \u03b81 and \u03b82 and the applied torque T1 and T2 defined in Figure 1(a), the equations of motion of the spur gear pair can be written as 1 1 1 1 1 1 1 ( ) ( ) ( ) , N n n n J t r k t t T F R\u03b8 \u03b4 = + = +\u2211 (1a) 2 2 2 2 2 2 1 ( ) ( ) ( ) , N n n n J t r k t t T F R\u03b8 \u03b4 = \u2212 = \u2212 \u2212\u2211 (1b) where the additional subscript n denotes the nth loaded tooth pair such that F1n and F2n represent the pinion and gear traction forces of the nth tooth pair in contact, and R1n and R2n are the corresponding contact radii as shown in Figure 2 for a tooth pair contacting at point C (The subscript n is omitted in the figure for simplicity purposes)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000166_14644193jmbd48-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000166_14644193jmbd48-Figure2-1.png",
        "caption": "Fig. 2 (a) Moving grids for contact zones, (b) moving grid setup, and (c) grid in tangent plane for \u00b5 calculation, and (d) principal directions and contact ellipse",
        "texts": [
            " This procedure is repeated for an M number of discrete positions (m \u2208 [1, M ]) spaced at an increment of \u03c6 (\u03c6m = m \u03c6) to span a complete gear mesh cycle. The average mechanical efficiency of the gear pair is given by \u03b7\u0304 = 1/M \u2211M m=1 \u03b7(\u03c6m). A commercial finite element (FE)-based hypoid gear analysis package [71] is used in this study as the contact analysis model. The contact model is capable of analysing both face-hobbed and face-milled hypoid gears. The model combines FE method away from the contact zone with a surface integral formulation applied at and near the contact zone [72]. As shown in Fig. 2(a), a fine contact grid is defined automatically on hypoid gear teeth to capture the entire contact zone. These grid cells are much finer than the regular size of finite element meshes elsewhere on the tooth surfaces and they are attached to the contact zones that result in an accurate contact analysis. A schematic view of these grid cells is shown in Fig. 2(b). Along the face width, there are 2n + 1 divisions, and at each division, there is a principal contact point (shown in dot) if contact occurs. Principal contact points are defined as the theoretical contact points of two undeformed contacting surfaces. In the profile direction, there are 2m + 1 grid cells within each division for capturing the entire contact zone formed due to tooth deflections and local surface deformations under load. Points that would be in contact only under load are called potential contact points in this study. The \u00b5 calculation is carried out in the grid of principal contact point in the tangent plane as shown in Fig. 2(c), which is a magnified view of the grid cell containing the principal contact point q. In Fig. 2(c), the surface defined by dotted lines with points 1\u2032\u20138\u2032 along the edges is the grid on the real tooth surface.The plane formed by solid lines with points 1\u20138 along the edges is the projection of the surface grid to the tangent plane at point q. Points 2 (2\u2032), 4 (4\u2032), 6 (6\u2032), and 8 (8\u2032) are the mid points at each edge of the grid. Vector t 26 that connects points 2 and 6 is approximated as the instant line of contact and vector t p26t is normal to t 26 in the tangent plane. n is the surface normal vector at the contact point q",
            "comDownloaded from unit vectors in the principal directions corresponding to the principal curvatures are defined as [72] e(i) = {\u03bb(i)}T \u23a7\u23aa\u23aa\u23a8 \u23aa\u23aa\u23a9 \u2202r \u2202s \u2202r \u2202t \u23ab\u23aa\u23aa\u23ac \u23aa\u23aa\u23ad , i = 1, 2 (3) Assume that q is the contact point of surfaces 1 and 2. Let ef and eh be the unit vectors of principal directions, and \u03baf and \u03bah be principal curvatures of surface 1 at point q. Likewise es and eq be unit vectors of principal directions, and \u03bas and \u03baq be principal curvatures of surface 2 at the same point q. These values of principal directions and curvatures can be obtained by solving equation (2). The angle \u03c3 formed by ef and es, and the angle \u03b1 that determines the orientation of the coordinate axes x and y with respect to ef shown in Fig. 2(d) are given as [74] \u03c3 = tan\u22121 es \u00b7 eh es \u00b7 ef , \u03b1 = 1 2 tan\u22121 [ g2 sin 2\u03c3 g1 \u2212 g2 cos 2\u03c3 ] (4) where g1 = \u03baf \u2212 \u03bah and g2 = \u03bas \u2212 \u03baq. Finally, two directions x and y are defined as x = ef cos \u03b1 + eh sin \u03b1, y = \u2212ef sin \u03b1 + eh cos \u03b1 (5) If the two contacting surfaces, 1 and 2, are in continuous tangency at the point of contact, the position and unit normal vectors of surfaces 1 and 2 must be equal. These conditions are described by the following equations [74] v(2) r = v(1) r + v(12), n\u0307(2) r = n\u0307(1) r + \u03c9(12) \u00d7 n (6) where v(i) r is the relative velocity vector of the contact point with respect to the surface as it moves over the surface i, n\u0307(i) r is the velocity of the tip of the surface unit normal in its motion over the surface i, and \u03c9(12) = \u03c9(1) \u2212 \u03c9(2) is the relative angular velocity. Equation (6) is then used for the derivation of curvature relations of mating surfaces. As shown in Fig. 2(d), velocity vectors of point q on surface 1 can be represented in the coordinate system Sa(ef , eh) as v(1) r = [ v(1) f v(1) h ] , n\u0307(1) r = [ n\u0307(1) f n\u0307(1) h ] (7) Similarly, the velocity vectors of point q on surface 2 are defined in the coordinate system Sb(es, eq) as v(2) r = [ v(2) s v(2) q ] , n\u0307(2) r = [ n\u0307(2) s n\u0307(2) q ] (8) According to Rodrigues\u2019 formula, vectors v(i) r and n\u0307(i) r are collinear for the principal directions and their relationship to the principal directions is given by n\u0307(i) r = \u2212\u03ba (i) I,IIv (i) r where \u03ba (i) I,II are the principal curvatures of surface i, i = 1, 2 [74]",
            " b44 \u23a4 \u23a5\u23a5\u23a6 \u23a7\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23a9 v(2) h v(2) f v(1) s v(1) q \u23ab\u23aa\u23aa\u23aa\u23aa\u23ac \u23aa\u23aa\u23aa\u23aa\u23ad = \u23a7\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23a9 \u2212(\u03c9(12) \u00b7 eh) \u2212 \u03baf (v(12) \u00b7 ef ) (\u03c9(12) \u00b7 ef ) \u2212 \u03bah(v(12) \u00b7 eh) \u2212(\u03c9(12) \u00b7 eq) \u2212 \u03bas(v(12) \u00b7 es) (\u03c9(12) \u00b7 es) \u2212 \u03baq(v(12) \u00b7 eq) \u23ab\u23aa\u23aa\u23aa\u23ac \u23aa\u23aa\u23aa\u23ad (9) where b11 = \u2212\u03baf + \u03bas cos2 \u03c3 + \u03baq sin2 \u03c3 , b12 = (\u03bas \u2212 \u03baq) cos \u03c3 sin \u03c3 , b22 = \u2212\u03bah + \u03bas sin2 \u03c3 + \u03baq cos2 \u03c3 , b33 = \u03bas \u2212 \u03baf cos2 \u03c3 \u2212 \u03bah sin2 \u03c3 b34 = (\u03baf \u2212 \u03bah) cos \u03c3 sin \u03c3 , b44 = \u03baq \u2212 \u03baf sin2 \u03c3 \u2212 \u03bah cos2 \u03c3 The solution of the matrix equation (9) yields the surface velocities in the principal directions. The surface velocities in the directions of contact line and in the direction that is normal to the contact line of surfaces 1 and 2, as shown in Fig. 2(d), are obtained by through coordinate transformations as{ V (1) p V (1) t } = [ cos q2 sin q2 \u2212 sin q2 cos q2 ] { v(1) s v(1) q } { V (2) p V (2) t } = [ cos q1 sin q1 \u2212 sin q1 cos q1 ] { v(2) f v(2) h } (10) JMBD48 \u00a9 IMechE 2007 Proc. IMechE Vol. 221 Part K: J. Multi-body Dynamics at OhioLink on October 30, 2014pik.sagepub.comDownloaded from where q1 and q2 are the angles defined in Fig. 2(d). Sliding and rolling velocities in the direction of the contact line are Vst = V (1) t \u2212 V (2) t and Vrt = V (1) t + V (2) t , respectively. Sliding and rolling velocities in the direction that is normal to the contact line are Vsp = V (1) p \u2212 V (2) p and Vrp = V (1) p + V (2) p , respectively. Finally, the resultant sliding and rolling velocities are given as Vstotal = [V 2 st + V 2 sp]1/2 and Vrtotal = [V 2 rt + V 2 rp]1/2, respectively. Normal curvatures in the direction of the contact line and in the direction that is normal to the contact line are given, respectively, as \u03ba(i) nc = \u03ba (i) I cos2 ( qi + \u03c0 2 ) + \u03ba (i) II sin2 ( qi + \u03c0 2 ) (11a) \u03ba(i) nn = \u03ba (i) I cos2 qi + \u03ba (i) II sin2 qi, i = 1, 2 (11b) Then the radii of curvature are simply the inverse of the corresponding normal curvature values in equation (11)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000648_978-3-642-17531-2-Figure7.11-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000648_978-3-642-17531-2-Figure7.11-1.png",
        "caption": "Fig. 7.11. Electrode variants for piezoelectric strip transducers: a) rectangular shape inducing bending moments, b) triangular shape inducing a point force at the electrode tip (pictures from (Preumont 2006))",
        "texts": [
            " an electric field along the polarization direction), the transverse effect induces a contraction ( 31 0e and 31 0d ), strip transducers also often called contractors. Unimorphs, bimorphs Strip transducers in the layout shown are commonly employed in laminated structures. The arrangement shown in Fig. 7.10 is termed a unimorph, as only one piezoelectric laminated layer is fused to the substrate. A bimorph consists of two active laminate layers, optionally separated by a substrate (only suggested in Fig. 7.10). Electrode shape Using a suitable electrode shape, the type and manner of force generation can be precisely selected. Fig. 7.11 shows two common variants. With a rectangular electrode geometry, an applied voltage induces mechanical bending moments at the electrode edges (Fig. 7.11a). With a triangular electrode geometry, a voltage induces a point force at the triangle tip (Fig. 7.11b). Note further that only the piezo material covered by the electrode area actively contributes to the force/moment. If the transducer is fixed at one end, the bending moments are absorbed by the support. 476 7 Functional Realization: Piezoelectric Transducer A more detailed mathematical description of strip transducers requires methods from continuum mechanics. These must however be excluded from the present work for reasons of space. The interested reader is referred to (Preumont 2006), (Kugi et al"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000050_nme.2959-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000050_nme.2959-Figure2-1.png",
        "caption": "Figure 2. Goldak double-ellipsoidal heat source.",
        "texts": [
            " The resulting highly non-linear system of equations is solved iteratively using a Newton\u2013Raphson method, with quadratic convergence to the solution. Copyright 2010 John Wiley & Sons, Ltd. Int. J. Numer. Meth. Engng 2011; 85:84\u2013106 DOI: 10.1002/nme This model proved to be more robust and accurate than two widely used effective capacitance models [23, 24] for problems with a narrow solidification range. In order to model the heat source, the three-dimensional double-ellipsoidal model moving along the welding path proposed by Goldak et al. [16] is used (Figure 2). One feature of the doubleellipsoidal model is that it can be easily changed to represent both the shallow penetration of arc welding processes and the deeper penetration of laser and electron beam processes. The heat flux distribution is assumed to be Gaussian along the longitudinal and transverse axes. The shape of the front half of the source is a quarter of one ellipsoidal source, whereas the rear half is that of the quarter of a different ellipsoidal source. Four parameters define each ellipsoid"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002084_j.ijplas.2015.09.007-Figure12-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002084_j.ijplas.2015.09.007-Figure12-1.png",
        "caption": "Figure 12. Distribution of the equivalent plastic strain in a NT45 specimen for different displacements to fracture: (a) mmu f 25.0= , and (b) mmu f 75.0= .",
        "texts": [
            " This point is located on the surface, near the gage section center for the SH specimens (See Fig. 10c). For the CH and NT specimens, this location (highlighted in Figs. 10a and 10b) typically corresponds to the intersection point of the specimen\u2019s axial plane of symmetry with the free curved boundary (outer radius of NT specimens, central hole boundary for all CH specimens). In NT specimens with high displacement to fracture, through thickness necking shifted the point of highest straining to the specimen center (Fig. 12). Except for the NT experiments with pronounced necking, the stress state remained more or less constant and the plane stress assumption held approximately true. Figure 13 shows the evolution of the equivalent plastic strain as a function of the applied displacement and the stress triaxiality for the NT, CH and SH experiments. A plot of the evolution of the Lode angle parameter is omitted due to its known dependence on the stress triaxiality under plane stress conditions. For tension with a central hole, the stress triaxiality is close to the theoretical value for uniaxial tension ( 33"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000600_j.mechmachtheory.2013.10.003-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000600_j.mechmachtheory.2013.10.003-Figure2-1.png",
        "caption": "Fig. 2. Deformation variables on the FS neutral curve (2D section).",
        "texts": [
            " Sf(Of; xf, yf, zf) and Sw(Ow; xw, yw, zw) are attached to the referred tooth on the FS at the engaged end and at the WG, respectively. xf is the symmetric line of the tooth, Of is the point on the neutral curve, xw is the major axis of the WG, and Ow is the rotational center of the WG. At the initial position, both xC and xf are coincident with xw. While xw is rotated to position \u03c6w relative to axis xC, in the anticlockwise direction, the coordinate system Sf(Of; xf, yf, zf) is moved to a new position as shown in Fig. 2. Here, \u03a6 is the rotational angle from xC to xf; \u03c6f is the angle from the radial vector of Of to xC; and \u03c6F and \u03c6 are the angles from the referred closed end of the FS to xC and xw, respectively. According to the kinematic theory of friction model for the HD, \u03c6w and \u03c6F satisfy \u03c6F \u00bc z2\u2212z1 z1 \u03c6w: \u00f04\u00de Here, z1 and z2 are the tooth numbers of the FS and the CS, respectively. The neutral curve equation in the polar coordinate system in Fig. 2 is expressed as follows: \u03c1 \u00bc rm \u00fe u: \u00f05\u00de Here, \u03c1 is the radial vector of the neutral curve of the deformed FS, and rm is the radius of the neutral curve of the FS before it is deformed. Similarly, the rotational angle displacement satisfies the following relationship: \u03c6 \u00bc \u03c6F \u00fe \u03c6w \u00bc z2 z1 \u03c6w \u00f06\u00de \u03c6 f \u00bc \u03c6F \u00fe \u03b8vz \u00bc \u03c6F \u00fe v \u03c1 \u00f07\u00de \u03a6 \u00bc \u03b8uz \u00fe \u03c6 f : \u00f08\u00de Here, u and v are the radial and circumferential displacements of Of, respectively. \u03c6uz and \u03c6vz are the rotational angles caused by radial and circumferential displacement, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003848_j.jmatprotec.2020.117032-Figure16-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003848_j.jmatprotec.2020.117032-Figure16-1.png",
        "caption": "Fig. 16. Two-sided hybrid part with tooth and carrier elements.",
        "texts": [
            " This shows, that regarding the current state of the art of commercially available AM machines, the presented process combination of AM and forming seems to be beneficial for small lot sizes in order to reduce invest in forming tools and machines. Regarding the results of this work, future investigations could include different tooth geometries for example for prototyping of gear components. A further development of hybrid parts is the additive manufacturing of structures on both sides of a metal sheet (Fig. 16). This offers the possibility to manufacture parts in three-dimensional design without support structure, which would be necessary in a fully additive manufacturing process using PBF-LB. The process chain in this case includes the AM process at two sides of the sheet metal. Therefore, distortion of the sheet metal, which results from the first AM process step, becomes relevant for PBF-LB of structures at the opposite side of the sheet metal. The results presented in this work show that a gear component can be manufactured in a process combination of PBF-LB/M and forming by deep drawing and upsetting"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001102_j.mechmachtheory.2015.09.005-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001102_j.mechmachtheory.2015.09.005-Figure9-1.png",
        "caption": "Fig. 9. Unit loads perpendicular to the tooth surface for a spur gear for multiple lines of contact (2D view).",
        "texts": [
            " The geometry of gear teeth is quite complex, therefore, the usage of numerical methods to study the load distribution along the path of contact is viewed as a possibility. In this second approach the dynamic effects will be disregarded, it will also be assumed that the deformation of the teeth is so small that the geometry of the teeth is the same in spite of the elastic deformation. The torque (Mw) that is transmitted by the driven gear is assumed constant. Several unit forces are distributed over the tooth flank in such a way that at the contact lines these unit forces are in the plane of action and perpendicular to the tooth surface, (Fig. 9). Taking advantage of finite element codes it is possible to obtain the displacements in the points of interest when the unit loads are applied. This process should be repeated for the driven and driving gears in order to obtain the displacement fields. In order to obtain the displacement matrix in the direction of interest the vector formed by the components of the displacement that are given by the FEM code must be projected in a direction perpendicular to the tooth surface, which is the dot product between the displacement vector and the correspondent unit force vector"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003887_j.etran.2020.100080-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003887_j.etran.2020.100080-Figure5-1.png",
        "caption": "Fig. 5. Configuration of SynRM and PMASynRM rotor [116].",
        "texts": [
            " To conclude, due to the low residual flux density of ferrite materials and the large magnetic airgap length of SPM machine, SPM ferrite machines are not likely to fulfil the requirements of high torque density and efficiency for high performance automotive traction applications. This explains why ferrite machines for high performance applications are invariably designed with the IPM configuration, which provides flux enhancing effects [22e25]. PMASynRMs are derived directly from SynRMs, as illustrated in Fig. 5. By adding proper amount of PMmaterials into flux barriers in the SynRM rotor lamination, the torque density, power factor and efficiency of the PMASynRM can be improved, which makes it a potential solution for ferrite IPM design [47e49]. E. Armando in Ref. [50] also pointed out that with even a small amount of PM, not only the torque output but also the constant power speed range could be improved greatly compared with SynRM design for washing machines. However it is not always the case that more PM results in higher torque"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001449_s10846-013-9955-y-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001449_s10846-013-9955-y-Figure1-1.png",
        "caption": "Fig. 1 Pure pitching motion",
        "texts": [
            " In order to obtain the airplane model equations, by omitting any flexible structure of the UAV, the fixed-wing UAV is then considered as a rigid body. Also we do not consider the curvature of the Earth, it is considered as a plane, because we assume that the UAV will only fly short distances. With the previous considerations, we can obtain the model by applying the Newton\u2019s laws of motion. 2.1 Longitudinal Dynamics The parameters involved in the longitudinal dynamic model (1)\u2013(5) are shown in Fig. 1. These parameters allow to analyzing the movement toward the front of an airplane [12], particularly the altitude control. V\u0307 = 1 m (\u2212D + T cos\u03b1 \u2212 mg sin \u03b3 ) (1) \u03b3\u0307 = 1 mV (L + T sin \u03b1 \u2212 mg sin \u03b3 ) (2) \u03b8\u0307 = q (3) q\u0307 = M Iyy (4) h\u0307 = V sin \u03b8 (5) where V is the magnitude of the airplane speed, \u03b1 describes the angle of attack, \u03b3 represents the flight-path angle and \u03b8 denotes the pitch angle. In addition, q is the pitch angular rate (with respect to the y-axis of the aircraft body), T denotes the force of engine thrust, h is the airplane altitude [12], and \u03b4e represents the elevator deviation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002838_978-3-319-54169-3-Figure2.5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002838_978-3-319-54169-3-Figure2.5-1.png",
        "caption": "Fig. 2.5 Analogy by a wheel climbing a ramp: a a motor with no resistive torque, b a motor with resistive torque (Goncalves et al. 2014)",
        "texts": [
            " Let us consider a motor mounted on a rigid base. Motion of the cart is eliminated (x\u0308 = 0) and according to (2.40) the mathematical model is ( J + m2d 2 ) \u03d5\u0308 = M0 ( 1 \u2212 \u03d5\u0307 0 ) . (2.41) The physical model which corresponds to (2.41) is a wheel climbing on a ramp. The slope of the ramp is related to the motor inertia defining the rate of the angular velocity. For a motor with no resistive torque when M = M0, the angular acceleration is constant and therefore, the angular velocity of the wheel increases by a constant rate (see Fig. 2.5a). The motor torque should be switched off as the desired angular velocity 0 is achieved. When considering the motor with resistive torque, the angular acceleration is no longer constant and decreases as the angular velocity increases. The system shown in 2.1 Simple Degree of Freedom Oscillator Coupled with a Non-ideal \u2026 19 Fig. 2.5b is used to represent the motor with resistive torque where it is more difficult to reach the energy level 0. The rate of velocity changing is no longer linear. When the motor is mounted on a flexible base, its motion is described with Eq. (2.40). It is clear that the angular acceleration is also a function of the cart motion x .Besides, themotion of the cart is a function of the acceleration and angular velocity of the motor (2.7). In Fig. 2.6 a system which is analog with the motor mounted on a flexible base is represented. Similar to Fig. 2.5a, wheel must climb a ramp to reach the level of energy defined by 0. In this case the ramp path is modified by the cart resonance frequency \u03c90. The resonance frequency is represented by the valley in the ramp path. The deep and the width of the valley in the ramp are related to the amplitude of the motion of the cart and in some cases the wheel can get stuck inside the valley in the ramp path. Numerical simulation is done for frequencies around the cart resonance frequency \u03c90. Figure2.7 shows that when 0 is slightly bigger than\u03c90 the angular velocity does not increase"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003810_j.addma.2020.101251-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003810_j.addma.2020.101251-Figure5-1.png",
