diff --git "a/designv11-6.json" "b/designv11-6.json"
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+[
+    {
+        "image_filename": "designv11_6_0003564_05698190490500743-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003564_05698190490500743-Figure3-1.png",
+        "caption": "Fig. 3\u2014Seal face with double-row spiral grooves in a splay pattern.",
+        "texts": [
+            " In the following article, the experimental investigations and industrial applications are described. GROOVES IN SPLAY PATTERN Wang, et al. (6) present a kind of noncontacting, zero-leakage face seal with double-row spiral grooves in a splay pattern (herringbone). A sketch of this kind of seal is shown in Fig. 1, where item 5 is the uncompensated rotating seat with double-row spiral grooves in a splay pattern on its faces, and item 4 is the balanced stationary primary ring. Figure 2 is a photograph of the rotating seat. The face with spiral grooves is shown in Fig. 3, where ri and ro are the inner radius and outer radius of the primary ring, respectively. The pressure distribution of oil film over the interface and the axial force balance of the primary ring are shown in Fig. 4. Fig. 1\u2014General structure sketch of face seals with spiral grooves: (1) shaft, (2) spring retainer, (3) antirotation pin, (4) primary ring, (5) rotating seat, (6) seal casing. D ow nl oa de d by [ U ni ve rs ity o f C al if or ni a Sa nt a C ru z] a t 2 1: 31 1 0 O ct ob er 2 01 4 Now the theoretical analyses are carried out, in which the basic assumption is same as that of Muijderman (2)",
+            " For a practical application, the normal width of a spiral groove, b1 \u2264 1 mm, and ratio of ridge width to groove width, \u03b3 = 1, are chosen. Then the number of spiral grooves can be selected by means of the following equation: k \u2248 \u03c0r2 sin \u03b1 b1 [18] For initial design, a radius of interface between oil and gas, r\u2217, near balance radius rb can be chosen. In addition, H \u2248 0.25 and \u03b1 = 10 \u223c 15\u25e6 are often adopted. So, the appropriate groove depth hg can be obtained from the equations given earlier. As shown in Fig. 3, there are three annular dams on the seal face. The outer annular dam, about 0.5 mm width, from r4 to ro, near the high-pressure side, is used to keep the particles in the sealing oil away from the seal gap. The inner annular dam, from ri to r1, near the low-pressure side, is used to prevent the \u201csecondary leakage\u201d of sealing oil, keeping the particles in the sealed gas away from the seal gap during operation and maintaining static sealing. The middle annular dam is used to prevent \u201cgas ingestion\u201d of sealed gas (Wang, et al"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003049_b:tril.0000044509.82345.16-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003049_b:tril.0000044509.82345.16-Figure1-1.png",
+        "caption": "Figure 1. Schematic diagram of test apparatus.",
+        "texts": [
+            " This was first carried out by Winer, who used an infrared (IR) microscope to measure and map thermal emission from the steel surface and the lubricant in a sliding EHD contact between a steel ball and a sapphire disc [33,34]. These emission measurements were then converted to temperatures using a combined calibration/analytical technique. This approach has also recently been applied to study the temperature rise of surfaces and fluid in a dimpled contact in very high sliding conditions [35]. In the current study, an EHD contact was formed between a 19 mm diameter AISI 52100 steel ball and a 3.5 mm thick sapphire disc, as shown in figure 1. Both disc and ball were independently driven to provide any desired sliding/rolling combination. The contact was contained in a temperature-controlled chamber (\u00b1 0.5 C) and the ball was half-immersed in lubricant to ensure fully-flooded conditions. A custom-built, infrared microscope was mounted on an XY table driven by micrometers attached to computer-controlled stepper motors. This microscope was focussed through the sapphire to within the contact and had a liquid N2-cooled InSb detector to sample the level of IR emission from the focus area"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001383_1.1288360-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001383_1.1288360-Figure1-1.png",
+        "caption": "Fig. 1 A HPS manipulator, as the connector chain of parallel manipulator",
+        "texts": [
+            "1 In addition, it can be easily proved that knowing the velocity state and the accelerator of a rigid body one can determine the acceleration of an arbitrary point of the rigid body. Further, Rico and Duffy @22# proved that AW * can be written in terms of the screws that represent the kinematic pairs of the linkages and the joint rates, i21v i , and their derivatives, i21v\u0307 i , as AW *5( i51 n i21v\u0307 i i21SW i1( i51 n21 F i21v i i21SW i ( j5i11 n j21v j j21SW jG . (5) This screw was called the \u2018\u2018accelerator\u2019\u2019 by Sugimoto @20#. Figure 1 illustrates an HPS manipulator where H, P, and S denote respectively a Hooke joint, and a prismatic and a spherical pairs. The first revolute pair in the Hooke joint is connected to ground, at point B, and the spherical pair is attached at the end effector or hand, at point P. Six such manipulators will be used as the connector chains of a parallel device ~see Fig. 2!, and the prismatic pair in each connector chain will be actuated, for more details see Fichter @24#. The velocity analysis of the parallel device is included for the sake of completeness and because it provides information necessary for the acceleration analysis"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003870_1.2401209-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003870_1.2401209-Figure1-1.png",
+        "caption": "Fig. 1 Rotor/magnetic/auxiliary bear placed for the Cartesian coordinates magnetic bearing.",
+        "texts": [
+            "org/about-asme/terms-of-use a w t 2 c c s a c s d a w z r o u 1 Downloaded Fr uxiliary bearing interactions. In particular, the issues associated ith short timescale/local and longer timescale/global temperaures are investigated. Variability of Contact Rotor Dynamics 2.1 A System Model. Before the transient thermal problem an be investigated it is necessary to determine the nature of the ontact forces that may arise in a rotor/magnetic/auxiliary bearing ystem. Therefore the simple rigid rotor within the magnetic/ uxiliary bearing combination shown in Fig. 1 is considered. For larity only one of the two magnetic bearing control axes is hown. The rotor makes contact with the auxiliary bearing in orer that rotor and magnetic bearing pole laminations are protected. The equations of motion for the auxiliary bearing are mbx\u0308b + cbx\u0307b + kbxb = fc cos \u2212 fc sin mby\u0308b + cby\u0307b + kbyb = fc sin + fc cos 1 nd for the rotor mrx\u0308r = fmx \u2212 fc cos + fc sin + mre 2 cos t mry\u0308r = fmy \u2212 fc sin \u2212 fc cos + mre 2 sin t 2 hich includes unbalance eccentricity e. The contact force is non- ero whenever r= xr\u2212xb 2+ yr\u2212yb 2 cr, where cr is the otor/auxiliary bearing radial clearance",
+            "org/ on 01/27/2016 Terms c t = 2 Ri R*fc t E*lb 3 where R* = Ri Ri \u2212 cr /cr 1/E* = 1 \u2212 r 2 /Er + 1 \u2212 b 2 /Eb 4 The nonlinear contact force/deflection characteristic follows from r \u2212 cr = fc t E*lb 2 3 + ln 4Rr Ri c t 2 5 The forces from the magnetic bearing may be determined from Amp\u00e8re\u2019s circuit law. To a first-order approximation, the forces in orthogonal directions are decoupled, which is acceptable for this study in which the contact dynamics will dominate. The decoupled version for the axes u=x ,y shown in Fig. 1 is fmu = \u2212 km V0 + Vc 2 cm \u2212 ur 2 \u2212 V0 \u2212 Vc 2 cm + ur 2 6 where cr cm. Since the magnetic bearing is an active element, the complete specification of the force will depend on the chosen control strategy. A number of options are available in this area, but a simple proportional-integral-derivative PID feedback law derived from measurement of rotor displacements xr ,yr is a typical practical case. The proportional and derivative gains determine the magnetic bearing stiffness and damping, while the integral gain allows centralization of the steady state rotor position with zero error"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002414_s0043-1648(03)00173-x-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002414_s0043-1648(03)00173-x-Figure3-1.png",
+        "caption": "Fig. 3. Waviness motifs parameters.",
+        "texts": [
+            " This method is characterised by spacing and height parameters, which calculation based on the unfiltered primary profile. The width of the motif AR and the vertical parameter R represent the mean values of roughness as described in the (Fig. 2). The upper envelope line is formed line is formed by the direct connection of the upper points of the roughness motifs. The evaluation of the waviness is based only on the upper envelope line. The waviness parameters are calculated in the same way as the roughness parameters through averaging of the width and height of the waviness motifs (Fig. 3). The 3D topographic measurements of chert surfaces before and after the friction with picrolite show a transfer phenomenon do to abrasion mechanism. Its location is non homogeneous on the surface, (Fig. 4a and b). The deposit made of debris of picrolite is orientated by the displacement of the sphere: scratches of small sizes appear. The deposit adheres to the peaks of the micro-relief where the contact is the more intense and it fills as well the valleys. This evolution of the surface is clearly illustrated by the extracted profiles, (Fig"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000595_1.2828771-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000595_1.2828771-Figure4-1.png",
+        "caption": "Fig. 4 Representation of generating ilnes in coordinate system Sf,",
+        "texts": [
+            " An illustrative example is given below to show the gener ation of Helipoid gears manufactured by the ZN type hob cutter. Example: A right-hand ZN worm-type hob cutter is used to manufacture the right-hand novel Helipoid gear. Table 1 sum maries the fundamental data of the hob cutter and Helipoid gear. The mathematical model of the ZN-type worm surface is well-known in industry and the ZN worm-type hob cutter is widely used in the gear manufacturing. The hob cutter's surfaces can be generated by a blade with straight-lined shape, per forming a screw motion with respect to the hob cutter's axis (Fig. 4) . The surface equation of the ZN-type worm proposed by Litvin (1994) are adopted and rewritten as follows: Xi, = p &m {0 + ^) \u00b1 u cos 6 cos {6 + ji), y^ = - p cos (6* 4- /.*) \u00b1 M cos 5 sin (6* -f- ju), and cos a cot XA _ . Zh = \u00b1p + M sm 0 -(- p6, (39) cos 8 By substituting Eqs. (32) into Eq. (33), the equations of the hyperbolid can be written as follows: and XfH = b cos ip + i sin 6 sin ip, yfh = fo sin (/3 \u2014 ^ sin 0 cos ip, ZfH = i cos 6, (34) where \u20ac and ip are parameters of the hyperbolid",
+            " The surface unit normal of the ZN-type worm is given as follows: Table 1 Parameters of tlie 214-type hob cutter and helipoid gear Number of teeth Module, normal Lead angle Pressure angle, normal Width N,=l m\u201e=2,0 1^=2,051\u00b0 a = 20\u00b0 Helipoid Gear N^=30 m\u201e=2,0 1^=70\u00b0 w - 20 mm 112 / Vol. 119, MARCH 1997 Transactions of the ASME Downloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/30/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use n^i = \u2014 [(p + p tan (5) sin (S + A*) \u00b1 M sin 5cos (6 + / /)] , k Wyi = [ \u2014(p + P tan 6) cos (9 + n) k u cos 6 M sin (5 sin (^ + /li) ] , (40) where k = [{p + p tan 6)^ + M^]' The upper sign indicates the surface generated by the generating line I shown in Fig. 4(^7) and the lower sign indicates the surface generated by the generating line II. In equation (39), parameter p is the screw parameters of the worm. Parameters u determines the location of current point A (or A') on the generating line; where u = \\MA\\ (or M = | M ' A ' | for the generating line II) as shown in Fig. 4. By applying the general gear mathematical model developed here, the Helipoid gears' tooth surface can be specified. By substituting equations ( 3 7 ) - (40) into Eqs. ( 4 ) - ( 6 ) and Eqs. (28) and (29), the tooth surfaces of the Helipoid gear are obtained and shown in Fig. 5. Conclusion Hobbing machines are widely used in industry for manufac turing different types of gears. Developing of 6-axis CNC hob bing machines makes the manufacturing of gears more efficient and flexible. Besides, it allows for novel type of gears to be developed"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001553_s0045-7825(99)00329-1-Figure7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001553_s0045-7825(99)00329-1-Figure7-1.png",
+        "caption": "Fig. 7. Coordinate systems applied for simulation of meshing.",
+        "texts": [
+            " Surface R 2 w is determined as the envelope to family of surfaces Rc that is generated in coordinate system Sw rigidly connected to the worm. The main goal of simulation of meshing is to determine the shift of the bearing contact and transmission errors caused by gear drive misalignment. The simulation of meshing is accomplished by application of TCA computer program developed by the authors. We apply the following coordinate systems: movable coordinate systems Sw and S2 rigidly connected to the worm and the worm-gear, and \u00aexed coordinate system Sf where meshing of worm and worm-gear is considered (Fig. 7). Coordinate systems Sa; Sb; Sp; and Se are auxiliary \u00aexed coordinate systems. Coordinate system Sq is applied for simulation of alignment errors DE, Dq, and Dc. The algorithm for simulation of meshing is based on equations that describe continuous tangency of interacting surfaces Rw and R2 [5]. Continuous tangency of Rw and R2 means that the surfaces being in mesh have a common position vector and the same unit normal at the current point of tangency. Surfaces Rw and R2 are represented in coordinate systems Sw and S2"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001575_1097-4628(20001121)78:8<1566::aid-app140>3.0.co;2-i-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001575_1097-4628(20001121)78:8<1566::aid-app140>3.0.co;2-i-Figure6-1.png",
+        "caption": "Figure 6 Three-dimensional tire model for explicit FEA.",
+        "texts": [
+            " Free rolling is defined as the state at which no longitudinal force occurs. The tire model is in contact with a road under vertical load of 4 kN traveling at 10 km/h. Angular velocity of the tire is varied from 8 to 10 rad/s in order to determine the free rolling radius. Figure 5 shows the driving force of the tire (referred to as longitudinal force) at different angular velocities. It is shown that free rolling occurs at angular velocity of 8.87 rad/s. Therefore, we can estimate the free rolling radius of 313.28 mm. Figure 6 shows a three-dimensional FE tire model by means of the same procedure as mentioned above. In the case of explicit FEA, the FE tire model must have a fine mesh (14,940 nodes, 11,160 elements) all over the circumferential direction in order to analyze a transit response of a tire. This causes more numbers of element and node than in case of the implicit FEA. Also, threedimensional FEA must be needed not only for a rolling analysis, but also for an inflation analysis. These cause to spend longer CPU times than in the case of the implicit FEA"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000732_s0301-679x(98)00043-7-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000732_s0301-679x(98)00043-7-Figure4-1.png",
+        "caption": "Fig. 4 Experimental apparatus for measuring the deformation of the rubber film",
+        "texts": [
+            " \u2202p\u0304 r\u2202u 5 0, we get 334 Tribology International Volume 31 Number 6 1998 teq 5 2 a(1 2 a)d sin b 2k0 H(h3 g 2 h3 r ) cos b \u2202p\u0304 \u2202s 2 6mdrv sin bJ 1 mrvSa hg 1 1 2 a hr D (13) From shear stress at the bearing surface, bearing torque in the groove region is calculated as follows Ts 5 E s3 s2 E 2p 0 tsr2du ds 5 2pE s3 s2 F 2 a(1 2 a)d sin br2 2k0 H(h3 g 2 h3 r ) cos b \u2202p\u0304 \u2202s (14) 2 6mdrv sin bJ 1 mr3vSa hg 1 1 2 a hr DG ds Bearing torque in the smooth region is Ts 5 E sj si E 2p 0 r2t du ds 5 2pE sj si m 1 h r3v ds (15) 5 2pmv 1 h sj 4 2 si 4 4 sin3g where t 5 m rv h is the shear stress in the smooth region. d 5 hg 2 hr, r 5 s sin g. Therefore, the bearing power consumption is given as Ploss 5 Tsv (16) Deformation characteristics of thin rubber film In order to theoretically obtain the static characteristics of the proposed bearing, we need to investigate the relationship between the deformation of a thin rubber film and water pressure. In this paper, we experimentally obtained this relationship. Fig 4 shows the experimental apparatus for measuring the deformation of the rubber film. The shaft is hori- zontally set to eliminate the effect of the weight of the air cylinder and load can be imposed on the bearing with an arbitrary magnitude. The axial deformation of the rubber film is measured by non-contact displacement probe. Fig 5 shows the relationship between dimensionless average pressure of the conical surface caused by load and the rubber deformation in the normal direction to the conical surface"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001121_physreve.65.011701-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001121_physreve.65.011701-Figure2-1.png",
+        "caption": "FIG. 2. Molecular rotation around the cone induced by the electric field in the TGBC phase.",
+        "texts": [
+            " Eelast is the elastic distortion energy of the nematic director in the smectic layers; we will indeed see that the director\u2019s components in a given block submitted to an electric field are not constant: a twist deformation is expected when the field is perpendicular to the helical axis, but other orientations can also give rise to splay distortions @13#. Figures 2 and 3 schematically describe the azimuthal angle w and tilt angle u induced in TGBC and TGBA phases 1-2 submitted to an electric field parallel to the helical axis. In the TGBC phase, the field component along the smectic layers Ex j 5EX cos uS is perpendicular to the spontaneous polarization PW S5e0xCuS uW Y j , where uW Y j is a unit vector parallel to OY j . Figure 2 schematically shows that, in the smectic layers, induced molecular rotations around the cone are expected because of the torque exerted by the field on the polarization. They correspond to the so-called Goldstone mode. In a given block, the rotation is not uniform: if the grain boundary exerts some anchorage on the director, we can reasonably assume that it is larger in the center of the block and weaker near the grain boundary. There appears then, a sort of twist deformation of the director, this deformation induces an elastic torque"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000517_1616-8984(199607)1:1<1::aid-seup1>3.0.co;2-6-Figure1-12-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000517_1616-8984(199607)1:1<1::aid-seup1>3.0.co;2-6-Figure1-12-1.png",
+        "caption": "Figure 1-12. Schematic input and output couplers interrogating the evanescent field via a grating. Lx is the area of interaction.",
+        "texts": [
+            " Guided modes will be refracted at this grating, leading to an out-coupling of radiation at a given angle. This angle depends on the wavelength, the grating constant, the optical parameters of the waveguide, and the refractive index of the analyte. To a first approximation, the grating does not influence the waveguide. Both input and output couplers are realized depending on whether radiation (incident) is coupled into the waveguide to be guided or leaves the waveguide in the grating region. The principle is shown schematically in Figure 1-12. A variety of set-ups have been developed [20]. Commercially available is a grating coupler system from Artificial Sensing Instruments (ASI) in Zurich, Switzerland. A further development is a set-up with a position sensitive CCD array which avoids mechanical angle scanning to find the optimum coupling angle [80] (see Figure 1-13). Another possibility is the bi-diffractive coupler. In Figure 1-14, the grating structure is shown schematically, representing a mixed grating with two grating constants [162], A second angle of outcoupling is achieved which differs from that of the normal reflection"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002460_63.85913-Figure8-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002460_63.85913-Figure8-1.png",
+        "caption": "Fig. 8. Predictive controller: Minimization of f\\; f ( k , ) weighted by n ( k , k , ) corresponds to reciprocal value of \u2018\u2018local\u2019\u2019 switching frequency in f = f,,. The \u201cglobal\u201d switching frequency f , ( r o ) is determined by C I n k k,)I, Et, (ki).",
+        "texts": [
+            " : ON-AND-OFF LINE OPTIMIZED PREDICTIVE CURRENT CONTROLLERS 455 switching state k which actually makes necessary a converter switching status change (because the relevant trajectory leaves the hexagon). In general more than one of the remaining seven (only six fork = 0 or k = 7) possible switching states will lead the control error back into the hexagon (Fig. 7). Among these a selection has to be made in an optimal sense. One possible optimization criterion is, e.g., the maximization of the dwell time [ t( k , ) ] of the trajectory within the hexagon, weighted by the number of necessary switchings n ( k , k,) to get from the old converter switching status k to the new one k, (Fig. 8 ) . This acts as a switching frequency minimization. But via n ( k , k , ) / t ( k , ) only the local switching frequency is minimized (as, e.g. , in a steepest descent method) and does not necessarily mean that the global minimum will be found (compare I in Fig. 8). On the other hand, a global optimization in practice cannot be performed due to the enormous computational effort connected herewith. Another optimization criterion could be, e.g., to minimize the (local) contribution of the considered part of the trajectory to the rms value of the control error. Also in this case the optimization criterion can be mathematically formulated easily. The control of AiN within the tolerance area (which is the side condition of the optimization) can only be guaranteed if at least one of the [ d ( A i , ) / d t ] k , leads back into the hexagon"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002968_j.conengprac.2003.12.013-Figure11-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002968_j.conengprac.2003.12.013-Figure11-1.png",
+        "caption": "Fig. 11. Nichols chart for every operating point.",
+        "texts": [
+            " But the performances have to be checked; this is done in the next section with graphical interpretations. 5.2. Results The efficiency of the method is now evaluated by considering the closed-loop plant with five bending modes; the obtained controller is applied to different models: they correspond to uncertainties on the rigid and bending modes parameters which have been recognized as worse case configurations. The frequency open loop responses of the frozen systems with the bending modes are first considered in a Black\u2013 Nichols chart for the 10 operating points (Fig. 11). The + indicates the decreasing and increasing gain margin specifications, and the dashed line corresponds to the attenuation required for the bending modes up to the second one. It can be seen that the frequency-domain specifications are almost satisfied, even in the case of parameter dispersions. Time responses of the closed-loop plant are then considered with respect to a typical worst case wind profile (Fig. 12) together with sensor noises. The specifications are represented by dark areas, whereas the time units are identical for all plots: the angle of attack i specification is almost satisfied for all cases (Fig"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003576_bf01076055-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003576_bf01076055-Figure2-1.png",
+        "caption": "Fig. 2. Voltammetric response of a modified glassy carbon electrode in 0.5M KCI. Scan rates: (1) 0.005Vs -l, (2) 0.05Vs -~. Ep, = 0.16V, Epc = 0.16V at 0.005Vs -I.",
+        "texts": [
+            "5 times when compared to the current values obtained with an emery polished GC electrode (electrodes without pretreatment). Even though catalytic activity (for example towards ferrocyanide oxidation) was observed with a GC electrode electrochemically pretreated in 0.5 M H2SO4, medium, adsorption type peaks (with AEp ~ 0) were not observed as in the 0021-891x/90 $03.00 + .12 9 1990 Chapman and Hall Ltd. present case. Further, it is significant to note that the G C electrode, after t ho rough washing with water, gave the response represented in Fig. 2 in pure 0.5 M KC1 with no ferro/ferricyanide in solution, thereby indicating the incorpora t ion o f surface redox groups on the G C surface. Catalysis o f such surface incorporated redox groups towards the model ferroferricyanide system showed far greater current response (several fold - typically ten times) as compared to unmodified electrodes. The redox behaviour exhibited by the electrode in Fig. 2, which is characteristic o f a surface reaction even in solutions devoid o f the redox species (ferroferricyanide), is new, N o reports exist in the literature suggesting the incorporat ion o f the above redox species even though a voluminous literature exists on this G C system. The Iinear plot o f i v against scan rate (Fig. 3) further confirms a surface reaction by the bound redox groups. The response o f the modified electrode, after a few polishings with emery strips, is represented in Fig"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000496_a:1022548914291-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000496_a:1022548914291-Figure1-1.png",
+        "caption": "Fig. 1. The Sagnac experiment.",
+        "texts": [
+            " These derivations are based on a Minkowski metric defined as To eliminate confusion for the non-specialist, and to more readily compare results with those of Einstein and others, we employ cgs, not geometrized, units where c = 2.998 X 10 \u00b0 cm/sec. 408 Klauber 1.4.1 The speed of light. In 1913 Sagnac [16] first demonstrated experimentally that rotating disks exhibit a remarkable property, the significance of which the present author believes has been completely overlooked ever since. That is, the local speed of a beam of light tangent to the disk circumference is not invariant, and not isotropic (as seen from the disk). Fig. 1 depicts the Sagnac experiment schematically. A light beam is emitted radially from the center of a rotating disk and is split by a half silvered mirror M at radius r. From there one part of the beam is reflected by mirrors appropriately placed on the disk such that it travels in one direction around the circumference. The other half of the beam travels the same route over precisely the same distance, but in the opposite direction. The beams then meet up again and are reflected back to the center where interference of the two beams results in a fringing, i",
+            " To compare with Brillet and Hall's reported single peak amplitude signal, one must then divide Eq. (35) by two. Using .465 km/sec in Eq. (35) and dividing by two, one gets At/t = 3.5X10\" . Fig. 12 can help to explain the reason for the discrepancy in this number and the reported value. In Fig. 12 the two light rays no longer travel solely on two perpendicular paths. In the Brillet and Hall experimental apparatus a similar configuration to that of Fig. 12 was used, apparently to accommodate the laser equipment which provided such extraordinary accuracy. (See Fig. 1 in Brillet and Hall.) Note that if the two shorter legs d were each 25% the length of the primary legs l, then the time t in Eq. (35) would be 1.25 times that of Fig. 11. Note also that the lower of the d legs is aligned perpendicularly to the velocity, whereas the lower path is intended to monitor light speed in the direction of the velocity vector. If both it and the upper d leg were 25% of the primary legs in length, one could therefore expect a 25% reduction in At as well. Hence the total signal At/t would be a reduced by a factor of "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001500_978-1-4899-1465-1-Figure8.24-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001500_978-1-4899-1465-1-Figure8.24-1.png",
+        "caption": "Figure 8.24. Motor connected to transmission cable and protected by surge capaci tors.",
+        "texts": [
+            " Engineers working with power equipment are not usually con cerned about lead lengths needed to interconnect various power de vices, as they contribute negligibly to the impedance and losses ofthe complete system. However, in engineering a surge protection system, ae Motor Control and Protection 181 one must remember that voltage surges are a high frequency phenom enon, not 60 Hz power, and lead lengths become important. This can be illustrated by an example of a typical installation showing the effect of varying lead lengths between the motor terminals and the surge capacitors. Figure 8.24 shows a 4000-V motor connected to a transmission line with Z = 25 {} and a surge voltage of 16 kV, wave front of 100 nsec, impressed on the system. Lead lengths connecting the motor terminals to the capacitors have the effect of adding inductance at the rate of 0.25 \"H per foot in series with the capacitor. Any internal inductance of the capacitor itself is assumed to be included with the lead length inductance for this example. The critical period from a voltage crest standpoint is the first 1 00 nsec during which the voltage is building up at the motor terminals"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002793_j.jsv.2005.03.024-Figure22-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002793_j.jsv.2005.03.024-Figure22-1.png",
+        "caption": "Fig. 22. Tyre cross-section.",
+        "texts": [
+            " This omission does not influence the belt vibration but it affects the force transmission to the hub in two ways. First the n \u00bc 1 cavity mode, which causes an audible tone around 250Hz within the passenger compartment, is neglected. The second is the stiffening of the belt due to cavity volumetric changes. Both of these effects are calculated here by considering the \u2018free\u2019 and \u2018forced\u2019 acoustic waves in the cavity, but an initial stage calculates the change in section area dA due to belt radial displacement w. Consider the tyre section of area A and inextensible side-wall of length ls seen in Fig. 22. The sum of the two end segments has an area A1 A1 \u00bc a2s \u00f02fs sin 2fs\u00de. (A.1) The central rectangle has area A2 \u00bc wsb. The side-wall radius and height are as \u00bc ls 2fs ; ws \u00bc ls sin fs fs . (A.2a,b) The total area is A \u00bc A1 \u00fe A2. (A.3) The fractional change in area arising from a belt displacement w is dA dw \u00bc dA1 dfs dfs dw \u00fe b, (A.4) where dA1 dfs \u00bc l2s 2f2 s sin 2fs fs 1 cos 2fs ; dw dfs \u00bc ls f2 s \u00f0fs cos fs sin fs\u00de. The general case of coupling between the carcass and the enclosed air, is obtained from the wave equation of the enclosed air excited by the change in cross-section dA, calculated above"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001366_s0304-3975(01)00117-7-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001366_s0304-3975(01)00117-7-Figure1-1.png",
+        "caption": "Fig. 1. A membrane structure.",
+        "texts": [
+            " Such an approach is typical for the area of Natural Computing, where one studies all kinds of computing inspired by (or gleaned from) nature. The membrane structure of a membrane system is a hierarchical arrangement of membranes (understood as three dimensional vesicles), embedded in a skin membrane, the one which separates the system from its environment. A membrane without any membrane inside is called elementary. Each membrane deEnes a region. For an elementary membrane this is the space enclosed by it, while the region of a non-elementary membrane is the space in-between the membrane and the membranes directly included in it. Fig. 1 illustrates these notions. As the reader can see, we give labels (positive integers) to membranes in order to be able to address them. Since each region is delimited (\u201cfrom outside\u201d) by a unique membrane, we will use the labels of membranes to also label the corresponding regions. Each region contains a multiset of objects and a set of (evolution) rules. The objects are represented by symbols from a given alphabet. Typically, an evolution rule is of the form ca\u2192 cbinjdoutdhere, and it \u201csays\u201d that a copy of the object a, in the presence of a copy of the catalyst c (this is an object which is never modiEed, it only assists the evolution of other objects), is replaced by a copy of the object b and two copies of the object d, where the copy of b has to \u201cimmediately\u201d enter the membrane labeled by j (hence to enter region j), providing that it is adjacent to the region where the rule is applied, a copy of object d is sent out of the current membrane, and a copy of d remains in the same region",
+            " Consequently, one can see this paper as investigating the power of communication in its purest form. In a membrane system with carriers no objects are created, and no objects are destroyed, and the whole computation process is accomplished by communication between regions (which is implemented by carriers). Thus, our result on the computational universality of membrane systems with carriers may be seen as a result on the power of communication in membrane systems. A membrane structure is pictorially represented by an Euler\u2013Venn diagram (like the one in Fig. 1); it can be mathematically represented by a tree or by a string of matching parentheses. The tree of the structure from Fig. 1 is given in Fig. 2. The same structure is also represented by the following parentheses expression: [1 [2 ]2 [3 ]3 [4 [5 ]5 [6 [8 ]8 [9 ]9 ]6 [7 ]7 ]4 ]1: Since the membranes are having labels, also here the pairs of corresponding parentheses have labels. It should be noted that the same membrane structure may be represented by diNerent parenthetic expressions. The multisets over a given Enite support (alphabet) are represented by strings of symbols. The order of symbols clearly does not matter, the number of copies of an object in a multiset is given by the number of occurrences of the corresponding symbol in the string"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002793_j.jsv.2005.03.024-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002793_j.jsv.2005.03.024-Figure1-1.png",
+        "caption": "Fig. 1. Side-wall geometry: (a) single side-wall section and (b) belt and side-wall sections.",
+        "texts": [
+            " The calculation shows two air transmission mechanisms, one of which is responsible for the cavity resonance around 250Hz that is detectable within the vehicle passenger compartment. The side-wall model is combined with the belt model [3] to make a full tyre model, this model is fitted to some experimental data to give estimates of the material properties and the force transmitted to the hub. The measurements include two previously untried techniques for line excitation of the belt and for transmitted force to the hub. Fig. 1 shows a tyre side-wall of length ls of radius as and uniform thickness ts, displaying the sign convention for positive directions, rotations, forces and moments. It is assumed that the side-wall is symmetric about the neutral axis and that the averaged material properties of the cross-section are known. Reference will only be made to these single material values for the cross-section. The side-wall is a curved, tensioned, Mindlin Plate (supporting bending and shear deformations) subjected to a net static pressure P",
+            " Below the side-wall ring frequency at 400Hz the phase of p=2 implies an evanescent wave. At 400Hz the rapid phase change marks the ring frequency, above which a longitudinal travelling wave occurs. This wave is controlled by the sidewall longitudinal stiffness. The third root has a phase of p=2 until the cut-on of the rotational travelling wave at 4 kHz. This means that it is an evanescent wave below this frequency. The large wavenumber implies rapid decay of vibration away from the belt towards the hub. Fig. 1 is a display of the side-wall subjected to displacements at the belt contact f1. If a lateral displacement uz1 or a vertical displacement wy1 is applied to the side-wall it causes responses at every point s, in both the circumferencial u and radial w directions. The force responses at s \u00bc 0 and ls are quantified in the \u2018dynamic stiffness\u2019 transfer function, which is force/displacement. The dynamic stiffness\u2019 can be calculated from the summation of the three pairs of waves that exist at each frequency",
+            " The longitudinal displacement is zero for the clamped boundary, and from Eq. (10) 0 \u00bc ITApLps\u00f0ls\u00dewp (22) and by expanding the matrices 0 \u00bc B6pwp, where B6p \u00bc \u00bda1A1 A1 a2A2 A2 a3A3 A3 . The six boundary conditions from Eqs. (16) to (22) can now be assembled into a single matrix Bpwp \u00bc w; Bp \u00bc B1p B2p B3p B4p B5p B6p 2 6666666664 3 7777777775 ; w \u00bc w1 u1 0 0 0 0 8>>>>< >>>>: 9>>>>= >>>>; . (23) This may be inverted to give the wave amplitudes wp \u00bc B 1p w. (24) The net transverse force/width F in the radial direction in Fig. 1 has contributions from the component internal shear forces/width Qs1 and tension forces/width N at s \u00bc 0 or s \u00bc ls F1 \u00bc \u00bdQs1 N1Fs s\u00bc0, (25a) F2 \u00bc \u00bdQs2 N2Fs s\u00bclS . (25b) The kinematic rotation Fs, is given in Eq. (2), [1] Fs \u00bc u as qw qs . (26) The shear force for the pth wave is the product of shear stiffness Ss and shear slope g and can be written in terms of wp using Eqs. (1), (8) and (44) of Ref. [3] Qp \u00bc Ss\u00f01 Ep\u00de qwp qs . (27) If only the static in-plane force is considered, i.e. N \u00bc Ns, then substitution into Eq. (25) of Eqs. (4), (7), (10), (11), (26) and (27), yield the net transverse force F at s F \u00bc IT \u00f0Ss \u00feNs\u00deDp SsEpDp Ns as Ap Lpswp. (28) The longitudinal forces N, in Fig. 1, are simply the product of the longitudinal stiffness As and the longitudinal strain N \u00bc As qu qs \u00fe w as . (29) This can be written in terms of wp using Eqs. (4), (7) and (10) N \u00bc AsI T DpAp \u00fe 1 as I0 Lpswp, (30) where I0 is the unit matrix. The radial and longitudinal forces in Eqs. (28) and (30) can be written in a single stiffness matrix Kp Fs \u00bc F N \u00bc KpLpswp, (31) where the stiffness matrix is Kp \u00bc \u00bdK1a K1b K2a K2b K3a K3b , (32) \u00bdKpa Kpb \u00bc ikp\u00f0Ss\u00f01 Ep\u00de \u00feNs\u00de Ns as Ap ikp\u00f0Ss\u00f01 Ep\u00de \u00feNs\u00de \u00fe Ns as Ap As ikpAp \u00fe 1 as As ikpAp \u00fe 1 as 2 6664 3 7775; p \u00bc 1; 2; 3"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000561_a:1009888213333-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000561_a:1009888213333-Figure1-1.png",
+        "caption": "Figure 1. Friction models.",
+        "texts": [
+            " The importance of joint friction on the dynamic behaviour of robots is such that any valid simulation model must include friction. One of the difficulties with modeling friction is the complexity of the phenomenon at low velocity and, in particular, of the stick-slip process. In the slip phase, friction is essentially a constant force opposing the motion. In the stick phase, the macroscopic relative motion is null and friction appears as a constraint maintaining the zero-velocity condition between the rubbing surfaces. One extensively-used model is the classical Coulomb model shown in Figure 1a. The model is static in the sense that it is purely algebraic and does not include any state. It is characterized by a static friction force (fs), a kinetic friction force (fk) and a velocity-dependent viscous friction force (slope bv). In the figure, the model is shown to have a static friction (breakaway) force fs larger than the kinetic friction. This is usually the case. One important property of that model is the non-unicity of the relationship between friction and velocity at v = 0. In reality, at zero velocity, the force of friction is anywhere between \u00b1fs and is defined by the constraint force needed to maintain the stick mode. One approach to obtain a one-to-one relationship is to use the linear approximation shown in Figure 1b. To be realistic, however, the slope must be steep and numerical problems may occur. In addition, the model exhibits no friction force at zero velocity and therefore cannot represent the stick-slip process properly. Figure 1c shows a modification of the model where the stick-to-slip transition occurs at the non-zero velocity vmin. This is usually required for computer implementation since a true zero is impossible, and agrees anyway with experimental observations [1]. In the gray area, the friction can have any value between zero and the static friction fs . Over the years, many solutions have been proposed to deal with friction modeling at low velocity. In general, two broad classes of models can be identified: static and dynamic",
+            " The other non-zero accelerations can be precomputed since the friction at those joints is known. From a numerical point of view, using zero velocity as the transition condition between the stick and the slip modes is not a realistic choice. Experimental observation shows that a motor abruptly stops below a given velocity. Moreover, computationally, using a zero velocity is not practical since a true zero is almost impossible in computer operations. For this reason, a numerical algorithm has to use a threshold velocity vmin,i (Figure 1) below which the acceleration is fixed to zero. The following equation shows the evolution of the state variables within one integration step: q(t) = q(t \u2212 T )+ t\u222b t\u2212T q\u0307 d\u03c4, (9) q\u0307(t) = q\u0307(t \u2212 T )+ t\u222b t\u2212T q\u0308 d\u03c4, (10) with q\u0308 =M(q)\u22121(\u2212g(q, q\u0307)+ T\u2212 Ff ), where T is the step time. Setting the acceleration q\u0308 to 0 implies that the velocity at time t will keep the previous time-step value. This is in contradiction with the sticking process. One option to avoid the numerical problems resulting from the residual velocity is to also set the velocity to zero, as is usually done when solving constrained motion"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003667_j.matcom.2006.01.001-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003667_j.matcom.2006.01.001-Figure1-1.png",
+        "caption": "Fig. 1. Space vector reference frames for motor variables.",
+        "texts": [
+            " In the special case of \u03c90 = 0, the general reference frame (x, y) becomes a stationary reference frame (\u03b1, \u03b2). Coordinates of a revolving reference frame aligned with the stator current vector are denoted here by d and q. The (d, q) frame rotates with the angular velocity \u03c9, usually referred to as the supply, excitation, or synchronous, radian frequency. Another reference frame employed in the subsequent considerations is the revolving frame (D, Q) aligned with the rotor flux vector. As illustrated in Fig. 1, both the (d, q) and (D, Q) frames revolve with the same velocity \u03c9. Thus, in the synchronous frame (d, q), \u03c90 = \u03c9, isd = Is, and isq = 0, with isd and isq denoting the direct-axis and quadrature-axis components of the stator-current vector, and Is being the magnitude of that vector. Within a short period of time required for estimation of the stator resistance, the stator flux vector in the (d, q) frame can be assumed constant. With d \u03bbs/dt = 0, from (1) to (4), vds + jvqs = RsIs \u2212 \u03c9 Lm Lr \u03bbqr + j\u03c9 [ \u03c3LsIs + Lm Lr \u03bbdr ] (6) where \u03c3 denotes the total leakage factor"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003940_1.2338060-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003940_1.2338060-Figure1-1.png",
+        "caption": "Fig. 1 Flexible body in space",
+        "texts": [
+            " Proper Formulation for the Dynamics of Aerospace tructures As discussed in the preceding section, the mean axes have been ortrayed as a useful tool in the treatment of such diverse aeropace structures as missiles, spacecraft, aircraft, and helicopters. A loser examination of pertinent investigations, however, paints a ifferent picture. Improper formulations of the equations of moion and/or misuse of the concept of mean axes do not inspire uch confidence in the usefulness of the approach. In this section, e propose to contrast the approach based on misuse of mean xes with a proper formulation of the same problem. From Meirovitch 8 , the motions of a flexible body can be escribed by means of a reference frame xyz Fig. 1 fixed in the ndeformed body and known as body. Then, the rigid-body moions are defined as three translations and three rotations of the ody axes relative to the inertial space XYZ and the elastic deforations as the displacements of points on the body relative to the ody axes. When expressed in terms of components along the ody axes, the rotational velocities are referred to as quasielocities, and the corresponding vector is denoted by . It is hown in Ref. 8 that, when expressed in terms of body-axes omponents, the translational velocities can also be treated as uasi-velocities; they are arranged in the vector V",
+            " Discrete forces can be treated as distributed by writing them in the form Fi t r\u2212ri , where r\u2212ri are spatial Dirac delta functions 11 , so that the virtual work can be written in the form W = D fT r,t + i=1 p Fi T t r \u2212 ri RP * dD 7 where RP * is a virtual displacement vector whose expression can be obtained by considering the velocity vector of a typical point P in the body in terms of components along the body axes as follows: vP = V + r + u + v = V + r\u0303 + u\u0303 T + v 8 where r is the radius vector from O to P and r\u0303+ u\u0303 is the skew symmetric matrix derived from the vector r+u. Using the analogy with Eq. 8 with the term u\u0303T ignored as small compared to r\u0303T , we obtain MAY 2007, Vol. 74 / 499 6 Terms of Use: http://www.asme.org/about-asme/terms-of-use w w v t o w a d o T a a s f a w n g l \u201c o t m n i a e w R t s a r o w 5 Downloaded Fr RP * = R* + r\u0303T + u 9 hich is the virtual displacement vector of point P Fig. 1 , in hich R* is the virtual displacement vector of the origin of xyz, is the virtual angular displacement vector of xyz and u is the irtual elastic displacement vector of point P relative to xyz, all in erms of body-axes components. Inserting Eq. 9 into Eq. 7 , we btain W = D fT r,t + i=1 p Fi T t r \u2212 ri R* + r\u0303T + u dD = FT R* + MT + D U\u0302T udD 10 here F = D fdD + i=1 p Fi, M = D r\u0303fdD + i=1 p r\u0303iFi, U\u0302 = f + i=1 p Fi r \u2212 ri 11 re the desired generalized forces. Closed-form solutions of hybrid sets of differential equations escribing the dynamics of flexible aircraft is not within the state f the art, so that one must be content with approximate solutions"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003446_1.1649980-Figure14-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003446_1.1649980-Figure14-1.png",
+        "caption": "Fig. 14 Cylindrical Co-ordinates for Reynolds Equation: Platetype Friction Component",
+        "texts": [
+            " The purpose here is to provide a single qualitative formula that one can use for enhancing the neural network model. Therefore, ideal assumptions are made in the following derivation to make the formulation manageable. First, the plate-type clutch is considered. Since the clutch plates are all annular disks, it is more convenient to use cylindrical coordinate system. Assuming that both the oil density and viscosity are constant across the oil film thickness direction, the Reynolds equation is formulated in cylindrical co-ordinate system ~see Fig. 14! as follows @27#: ] ]r S rrh3 h ]p ]r D1 ] ]u S rh3 hr ]p ]u D 56rr~Ur12Ur2!16r~Vu12Vu2! ]h ]u 16rh ] ]r @r~Ur11Ur2!#16h ] ]u @r~Vu11Vu2!# 16rh~Ur11Ur2!112rrW2112h ]r ]t r (A1) where the speed components Ur1 , Ur2 , W1 , Vu1 , Vu2 are all defined in the nomenclature and Fig. 14. Ur1 and Ur2 are the surface velocities in the radial direction of the clutch plates. Vu1 and Vu2 are the surface velocities in the u-direction. W2 is the moving velocity of the upcoming plate in the z direction, which is actually the changing rate of the oil film thickness. Noticing the disks only move in the tangential direction, all the terms related with the radial movement can be dropped. Assuming the plateclutch system is axis-symmetric, and the oil density keeps as a rom: http://dynamicsystems"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003658_.2005.1467063-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003658_.2005.1467063-Figure1-1.png",
+        "caption": "Figure 1: The schematic diagram of the TRMS.",
+        "texts": [
+            " An objective function is created to tune the PID controller within the augmented strategy that gives the smallest overshoot, fastest rise time, quickest settling time and very small steady state error. In order to combine all these objectives, multiple objective functions are used to minimise the output error of the controlled system. Since their introduction by Holland in 1975 [6] as evolutionary algorithms, there has been growing interest among scientists and engineers in the use of GAs in identification and control applications [1, 3, 4, 9, 10]. The TRMS, shown in Figure 1, is a laboratory set-up designed for control experiments [5]. In certain aspects it behaves like a helicopter. The TRMS rig consists of a beam pivoted on its base in such a way that it can rotate freely both in the horizontal and vertical directions producing yaw and pitch movements, respectively. At both ends of the beam there are two rotors driven by two d.c. motors. The main rotor produces a lifting force allowing the beam to rise vertically making a rotation around pitch axis (vertical 0-7803-8936-0/05/$20"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001678_3.21494-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001678_3.21494-Figure1-1.png",
+        "caption": "Fig. 1 Interception conflict geometry.",
+        "texts": [
+            " 5) The pursuer controls its lateral acceleration via a first-order system. Remark 2: This first-order system represents a closed-loop control of the missile's acceleration. It follows from the preceding remark that the time constant of this representation can vary with the speed of the missile at the acquisition time. This is typical for missiles with no measurements adequate for gain scheduling (e.g., pitot sensors). In these cases variations in the time constant can be quite significant. Referring to Fig. 1 we obtain the following equation. For small YP and ye, Y = Ye-Yp = Ve cos(ye,)ye - Vp cos(ypo)yp (8) This is obtained by noting that for \\yp\\ <\u00a3 I we have sin(\u00bbo + YP) \u2122 sin(^o) + COS(YPO)YP A similar condition holds for the evader E. We have also used the fact that the collision condition is expressed as Vp sin(ypo) - Ve sm(yeQ) = 0 Since the controls are the lateral accelerations, we define xi = -Y, x2 = -Y, x3 = Vp cos(yPQ)yp and readily obtain the following state space formulation: (9) jc3(0 = -0(0*3(0 + a(t)u(t) x4(t) = w(t) where w(t) is the evader's jerk and u(t) is the commanded interceptor's acceleration"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003664_s0263574704000359-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003664_s0263574704000359-Figure1-1.png",
+        "caption": "Fig. 1. Schematic of the HSM.",
+        "texts": [
+            " Measurement of postures can be automated, thereby making the experimental procedure simple. This paper is organized as follows: Hexa Slide Manipulator (HSM) and its kinematics are described in Section 2. Section 3 discusses the calibration device along with measurement procedure and formulation. Results of computer simulations are presented in section 4. Section 5 concludes the study. This section introduces the parallel robot, HSM, to which the proposed calibration scheme is applied and presents its kinematics. The schematic of the HSM is shown in figure 1 and the geometric parameters are defined in figure 2. It is a 6 DOF fully parallel manipulator of the PRRS type. In figure 2, Aio and Ail denote the start and the end points of the ith (i = 1,2, . . . ,6) rail axis. Ai denotes the center of ith universal joint and it lies on the line segment AioAil. Rail axes are identical and the nominal link length, , is equal for all kinematic chains. The articular variable, \u03bbi , is the distance between the points Aio and Ai. Bi denotes the center of ith spherical joint at the mobile platform"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003446_1.1649980-Figure15-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003446_1.1649980-Figure15-1.png",
+        "caption": "Fig. 15 X-Y-Z Co-ordinates for Reynolds Equation: Band-type Friction Component",
+        "texts": [
+            " For band brake, there are very significant film thickness and pressure distributions from one end to the other end during the band brake engagement. Therefore, the pressure and oil film thickness cannot be assumed constant across the tangential direction of the band. Determined by the geometry characteristics of the band brake system, it\u2019s more convenient to apply Reynolds equation in rectangular coordinates @27#: ] ]x S rh3 h ]p ]x D1 ] ]z S rh3 h ]p ]z D 56r~U12U2! ]h ]x 16r~W12W2! ]h ]z 16h ] ]x $r~U11U2!%16h ] ]z $r~W11W2!% 112rV2112h ]r ]t (A9) The speed components U1 , U2 , W1 , W2 , V2 are defined in the nomenclature and Fig. 15. U1 and U2 are the surface velocities in the x-direction ~width direction of the band brake!. W1 and W2 are the surface velocities in the z-direction ~tangential direction of the band and drum!. V2 is the moving velocity of the band in the z direction, and it is actually the changing rate of the oil film thickness. In addition, since the changes of oil temperature and pressure are not dramatic enough to cause observable shifting of oil density, the oil density is assumed to be constant throughout the MARCH 2004, Vol. 126 \u00d5 151 6 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F engagement process. Based on these assumptions, and noticing that neither of the two contact surfaces moves in the x-direction, Eq. ~A9! is further simplified as ~see Fig. 15!: ] ]x S h3 h ]p ]x D1 ] ]z S h3 h ]p ]z D56vRo ]h ]z 112 ]h ]t (A10) Noticing z5Rou , the above equation can be rewritten as: ] ]x S h3 h ]p ]x D1 1 Ro 2 ] ]u S h3 h ]p ]u D56v ]h ]u 112 ]h ]t (A11) The pressure distribution can be estimated based upon the band tension, which is obtained by solving following differential equation @7#: dTb~u ,t ! du 5@tviscous1tasperity#WbRo (A12) Since the asperity contact has not been well established at the early stage of the engagement, the asperity friction force can be ignored"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001500_978-1-4899-1465-1-Figure7.24-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001500_978-1-4899-1465-1-Figure7.24-1.png",
+        "caption": "Figure 7.24. Brushless de control switching logic signals compared with line-to-line and line-to-neutral voltages.",
+        "texts": [