        "caption": "Fig. 5. Denominations of specimen type depending on specimen orientations with respect to build direction Z. Please remember that each specimen can be tested in two ways according to the scheme of Fig. 4).",
        "texts": [
            " While the presence of the correction coefficient Cmg may be considered a weakness of the test method, it is counterbalanced by the many benefits of specimen miniaturization. On the other hand, when the specimen in the loading apparatus of Fig. 3 (bottom) is flipped vertically, the stress distribution due to the applied bending loading M is presented in Fig. 4 (bottom). The peak tensile stress occurs at the notch root and its value can be used to compute the stress concentration factor Kt of the miniature specimen geometry as follows: Kt = \u03c3max,FE /(M/W) = 1.63, where \u03c3max,FE is the maximum principal stress computed by elastic finite element analysis. Fig. 5 shows four orientations of the mini specimen on the build plate that were used in this experimental campaign and their respective denominations. Eight sets of miniature specimens of L-PBF AlSi10Mg were fabricated in a single build (i.e. about 90 miniature specimens), removed by wire cutting from the build plate and tested without any post-processing. Four sets were aimed at smooth fatigue characterization, with miniature specimens tested as specified in Fig. 4 (top). Four other sets were aimed at notched fatigue characterization therefore miniature specimens were tested as specified in Fig",
            " On the other hand, the flat surface of Type A + specimen is obtained when separating the specimen from the build plate by wire cutting. The applied stress direction Type A + and Type A- specimens is parallel to the build layers similarly to Type B specimens. When considering the four specimen sets for notched fatigue testing, the quality of curved surfaces depends on local orientation with respect to the build direction and the local surface curvature. The different sets of miniature specimen produced and tested for this work, see Fig. 5, allow the investigation of the influence of aspect such as i) as-built surface roughness and ii) quality of an as-built curved geometry on the fatigue behavior of L-PBF AlSi10Mg. The quality of the semicircular notch significantly differs among specimens. Especially relevant in fatigue is the quality of the notch root because it is the location where fatigue cracks initiate. The notch geometry of Type B is accurately semicircular because obtained by laser contouring, layer upon layer. The notches of Type A + and Type A- specimens are instead influenced by features of the PBF technology, namely: i) stair stepping and ii) surface orientation with respect to build direction",
            " Since stair stepping is position\u2013dependent along a curved surface, [36], while fatigue crack initiation occurs always at the notch root, stair stepping can be severe or mild or absent. This section presents initially the smooth fatigue test results and then the notched fatigue test results of the as-built L-PBF AlSi10Mg with as-built surfaces. In this section the term directional is attributed to the fatigue behavior determined with the miniature specimens because the specimen orientation during fabrication shown in Fig. 5 is expected to significantly affect the measured fatigue behavior. So differences in fatigue response among different specimen sets will not be generically attributed to material scatter rather it is discussed keeping in mind the peculiar surface quality associated to the specific fabrication direction. The fatigue data of the four types of miniature specimens tested as shown in Fig. 4 (top) are shown in Fig. 6. They are plotted as maximum local stress \u03c3max (including the coefficient Cmg) vs. cycles to failure Nf where failure was defined by the 10% drop of the initial value of the applied load due to fatigue crack initiation",
            " Surface roughness associated to the L-PBF processing of metal parts is considerably higher than after conventional milling or grinding, [26]. The quality of as-built PBF surfaces is typically quantified on the base of roughness measurements with the standard instrumentation. Average roughness, i.e. Ra, is found to range from Ra = 4 to 20 \u03bcm. The surface roughness depends on melting energy, powder particle size distribution, layer thickness, [1,2,36]. Therefore, the flat surfaces of the miniature specimens of Fig. 5 have different qualities as they are obtained in a different way. Measurements recently obtained with a Taylor Hobson Talysurf CCI optical profiler with 50\u00d7 objective quantified limited differences among specimens. The minimum average roughness was Sa = 2.31 \u03bcm for the top layer of Type A- specimen. A maximum value of Sa = 7.4 \u03bcm for the flat surface of Type A + specimen was the result of specimen separation from the build plate by wire cutting. An average roughness of 4.5 \u03bcm was determined on flat surfaces of Type B and Type C specimens",
            " Fig. 14 shows fatigue data for the vertical specimens with as-built surfaces and the machined and polished, horizontal specimens plotted in terms of stress amplitude vs. cycles to failure. Surface polishing enhanced the fatigue strength but the degree of improvement was inconsistent, [18]. In addition, data scatter was more significant in the polished specimens and it was attributed to defects in the bulk of the material. On the other hand, fatigue data obtained with the miniature specimens of Fig. 5 under cyclic bending and a stress ratio R = 0 require a conversion to be plotted in the diagram of Fig. 14 where stress amplitude is for R=-1. The equivalent stress amplitude at R=-1 \u03c3a,R=-1 is readily determined from stress amplitude at R = 0, \u03c3a,R=0, using the Haigh linear formula defined as \u03c3a,R=-1 = \u03c3a,R=0 /(1\u2212\u03c3m,R=0)/Rm (2) where \u03c3a,R=0 = \u03c3m,R=0 = 0.5 \u03c3max,R=0 and ultimate strength Rm = 440 MPa. Fig. 14 shows the good correlation of the converted Type C specimen data (i.e. long axis parallel to build) and Mower\u2019s data when surfaces were in the as-built state"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001842_s00170-015-7647-4-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001842_s00170-015-7647-4-Figure3-1.png",
        "caption": "Fig. 3 Quarter piece of a mandrel with cooling channels through the die bridges [5]",
        "texts": [
            " (2012) investigated the use of press-hardening tools with conformal cooling channels which are manufactured by selective laser melting [15]. Also, deep drawing dies are manufactured in the same way. Here, inner channels for lubrication are implemented. The lubricant exits the ring in the channels and is distributed homogenously in the area of the flange and the draw ring. The authors of the present work have introduced dies manufactured by selective laser melting for hot aluminum extrusion applications (Fig. 3) [7]. Due to the design of the extrusion press and the die holder, a supply of the coolant is only possible from the exit face of the die. Due to this, the cooling channels follow the bridges and have to pass quite a long way. The manufacturing by laser melting provides the possibility to integrate multidirectional channels for supplying a coolant and to integrate thermocouples for temperature measurement into hot extrusion dies. By applying the cooling close to the main forming zone and close to the die bearings, a significant reduction of the temperature of the die as well as the profile is possible and thermally induced surface defects on the profile can be avoided"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001756_tmech.2015.2453122-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001756_tmech.2015.2453122-Figure5-1.png",
        "caption": "Figure 5. Schematic view of the catheter with the force angle.",
        "texts": [
            " We use the catheter tip pose for the estimation of the contact force following the procedure mentioned above. To demonstrate that the proposed method is able to converge to a unique solution under medical conditions, the initial curvatures and contact forces experienced by the catheter in an ablation procedure have been selected. The magnitudes of the forces are considered to be 0.15, 0.25 and 0.35 N, thereby simulating the range of contact forces used in intra-cardiac ablation [1], [23]. The direction of the applied forces, which is characterized by the angle \u03b1, spans 180 degrees, as shown in Fig. 5. Figures 6, 7 and 8 show the estimated force versus the real external force applied at the tip of the catheter for initial curvatures of the distal shaft of 0.01, 0.02 and 0.03 mm-1, respectively. For all of the simulations shown in Fig. 6, values of zero have been selected as the initial guess of the rootfinding algorithm for the estimated forces in both directions. As depicted in this figure, the algorithm is able to accurately estimate the applied forces in the x and y directions. These results imply the one-to-one relation between the tip pose and the estimated forces using the proposed approach for the practical range of the ablation procedure"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002285_978-3-319-72526-0_9-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002285_978-3-319-72526-0_9-Figure1-1.png",
        "caption": "Fig. 1 SLM fabricated functionally graded Inconel 718 using a variation of 250 and 950 W laser sources",
        "texts": [
            " The effect of heat treatment on microstructure and high temperature mechanical behaviour is also evaluated and compared with conventional wrought Inconel 718. For manufacturing of the SLM specimens, (see Table 1 for process parameters) an SLM 280HL facility (SML Solutions Group AG, Germany) featuring two YLR-lasers with a wavelength of 1070 nm and a maximum output power of 400 and 1000 W was employed. Laser power of 250 and 950 W was used to produce different areas within functionally graded cylindrical rods of 140 mm \u00d7 \u00d8 14 mm (Fig. 1), further referred as FGM samples. The Z-axis was defined parallel to the building direction, whereas each layer was deposited parallel to the XY-plane with the laser scanning at 45\u00b0 between X and Y. Post heat treatment was applied to examine the effect on microstructure and mechanical properties of Inconel 718 with tailored microstructure. The samples were investigated under \u201cas-processed\u201d and \u201cheat treated (HT)\u201d conditions, complying with AMS 5664E requirements [11] (see Table 2 for heat treatment details)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002202_1.4894855-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002202_1.4894855-Figure5-1.png",
        "caption": "FIG. 5. Fluid velocity field and streamlines in body frame of the swimmer model with beating pattern (A). Snapshots are taken at t = 0.5\u03c0 and 1.5\u03c0 for (a) synchronized beating \u03c6 = 0, (b) antiplectic wave \u03c6 = 0.2\u03c0 , and (c) symplectic wave \u03c6 = \u22120.2\u03c0 . Total number of cilia is N = 80.",
        "texts": [
            " The doubly infinite ciliary field is approximated using 18 copies of the computational domain (9 on each side) in each direction. More details on the convergence properties of this computation can be found in Ding et al.26 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 129.21.35.191 On: Fri, 19 Dec 2014 13:51:09 The fluid velocity fields generated by the ciliated cylinder with beating pattern (A) are shown in Fig. 5 for three types of metachronal coordination: (a) all the cilia beat in a synchronized way ( \u03c6 = 0); (b) the collective ciliary beat generates an antiplectic metachronal wave ( \u03c6 = 0.2\u03c0 ); (c) the collective ciliary beat generates a symplectic metachronal wave ( \u03c6 = \u22120.2\u03c0 ). When the cilia beat in synchrony, they generate a relatively large flow field during their effective stroke but the flow is reversed during the recovery stroke. When the cilia beat in metachrony, the magnitude of the fluid velocity field at any time is relatively smaller than that produced by the synchronized cilia but the flow field is characterized by vortex-like structures generated by the metachronal wave",
            " In Taylor swimming sheet, the average swimming velocity scales inversely proportional to the wavelength. Here, the wavelength is equal to the distance between two neighboring cilia divided by the phase difference \u03c6 and times 2\u03c0 .26 For convenience, we examine how the performance of the swimming and pumping systems depends on the phase difference \u03c6. Fig. 6 compares the swimming velocity U (ciliated cylinder) and pumping flow rate Q (ciliated carpet) for the three cases \u03c6 = 0, 0.2\u03c0 , and \u22120.2\u03c0 depicted in Fig. 5. In each case and in the context of each model, we compare cilia patterns (A) and (B). Clearly, the maximum values of U and Q occur for \u03c6 = 0 (Fig. 6(a)), however the average speed \u3008U\u3009 and average flow rate \u3008Q\u3009 are substantially increased when \u03c6 = 0.2\u03c0 and somewhat decreased when \u03c6 = \u22120.2\u03c0 (Fig. 6(b)), suggesting the existence of optimal metachronal waves that maximize swimming and pumping. We examine the dependence of the average swimming speed (ciliated cylinder) and average flow rate (ciliated carpet) over one cycle on all phase differences \u03c6 from \u2212\u03c0 to \u03c0 , for the two cilia patterns (A) and (B), see Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003686_tie.2019.2959504-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003686_tie.2019.2959504-Figure5-1.png",
        "caption": "Fig. 5. Open-circuit flux distribution of 12-stator-pole/10-rotor-tooth DF-FSPM machine and definition of dq-axes of stator-armature machine part. (a) Open-circuit flux distribution, rotor position = 9 mech. deg. (b) Dq-axes of stator-armature machine part.",
        "texts": [
            " The electrical angular distance between two adjacent stator coils can be calculated as follows: 360es r sN N  (3) On the other hand, the electrical angular distance between two adjacent rotor coils can be calculated by  360 2er s rN N  (4) It is worth noting that when the rotor rotates anticlockwise, the back-EMF of a stator coil leads its anticlockwise adjacent coil by \u03b1es. However, since the stator rotates clockwise with respect to the rotor, the back-EMF of a rotor coil delays its anticlockwise adjacent coil by \u03b1er. The d- and q-axes of the stator-armature machine part can be defined in terms of the stator flux linkage characteristic. As shown in Fig. 5(a), positive maximum stator flux linkage is obtained when the angle between the midline of rotor tooth (red arrow) and stator coil axis (blue arrow) is 9 mech. deg. Hence, the d-axis of the stator-armature machine part is 9 mech. deg. shifted from the midline of rotor tooth, as shown in Fig. 5(b). The q-axis leads the d-axis by 90 elec. deg. (viz. 9 mech. deg.), which coincides with the midline of rotor tooth. The d- and q-axes of the rotor-armature machine part can be defined in a similar way. As shown in Fig. 6(a), positive maximum rotor flux linkages are obtained when the rotor coil axis (red arrow) aligns to the midline of stator slot (blue arrow). Therefore, the midline of stator slot is defined as the d-axis of the rotor-armature machine part, as shown in Fig. 6(b). The q-axis leads the d-axis by 90 elec"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002139_b978-0-08-100433-3.00004-x-Figure4.1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002139_b978-0-08-100433-3.00004-x-Figure4.1-1.png",
        "caption": "Figure 4.1 Computer-assisted design model (shaded) and associated stereolithographic representation (wireframe facets). This model of a low-volume prototype cover indicates visible (A-class) and non-visible (B-class) surfaces, which inherently have different surface roughness objectives.",
        "texts": [
            "4): \u2022 A surgical implant, whereby an orientation map of average roughness is presented for feasible orientations to identify the optimal implant orientation for surgical objectives \u2022 Low-volume prototype cover, whereby a custom roughness weighting is applied to discourage facets with high roughness from occurring on visible surfaces \u2022 Hydraulic valve assembly, whereby surfaces of relevance to functional objectives are assessed to enable robust identification of optimal build orientation AM is defined by the ASTM [16] as the \u2018process of joining materials to make objects from 3Dmodel data, usually layer upon layer, as opposed to subtractive manufacturing methodologies, such as traditional machining\u2019. AM begins with a computer-assisted design (CAD) representation of the intended component geometry. This data are then converted to stereolithographic (STL) format to be compatible with AM processes (Fig. 4.1). The STL format represents the CAD data with a discrete number of triangular facets and their associated surface norms (Table 4.1). The STL representation is processed as required to provide specific tool path and processing instructions for the specific AM method [17,18]. AM processes can be characterised according to the method by which support is provided, the resolution of the manufactured geometry to the intended geometry, and the relevant processing parameters of manufacture [18e20]. Of the AM processes of commercial interest, SLM is extremely important because it allows the manufacture of large-scale functional components with engineering-grade metals with high complexity and a relatively low unit cost [21]",
            " Geometric error refers to a discrepancy between the CAD representation of the intended product and the geometry of the actual manufactured product. Geometric error in AM can be attributed to either error in the STL representation of the CAD geometry or error in the AM manufacture of the STL representation (Fig. 4.2). Because of the discrete nature of the STL format, error may occur in the representation of the original CAD data. If the original CAD data are prismatic, the discrete facets of the STL represent the CAD data without error (Fig. 4.1). If the original CAD data are curvilinear, the STL representation of the original CAD data includes some approximation error (Fig. 4.2); this error diminishes with an increasing number of facets [6]. It is desirable to minimise the number of facets to reduce computational demands; if possible, however, the number of facets should be sufficiently high that the associated STL representation error is negligibly small. AM involves the successive addition of material to manufacture an intended geometry"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001765_tcyb.2015.2509863-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001765_tcyb.2015.2509863-Figure3-1.png",
        "caption": "Fig. 3. Furuta pendulum built at the Instituto Polit\u00e9cnico Nacional, CITEDI.",
        "texts": [
            " The experimental setup is briefly described, and the controllers used in the comparison are introduced. Then, details of the experiments are given, and the results of the real-time implementation are shown and discussed; the performance comparison is conducted considering the maximum error, the root mean square (RMS) value of the tracking error e(t), and the RMS value of the applied torque \u03c4(t). The experimental tests have been performed using a Furuta pendulum built at the Instituto Polit\u00e9cnico Nacional, CITEDI, as shown in Fig. 3. The experimental platform consists of a PC with MATLAB/simulink and real-time windows target toolbox software, a sensoray 626 data acquisition board, and a model 30A20AC servoamplifier manufactured by advanced motion controls, a servomotor used as an actuator to directly apply torque to the arm, and two optical incremental encoders that sense the relative angular position of each joint. The joint velocities are estimated using the following algorithm: q\u0307(kT) = q(kT) \u2212 q((k \u2212 1)T) T (72) where T = 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000898_j.mechmachtheory.2011.08.010-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000898_j.mechmachtheory.2011.08.010-Figure8-1.png",
        "caption": "Fig. 8. Distribution of contact forces in case of M=300 kNm and irregular geometry of outer raceways as defined by 2 waves and different clearances.",
        "texts": [
            " This can be seen by comparing the contact forces and the contact pressures for these cases in Table 2 and by comparing Figs. 6b, 7a and b. Such results are expected, since this kind of irregular geometry somehow follows the \u201cshape\u201d of the contact load distribution in case of a bearing with a clearance. This means that there are no sudden changes in geometry, which would cause local increases of contact loads. The influence of the irregular geometry of the outer raceways, as defined by 2 sine waves and the influence of the amplitude of the deformation, can be seen in Fig. 8a and b. The load distributions on these figures show that such deformation generates so called \u201chard spots\u201d. These are spots along the raceway where local deformations of rings cause large contact loads. This happens because sudden changes in geometry can lead to cases when only few rolling elements are able to take over external bearing loads. This means that these rolling elements are exposed to significantly higher contact loads than the rest of the rolling elements. As it can be seen from the results presented in Table 2, the deformation with 2 sine waves and an amplitude of 0"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001918_j.precisioneng.2017.05.014-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001918_j.precisioneng.2017.05.014-Figure2-1.png",
        "caption": "Fig. 2. A schematic description of the mathematical model.",
        "texts": [
            " This mesh is eferred to as a data surface mesh in this paper. Every triangular element is defined by three nodes. The first step is to obtain the nominal vector from a node from the reference surface mesh to the data surface mesh. Fig. 1 shows three nodes (A, B and C) defining an element from the data surface mesh, and Node P, which is an arbitrary node from the reference surface mesh. The main task is to identify the element from the data surface mesh which the projection of Node P (denoted Node O in Fig. 2) belongs to, in order to invert the coordinates of Node P in the opposite direction of the Plane \u02db. The position of Node P is checked relative to all elements of the data surface mesh using a search algorithm. The mathematical model for defining the distance from a point to a plane is determined by Fig. 2. Knowing the coordinates of nodes A, B, C and P from the reference and data surface meshes, the direction vectors \u2192 AB, \u2192 AC and \u2192 AP can be given by: \u2192 AB = (B(x) \u2212 A(x))i + (B(y) \u2212 A(y))j + (B(z) \u2212 A(z))k (1) \u2192 AC = (C(x) \u2212 A(x))i + (C(y) \u2212 A(y))j + (C(z) \u2212 A(z))k (2) \u2192 AP = (P(x) \u2212 A(x))i + (P(y) \u2212 A(y))j + (P(z) \u2212 A(z))k (3) or in abbreviated forms: precision additive manufacturing through compensation. Precis \u2192 AB = a1i + a2j + a3k (4) \u2192 AC = b1i + b2j + b3k (5) ING Model P Engine A u \u2192 o \u2192 \u2192 w | \u2192 v d t a t t S t c l n w d d n w t ( ARTICLERE-6587; No"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000811_j.matdes.2012.12.062-Figure6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000811_j.matdes.2012.12.062-Figure6-1.png",