+            " The proper Hall de vice positioning can be achieved by aligning the Hall device outputs relative to the three-phase generated voltages of the motor. However, the three line-to-line voltages are usually the ones available to be mea sured because the motor neutral is normally not brought out to a ter minal. Therefore, much of the brushless dc literature displays the logic timing diagram relative to line-to-line voltages rather than phase volt ages. Consequently, the logic signals for Q! are repeated in Fig. 7.24 Adjustable-Speed Drives 149 compared with the line voltage Vab and Van is included for reference. The 30\u00b0 phase shift between Vab and Van is evident in the figure. The other five logic signals will have similar displacements relative to V be and Yea' The preceding discussion has focused on one particular type of brushless dc drive. The motor voltage was assumed to have an ideal sinusoidal shape and the current was controlled to be rectangular pulses. The sinusoidal voltage/rectangular current drive requires some means of current control to regulate the motor torque"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003764_bf02953383-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003764_bf02953383-Figure1-1.png",
+        "caption": "Fig. 1 Thrust bearing with variable gap geometry.",
+        "texts": [
+            " The main design principles with variable gap geometry are: The control function of the restrictor is assigned partially or completely to the gap itself. As a result, the pressure drop in the restrictor is reduced, and higher pressures are avail able in the gap, leading to an increased load capacity. A large load capacity, and especially, a high bearing stiffness, are obtained when the convergence of the gap in the flow direction is made to become an increasing function of the external load. A cross section of an air-bearing pad is represented in Fig. 1. The type represented is one with a variable gap geometry, obtained by a membrane deflected by the difference of the pressure acting on its upper and lower sides. In case of equal pressures on both sides of the membrane, no elastic deformation of the latter occurs, it remains in its original (conical) position. Such a situation arises when the load on the the bearing is so large that the outer rim of the bearing touches the opposite bearing surface(Fig.la)_ In that case the pressures on both sides of the membrane are the same"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003024_1.2103093-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003024_1.2103093-Figure1-1.png",
+        "caption": "Fig. 1 Schematic of a brush seal",
+        "texts": [
+            " Deformed geometries may be exported directly to the mesh generation software, allowing iterative solution of the coupled aerodynamic/mechanical problem. DOI: 10.1115/1.2103093 Brush seals are a relatively new type of aerodynamic seal for turbomachinery applications. They have found increasing industrial use in gas turbine aero and power generation engines over the last decade. A brush seal is a set of fine diameter fibers densely packed between retaining and backing plates. There are three main components: bristle pack, front plate, and backing plate Fig. 1 . It is convenient to divide the bristle pack into two regions: the overhanging region, as indicated, and the outer portion. The backing plate is positioned downstream of the bristles to provide mechanical support for the bristles under the differential pressure loads. The inherent flexibility enables the seal to survive large rotor excursions, resulting from vibration, thermal, and centrifugal growth, and rotor imbalance or eccentricity during normal operation, without sustaining appreciable permanent damage"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002793_j.jsv.2005.03.024-Figure13-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002793_j.jsv.2005.03.024-Figure13-1.png",
+        "caption": "Fig. 13. Net force transmission to the hub due to a displacement on the contact patch.",
+        "texts": [
+            " In fact there will be a slight fluctuation in width about a mean value. The effect of this fluctuation is modelled by averaging nine transfer functions. Fig. 12 shows the effect of a 0.3% standard deviation in the plate strip width ls. For this 100mm side-wall, the standard deviation of the width was therefore 0.03mm. It is interesting to see that the effect of the width fluctuation has a similar effect as an increase in damping. A realistic side-wall model can therefore be made without using particularly high damping values. Fig. 13 shows a loaded tyre of belt radius a and a contact patch of length lct, where lct \u00bc 2ycta. The total force transmitted in the vertical direction Fs is the sum of three components Fs \u00bc F ct \u00fe Fb \u00fe Fa. (49) Fa is the force transmitted by the \u2018free acoustic wave\u2019 in the cavity, and is calculated in Appendix A.1. F ct \u00bc 2Krlctw\u00f00\u00de is the force transmitted through the side-wall at the contact patch. The force from the vibration of the unloaded belt Fb is an integral over the free belt length lb, weighted by cos y Fb \u00bc \u00f02Kr \u00fe Ka\u00dea Z 2\u00f0p yct\u00de yct w\u00f0c\u00de cos ydy\u00fe 2Kca Z 2\u00f0p yct\u00de yct u\u00f0c\u00de sin ydy, (50) where Kr and Kc are the side-wall stiffness\u2019 in the radial and circumferential directions"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003842_s00158-006-0055-5-Figure7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003842_s00158-006-0055-5-Figure7-1.png",
+        "caption": "Fig. 7 Lalanne\u2019s rotor model (Lalanne and Ferraris 1998)",
+        "texts": [
+            " u denotes the residual unbalance of the disk. In this study, only the diagonal terms of the stiffness and damping coefficients (kxx, kyy, cxx, cyy) are considered and do not consider inequality or equality constraints. When a journal bearing is used in the rotor\u2013bearing system, crosscoupled terms of stiffness and damping coefficients (kxy, kyx, cxy, cyx) need to be selected as design variables. The proposed methodology is first verified by a simulation study. A simple rotor\u2013bearing model (Lalanne and Ferraris 1998) as shown in Fig. 7 and detail specifications shown in Table 1, is composed of a shaft of 1.3 m in length and 0.1 m in diameter and has three disks. Two bearings support the shaft at each side end. The dynamic coefficients of two bearings have the same values, and hence, only the diagonal terms are considered. An unbalance mass was added on disk 2 (6th node) with magnitude of 200 g\u00b7mm and angle of 0\u25e6. The unbalance responses at the 2nd and the 12th node were selected as simulated measured responses. To consider the uncertainty of the analytical model and to examine the robustness of identification, 10% of Gaussian noise was applied to the simulated responses"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001965_s0167-8922(03)80088-3-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001965_s0167-8922(03)80088-3-Figure3-1.png",
+        "caption": "Figure 3. General geometries of ring and roller specimen (dimension in mm, not to scale)",
+        "texts": [
+            " However, early tests showed that as micropitting evolved, high frequency components in the evolving topography provided a vibratory excitation at around 30 times the rotational speed and led to corresponding vibratory radial displacements of the counterface shatts. Wear on the test specimens became nonuniform and developed a ridged appearance. In order to remove this problem, the rig was equipped with three damper rings, located on the shafts with a small radial clearance. Squeeze film action provided a source of damping akin to that of the hydrostatic system of earlier rigs and led to uniformly worn specimens. A test roller and three counterface rings are employed for each test. The general geometries of both roller and rings are shown in figure 3. Both specimens were manufactured from 16MnCr5 steel to DIN 17210, commonly used in gear industries. Both specimens were gas carburised and heat treated to the specified hardness of 660-700 HV and 730- 770HV for roller and ring respectively with minimum case depth of 0.9 mm for both specimens. The average roughness of each specimen was between Ra = 0.35 ~tm and 0.5 Bm for roller and tings respectively. A poly-alpha-olefin (PAO) base stock was employed in this work. The viscosity of the lubricant was 13"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003629_ramech.2006.252627-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003629_ramech.2006.252627-Figure2-1.png",
+        "caption": "Fig. 2. Kinematics of a two-wheeled mobile robot under consideration of side-slip",
+        "texts": [
+            " The robot is equipped with two single-chip two-axis acceleration sensors measuring tangential and lateral acceleration, 1\u20134244\u20130025\u20132/06/$20.00 c\u00a9 2006 IEEE RAM 2006 a single-chip gyro sensor and wheel encoders for each side. Therefore, seven measurement channels sampled at the same sampling rate of 2ms are available. An Analog Devices Blackfin DSP running at 600MHz provides sufficient calculation performance to execute both the predictive control algorithm and the navigation system. The kinematics of the unicycle-type mobile robot under consideration of side-slip, Fig. 2, are given by x\u0307 = v cos(\u03d5 + \u03b1) = vt cos \u03d5 \u2212 vn sin\u03d5 y\u0307 = v sin(\u03d5 + \u03b1) = vt sin\u03d5 + vn cos \u03d5 \u03d5\u0307 = \u03c9, (1) where x and y denote the inertial coordinates of the robot\u2019s center of gravity, \u03d5 denotes its the inertial attitude angle, \u03b1 is the side-slip angle, v the effective velocity with components vt and vn and \u03c9 denotes the yaw rate. To calculate the robot\u2019s position and orientation x, y and \u03d5, estimation of vt, vn and \u03c9 and subsequent integration using (1) is necessary. As mentioned in the introduction, the general idea is to use data from inertial sensors rather than data from odometric sensors only during periods where odometry is likely to be unreliable, i"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002472_j.jsv.2004.04.037-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002472_j.jsv.2004.04.037-Figure2-1.png",
+        "caption": "Fig. 2. Global coordinate systems of a gear pair.",
+        "texts": [
+            " From the equilibria of the generalized forces for each gear, the coupled equation of motion of a gear pair can be expressed by (a detailed derivation can be found from [3]) MG0 \u20acqG0 \u00fe CG0 \u00fe GG0 _qG0 \u00fe KG0 qG0 \u00bc QG0 ; (2) where MG0 ; CG0 ; GG0 and KG0 are the inertia, damping, gyroscopic and stiffness matrices and they are given in Appendix A by Eqs. (A.1)\u2013(A.4). It can be noticed that the gear meshing stiffness and damping are coupling mechanisms. And QG0 is the external force vector, which is generally a function of gear unbalances, geometrical eccentricities and transmission errors [9]. But the gear meshing damping and the general forces due to gear geometrical eccentricities and transmission errors are not considered in the proceeding analysis. With respect to the global coordinate system as shown in Fig. 2, a generalized displacement vector of a gear pair can be defined by qG \u00bc uG 1 vG 1 yG X1 yG Y1 uG 2 vG 2 yG X2 yG Y2 yG Z1 yG Z2 T : (3) Then, through a coordinate transformation considering a pressure angle, the global equation of motion of a gear pair can be expressed by MG \u20acqG \u00fe CG \u00fe GG _qG \u00fe KG qG \u00bc QG : (4) Fig. 3 shows the structure of the global coupled gear mesh stiffness matrix, KG : kl1,2 and klc represent the pure lateral components and the coupled component between the lateral vibrations and kt1;2 and ktc the pure torsional components and the coupled component between the torsional vibrations, respectively"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002068_bf00052455-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002068_bf00052455-Figure5-1.png",
+        "caption": "Fig. 5. Backlash force law.",
+        "texts": [
+            " (6) Cki The vector cki follows from Figure 4, 5ki is the relevant skew-symmetric tensor (gtb _= a \u00d7 b). The vector ~b k E ~6 represents a unit vector in the direction of relative displacement. In that direction we have a generalized force ffk according to the given force law. It can be projected into the body coordinate frames for Hi, H i (Figure 4) by f/ T T = CkiCkffk , fj = Ck jCkCk . (7) ~k =- c'Zk + dS'k. (8) Of course, any nonlinear relationship might be applied as well as the force law with backlash according to Figure 5. Gear meshes with backlash are modeled with the characteristic of Figure 5. In this case care has to be taken with respect to the two possibilities of flank contact on both sides of each tooth [20]. Oil reduces the impact forces of the hammering process. Some application tests have been performed with the nonlinear oil model of Holland [7]. On this basis a simplified model has been derived to approximate the oil influence (Figure 6). The model assumes an exponential damping behavior within the backlash s. Bearings are very important coupling elements in drivelirles. Roller bearings are approximated by the force laws in (x, y)-directions ~kx = cx% + dx+x, (kv = Cy~y + dy;~ u"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure3.18-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure3.18-1.png",
+        "caption": "Figure 3.18. A general displacement viewed as consecutive rotations about nonintersecting axes.",
+        "texts": [
+            "161) the resultant rotation about the base point 0 is decomposed into two con secutive rotations R 1 and R 2 about concurrent axes a 1 and a2 , such that a 1 is any given direction and a 2 is perpendicular to the translation vector b*. Since T*=T 1 +T2 R1, (3.161) may be written as d*=T 1x+b*+T 2 x, where X= R I X is the position vector from 0 to the final position r of the particle p Finite Rigid Body Displacements 213 after the first rotation alone. Since a 2 \u00b7 b* = 0, we may apply the parallel axis theorem in Fig. 3.17b to find a parallel line through another base point 0' such that d = b* + T 2 x = T 2 x' is a pure rotation about 0', where x' is the location of P' from 0'. Thus, as shown in Fig. 3.18, the given displacement d*(P) is the sum of two pure rotational displacements d 1 = T 1 x and d2 = T 2 x' about 0 and 0', so that (3.162) Hence, any given rigid body displacement (3.161) may be represented by the sum of two consecutive pure rotational displacements about, in general, non intersecting axes a 1 and a 2 , where a 1 is any assigned direction and a 2 is perpen dicular to the parallel translation vector of the assigned displacement. We have learned that every rigid body displacement may be reduced to a unique screw displacement"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002291_robot.1994.351239-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002291_robot.1994.351239-Figure5-1.png",
+        "caption": "Figure 5 : Identifying an obstacle free region The first two demonstrations define the initial region RR. Additional demonstrations extend the boundaries with the segments that are exterior to R F ~ as shown by the solid segments of demonstration 3.",
+        "texts": [
+            " Thus the sequence of regions Rijlm for m=1,2, ... M are guaranteed to be obstacle free using the same argument presented for an individual region. The obstacle free regions identified from one pair of demonstrations can be determined by finding the intersections between the trajectories. Combining the obstacle free regions from all possible pair combinations result in the obstacle free region, RF. The procedure used to define the boundaries of RF is presented in the following steps with references to figure 5 . Implementation requires finding the intersection points between trajectories, which is implemented using the sweep line algorithm [8]. Average the beginning and ending position of each trajectory to find the starting and target positions. Append segments to each trajectory so they all start and end at common positions. Find the intersections within the individual trajectories and remove the loops in as explained in equation 2 to define the modified trajectories X'i. Use the first two demonstration trajectories, x'l and x'2, to define initial boundaries of the obstacle free region, RFi",
+            " If x' 1 starts off as the right side, then at the first intersection between the trajectories x\u20192 switches to the right and x\u2019l switches to the left. A single test line is used to identify the right and left boundaries at one location. The complete right and left sides are defined by switching between the trajectories at every subsequent and preceding intersections. An additional demonstration can extend the boundaries of the obstacle free region with segments that are external to R F ~ , as shown in figure 5. The intersections between the new trajectory and the right and left boundaries of R F ~ are found. The new trajectory switches between interior and exterior of RFi at every intersection with the boundaries. The new trajectory starts on the interior of RFi if its first segment of the trajectory is on the interior of the vertex at the starting position. Thus, by keeping track of the intersections and the starting direction of the new trajectory, the segments that are exterior to R F ~ can be found"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000858_s0379-6779(98)00128-3-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000858_s0379-6779(98)00128-3-Figure2-1.png",
+        "caption": "Fig. 2. Voltammetric response at a platinum disk electrode (diameter 1 mm) previously coated with a polymer obtained by oxidation at: (a) 1.60 V and (b) 1.90 V of a solution of 4.95 \u00d7 10 -3 M of I in 0.2 M Bu4NBF4 in CHzC12, and (c) 1.80 V of a solution of 5 \u00d7 10 -3 M fluorene in 0.2 M Bu4NBF4 in CH2C12. Supporting electrolyte: 0.2 M BuaNBF4 in CH2C12. Scan rate: 100 mV s - '. Amount of charge used for the synthesis: 0.75 mC. Initial potential: 0.0 V, switching potential: (a) and (b) 1.75 V, (c) 1.65 V.",
+        "texts": [
+            " This may be explained by the fact that fluorene diffuses more quickly than I, ip(fluorene) is higher than i(E ~ ) of I but the oxidation of the second fluorene unit of I leads to an i(E 2) higher than ip(fluorene). Fig. 1 shows typical a cyclic voltammogram of I at stationary platinum electrodes in CH2C12 solution containing 0.2 M Bu4NBF4 and 2.37 \u00d7 10 -3 M 9,9'-spirobifluorene for the electrode potential swept continuously between 0.0 and 1.7 V. Polymerization has also been performed by oxidation of I at fixed potential. Fig. 2 presents the redox behaviour of poly(I) deposits obtained by oxidation at 1.6 and 1.9 V in CH2C12 solution containing 0.2 M B u 4 N B F 4 and 4.95 \u00d7 10-3 M 9,9'-spirobifluorene. The electrolytic medium is also CH2C12 solution containing 0.2 M Bu4NBF4 in the absence of any electroactive species. Whatever the potential of polymerization, the electrochemical behaviour of poly (I) presents three main waves, the first one decreasing and the third one increasing when increasing the potential of polymerization. The stability of the redox behaviour of poly(I) is better when only the two first waves are reached. For information, Fig. 2(c) shows the electrochemical behaviour of polyfluorene in the same electrochemical medium. This one consists only in one redox system in the potential range lying between 0.0 and 1.65 V. This figure shows also that, globally, the electrochemical response of poly (I) is twice the one of polyfluorene as soon as the three deposits (where the electrochemical response is presented) were obtained in solutions of the same concentration and during a polymerization process consuming the same amount of charge (7"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001580_physreve.66.015102-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001580_physreve.66.015102-Figure1-1.png",
+        "caption": "FIG. 1. Diagram of the 2D injection cell used in the experiments.",
+        "texts": [
+            " Irreversibility here means that if the constraints due to the cavity are removed, the crumpled wire does not restore the initial situation. We will show that the structure of this 2D crumpling process is remarkably different from crumpling processes of sheets in 3D. We have also succeeded in explaining the experimental data with a hierarchical crumpling model based on a cascade of loops of decreasing sizes. The apparatus used to obtain the digital images of the 2D configurations of crumpled wires ~CW! is shown in Fig. 1. It consists of a transparent cell formed by the superposition of two disks of Plexiglas with a total height of 1.8 cm, an external diameter of 30.0 cm, and a circular cavity of 20.0 cm diameter and 0.11 cm height, which can accommodate configurations of a single layer of CW of diameter ~gauge! z 50.10 cm. In order to reduce friction, the cavity of the cell was polished and the 19AWG copper wire used in the experiment had a varnished surface. The cavity and the wire operated in a dry regime, free of lubrication. Radial channels 1063-651X/2002/66~1!/015102~4!/$20.00 66 0151 were made to provide three different ways of injecting the wire into the cell at the angles of 10\u00b0, 90\u00b0, and 180\u00b0 ~Fig. 1!. The photographs were taken with an Olympus C-3040ZOOM digital camera with a resolution of 3 megapixels that was connected to a computer and assembled 30 cm over the cell. To avoid picture artifacts by light reflections, a cylindrical screen was placed around the cell. An injection experiment begins fitting a straight wire in the opposite channels and subsequently pushing manually and uniformly the wire on both sides of the cell toward the interior of the cavity. The injection velocity at each channel in these experiments was typically of the order of 1 cm/s"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001995_310-Figure10-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001995_310-Figure10-1.png",
+        "caption": "Figure 10. Contour of the flow field along the cutting front and the change of pressure and Mach number of the jet from a supersonic nozzle: assistant gas N2, P0 = 7 bar, Dn = 1.5 mm, WL = 2 kW, v = 1.6 m min\u22121 and z0 = 2.5 mm and nozzle displacement with kerf (a) 1.4 mm and (b) 0.6 mm.",
+        "texts": [
+            " Figure 8 shows the macrograph of the laser cut edge of 5 mm thick stainless steel under the conditions of this group of cutting parameters. The horizontal line on the surface of the cut edge is pushed down to near 3 mm and surface roughness of the cut edge at 1 mm above the cut edge bottom is decreased to Ra = 2.65 \u00b5m. When the displacement of the nozzle with the cut kerf is increased from 0.9 to 1.4 mm (i.e. the overlap of the gas jet with the cut kerf is increased to 1.4 mm as shown in figure 9) and other conditions remain unchanged, the flow field inside the cut kerf is improved greatly (shown in figure 10(a)) compared with the conditions in figure 1. Not only is the curved shock weakened from P2/P1 = 1.46 to 1.22 but the incident point also moves along the cutting front from 3.5 to 4.3 mm. The flow field distribution along the cutting front becomes smooth and the exit momentum thrust increases. Therefore, the ability to eject the molten slag increases greatly. However, when the displacement of the nozzle with the cut kerf decreases from 0.9 to 0.6 mm and the other conditions remain unchanged, the flow field inside the cut kerf deteriorates, as shown in figure 10(b). The incident point moves up along the cutting front from 3.5 to 2.8 mm and the strength of the curved shock increased from P2/P1 = 1.46 to 1.82. The exit pressure along the cutting front increases from 1.13 into 1.23 bar and the exit Mach number decreases from 1.78 into 1.70. All these effects cause the quality of cut edge to worsen. Even if the inlet stagnation pressure is increased to 15 bar, the flow field does not greatly improve because the curved shock is pushed down to only 3.05 mm and its strength decreases to P2/P1 = 1"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000454_s0191-8141(99)00079-6-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000454_s0191-8141(99)00079-6-Figure3-1.png",
+        "caption": "Fig. 3. Geometrical elements of an isoclinal fold.",
+        "texts": [
+            " This function can be helpful in some cases, but it is more complicated than Eq. (1). The power functions do not generate proper isoclinal forms (except when n41) and isoclinal rounded folds (e.g. semicircular or semi-elliptical folds) are only roughly approximated by these functions. Hence, another type of function must be considered to \u00aet isoclinal folds. A limb pro\u00aele of these folds can be approximated by the expressions: y b 0@1\u00ff 1\u00ff x2 x2 0 s 1A within 0,x0 4a x x0 within bRyRy0 4b where y0 b C (Fig. 3). Eq. (4a) is a quarter of an ellipse with semi-axes x0 (on the x-axis) and b (on the y-axis), and centred at the point 0,b ; Eq. (4b) represents a line segment of length C which is a prolongation of the ellipse arc (Fig. 3). Fig. 4 shows some isoclinal fold morphologies described by Eqs. (4a) and (4b) (within the interval \u00ffx0,x0 to represent complete folds), for x0 1 and several values of C/y0 and y0. For y0 b (or C=y0 0) folds are elliptical; for x0<b (or C=y0<1\u00ff x0=y0) folds have a single hinge point; for x0 b, folds contain a semi-circle; for x0 > b, the shape is that of double hinge folds; for b 0 (or C=y0 1), the shape is that of box folds. Another function that can be used to analyse fold geometry is xp x p 0 y p y p 0 1: 5 This function was used by Lisle (1988) to approximate the form of coarse clastic sediment particles",
+            " The next step is to \u00aend the \u00aetting function or functions whose area equals the area of the natural fold analysed. In the case of alloclinal folds, when Eq. (1) is used, the integration of this function allows us to determine the n value of the \u00aetting function; this value is given by: n A x0y0 \u00ff A : 6 In the case of isoclinal folds, the \u00aet by functions of the type (4) should be made by determining the parameter C, which can be derived from the formula of the area beneath the curve of Eqs. (4a) and (4b), and is given by C 4A\u00ff px0y0 x0 4\u00ff p 7 where x0 and y0 b C can be measured on the natural fold (Fig. 3). A graphical solution to obtain the value of the respective fold shape parameter, m or p, using Eq. (3) or Eq. (5), is shown in Fig. 5. In this \u00aegure all the fold shape parameters (n, C/y0, m and p ) have been included and mutually correlated through the area. In order to avoid the fold size e ect in the determination of the parameters, a normalised area, de\u00aened as a 2A=x0y0, and a normalised value of C (C/y0) have been used in this \u00aegure. Hence, a \u00aet by the area balance method permits the determination, from the normalised area below a natural fold pro\u00aele, of the corresponding value of n, m, p and C/y0, and there- fore, of all the particular functions that can be used to describe the fold geometry",
+            " 2] de\u00aened by three parameters (x0, y0 and n ), which can be reduced to two ( y0/x0 and n ) if the fold size is not considered. y0/x0 characterises the fold amplitude and the exponent n characterises the fold shape. Therefore, depending on the value of n we have: n<1, cuspate folds; n 1, chevron folds; n 2= p\u00ff 2 11:75, sinusoidal folds; n 2, parabolic folds; n41, box folds. Eq. (3) is a more complicated choice to approximate alloclinal folds. The limb pro\u00aeles of isoclinal folds are approximated by functions [Eqs. (4a) and (4b), Fig. 3] which represent a quarter of an ellipse and a vertical segment of length C to describe the isoclinal part of the limb. In this case, y0/x0 also characterises the fold amplitude and the fold shape is de\u00aened by C/y0, which varies from 0 (elliptic folds) to 1 (box folds). Both alloclinal and isoclinal folds can be also approximated by superellipses (Gardner, 1965; Lisle, 1988) [Eq. (5)], although these functions are more complicated than Eqs. (1), (4a) and (4b) and in most cases give a worse approximation than Eq"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002594_robot.2001.932799-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002594_robot.2001.932799-Figure5-1.png",
+        "caption": "Figure 5. Force Reflection Mechanism",
+        "texts": [
+            " The rotational angle is much smaller than 1 radian. change. The first assumption is reasonable because the skin is very thin and there is only muscle and fat between the skin and the bone. The second assumption is trivial. Since the side surface of the needle is not sharp like the tip and its motion is constrained by internal tissues except in the movement of the inserted direction, the third one is acceptable. Using these assumptions, the correction force is calculated using the torque derived from the force at the needle tip. Figure 5 shows the initial needle direction vector Vi and the current needle direction vector Vc. Vi is derived by multiplying the needle inserted unit vector with the needle length. Vc is derived from the current tip point and the gimbal point of the needle. The correction forcepc can then be derived from the difference of these two vectors. The upper limit of this force is 2N since the haptic device can only generate 8.5N and the limit of the tissue penetration force is 6N. Since the tissues between skin and bone are muscle and fat, the stiffness for the correction force is determined from muscle and fat and this force is calculated by multiplying the correction vector by a stiffness and a constant"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001500_978-1-4899-1465-1-Figure8.16-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001500_978-1-4899-1465-1-Figure8.16-1.png",
+        "caption": "Figure 8.16. Inherent-overheating protector.",
+        "texts": [
+            " These range all the way from relatively simple current relays which sense motor current and trip on overcurrent, to solid-state devices which receive multiple inputs and use this infor mation to model the motor's thermal characteristics in order to pre dict temperature rise in critical parts of the motor. Each of these de vices has its place, depending on the application need, the cost of motor failure, and the cost of the associated downtime. Some of the more commonly used protective devices are described in the follow ing sections. Inherent-overheating protectors are widely used on fractional horsepower motors and their use extends up into the lower end of the integral horsepower ratings. A sectional view of such a device is shown in Fig. 8.16. A disk-type thermostat is the major operating element. The thermostat element is a bimetal disk which is dish-shaped with the highly expansive metal on the concave side at normal tempera tures. As the disk is heated, the bimetal element expands, but is re strained by the less expansive metal on the outside. At some critical value, the disk snaps into a convex shape, opening the electrical con tacts which interrupt current to the motor. The motor current also ac Motor Control and Protection 169 passes through a heater element which is located inside of the thermal protector"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003966_j.physleta.2005.12.029-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003966_j.physleta.2005.12.029-Figure1-1.png",
+        "caption": "Fig. 1. The planar, circular restricted three-body problem, on a inertial coordinate system (\u03be, \u03b7) and on a rotating coordinate system (x, y). Note that on the rotating coordinate system the positions of the two massive bodies are fixed.",
+        "texts": [
+            " In this problem there is a system of two massive bodies with masses m1 and m2, m2 m1, in circular orbits around their center of mass and a third massless body moving under influence of this system without perturbating it. We can choose units of mass such that G(m1 +m2) = 1. In this way, we can take the masses of the two massive bodies respectively as 1 \u2212 \u00b5 and \u00b5, where \u00b5 = Gm2 (note that in this units m2 < m1 implies \u00b5 < 1/2). If we consider the center of mass of the two massive bodies as the origin of the coordinate system, The massive bodies with masses \u00b5 and 1\u2212\u00b5 are situated respectively at the positions (1 \u2212\u00b5)R and \u00b5R of a rotating x-axis (see Fig. 1), where R is the distance between the massive bodies. We have (1)R = ( G(m1 + m2) \u03c92 )1/3 for this distance, where \u03c9 is the angular velocity of the rotating frame. By using the unit of mass above defined and a unit of time such that \u03c9 = 1, we have R = 1. In these units, the equations of the motion for the third body read (2)x\u0308 = 2y\u0307 + x \u2212 \u2202V \u2202x , (3)y\u0308 = \u22122x\u0307 + y \u2212 \u2202V \u2202y , where (4)V = \u2212 (1 \u2212 \u00b5) r1 \u2212 \u00b5 r2 with (5)r1 = \u221a (x + \u00b5)2 + y2, (6)r2 = \u221a[ x \u2212 (1 \u2212 \u00b5) ]2 + y2. To obtain Hill\u2019s equations, we perform the transformation (7)x \u2192 (1 \u2212 \u00b5) + \u00b51/3x, (8)y \u2192 \u00b51/3y"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002463_0954410041322005-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002463_0954410041322005-Figure3-1.png",
+        "caption": "Fig. 3 Aircraft performing a steady, banked turn in the horizontal plane",
+        "texts": [
+            " Scheme C is often used for computer animation purposes. The way in which flocking rules are implemented depends on the dynamics and control of the system at hand. In the present work for application to aircraft, the system dynamics are represented by a point mass moving at constant speed in the horizontal plane and control is via acceleration in the horizontal plane normal to the direction of motion. This corresponds to aircraft flying at constant speed using bank to turn. An aircraft performing a level turn is shown in Fig. 3. Using Newton\u2019s second law for angular motion it can be G05503 # IMechE 2004 Proc. Instn Mech. Engrs Vol. 218 Part G: J. Aerospace Engineering at University of Bath - The Library on June 18, 2015pig.sagepub.comDownloaded from shown [25] that the turn rate, _c, is given by _c \u00bc g ffiffiffiffiffiffiffiffiffiffiffiffiffi n2 1 p V? \u00f01\u00de and the turn radius, R, by R \u00bc V2 ? g ffiffiffiffiffiffiffiffiffiffiffiffiffi n2 1 p \u00f02\u00de where n is the load factor, defined as n \u00bc L W \u00bc 1 cosf \u00f03\u00de and g is the acceleration due to gravity"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure4.1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure4.1-1.png",
+        "caption": "Figure 4.1. A motion x(P, t) of a gear particle Preferred to the moving frames l{J 1 and lp 2 , and to the fixed ground frame lfJo-",
+        "texts": [
+            " Let us begin with an example. Motion Referred to a Moving Reference Frame and Relative Motion 231 A particular reference frame usually is chosen to simplify the form or the derivation of equations and to ease calculations. A vector v, for example, may be a constant vector in one reference frame, and a function of one or more variables in another. Therefore, the derivatives of the same vector referred to different reference frames will be different. This will be illustrated in the following example. The Fig. 4.1 of the motor on a rotating table shows three reference frames: the frame fPo = { F; Ik} is fixed in the ground E; frame fP 1 = { F; ik} is in the table T; and frame qJ 2 = { 0; i~} is imbedded in the gear G of radius r. A point P on the rim of G has a position vector x from its center. Of course, in each of these frames the same vector x has a unique representation x = xkek in which the scalar components xk describe the behavior of x when referred to the reference frame with basis vectors ek. But in another frame, i.e., when x is referred to a different basis, the components will be different. In the present case, it is easily seen from the geometry in Fig. 4.1 that x = rk' is a constant vector in qJ 2 ; x = r(sin (} i +cos(} k) = x((J) in qJ 1 ; x = r sin (}(cos 1{1 I+ sin 1{1 J) + r cos(} K = x((J, 1{1) in fPo\u00b7 (4.1a) (4.lb) ( 4.lc) We thus see that the position vector x is a function of 1{1 and (} in qJ 0 ; it depends on (} in frame qJ 1 ; and in qJ 2 , it is a constant vector. It follows from ( 4.1) that the rate of change of x with respect to (} is given by lOin fP2; :: = r( cos (} i - sin (} k) in qJ 1 ; r cos (}(cos 1{1 I+ sin 1{1 J)- r sin(} Kin qJ 0 ; (4",
+            " The slot makes an angle of 30\u00b0 with the horizontal drive shaft, as illustrated. Find for the instant shown the velocity and the acceleration of P relative to the plate and to the link. Solution. Let the frame f/J = { F; I, J, K} be fixed in the plate, and let <p = { 0; i, j, k} = { 0; I, J, K} be a parallel frame fixed in the slotted link. The link frame Is moving on a straight line in f/J with the assigned constant velocity Vcu = 5(cos 30o i- sin 30o j) =~ (j3i -j) ftjsec, ( 4.55a) as indicated in Fig. 4.1 6. Of course, a0 F = 0. Thus, with these data in mind, the absolute velocity and acceleration of the pin P relative to the plate frame at F are obtained by application of the kinematic chain rules ( 4.51 ). With the present labels, we have V PF= V PO+ VoF> aPF= apo\u00b7 (4.55b) Each of these vector equations involves two unknown vector quantities; hence, additional information about their components must be furnished in order to solve ( 4.55b) for the unknown vectors. This is done by considering the nature of the motion of the pin in the separate frames",
+            " The crane is turning simultaneously with an angular speed w = 2 radjsec, which is decreasing at the rate dJ= -1 radjsec2 relative to the ground frame<!>= {F;lk}. If there is no slippage between the cable A and the pulley P, what are the absolute angular velocity and angular acceleration of P in <!> at the instant of interest? Problem 4.12. 4.13. A cross-sectional view of a motor-driven bevel gear mounted on a rotating table is shown in the figure. This assembly corresponds to the device shown pictorially in Fig. 4.1. The bevel gear G has a pitch angle a and it engages another bevel gear B whose axis of rotation coincides with the axis of the table. The motor drives G at a constant angular velocity ro, as indicated. The gear B may be driven independently at a constant angular velocity n = QK by the engagement of its drive clutch C in the machine. (a) What is the total angular velocity of the table T when the clutch is 322 Chapter 4 engaged? (b) What is the absolute angular velocity ofT when B is fixed in the machine frame l/J = { F; Ik}"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000462_jsvi.1999.2324-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000462_jsvi.1999.2324-Figure3-1.png",
+        "caption": "Figure 3 (a). A clamped}clamped uniform beam carrying a two-d.o.f. spring}mass system (m(1) e \"1)53875 kg, J(1) e \"1)53875 kg m2, k(1) y \"6)34761]106 N/m, x(1) i \"0)2 m, x(1) k \"0)4 m, \u00b8\"1)0 m, a(1) 1 \"0)06667 m, a(1) 2 \"0)13333 m). (b) A general restrained uniform beam carrying a two-d.o.f. spring}mass system [19] (m(1) e \"500)0 kg, J(1) e \"177)0833 kg m2, k(1) y \"1)0]1010 N/m, x(1) i \"1)4 m, x(1) k \"2)6 m, \u00b8\"4.0 m, a(1) 1 \"0)6 m, a(1) 2 \"0)6 m, K 1 \"K 2 \"1)0]1010 N/m, b 1 \"b 2 \"1)0]1010 N m/rad, E\"2)0]1011 N/m2, A\"0)15 m2, I\"0)003125 m4, o\"7860 kg/m3).",
+        "texts": [
+            "ective springs with spring constant k(v) eff, ij (i, j\"1, 2), the overall mass matrix [MM ] is not a!ected by the spring masses: uN 1 uN 2 2 uN 2i~3 uN 2i~2 2 uN 2k~3 uN 2k~2 2 uN 2n [K1 ]\"C kM 2i~3, 2i~3 (#k(v) eff, 11 ) kM 2i~3, 2k~3 (#k(v) eff, 12 ) kM 2k~3, 2i~3 (#k(v) eff, 21 ) kM 2k~3, 2k~3 (#k(v) eff, 22 ) D uN 1 uN 2 2 uN 2i~3 uN 2i~2 F uN 2k~3 uN 2k~2 F uN 2n , (39) [k eff ]\"C k(v) eff, 11 k(v) eff, 12 k(v) eff, 21 k(v) eff, 22 D . (40) 7. NUMERICAL RESULTS AND DISCUSSIONS The dimensions and the material constants for the uniform beam studied in this paper (except the one shown in Figure 3(b) of section 7.1) are total length \u00b8\"1)0 m, diameter d\"0)05 m, Young's modulus E\"2)069]1011 N/m2, mass density o\"7)8367]103 kg/m3, mass per unit length m\"oA\"15)3875 kg/m, cross-sectional area A\"nd2/4\"1)9635]10~3 m2, moment of inertia I\"nd4/64\"3)06796]10~7 m4, total mass of the beam m b \"m\u00b8\"15)3875 kg. In order to con\"rm the reliability of the theory presented in this paper and the computed programs developed based on the related algorithm, a clamped}clamped uniform beam carrying a two-d.o.f spring}mass system located at x(1) i \"0)2 m and x(1) k \"0)4 m with a(1) 1 \"0)06667 m and a(1) 2 \"0)13333 m presented in Figure 6 of reference [18] and a general restrained uniform beam carrying a two-d.o.f. spring}mass system presented in Figure 1 of reference [19] are studied here (see Figures 3(a) and (b)). For the uniform beam shown in Figure 3(a), besides the dimensions and the material constants mentioned above, the other given data are: m(1) e \"0)1 m b \"1)53875 kg, k(1) y \"100(EI/\u00b83)\"6)34761]106 N/m (for each spring) and J(1) e \"0)1 (m b \u00b82)\"1)53875 kg m2. The \"rst \"ve natural frequencies of the constrained beam are shown in Table 1(a), where are values of u6 s (s\"1, 2, . . . , 5) listed in the third row were obtained from FEM1 (i.e., the two-d.o.f. TABLE 1 (a) \u00b9he ,rst ,ve natural frequencies uN s (s\"1}5) of a uniform clamped}clamped beam carrying a two-d",
+            " For this reason, in addition to the modal displacements of the beam itself, the translational movement and the rotational angle of each two-d.o.f. spring}mass system will appear in the modal displacements obtained from the FEM1. Therefore, the curves in Figure 4(a) were plotted by excluding all the modal displacements of the two-d.o.f. spring}mass systems and &&double'' normalizations for the mode shapes obtained from the FEM1 were required sometimes. For example, in the third mode of the vibrating system shown in Figure 3(a), the largest modal displacement is the translational movement of the lump of the spring}mass system. Hence the third &&normal'' mode shape obtained from the computer output based on the FEM1 is the thin solid line with amplitude >I 3 (0)6):0)34766 as shown in Figure 4(a) (iii). A good agreement with the other two curves was obtained when a second normalization was made, i.e., all the modal displacements of the thin solid line were divided again by 0)34766. The \"nal result is shown by the wider solid line of Figure 4(a) (iii). Another example to be used to check the reliability of the theory and the computer programs is the uniform beam supported by two linear springs and two rotational springs at both ends as shown in Figure 3(b). All the given data and the boundary conditions of the bema are exactly the same as those in referenece [19]. For reference, all the given data are shown in the legend of Figure 3(b). The \"rst \"ve natural frequencies and the asociated mode shapes are shown in Table 1(b) and Figure 4(b). From Table 1(b) and Figure 4(b), one sees that all the \"rst \"ve natural frequencies and the corresponding moe shapes obtained from the FEM2(b) and ANCM(b) are in close agreement with those show on in reference [19]. From all the reasonable facts indicated in this section, it is believed that the results presented in this paper should be reliable. TABLE 2 \u00b9he ,rst ,ve natural frequencies uN s (s\"1}5) of a uniform cantilever beam carrying a two d"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003019_ajassp.2005.626.632-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003019_ajassp.2005.626.632-Figure3-1.png",
+        "caption": "Fig. 3: Groove Design and the Main O-ring Dimensions",
+        "texts": [
+            " The interaction of all the operating parameters have to be taken into consideration, but in the same time the contribution of these parameters to the magnitude of friction force will makes the mathematical analysis as impossible or very hard, due to the simple reason that the above factors cannot be quantified and because they overlap and act cumulatively, so it is difficult to establish an exact or accurate statement regarding the expected friction level [4]. The initial phase of calculation of the friction force is based on considering the contribution of the most important working factors (Fig. 3), by considering these factors and their contribution we can initially estimate and express the friction force in O-ring by using the following relationship: f 3F C D b p i= \u00d7\u00b5\u00d7 \u03c0\u00d7 \u00d7 \u00d7 \u2206 \u00d7 (1) Where, p is total pressure difference acting on the gasket, that is equal with the sum between the difference of the working pressures in two separated chambers by the sealing element and the pressure due to deformed assembling (0.05 \u2013 0.06). I: when more than one O-ring are used in the system, then the friction force for all rings must be combined in order to determine the total friction force",
+            "1: O-ring Dimensions The importance of the initial squeeze in the O-ring groove (rectangular groove), is essential to ensure its function as a primary or secondary sealing element, initial squeeze will serve to achieve the initial sealing capability and to assure the defined frictional forces as same as to compensate for the compression set, depending on the nature of application, the following values can be applied for the initial squeeze as a proportion of the cross section d2: 6-20%- for dynamic applications 15-30%- for static application Groove Design: As compared with the Triangular or with the Trapezoidal grooves that are characterized with the difficult manufacturing processes, the rectangular groove is preferred for all new designs; rectangular designs with beveled groove flanks up to 5\u00ba are permissible. The groove choice is based on the guide values for the initial squeeze and on the relationships between the Shore A hardness, loads and cross- sections. The recommended and specified groove width already takes into account the swelling value for O-rings as described in DIN 3771 part 5, September 1989, where 8% swelling is permissible for moving parts and 15% for stationary parts [2]. Figure 3 shows some of the required dimensions and characteristics of the rectangular groove. The Shaft Design: is of a vital significance for the performance as well as for the useful life of the seal, so the shaft run out and the eccentricity between the shaft and housing bore centers should be avoided or kept within a minimum [7]. Principles of Sealing Mechanism: The demand for higher reliability and efficiency rates for both hydraulic and pneumatic systems necessitate an extensive research and development programs in sealing technologies",
+            " Tray, (2) Auxiliary Masses (3) Stopper Mechanism, (4) Cylinder, (5) O-ring, (6) Ram, (7) Cover, (8) Sleeve, (9) Frame and (C) Comparator, (M) Manometer, (S) Source, (F) Filter, (R) Regulator * Sealing performance can be also shown by the amount of squeeze, because the increased amount of squeeze above the established limits it can cause a high friction and excessively high actuating forces, also for low-squeeze below the limits means lowering the sealing pressure and increasing the leakage tendency. Designing or selection of O-ring seals for low-pressures is not simply a matter of reducing the amount of squeeze, but it involves the difficulty of balancing between the material hardness, dimensional tolerances, stress relaxation and friction characteristics. The width and contact pressure evaluation in O-ring sealing as in Fig. 3, has to follow a rigorous procedure in order to show the important component of the friction from the sealing element. For this reason, a theoretical model was proposed and experimental measurements were performed to ensure and to compare the results. The appearance of an identical pressure distribution between the O- ring and the cylinder with diameter D3=DN, respectively between the O-ring and the ram with diameter d4 (Fig. 4), the pressure distribution appears having the resulting force Fn (the normal force from the section",
+            " Also from the same figure, we can obtain: 2 3 4 2 (D d )b sin 1 2r 16r \u2212 \u03b3 = = \u2212 (4) The friction force due to ring deformation at assembly is: Ff=\u00b5 D3Fn (5) Replacing equations (2,3,and 4) in equation number (5), we get the developed expression of the friction force: 2 3 4 3 4 3 2 D d (D d ) Ff 2 D rE 1 1 4r 16r \u2212 \u2212 = \u03c0 \u2212 \u2212 (6) The validity of expression 6 ( 2 3 4 3 4 3 2 D d (D d ) Ff 2 D rE 1 1 4r 16r \u2212 \u2212 = \u03c0 \u2212 \u2212 ) was tested with an experimental device (Fig. 5), which was used for obtaining the experimental results. The Ram has five different sizes of sockets or grooves to increase the possibility of testing different number of O-ring sizes (Fig. 5). Each groove is designed for a specific diameter, The ram and cylinder geometry is characterized by the values of the diameters, both diameters are clearly shown in Fig. 3 and 4, in our case the cylinder diameter D3 = 28.03 mm, the inside ram diameter d4 having five different sizes, in our case (d4 = 21.41, 21.45, 21.59, 21.74 and 22.10 mm), all of these sizes were tested and the obtained results are indicated in Fig. 7 (in absence of the pressure), in which each size has its proper value of friction, Fig. 8 indicates the measured values for different O-ring sizes where the pressurized agent was involved. Experimentally we follow to ensure the validity of using the developed relationship for calculating the friction force, the results obtained through the use of this formula are used to show the degree of agreement between the computed and measured values for each inside diameter"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001131_etep.4450030405-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001131_etep.4450030405-Figure5-1.png",
+        "caption": "Fig. 5. Complex transformation a) (Fictitious) magnetizing currents depending",
+        "texts": [
+            " ( 1) to (4) it is evident that the curve of the (di,/dz)-space phasor relative to the respective gc-space phasor in the complex plane is a circle with a radius depending on the difference of the reactances &.dim and Xq,diff and a (real) offset depending on x,. Consider a curve of magnetization of the PSM as given in Fig. 4. Assume the d-axis coinciding the a-axis or phase direction A, respectively ( y= kx; k = 0, 1, . . .). The magnetic operating point in the d-axis is defined by the permanent magnetization (represented by ificrM). leading to xd.diff. The quadrature-axis reactance xq,diff = xq is assumed to be not influenced by saturation effects. Now the general case (arbitrary y) is considered (Fig. 5). The special assumptions of Fig. 4 are represented by the points PA and Pi in Fig. 5. on Y ( S Pplane) b) Locus of (di,/d?) (us is assumed in the real axis) due to the magnetization given in a) (a, &plane) + y In Fig. 5 the complex plane of the magnetizing current space phasor (plane p ) is set against the complex plane of the space phaszr of the current changes (plane v). Both planes are connected via a complex transformation p + y. The parameter of the complex curves is in bo& cases the rotor angular position y Both planes are stator-oriented (real axis a in phase axis A). The (fictitious) magnetizing current ifict,rsl in plane p results from the permanent magnetization, represented by ifict,M(y), and the constant stator offset current iotr+",
+            " Performing a (di,/dz)-measurement due to a us-test space phasor when no offset current is applied (normal \u201cInform\u201d measurement; magnetization curve C ( y ) inp) yields a circIe C(2y) in plane y which is run thou$ twice during a full electrical revolution of the rotor ( y= 0 +2x) . Assuming a fictitious motor with permanent magnetization (ificr.M + ion+) ely (Qi in p) yields the circle &+(2y). Another fictitious motor with permanent magnetization (ifict.M - ioff+)dr(CL in p) leads to a circle L ( 2 y ) . The (di,/d?)-space phasor gf the real motor under a modified operating point by a constant offset current LOR+ (curve &bff+ in p) yields a curve y) in y which is no longer a circleTFig. 5b). However, it can be approximated in certain sections to the mentioned fictitious motor curves: ETEP Vol. 3, No. 4, JulytAugust 1993 279 E TEP sector 3; c p : C;,,+ = g; sectors S ; . S i c ~ : ~ b f f + a C \u2019 * _ C o f r + a ; r i n S ; , s l c v ; sector Sl c p : _CLff+ a ,Cl * a _C+ in S+ c y ; - _Coff+ = _C- in 2- c 11. - The curve derived in Fig. 5b) can indeed be measured using a digital signal processing system (Fig. 7). The real part of coff+ represents the relations given in Fig. 2, the imaginary part is likewise a function of y and CM hence be used to estimate the rotor angular position. The curve has zero-crossings at y= 0, IC and at a certain angle between x / 2 and x (Fig. 9a). For acorrect evaluation, a second measurement with the negative offset current ioff- has to be performed. Subtracting \u20acoff+ and coff- eliminates disturbing offsets and space harmonics (Fig"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000732_s0301-679x(98)00043-7-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000732_s0301-679x(98)00043-7-Figure1-1.png",
+        "caption": "Fig. 1 Water-lubricated hydrostatic conical bearing with a rigid or compliant surface",
+        "texts": [
+            " Furthermore, it is reported by Lowe3 and Heshmat4 that hydrostatic and hydrodynamic bearings 332 Tribology International Volume 31 Number 6 1998 with a compliant bearing surface can achieve larger load capacity or higher stability at high speeds than the rigid surface bearing. In this paper, the comparison between rigid and compliant surface conical bearings is also performed and the effect of a compliant surface on the static characteristics is clarified. Structure and operating principle of the bearing Fig 1 shows a water-lubricated hydrostatic conical bearing with a rigid or compliant bearing surface as proposed in this paper. In the compliant surface bearing, a thin rubber film is formed on the bearing surface and the rubber surface is ground by an internal grinder. Eight spiral grooves are formed on the cone surface of the shaft and feeding holes are also drilled at the edge of each spiral groove. Pressurized water is fed to the inside of the shaft and introduced into the bearing clearance through feeding holes"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000575_la9705571-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000575_la9705571-Figure1-1.png",
+        "caption": "Figure 1. Schematic view of the Langmuir trough. The Teflon Wilhelmy plate is not shown.",
+        "texts": [
+            " Thereferenceelectrode can then be connected to the capillary. A perforated platinum disk connected to the base of the capillary works as a counter electrode. The electrode in the upper phase (water) can be brought close to the interface with a micromanipulator. Since the interfacial area is larger than usual in liquid/liquid electrochemistry, the ohmic drop in the aqueous phase can be neglected, and no four-terminal setup is needed but any threeterminal potentiostat will do. A schematic view of the trough is given in Figure 1. Thephospholipids distearoylphosphatidylcholine (DSPC) and dipalmitoylphosphatidylcholine (DPPC) (Sigma, 99%) were chosen for detailed study in preliminary tests, because they gave the best water/oil isotherms among the lipids we investigated; they were used as received. Phosphate-buffered saline solution (pH ) 7.6) was prepared from Na2HPO4, KH2PO4 (J. T. Baker, reagent purity), NaCl (FF-Chemicals Ltd., Finland, p.a.), and KCl (Merck, p.a.). Acetic acid buffer solution (pH ) 4.05) was prepared fromCH3COOH(Titrisol,Merck) andCH3COONa (FFChemicals Ltd"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002965_1047568.1047569-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002965_1047568.1047569-Figure4-1.png",