        "caption": "Fig. 6. (a) CAD model of Batch 1 tensile samples and (b) tensile properties of Batch-1 as-deposited samples as a function of deposition direction.",
        "texts": [
            " However, the cooling rate during the HIPping cycle was slow (5 C/min), which led to the precipitation of the carbide particles along the grain boundaries and their coarsening as well (shown by arrows in Fig. 5b). Both conditions were examined using X-ray diffraction, which confirmed the presence of martensite, ferrite and the Fe and Cr-rich carbide M23C6. Two sets of SC420 samples were fabricated to assess the mechanical properties development. The effect of the build size, deposition direction (horizontal or vertical), and of the post-fabrication HIPping on the mechanical properties of SC420 was assessed. In Batch-1 the sample size was small 13 13 70 mm (vertical) and 13 70 13 mm (horizontal), Fig. 6a. Each build was used to prepare a single tensile sample. For each of the horizontal and vertical conditions 3 samples were fabricated; no post heat treatment was performed on these samples. As the volumes of the vertical and the horizontal samples were the same, the differences in mechanical properties can be attributed to the different deposition direction. In the vertical sample, each layer took only 30 s to deposit, whereas in the horizontal sample each layer took 200 s to deposit, which suggests that the thermal history between the layers was different",
            " It appears that the vertical samples generally retained the heat throughout the build (via a heat sinking effect by the substrate), which annealed the sample during the deposition, leading to an elongation of 13%, which compares with a reported elongation of 15% in a forged grade of 420 martensitic stainless steel in the annealed condition compared, and only 8% in the tempered condition [2]. Conversely, during horizontal deposition, deposition of each layer took a considerably longer time, which led to the dissipation of the heat. This resulted in poor elongation of 2\u20134% only. The yield strength and tensile strength were similar irrespective of the deposition direction (Fig. 6b). This result is in contrast with the literature data that suggested that the tensile strength and yield strength were reported to be lower after annealing [2], as it does not seem that the annealing effect in the vertical builds resulted in poorer strength. In Batch-2 the build size was 25 35 70 mm and 70 35 30 mm for the vertical and horizontal samples, respectively. From each build (Fig. 7) 6 samples were extracted using Electro Discharge Machining (EDM); among these, 3 samples were tested in the asdeposited condition and 3 samples were HIPped"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002000_s11663-014-0183-z-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002000_s11663-014-0183-z-Figure9-1.png",
        "caption": "Fig. 9\u2014Plot showing dependence of the PDAS on the temperature gradient and solidification velocity and the polynomial fit obtained for the plotted data.",
        "texts": [
            " A similar relationship can be developed for low Pe\u0301clet numbers and can be written as[26] w \u00bc 6\u00f0DT0kDC\u00de0:25V 0:25G 0:5 1 DG VDT0k 0:5 : \u00bd11 In the above models, the PDAS essentially follows the proportional relation as given by Eq. [1]. However, it has been established that these models cannot provide a precise prediction for the PDAS and are only useful in obtaining a qualitative estimate for the PDAS.[27] The result of the statistical data fitting for the PDAS conducted in the current study is shown in Figure 9. For the plot shown, the R-squared value, describing the goodness of fit, is 0.72. The coefficient \u2018a\u2019 is found to be 0.00039 with 95 pct confidence bounds at (0.00038, 0.00040). METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 45B, DECEMBER 2014\u20142285 The proportional relation between the PDAS, the temperature gradient, and the solidification velocity is thus experimentally verified. Our model based on the raster scan pattern utilized in SLE and the line heat source assumption adopted for the simulation results in the same form of the growth relation as that developed for marginal stability under constrained growth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000751_tmech.2012.2209673-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000751_tmech.2012.2209673-Figure5-1.png",
        "caption": "Fig. 5. Different types of complex end-effector motion used to evaluate the parameter estimation in Section IV-B5. (a) \u201cPull.\u201d (b) \u201cGradual Tangent Pull.\u201d (c) \u201cTwist and Pull.\u201d",
        "texts": [
            " Noise from the control signal appears not to cause a significant effect on the parameter estimation if the noise level is not extremely high. 5) Parameter Estimation Under Complex Motions: The merit of this multiaxial estimation framework over uniaxial estimation is the ability to estimate the tissue parameters under BOONVISUT AND C\u0327AVUS\u0327OG\u0306LU: ESTIMATION OF SOFT TISSUE MECHANICAL PARAMETERS FROM ROBOTIC MANIPULATION DATA 1607 complex surgical manipulations. This set of simulations was conducted to evaluate the effectiveness of the method when the robot had nontrivial motions during a surgical manipulation. Fig. 5 shows the two more different motions used in the simulations. In the first test motion, the gripper horizontally pulled the tissue by simultaneously rotating the gripper. And in the second case, the gripper pulled the tissue horizontally in the tissue plane while rotating the tissue to twist it. The results in Table V show that the method can still estimate the parameters with good accuracy under such complex motions. In order to validate the proposed method, hardware experiments were conducted",
            " The tissue phantoms used in the experiments were similar in shape and size to the models used in the simulation studies described in Section IV-A. Specifically, the tissue phantoms were square in shape, with dimensions of 10 cm \u00d7 10 cm \u00d7 1 cm. The tissue phantoms were placed horizontally while being grabbed and retracted by a gripper toward right. We considered two cases where the phantoms were anchored to a wall on one side (left) and two adjacent sides (left and back). The retraction actions were achieved by moving the gripper in 1\u20132 mm increments, toward right, producing about 10% elongation of the tissue phantom as shown in Fig. 5. The \u201cPull\u201d trajectory was performed in 10 steps with 2 mm increments; the \u201cGradual Tangent Pull\u201d trajectory was performed in 20 steps with \u223c1 mm increments; and the \u201cTwist and Pull\u201d trajectory was performed in 10 steps with \u223c2 mm increments. Sixteen artificial fiducials were marked on the top surface of the tissue and were tracked by a calibrated stereo camera pair to measure their deformations during retraction. The silicone surface was labeled with rubber beads 1 mm in diameter which were used as the fiducials"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002084_j.ijplas.2015.09.007-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002084_j.ijplas.2015.09.007-Figure5-1.png",
        "caption": "Figure 5. (a) Schematic of the V-bending device, (b) view of the punch testing device; max. principal strain field measured through stereo DIC in (c) a V-bending experiment and (d) in a punch test.",
        "texts": [
            "05mm/min is used for the shear (SH) specimen to achieve a comparable equivalent plastic strain rate ( 1210 \u2212\u2212\u2245 sp\u03b5& ) in all experiments. In the case of the SH experiments, two cameras are used to observe the surface displacement fields at two different magnifications: the field of view of a first camera includes the whole specimen to compute the overall displacement with a 25mm-long extensometer (distance between blue dots on Fig. 4d); the second camera is positioned closer to the specimen to measure the strain in the shear gage sections. V-bending experiments are performed to characterize the plane strain fracture response. Figure 5a shows a newly developed V-bending device by Roth and Mohr (2015). It features a support point spacing of 3.8 mm and makes use of a sharp central punch with a tip radius of less than 0.4 mm. The particular feature of the loading device is that the punch (part \u2460) remains stationary while the outer support rollers (parts \u2461) move downwards. This set-up has the advantage (over conventional moving punch set-ups) that the surface strains can be accurately measured through stereo digital image correlation",
            " The digital image correlation software VIC3D is used to compute the surface strains in the area above the punch. The random speckle pattern featured an average speckle size of 8 pixels. After verifying that plane strain conditions prevail on the specimen surface M ANUSCRIP T ACCEPTE D )( rz \u03b5\u03b5 << , the logarithmic axial strain f r\u03b5 at the instant of crack formation is reported as the main experimental result. The onset of fracture is identified either through a 30N drop in force or the appearance of macroscopic surface cracks (visible by eye). The miniature punch testing device shown in Fig. 5c is used to subject a 60mm diameter disc specimen (Fig. 4f) to equi-biaxial tension. The specimen is positioned onto a female die with a 25.4 mm inner diameter and held in place through a clamping ring (part \u2460) with eight M6 screws. In order to reduce friction during the punch test six 0.08 mm thick Teflon sheets are put between the punch (part \u2461) and the specimen. As for the V-bending experiment, the punch is kept stationary while the die moves downwards at a speed of 2.0 mm/min. Stereo digital image correlation is used to determine the surface strains"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003923_tvt.2020.2974019-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003923_tvt.2020.2974019-Figure2-1.png",
        "caption": "FIGURE 2. (a) Exploded view of CVS headset. (b) Schematic showing the principal elements of the earpiece.",
        "texts": [
            " 1) is easily operated and consists of a headset, fashioned like music headphones, with aluminum earpieces to conduct heat and a control unit that powers the device and allows for patients to start treatments. The temperature in each ear insert is separately controlled allowing for a wide variety of time-varying waveforms. However, the device has fail-safe and patient-lockout protections, so the patient can only activate the neuromodulation protocols and number of daily treatments prescribed on the SD cards inserted into the control unit. The CVS device is based on a Peltier unit, an array of diodes comprised of n-type/p-type semiconductor junctions comprised of bismuth telluride (see Fig. 2). The Peltier module used in the CVS device is composed of an array of diodes in a cast epoxy cube to reduce susceptibility to shear stress (TE Technology, Traverse City, MI). When direct current is passed in one direction through the array, one side heats up with respect to the other. Reversing the direction of current flow also reverses the temperature gradient across the array. A pulse-width-modulation algorithm is used to power the Peltier devices so that the actual temperature, as measured by a thermistor in the earpiece, matches the waveform target temperature. The anodized, aluminum earpiece is attached to one side of the Peltier array and an aluminum heat sink is attached to the other. The Peltier device mates to the heat sink via a solid aluminum standoff. Fig. 2b shows an enlarged view of the connections to the Peltier device as well as the location of a thermistor temperature sensor, which is used in the control circuit that sets the temperature of the earpiece. The groove in the ear insert is designed to allow for pressure equalization within the ear canal. The earpiece is covered on its lower base by an ethylene-vinyl copolymer skirt that works to thermally insulate the earpiece from the outer portions of the ear canal and concha. Fig. 3 shows a thermograph of the components in fig. 2b. The thermistor in each earpiece samples the temperature at the tip at a rate of 4 Hz. The thermistor provides feedback to the control circuit that sets the temperature of the earpiece. The heating and cooling systems are deactivated if either thermistor detects temperatures 1 \u25e6C below or above the minimum and maximum temperatures defined by the thermal waveforms, respectively, or if a thermistor fails. The temperature control circuit accesses a temperature calibration file matched to a specific thermistor whenever the system is powered on"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001079_j.procir.2014.06.151-Figure9-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001079_j.procir.2014.06.151-Figure9-1.png",
        "caption": "Fig. 9: Notch geometry",
        "texts": [
            " These disorientation areas have appeared during the bulge formation during the cladding. Within the bulky area the heat propagation is changing and consequently there are deviations regarding the appropriate value and orientation of the thermal gradient. To overcome such defects the input of the inductive heating and also the local cooling must be adjusted to reestablish the former gradient for SX gladding in these areas. In order to clad cracks on blades, feasible notch geometries have to be determined. In Fig. 9, the used notch geometry is shown. Tests have been used to evaluate the interaction grades between notch geometry, induction system and powder supply. Table 2 shows the used parameter for the initial test. These parameters were the result of the previous experiment for the single crystal tip cladding. Preheating was set to 650\u00b0C to form the required thermal gradient inside the notch. The required preheat temperature was calculated before to fit for The microstructure of N1 approximates to the single crystal solidification even in the cross section, but there are cracks and pores in it"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001115_j.wear.2015.01.047-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001115_j.wear.2015.01.047-Figure8-1.png",
        "caption": "Fig. 8. Rolling friction due to micro-slip in pure rolling motion. (a) Front view of the rolling contact, and (b) top view of the contact ellipse.",
        "texts": [
            " As p becomes small at the edges of the contact (Hertz pressure distribution), little slip zones are not likely to generate much wear. For larger slip zones i.e. higher \u03c4 (Fig. 7), the surface may start to slip in the middle of the contact where the normal pressure p is higher, which could be more critical regarding smearing. Hence, the best configuration would be to maximize the tangential strain in order to reduce the slip zone magnitude. The rolling micro-slip arises from the curvatures of the roller profile (Fig. 8). Then, if the tangential stress generated is significant, the contact would be an association of transverse sliding and rolling microslip. The calculation sheet can meet the two components separately on the same draft, in order to compare the stress they generate. For dry contact condition (m 0.8), the three microslip zones are very small and located near the contact edges. Then, the maximum shear stress is also very low. Thus, for creep ratios around 0.01\u20130.05 the rolling microslip shear stress is negligible compared to that of the transverse sliding",
            " These results are very different from classic pure sliding tests because the rolling component influences the wear mechanisms in several ways: it flattens the adhesive transfer at each cycle and it reduces the instantaneous sliding amplitude of the slipping surfaces. Anyway, in dry test conditions, smearing occurs extremely quickly. Also, other wear tests revealed that adhesive wear even happens for lighter conditions (Fn down to 2 N). A special case arises for pure rolling motion (\u03c4\u00bc0). Observations reveal that smearing even occur without transverse creep (Fig. 15). The wear track is strip shaped along the rolling direction. That observation is directly related to the existence of slip bands due to roller's curvature (Fig. 8). These observations show that the wear pattern is similar to that of the usual bearing parts: without lubrication, smearing quickly arises from the micro-slip zones. This results in a progressive transfer of small particles from both surfaces. These transfer patches grow at each cycle and lead to the global degradation of the track. Besides, the PRS contact geometry seems more hazardous than usual bearings because of the transverse sliding component. Lastly, the curvature of the roller influences the contact width and then the rolling micro-slip zones",
            " Darker colors are usually related to different chemical products [21], and thus to more stressed areas. Therefore, observations confirm the theoretical dissymmetric stress distribution due to creep. Lastly, the same test performed without creep (Fig. 17b) reveals a much lighter quantity of tribochemical film. This is due to density of asperities in contact that is necessarily lower without a sliding component. Besides, the picture also reveals a tribofilm distribution divided into three darker bands on the middle and on the edges, that corroborates the theoretical analysis (Fig. 8). Low grease thickness tests have been performed to reproduce the situation of insufficient lubrication that may occur in the PRS mechanism. Fig. 16 shows the comparison of Ft/Fn between small and large grease thickness. The evolution of Ft/Fn first fits the large thickness one, and then raises quickly after a certain number of cycles that varies from one test to another. Wear track These results show that a very slight difference in initial grease thickness can significantly influence the smearing lifetime"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003426_s00170-018-3127-y-Figure14-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003426_s00170-018-3127-y-Figure14-1.png",
        "caption": "Fig. 14 3D contour of the residual stress distribution, a longitudinal direction of single-track flat model, b transverse direction of single-track flat model, c longitudinal direction of double-track flat model, and d transverse direction of double-track flat model",
        "texts": [
            " 13 indicates, a qualitative agreement is achieved between the simulated residual stresses and measured values. The simulated results in the clad layer are higher than those obtained from the experiments. The differences between the prediction and measured results can be attributed to two reasons. First, the curved clad surface and un-melted powders as well as the XRD machine errors could lead to deviation during the measurement. Second, the stress-strain curve adopted in this study and the lack of high temperature material properties could decrease the prediction accuracy of the FE model. Figure 14 shows the 3D residual stress contour of the single and double flat models. As Fig. 14a and b shows, both the longitudinal and transverse stresses in the cladding layer are tensile in nature. Compressive stress in the substrate at a distance away from the cladded layer was observed to balance the residual stress. The longitudinal and transverse residual stresses had a symmetry distribution according to the center of the clad. As the advancing direction of the cladding process, the longitudinal residual stress was higher than the transverse residual stress. Figure 14c and b plots the 3D contour of the residual stress distributions of the double-track flat model. The symmetry distribution pattern of the residual stress disappeared in the double-track flat model. The nature of the longitudinal and transverse residual stresses was still tensile in the cladded layer. Compressive transverse and longitudinal stresses were observed at the substrate\u2019s edges in order to equilibrate the tensile stress in the cladded layer. The highest longitudinal residual stress and transverse residual stress were both distributed at the overlapping region"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001496_tcst.2015.2454445-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001496_tcst.2015.2454445-Figure1-1.png",
        "caption": "Fig. 1. Takeoff slope and quadrotor. (a) Reference frames. (b) Quadrotor geometry.",
        "texts": [
            " The vector n must be constant for the section of the landing slope needed for landing, depending on the size of the quadrotor and the desired sliding trajectory. This last requirement of continuity results in a landing plane that is vertical so that the contact of the left and right landing gears occurs simultaneously, and the quadrotor does not pivot around a single contact point. Although the proposed hybrid controller framework can be extended to three dimensions using the same mathematical modeling principles, the authors feel it would not bring added benefits. Fig. 1(a) presents a graphical description of the quadrotor geometry and the landing environment. The ground is modeled as a flat surface at an angle \u03b2 with the horizontal. A body-fixed frame {B} = {CM, iB, kB} is attached to the quadrotor\u2019s center of mass (CM), with the vector kB pointing upward, along the thrust direction. The inertial frame {I} = {O, i , k} is defined by the vectors i and k that point north and up, respectively. An additional frame {L} = {O, iL , kL}, denoted by slope frame, is attached to the origin of {I} and rotated with respect to {I} by an angle \u03b2. The angle \u03b8 denotes the rotation angle from the inertial frame to the body frame. The planar model of the quadrotor shown in Fig. 1(b) has two counterrotating motors for propulsion, generating the aerodynamic forces F1 and F2, and a landing gear with two points of contact with the ground, denoted by A and B. The distance from the CM to each motor and to each contact point are denoted by r and , respectively. The angle with vertex in CM and subtended by the motor and contact point is denoted by \u03b3. The shorthand g = cos(\u03b3 ) is introduced to simplify mathematical expressions. To simplify the description of the various quadrotor dynamics, the state of the quadrotor is expressed in different coordinate systems, according to its operative mode",
            " In situations where contact with the ground occurs, the quadrotor state is described by the tuple (\u03be, \u03b6, \u03b8) and its derivative, wherein \u03be, \u03b6 are the coordinates of point A in the slope frame and \u03b8 is the quadrotor tilt angle. This change of coordinates given by \u03be = x cos \u03b2 + z sin \u03b2 + cos(\u03b8 + \u03b3 + \u03b2) \u03b6 = \u2212x sin \u03b2 + z cos \u03b2 \u2212 sin(\u03b8 + \u03b3 + \u03b2) helps to decouple the translational motion of the contact point along the slope, captured by \u03be , from the rotational motion of the quadrotor around the contact point, embedded in \u03b8 . A depiction of the inertial and the slope frames is presented in Fig. 1(a), together with a representation of the vehicle location in each frame. For the development of the quadrotor hybrid automaton, we consider five operating modes, corresponding each mode to the different dynamics that the vehicle is subject to. The modes are distinguished by the number of contact points of the landing gear with the ground and the existence of relative movement between the contact point and the ground. The operating modes are defined as follows. 1) FF: In this operating mode, the quadrotor is in FF and no contact with the landing slope occurs",