+        "caption": "Fig. 4. Dynamic 3-D visualization of a Khepera and its infrared sensors.",
+        "texts": [
+            " These abstractions help simplify individual robots into higher-level entities needed for generic behavior programming. Pyro also provides facilities for the visualization of various aspects of a robot experiment. Users can easily extend visualization facilities by providing additional Python code as needed in a particular experiment. For example, we can easily create a graph to plot some aspect of a brain, or sensor, with just a few lines of code. In addition, Pyro can, through Python's OpenGL interface, generate real-time 3D views. Figure 4 shows a visualization of a Khepera robot and its infrared readings. In keeping with the spirit of the Pyro project, we created an abstract API so that 3D shapes can be drawn in this window without knowing anything about OpenGL. The Python language has generated much interest in recent years as a vehicle for teaching introductory programming, object-oriented programming, and other topics in computer science. For example, Peter Norvig has recently begun porting the example code from Russell and Norvig's \"Artificial Intelligence: A Modern Approach\" [1995] into Python"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001799_s0168-874x(02)00056-2-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001799_s0168-874x(02)00056-2-Figure2-1.png",
+        "caption": "Fig. 2. The geometric relationship between the rocker and the workpiece in rotary forging.",
+        "texts": [
+            " In rotary forging, the relative movement between the workpiece and the conic upper die (namely the rocker) is a spiral feed, and the outline and the shape of the contact zone can be obtained geometrically. In fact, the contact outline is a cross line obtained from the spiral surface of the workpiece and the conical surface of the rocker. The shape of the contact zone is a part of the conical surface of the rocker. The non-contact surface is a part of the spiral surface during the actual rotary forging process. As shown in Fig. 2, in cylindrical coordinate system, the conical surface of the rocker can be expressed as F(r; ; z) = z2(1\u2212 tg2 )\u2212 r2 sin2 tg2 + 2rz cos tg ; (7) where is an angle of the rocker axis deviating from the machine axis. In rotary forging, the upper surface of the workpiece is a part of the Archimedes spiral surface. It can be expressed as M (r; ; z) = z \u2212 S 2 ; (8) where S is the feed per revolution. Thus, the outline of the contact zone is a cross line of the curved surface (Eq. (7)) and the curved surface (Eq"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003972_robot.2006.1642071-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003972_robot.2006.1642071-Figure4-1.png",
+        "caption": "Fig. 4. Model of viscoelastic object",
+        "texts": [
+            " The differences are shown as in Figure 3. Third, we compare the stability in aspect of the difference of manipulated variables. Since we deal with soft objects, we can use not only a driving force but also an input position as a feedback signal. Finally, we compare the stability in case of viscoelastic and elastic object as a soft object to validate the stability analyses. In this section, we describe the model of a soft material. Based on the particle model, we formulate the motion and deformation of soft material. Figure 4 shows a simplified model for the soft object manipulation. In this model, we use linear mass-damper-spring components and consider the motion and deformation of the soft object along the x-axis. Let Pi represent the i-th mass point. Let xi and vi represent the position and velocity of Pi at time t, respectively. Note that the number of masses is not serialized along the x-axis to utilize the symmetry of the model in analysis. In Figure 4, P0 and P2 are manipulated points, while P1 and P3 are positioned points. We regulate the positioned points to the respective desired points by controlling the manipulated points to control the motion and the deformation simultaneously, as shown in Figure 2. Let kij and bij be the elastic and viscosity coefficients, respectively, of the soft interface between i-th and j-th masses, and mi represent the mass of Pi. Additionally, let Lij be the natural length of the soft interface between i-th and j-th masses"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure3.15-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure3.15-1.png",
+        "caption": "Figure 3.15. The composition of consecutive rotations about nonintersecting lines in (a) is equal to a rotation about a 2 and a normal translation b0 in (b).",
+        "texts": [
+            " The special case of reversed rotations about parallel axes also is described; and it will be shown how any given displacement may be represented as the sum of rotational displacements about nonintersecting axes. We shall begin with two consecutive pure rotations about nonintersecting Finite Rigid Body Displacements 211 axes. The displacement of a particle P in a pure rotation T 1 about an axis a 1 is given by d 1 = x 1 - x = T 1 x, where x and x 1 are the initial and final positions of P from the base point 0, as shown in Fig. 3.15a. The subsequent dis placement of P in another pure rotation T 2 about a nonintersecting axis a 2 through the base point 0' is given by d2 = T 2 x~, where x~ is the location of P from 0'. But the same displacement, by the parallel axis theorem, may be accomplished by the same rotation T 2 about a parallel axis through 0 together with a translation b0 perpendicular to a 2 . Therefore, as described in Fig.3.15b, d 2 =x2 -x 1 =T2 x~=b0 +T2 x 1 , wherein x2 is the ultimate position vector of P from 0. With (3.87), we have x 1 = R1 x and x2 = b0 +R2 x 1 ; hence, x2 =b0 +R*x, where R*=T*+l=R2 R 1 in terms of the rotation tensors. Therefore, the resultant displacement due to the rotations alone is given by d(P) = x2 - x = b0 + T*x with b0 \u00b7a2 =0. (3.160) In words, the displacement resulting from the composition of two consecutive pure rotations about nonintersecting axes is equivalent to a rotation about a line through the first base point 0 together with a parallel translation which is equal to a pure rotation of 0 about the axis at 0'"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001500_978-1-4899-1465-1-Figure6.6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001500_978-1-4899-1465-1-Figure6.6-1.png",
+        "caption": "Figure 6.6. Cross-sectional view of a rotor for a reluctance-synchronous motor.",
+        "texts": [
+            " A capacitor is permanently in series with the auxiliary winding and the auxiliary circuit remains excited under both starting and running conditions. Motors of this type designed for continuous duty have low starting torque and consequently are usually applied in fan and blower applications. These two types of synchronous motors are included in this sec tion on fractional-horsepower motors because they are usually built in ratings 1 hp and below. Neither type of motor has an excited field as is used on larger synchronous machines. The reluctance-synchronous motor has a rotor structure with salient poles. Figure 6.6 displays one such rotor with this type of construction which has been described by Honsinger in U.S. Patent No. 3,045,135. The rotor has a cast alumi num cage for starting and accelerating. As the rotor nears synchro- Single-Phase and Synchronous Motors nous speed, it pulls into step as the salient poles \"attach\" themselves to the rotating magnetic field and the motor operates at synchro nousspeed. The permanent-magnet synchronous motor has its permanent magnets embedded inside of the rotor structure and surrounded by a squirrel cage to provide starting torque"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001297_1.2834570-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001297_1.2834570-Figure5-1.png",
+        "caption": "Fig. 5 Line EHL contact crack initiation and propagation model",
+        "texts": [
+            " The dry experimental re sults illustrate that a spall will initiate in the absence of a lubri cant. Therefore, spall initiation is due to the cyclic plastic strain accumulation process. Due to excessive computational require ments for calculation of stresses and plastic strain in a point contact analysis, a line contact model was developed. In this investigation, spalls develop when minute pieces of metal flake off the rolling surface. The line contact was divided into many small metal cells, as shown in Fig. 5. Each cell is a representa tive volume element (RVE) in the continuum mechanics point of view, where the RVE is small enough that every physical quantity can be regarded as evenly distributed constants but large enough that it represents an average of the microprocess (Krajcinovic, 1985, Lemaitre, 1992). For each cell a damage variable is defined: D = So So (1) where Sn is the damaged area and ^o is the total area of the cell, with the criteria. Fig. 3 Experimental result for a dent-initiated spall after 0"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001521_iros.1994.407377-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001521_iros.1994.407377-Figure4-1.png",
+        "caption": "Figure 4: Approximation of a circle by a polygon. a,,, is the largest permissible angle between successive path segments according to Rmin",
+        "texts": [
+            " For the class of omni-directional robots a generated path, as discussed in this paper so far, is always executable, since the robot can move in any direction. A car-like robot, on the other hand, cannot move in lateral direction. Feasible motions are forward, backward and limited turns. In order to generate paths which are feasible for a car-like robot the unconstraint gradient search algorithm has been modified. In the following, Rmin denotes the minimum turning radius and 2 the length of each path segment during gradient search. By means of simple geometric relations, a circle with the radius Rmin can be approximated by a polygon using 2 (Fig. 4). Based on this approximation we define a,, as the largest permissible angle between successive path segments. In each gradient search step we limit the angle between successive path segments a according to the following formula: With respect to Rmin the computed gradient path is adjusted if necessary so that the resulting path is feasible. The effect of this modified gradient algorithm for different starting orientations is illustrated in Fig. 5 . Note that the objective is not to generate maneuvers for such a vehicle but to compute feasible paths in a predefined motion direction (usually forward motion direction)"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003319_s0167-8922(08)71045-9-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003319_s0167-8922(08)71045-9-Figure1-1.png",
+        "caption": "Fig. 1 Test bearing.",
+        "texts": [
+            " Here we define the initiation time Ta of crack propagation, the propagating time Tv-Ta and the life L as follows: Ta is the time at which acoustic emissions increase at the position of failure on the raceway of an outer race; Tv-Ta corresponding to the propagation phase is the period from the initiation time to the time when vibration acceleration increases; and L is the running time until a test is automatically stopped by a vibrometer when acceleration exceeds a preset level. Lundberg and It is well known that acoustic signals emit On the contrary, 2 EXPERIMENT The test bearing simulated a thrust ball bearing as shown in Fig.1 consisting of an inner race, three balls, a retainer and an outer race. Balls in the test bearing rolled on a flat of the outer race to accelerate the fatigue test. The bore diameter and the outer diameter of the inner race were 25 mm and 42 mm respectively, and those of the outer race were 25 mm and 47 mm. Balls were 6.350 mm in diameter. The inner race had a raceway groove, which the outer race did not have. The pitch circle diameter of the raceway groove of the inner race was 33.5 mm. The retainer was machined, and had a bore diameter of 25"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003344_bf00311967-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003344_bf00311967-Figure3-1.png",
+        "caption": "Fig. 3A, B. Toxotes chatareus. Branchial basket and hyoid arch, drawn from an alizarinred-stained preparation A. Lateral view B. dorsal view. gl-hy glossohyal, cop copula, i-hy interhyal, ph-br pharyngobranchial, e-br epibranchial, c-br ceratobranchial, u-hy urohyal, br-st branchiostegal, e-hy epihyal, c-hy ceratohyal, h-hy hypohyal, hy hyoid, gl-hy glossohyal, h-br hypobranchial, cent cart central cartilage",
+        "texts": [
+            " The suspensory apparatus is shown in Fig. 2. The palatinum and the ecto- and entopterygoid are provided with teeth (see also Fig. 8B). The entopterygoid nearly reaches the parasphenoid and forms a shelfjust below the eye. This shelf is not identical with the subocular shelf found in some other teleosts (Smith and Bailey 1962), which is a derivative of the infraorbitals. The maximum angle of suspensorial abduction is about 20 \u00b0. 4. The hyoid apparatus is made up of the hyoid bars, the interhyals, and the branchial basket (Fig. 3). Teeth are 50 found on the glossohyal, the pharyngobranchials 2 and 3 4 , and on the ceratobranchials 5, which are not fused. The maximum angle between the hyoid bars and the sagittal plane in an abduced head is about 35 \u00b0 (cf. Milburn and Alexander 1976: about 30\u00b0). 5. The neurocranium consists of a number of bony elements identical to other percids (see Barel et al. 1976). The vomer possesses small teeth (Figs. 6E, 8B). The levation range of the neurocranium is about 10 \u00b0 in the medial plane"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001403_robot.1993.292088-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001403_robot.1993.292088-Figure2-1.png",
+        "caption": "Fig. 2 Free-body diagram of the platform and of the two parts of one of the legs.",
+        "texts": [
+            " More detailed analyses lead to parallel algorithms whose complexity is of the order of log(n) For parallel manipulators, the situation is quite different since the end-effector - the platform - is not the end link of a kinematic chain. However, as opposed to the results obtained above for the inverse kinematics, it is not obvious from the outset that the parallel structure of the mechanism will lead to a parallel algorithm for the inverse dynamics. Let us first consider the free-body diagrams of the platform and of the two parts of one of the legs, which are shown in Fig. 2. In Fig. 2(a), the platform is represented with all the forces acting on it. Point Gp denotes the mass center of the platform. Since each of the legs is attached to the platform via a spherical joint, no torque can be applied to the platform by the legs. Moreover, for reasons that will become clearer in the next subsection, each of the contact forces between the legs and the platform has been decomposed as one force acting in the direction of the leg, noted fi and one force acting in a plane orthogonal to the direction of the leg, noted gj. Since the direction of the leg is known from the kinematic analysis, force fi contains only one unknown - its magnitude - and force gi contains two unknowns. Hence, there are 18 unknowns in the free-body diagram of Fig. 2(a) which PI. means that they cannot be solved directly. In Fig. 2(b), the freebody diagram of the upper part of the ith leg is represented. Point Gil denotes the mass center of this link. Forces f i and gi are still present, in virtue of Newton\u2019s third law. Moreover, the forces and moments applied to the upper part of the leg by the lower part of the leg are denoted as follows: force di is the force acting in a plane orthogonal to the leg, force hi is the force acting in the direction of the leg - the force applied by the actuator -, moment ni is the moment acting in a plane orthogonal to the leg and moment oi is the moment acting in the direction of the leg. Again, the force and moment acting in the plane orthogonal to the leg contain two unknowns while the force and moment acting in the direction of the leg contain only one unknown, i.e., their magnitude. Finally, the free-body diagram of the lower part of the leg is represented in Fig. 2(c). Point Gi2 is the mass center of this link. Since the link is connected to the base via a Hooke joint, only a moment in the direction of the leg can be applied by the base link to the lower part of the leg. This moment is denoted li. Furthermore, the force applied by the base to the lower part of the leg is decomposed into two forces: force ci is the force acting in the direction of the leg and force ei is the force acting in a plane orthogonal to the direction of the leg. Hence, the inverse dynamics problem can be formulated globally using 13 free-body diagrams involving a total of 78 scalar unknowns which are nothing but the components of the forces and moments defined above",
+            " Applying Newton and Euler's equations to each of the free-body diagrams, 78 linear equations are obtained, which is consistent with the fact that the problem a t hand is dynamically determined. compute g, compute g2 J( fl:o!E J. compute J. h, cojpute h, 3.1 Parallel algorithm for the inverse dynamics compute g6 1 ... As mentioned above, the parallelization of the inverse dynamics procedure is not as straightforward a8 in the case of the inverse kinematics. Indeed, the free body diagram of the platform cannot be solved directly from the outset. However, a closer look at the free-body diagrams of Fig. 2(b) and (c) reveals that some of the unknowns appearing on these diagrams can be solved for directly and independently from the other legs, if the unknown forces and torques are judiciously decomposed. This decomposition is the one presented above, i.e., each of the unknown forces and torques associated with one particular leg is decomposed into a vector in the direction of that leg and a vector acting in a plane orthogonal to the leg. The application of the Newton-Euler equations in the plane orthogonal to the direction of one given leg to both the upper and the lower part of the leg then leads to a system of 8 equations in 8 scalar unknowns which can be solved independently from the other legs"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003250_aim.2003.1225428-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003250_aim.2003.1225428-Figure4-1.png",
+        "caption": "Figure 4. Structure of the Fin Type of Microrobot",
+        "texts": [
+            " Although the structure of the microrobot is easy, and does not need offer of the energy &om the exterior as a feature of this proposal, it is difficult to obtain big propulsive force. 2.2 The Guided Type of microrobot The structure of a guided type of microrobot is shown in Figure 3. It is made to circle by the magnetic field of external revolution, carrying out surfacing guidance of the main part. By using the wheels, it becomes the structure of washing the inside of a pipe. As the feature of this proposal, the structure is easy and making it move by wireless is mentioned. 2.3 A Fin Type of Microrobot in Pipe Figure 4 shows the structure of a fine type of proposed microrobot. This microrobot consists of the main body made of styrol material shaped as a sphere, a fin made of film sheet (100pm thickness), a permanent magnet and an exchange magnetic field. When current flows in a coil, an alternate magnetic field parallel to the promotion advance direction is applied in a coil, and this moves by impelling force arising by a permanent magnet carrying out rotation vibration, and carrying out rotation vibration also of the fin in connection with it"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002606_iros.1997.655141-Figure7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002606_iros.1997.655141-Figure7-1.png",
+        "caption": "Figure 7: Schema of the verification experiment setUP.",
+        "texts": [
+            " Intrinsic calibration of the vision system was performed and radial distortion defects corrected for the whole set of images. We have assumed that all other optical deformations were negligible. Since we can't, know a priori the numerical values of X and T parameters, the estimation accuracy has been checked out by moving the robot camera. Using this method enables to test independently each estimated parameter of X. This verification includes two parts and requires a particular set-up described as follows (see fig.7). The robot camera is placed at about 50cm of a perforated wood plate (with a hole of lcm diarneter). A LED is fixed on the robot superstructure at about 1.2m behind the plate. The robot camera, the LED and the wood plate are then situated in a configura- 1063 tion where the LED is visible through the hole. This causes the LED, the hole and the camera optical center 0, to be aligned. Knowing the X transformation allows to move directly the camera instead of the gripper inside the robot workspace"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003591_s0022-5193(86)80192-8-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003591_s0022-5193(86)80192-8-Figure4-1.png",
+        "caption": "FIG. 4. Upper part: The geometric arrangement of cross-bridges (denoted by arms) and attachment sites (denoted by dots) is schematically shown. Lower part: The distribution of cross-bridges between nearest attachment sites is represented. In the case of muscle, M and A denote the thick and thin filaments. In the case of flagella, A and B denote the a-subtubule of the ith doublet and the b-subtubule of the i+ lth doublet.",
+        "texts": [
+            "5 pN) and 24 (nm) means a stroke distance of the radial spoke. Here we assume that the periodic mechanical potential is in the direction of the sliding coordinate as is shown in Fig. 3(b). The following two sections give a relationship between sliding displacement (x) and x values of individual cross-bridges in the flagellar segment. (B) GEOMETRIC CONSIDERATIONS There is need for the three-state model to be modified based on the geometric arrangement of both cross-bridges and attachment sites on each adjacent outer doublet of the flagellar axoneme (Fig. 4). That is, in muscle the value of cross-bridge spacing (42.9 nm) is different from that of attachment site spacing (37 nm) (Huxley & Brown, 1967) called \"vernier effect\" (Thorson & White, 1969; Nishiyama & Shimizu, 1979), while in flagella the value of the cross-bridge interval (24 nm) is almost equivalent to that of attachment site interval (24nm) (Takahashi & Tomomura, 1978). This suggests that the cross-bridge distribution along nearest attachment sites in a segment of length As, which is long enough to include a few 416 M"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000868_ie980219a-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000868_ie980219a-Figure1-1.png",
+        "caption": "Figure 1. The experimental setup.",
+        "texts": [
+            " However, impinging and canceling of the x-component of the jet velocities occurs very near the die face. The coordinate system selected for the experiments is shown in Figure 2. The origin of the system is at the center of the face of the die. The x-direction is transverse to the major axis of the nosepiece and slots, and the z-direction is perpendicular to the face of the die. The y-direction (which is perpendicular to the plane of Figure 2) is parallel to the major axes of the nosepiece and slots. The z-axis is directed vertically downward (see Figure 1). Air was metered through a Fisher & Porter flowmeter; this metered air was then fed to a die mounted in a test stand. The air flow rate, at standard conditions of 21 \u00b0C and 1 atm pressure, was maintained at either 1.67 \u00d7 10-3 or 3.33 \u00d7 10-3 m3/s (100 or 200 L/min). The corresponding Reynolds numbers (for a blunt die with b ) 0.65 mm) are 3800 and 7600. For all runs, the air temperature was maintained at ambient (21 \u00b0C). Harpham and Shambaugh1 showed that a die of the type used in our experiments has a large enough l /w to approximate an infinite-length die for positions away from the die ends"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001582_bf00262816-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001582_bf00262816-Figure1-1.png",
+        "caption": "Fig. 1 Oar angles and force measured to determine mechanical power during 3 min of moving-water tank rowing. Measurements were determined by a potentiometer mounted on the oarlock and strain gauges mounted inboard from the oarlock (see text for description)",
+        "texts": [
+            " The actual rowing time was divided into two, 3-rain bouts separated by 60s of rest. The rest period was used to obtain a blood sample for the determination of lactate accumulation. Subjects were asked to row at an intensity approximately equal to the middle portion of a rowing race when power output is generally constant and rowing at this intensity is 90% or more of l?O2~oak (Secher 1983; Steinacker 1993). To maintain a constant power output, feedback regarding the force exerted during each stroke and each 30-s cadence was provided to the subject by a visual monitor. Figure 1 illustrates the oar angle and forces measured for the determination of rowing mechanical power. Oar angle during the stroke was determined by a potentiometer attached to the oar lock and calibrated before testing with a goniometer (Ishiko et al. 1983). Forces on the handle were assessed by placing two strain gauges on the oar parallel to the blade and two gauges perpendicular to the blade to form a four-arm Wheatstone bridge. The four strain gauges were mounted inboard from the oar lock to measure strain on the handle during a stroke",
+            " Positional and force data were collected at 60 Hz with a customized Basic computer program, using an analog to digital board (DT2801A, Data Translation, Marlboro, Mass.) and stored on a computer. The oar force and positional data were smoothed by employing a five-point moving average (Wood 1982). Work performed during one stroke was calculated by the integral of force with respect to displacement of the oar (Mason et al. 1988). The work performed during each stroke was summed to attain the total work performed during the sampling period and was described by the following equation: ~6f Work = ~ rd~) ~s where: T = oar handle torque x sin (oar angle) (Fig. 1). Work was integrated from the starting position of the oar (q~s) continuously through the exercise bout until the final oar position of the exercise bout (~bf). Work in newton, meters was then converted to kilojoules (Astrand and Rodahl 1986). The initial non-linear rise in lactate observed at the beginning of exercise was minimized by allowing the rower to exercise at a constant power output for 3 rain before blood collection. This workload was at a power output the subject felt was similar to the middle portion of a 2000-m race"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001059_12.403696-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001059_12.403696-Figure1-1.png",
+        "caption": "Figure 1. Diagram of a typical notch flexure hinge (left) and a flexure hinge similar to a leaf spring (further referred as beam hinge) y is the nominal axis of rotation",
+        "texts": [
+            " To achieve a high life cycle the deformation should remain in the elastic strain. Looking at a conventional flexure hinge, a cantilever beam with a circular \u2217 Correspondence: Email: a.raatz@tu-bs.de; http://www.iwf.ing.tu-bs.de; Langer Kamp 19b, 38106 Braunschweig Microrobotics and Microassembly II, Bradley J. Nelson, Jean-Marc Breguet, Editors, Proceedings of SPIE Vol. 4194 (2000) \u00a9 2000 SPIE \u00b7 0277-786X/00/$15.00 157 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/17/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx notch (fig. 1) (further referred as notch hinge), the deformation takes place nearly only at the point of the smallest crosssection. Flexure hinges made of metallic alloys used for springs have limited mobility because these materials only allow low elastic strains. Hinges made of these materials are mostly used in precision engineering e.g. in bearings for highly accurate measuring instruments. These hinges have the geometry of leaf springs which allow deformation over the whole hinge length. Therefore, the possible deflections are higher and can be suited to the needs by varying the length",
+            " Because all pixels of the area are containing information for correlation, the accuracy of determining the position is higher compared to feature based algorithms. A camera with 782x582 pixels is used and the measurement area was 15x11 mm\u00b2 with a window size of 31x31 pixels. The resolution can then be expected to be 0.1 \u00b5m.12 Proc. SPIE Vol. 4194162 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/17/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx Thereby, two different joint types were examined. The notch flexure hinge according to fig. 1, left and beam flexure hinge according to fig. 1, right. It permits larger angle deflections, because the deformation extends over the entire length lM, but has also a larger movement of it\u2019s center of rotation. (notch hinge: l1 = 25 mm, R = 6 mm, l2 = 12 mm, t = 0.38 mm, h = 5 mm, b = 5 mm) (beam hinge: l1 = 19 mm, lM = 12 mm, l2 = 6 mm, t = 0.38 mm, h = 5 mm, b = 5 mm) The results of measurement compared to the calculated ones are shown in the diagrams 7 and 8. Generally the deviations for the zB coordinate are smaller (differences less than 2%) than for the xB coordinates, which are on average about 4%"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000327_t-aiee.1926.5061221-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000327_t-aiee.1926.5061221-Figure1-1.png",
+        "caption": "Fig. 1; and the rate at which that inductance changes n CIRCUITS with respect to x. General Case. From Appendix B, the general equaEquation (65) can be written in the following form: tion for fx for the case of n circuits is given in the fol-",
+        "texts": [
+            " It By conservation of energy, the increment in energy is the purpose here to give the general equation for a received from the electrical source during the change system of n circuits which may contain iron, either d x must equal the sum of the mechanical work plus saturated or not, but assumed to have no hysteresis, increment in stored magnetic energy. Thus, I d Q = f dx + d fidd 0 from which, by equations in Appendix A, fd x =- a d x dX joules (59) 0 In Fig. 2, i---4= S ; d x = h | |XOXThus, (c) Mechanical work - f d x = o a b' FIG. 1 In equation (59), d x is a constant in the integration. Hence and thus having inductances which are functions of S both position and current; and in a subsequent paper fz =- d X joules/cm. (60) in the near future, to apply the results to the case of 0 ax mechanical forces in synchronous machines under short- which is the same as equation (5), Appendix A. circuit condition. Or, Two cases will be taken up in order; single circuit, and n circuits. f =-22.5f a d lb. (60a) SINGLE CIRCUIT O The magnet in Fig. 1 is assumed to be excited to a This is the general equation for force by a single point a on the saturation curve Fig. 2. Let = magnetic linkages X 10-1 = L i = value of a at which the force is to be determined; dw viz., L I L = inductance in henrys, defined as linkages-per- ampere X 10-, and is a function of the current. i = current in amperes. I = value of i at which force is to be determined. fx = mechanical force exerted on the armature by the magnetic field, in the direction of x. x = distance in cm. from arbitrary reference. Although the electromagnet in Fig. 1 is a special case involving, as a result of symmetry, only one space FIG. 2 coordinate, the general case is fully treated in Appendix A, equations (5) and (6). circuit in which the inductance is a function of both Applying the principle of virtual displacement to the position and magnetic flux, and is therefore applicable system in Fig. 1, let there be a displacement d x of the to electromagnets involving saturation. armature, thus allowing the force fx to do work. Then, Equation (60) is applied as follows: referring to Fig. 2, the curve o a corresponds to position Let, x; curve o b, to position x + dx: i =f (co, x) 242 DOHERTY AND PARK: Transactions A. I. E. E. With co as parameter, plot where i = F (x) N = number of series turns. as in Fig. 3.7 From this, plot a = 61, + cRi turns2/henry (63) a i (R = magnetic reluctance coefficient, which is made --=s (co) up of (Ro, applying to the air portion of the magnetic circuit; Gi, to the iron portion",
+            " Thus the change in current due to such a change in x would be due wholly to the change in reluctance of the air path. This increment is indicated by h in Fig. 2, and corresponds to a change from x to x + d x, at a constant value of co8- i These relations will now be written into equation (60). By definition, (A)~~~~~~~~~~~~~co t = L amperes (61) FIG. 4 and NT2 1 ulp leL0 (65) L = p henrys (62) = 2 L 2 joules/cm (5 _________ ~~~~~~~~~Thus,for those cases where the above assumptions 7. It is mnore convenient in the particular case of Fig. 1 to approximately hold, the force is expressed in the follow- plot i as F (x - x) instead of F (x).inknwancovietersthatulmgtc 8. In calculating force, it makes no difference in the valueinkowadcnvietersthatulmgtc whether it is assumed that the change d x is made at constant 9. Thus, equation (65) holds only in so far as Ro and the linkages, as abovre, or at consta,nt current. Referring to Fig. 2, d iR the difference in mechanical work is represented by the second ratio d\u00b0are independent of co. order area a b b', which vanishes in the limit",
+            " In my own ru = resistance of circuit u in ohms. experience I have seen several cases where this rule led to comL, = M f= the self inductance in henrys of c ircsuit pletely erroneous results when applied to pra.ctical machines. withut sturaion In one instance, a complete change in sign of the force was ilnvolved, a repulsion was predicted, whereas actually an attrac- M = the mutual inductance in henrys of circuits tion was found. The magnetic circuit shown in Doherty and u and v without saturation. Park's Fig. 1 is one for which application of the fifty-fifty rule Feb. 1926 MECHANICAL FORCE BETWEEN ELECTRIC CIRCUITS 251 would give the wrong sign if the iron is saturated. With eon- to no saturation. There thus seems to be an omission in the stant current, motion of the armature upward decreases the authors' proof, which might be rectified as follows: magnetic energy, and yet the armature is attracted and not Let repelled. Lo = inductance corresponding to air-gap alone:i. e. inductance The great contribution of Doherty and Park in this paper lies corresponding to infinite permeability",
+            " For simplicity, considering only two cir- x\\ Lo' / x \\L0 J cuits, the authors would write the magnetic energy, Hence, since Lo appears in the authors' formulas only in the factor E = f i1 d w, + f i2 d w2 0 0 ( ) To bring out more definitely that i1 and i2 are functions of both Lo variables, wI and w2 I shall write this as, , Q02 therefore Lo' may replace Lo throughout. E = f il (Wl W2) d wx + f i2 (wOI W2) d W2 R. H. Park: In order to test the ease of applicability of the () ~~~~0 formulas developed and the agreement of calculated and ob- Now 2intcnttnhfsitr,umserved results, a calculation and test was made in a particular as co, varies, and co, is not a constant in the second integral. However, whatever relation is adopted between 022 and w I in the case. first integral, the same relation must be used in the second if The circuit employed (see Fig. 1 herewith) consisted of two the correct value for magnetic energy is to be obtained. magnetic yokes separated by a brass strip and excited by direct Now integrals of this kind are of frequent occurrence in mathe- current in two coils connected in series matical physics, and they are usually denoted by line integrals In order to determine the attractive force of the yokes, a written thus: weight was attached to the lower yoke and the exciting current was reduced until the yokes separated. 921 = 02 In order to calculate the force, the flux linkages co were measured E = f i1 d w, + i2 d 02 with a ballistic galvanometer for different air-gap and excitation",
+            " This may be looked upon as a generalization for the case of From a theoretical point of view, we know that until the saturasaturatioi, of the well-known fact for the linear case, that the tion of the core is sufficient to change appreciably the distribumutual inductance of circuit No. 1 upon circuit No. 2 is equal to the mutual inductance of circuit No. 2 upon circuit No. 1. .__.a_ On the fourth page first column of their paper, the authors give tio of thXil nar h uvso hudbier a numnber of formulas applying to their Fig. 1, and state that the quantity Lo, wshich appeairs there, is the inductance corresponding It may be observed that the experimental results agree with to no saturation. However, in their derivation of these formulas, 8 if I understand their derivation correctly, Lo is taken as the this requirement, the curves of a being linear except at very inductance corresponding to the air gap alone. That is, Lo is the inductance corresponding to infinite permeability, and not high saturation. 2.52 DOHERTY AND PARK: Transactions A"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure3.1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure3.1-1.png",
+        "caption": "Figure 3.1. An equivalent image rotation.",
+        "texts": [
+            "76) are given by cos 8 = 1 + !Tkk (3.78a) and (3.78b) and ( 3. 77b) yields for 8= \u00b1n. (3.79) 170 Chapter 3 (3.76) may be written as (3.80) wherein we recall (3.50b). For example, T[231 =(T23 -Td/2. Equations (3.75) and (3.76), or (3.80), determine 0 and a to within their signs. However, a right-hand rotation through an angle (J = -0, or equivalen tly, 2n- 0, about an axis a= -a clearly is equivalent to a right-hand rotation through an angle 0 about the axis a. In the former case, we visualize in Fig. 3.1 that the rotation through a negative angle about a negative direction is just the mirror reflection of the latter; hence, the pair { - 0, -a} is called the image rotation of the pair { 0, a}. Since these describe equivalent rotations, it is clear that (3.75) and (3.76), hence (3.80), determine the angle and axis of rotation uniquely. Moreover, it is plain that every rotational displacement may be accomplished by a rotation through an angle which is not greater than a straight angle; so, no generality is sacrificed by our requiring hen ceforward that 0 ~ 0 ~ n"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000425_s0003-2670(99)00040-9-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000425_s0003-2670(99)00040-9-Figure2-1.png",
+        "caption": "Fig. 2. Schematic diagram of the home-made flow-through cell: (1), (7) copper cover; (2) copper flow-through cell body; (3), (6) polytetrafluoroethylene O-ring; (4) glass support; (5) O2-sensitive reverse-phase optode membrane. Cell volume is 80 ml.",
+        "texts": [
+            " N2\u00b1O2 gas mixtures of various speci\u00aeed compositions, spanning the range 0\u00b1100% O2, were generated using two mass \u00afow controllers (Brooks Instrument B.V., the Netherlands) and a gas mixing chamber [54]. These gas mixtures were subsequently used to prepare various concentrations of oxygenated-organic solvents. The dissolved O2 concentrations in the organic solvents were calculated using O2 solubility data [55,56]. The optode membrane was mounted in a specially designed home-made \u00afow-through cell illustrated in Fig. 2 and positioned in either a Perkin-Elmer LS-50B luminescence spectrometer (Buckinghamshire, UK) coupled with a microcomputer or a spectro\u00afuorimeter consisting of a lamp power supply (Model LPS-220), a xenon lamp (Model A1010), and a photomultiplier detection system (Model 710), from Photon Technology International (Ont., Canada). Different concentrations of oxygenated-organic solvents were injected into the \u00afow-through cell at \u00afow rates of 2.0 ml min\u00ff1. All \u00afuorescence measurements were made at room temperature of 238C and atmospheric pressure"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003657_j.cma.2005.02.033-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003657_j.cma.2005.02.033-Figure6-1.png",
+        "caption": "Fig. 6. Linear graph of 2-link manipulator; the branches shown in bold (r3 r6 and h7 h8) correspond to a joint coordinate tree.",
+        "texts": [
+            " For a system with closed kinematic chains, one or more joints must be placed in the cotree. Projecting the branch transformations for these cotree joints onto their reaction spaces directly gives the kinematic constraint equations in terms of joint coordinates. For an open-loop system, all joints can be placed in the tree and the joint coordinates are independent. No kinematic constraint equations are generated since there are no cotree joints. This is the case for the 2-link manipulator with edges r3 r6 and h7 h8 selected into the tree shown as bold edges in Fig. 6. The branch coordinates then coincide with qb. The velocity transformations can be generated from the branch transformations for the rigid bodies now residing in the cotree. For body 2 of the 2-link manipulator v2 \u00bc v7 v3 \u00fe v4 \u00fe v8 v5; \u00f021\u00de x2 \u00bc x7 x3 \u00fe x4 \u00fe x8 x5; \u00f022\u00de where for example, v5 = x2 \u00b7 r5 is the translational velocity of arm r5 and x2 is the angular velocity of m2 given by (22). Projecting the vectorial branch transformations (21) and (22) onto the motion space defined by \u0131\u0302; |\u0302; and k\u0302 gives the three velocity transformation equations (9)",
+            " Although the absolute angular coordinates are a special case of indirect coordinates, they are covered here to demonstrate the concept of selecting two trees for the graph, a feature which is not new but which is required in order to use indirect coordinates, as shown later in this paper. One tree is used to generate translational equations and the other to generate rotational equations. By selecting joints into the tree for translation and rigid bodies into the tree for rotation, the branch coordinates take the form of absolute angular coordinates qh. Once again, all arm elements are selected into both trees. For the 2-link manipulator, the translational tree consists of the arm elements plus joints h7 and h8, as shown by the bold edges in Fig. 6. The rotational tree consists of arm elements plus bodies m1 and m2, as shown in Fig. 5. Since there are no translations associated with revolute joints, the only unknown tree displacements appearing in the branch coordinates are h1 and h2, the absolute angular coordinates. Even though there are revolute joints in the rotational cotree, their rotational branch transformations are orthogonal to the reaction space \u00f0\u0302\u0131; |\u0302\u00de of these joints. Thus, a null set of kinematic constraint equations is obtained for these independent coordinates"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002793_j.jsv.2005.03.024-Figure14-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002793_j.jsv.2005.03.024-Figure14-1.png",
+        "caption": "Fig. 14. Schematic arrangement for tyre tests.",
+        "texts": [
+            " Three types of test were made; the first uses a line excitation to select only the zero-order waves on the belt, the second test uses point excitation on the belt, the third test attempts to measure the force transmitted to the hub from excitation on the belt. Measurements were made for all the transfer functions described above and the parameters of the model were varied until a reasonable fit was made to the transfer functions with a single data set. This final parameter choice used in all the predictions is given in Tables 2 and 3. Fig. 14 shows a schematic diagram of a test arrangement on a pressurised tyre on a hub bolted horizontally to a steel block weighing 200 kg. This type of mounting is needed for measurements of transmitted force. The excitation was band-limited white noise from an electro-dynamic exciter. For most tests the loading was applied on a line across the belt, designed to preferentially excite the one-dimensional, m \u00bc 0, belt waves. This load spreader was made of plywood of 0.01m width, and was glued to the belt",
+            " The most important of these effects is the n \u00bc 1 acoustic cavity mode occurring when an acoustic wavelength fits around the cavity. However the n \u00bc 1, belt flexural mode and the n \u00bc 0 ring mode have longer wavelengths than the acoustic wave and therefore transmit forces to the hub via the stiffness of the entrapped air. Some tests were made of the theoretical predictions for transmitted force via the two side-wall components in Eq. (49), and the three structural/acoustic modes from Appendix A. The belt in Fig. 14 was excited by 0.2m line force along the centre line. The displacement directly above the edge of the side-wall was obtained from the acceleration, and the force transmitted to the hub was measured using the piezo-electric transducers. The force/displacement or \u2018dynamic stiffness\u2019 was thereby obtained and are compared with the theoretical prediction in Fig. 20. Fig. 21 gives the four components of the theoretical prediction, which will be discussed before considering the measurements. The contact length in Fig"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001869_irds.2002.1043954-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001869_irds.2002.1043954-Figure5-1.png",
+        "caption": "Figure 5: h e - b o d y diagram of one strand in symmetric tension",
+        "texts": [
+            " (1) This equation has two unknown variables, F1b and F26, which can be uniquely solved in general. The condition of impending motion can be obtained from the free-body diagram of one strand as shown in Figure 4. The impending motion occurs when (FIaZla + F&b> . Zt = P(fian -k flbn). (2) From (2), it is possible to obtain the general sliding condition, but it is quite complicated. Since the desired knot trajectory lies in the normal direction to the tissue, we shall only consider the symmetric shown in Figure 5. At the equilibrium, the force and moment equations about p and p' are c=e(P = PI = ,927 7 = 71 = 7 2 , F1a = F2a), as (4) (5) Coulomb\u2019s law states the sliding occurs when It can be further simplified to (7) 1 1 tanp tany > 2P, --- which results in the following sliding condition (8) tany 2p tany + 1 o < p < tan-\u2019( ). This means that the sliding begins when the angle ,8 is sufficiently small to satisfy the inequality condition which depends on the coefficient of friction between the strands and y"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003292_s0167-8922(08)70696-5-Figure40-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003292_s0167-8922(08)70696-5-Figure40-1.png",
+        "caption": "FIG. 40",
+        "texts": [],
+        "surrounding_texts": [
+            "I n o rde r t o overcome many o f t h e mounting and dismount ing problems SKF, i n 1940, in t roduced an o i l - i n j e c t i o n techn ique which i s now w ide ly used i n many branches o f eng ineer ing . O i l under h i g h pressure i s i n j e c t e d between the bearing i nne r r i n g and s h a f t j o u r n a l du r ing mounting o r dismount ing. An o i l f i l m i s formed which bo th separates and l u b r i c a t e s the con tac t sur faces . The o i l separates the con tac t sur faces except f o r a narrow zone a t each end o f t he r i n g . The su r face pressure i s g rea te r i n these zones due t o the i n f l u e n c e o f t he s h a f t m a t e r i a l beyond t h e end o f t h e r i n g and t h e zones a c t as an o i l l ock which r e t a i n s t h e o i l between the con tac t sur faces . When the o i l p ressure i s released the o i l i s f o rced a u t o m a t i c a l l y back through t h e supp ly duc ts , thereby r e s t o r i n g the o r i g i n a l f r i c t i o n . The advantage o f u s i n g o i l - i n j e c t i o n i s t h a t t he f o r c e requ i red t o move the component i s s i g n i f i c a n t l y reduced and t h a t by e l i m i n a t i n g d i r e c t con tac t and the r e s u l t i n g f r i c t i o n between the con tac t sur faces , t he p o s s i b i l i t y o f damage t o the sur faces o c c u r r i n g du r ing the mounting o r dismount ing process i s minimised. 170 A f u r t h e r advantage i s t h a t components can be dismounted o r ad jus ted w i t h o u t the r i s k o f the f i t d e t e r i o r a t i n g . I f the bear ing r i n g i s mounted on a tapered j o u r n a l w i t h a s e l f - r e l e a s i n g taper , the r i n g w i l l be e j e c t e d w i t h some f o r c e when the o i l i s i n t roduced and some f o r o f a x i a l r e s t r a i n t such as a n u t w i l l be necessary. I f , however, a l ock ing taper i s used then an ex te rna l f o rce a d d i t i o n a l t o the o i l i n j e c t i o n fo rce w i l l be requ i red . F igures 41, 42 and 43 show t y p i c a l arrangements. Position of distribution groove in a tapered and a cylindrical seating for a rolling bearing Cylindrical seating 171 Cylindrical mating surface having two distribution grooves F I G . 43 HMV nut and stop rings in position to press loose an adapter sleeve HMV nut for driving up a bearing on an adapter sleeve HMV nut used to free a withdrawal sleeve F I G . 46"
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0003475_j.ultras.2004.01.001-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003475_j.ultras.2004.01.001-Figure1-1.png",
+        "caption": "Fig. 1. Laboratory ultrasonic grinding mill for processing of powder materials: (a) scheme: 1\u2013\u2013ultrasonic generator; 2\u2013\u2013vibrator; 3\u2013\u2013steplike horn; 4\u2013\u2013container; 5\u2013\u2013metallic balls; 6\u2013\u2013gas inlet and 7\u2013\u2013thermocouple, (b) photo of chamber with transparent walls.",
+        "texts": [
+            "001 ments of powder materials those in turn lead to sharply acceleration of diffusion, mass-transfer processes, solidstate reactions and structure changing [9,10]. In this paper we report on some construction details of ultrasonic mill and obtained results concerning to formation of an fcc substitution solid solution of Fe, Ni and Cu, interstitial solid solution of Fe and C by ultrasonic milling and ultrasonically induced fcc\u2013hcp phase transformation of Fe4N. The schema of apparatus is shown on Fig. 1(a) [11]. It consists of ultrasonic generator (1 kW power output, 20 kHz frequency), magnetostrictive vibrator and step-like shape ultrasonic horn (tip diameter was 13 mm) made from the quenched high carbon steel. A cylindrical chamber of 14 mm in diameter for ultrasonic treatment also was made from high carbon steel and quenched. Used apparatus was similar to the one described in [7] with power supply 500 W. However, a certain quantity of steel balls (ShKh15) with different diameters (12 and 3 mm) was enclosed (Fig. 1(b)). An acoustic system was forced (F \u00bc 20 N) against balls. After that the ultrasonic vibrations were turned on and balls began to revolve and collide. Since a dependence of vibration amplitude of ultrasonic horn tip on static loading and power supply is well known fact the peak-to-peak amplitude was measured by vibrometer. Used ultrasonic generator permits to sustain it in forced condition on level equals 10 lm. The chamber was cooled by flowing water during processing. Temperature within the chamber, which was measured during treatment by thermocouple, was not exceeded 60 C"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000771_s1350-4533(97)00022-2-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000771_s1350-4533(97)00022-2-Figure1-1.png",
+        "caption": "Figure 1 Two-link conceptual body model.",
+        "texts": [
+            " In the analysis of the skeleton system mechanics\u2019 requirement to determine the joint stiffness, the function of muscle stiffness is simulated as a feedback controller. The complexity of the controller in the gait model limits the analysis of its time-varying property. So far, no attempt has been made to include the muscle joint stiffness as a basic component of the skeleton system gait model, and to analyze stiffness timevarying properties. That is the purpose of this study. Our idealized model, shown in Figure 1, consists of two rigid bars, which represent the stand leg and upper bodym respectively, and two masses associated with each bar. The mass of the body segment is concentrated at one point, the center of gravity of the body segment. The dimensions and mass of the foot are much smaller than that of the leg and upper body, so they are neglected. We assume that the ankle is hinged directly on the ground through a revolute. Although this is not an accurate model of the stand leg, our purpose here is to demonstrate the method with a simple model; a movable ankle is coincided in a separated 8DOF Model24"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000831_s0167-6911(98)00058-9-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000831_s0167-6911(98)00058-9-Figure1-1.png",
+        "caption": "Fig. 1. Inverted pendulum system.",
+        "texts": [
+            " (5), this robust area is governed by \u2016 H ij\u2016Robust area 6\u2212 [A0]\u2212 \u2016H ij \u2212 A0\u2016 \u2212 for all i and j: (24) The uncertain fuzzy control system is stable if the uncertainty \u2016 H ij\u2016, with \u2016 H ij\u2016max as its maximum value, satis es the following condition: \u2016 H ij\u20166\u2016 H ij\u2016max6\u2016 H ij\u2016Robust area : (25) For the particular case of the simpli ed system of Eq. (8), the robust area is governed by \u2016 H j\u2016Robust area 6\u2212 [A0]\u2212 \u2016H j \u2212 A0\u2016 \u2212 for all j: (26) The uncertain fuzzy control system is stable if the uncertainty \u2016 H j\u2016, with \u2016 H j\u2016max as its maximum value, satis es the following condition: \u2016 H j\u20166\u2016 H j\u2016max6\u2016 H j\u2016Robust area : (27) A fuzzy controller is designed using the proposed methodology to balance an inverted pendulum on a cart [6]. The inverted pendulum system is shown in Fig. 1. The equation of motion is given by x= g sin(x)\u2212 amlx\u03072 sin(2x)=2\u2212 a cos(x)u 4l=3\u2212 aml cos2(x) ; (28) where x and x\u0307 are the angular displacement about the vertical axis (in rad) and the angular velocity (in rad s\u22121) respectively, g=9:8m=s2 is the acceleration due to gravity, a=1=(m +M); m=2kg is the mass of the pendulum, M =8kg is the mass of the cart, 2l=1m is the length of the pendulum, and u is the force applied to the cart. It was reported in [6] that the system of Eq. (28) can be approximated by a fuzzy plant model with the following two rules: Rule 1: IF x is about 0 THEN \u02d9\u0303x= A\u0303 1 x\u0303+ B\u0303 1 u: Rule 2: IF x is about \u00b1 =2(|x|\u00a1 =2) THEN \u02d9\u0303x= A\u0303 2 x\u0303+ B\u0303 2 u; (29) where x\u0303= [ x\u03031 x\u03032 ] ; x\u03031 = x; x\u03032 = x\u0307; A\u0303 1 = [ 0 1 g 4l=3\u2212 aml 0 ] ; A\u0303 2 =   0 1 2g (4l=3\u2212 aml 2) 0  ; B\u0303 1 = [ 0 \u2212 a 4l=3\u2212 aml ] ; B\u0303 2 =   0 \u2212 a 4l=3\u2212 aml 2  ; =cos(88\u25e6); x\u2208 ( \u2212 2 ; 2 ) : The membership functions, about 0 = 1 \u2212 |x|=d and about\u00b1 =2 = |x|=d, are shown in Fig"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003355_tmag.1982.1061919-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003355_tmag.1982.1061919-Figure2-1.png",