            " During the FF and TLs landing phases, the forces are similar in magnitude, reflecting a control of constant tilt angle. In TL, however, F2 drops drastically, when forcing the rotation of the quadrotor and consequent landing. Nonetheless, F1 and F2 are always positive and within the limits of the quadrotor actuation. The evolution of the distance of both landing gear extremities to the slope is shown in Fig. 16. In FF, both distances decrease at the same rate until contact with the ground happens at 8 s and the quadrotor enters the TLs state. After the transition, the contact point A [see Fig. 1(b)] remains on the slope for the duration of the maneuver. The contact point B on the landing gear gains a slight distance and then remains approximately constant, as the quadrotor tilts to track \u03b80 and goes up the slope. Once in the TL operating mode, the distance of point B diminishes, as the quadrotor rotates, until both points are in contact with the landing slope. The distance is computed from the quadrotor position and attitude, knowing the slope\u2019s location and incline. The small resulting errors are due to imperfections in the landing slope surface"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001443_ls.1271-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001443_ls.1271-Figure1-1.png",
        "caption": "Figure 1. Types of elastohydrodynamic contact.",
        "texts": [
            " Received 26 March 2014; Revised 22 April 2014; Accepted 12 May 2014 KEY WORDS: elastohydrodynamic lubrication; EHL; EHL film thickness; EHL friction Lubricated machine components can be divided into those whose elements slide together and those having elements that roll against one another. In the former, such as piston ring/liners and plain bearings, the elements are generally designed to conform closely, so as to spread the applied load over a large fluid film area and thus reduce the contact pressure. By contrast, in rolling-sliding components such as rolling bearings, involute gears, cam/follower systems and constant velocity joints, as shown in Figure 1, the elements must have curved surfaces and be non-conforming so as to be able to roll. If these contacting elements are metallic or ceramic and so have a high elastic modulus, the resulting contacting area is very small. In consequence, these contacts experience very high pressures, often of the order of several gigapascals (1GPa = 10 kbar). The lubrication of conforming lubricated contacts is well described by the hydrodynamic lubrication theory first developed by Reynolds in 1886.1 However, for many years after this, it was not understood how non-conforming contacts could operate successfully, since Reynolds\u2019s hydrodynamic theory *Correspondence to: Hugh Spikes, Tribology Group, Department of Mechanical Engineering, Imperial College London, London, UK"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002213_j.mechmachtheory.2014.06.006-Figure10-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002213_j.mechmachtheory.2014.06.006-Figure10-1.png",
        "caption": "Fig. 10. State 6 of the derivative queer-square mechanism (\u03b11 b 0, \u03b12 b 0, \u03b211 = \u03b212, \u03b221 = \u03b222).",
        "texts": [
            " (27), are illustrated as \u03b11b0;\u03b211 \u00bc \u03b212N0 \u03b12N0;\u03b221 \u00bc \u03b222b0 : \u00f030\u00de In state 5, limb1s is lower than the base OA1A2, limb2s is higher than the base and the platform E1F1E2F2 locates in the position higher than limb1p but lower than limb2p. Through rotating the negative values for angles \u03b11 and \u03b12 from the singular position, limb1s and limb2s have a relatively lower position compared to the base where state 6 is. The angle ranges in state 6 are given as \u03b11b0;\u03b211 \u00bc \u03b212b0 \u03b12b0;\u03b221 \u00bc \u03b222b0 : \u00f031\u00de In state 6, the limb1s, limb2s, limb1p and limb2p are lower than the base, and the platform E1F1E2F2 is lower than the limb1s, limb2s, limb1p and limb2p, as illustrated in Fig. 10. In state 6, through rotating the negative angles \u03b11 and \u03b12, limb1s, limb2s, limb1p and limb2p all have a relatively lower position compared to the base. Platform motion\u2013screw system in states 3\u20136 can be solved by combining Eqs. (17)\u2013(22) and Eq. (27). The result of the platform motion\u2013screw system in states 3\u20136 is illustrated as S f n o \u00bc S f1 \u00bc 0 0 0 \u2212 s\u03b11c\u03b211 s\u03b211c\u03b11 1 0 T S f2 \u00bc 0 0 0 \u2212 s\u03b11 c\u03b11 0 1 T 8>< >: 9>= >; : \u00f032\u00de Since the first three components of the screws in the platform motion\u2013screw system are all equal to zero, the platform of the derivative queer-square mechanism has two dimensional pure translations in states 3\u20136"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001267_tmag.2011.2178100-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001267_tmag.2011.2178100-Figure3-1.png",
        "caption": "Fig. 3. Finite-element model for calculating the electromagnetic field and the magnetic forces of the PMDC commutator motor under no-load condition: (a) mesh model and (b) distribution of the electromagnetic field at the rotor position of 0 degrees.",
        "texts": [
            " The present motor ran under no-load condition, and the no-load current of 1.8 A is applied into the finite-element model with a linear commutation in the commutation zones. By using the finite-element software ANSYS 12.1, the nonlinear properties of the materials of the stator (low-carbon steel) and the rotor (cold-rolled silicon steel) are included in the model to calculate the electromagnetic field. The boundary condition on the outer surface of the stator is set to be zero vector potential in the Z direction. The finite-element model shown in Fig. 3(a) contains 23 457 nodes and 11 450 PLANE233-type elements. In order to rotate the rotor anticlockwise at an incremental angle of 0.5 degrees, the rotor and the stator are meshed individually and then coupled together along the outer surface of the rotor. Fig. 3(b) shows the distribution of the electromagnetic field in the whole cross section of the PMDC commutator motor at the rotor position of 0 degrees. Fig. 4 shows the radial and tangential magnetic fields with and without the static eccentricity in polar coordinates, respectively. The location of the compared magnetic fields is in the air-gap near the inner surfaces of the permanent-magnets (see the dotted circle of which the radius is 20.9 mm in Fig. 2). Fig. 4 shows that the eccentricity increases (decreases) the magnetic fields in the narrower (wider) air-gap region, especially at the corners of the rotor teeth"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001319_1.4864956-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001319_1.4864956-Figure3-1.png",
        "caption": "FIGURE 3. Solid model of the viewport used to accommodate imaging by thermal cameras (a); an assembly of the viewport, the machine\u2019s door and a thermal camera (b); and a side cross-section of the build chamber (c). In (c) the recoating arm would travel in and out of the plane of the page.",
        "texts": [
            " Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 130.237.165.40 On: Fri, 14 Aug 2015 23:40:21 outside the build chamber, but view into the working plane. The easiest path to accomplish this on the system at NIST is through the front door of the machine. The existing viewport of the machine (a simple window with IR-blocking glass) will be replaced with a metal structure that protrudes into the build chamber a bit, allowing the camera to be positioned closer to the working plane. Figure 3 shows a solid model of the modified viewport, and its assembly with the machine\u2019s door. The viewport was designed to maintain safe machine operation and allow the camera to get as close to the build platform as possible. The viewport will be made of metal to ensure any stray or reflected light from the laser will be blocked, but will have a 75 mm diameter sapphire window to allow viewing by the camera. The sapphire window will be at the end of a metal tube or sleeve, and the camera optics will fit within that tube",
            " These considerations will allow the chamber to maintain proper pressure and atmosphere and will allow the machine\u2019s safety systems to operate as they are intended. The camera will be supported by a tripod at a 45\u00b0 angle. Ordinarily this would be noteworthy because that angle would affect the emissivity of the object being viewed. However, the hyperspectral camera will image the same object at the same 45\u00b0 angle, providing an in situ characterization of the emissivity. The primary concern with getting the camera close to the build platform is the clearance of the recoating arm. Figure 3c shows that the tube can protrude into the chamber by several centimeters while still allowing the recoating arm to safely pass by. The primary benefit to imaging through the existing viewport is that it will not require any permanent modification to the machine. However, using the viewport requires a rather shallow imaging angle that because of the depth of focus will limit the field of view. NEXT STEPS Once all of the components are manufactured and in place, process parameters and camera settings must be determined before experiments are conducted"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001968_978-94-007-6101-8-Figure2.6-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001968_978-94-007-6101-8-Figure2.6-1.png",
        "caption": "Fig. 2.6 RPY angles for the case of an airplane",
        "texts": [
            " The vectors s and a are unit vectors which are perpendicular with respect to each other, so that we have: s \u00b7 s = 1 a \u00b7 a = 1 s \u00b7 a = 0 Three elements are, therefore, sufficient to describe the orientation. The orientation is often described by the following sequence of rotations: R : roll\u2014about z axis P : pitch\u2014about y axis Y : yaw\u2014about x axis This description is mostly used with orientation of a ship or airplane. Let us imagine that the airplane flies along z axis and that the coordinate frame is positioned into the center of the airplane. Then, R represents the rotation \u03d5 about z axis, P belongs to the rotation \u03d1 about y axis and Y to the rotation\u03c8 about x axis, as shown in Fig. 2.6. All rotations are performed with respect to a fixed reference frame. 22 2 Rotation and Orientation The meaning of RPY angles for the case of robot gripper is shown in Fig. 2.7. As it can be realized from Figs. 2.6 and 2.7, the RPY orientation is defined with respect to a fixed coordinate frame. In Sect. 2.1 we learned, that consecutive rotations about different axes of the same coordinate frame can be described by the premultiplication of the rotation matrices, or with another words the rotations are performed in the reverse order"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000782_j.mechmachtheory.2012.11.006-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000782_j.mechmachtheory.2012.11.006-Figure7-1.png",
        "caption": "Fig. 7. Reference system for misalignment definition.",
        "texts": [
            " This parameter is crucial for the dynamic response of planetary gear sets [32,33]. Misalignments can be defined for a gear pair in terms of relative position and orientation of the gears. Since rotation around the axes is allowed and gear bodies are assumed to be rigid, misalignment can affect the other 5 degrees of freedom. Three translational or parallel misalignments and two rotational or angular misalignments can be identified. Directions discussed by Houser et al. [34] are used to define the axis system shown in Fig. 7 and described hereafter. The three orthogonal directions are chosen as the Line Of Action (LOA) in the direction of the normal contact force in the transverse plane as well as tangent to the base circles of the gears, the Offline Line Of Action (OLOA) orthogonal to the LOA still in the transverse plane and the axis of rotation direction and finally the axis of rotation. Since the TE is calculated in LDP along the LOA and this direction is normal to mating teeth surfaces, this axis system is particularly convenient as it allows understanding how fields of displacement caused by parallel and angular misalignments affect TE and mesh stiffness"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000865_j.snb.2011.01.050-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000865_j.snb.2011.01.050-Figure1-1.png",
        "caption": "Fig. 1. Scheme of electron flow and current generation in o",
        "texts": [
            " To discern the role of individual components, three different electrodes, bare Au, c-MWCNT/Au and GNPs/c-MWCNT/Au were analyzed in H2O2 solution. Cyclic voltammograms of bare Au electrode, c-MWCNT/Au electrode and GNPs/c-MWCNT/Au electrode were recorded in 50 mM Tris\u2013HCl buffer pH 8.5 containing 0.1 mM H2O2. Potential range of 0.0 to +1 V s\u22121 with scan rate 50 mV s\u22121 was tested in potentiostat\u2013galvanostat. On addition of 0.1 ml of 10 mM oxalic acid, it was oxidized to CO2 and an electroactive H2O2, which was splited into 2H+ + O2 + 2e\u2212 under a potential of +0.4 V. The flow of e\u2212 i.e., current was measured in mA (Fig. 1). To determine the working conditions of the electrode, the pH of the reaction buffer was varied in the range 3.0\u20137.5 at an interval of pH 0.5, using 0.05 M sodium succinate buffer between pH 3.0 and 6.0 and 0.05 M sodium phosphate buffer between pH 6.5 and 7.5. Similarly, the optimum temperature was studied by incubating the reaction mixture from 20 \u25e6C to 50 \u25e6C at the interval of 5 \u25e6C and optimum response time by measuring the current at 2\u201312 s at an interval of 1 s. The optimized conditions were then used to measure at different concentrations of substrate (oxalic acid) in the range 1\u2013800 M"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001885_j.matpr.2015.10.028-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001885_j.matpr.2015.10.028-Figure4-1.png",
        "caption": "Fig. 4. a) Mandrel of an extrusion die manufactured by laser melting, b) geometry of the channels (negative), c) detail top of the mandrel with deflectors and die cap (according to [8])",
        "texts": [
            " High thicknesses lead to rough surfaces but a quick manufacturing time while thin layer thicknesses cause the contrary. After transferring the data to the machine, the process starts by deposition a thin layer of the metal powder. The powder is locally melted and solidified layer by layer by using an energy source. After generating the geometry in one layer the building platform is lowered by the thickness of one layer and then a new layer of powder can be deposited. These processes repeat as often as the whole geometry is built up [11]. A mandrel of an extrusion die (Fig. 4 a)) was manufactured in a powder bed of CL50WS (similar to the hot working steel 1.2709) in a nitrogen atmosphere by using a laser cusing machine m3 linear (by Conept Laser GmbH). The fabrication of the die, with a volume of 116 cm\u00b3 and a deposition rate of 3.8 cm3/h, took around 30 h (1580 layers \u00e0 30 \u03bcm). The fitting surfaces and die bearings had an allowance of 0.3 mm and were mechanically refinished. The mandrel was heat treated (ageing 500 \u00b0C, 8h) to a final hardness of 55 HRC [11]. Due to the design of the extrusion press, a supply of the cooling medium and the measuring setup is only possible from the exit end face of the die. For feeding the coolant into the mandrel, a multidirectional course of the cooling channel through the mandrel was designed. Two opposite bridges of the mandrel include the cooling channel while in the other two, a channel for thermocouples is positioned (Fig. 4 b)). On top of the mandrel small deflectors were added which prevent a pull out of the thermocouples due to a possible contact between the extrudate and the thermocouples especially during the beginning of the extrusion process (Fig. 4 c)). Due to the step effect and the used powder, parts manufactured by additive manufacturing processes have a rough surface which has to be mechanically refinished in areas which are in contact to other areas, sealing surfaces and the die bearings. The question is, whether the rough surfaces in the die inlet influence the material flow and if these areas can stay as manufactured or if they have to be mechanically refinished. In order to prove this, a visioplastic analysis was carried out. The idea was, to compare the material flow along two different die surfaces which are conventionally and additively manufactured"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003684_tcst.2019.2952826-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003684_tcst.2019.2952826-Figure1-1.png",
        "caption": "Fig. 1. Schematic of a quadrotor with a suspended payload.",
        "texts": [
            " In Section V, the stability of the closed loop is analyzed. Real-time experimental results are presented in Section VI. Finally, Section VII gives some conclusion remarks. In this brief, R n denotes the n-dimensional Euclidean space. The symbols c\u00b7 and s\u00b7 represent sin(\u00b7) and cos(\u00b7), respectively. The n-dimensional identity matrix is defined as Ii \u2208 R i\u00d7i . The mapping R n \u2192 R n\u00d7n : y = diag{x} produces diagonal matrix y \u2208 R n\u00d7n from x \u2208 R n with y(i, i) = x(i), i = 1, 2, . . . n. The schematic of a quadrotor UAV with a suspended payload is shown in Fig. 1. The major symbols used in this brief are listed in Table 1. The dynamic model of the quadrotor UAV with a suspended payload can be given by the following equations: \u03c4 = J \u03b7\u0308 + N\u03b7(\u03b7\u0307) (1) F\u0304 = M(\u03c7)\u03c7\u0308 + C(\u03c7, \u03c7\u0307 )\u03c7\u0307 + Vm(\u03c7)+ \u03ba\u03c7 (\u03c7\u0307) (2) where F\u0304(t) = [ F(t)T 0 0 ]T \u2208 R 5 with F = f [ c\u03c6s\u03b8c\u03c8 + s\u03c6s\u03c8, c\u03c6s\u03b8 c\u03c8 \u2212 s\u03c6c\u03c8, c\u03b8c\u03c6 ]T and the torque produced by the four rotors is represented by \u03c4 (t) = [ \u03c4x(t), \u03c4y(t), \u03c4z(t) ]T \u2208 R 3. Here \u03c4 (t) and f (t) are the inputs of the system. For the inner-loop (rotational motion of the quadrotor) subsystem in (1), N\u03b7(\u03b7\u0307) = \u2212\u03b8\u0307 \u03c8\u0307(Jy \u2212 Jz), \u2212\u03c6\u0307\u03c8\u0307(Jz \u2212 Jx ), \u2212\u03b8\u0307 \u03c6\u0307(Jx \u2212 Jy) T "
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000644_j.1538-7305.1965.tb04141.x-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000644_j.1538-7305.1965.tb04141.x-Figure7-1.png",
        "caption": "Fig. 7 - (a) Thevenin equivalent circuit: series combination of voltage source and a monotonically increasing current-controlled resistor whose characteristic passes through the origin. (b) Norton equivalent circuit: parallel combination of current source and monotonically increasing voltage-controlled resistor whose characteristic passes through the origin.",
        "texts": [
            " Dually, if we pick a branch and insert two terminals in series with it, we obtain a two-terminal network: we shall call the characteristic of this two-terminal network the branch-input characteristic of \\n. Theorem II (Thevenin and Norton equivalent circuits): Consider a network \\n satisfying the requirements of Theorem I together with the same kind of source distribution. Then (a) the input characteristic of m at any node pair is that of a currentcontrolled resistor whose characteristic is a continuous, monotonically increasing function defined on (- co, co ). This characteristic may be represented by the Theuenin equivalent circuit of Fig. 7(a): a series combination of a voltage source and a monotonically increasing current-controlled resistor whose characteristic passes through the origin. (b) The branch-input characteristic of m. at any branch is that of a voltage-controlled resistor whose characteristic is a continuous, monotonically inCreasingfunction defined on (- co, co ). This characteristic may be represented by the Norton equivalent circuit of Fig. 7 (b): a parallel combination of a current source and a monotonically increasing voltage-controlled resistor whose characteristic passes through the origin. Let us consider some special cases of Theorem II. Corollary 3: Consider a connected network of nonlinear (possibly timevarying) resistors satisfying assumptions (a), (b) and (c) of Theorem 1. (a) If, in addition, the characteristics of the tree branches of 3 are strictly increasing, then the input characteristic at any node pair is that of a strictly increasing current-controlled resistor"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003694_rcs.2081-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003694_rcs.2081-Figure7-1.png",
        "caption": "Figure 7. Results of FEM simulation for the module integrated with the variable-stiffness sheath via static structural analysis. (a) Deformation nephogram of the module (b) Deformation nephogram of the module (c) Three-dimensional models and corresponding boundary conditions of the module.",
        "texts": [
            " It is clearly seen that when the voltage increases from 0 to 10 V, the deflection reaches to the minimum during the heating procedure, meaning that stiffness of the sheath reaches to the maximum. The maximum maxD and minimum minD of the deflection for force 0.5 N, 1 N and 1.5 N are separately 8.1405 mm and 3.1686 mm, 16.2810 mm and 6.3372 mm, 24.4215 mm and 9.5058 mm, and the increment of stiffness (i.e., the decrement of deflection max min/ 1D D \u2212 ) is 156.9%. Similarly, the static structural analysis for the module integrated with the proposed variable-stiffness sheath is performed. Three-dimensional models of the module and boundary conditions are shown in Figure 7(a). Figure 7(b) and 7(c) show deformation nephograms of the module under 0.5 N force, separately in an unactuated state (flexible state) and a fully actuated state (rigid state). As shown in Figure 8, according to the deflection-voltage simulation curves of the module, the maximum maxD and minimum minD of the deflection for force 0.5 N, 1 N and 1.5 N are separately 12.2352 mm and 6.7408 mm, 24.4704 mm This article is protected by copyright. All rights reserved. and 13.4816 mm, 36.7056 mm and 20.2224 mm. And the increment of stiffness max min/ 1D D \u2212 is 81"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002608_j.tafmec.2019.04.005-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002608_j.tafmec.2019.04.005-Figure1-1.png",
        "caption": "Fig. 1. CT specimen geometry and dimensions (mm).",
        "texts": [
            " Material of powder particles to produce SLM parts was the maraging steel AISI 18Ni300 with the chemical composition indicated in Table 1. The specimens were manufactured using a scan speed of 200mm/s, adding layers of 40 \u03bcm thickness with hatch spacing of 100 \u03bcm and 25% overlapping, growing towards the direction corresponding to the application of the load in the mechanical tests. After manufacturing the specimens were mechanically polished. The specimens\u2019 geometry and respective dimensions are indicated in Fig. 1. Two different batches of tests were performed: as-built SLM specimens and also SLM specimens subjected to a post-manufacturing heat treatment. The purpose of the heat treatment was to increase the hardness and reduce the residual stress level. A slow and controlled heating was performed during 2 h up to 635 \u00b0C, followed by maintenance at 635 \u00b0C for 6 h. Then, the specimens were submitted to a controlled cooling in the oven for 3 h up to 360 \u00b0C. The final cooling to room temperature was carried out in the air"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000559_icar.2011.6088631-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000559_icar.2011.6088631-Figure4-1.png",