+        "caption": "Fig. 2. A graphical illustration of the rotation segment.",
+        "texts": [
+            " This line is called the cluster knot. We distinguish three types of wall clusters, depending on the position of the cluster knot (see Fig. 1). It can be shown that only two continuous magnetization modes are possible in the domains [I41 by virtue of the incompatibility of space-charge density singularities within soft magnetic materials. The first mode is a simple quasi-uniform sector, in which the rotation of the magnetic dipoles is infinitely small close to the cluster knot. The other mode, the so-called rotation segment (Fig. 2), is characterized by a circular rotation of the magnetization around the cluster knot. There are two types of domains to be distinguished, namely the rotating domains and the uniform domains. A rotating domain contains one rotation segment, surrounded on both sides by uniform sectors. On the contrary, no rotation segment is present in a uniform domain, which consists of one uniform sector only. It can be shown [15] by applying the procedure shown in [I41 that, in contradistinction to the free wall cluster, no rotation segment can exist in an edge cluster"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003236_tmag.2005.854972-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003236_tmag.2005.854972-Figure1-1.png",
+        "caption": "Fig. 1. Four-pole rotor winding scheme of one circuit. Front and rear connection are reported in continuous and dotted lines.",
+        "texts": [
+            " The investigated motor belongs to the first type, and it has been derived starting from a four-pole conventional induction machine. A wounded four-pole rotor has been employed in order to improve stability and force generation of the system. This configuration allows the application of known techniques of vectorial control used in conventional induction machines. The studied prototype is a low-power three-phase bearingless four-pole induction machine with winded rotor. The rotor arrangement consists of four equal circuits, and one of them is shown in Fig. 1. The stator coils are used both to produce the torque and to control the radial force [1]\u2013[4]. Fig. 2 shows, in small letters, the stator windings of a standard 36-slot four-pole motor, distributed on the stator cross section. The geometrical winding axis is also represented. The single and double apex indicates, respectively, the half-windings \u201cunder\u201d the first and the second couple of poles. Also in Fig. 2, the conventional name Digital Object Identifier 10.1109/TMAG.2005.854972 of the half windings for the bearingless machine is reported in bigger letters"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003594_j.mechatronics.2005.06.004-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003594_j.mechatronics.2005.06.004-Figure4-1.png",
+        "caption": "Fig. 4. Two-link robotic manipulator.",
+        "texts": [
+            " Although Huang and Lian [17] once proposed the mixed fuzzy control strategy and applied it in controlling the active dynamic absorber for a MIMO system, presenting good control performance in verified experimental results, the stability of the mixed fuzzy control system is unproven by theoretical or numerical analysis. Clearly, the MFC is very suitably employed in controlling practically complicated MIMO systems. However, the stability of the mixed fuzzy control system still needs to be further determined to guarantee that the system is able to operate stably during all control processes. To evaluate the control performance and the stability behavior of a MFC for MIMO control systems, this work presents a two-link robotic manipulator for a MIMO system, as shown in Fig. 4. Where m1 and m2 are the masses of links 1 and 2, respectively; l1 and l2 are the length of the links 1 and 2, respectively. The dynamic equation of the robotic manipulator is M\u00f0q\u00de\u20acq\u00fe C\u00f0q; _q\u00de _q\u00fe G\u00f0q\u00de \u00bc s \u00f07\u00de where q \u00bc \u00bd q1 q2 T is an 2 \u00b7 1 vector of joint position, _q \u00bc \u00bd _q1 _q2 T is an 2 \u00b7 1 vector of joint velocity, \u20acq \u00bc \u00bd \u20acq1 \u20acq2 T is an 2 \u00b7 1 vector of joint acceleration, s \u00bc \u00bd s1 s2 T is an 2 \u00b7 1 vector of the control input torque; M(q) is an 2 \u00b7 2 inertial matrix that can be described as M\u00f0q\u00de \u00bc 1 3 m1 \u00fe m2 l21 \u00fe 1 3 m2l 2 2 \u00fe m2l1l2 cos q2 1 3 m2l 2 2 \u00fe 1 2 m2l1l2 cos q2 1 3 m2l 2 2 \u00fe 1 2 m2l1l2 cos q2 1 3 m2l 2 2 \" # C\u00f0q; _q\u00de is an 2 \u00b7 2 matrix of Coriolis and centrifugal forces that can be described as C\u00f0q; _q\u00de \u00bc 1 2 m2l1l2\u00f02 _q2\u00de 1 2 m2l1l2 _q2 sin q2 1 2 m2l1l2 _q1 sin q2 0 \" # and G(q) is an 2 \u00b7 1 gravity vector that can be represented as G\u00f0q\u00de \u00bc 1 2 m1 \u00fe m2 gl1 cos q1 \u00fe 1 2 m2 gl2 cos\u00f0q1 \u00fe q2\u00de 1 2 m2 gl2 cos\u00f0q1 \u00fe q2\u00de \" # where g represents a gravity acceleration constant"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000596_1.2805411-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000596_1.2805411-Figure1-1.png",
+        "caption": "Fig. 1 Electromechanical actuator",
+        "texts": [
+            " This result is closely related to the one of Hac (1992) but without computing the bilinear part of the DDO (Nj = 0 ) . The design is the reduced to the pole placement of the matrix H using the linear DDO design given by Darouach et al. (1994) or Kurek (1983) for example. 5.2 Electromeclianical Actuator (Malasse et al., 1994; Rugh, 1981). The second numerical example is an electrome chanical actuator frequently used in robotics and constituting of a direct-current motor with an elastic coupling and the load shaft as shown in the Fig. 1. This plant can be described by the following bilinear statespace model X = Ax -I- DiM,x + BU -I- F^; y = Cx where 1,/L, 0 0 0 0 0 -F IJ 1 UN 0 0 0 0 0 0 0 -K/(NJ\u201e,) 0 0 fCrfJc 0 0 0 - 1 -FJJ, X = la , F = 0 0 0 0 \u20221/7, D, = C = 0 -kJL, i^a'^m ^ 0 0 0 0 0 0 \" 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0\" 0 0 0 0 0 0 0 0 0 0 0 0 . 0 0 1 , B = \"0 0 0 0 .0 r and U = *\u2022\u20ac -^a. = 0 1/L, 0 0 0 \u00ab i _M2 The state variables are the armature current ia(t), the motor Journal of Dynamic Systems, IVIeasurement, and Control SEPTEMBER 1998, Vol"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001854_cdc.2001.980101-Figure11-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001854_cdc.2001.980101-Figure11-1.png",
+        "caption": "Figure 11: Twin rotor experimental model",
+        "texts": [
+            " In the case of the proposed method, the overshoot and the undershoot increase as e increases, but the system remains stable and the tracking error converges to zero as shown in Fig. 2 and Fig. 3. In the case of the approximate method, the system becomes unstable \u20acor e = 0.5,O.g. . , . . . , . . /-. Figure 6 A M x ( t ) Figure 5: PM:(x,y) Figure 7 AM:y(t) ., . ., . > . Figure 9: AM:(z,y) 21 9 4.1 Experimental setup and model The general view of our experimental setup is shown in Fig. 10. The twin rotor helicopter model is mounted on a base as shown in Fig. 11. The arm AB can rotate around the center 0 freely, and a1 and a2 are the yaw and the IOU angles, respectively. The airframe CD can also rotate freely on the axis AB, and 6' is the pitch angle. Thus, the model has three degrees of freedom. The rotors are driven separately by two DC motors. The actuator part is illustrated in Fig. 12. The angle 4 produces the coupling property. By the way, 4 is zero in (41 and [7]. The maSS of each rotor is A/2, and the distance from the point B to the center of mass of each rotor is r"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000631_10402009908982280-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000631_10402009908982280-Figure2-1.png",
+        "caption": "Fig. 2-Thermoelastlc deformations (0: original profile, P: deformed due to pressure, 1: further deformed due to frictional heating).",
+        "texts": [
+            " At a surface location x,, the heat flux is proportional to the contact pressure, p(x,), over a differential area AA, or to the surface nodal force, F,: An adiabatic boundary condition shown in Eq. 131 can be assigned to S2 and S3, as validated by the symmetric extensions of the digitized profile. A prescribed temperature, To, may be proper for the base, S,, of the model. Thermoelastic Contact Conditions Under the contact pressure and frictional heat, surface asperities should experience elastic and thermal deformations while the feedback of the deformations alters the pressure distribution and heat generation. Figure 2 enlarges one of the asperities shown in Fig. I(b). At any point x,, the sum of the elastic deformation, u; the thermal deformation, u,', separation, s,, and the rigid-body motion, or, can be expressed as: ukp 2 O,U: ? o,sk 2 0 with The rigid-body motion, or, in Eq. [6] may be negative if the thermal deformation is larger than the elastic deformation. By making a non-negative and by introducing slack variables Y,, at any point x,, the inequality constraint shown in Eq. [6] changes into an equality (17): ~ ( k p -\"; + S k Yk = O for small thermal deformation, and x c S, 181 u[-U[ + s k + a - Y k = O for large thermal deformation, and x = S, P I The tangential traction on the surface is assumed proportional to the normal traction"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000977_20.717790-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000977_20.717790-Figure6-1.png",
+        "caption": "Fig. 6. Mesh of the switched reluctance motor for a rotary angle of 4 degrees",
+        "texts": [
+            " The classical iterative methods are not suited to solve the matrix system and, to get the solution, other techniques, such as the normal equation method or minimal residual are to be employed. Moreover, the convergence becomes more and more difficult as the number of DOFs of the model is increased. Various numerical experiences have shown that Lagrange multipliers method is not efficient for realistic applications when using a classical solver. 3362 The mesh interpolation method seems to be more suited for the analysis of realistic applications than the Lagrange multipliers method. To investigate the proposed approach, we have chosen a model of a switched reluctance motor (Fig. 6). The motor has four stator and two rotor poles. Each pair of stator coils makes up a phase. To avoid the mesh splitting, a regular mesh was used on the coupling interface. The mesh is conformal generated for a specified position of the rotor. Then, to allow the rotor sliding, the nodes on the coupling interface are duplicated. When the rotor position changes, the coordinates of the rotor nodes are calculated by the rotary angle. To connect the independent meshes, which are generally non-conformal, the sliding parameter based method was used"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001349_s0094-114x(00)00051-3-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001349_s0094-114x(00)00051-3-Figure1-1.png",
+        "caption": "Fig. 1. Seven-jointed spherical-revolute-spherical manipulator: (R?R?R)sph ? R?(R?R?R)sph.",
+        "texts": [
+            " . . ; $sub6 ; $r1 ; $r2 ; . . . ; $rk\u00ff6 becoming degenerate. Two examples are presented to illustrate the developed methodology. Hollerbach [16] proposed the ``optimal'' layout of a seven-jointed manipulator for the elimination of singularities as (R?R?R)sph ?R?(R?R?R)sph, where R is a revolute joint, sph denotes a spherical joint group, and ? refers to two successive joints being perpendicular to one another. Denavit and Hartenberg parameters [17] for the manipulator are presented in Table 1. Fig. 1 shows the layout of the manipulator. Choosing a reference frame that is located at the intersection of the wrist spherical group and oriented with zref in the direction of $5 and yref in the opposite direction to that of $4 allows the joint screws to be found as ref$1 S2C3C4 C2S4 \u00ffS2S3 \u00ffS2C3S4 C2C4 \u00ffS2S3C4g \u00ff S2S3h \u00ffS2C3g \u00ff S2C3C4h\u00ff C2S4h S2S3S4g 8>>>>><>>>>>: 9>>>>>=>>>>>; ; ref$2 \u00ffC4S3; \u00ffC3; S3S4; \u00ffC3C4g \u00ff C3h; S3g S3C4h; C3S4gf gT; ref$3 S4; 0; C4; 0; \u00ffS4h; 0f gT; ref$4 0; \u00ff1; 0; \u00ffh; 0; 0f gT; ref$5 0; 0; 1; 0; 0; 0f gT; ref$6 S5; \u00ffC5; 0; 0; 0; 0f gT; ref$7 \u00ffC5S6; \u00ffS5S6; C6; 0; 0; 0f gT ; 8 where Cij cos hi hj and Sij sin hi hj "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002971_bf02169679-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002971_bf02169679-Figure1-1.png",
+        "caption": "Figure 1. A pendulum subject to a bounded comml torque.",
+        "texts": [
+            " For this example, the Riccati equation (19) reduces to 2aP - b z P z + QR = 0. (36) The positive solution to equation (36) is given by P = a /b z + [(a/b2) 2 + QR] '~. (37) Thus, by appropriate choice of QR > 0, we can obtain any P that satisfies P > 2a/b z. Condition (34) becomes b2p2 <_ (c/r)2; hence, an appropriate P exists iff r < Iblc/2a. 5.2. Stabilization o f an inverted pendulum with a bounded controller Consider a pendulum P (or one-link manipulator) subject to a bounded control torque T; see figure 1. Its motion is described by I0\" - mgtsin 0 = T (38) where I is the moment of inertia of P about its axis of rotation, m is the mass of P, l is the distance between the center of mass of P and O, and g is the gravitational acceleration constant of the planet (or moon) in which P resides. We consider the situation in which tT(t)l <- T (39) where the control torque bound :F is specified and satisfies 1\" > mgl. (40) If we let A A A Xl = O,X 2 = O, U = T/1, then )~1 ---- X2 \"~2 = psin Xl + U where a p = mgl / I and lu(t)l ~ ~ zx T/I"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002460_63.85913-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002460_63.85913-Figure4-1.png",
+        "caption": "Fig. 4. Trajectories of the current control error A i N shown for JgUl close to 1 ~ ~ 1 , The \u201caxis\u201d C i5 parallel to ( k , ) for k , = 0, 7 . For iTB and hexagon see section 3.",
+        "texts": [
+            " As can be easily estimated, for practical applications the inductive voltage drop L ai,,,/dt can be neglected in comparison to g N in many cases (see Fig. 3 : A$ + 0). Under stationary operating conditions one can assume sinusoidal quantities forming g N and j $ . There the space vector of the current control error A I N due to (2) is rep- KOLAR et al.: ON-AND-OFF LINE OPTIMIZED PREDICTIVE CURRENT CONTROLLERS 453 resented in a coordinate system whose origin lies in the tip of j ; . The trajectories of AiN ( k , ) are trochoids which degenerate to circles for k, = 0 or k, = 7 (Fig. 4). used to compare the different current controllers can be calculated from the space vector Aihi. At first we define: The rms value of AiN eff of the current ripple which is c A i 2 = + + ( 5 ) 454 IEEE TRANSACTIONS ON POWER ELECTRONICS. VOL. 6, NO. 3. J U L Y 1991 Equation ( 5 ) characterizes the power dissipation of the system due to current control errors and can also be expressed by the space vector Ai, : CAi2 = (AiN)* . (6) Accordingly, AiNc,, = dk dt (7) is used as a quality criterion. For converter switching frequencies in the kilohertz range for rms value calculations the trajectories of Ai, can be replaced by straight lines with very good approximation (the error lies in the 0"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002068_bf00052455-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002068_bf00052455-Figure4-1.png",
+        "caption": "Fig. 4. Elastic coupling.",
+        "texts": [
+            " The spatial possible motion of the joint can be described by (#iqJ~) with the relative displacements qj~ in the not constrained directions of the joint i. A complementary matrix ~ E ~ 6 , 6 - f i exists for the constrained directions of the joint. It is always ~ = 0, and the constraint forces are written as fJi -~ ~)c)~i, )~i E ]~6-fl. (5) The Lagrangian multipliers ), follow from d'Alembert's principle and a Lagrangian treatment of the equations of motion. Elastic couplings in drivelines are characterized by some force law in a given direction between two bodies (Figure 4). The relative displacement and displacement velocity may be expressed by T T 7k = Ck ( - C k i P i + Ckjpj ) , ~/k -~- ~)k ( - -Cki Vi \"q- C k j V j ) ( E 0 ) ~ 6'6 Ck~ = -T E C . (6) Cki The vector cki follows from Figure 4, 5ki is the relevant skew-symmetric tensor (gtb _= a \u00d7 b). The vector ~b k E ~6 represents a unit vector in the direction of relative displacement. In that direction we have a generalized force ffk according to the given force law. It can be projected into the body coordinate frames for Hi, H i (Figure 4) by f/ T T = CkiCkffk , fj = Ck jCkCk . (7) ~k =- c'Zk + dS'k. (8) Of course, any nonlinear relationship might be applied as well as the force law with backlash according to Figure 5. Gear meshes with backlash are modeled with the characteristic of Figure 5. In this case care has to be taken with respect to the two possibilities of flank contact on both sides of each tooth [20]. Oil reduces the impact forces of the hammering process. Some application tests have been performed with the nonlinear oil model of Holland [7]"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001383_1.1288360-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001383_1.1288360-Figure2-1.png",
+        "caption": "Fig. 2 An in-parallel manipulator",
+        "texts": [
+            " Further, Rico and Duffy @22# proved that AW * can be written in terms of the screws that represent the kinematic pairs of the linkages and the joint rates, i21v i , and their derivatives, i21v\u0307 i , as AW *5( i51 n i21v\u0307 i i21SW i1( i51 n21 F i21v i i21SW i ( j5i11 n j21v j j21SW jG . (5) This screw was called the \u2018\u2018accelerator\u2019\u2019 by Sugimoto @20#. Figure 1 illustrates an HPS manipulator where H, P, and S denote respectively a Hooke joint, and a prismatic and a spherical pairs. The first revolute pair in the Hooke joint is connected to ground, at point B, and the spherical pair is attached at the end effector or hand, at point P. Six such manipulators will be used as the connector chains of a parallel device ~see Fig. 2!, and the prismatic pair in each connector chain will be actuated, for more details see Fichter @24#. The velocity analysis of the parallel device is included for the sake of completeness and because it provides information necessary for the acceleration analysis. The inverse velocity analysis problem can be stated as follows: \u2018\u2018Given the velocity state of the end effector, determine the joint rates of the active prismatic pair as well as of the remaining passive pairs.\u2019\u2019 In the opposite direction, the forward velocity analysis is stated as follows: \u2018\u2018Given the joint rates of the active prismatic pairs, determine the velocity state of the end effector"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001838_1.2889636-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001838_1.2889636-Figure4-1.png",
+        "caption": "Fig. 4 Electro-magnetic excitation device",
+        "texts": [
+            " Ha,(jO)) = H,p{j(o)-a)} H^(j(B) = 0 H^(jOl) H^(jo>) rotor system, the magnitude of residues in the reverse dFRFs defined in the stationary (rotating) coordinate are relatively small compared to those in the normal dFRFs. In order to investigate the practicality of the proposed diag nostic method, it is tested with a laboratory flexible rotor-bear ing system. The test rig consists of two rigid disks, and a uni form flexible shaft supported by two high-speed self-aligning type of ball bearings. The dimensions and disk data of the test rig are shown in Fig. 3. Figure 4 depicts the electro-magnetic exciting device devel oped for the complex modal testing. It consists of four identical electro-magnets attached to a cross-type panel, a tool dynamom eter to measure the excitation force on the rotor, and the support structure. Four identical radial electro-magnets are equally spaced around a circle of 160 mm in diameter. Each magnet cores are made of laminated stacks of 0.35 mm thick silicon steel plate and 1160 turns of winding coil. A hybrid controller with analog electronic circuits controls the excitation force level up to 40QN"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001553_s0045-7825(99)00329-1-Figure11-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001553_s0045-7825(99)00329-1-Figure11-1.png",
+        "caption": "Fig. 11. Generating cone surface.",
+        "texts": [
+            " Investigation of meshing and contact of misaligned gear drive is accomplished by computer program developed by the authors and obtained for a gear drive with the design parameters represented in Table 1. The results of computation show that the function of transmission errors is indeed a parabolic one (Fig. 9). Contact paths on gear tooth surface have been obtained for cases of errors of alignment Dc, DE, and Dq. Correction of the worm lead angle Dpw allows to compensate the shift of the bearing contact caused by errors of alignment (Fig. 10). The term ``Klingelnberg'' means that the hob is provided with surface Rh generated by a cone (Fig. 11) [5]. The process of generation of Rh is similar to the one described in Section 5 for worm generation, wherein only the screw motion of Rh is applied and plunging is not provided. Hob surfaces R i h (i I; II) assume the form of Eqs. (2) and (3). After respective derivations, they are obtained as follows: r i h u i t ; h i t ;wt u i t cos a i t cos ct sin h i t sin wt cos a i t cos h i t cos wt sin a i t sin ct sin wt a i sin ct sin wt Et cos wt u i t cos a i t cos ct sin h i t cos wt \u00ff cos a i t cos h i t sin wt sin a i t sin ct cos wt a i sin ct cos wt \u00ff Et sin wt u i t cos a i t sin ct sin h i t sin a i t cos ct \u00ff phwt a i cos ct 26666666664 37777777775 ; 31 f u i t ; h i t a i sin a i t Et sin a i t cot ct \u00ff ph sin a i t tan h i t \u00ff Et \u00ff ph cot ct cos a i t cos h i t \u00ff u i t 0: 32 The unit normal to the hob thread surface Rh is represented as n i h h i t ;wt L1t wt n i t h i t 33 that yields n i h h i t ;wt sin wt sin a i t cos ct sin h i t cos a i t sin ct sin a i t cos h i t cos wt cos wt sin a i t cos ct sin h i t cos a i t sin ct \u00ff sin a i t cos h i t sin wt sin a i t sin ct sin h i t \u00ff cos a i t cos ct 2664 3775: 34 The face worm-gear surface R2 is generated by the hob"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure1.10-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure1.10-1.png",
+        "caption": "Figure 1.10. Motion of a particle along a space curv(:.",
+        "texts": [
+            " The arc length and the unit tangent vector to the particle's path are obvious intrinsic geometrical quantities associated with the velocity vector in (1.14), for example. Therefore, (1.14) is an intrinsic equation for the velocity. To derive the general formulas for the intrinsic velocity and acceleration, it is natural that we should begin by thinking of the motion as a function of the distance s(t) traveled by the particle along its path. Let us consider a par ticle P moving along an arbitrary path C in space, as shown in Fig. 1.10. At any instant t its distance along C from any reference point Q on C is s(t). Hence, relative to our Cartesian frame tP = { 0; ik} in which the usual coor dinates of a point are {xd = (x, y, z), the position vector of the particle may be written as a function of the time-varying distance traveled along the path: x(P, t)=x(s(t))=x(s)i+ y(s)j+z(s)k. ( 1.60) Then with dx(s) = dx(s) i + dy(s) j + dz(s) k, it is seen that dx \u00b7 dx = ds2, the elemental arc length of the curve. Therefore, the vector dx/ds is a unit vector. It may be seen in Fig. 1.10 that this unit vector is tangent to the path in the direction of increasing values of s. Thus, the vector t(s) defined by (1.61a) and t. t = 1 (1.61b) is called the tangent vector of C. We must insist that C be continuous without corners so that t(s) is defined uniquely at each point on C. Recalling that the scalar components of a unit vector are the direction cosines of the vector, we see that dxkjds are the three direction cosines of the tangent to the path at P. These results are easily visualized for a plane motion, and it may be helpful for the reader to study the equations ( 1"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003893_0301-679x(83)90004-x-FigureI-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003893_0301-679x(83)90004-x-FigureI-1.png",
+        "caption": "Fig I Test samples o f (a ) f lat and (b ) spherical laminates",
+        "texts": [],
+        "surrounding_texts": [
+            "Properties and prospective applications of ultra thin layered rubber-metal laminates for limited travel bearings E. I. Rivin*\nLimited and/or oscillating motions represent the most severe operating conditions for conventional bearings, both sliding and antifriction. Thinlayered rubber-metal laminates seem to be ideal substitutes for conventional bearings for oscillating motions. This paper describes experimental investigations of the compression and shear properties of flat and spherical laminates. The very high compression stiffness and strength of the laminates are accompanied by low shear stiffness. Strong non-linearity of the hardening type in compression is accompanied by weak non-linearity of the softening type in shear. Substantial non-linearity in compression starts as early as at relative compression 0.001. Applications of thin-layered laminates for compensating couplings, U-joints, gears, vibration isolators and impact cushioning in joints of mechanisms are described. Expressions have been derived for efficiency of couplings and joints equipped with laminates\nKeywords: bearings, I/m/ted travel bearings, rubber-metal laminates\nConventional machine design textbooks are based on the use of external friction to formulate important relationships in mechanisms, such as expressions for energy efficiency (eg cylindrical joints of limited displacement, gears, U-joints, couplings), conditions for self-locking in wedge-type mechanisms, etc. In many of these mechanisms only limited motion occurs in the joint, as is the case in U-joints, Oldham couplings, and gear meshes. Accordingly, conditions for full hydrodynamic lubrication do not develop in such joints. Near the points where the relative velocity of the contacting surfaces changes direction, the friction characteristics are similar to dry (Coulomb) friction. In other areas of the engagement cycle there is a mixture of boundary and elastohydrodynamic lubrication (ehl). Occurrences of dry and/or boundary lubrication conditions lead to reduced energy efficiency and to increased levels of vibration and noise in the mechanisms caused by the impulsive character of friction forces at the point of reversal of relative velocity in a joint or in a gear mesh. Intensive heat generation causes thermal expansion of components and the possibility of jamming; thus, initial clearances are required. An efficient lubrication system, together with very hard contacting surfaces, is required to reduce wear, etc.\nRecently, it has been demonstrated that it is possible to replace external friction in some structural joints by the judicial application of elastomeric materials with restricted free surface area, mostly in thin-layer form 1-4 . Such an approach could have a great impact on design engineering. Some of the prospective advantages of thin-layered elast 9- mers in mechanism applications are: substantial reduction of energy dissipation (ie improvement in efficiency); elimination of the lubrication system and the dirt-protection (sealing) system; reduction in vibration and noise generation\n*Department of Mechanical Engineering, Wayne State University. Detroit, M148202, USA\nand transmission;easing of material, heat treatment and machining specifications for contacting surfaces; elimination of clearances in joints.\nHowever, these bright prospects have not yet materialized fully, largely because of a lack of information on the basic properties of thin-layered elastomeric materials, especially of the most promising ultrathin-layered materials where the thickness of a single elastomeric layer is in the range 0.01-0.50 mm.\nThis paper presents experimental data on properties of ultrathin rubber-metal laminates, together with discussions of some possible applications. The discussion in this paper is mostly confined to the static properties of the laminates. Many other issues, such as thermal and fatigue resistance, optimal material selection etc, certainly have to be addressed by future researchers. However, since energy losses in the laminated connections are, as will be shown below, several orders of magnitude less than in the conventional connections, then both the heat dissipation problem and the closely related (in elastomers) fatigue problem do not seem a priori to be critical.\nExperimental arrangement to determine stiffness characteristics of ultrathin-layered rubber-metal laminates Two types of laminates have been tested: (a) fiat and (b) spherical (Fig 1). The laminates consisted of n layers of metal and n - 1 layers of rubber. Metal layers in the experimental laminates were made of 0.05 mm brass foil or 0.1 mm steel foil; rubber was bonded to the metal layers.\nThe issues considered when selecting the rubber were:\n(a) A structural laminate should have the maximum possible compressive stiffness k z to assure minimum dimensional variation under load. On the other hand, the shear stiff-\n0301-679X/83/010017-09 $03.00 \u00a91983 Butterworth & Co (Publishers) Ltd 17",