        "caption": "Fig. 4. Inertial and Body\u2013Fixed Frame",
        "texts": [
            " The altitude of the system is controlled by increasing or decreasing the rotors\u2019 thrust, while the planar displacements are controlled by simultaneously controlling the rolling or pitching of the system and the total thrust. These main operational principles are illustrated in Figure 3. Let I = {Ex,Ey,Ez}, be the inertial Earth\u2013Fixed Frame (EFF) and B= {B1,B2,E3} the coordination system on the Body\u2013Fixed Frame (BFF). Let the vector of translational and rotational motions q = [\u03be ,\u03b7 ]T , where \u03be = [x,y,z]T the translational displacements and \u03b7 = [\u03c6 ,\u03b8 ,\u03c8]T the roll, pitch, yaw angles respectively. In Figure 4, the main coordination frames utilized are presented. Three auxiliary frames have been utilized in order to model the pitch and yaw motion. The first two auxiliary frames are obtained from the differential tilting of the rotors to drive the yaw motion, Y1 = {iY1 x , iY1 y , iY1 z }, Y2 = {iY2 x , iY2 y , iY2 z }. The third auxiliary frame is obtained from the tilting of the rotors in order to drive the pitch motion, P = {iPx , iPy , iPz }. Let \u03b3 , be the angle of the equally and contrary tilted rotors in order to drive the yaw motion and \u03b1 the equal tilting of the rotors in order to regulate the pitch motion"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003841_1.j059216-Figure12-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003841_1.j059216-Figure12-1.png",
        "caption": "Fig. 12 Impact configuration: front (a) and lateral (b) views.",
        "texts": [
            "J 05 92 16 whereas surface-to-surface and single-surface interactions have been set up by using the friction coefficients of the materials in contact. Amaster-surface to slave-node contact algorithm has been defined between the impact surface (the rigid wall) and the lower part of the fuselage section. Finally, the initial vertical velocity,matching the experimental one, has been assigned to all nodes of the model in order to simulate the 4.26 m vertical drop test, and the gravity acceleration has been applied to the whole structure as well. The overall FE model, consisting of 2,031,764 nodes and 2,426,312 elements, is shown in Fig. 12. As a quality check of the model, the total mass of the fuselage model is approximately 925 kg, confirming the total testing one of 927 kg. As aforementioned in Sec. III.A, the adopted average mesh size is equal to 10 mm, which allows obtaining a very good solution accuracy to computational cost ratio. Furthermore, according to [62], the total number of elements used to discretize the fuselage section can be considered an appropriate value for this kind of simulation. Another aspect influencing the simulation is the integration method chosen for the generic element"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001374_j.actamat.2016.02.005-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001374_j.actamat.2016.02.005-Figure3-1.png",
        "caption": "Fig. 3. a) A schematic of the in-situ loading neutron diffraction measurement setup. The signal from the planes perpendicular (i.e., their plane normals parallel) to the build/axial direction and along the cross-member is received in the east bank of detectors. Likewise, the signal from the planes perpendicular to the transverse direction is received by the west bank of detectors. The red arrows correspond to the direction of the applied compressive load on the theta sample which places the cross-member in tension. Note the beam \u201cwindows\u201d which allow the passage of the incident and diffracted beams to and from the region of interest with minimal attenuation; b) The location of the neutron diffraction mapping points along the cross-member (see red diamonds). A.D., T.D., and N.D. refer to the axial, transverse and normal directions, respectively. Also shown here is the location on the ring section (see yellow square) from where the EBSD measurements were taken.",
        "texts": [
            " The build sequence schematics for the spot and line builds are presented in Fig. 1a and b, respectively. The spot heat source scheme consisted of melting the material one spot at a time in a pattern to control the bulk heat input according to the scheme described by Kirka [31]. The line heat source scheme on the other hand, consisted of a snake raster pattern that was rotated 90 after each new layer. The build direction of the sampleswas parallel to the long axis of the cross-member (see axial direction in Fig. 3). A layer thickness of 50 mmwas used for both builds and the total build process took 24 h with an average time per layer of 70 s. The samples were allowed to cool for 7.2 h under vacuum and no post-process heat treatments were performed. More details about the build parameters employed are presented in Ref. [30] (also see the supplementary document). In order to obtain the axial and transverse lattice strains from the cross-member during the in-situ neutron diffraction experiments, these theta-shaped specimens were designed housing four beam windows (see Fig. 3). In terms of sample dimensions, the cross-member was designed to have a 4 4 mm2 cross-sectional area with a total length of 40.4 mm and gauge length of 28.4 mm. The samples had outer and inner ring diameters of 60 and 2 JEOL USA, Inc. 11 Dearborn Road, Peabody, MA 01960. 44 mm, respectively. The beam windows were 9 mm long and 6mmwide, and the ring thickness was 15 mm to accommodate the beamwindows. The samples were designed to initiate the failure in the cross-member. To perform the EBSD analyses, a JEOL 6500F Field Emission GunSEM2 equipped with an EDAX Apollo Silicon Drift Detector and Hikari EBSD camera was used",
            " The electron gun was set to an accelerating voltage of 20 kV and tip current of 4 nA for collecting the EBSD data. Prior to conducting EBSD analysis, all specimens were given a final colloidal silica (0.04 micron) polish. The postprocessing of the collected data was performed using the TSL OIM Analysis software and no additional data clean-ups were performed. The data were obtained from both the cross-members (top, middle and bottom locations as shown in Fig. 2 with yellow squares; both//and \u22a5 to the Build Direction, BD) and the ring sections (from the portion near the loading mounts, yellow square in Fig. 3b,//to BD) of the specimens. Data collection was performed using a hexagonal grid with varying sampling areas (from ~1840 1820 mm2 on the cross-member \u22a5 to BD, to ~3670 3640 mm2 on the cross-member and on the ring section//to BD) and step sizes (from 2 mm on the cross-member \u22a5 to BD, to 5e6.5 mm on the cross-member and on the ring section//to BD). Synchrotron x-ray diffraction (SXRD) measurements on the cross-members extracted from un-deformed samples were performed at Beamline 11-ID-C, Advanced Photon Source (APS), Argonne National Laboratory, in an effort to obtain the as-built textures",
            " The in-situ lattice strain evolutions of the cross-members were measured using neutron diffraction at the VULCAN Beamline [35], Spallation Neutron Source (SNS), Oak Ridge National Laboratory (ORNL). The measurements were conducted in high-intensity (HI) mode that offers a neutron flux of up to 6.7 107 n/s/cm2 to achieve good count statistics in a reasonable amount of time, and a 2 2 2 mm3 gauge volume was used to ensure full burial of the neutron beam inside the sample. For these measurements, the theta-shaped specimens were situated such that the cross-members were at a 45 angle with respect to the incident neutron beam, Fig. 3. With this setup the axial and transverse components of strain were simultaneously detected making use of the two detectors (west and east banks) positioned at \u00b190 to the incident beam. The incident and diffracted beams were allowed to enter and exit through the as-built beam-windows with minimum attenuation. The samples were loaded by applying compression on the mounting flats of the ring (indicated by the red arrows in Fig. 3) which were translated into tensile stresses along the cross-member [30]. Initially the samples were held in place with a compressive pre-stress of 0.4 kN cumulative load. This translated into a ~7 MPa tensile stress on the cross-member [30] and was taken as the \u201creference state\u201d when calculating the lattice strains. The in-situ deformation was then carried out under load-control for a total of 15 loads up to maximum cumulative load levels (i.e., total loads experienced by the whole structure) of 66 and 58 kN for the spot and line builds, respectively; followed by an unload in 4 steps back to 0",
            " Accordingly, the highest loads (66 and 58 kN for the spot and line builds, respectively) applied during the in-situ neutron diffraction measurements corresponded to 3.5% of macroscopic engineering strain on the cross-members [30]. In this context, the strains on the cross-members were incremented from the reference state (~0% strain) in 0.1% steps up to 1% strain followed by 0.5% increments up to 3.5% strain. For each load level, five points were mapped along the cross-members, i.e., Center, \u00b12 and\u00b1 4mm from the center, at 8min per location (Fig. 3b). The data reduction and single peak fittings were performed using the VULCAN Data Reduction and Interactive Visualization Software (VDRIVE) [36]. EBSD grain orientation and grain aspect ratio maps from both builds (cross-members and ring sections) are presented in Figs. 4 and 5, respectively. Since qualitatively similar microstructures were observed along the crossmember (top, middle and bottom, Fig. 2), only the results from the middle points (as representative) are presented in Figs. 4 and 5 for brevity",
            " Additionally, the presence of stronger textures in the spot build relative to the line build can also be visualized by the sharper poles in the spot build as opposed to the more diffuse textures observed in the line build. The diffraction patterns obtained from the cross-members during in-situ neutron diffraction measurements are presented in Fig. 8a and b for the spot and the line builds, respectively; covering both the axial/build and transverse directions. In Fig. 8 each run number corresponds to a different pattern, i.e., different load, along a given sample direction, i.e., axial/build or transverse. Also, each pattern corresponds to the ones obtained from the centers of the cross-members (see Fig. 3b). In agreement with the PFs presented in Fig. 7, a prominent presence of the (200) reflection is observed along the axial/build and transverse directions in both builds. Additionally, a strong presence of the (220) reflection along the transverse direction of both builds can be seen, again consistent with the bulk texture measurements from SXRD. Furthermore, when the relative intensities of individual reflections, e.g., (311) vs (200), are compared between the builds, a stronger presence of (200) along the axial/ build direction is observed in the spot build, compared to the line build, which is consistent with the PFs presented in Fig",
            " 10a and b as a function of the applied cumulative loads for the spot and the line builds, respectively; covering the axial and transverse directions. Following in Fig. 10c and d are presented the evolution of the axial lattice strains as a function of the applied macroscopic strains on the cross-members, obtained from DIC [30], for the spot and line builds, respectively. In these figures the data points correspond to the average response of the five mapped locations on the cross- members (Center, \u00b12 and \u00b1 4 mm, Fig. 3b) and the error bars to their standard deviation. The relative changes in d-spacing values (Dd) differ for each reflection for the same change in load, pointing to elastic anisotropy. This highly anisotropic micro-mechanical behavior is observed in both builds, revealed by the large variation between the lattice strain responses of different hkl planes, consistent with the high elastic anisotropy of Ni-alloys [40]. Within this context, the (111) and (200) reflections mark the two extremes being the elastically stiffest and the most compliant planes, respectively [41]"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002506_iros.2015.7354046-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002506_iros.2015.7354046-Figure1-1.png",
        "caption": "Fig. 1: The body fixed reference frame and the inertial reference frame used for deriving the model of the quadrotor",
        "texts": [
            " Section III presents the FDI system which is designed for the case of one total rotor failure. The fault-tolerant control system is introduced in Section IV. The performance of the approach is shown in Section V. Finally, Section VI concludes the paper. This section first presents the translational and rotational dynamics of the quadrotor, followed by some simplifications used for design of the controller and fault detection system. Finally, the new definition of the LOE factors is presented. The reference frames of the quadrotor are shown in Fig. 1. The earth frame is denoted as {\u03a3e}(Oe, xe, ye, ze) and the body frame of the quadrotor , which is fixed to the quadrotor, is denoted as {\u03a3b}(Ob, xb, yb, zb). Both ze and zb point down. The rotation of \u03a3b with respect to \u03a3e is described by the rotation matrix R as follows: R = C\u03b8C\u03c8 S\u03c6S\u03b8C\u03c8 \u2212 C\u03c6S\u03c8 C\u03c6S\u03b8C\u03c8 + S\u03c6S\u03c8 C\u03b8S\u03c8 S\u03c6S\u03b8S\u03c8 + C\u03c6C\u03c8 C\u03c6S\u03b8S\u03c8 \u2212 S\u03c6C\u03c8 \u2212S\u03b8 S\u03c6C\u03b8 C\u03c6C\u03b8  where S(.), C(.) and T(.) denote sin(.), cos(.) and tan(.), respectvely. \u03c6, \u03b8 and \u03c8 are the roll, pitch and yaw angles. 978-1-4799-9994-1/15/$31"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000845_j.scient.2012.01.004-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000845_j.scient.2012.01.004-Figure5-1.png",
        "caption": "Figure 5: Beam element geometry and structural degrees of freedom.",
        "texts": [
            " Arranging for unknown temperatures, a system of algebraic equations will result: [Rinv] {T } =  Q\u0307  , (23) which can be readily solved. {T } = {Ti, Tb, To}T is the vector of unknown temperatures and  Q\u0307  is the vector of transient thermal loads. Components of [Rinv], the inverse thermal resistance matrix, and  Q\u0307  , are given in the Appendix. Since the bearing is mounted between the shaft and housing, bearing ring temperatures are applied as thermal loads to the shaft and housing. Shaft and housing are treated as Timoshenko beamelements of a pipe type, with five structural and one temperature degrees of freedom (Figure 5). In finite element notation, the equation of motion of the beam can be written as: [M] {q\u0308} + [G] {q\u0307} + ([K ] + [MC ]) {q} \u2212 {Fth} = {F} , (24) [M], the mass matrix [G], the gyroscopic matrix, [K ], the stiffness matrix, and [MC ], the centrifugal matrix, are taken from [15]. {q} is the vector of structural degrees of freedom. F is the vector sum of distributed and concentrated forces applied on the beam. {Fth} is the vector of the thermal load and is evaluated in the thermal model below. The heat transfer equation for the finite element formulation of the beam as a two-node two-degree-of-freedom thermal element is presented here: C t e   T\u0307 e +  K tb e  +  K tc e   T e =  Q c e  , (25) {T e} is the vector of nodal temperatures,  C t e  is the thermal damping (specific heat) matrix,  K tb e  is the diffusion conduc- tivity matrix,  K tc e  is the surface convection matrix and  Q c e  is the convection surface heat flow vector"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002251_j.isatra.2016.08.002-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002251_j.isatra.2016.08.002-Figure2-1.png",
        "caption": "Fig. 2. Schematic diagram of an AUV in body coordinates with respect to the inertial frame [47].",
        "texts": [
            "101 Motion of a vehicle is introduced by rotational and translational movement vectors in the body fixed frame with respect to an inertial frame by the following definitions: \u03b7\u00bc \u03b71 \u03b72 h iT ;\u03b71 \u00bc x y z T ;\u03b72 \u00bc \u03d5 \u03b8 \u03c8 h iT ; v\u00bc v1 v2\u00bd T ; v1 \u00bc u v w\u00bd T ; v2 \u00bc p q r\u00bd T ; \u03c4\u00bc \u03c41 \u03c42\u00bd T ; \u03c41 \u00bc X Y Z\u00bd T ; \u03c42 \u00bc K M N\u00bd T \u00f024\u00de where \u201cT\u201d denotes the transpose operator. Meanwhile v shows the linear and angular velocities in the body frame and \u03b7 shows the relative angles and positions in the inertial frame. Forces and moments imposed on the vehicle in motion are also represented by \u03c4. Definitions provided in (24) are in accordance with Fig. 2 and Table 1. Kinematics equations, indicating the relation between two frames, are as follows: Assuming that centers of gravity and buoyancy in three axes are as follows: rG \u00bc xG yG zG 2 64 3 75; rB \u00bc xB yB zB 2 64 3 75 \u00f026\u00de And assuming that m is the vehicle mass and Ix, Iy and Iz are vehicle moments of inertia, the AUVs governing dynamic equations can be achieved as follows [48]: m\u00bd _u vr\u00fewq xG\u00f0q2\u00fer2\u00de\u00feyG\u00f0pq _r\u00de\u00fezG\u00f0pr\u00fe _q\u00de \u00bc X X m\u00bd_v wp\u00feur yG\u00f0r2\u00fep2\u00de\u00fezG\u00f0qr _p\u00de\u00fexG\u00f0qp\u00fe _r\u00de \u00bc X Y m\u00bd _w uq\u00fevp zG\u00f0q2\u00fep2\u00de\u00fexG\u00f0rp _q\u00de\u00feyG\u00f0rq\u00fe _p\u00de \u00bc X Z back controller for pitch and yaw channels of an AUV with 6/j"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002387_9781118773826-Figure4.3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002387_9781118773826-Figure4.3-1.png",
        "caption": "Figure 4.3 Nyquist plot in the complex plane and Randles equivalent circuit (top right) used for the fi tting.",
        "texts": [
            " In this plot, the impedance function is represented as a vector with magnitude Z 0 , and a direction given by the phase angle . Another popular presentation of impedance results is given by the Bode plot, in which both the absolute value of the impedance and the phase shift are plotted in the y-axis versus the frequency, which is represented in the x-axis. Albeit having the disadvantage of not explicitly showing the frequency information, the Nyquist plot continues to be the most used representation for impedance data, especially in electrochemical studies. Figure 4.3 shows a typical example of a Nyquist plot of a generic electrochemical reaction taking place at an electrode. Th e corner insert schematizes the electrical equivalent circuit representing its behavior, called Randles\u2019 equivalent circuit [56]. Each point plotted in the spectrum corresponds to a diff erent recorded frequency. Low frequency data are on the right side of the plot and high frequencies are on the left . Th e theoretical electrical circuit (Randles\u2019 equivalent circuit) comprises a resistance R 1 in series with the R 2 C element which also includes a Warburg impedance (term W)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001742_0954406214531943-Figure10-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001742_0954406214531943-Figure10-1.png",
        "caption": "Figure 10. The full finite element model of the linear guideway.",
        "texts": [
            " It can be seen that the contact deformation and stiffness obtained with FEM are slightly different than the analytical results, but the tendencies of variation are consistent. at UNIV OF CONNECTICUT on June 15, 2015pic.sagepub.comDownloaded from Modeling of the full finite element model of guideway To create the full finite element model of the linear guideway, each ball bearing in the grooves should be molded using contact elements introduced in the above section, and the created model is shown in Figure 10. There are 1,380,934 elements and 1,380,934 nodes in the model, during which there are 93,312 contact elements and 13,392 target elements. The load interval is chosen from 0 to 20 kN, the relative deformation H and vertical stiffness KF are calculated using the full finite element model, and the results are shown in Figure 11. The expression of vertical stiffness of guideway is KF P H \u00f025\u00de It can be seen from Figure 11 that the calculation results are consistent with the statics experiment. However, due to the huge number of contact elements in the model, the calculations need to consume a lot of time"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000857_j.cma.2013.12.017-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000857_j.cma.2013.12.017-Figure7-1.png",
        "caption": "Fig. 7. Sketch of coordinate transformation from Sc\u00f0xc ; yc ; zc\u00de to S1\u00f0x1; y1; z1\u00de.",
        "texts": [
            " This equation is satisfied and the gear tooth surface indeed exists if it remains tangent to its generating tool surface. The sufficient conditions of existence of the envelope to a family of surfaces (conditions of nonundercutting) can be found in [9]. In this work, the differential geometry approach for determination of the equation of meshing has been used [9]. The following equations of meshing relate surface parametric coordinates u and h, for the main generating surface, and k and h, for the edge generating surface, with the generalized parameter of movement w1 (see Fig. 7): f \u00f0u; h;w1\u00de \u00bc @r\u00f0P\u00de1 @u @r\u00f0P\u00de1 @h ! @r\u00f0P\u00de1 @w1 \u00bc 0 \u00f017\u00de f \u00f0k; h;w1\u00de \u00bc @r\u00f0P\u00de1 @k @r\u00f0P\u00de1 @h ! @r\u00f0P\u00de1 @w1 \u00bc 0 \u00f018\u00de The parametric representation of the family of face-milling cutter generating surfaces in reference coordinate system S1\u00f0x1; y1; z1\u00de, fixed to the generated gear, is given by Eqs. (19) and (20). The coordinate transformation from coordinate system Sc\u00f0xc; yc; zc\u00de, fixed to the cutter, to coordinate system S1\u00f0x1; y1; z1\u00de, fixed to the being-generated gear, is represented in Fig. 7 and given by matrix M1c . r\u00f0P\u00de1 \u00f0u; h;w1\u00de \u00bc x\u00f0P\u00de1 \u00f0u; h;w1\u00de y\u00f0P\u00de1 \u00f0u; h;w1\u00de z\u00f0P\u00de1 \u00f0u; h;w1\u00de 1 2 66664 3 77775 \u00bcM1c\u00f0w1\u00der\u00f0P\u00dec \u00f0u; h\u00de \u00f019\u00de r\u00f0P\u00de1 \u00f0k; h;w1\u00de \u00bc x\u00f0P\u00de1 \u00f0k; h;w1\u00de y\u00f0P\u00de1 \u00f0k; h;w1\u00de z\u00f0P\u00de1 \u00f0k; h;w1\u00de 1 2 66664 3 77775 \u00bcM1c\u00f0w1\u00der\u00f0P\u00dec \u00f0k; h\u00de \u00f020\u00de M1c\u00f0w1\u00de \u00bc cos w1 sin w1 0 rp\u00f0sin w1 w1 cos w1\u00de \u00fe rc cos w1 sin w1 cos w1 0 rp\u00f0cos w1 \u00fe w1 sin w1\u00de rc sin w1 0 0 1 0 0 0 0 1 2 6664 3 7775 \u00f021\u00de Finally, by introducing Eqs. (19) and (20) into Eqs. (17) and (18), respectively, analytic expressions of equations of meshing corresponding to being-generated gear tooth surfaces are derived, which are shown in Eqs"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003412_j.isatra.2020.10.040-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003412_j.isatra.2020.10.040-Figure5-1.png",
        "caption": "Figure 5: Fo rated by the relative wind",
        "texts": [
            " Moreover, the Journal Pre-proof r, the forces generated by the horizontal stabilizer due to the relative wind speed vair xz ( uted as follows f drag hxz = \u22121 2 \u03c1sh ( vair xz )2 cd hxz (\u03b1air), f li f t hxz = p f li f t hxz + a f li f t hxz = 1 2 \u03c1sh ( vair xz )2 cl hxz (\u03b1air) \ufe38 \ufe37\ufe37 \ufe38 p f li f t hxz + 1 2 \u03c1sh ( vair xz )2 ce\u03b4e \ufe38 \ufe37\ufe37 \ufe38 a f li f t hxz , air), cl hxz (\u03b1air), ce \u2208 R are aerodynamic coefficients non-dimensionalized with respect n (27) is a function of the elevator deflection and weights its influence on the aircraft is work assumes that the forces generated by the relative wind speed vair xy in the horizonta le for control purposes. Thus, the generalized forces applied to the system due to the e given by \u03d1h = (Jh)\u2032 Force w.r.t I\ufe37\ufe38\ufe38\ufe37 RIB fh , fh = RB \u03b1air  f drag hxz 0 f li f t hxz  , inear velocity Jacobian Jh = \u2202vIh /\u2202q\u0307 is related to the aerodynamic center of the horizo vIh = d pIh /dt = Jh q\u0307, pIh = \u03be + RIBdBh , and dBh \u2208 R3\u00d71 is the distance from the body fr tabilizer aerodynamic center. e aerodynamic forces acting on the aircraft due to the vertical stabilizer (see Figure 5 f drag vxy = \u22121 2 \u03c1sv ( vair xy )2 cd vxy (\u03b2air), f li f t vxy = p f li f t vxy + a f li f t vxy = 1 2 \u03c1sv ( vair xy )2 cl vxy (\u03b2air) \ufe38 \ufe37\ufe37 \ufe38 p f li f t vxy + 1 2 \u03c1sv ( vair xy )2 cr\u03b4r \ufe38 \ufe37\ufe37 \ufe38 a f li f t vxy , air), cl vxy (\u03b2air), cr \u2208 R are aerodynamic coefficients non-dimensionalized with respect n (31) is a function of the rudder deflection \u03b4r and weights its influence on the aircr out the text the subscripts \u201ch\u201d and \u201cv\u201d will be used to denote the horizontal and vertical stabilizer, Jo ur na Pr epr oo f superscripts \u201ca\u201d and \u201cp\u201d will be used to denote passive and active aerodynamic forces, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000618_j.mechmachtheory.2009.11.007-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000618_j.mechmachtheory.2009.11.007-Figure2-1.png",
        "caption": "Fig. 2. A 6 d.o.f hybrid robot composed of two different parallel modules.",
        "texts": [
            " In this paper we propose the exploitation of this method for the dynamic modeling of hybrid structures. The hybrid robots treated in this paper are composed of serially connected non-redundant parallel modules like the Logabex LX4 robot (Fig. 1) [16] and biomimetic robots snakes robots [17,18]. The serial form of these hybrid manipulators overcomes the limited workspace of parallel manipulators and improves overall stiffness and response characteristics. The proposed methodology can be easily applied to hybrid robots that are constructed of different parallel modules (Fig. 2) [19], or by combination of serial and parallel modules (Figs. 3 and 4) [20]. Among the very few work approached the dynamic modeling of hybrid robots, we can find Freeman and Tesar [21], Sklar and Tesar [22] who used the principle of D\u2019Alembert with the equivalent tree structure of the closed structure, and Chung et al. [23] who calculate at first the local dynamics of each module with respect to the independent joint coordinates and then the dynamics of the hybrid robot is calculated by using the concept of the virtual joints that are attached to the base of each module"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000024_0278364909104296-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000024_0278364909104296-Figure1-1.png",
        "caption": "Fig. 1. The sagittal-plane \u201ccompass-gait\u201d bipedal robot.",
        "texts": [
            " The humanoid form of locomotion known as dynamic bipedal walking is based on \u201ccontrolled falling\u201d, where each leg\u2019s step cycle involves a fall towards the ground until foot impact transfers this falling motion to the other leg (enabling a hybrid sense of stability for the walking gait). This is quite different from the \u201cquasi-static\u201d locomotion of the popular Honda Asimo and Sony Qrio robots. These bipeds maintain a static sense of stability during each step cycle, resulting in unnatural and inefficient shuffling motion (Kuo 2007). The first significant studies in dynamic bipedal walking concerned simple models constrained to the sagittal plane (two-dimensional space), such as the uncontrolled two-link \u201ccompass-gait\u201d biped of Figure 1, to roughly approximate human dynamic motion. McGeer (1990) discovered the existence of stable \u201cpassive\u201d limit cycles down shallow slopes for the compass-gait biped, and passive dynamic walking was further studied by Goswami et al. (1996). Chevallereau et al. (2003) proved that stable limit cycles could be generated for underactuated planar walkers using a control method known as hybrid zero dynamics (Westervelt et al. 2003 Morris and Grizzle 2006), in which output linearization is employed to zero hybrid-invariant output functions (i"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002727_tnnls.2018.2844173-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002727_tnnls.2018.2844173-Figure1-1.png",
        "caption": "Fig. 1. Body-fixed and inertial frame of the helicopter.",
        "texts": [
            " The rest of this paper are arranged as follows. The mathematical foundation is introduced in Section II, and the proposed identifier with a deep CNN is presented in Section III. The introduction of the adaptive backstepping controller and the rigorous proofs of the stability are expressed in Section IV. Section V presents the details of experiment setting and the corresponding experimental results. In this section, we briefly go over how to explain the kinematics equations of unmanned helicopter (shown in Fig. 1) in terms of quaternion [26]. The attitude of the helicopter can be denoted by a quaternion, a four-element vector with one real and three imaginary components, so that q = e1i + e2 j + e3k + e4 = [ e1 e2 e3 e4 ]T = \u23a1 \u23a3 u sin \u03b1 2 [0.6 pc] cos \u03b1 2 \u23a4 \u23a6 = [ \u03b5 \u03bb ] \u2016q\u2016 = e2 1 + e2 2 + e2 3 + e2 4 = 1 (1) where u = [ux uy uz]T is a unit vector with its norm to be equal to unity. \u03b5 represents a vector, and \u03bb is a scalar. The direction cosine matrix is parameterized by quaternion q , representing the transformation from the inertial frame into the body-fixed frame",
            " These submodels give a better representation of the locally dynamic properties of the adjacent states either in the time dimension or variable dimension and are effectively combined together to construct a global nonlinear model of the hidden states or uncertainties in system dynamics. In addition, we present a method for optimizing the parameters of the proposed dynamic model. A two-step optimization strategy is adopted. The parameters of the first-principlesbased model are first optimized while keeping the uncertainties keeps fixed. Then, the weights and biases of deep CNN are optimized by using stochastic gradient descent (SGD) [45]. Considering the unmanned helicopter shown in Fig. 1, it contains six degrees of freedom, which are the position r = [rx ry rz]T \u2208 R 3 and the attitude [\u03c6 \u03b8 \u03d5]T \u2208 R 3 expressed in the Cartesian coordinates, respectively. Particularly, to eliminate kinematic singularity, we use the unit quaternion q = [e1 e2 e3 e4]T \u2208 R 4 to replace the Euler angle [\u03c6 \u03b8 \u03d5]T \u2208 R 3 in the proposed dynamic model. Here, we assume that the origin of the body-fixed frame to be at the center of mass of the helicopter, and then, the linear velocity and the angular velocity with respect to the origin can be denoted with v = [vx vy vz]T \u2208 R 3 and \u03c9 = [\u03c9x \u03c9y \u03c9z]T \u2208 R 3, respectively"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000648_978-3-642-17531-2-Figure6.12-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000648_978-3-642-17531-2-Figure6.12-1.png",
        "caption": "Fig. 6.12. Voltage-drive electrostatic plate transducer with variable electrode separation and series resistor",
        "texts": [
            " The electrostatic force thus now follows the rule 2 2 2 2 1 1 ( , ) 2 2( ) ( ) el S S S serialserial x F x u u u x xx CC . Advantages, disadvantages, limitations Electrically increasing the armature travel maintains a compact geometry. Due to the voltage divider behavior of this method, however, a higher control voltage is required than in the case of direct transducer control. In addition, parasitic capacitances still limit stable operation (Chan and Dutton 2000). Transducer with a voltage source and serial resistance Fig. 6.12 depicts an arrangement consisting of a voltage-drive plate transducer with a series resistor R . In Sec. 5.5, the dynamics of a lossy elementary transducer were discussed in detail; these can now be demonstrated concretely in this transducer type. As previously explained, mechanical energy is dissipated in the electrical loop via electromechanical coupling, resulting in passive damping of the mechanical single-mass oscillator. Thus, the resistance value should be considered an important design degree of freedom"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002687_tmag.2017.2665580-Figure5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002687_tmag.2017.2665580-Figure5-1.png",
        "caption": "Fig. 5. Load flux plot distributions with different excitations simulated by the FEA. (a) PM with 12A AC current. (b). PM, 4.3 A DC, and 11.2 A AC current.",
        "texts": [],
        "surrounding_texts": [
            "0018-9464 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.\n978-1-5090-1032-5/16/$31.00 \u00a92016 IEEE\nthe phase difference of 120 degree.\nTo analyze the machine performance, FEA model of the proposed machine is designed and the main parameters are shown in Table I.\nThe proposed machine fed with DC biased current can be considered as the combination of a quasi FRPM with a DCbiased current vernier reluctance machine (DC-biased-VRM). Therefore, the principle can be explained by the superposition of FRPM and DC-biased-VRM using flux modulation principle [6]-[8]. To illustrate the principle clearly, the harmonics are neglected and only the fundamental components are considered.\nFirstly, a multipole stationary magnetic motive force (MMF)\nproduced by stator located PMs can be expressed as\n1 cos( )PM PM pmF F P  (2)\nwhere PPM is the fundamental pole pair number of PM MMF.\nSimilarly, by injecting DC current into the specified arranged armature winding, another stationary MMF can also be produced\n1 cos( )dc dc dcF F P  (3)\nwhere Pdc is the fundamental pole pair number of stationary MMF produced by DC current.\nSecondly, the salient rotor structure acts as a permeance modulation function. Only considering the 1st order harmonic, it can be expressed as:\n0 1 sin( ( ))r r rP P P N w t   (4)\nThe resultant exciting fields by multiplying the stationary\nMMF by the permeance modulation function are\n 1 1 0\n1 1\n1 1\n( ) cos( ) cos( )\nsin(( ) )1\nsin(( ) )2\ng dc PM r PM PM dc dc\nPM r PM r r\nPM r PM r r\nB F F P F P F P P\nF P N P N w t\nF P N P N w t\n \n\n\n    \n     \n   \n(5)\nIt can be found that the fields contain stationary components (the first one), and the rotating components (the second one). Generally, the rotating fields can induce back-EMF in armature winding.\nTherefore, in order to produce non-zero torque, the armature winding pole pair number Pa, and the electrical frequency we, should be agreement with the rotating fields, that is to say, the following equation should be satisfied\na pm rP P N  (6)\na dc rP P N  (7)\n(2 ) 60 e r r r\nn w N w N   (8)\nwhere Nr is the rotor slot number, and wr is the mechanical\nfrequency.\nBased on Eq. (5) and (6), the pole pair numbers of the proposed machine can be determined and are listed in Table II.\nThe maximum torque per current control of the proposed machine is zero d-axis current control. The electromagnetic torque expression under Id=0 control is\n( )em r pm dc q r pm ac r dc m acT N I N I N I L I      (9)\nwhere \u03c8pm, \u03c8dc are the flux linkage by PM and DC current, respectively. Lm is the equivalent magnetizing inductance.\nIt can be found that with the proposed DC-biased current configuration, in addition to the PM torque component, another torque component which is proportional to the square of current is introduced.\nFig. 2 compares the no load flux distributions with different excitations simulated by the FEA. In Fig. 2 (a), the PMs are removed, the main flux produced by DC current bypasses the PMs, but through the adjacent iron shoe, this condition is similar to the no load situation in VRM. Another condition is the sole PM excitation in Fig. 2 (b) which is similar to the no load situation in FRPM, when the stator PM aligns with the center of the rotor slot, the magnetic flux forms mostly leakage flux, while when the stator PM aligns with the rotor tooth, the magnetic flux leakage is the least. It can be inferred that, due to the large flux leakage, the open circuit back-EMF will be small, which is helpful for the short circuit current reduction during short-circuit condition. To some extent, when both the DC current and PM are excited, the flux distribution at this time can be roughly considered to be a superposition of the two cases, as shown in Fig. 3 (c), but it is worth noting that at this time due to the impact of magnetic field generated the DC current, the total flux leakage by the PM is reduced.\nIn order to further illustrate the field distributions with different excitations, the air gap flux densities are analyzed. As shown in Fig. 3, the flux density waveforms are particularly irregular, however, by harmonic analysis, it can be found that",
            "0018-9464 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.\n978-1-5090-1032-5/16/$31.00 \u00a92016 IEEE\nthe main working magnetic field, the 4th in the hybrid excitation is greatly enhanced, which proves the flexible flux adjustment ability.\nB. Virtual Back-EMF\nFig. 4 compares the back-EMFs with different DC currents. It can be seen that the fundamental component can either increase or decrease with the injected DC current. This illustrates the flexible field adjustment ability.\nIn addition, it can be found that the main harmonics include not only the 5th, the even-order harmonics also appear. Moreover, the injected DC current can change the total harmonic distortion (THD), when with a DC current of 4 A, minimum THD (5.5%) is obtained.\nWhen three phase balanced AC currents are fed into the armature winding, average torque will be produced. The flux distributions with traditional pure AC current and novel DCbiased current are simulated with FEA. Comparison results shows that the flux distributions are quite different. When with PM and AC current excitations, considerable flux leakage exists when the stator PM is aligned with the center of the rotor slot. While when with DC-biased current, because both the magnetic fields produced by DC and AC current flow through the stator tooth iron near the PM, the leakage flux is reduced further.\nDefining the DC current ratio is\ndc rmsk I I (10)\nwhere k is the DC current ratio. The high k, the high biased level in the phase current waveform.\nThe AC component in phase current can be determined by\n21ac rmsI k I  (11)\nThe traditional pure sinusoidal current can be regarded as a case of zero DC current ratio. Fig. 6 shows the simulated average torque variation with the DC current ratio when the phase current is 12 A. It can be seen that the torque increases with the DC ratio, then reaches a maximum value, and after that the torque begins to decrease. Under the constant phase current, that is constant copper loss, from Eq. (9), the optimum DC ratio for maximum torque is related to the PM flux linkage,\n\u03c8PM, and the magnetizing inductance, Lm. For this designed machine, the optimal value of k is 0.36.\nThe structure of uneven rotor tooth distribution is adopted to reduce the torque ripple. As shown in Fig. 7, all the rotor teeth have the same width and length, but the odd number rotor teeth are rotated 1.5 mech. degree clockwise. The electromagnetic torque waveforms with pure and with a DC ratio of 0.36 are compared in Fig. 8 (a). The average torque increases from 3.22 Nm to 3.57 Nm, about 11% improvement,",
            "0018-9464 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.\n978-1-5090-1032-5/16/$31.00 \u00a92016 IEEE\nwhat is more, the torque ripple is reduced form 15.6% to 7.5%. The corresponding current waveforms are compared Fig. 8 (b). For the hybrid excitation, the DC/AC component is 4.3/11.2 A.\nFig. 9 reveals the average torque variation with current based on the maximal torque control strategy. As shown, with pure sinusoidal current, the torque increase ratio decreases gradually, while with the hybrid excitation, the torque can maintain a high increase as the emerging torque component is proportional to the square of the current, that is to say, the emerging torque component produced by DC and AC current grows faster than PM torque. Therefore, the proposed current configuration can improve the machine over load capacity.\nThe electromagnetic performance of machines in Fig.1 are compared while keeping the same geometrical parameters, the same coil turns, and the same phase current. The results in Table III show that the proposed machine exhibits higher back-EMF, higher output torque both in pure AC current configuration and DC-biased current configuration. The reason is that in the proposed consequent pole structure, only half of stator tooth iron shoes suffer from the saturation. Besides, the consequent pole can reduce the equivalent air gap length. Therefore, the performance of the consequent pole structure is better than that of the existing machine.\nThis paper proposes a novel hybrid excitation, stator-PM, consequent pole vernier machine with dc-biased sinusoidal current. The principle and electromagnetic performance are analyzed. It is found that the injected DC current can adjust the exciting field flexibly. Besides, due to the inherent structure, small short-circuit fault current would be expected due to low back-EMF under open-circuit. Furthermore, it is found that the proposed DC-biased current configuration can increase the torque density in the case of the same copper loss, and hence will have a higher efficiency. In addition, the motor overload capacity is stronger.\n[1] A. M. EL-Refaie, \u201cFractional-slot concentrated-windings synchronous\npermanent magnet machines: opportunities and challenges,\u201d IEEE Trans. Ind. Elec., vol. 57, no. 1, Jun. 2010. [2] J. Cros and P. Viarouge, Synthesis of high performance PM motors with\nconcentrated windings,\u201d IEEE Trans. Energy Convers., vol. 17, no. 2,\npp. 248-253, Jun. 2002. [3] M. Cheng, W. Hua, J. Zhang, and W. Zhao, \u201c Overview of stator-\npermanent magnet brushless machines,\u201d IEEE Trans. Ind. Electron., vol. 58, no. 11, pp. 5087\u20135101, Nov. 2011. [4] S. Jia, R. Qu, J. Li, D. Li, and H. Fang, \u201cHybrid excited vernier PM\nmachines with novel DC-biased sinusoidal armature current,\u201d in Proc. of IEEE Conference of ECCE\u20192016. [5] A. Kohara, K. Hirata, N. Niguchi, and Y. Ohno, \u201cFinite element analysis\nand experiment of current superimposition variable flux machine using permanent magnet,\u201d IEEE Trans. Magn., vol. 52, no. 9, pp. 8107807, Sep. 2016. [6] Z. Q. Zhu and D. Evans, \u201cOverview of recent advances in innovative electrical machines\u2014with particular reference to magnetically geared\nswitched flux machines,\u201d in Proc. ICEMS., Oct. 2014, pp. 1\u201310.\n[7] S. Jia, R. Qu, J. Li, and D. Li, \u201cPrinciples of stator DC winding excited vernier reluctance machines,\u201d IEEE Trans. Energy Convers., Vol.31,\nNo.3, Sep., pp: 935-946, 2016.\n[8] S. Jia, R. Qu, J. Li, and D. Li, \u201cFlux modulation principles of DC-biased sinusoidal current vernier reluctance machines,\u201d in Proc. of IEEE\nConference of ECCE\u20192016."
        ]
    },
    {
        "image_filename": "designv10_5_0002832_tie.2017.2677330-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002832_tie.2017.2677330-Figure1-1.png",
        "caption": "Fig. 1. AV-FPSO system.",
        "texts": [
            "org/publications_standards/publications/rights/index.html for more information. Index Terms\u2014Synchronized tracking control, accommodation vessel, floating production storage and offloading, neural network, robust H\u221e control, artificial potential. I. INTRODUCTION W ITH the increasing demand for exploration and exploitation of offshore oil and gas, more and more offshore operations have to take place in deeper water area. In order to ensure smooth operation for such offshore work, Floating Production Storage and Offloading (FPSO) shown in Fig. 1 as working platform always requires the accompany of Accommodation Vessels (AV), which are used to provide the space for logistic support and opened deck. Since personnel transportation and equipment transfer between AV and FPSO are achieved by gangway shown in Fig. 1, AV must be This work was supported in part by the Doctoral Scientific Research Staring Fund of Binzhou University under Grant 2016Y14 and in part by Keppel-NUS Collaboration Lab under Singapore National Research Foundation under Grant R-261-507-004-281. G. X. Wen is with the Department of mathematics, Binzhou University, Binzhou, 256600, Shandong, China and also with the Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117576 (E-mail:gxwen@live.cn)"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000492_tie.2011.2168795-Figure25-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000492_tie.2011.2168795-Figure25-1.png",
        "caption": "Fig. 25. Magnitude of the third harmonic of magnetic flux density for motor B.",
        "texts": [],
        "surrounding_texts": [
            "This paper has presented a no-load core loss analysis of three-phase energy-saving small-size induction motors fed by sinusoidal voltage, using a combination of the timestepping FEM and an analytical approach, which offers rapid computation. In this field-circuit approach, the distribution and changes in magnetic flux densities of the motor are computed using a time-stepping FEM. A DFT is then used to analyze the magnetic flux density waveforms in each element of the model obtained from several snapshots taken over a voltage cycle of the time-stepping solution. Rotational aspects of the field are accounted for by introducing a correction to the first harmonic of the alternating losses. The core losses in each element are evaluated using the specific core loss expression, in which the frequency-dependent parameters and flux are derived from a test conducted on a sample laminated ring core. The results are compared with measurements, and good agreement is observed for both methods. However, the field-circuit timestepping method is quite time consuming, so for optimization, the rapid analytical method is to be recommended. APPENDIX A FLUX DENSITY HARMONICS See Figs. 25\u201327. APPENDIX B CORE LOSS SPECTRUM See Figs. 28 and 29."
        ]
    },
    {
        "image_filename": "designv10_5_0000874_j.wear.2013.01.047-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000874_j.wear.2013.01.047-Figure1-1.png",
        "caption": "Fig. 1. Structure of the roller linear guide.",
        "texts": [
            " By using the Archard wear theory, we analyze the wear process of roller linear guides and realize the calculation model of the displacement of the slider, which is due to the wear loss of the slider\u2019s raceway, to predict the wear of the roller linear guide. Finally, through simulations and experiments on a specialized test system, we verify the effectiveness of the proposed models on stiffness and wear prediction. 2. Contact stiffness of roller linear guides 2.1. Load and elastic deformation of the roller The roller linear guide is mainly composed of a rail, slider, roller, cage assembly, and endplate ,and transports the slider by using four rows of recirculating rollers (Fig. 1). Cages are located between the rollers to prevent rollers from interacting. The endplate is fixed on the end of the slider to ensure the recirculating motion of the rollers. When the roller linear guide is used in machine tools and machining centers, the load mainly includes the vertical load on the upper surface of the slider, the horizontal load on the side surface of the slider, and the turning torque around the motion direction of the load. Deformation is generally applied to the roller to form a pre-load on the roller linear guide and eliminate the gap between the roller and raceway, thus increasing the stiffness of roller linear guides"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000509_1.4005952-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000509_1.4005952-Figure2-1.png",
        "caption": "Fig. 2 Idealized point/elliptical contact EHL",
        "texts": [
            " 1, in which it is assumed that the contact line is infinitely long in the y-direction, and the load is uniformly distributed, so that the problem can be simplified to that of two-dimensional (2D) plain strain if the surfaces are assumed to be smooth. The original geometric gap between the two surfaces without deformation can be approximated by the following expression based on its Taylor expansion series: f \u00f0x; y; t\u00de \u00bc x2 2Rx (1) where Rx is the effective radius of curvature in the direction of rolling perpendicular to the contact line. An idealized EHL point contact is illustrated in Fig. 2, which is three-dimensional (3D) in nature. In the same way the original gap between the two surfaces can be given roughly by f \u00f0x; y; t\u00de \u00bc x2 2Rx \u00fe y2 2Ry (2) However, in reality the contact geometry of mechanical components is often more complicated. Typical \u201cline contact\u201d components, such as gear teeth and bearing rollers, are usually designed to have a crown along the contact length direction in order to accommodate possible misalignment, fabrication errors, and nonuniform load distribution"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001880_j.applthermaleng.2014.02.008-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001880_j.applthermaleng.2014.02.008-Figure3-1.png",
        "caption": "Fig. 3. The measured temperature positions and boundaries of solving region.",
        "texts": [
            " The temperature on the frame of the machine was tested by infrared thermoprobe, and the wind speed on the shell surface was measured by anemometer EY3-2A. 3. Thermal field modeling and boundaries of the solving region 3.1. The thermal field modeling The 3-D model of the motor is employed in this paper, and the FEM solution was achieved by the software \u201cANSYS\u201d. Thermal models in Fig. 2 have been developed for the prototype motor, which allows us to estimate the stator and rotor temperature. The proposed model is intended to compute the motor temperature in steady-state condition. In Fig. 3, S1eS7 are the boundaries of the solving region. The region S1 is the face of the motor frame, S2 is the internal surface of the connecting box, S3 is the contact surface of motor frame and stator, S4 is the end face of the stator, S5 is the internal surface of the stator and the outer surface of the rotor, S6 is the end face of the rotor, S7 is the end face of the end-ring. The measured positions are also given in Fig. 3A, B, C are three points of the radiating fins. The sensor D is mounted on the stator wedge and is faced with air-gap, which allows us to get the airgap temperature near the stator. Two sensors, E and G, are inserted inside a stator slot center, and the difference between them is that point G is near the junction box and point E is located in the opposite side of the junction box. Sensor F has been positioned on the rotor bar, while in the condition of broken bars fault, the sensor F is included in the hole positioned in the broken rotor bar"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003379_j.commatsci.2020.109788-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003379_j.commatsci.2020.109788-Figure3-1.png",
        "caption": "Fig. 3. Laser-particle interaction in the (a) experiment and (b) DEM.",
        "texts": [
            " Then, the temperature distributions as well as the thermal histories are obtained by the moving heat source model. Finally, the obtained temperatures are combined with the established phase-field model to simulate the solidification process in DED-AM. The powder was ejected from the nozzles at a certain velocity along the coaxial direction of the nozzles. During the flight process in the laser beam, both consumptions and absorptions of laser energy can be obtained and the powder particles are heated during the flight, as displayed in Fig. 3. The heat absorbed by the flying particles depends on many factors, e.g., laser power density, material properties, gas velocity, and residence time [13]. Moreover, the spatial distribution of particles in the laser beam also affects the absorption of heat. It has been proved that the distribution of the powder stream is one of the important parameters to obtain the optimum conditions of the DED, and some studies [19\u201321] analyzed the powder stream characteristics using the computational fluid dynamics method. In this study, we focused on the distribution of powder particles in the beam\u2013powder interaction zone. In that zone, the effect of gas on the particle movements was not considered based on Ref. [22]. To consider the interaction between the powder particles and laser beam, we made the following assumptions: (1) the powder particles are spherical, (2) gravity is neglected, and (3) the initial velocities of all powder particles are the same. As shown in Fig. 3(b), a series of spatially distributed particles generated by the EDEM software, which is based on the discrete element method (DEM), is used. The effect of gravity on particle flight was not considered owing to the short distance. According to the DEM, the movement of an individual particle can be expressed by translational and rotational motions given by where mi, Ii, vi, and \u03c9i are the mass, moment of inertia, translational velocity, and angular velocity, respectively; Fn,ij and Fs,ij are the normal and tangential contact forces, respectively; Ri is a vector from the center of the particle to the contact point and \u03bcr is the rolling friction coefficient"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001968_978-94-007-6101-8-Figure2.5-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001968_978-94-007-6101-8-Figure2.5-1.png",
        "caption": "Fig. 2.5 Orientation of robot gripper",
        "texts": [
            "24) 0R2 = 0R1 1R2 This is different from the previous chapter, where we considered consecutive rotations about different axes of the same coordinate frame. The consecutive orientations of several coordinate frames are described by the postmultiplication of the rotation matrices. We must have in mind, that consecutive orientations are related to the previous (relative) coordinate frame. The notion of orientation is in robotics mostly related to the orientation of the robot gripper. A coordinate frame with three unit vectors n, s, and a, describing the orientation of the gripper, is placed between both fingers (Fig. 2.5). The z axis vector lays in the direction of the approach of the gripper to the object. It is denoted by vector a (approach). Vector, which is aligned with y axis, describes the direction of sliding of the fingers and is denoted as s (slide). The third vector completes the right-handed coordinate frame and is called normal. There is n = s\u00d7 a. The matrix describing the orientation of the gripper with respect to the reference frame x0, y0, z0 has the following form: R = \u23a1 \u23a3 nx sx ax ny sy ay nz sz az \u23a4 \u23a6 (2",
            " The axes z4 and z5 are placed into wrist center Q. The x4 axis is perpendicular to the plane defined by the axes z3 and z4, while the x5 axis goes perpendicularly to the axes z4 and z5. The robot end-point or robot gripper point is denoted by the letter P. The axes of the corresponding frame are parallel to the axes of the precedent coordinate frame. The fingers of the gripper are rotated in such a way that the unit vectors n, s, and a are placed into the robot end-point. We got acquainted with these vectors already in Fig. 2.5. In order to make Fig. 5.2 more clear, the y axes have been not drawn. From Fig. 5.2 it is not difficult to read the DH parameters, which are inserted into the table. The lengths of the segments d1, a2, d4, and d6 are denoted in Fig. 5.2. i ai \u03b1i di \u03d1i 1 0 \u03c0/2 d1 \u03d11 2 a2 0 0 \u03d12 3 0 \u2212\u03c0/2 0 \u03d13 4 0 \u03c0/2 d4 \u03d14 5 0 \u2212\u03c0/2 0 \u03d15 6 0 0 d6 \u03d16 We write the matrices (4.3) with the DH parameters of each line. The matrices describe the relative poses of the neighboring coordinate frames: 0A1 = \u23a1 \u23a2\u23a2\u23a3 c1 0 s1 0 s1 0 \u2212c1 0 0 1 0 d1 0 0 0 1 \u23a4 \u23a5\u23a5\u23a6 (5"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002003_we.1721-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002003_we.1721-Figure1-1.png",
        "caption": "Figure 1. Schematic of an indirect drive train concept, out of American Gear Manufacturers Association Standard.14",
        "texts": [
            " For further reading, a review about smart rotor control can be found in the work by Barlas and van Kuik.13 Generally, there are two main drive train concepts widely used, the indirect-drive and direct-drive concept. The main difference is the integration of a gearbox to transform the low rotational speed from the rotor to a high rotational speed for the generator. Today, the concept without a gearbox is of great interest for offshore wind power plants to make the turbine more reliable due to the high repair costs in case of an error. The indirect drive is the current dominating design (Figure 1), where all components are mounted in line with a gearbox to transfer the low rotational speed from the rotor to a high rotational speed of 1500 rpm needed for 50 Hz (two-pole Wind Energ. (2014) \u00a9 2014 John Wiley & Sons, Ltd. DOI: 10.1002/we pair generator). With this approach, all components are assembled on a bedplate, which must be stiff enough to prevent misalignment between components. An advantage of this concept is the usage of standard components available on the market. The disadvantage is that the relative high weight comes with the stiff bedplate structure to support all functional components and to prevent misalignments in the DTS"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002941_j.ymssp.2016.07.007-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002941_j.ymssp.2016.07.007-Figure2-1.png",
        "caption": "Fig. 2. (a) A composite picture showing the sun gear, two of the three planet gears, the ring and a section of the carrier which comprise the fundamental elements of the epicyclic gearbox. (b) A photograph of the gearbox, with the planet gear tooth seeded with a defect marked. (c) An enlarged photograph of the planet gear tooth seeded with a defect visible. (d) A schematic showing an approximation of the amount of material removed from the entire face width of the gear tooth.",
        "texts": [
            " The motor was supplied with 430 VRMS direct on line via an autotransformer. The motor was connected via a ROTEX 48 coupling to the carrier of a Bonfiglioli 301 L1 PC 5.77 B3 in-line epicyclic gearbox with ratio 5.77. The gearbox was comprised of a 13 tooth sun gear, a 62 tooth fixed ring gear and three planets, each with 24 teeth. A composite picture showing the sun gear, two of the three planet gears, the ring and a section of the carrier which comprise the fundamental elements of the epicyclic gearbox is given in Fig. 2(a). Load to the systemwas provided by a 1.5 kW, 2 pole ABB M3BP 090 SLB 2 three phase induction motor with a nominal speed of 2900 RPM and nominal torque of 4.9 Nm, connected to the sun gear of the gearbox via a Rotex 42 coupling. The load motor was supplied via an ABB ACS800 variable speed drive which controlled the load on the system via Direct Torque Control. Data was collected with a National Instruments cDAQ-9138 measurement unit with dedicated measurement cards associated with each of the sensors used",
            " For each experiment, a minimum of 180 s of data was recorded. During post-processing, all signals were synchronized to ensure that they occurred at simultaneous time stamps using spline interpolation. Once measurements from the healthy system had been recorded, the gearbox was deconstructed and a defect was seeded into a tooth on one of the planet gears. Specifically, material was removed from the tooth surface using a milling machine, in order to simulate a tooth defect such as destructive pitting. Images of the seeded fault are given in Fig. 2 (b\u2013d). Fig. 2(b) shows a photograph of the defective tooth in situ, highlighting that material was removed from the entire tooth flank. Fig. 2(c) shows an enlarged view of the defective tooth. Fig. 2(d) shows a schematic, giving an approximate magnitude of the defect; it was estimated that the gear tooth deviated from its ideal profile by a maximum of 0.5 mm at approximately the pitch point. Once the tooth fault had been seeded into the planet, the gearbox was reassembled and the tests were repeated with the defective gearbox. The gearbox was reassembled in such a way that the defective tooth in the planet gear meshed with the sun gear when the system was rotating in its nominally positive direction"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001860_1464419315569621-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001860_1464419315569621-Figure4-1.png",
        "caption": "Figure 4. Load share of a typical roller-to-races\u2019 contact during a cage cycle under steady-state conditions for \u00bc 5 m.",
        "texts": [
            " The dominant base natural frequency of the limit cycle vibrations can best be observed in its frequency spectrum, shown in Figure 3(a) and (b) for the interference fitted and zero clearance bearings, respectively. The spectra in Figure 3 are the direct result of the effective dynamic stiffness of the bearing, affected by the contact deformation of the rolling element complement in their orbital motion about the centre of the bearing. The extent of contact stiffness variation of roller complement-to-races contact is best observed by load share of a typical rolling element during a steady-state cage cycle. This is shown in Figure 4 for the case of 5 mm interference fit. It is clear that a typical roller-to-raceways\u2019 contact is subjected to increased loading beyond the initial preload in the loaded region of the bearing in the region bounded by the section lines YY to XX in the figure (such as roller positions A1, B1 and C1). Conversely, reduced contact deformation occurs in the bearing arc XX to YY. Sufficient preload, as shown in the figure, ensures no loss of contact load (i.e. W> 0). Clearly, a reducing preload could result in loss of contact for some of the roller complement. This occurs for the case of mutual separation of bearing rings beyond zero clearance (i.e. poorly preloaded bearings). The spectrum of vibration, contained in the time history of Figure 4, is obtained after steady-state conditions are reached for several cage cycles. This is shown in Figure 5. Two frequency contributions make the basis of the spectrum (Figure 5(a)). These are the aforementioned base natural frequency of the bearing and the cage rotational frequency (the lowest bearing frequency: resulting from the cyclic repetition of the circumferential disposition of complement of rollers). Multiples of cage frequency occur because of the off-loading of roller-to-raceway contact reactions beyond the original applied preload",
            " This paper is focused on the determination of contact conditions under the prescribed dynamic analysis. To determine friction and generated heat a numerical solution of the thermo-elastohydrodynamic lubricated contact of roller-to-raceway is required. With the contact load variation determined in the previous section and the relative contact velocity of roller to raceway known under a given bearing operating condition, the solution can be obtained for a typical roller during the steady-state repetitive cage cycle in Figure 4. Reynolds equation is solved simultaneously with a contact thermal model. Reynolds equation of the following form is used to obtain the generated contact pressures @ @X h3 @p @X \u00fe @ @Y h3 @p @Y \u00bc 12 U @ @X h\u00bd \u00fe @ @t h\u00bd \u00f06\u00de where X is the direction of entraining motion of the lubricant into the contact and Y denotes the side leakage direction along the length of the roller. The side-leakage flow is considered to be negligible for the usually starved roller-to-races contacts, thus the remaining Couette flow (first term on the right-hand side of equation (6)) is that due to the lubricant at Kungl Tekniska Hogskolan / Royal Institute of Technology on September 10, 2015pik",
            " The data corresponds to the rear support roller bearing of the transmission input shaft of a heavy duty truck, equipped with a diesel engine delivering 2200 Nm (max) torque at the nominal engine speed of 209 rad/s. Results of thermo-elastohydrodynamic conditions are provided for both the traditionally assumed fully flooded inlet condition and those with the boundary conditions developed here. In addition, the contact load variation in a cage cycle within the limit cycle oscillations is taken from Figure 4. The squeeze velocity is initially set to zero and obtained thereafter as: @h @t \u00bc hk0 hk0 1 t , where the superscript k0 denotes the time step of simulation and t is the time-step size. Figure 9 shows the variation of squeeze velocity during a cage cycle for a typical roller-to-race contact. The variation closely follows the characteristic load per roller under bearing small amplitude oscillations. The aforementioned parameters are used to determine the lubricant film thickness and shape, as well as the corresponding pressure and temperature distributions in any roller-to-raceway contact at any instant of time. These correspond to the passage of a typical roller through various regions of the bearing, shown in Figure 4. Typical results are shown in Figure 10, for a roller traversing the loaded region of the bearing; positions A1, B1 and C1 in Figure 4. The horizontal axis in this figure is the distance along the direction of entraining motion (along the half width of the Hertzian contact footprint). The results in Figure 10 demonstrate the prevalent elastohydrodynamic regime of lubrication by the conformance of the lubricated pressure profiles to the dry elastostatic Hertzian condition (also included in the figure), except for the inlet trail and the pressure spike in the vicinity of the contact exit. These are important in the determination of film thickness, shear rate and ultimately the generated friction",
            " The increased film thickness results in reduced friction because of a decrease in boundary friction contribution (for the cases A1 and C1 when compared with the case B1) as shown in Table 3. The table also provides the total friction due to the prevailing mixed regime of lubrication (boundary and viscous shear of the thin non-Newtonian film). It can also be observed that with realistic boundary conditions a slightly starved contact results which marginally increases the predicted friction from its idealistic fully flooded inlet condition (by an average of 12.5%). The instantaneous kinetic coefficient of friction can also be obtained since the contact load is known from Figure 4 (marked by positions A1, B1 and C1). This is around 0.01, which is far less than the impractical dry contact Coulomb friction value of steel counterfaces of about 0.15\u20130.2, which is often used in dry contact analysis. Figure 11 shows the temperature distributions through mid-plane of contact, corresponding to the results in Figure 10. The temperature closely follows the same trend as the pressure distribution. An interesting point is that the reduced thermal wedge effect in Figure 11(B1), with lack of a dimple (Figure 10(B1)) is a clearly an effect of contact kinematics, not the underlying cause for the squeeze caving phenomenon"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002139_b978-0-08-100433-3.00004-x-Figure4.13-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002139_b978-0-08-100433-3.00004-x-Figure4.13-1.png",
        "caption": "Figure 4.13 Functional housing for an engineering application, indicating mounting holes ( 4) and features ( 4) that contribute to the surface roughness objective.",
        "texts": [
            " The orientation map clearly identifies global minima and maxima and enables an informed trade-off when compromising between competing objectives such as build time and support material consumption. It is apparent that the minima for both Ra_r (a1 \u00bc 170 degrees, a2 \u00bc 0 degree) and Ra_w_r (a1 \u00bc 160 degrees, a2 \u00bc 0 degree) occur at slightly different locations, indicating that the Ra_w_r successfully identifies a more favourable orientation for the design objectives. The hydraulic housing shown in Fig. 4.13 is to be manufactured by SLM for low- to medium-volume production. For this functional engineering application, there are no aesthetic requirements for surface finish. However, it is technically necessary that the surface finish of the mating features and mounting holes be minimised to ensure robust technical function. For this scenario, the average surface roughness, Ra_ave, is not an appropriate surface roughness objective because the surface roughness of features other than the mating features is inconsequential to component function"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001228_j.robot.2011.11.014-Figure4-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001228_j.robot.2011.11.014-Figure4-1.png",
        "caption": "Fig. 4. EE-path and singular curves of the 2 DOF 2RRR/RR RA-PKM.",
        "texts": [
            " The tree-topology open loop system contains the remaining n = 6 joint angles, giving rise to a system of n = 6 motion equations (3). Imposing the constraints shows that the PKM possesses the DOF \u03b4 = n \u2212 r = 2, and the minimal coordinate formulation (7) gives \u03b4 = 2 independent equations. Using the formulation in redundant coordinates (10) is a system of n = 6 equations of which \u03b4 = 2 are independent. The projected 6 \u00d7 3 control matrixA has rank 2. The manipulator is controlled along the EE-path in Fig. 4. As described in Section 2.2 the non-redundantly actuated PKM, i.e. when only \u03b4 = 2 joints are actuated, exhibits inputsingularities. That is, if two actuator coordinates are used as independent coordinates q2, the orthogonal complement (6) and so the PKM model (7) is not valid at these input-singularities. The corresponding singularity curves are depicted in Fig. 4 for three different combinations of actuator coordinates q1, q2, q3. Apparently the EE path passes twice the singularities of each selection of q2. The trajectory of the actuated joints qa =  q1, q2, q3  and q is determined via the inverse kinematics from the EE-path, and according to velocity and acceleration limits. Controlling the RAPKMusing the proposed CTC scheme (24) leads to the drive torques in Fig. 5. The corresponding joint tracking errors are shown in Fig. 6 that are acceptable taking into account the encoder resolution",
            " The pseudoinverse (15) of the control matrix AT in (24) requires identification of \u03b4 joint coordinates that determine theA1 submatrix. Based on the infinity norm of A1 one of the three combinations q(1) 2 = (q1, q2), q(2) 2 = (q1, q3), and q(3) 2 = (q2, q3) is selected for which \u2225A1\u2225\u221e is minimal. Fig. 7 shows the selections during the motion. With this formulation the RA-PKM can be controlled through the parameterization-singularities of the minimal coordinates model (7). The latter becomes unstable when the EE path approaches the singularity curves in Fig. 4. Fig. 8 shows the computed control commandswhenq2 = (q1, q2) is used in (7). The RA-PKM has to cross the singular curve (red curve in Fig. 4) once at the start and once just before the endof the EE-trajectory. Apparent in the critical configuration (7) does not admit to compute any sensible control torques leading to instabilities. This is visible in the measured joint errors in Fig. 9 (notice that the EE motion had to be limited manually). The significance of a complete linear feedback should be emphasized (Remark 1). Fig. 10 shows the error evolution when only the tracking error of \u03b4 = 2 independent actuator coordinates q2 =  q1, q2  are fed back"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000284_1.36426-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000284_1.36426-Figure2-1.png",
        "caption": "Fig. 2 Fundamental ellipse (continuous line) and a generic admissible orbit (dashed line).",
        "texts": [
            " Its eccentricity vector is given by eF r1 r2 =c i\u0302c, whereas its semimajor axis is expressed on the basis of simple symmetry considerations as [1] aF r1 r2 =2 D ow nl oa de d by C L A R K SO N U N IV E R SI T Y o n Se pt em be r 24 , 2 01 3 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /1 .3 64 26 The orbit parameter pF is determined accordingly as pF aF 1 e2F . The eccentricity vector of a generic orbit passing through P1 and P2 can be represented as the sum of the constant eccentricity component of the fundamental ellipse eF, parallel to the chord, plus a transverse component, in the direction perpendicular to both the chord and eF (Fig. 2), e eF tan ! i\u0302h eF (4) where i\u0302h is the unit vector parallel to the angular momentum vector (that is, perpendicular to the orbit plane), and ! is the rotation of the periapsis with respect to the eccentricity vector of the fundamental ellipse (! in Battin\u2019s notation). It is possible to show that the semilatus rectum p of the corresponding orbit is given by [1] p ! pF r2 r1 eF tan ! r1r2 c sin (5) where the sign function is defined as x 1 if x > 0 1 if x < 0 Note that the original formulation of Eq",
            " To derive a general parametrization of the orbits that is also valid when the minimum eccentricity is zero, the transverse component eT eF tan ! that appears in Eq. (7) will be used in the sequel as the free parameter, rather than the periapsis rotation !. The orbit parameter it thus expressed as p eT pF eT r1r2 c sin (10) where the last expression does not feature the highly nonlinear sign function and accommodates for circular fundamental ellipses. Finally, the semimajor axis is given by a eT p eT 1 e2F e2T Letting !c be the angle between the reference direction r\u03021 and the chord i\u0302c (Fig. 2), it is possible to express i\u0302c as cos!c; sin!c; 0 T and i\u0302p sin!c; cos!c; 0 T . The coordinates of the generic eccentricity vector e eT are thus given by e eT e cos!; e sin!; 0 T eF cos!c eT sin!c; eF sin!c eT cos!c; 0 T The argument of the periapsis of the generic orbit is determined from the equation ! eT tan 1 eF sin!c eT cos!c; eF cos!c eT sin!c (11) where tan 1 y; x is the four-quadrant inverse tangent function. The true anomaly of P1 and P2 will thus be given by 1 ! and 2 !. It is now possible to evaluate the time-of-flight between P1 and P2 as a function of eT by use of Kepler\u2019s time equation"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003364_tac.2020.2973609-Figure8-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003364_tac.2020.2973609-Figure8-1.png",
        "caption": "Fig. 8. (a) Schematic of the curved space mapping Chromo-Modal Dispersion (CMD) device and the functions it performs (inset). (b) Warping of spatial dispersion by a parabolic mirror. Diagrams on the right-hand side show, from top to bottom, the mapping of optical frequency into 1-D space, 2-D space, and 1-D polar coordinate space [37]. SLM: spatial light modulator; MMF: multimode fiber or waveguide.",
        "texts": [
            " The strength, sign, and the delay versus frequency curvature can be widely reconfigured by adjusting the alignment of the grating and the waveguide. The CMD device provides field reconfigurable tuning of the group delay and offers a means to achieve the type of phase filters needed for engineering the spectrotemporal structure of wideband optical waveforms in a reconfigurable fashion. Also recently, linear-to-curved-space mapping is combined with the CMD to achieve a new dispersive device that offers arbitrary tuning of dispersion curvature [37] (see Fig. 8). The ROADM is a tunable wavelength-division multiplexing filter with a channel monitor and attenuator/ amplifier that can be remotely reprogrammed to change the channel access. Having a wavelength selective switch, they can be used in parallel in conjunction with a set of tunable delays to form a quantized form of the group delay profile. As long as the spectral resolution of the channels in the ROADM is fine enough for the target application, this can be an effective approach to implement an easily reconfigurable arbitrary group delay profile"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000083_j.mechmachtheory.2009.01.010-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000083_j.mechmachtheory.2009.01.010-Figure7-1.png",
        "caption": "Fig. 7. (a) Contact between a tooth pair and (b) discretization of the contact region.",
        "texts": [
            " Further information about conical gear drives in approximate line contact can be found in the paper [14]. One efficient model for calculating the contact stress distribution on the tooth flank from the load-deformation relation is the influence coefficient method. The method is based on the principle that the total deformation at each point on the tooth flank is the results of the superpositioning of individual loads acting on the contact region, which is subdivided into discrete rectangular segments that are equal in area. Deformation in a loaded tooth pair is illustrated in Fig. 7. The tooth pair is initially in contact at point Oy, as indicated by the solid curves in Fig. 7a. When the teeth are loaded with a normal force F, two opposing points Q1 and Q2 on the corresponding tooth-flank, with an initial separation h, will be brought into contact, as shown by the dashed curve. We obtain the following relations for the tooth contact conditions, the contact pressure p and the elastic deformation w1 and w2 for gear tooth 1 and 2 at the specified point: (i) with two points in contact: p > 0; w1 \u00few2 \u00fe h \u00bc d; \u00f032\u00de (ii) without two points in contact: p \u00bc 0; w1 \u00few2 \u00fe h > d; \u00f033\u00de where the total relative approach d is the sum of the individual approach d1 and d2 of the teeth in the direction of the contact normal, i",
            " We focus on the deformation of gear teeth (assumed to be free from manufacturing error) under loading, whereby the Hertzian contact and the bending deflection of the teeth are the dominant factors. The total elastic deformation w1 or w2 is expressed as the sum of contact deformation wH and tooth bending deflection wB, i.e., wi \u00bc wH;i \u00fewB;i; i \u00bc 1;2: \u00f035\u00de The distribution of the contact stresses in the contact region can be calculated utilizing the method of discretization, where a set of finite numbers represent uniform contact stresses pj (j = 1,2, . . . ,n). These act at discrete segments equal in area s, as shown in Fig. 7b. The center of each segment is also the contact point with the corresponding tooth flank. The coordinates are expressed in the coordinate system Sy (xy,yy,zy) defined in Fig. 5. Assuming linear elasticity of the gear tooth, the total elastic deformation wk at point k of the corresponding opposing tooth flanks can be expressed as a linear summation of the contact deformation and the bending deflections caused by all the contact stresses pj, i.e., wk \u00bc w1k \u00few2k \u00bc Xn j\u00bc1 \u00f0fH;kj \u00fe fB;kj\u00depj: \u00f036\u00de The factors fH,kj and fB,kj in Eq",
            " We thus have two influence coefficient matrices A1 and A2, two pressure vectors P1 and P2, and two separation vectors H1 and H2. Eq. (39) can now be extended to the following relation: A1 0 In1 1 0 A2 In2 1 s1I1 n1 s2I1 n2 0 2 64 3 75 P1 P2 d 2 64 3 75 \u00bc H1 H2 F 2 64 3 75: \u00f040\u00de The influence coefficient fH in Eq. (36) is determined based on the Boussinesq half-space force-displacement relations [27]. The contact problem, the elastic contact deformation wHi of tooth i at point k(xk,yk) caused by the distributed contact stress pj(xj,yj) acting over the area X (see Fig. 7b), can be formulated by the integration equation wHi\u00f0xk; yk\u00de \u00bc 1 t2 i pEi Z Z X pj\u00f0xj; yj\u00deffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0xk xj\u00de2 \u00fe \u00f0yk yj\u00de 2 q dxjdyj; i \u00bc 1;2; \u00f041\u00de where mi and Ei represent the Poisson\u2019s ratio and the modulus of elasticity for tooth i, respectively. The sum of elastic contact deformation of gear tooth 1 and 2 is thus wH;k \u00bc wH1 \u00fewH2 \u00bc 1 t2 1 pE1 \u00fe 1 t2 2 pE2 Z Z X pj\u00f0xj; yj\u00deffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0xk xj\u00de2 \u00fe \u00f0yk yj\u00de 2 q dxjdyj; i \u00bc 1;2: \u00f042\u00de The contact region is discretized into rectangular segments equal in size, 2A 2B; see Fig. 7b. Eq. (42) can now be rewritten in linear algebraic form, combined with the influence coefficients fH,kj, wH;k \u00bc wH1;k \u00fewH2;k \u00bc Xn j\u00bc1 fH;kjpj; k \u00bc 1;2; . . . ;n: \u00f043\u00de The influence coefficients fH,kj are expressed as [18\u201320] fH;kj \u00bc 1 t2 1 pE1 \u00fe 1 t2 2 pE2 \u00bdg\u00f0 x\u00fe A; y\u00fe B\u00de \u00fe g\u00f0 x A; y B\u00de g\u00f0 x A; y\u00fe B\u00de g\u00f0 x\u00fe A; y B\u00de ; k \u00bc 1;2; . . . ; n \u00f044\u00de with the general function g\u00f0x; y\u00de \u00bc xln ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0x\u00de2 \u00fe \u00f0y\u00de2 q \u00fe y \u00fe yln ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0x\u00de2 \u00fe \u00f0y\u00de2 q \u00fe x ; \u00f045\u00de where x; y indicate the relative coordinates of any point j with respect to the considered point k, x \u00bc xj xk; y \u00bc yj yk"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0000157_s00521-010-0382-8-Figure3-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0000157_s00521-010-0382-8-Figure3-1.png",
        "caption": "Fig. 3 A conservative approach to determining a space that is well approximated by a discrete network (assuming unit disk communication) is to surround each device with a half-communication radius disk (a). The union of all such disks is a space well approximated by the network (b), and a Voronoi decomposition of the space (red lines) can be used to determine which portions of the space are to be approximated by which discrete devices",
        "texts": [
            " For example, Kleinrock and Silvester [23] show that at two or more expected neighbors, reasonable forward progress can be expected in each hop through the network; for distributed distance measures, a good threshold is 10 expected neighbors [5]. Assuming that the expected number of neighbors is sufficient, the responsibility of devices for approximating portions of the space can be determined using a Voronoi decomposition. Going in the other direction, a conservative approach to determine a space that is well approximated by a discrete network is to surround each device with a disk whose radius is 1 2 r (Fig. 3). The union of all such disks is a space well approximated by the network: there is a straight-line path connecting any pair of devices that can communicate directly, and when two devices are in disconnected components of the network, there is no path connecting them through the space. 2.2 Extending the amorphous medium to moving devices At a surface level, extending the amorphous medium abstraction to moving devices is straightforward: merely add a function for moving devices to the language. Many swarm robotic applications are also focused not on the robots, but on the space through which they move"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002669_j.isatra.2016.04.024-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002669_j.isatra.2016.04.024-Figure1-1.png",
        "caption": "Fig. 1. Furuta pendulum and its generalized coordinates [22].",
        "texts": [
            " If the next inequality is fulfilled P\u00feP ~\u039bPrG \u00f026\u00de that is equivalent (by Shur complement [21]) to G P P P ~\u039b 1 \" # Z0 \u00f027\u00de The MI in (25) can be presented as \u03a6> \u00f0K\u00deG\u03a6\u00f0K\u00de \u00f01 \u03c1\u00deP\u00fe\u03f0Ir Q \u00f028\u00de Then, the solution of (17) is relaxed to the solution of (27) and (28). The DSTC is testing in a Furuta Pendulum, with dynamic model is given by the Euler\u2013Lagrange formulation as M q\u00f0 \u00de \u00bc M11 q\u00f0 \u00de M12 q\u00f0 \u00de M12 q\u00f0 \u00de M22 q\u00f0 \u00de \" # ; N q; _q\u00f0 \u00de \u00bc N1 q; _q\u00f0 \u00de N2 q; _q\u00f0 \u00de \" # here M11 q\u00f0 \u00de \u00bc Jeq\u00feMpr2 cos 2 q1 M12 q\u00f0 \u00de \u00bc 1 2Mprlp cos q1 cos q2 M22 q\u00f0 \u00de \u00bc Jp\u00feMpl 2 p N1 q; _q\u00f0 \u00de \u00bcMpr 2r cos q1 sin q1 _q2 1 \u00feMpr 1 4 lp cos q1 sin q2 _q2 2 N2 q; _q\u00f0 \u00de \u00bc 1 2Mplp sin q1 cos q2 _q2 1\u00feg sin q2 where q\u00bc \u00bdq1 q2 > are the generalized coordinates described in Fig. 1. q1 is the angular rotation of the Furuta pendulum measured in the horizontal plane and q2 is the angular rotation of the second arm that describes the Furuta pendulum, Mp is the mass of the pendulum, lp is the length of pendulum center of mass from the systems based on recurrent Super-Twisting-like algorithm. ISA pivot, Lp is the total length of the pendulum, r is the length of the arm pivot to pendulum pivot, g is the gravitational acceleration constant, Jp is the pendulum moment of inertia about its pivot axis and Jeq is the equivalent moment of inertia about motor shaft pivot axis"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002129_j.ijfatigue.2016.02.011-Figure7-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002129_j.ijfatigue.2016.02.011-Figure7-1.png",
        "caption": "Fig. 7. Different modes of loading of LoF defect in the perpendicular and parallel specimen.",
        "texts": [
            " SEM\u2013EDS analysis indicated higher oxygen content within III and thus the crystal-like features are attributed to thin layers of oxide. The \u2018\u2018bumps\u201d within III are further assumed to be dendrites covered with a thin oxide layer. The three features were sometimes observed within the same LoF defect. LoF defects were observed for specimens in both orientations (Fig. 2) but their occurrence in the parallel specimens was less frequent. This could be explained by the prevalence of the LoF defect in the x\u2013y plane (Fig. 7), i.e. along the parallel specimen leading to that the LoF defects in the two orientations will experience different types of loading. In the perpendicular orientation the defect will experience a separating type of loading where the loading will be perpendicular to the plane of LoF, see Fig. 7, and the crack will consequently open as a result of the loading. However, in the parallel orientation, the loading direction is parallel to the plane in which the LoF is located, and hence the LoF will be less detrimental to the fatigue life. The LoF defects in the x\u2013y plane could in cases of parallel loading direction (Fig. 7) have a more crack-like appearance, see Figs. 4e and 4f, compared to the LoF of perpendicular loading direction, see Fig. 6a\u2013f. Similar influence of the LoF defects has been reported Kobryn and Semiatin [21] for tensile specimens. The effect of pores on the fatigue properties is complex. Specimens that exhibited pores on the fracture surfaces showed sometimes only little decrease in fatigue life while other specimens showed a significant decrease, compared to specimens without defects. Careful fractographic evaluation revealed that specimens having low fatigue life also had a more pronounced plateau around the pore, clearly indicating that the crack was initiated at the pore"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0001094_s00170-015-8051-9-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0001094_s00170-015-8051-9-Figure2-1.png",
        "caption": "Fig. 2 Setup for laser scanning: a general view, b the moving mirror and the laser head, c principal schema",
        "texts": [
            " The difference of the scale readings of the vertical micrometer screw gives the thickness. The obtained sandwich-like targets consist of a thin powder layer on a thick substrate of the same material. Laser scanning of such a target simulates additive fabrication of a massive part by SLM. A sealed CO2 laser tube of 30 W maximum output power is used as the laser source operating in continuous mode at 10.6 \u03bcmwavelength where quartz glass absorbs well. The tube is integrated into commercial machine for laser engraving Qualitech 203 shown in Fig. 2. Laser beam 2 (see Fig. 2c) from sealed CO2 tube 1 is deflected by fixed mirror 3 and moving mirror 4 mounted on the rail moving along axis Y. The rail is seen in Fig. 2b as a horizontal beam of rectangular cross-section. Laser head 5 moves along this rail in X direction. The laser head contains a mirror on the top and a ZnSe lens of 2 in. focal length on the bottom. Target 6 is placed on the working table. Protective gas is not used in the experiments because the studied material does not react with atmospheric air even at high temperatures. The minimum scanning velocity is limited by 10 mm/s in the used laser setup. To reduce the apparent scanning velocity, a zigzag path of the laser beam is programmed with a small amplitude compared to the spot size. This gives the displacement lower than the path, so that the mean velocity reduces. The resulting mean scanning velocity is measured by a stopwatch. The power of the laser beam is controlled by the current of the pumping gas-discharge in the tube. The scale of the ammeter (on the right in Fig. 2a) is calibrated in Watts by a laser power meter with a wide-band sensor. The laser spot diameter is estimated by the width of the laser trace on the surface of the target. Figure 3 shows cross-sections of the targets scanned by laser at various powers P and velocities v. The targets initially contained a 200-\u03bcm layer of powder on the top. The powder irradiated by laser was heated and fused forming a bead on the substrate. The rest of non-consolidated powder was removed. When the top surface of the target is placed in the focal plane (see Fig"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0002764_j.msea.2019.138065-Figure1-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0002764_j.msea.2019.138065-Figure1-1.png",
        "caption": "Fig. 1. Orthogonally additive-manufactured cylindrical dog-bone tensile specimens. (a) Vertically fabricated specimen with its tensile axis parallel to building z-direction (AM-V). (b) Horizontally fabricated specimen with its tensile axis perpendicular to building z-direction (AM-H).",
        "texts": [
            " The following manufacturing conditions were employed: a spot size of ~70 \u03bcm, a layer thickness of ~40 \u03bcm, nitrogen atmosphere, and a scanning speed of 1200mm/s. The materials were made using an orthogonally additive manufacturing technology and had a gauge length of 10mm and a diameter of 5mm. The metal powder had a chemical composition similar to the 15-5PH commercial alloy (Table 1). Two types of dog-bone tensile specimens were manufactured: (1) One sample was fabricated with its tensile axis parallel to the z-direction (Vertical sample, denoted as AM-V in Fig. 1), (2) The other sample was fabricated with its tensile axis perpendicular to the z-direction (Horizontal sample, denoted as AM-H in Fig. 1). A commercial 15-5PH stainless steel (denoted as CA) was studied as a reference for comparison. Microstructural features of AM-V, AM-H, and CA were examined using optical microscopy (BX51M, Olympus, denoted as OM). For this observation, specimens were mechanically polished with a diamond suspension of 1 \u03bcm followed by electro-polishing at 5 V for 3 s and etching at 2 V for 30 s with a 30% Nital etching reagent. Electron backscatter diffraction (NordlysNano, Oxford Instruments, denoted as EBSD) was used to examine the morphology of retained austenite and crystallographic information of phase constituents"
        ],
        "surrounding_texts": []
    },
    {
        "image_filename": "designv10_5_0003386_j.ast.2020.105974-Figure2-1.png",
        "original_path": "designv10-5/openalex_figure/designv10_5_0003386_j.ast.2020.105974-Figure2-1.png",
        "caption": "Fig. 2. Possible configurations of aerial transportation system with different quadrotor attitudes.",
        "texts": [
            " Hence, it is not desirable to drive the quadrotor with fast spin and the cable twisting will be negligible in the transportation mission. Furthermore, as shown in Assumptions (ii) and (iv), the payload is treated as a point mass and the cable mass is neglected. Therefore, it is reasonable to omit the effect of the payload on quadrotor in the yaw direction. As shown in Fig. 1, the view of the transportation system in yb zb and xb zb planes are similar. Both cases may have the possible configurations shown in Fig. 2 with different roll or pitch angles. Without loss of generality, the motion is restricted to yb zb plane in the following analysis. That is, the effect of the roll angle on the stable configuration of the four-cable-suspended payload will be investigated. Since the stable configurations are symmetric with the roll angles \u03c6 and \u2212\u03c6, only the situation where \u03c6 \u2265 0 is discussed. As shown in Fig. 2, the possible stable configurations can be categorized into three cases. Note that the tension of each cable in Fig. 2(a)\u2013(c) can be considered as the projection of the resultant force of two adjacent practical cables in yb zb plane. (a) When the roll angle is zero, the payload will stay right under the quadrotor in the stable configuration. The tensions in these two cables are F1 = F2 = mg 2 cos\u03b21 (7) where \u03b21 = \u03c0 2 \u2212 \u03b1 with \u03b1 = arccos l y L . Note that L is the equiv- alent cable length L = \u221a l2 \u2212 l2x . To analyze the robustness of the configuration in Fig. 2(a), suppose there exists a small disturbance d acting on the payload along the horizontal direction as shown in Fig. 3(a). In this case, the tensions in the cables satisfy the following equations F1 sin\u03b21 + d = F2 sin\u03b21 (8) F1 cos\u03b21 + F2 cos\u03b21 = mg (9) The solutions to Eqs. (8) and (9) are F1 = mg 2 cos\u03b21 \u2212 d 2 sin\u03b21 , F2 = mg 2 cos\u03b21 + d 2 sin\u03b21 (10) From Eq. (10), it can be found that F1 = 0 holds if d equals to mg tan\u03b21 and d = \u2212mg tan \u03b21 implies F2 = 0. That is, the system cannot remain in the configuration in Fig",
            " Since the cable of concern has a huge modulus of elasticity for tension, the impact damping is also huge, which means that the system energy will decrease rapidly at this point. Hence, even if the system starts from the initial position shown in Fig. 4, it will quickly converge to a simple harmonic motion along the red solid curve in Fig. 4. Different from the systems with one cable, there exists coupling between the quadrotor attitude and the payload motions in the developed aerial transportation system. Next, the influence of the torques acting on the quadrotor from the payload in the stable configurations shown in Fig. 2 will be discussed. It is clear that F1 is equal to F2 and no additional torque exists in the unperturbed Case (a). For Case (a) with disturbance shown in Fig. 3(a), the torque acting on the quadrotor from the payload is \u03c4a = \u2212F1l y sin\u03b1 + F2l y sin\u03b1 = dly sin\u03b1 sin\u03b21 (14) In the perturbed case with a small roll angle, the disturbance torque can be expressed as \u03c4b = mg sin\u03b22 + d cos\u03b22 \u2212 mg sin\u03b23 + d cos\u03b23 sin(\u03b22 + \u03b23) l y sin\u03b1 = \u2212mgly sin\u03c6 tan\u03b1 + dly cos\u03c6 tan\u03b1 (15) In the case with a large roll angle, the resulting torque on the quadrotor with an unperturbed payload is \u03c4c = \u2212F1l y sin\u03b1\u2217 = \u2212mgly cos\u03c6 (16) Therefore, the following conclusions can be drawn. (i) The disturbance acting on the payload has an effect on the attitude motion of the quadrotor. (ii) For the configurations shown in Fig. 2, the torque acting on the quadrotor from the payload changes from \u2212mgly sin \u03c6 tan\u03b1 to \u2212mgly cos\u03c6 when \u03c6 = \u03c0 2 \u2212 \u03b1. It should be noted that sin \u03c6 tan\u03b1 < sin \u03c6 tan( \u03c0 2 \u2212 \u03c6) = cos\u03c6 holds in the case of \u03c6 < \u03c0 2 \u2212\u03b1. Hence, considering cos \u03c6 \u2264 1, a possible bound of the torque acting on the quadrotor in the stable configurations is mgly . In the previous section, the disturbance forces and torques caused by the payload are only analyzed in stable configurations. However, when the payload is swinging, the disturbance is larger"
        ],
        "surrounding_texts": []
    }
]