+            "ness kx should be as low as possible for better compensation of misalignment and/or lower resistance to the working displacement. Thus, a maximum value for the ratio kz /k x is desirable.\n(b) Compressive stiffness k z depends highly on the deviation of Poisson's ratio from v = 0.5 - the ultimate value for a volumetric incompressible material. The ratio v is closest to 0.5 for soft rubber and the deviation increases with increasing rubber durometer H; eg for chlorophroe rubber v = 0.4997 fo rH = 0.4990 fo rH = 751 .\n(c) The compressive stiffness k z of thin-layered laminates increases for harder rubbers more slowly than their modulus. This is because higher hydrostatic pressures in the harder rubber cause noticeable stretching of the metal interleaves, equivalent to limited slippage on the bonded surfaces.\n(d) Shear stiffness kx does not depend on factors (b) and (c) and depends only on shear modulus G.\nOn the basis of these factors, soft rubber (H = 42*) was the main choice for this work. However, two control samples were fabricated and tested using rubber with H = 58* and H = 75*. The parameters of the type (a) flat samples tested are listed in Table 1, and of the type [b) spherical samples in Table 2.\nFlat samples were tested in compression to determine compression stiffness k z versus specific compressive load Pz, and in shear to determine shear stiffness k x versus specific shear loadPx. Spherical samples were tested in compression, in shear around the x axis (k= in a-direction, Fig lb), and in torsion around the z-axis (k-/in ~,-direction, Fig lb).\nTests were performed on universal precision testing machines - an Instron TT-DM (0.1 MN maximum capacity) and TT-KM (0.25 MN maximum capacity). These machines have very high structural stiffness and sensitive extenso. meters. However, both parameters were found to be inadequate for testing ultrathin-layered laminates in compression. Ultra-sensitive displacement transducers (Fig 2(a)) were used to eliminate the influence of the testing machine structural stiffness on test results. The transducer was\nmachined from a solid block of low-hysteresis (spring) steel, thus eliminating friction in the joints which could affect transducer sensitivity. Four strain gauges provided compensation for machining asymmetry and thermal effects. Using good strain-gauge amplifiers, these transducers can reliably measure displacements as small as 0.05-0.1/am. Standard extensometer amplifiers were used with the testing machines to give resolutions of 0.25/am actual displacement per mm on graph paper. Signals from two transducers (Fig 2Co)) were averaged to reduce the adverse influence of machining errors and of the asymmetry of motion of the left and right driving screws of the testing machines. The shear stiffness of the flat samples were measured under variable compression. To alleviate friction effects, a standard set of rollers in a cage and hardened and ground end plates (Fig 3(a)) were used to apply compression force Pz. In measuring shear ka and torsional k~/stiffness of the spherical samples, two identical samples with intermediate solid double-convex lens-shaped block were used for a similar purpose (Fig 3(b)). Compression load on the spherical samples was applied through solid concave lens-shaped blocks. When the double-sample set was used, as in Fig 3, the measured value of compression stiffness was kz]2, and of shear and torsional stiffness, 2k= and 2k7, respectively.\nExperimental results\nCompression stiffness\nCompression stiffness versus specific compression load Pz = Pz]A, where A is the surface area of the sample, is shown in Fig 4 in a double4ogarithmic scale. Compression stiffness is expressed in terms of differential (local)\n= Hardness was measured on standard cylindrical samples (2.54 cm diameter, 1.27cm high) made from a given rubber. The actual hardness of a thin layer cannot be directly measured,\" it can be different from the hardness of standard samples made of the of the same rubber blend. The actual hardness can be judged by the measured shear modulus shown in Fig 6.\n18 TRI BOLOGY international February 1983",
+            "compression modulus E referred to the total thickness of rubber in the sample hr:\nApzhr E - (1)\nAz\nand was calculated from the load-deflection diagrams. Here Az is the increment in compression deformation caused by an increment &Pz of the specific compression force. With such a format of stiffness expression, data plotted in Fig 4 does not depend on n and A. As shown in Table 1, all the samples have different values of surface area. The comparison of the properties of such samples in a dimensionless format, as given in Fig 4, became possible after it was shown experimentally that, with the shape factor S > 20, compression stiffness is proportional to the loaded surface area of the sample (the shape factor S is the ratio of one loaded surface area to the force-free surface area of the sample). The nonlinearity starts from the smallest deformations which could be measured, in some cases from e = Az/hr = 0.001. Modulus E increases as much as one decimal order of magnitude when compression load increases about 1.5 decimal orders of magnitude. The effect is similar (but much more pronounced) to the nonlinearity for laminates with rubber layers 2--4 mm in thickness described in Ref 5.\nSamples with metal layers made of brass failed at the specific compression load Pz = 45 MN/m 2 and those with steel metal layers at Pz > 250 MN/m 2 . In all cases, failure was due to rupture of the metal layers; the rubber remained intact. This suggests that, by using stronger metals for the metal layers,\nI000\n500\nt~ 200\nIOO\n50\nN o (Toble I)\nI-o 2-0 :5-~' 4 - 0 5 - - A 6--w 7--z~ 8 - - I 9 - - 0\ni I I i I l l I ~ I I ~ I n ~1 1 5.0 I0.0 2 0 5 0 I00 2 0 0\nPz ' MN/m2\nFig 4 Compression modulus of the ultrathin-layered rubber-metal laminates\nthe compression strength of thin-layered laminates could be substantially increased. It is worth mentioning that the maximum (destructive) compression load did not depend in these experiments on rubber durometer.\nFrom the data in Fig 4, some important conclusions can be reached about the properties of laminates:\n\u2022 Thin-layered rubber-metal laminates in compression demonstrate a very substantial nonlinearity of the hardening type.\n\u2022 Compression modulus E depends monotonously on thickness t r of a rubber layer for a given durometer (the thinner the layer, the higher the modulus). The dependence is very steep (see Fig 5, data for Pz = 30 MN/m 2). \u2022 Compression modulus E increases with the increasing durometer of the rubber, but not as fast as the shear modulus G of the rubber. This is clear from Fig 5, where ratios E/G are plotted. This conclusion cannot be considered as final because it is based on limited data. The effect might be caused by a more pronounced contribution of metal stretching with increased rubber durometer, as well as by lower values of v for the higher durometer rubbers.\n\u2022 Absolute values of compression stiffness for thin-layered laminates are very high. Thus, for sample 7 at Pz = 100 MN/m 2 , E = 1800 MN/m 2 , which is equivalent to 1/am deflection per 1.06 MN/m: compressive force. This is in the same range as the values of contact stiffness in a joint between two flat, ground-steel surfaces ~'7 .\nShear stiffness\nShear stiffness was expressed in t e r m s o f shear modulus G and is plotted in Fig 6 versus s h e a r f o r c e Px. Analogously t o F i g 4 , s h e a r modulus was calculated in a differential format:\nZ~O x \"h r G - - - (N/m 2) (2)\nAx\nTRI BO LOGY international February 1983 19"
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0000517_1616-8984(199607)1:1<1::aid-seup1>3.0.co;2-6-Figure1-6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000517_1616-8984(199607)1:1<1::aid-seup1>3.0.co;2-6-Figure1-6-1.png",
+        "caption": "Figure 1-6. Mode beat or difference interferometer (according to [305]). TM and TE modes are coherently excited by a laser and their phase difference can be measured by two Wollaston prisms and four detectors (D) given by the relationship shown on the figure.",
+        "texts": [
+            " Guided radiation will propagate in these two arms with a different phase velocity, leading to a phase shift which can be measured behind the chip as an intensity depending on the refractive index of the superstrate medium on top of one of the arms, the wavelength, the interaction length, and the waveguide properties. A special application is the Young interferometer, the principle of which is demonstrated in Figure 1-5. The refractive index of liquids and gases can be determined by refractometry. The set-up was tested with sugar solutions and test gases (CO2, N2) [78]. The other approach to using interference is realized in the mode beat or difference interferometer using a planar (film) waveguide [410]. Its TE and TM modes interact differently with an analyte (Figure 1-6). Their phase difference can be measured. This instrument was investigated also by Hoffmann-La Roche [220] and applied to bioanalytical problems [161]. This principle can be realized by two other approaches: 1.2 Principles of Optical Transduction 13 (a) a bent fiber or a bent step-index single-mode fiber half-coupler [281]; or (b) a D-shaped fiber as a type of polarization interferometer [244]. A review of interferometers and the light sources used is given in [21]. For further The evanescent field extends into a layer next to a waveguide and can couple to modes of an adjacent second waveguide"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002661_s0013-4686(03)00227-5-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002661_s0013-4686(03)00227-5-Figure4-1.png",
+        "caption": "Fig. 4. Cyclic voltammograms of the PdPCNF/Al electrode in 0.5 M nitrate solution of (a) Ba, (b) Ca, (c) Mg and (d) K, potential scan rate: 150 mV s 1.",
+        "texts": [
+            " On the basis of the results obtained from the similar studies for the other alkali metal cations and ammonium we concluded that the PdPCNF film shows the following surface affinity ranking: Cs /Rb /NH4 /K / Na /Li . This ordering parallels the observed change in E0? or thermodynamic tendency of the film for cations, due to the size of the hydrated cation and thus its ability to enter into the crystal lattice during the electrochemical reduction process as follows: PdII[FeIII(CN)5NO] M e 0 MPdII[FeII(CN)5NO] Similarly the effect of alkaline earth metal cations on the electrochemical behavior of the PdPCNF/Al electrode was investigated. As seen in Fig. 4, the cyclic voltammograms of the PdPCNF/Al electrode obtained in aqueous solutions of alkaline earth metal cations: Mg2 , Ca2 and Ba2 with 0.5 M concentration, exhibit a broadened shape at more negative peak potential. This may be attributed to the large radii of the cations. Upon addition of KNO3 to such solutions, peak potential steadily shifted to positive direction and the K -associated peak appeared. 3.2.3.3. Charge transfer rate in the film. For a PdPCNF/ Al electrode, the peak-to-peak separation potential (DEp /Epa /Epc) of the cyclic voltammogram recorded for scan rates up to 200 mV s 1 was a maximum at 50 mV in the presence of KNO3 as supporting electrolyte"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002333_a:1025991618087-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002333_a:1025991618087-Figure2-1.png",
+        "caption": "Figure 2. The model of interaction between the feet and the trampoline bed.",
+        "texts": [
+            " Let us denote that a single somersault begins/ends the instant the athlete drops on the trampoline and touches the bed with his feet. The jump can then be divided into two phases: the support phase when the feet push on the bed, and the flying phase when the trampolinist does not touch the bed. During the flying phase, the only external forces on the system are the gravity forces, and in the support phase the reaction from the trampoline bed on the feet (segment 4) must be added. The latter are modeled in terms of the horizontal (Rx) and vertical (Ry) reactions, and the moment (MA) with respect to the ankle joint A (Figure 2). The derivation of equations of motion for the above modeled system belongs to standard multibody codes, often called joint coordinate method [11], well described in the literature; see also e.g. [4, 9, 12, 13]. Here we use an extended version of this minimal-form formulation of multibody dynamics, called augmented joint coordinate method, which leads to the motion equations identical with the result of the previous method, and yields in addition an efficient scheme for the determina- tion of joint reactions",
+            " In addition, the distance between the joints H and S is ls = 0.486 m. As said, the trampoline bed was treated as a weightless canvas with some stiffness and damping characteristics. We measured these characteristics in the way shown in Figure 4. The vertical stiffness was estimated by measuring the static response yA to the load G (Figure 4a). Then, for a given vertical deflection yA, the response xA to a horizontal force Px (Figure 4b) and the response \u03b8A to a moment MA = Gd cos \u03b8A (Figure 4c) were measured (see also Figure 2). Some results of the measurements are shown in Figure 5. As it can be seen, in the vertical direction the trampoline behaves as a hardening spring, and the results do not significantly depend on how far from the bed center the load is placed. The horizontal force Px shows linear dependency on xA, while its dependency on yA is negligible. Finally, for a given yA, the dependence of MA on \u03b8A is linear, and the stiffness coefficient k\u03b8 increases (linearly) in function of yA. The damping characteristics of the trampoline were estimated as follows",
+            " To achieve high precision of determination of feet positions x\u2217 Ad(t), y \u2217 Ad(t) and \u03b8\u2217 Ad(t) during this phase, required to precisely estimate the reactions from the bed according to Equation (18), we used a shadow registration method and the assisted high-precision equipment described in [16]. The cubic spline interpolation was used to generate continuous xAd(t), yAd(t) and \u03b8Ad(t) consistent with x\u2217 Ad(t), y\u2217 Ad(t) and \u03b8\u2217 Ad(t), and these analytically given functions were then differentiated to obtain x\u0307Ad(t), y\u0307Ad(t) and \u03b8\u0307Ad(t) as used in Equation (18) to determine Rxd(t), Ryd(t) and M\u03b8d(t) (Figure 2). The estimated reactions from the trampoline are seen in Figure 9. The inverse dynamics problem for the system at hand aims at determining the applied torques of muscle forces in the joints that result in the specified (observed) motion. The nature of the stunts and the rules the human body is maneuvered and controlled can be studied this way. The dynamic simulation (direct dynamics problem) [4] in which the calculated control is used as the input signal is then studied. For the same biomechanical model used, the outputs of the direct dynamics simulation should approximately match the movement pattern that served as input to the inverse dynamics problem"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003764_bf02953383-Figure12-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003764_bf02953383-Figure12-1.png",
+        "caption": "Fig. 12",
+        "texts": [
+            " 8 Gap width Stiffness Load Flow rate Gap type N 1O\u00b7-3N/pm N N gr/spm -~ -m~ m'\u00b7 p.pm Parallel 10 16.6 9.0 460 0.25 0.32 5 4.6 2.5 510 0.28 0.18 Convergent 10 64.4 35.1 870 0.47 0.45 hv =21pm 5 77 42.0 1240 0.768 0.27 Compliant 10 52.2 28.4 670 0.36 0.42 hv =21pm 5 130 70.8 1130 0.62 0.27 tion for relatively large gap widths. The stiffness, load capacity and gas flow are compared in Table l(nominal diameter =98mm, pad angle =1.11rad, pad width =60mm, diameter restrictor=cO.9mm, supply pressure=0.7M Pal. The result of this theoretical approach is given in Fig.12a and b. Bearings with parallel gaps below 20 lim tum out to be statically unstable even for small size irregularities(hb =2. Slim). This is illustrated in Fig.12a where, in some cases, the stiffness of the bearing(slope of force displacement curve) changes its sign with the gap width. The force-displacement characteristics for convergent gap bearings, on the other hand, do not show any region of negative stiffnesses for irregularities remaining smaller than the gap difference hv . The passage of this kind of irregularity results, in this case, merely in some relatively small change in the gap width. 3.2 Influence of Bearing Surface Irregularities Bearings with parallel gaps are quite sensitive to irregu larities (scratches, bumps, etc",
+            " The gap width remains unchanged as well. However, as soon as the bearing surface irregularity or \"bump\" reaches the restrictor area, an instant drop of the load carrying capacity occurs, yielding a sudden mechanical contact of both bearing surfaces. Bearings with convergent gap geometries are far less sensi tive to this disturbing phenomenon. To quantify the sensitiv ity of various bearing geometries with respect to bearing surface irregularities, two particular types of irregularity have been selected as shown in Fig.12. Using a model insur ing viscous gas flow and neglecting throttling at the entrance, the load force is evaluated for various gap widths ho as well as for a set of different heights of the bumps hb \u2022 86 R. Snoeys and F. AI-Bender Theoretically, Kf(w) was determined by solving the time dependent Reynold's equation for a fixed conical gap geome try, by a predictor-corrector method. The results obtained from the theoretical model were experimentally verified by means of a test set-up as shown in Fig"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000299_301-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000299_301-Figure1-1.png",
+        "caption": "Figure 1.",
+        "texts": [
+            " Firstly, the force on the element of conductor is at right angles to the direction of the magnetic field instead of being along it, and secondly, the force depends on the direction of the current and consequently the element of conductor cannot be treated as a point but must have finite extension in the direction of the current, A new treatment of electric and magnetic induction 581 To measure this force we suppose the element ds of conductor carrying a current i to be placed in the medium where it will occupy a small evacuated cylindrical volume making an angle 0, say, with the direction of the magnetization (figure 1). Any force on it will cause it to move in a direction which will be perpendicular both to the element itself and to the magnetic field, and in order to measure it we imagine the medium removed in the direction of the force so that we have a thin rectangular-shaped cavity, one side being finite and parallel to the element of conductor, another finite and parallel to the direction of the force, and the third, perpendicular to the other two, can be made as small as we please. We could call this force per unit current per unit length of conductor the Internal Electromagnetic Force"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002276_fld.640-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002276_fld.640-Figure2-1.png",
+        "caption": "Figure 2. Representation of the (s \u2212 1)th and sth element of the \u2018pendulum.\u2019 Note that each element has a sti ness coe cient, Ks, and a damping coe cient, Cs, associated with it.",
+        "texts": [
+            " Fluids 2004; 44:313\u2013330 We assume that the lament is of total length L and has total mass is M . Furthermore, we assume that it is composed of N equal length, homogeneous, lament elements. Thus, each element is of length l\u0303=L=N and of mass m\u0303=M=N . The elements are xed to one another at their hinge (or fulcrum) points. The whole lament (or ag) is thus assumed to be approximated by a form of an \u2018N -tuple pendulum\u2019 in which each hinge, denoted by a subscript, s, has a positive spring sti ness coe cient, K\u0303 s, and a positive damping coe cient, C\u0303s, associated with it. Figure 2 shows a representation of (s \u2212 1)th and sth elements of the \u2018pendulum\u2019. In order to model the motion of the \u2018N -tuple pendulum\u2019, we form a system of equations using Lagrange mechanics in similar manner to that of Fenlon et al. [5, 6]. We must therefore determine the kinetic and potential energies and the non-conservative forces acting on the elements. It is relatively straightforward to show that the kinetic energy T of a lament of N such elements is given by T = 1 2 m\u0303l\u0303 2 N\u2211 i=1 i\u22121\u2211 j=1 i\u22121\u2211 k=1 \u0307j\u0307k cos( j \u2212 k) + 1 2 m\u0303l\u0303 2 N\u2211 i=1 i\u22121\u2211 j=1 \u0307i\u0307j cos( i \u2212 j) + 16 m\u0303l\u0303 2 N\u2211 i=1 \u03072i (4) where s is the angle subtended by the element, s, with respect to the x co-ordinate axis",
+            " If the length of the lament is altered the corresponding non-dimensional coe cients also change. Most notably if the length L is reduced then the lament becomes e ectively \u2018sti er\u2019 and more \u2018damped\u2019. Conversely by increasing the length the lament becomes \u2018soft\u2019 and underdamped. We note that the non-dimensional damping parameter Cs changes non-linearly with length. Copyright ? 2004 John Wiley & Sons, Ltd. Int. J. Numer. Meth. Fluids 2004; 44:313\u2013330 Filament boundary and initial conditions With reference to Figure 2 implicit in the Euler\u2013Lagrange equation set is the fact that 0 = 0 and plays no part in the calculations although 1 may be non-zero. We should note however that the potential in the sti ness terms would wish to make 1 \u2192 0, that is along the direction of ow. It is an interesting test to see whether alternative vortex formulations could be formed when a zero imposition is placed on 1. Early indications with heart valve simulations studies suggest that the e ect is not large. It is crucial to impose initial conditions which do not lie in or too close to either of the \u2018attracting basins\u2019 (namely, the oscillating and non-oscillating modes) when determining the interface between stationary and oscillatory states"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003231_491596-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003231_491596-Figure1-1.png",
+        "caption": "Fig. 1.\u2014Schematic of disk reprocessing in X-ray pulsars. The hard (power-law spectrum) X-ray beam sweeps around and illuminates the accretion disk, which reradiates a soft X-ray (blackbody) component. The observer sees pulses from both the power-law and blackbody components, but these differ in pulse shape and phase.",
+        "texts": [
+            " (2005) conclude that the occulation of the source is caused by the inner regions of the disk near the magnetospheric radius 108 cm. 1.2. Disk Reprocessing and the Soft X-Ray Emission In Her X-1, reprocessing of the hard X-rays from the neutron star by the inner accretion disk produces a soft (<1 keV) X-ray component that pulses out of phase with the hard (>2 keV) pulses (e.g., Endo et al. 2000; Ramsay et al. 2002). Thus, the X-ray beam from the neutron star acts as a \u2018\u2018flashlight\u2019\u2019 that illuminates the inner disk (Fig. 1). Many luminous X-ray pulsars, including LMCX-4 and SMC X-1, have similar soft spectral components that are also likely caused by disk reprocessing (Hickox et al. 2004). We expect the flux of such a soft component to pulsate as the pulsar beam sweeps around and illuminates the disk. The soft pulses will have the same period as those from the hard X-ray beam but will have a different shape and relative phase. Moreover, precession of the accretion disk will change the observer\u2019s view of the inner region, and so the shape and phase of the reprocessed component should vary with superorbital period"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002495_12.497801-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002495_12.497801-Figure1-1.png",
+        "caption": "Fig. 1 Schematic arrangement of X-ray transmission imaging system and high-speed video camera for simultaneous observation ofkeyhole behavior, bubble and porosity formation, and melt flow and plasma/plume behavior during laser welding.",
+        "texts": [
+            " 4831 (2003) \u00a9 2003 SPIE \u00b7 0277-786X/03/$15.00 281 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 11/20/2012 Terms of Use: http://spiedl.org/terms butt-joint surface on porosity formation. The effect of pulsed laser welding conditions on porosity formation was also examined with a high-quality 5.5 kW CO2 laser. The formation behavior of a keyhole, bubbles and pores was observed during laser welding by in-situ observation system with microfocused X-ray. The system36 is schematically represented in Fig. 1. The welding phenomenon was observed by high-speed video cameras (the maximum imaging speed: 400 f/s and 8,000 f/s) or ultra-high speed video camera (the maximum imaging speed: 40,500 fls). The frame speeds used chiefly to clearly observe bubble motion are 200, 1000 or 4,000 f/s. Laser welding was performed in He, Ar, Ar-He mixture and N2 gas shielding using a pipe and atmosphere utilizing a box. The laser power and welding speed used mainly are 3 or 10 kW and 10 or 25 mm/s, respectively. Fractured surfaces of laser weld metals were observed by SEM (Scanning Electron Microscope) to reveal the \u2014\u20141 characteristics of pore inside surfaces, and the surfaces were analyzed with EDX (EDS: Energy Dispersive X-Ray Spectrometer) or EPMA (Electron Probe Micro-Analyzer) to know the distribution of Al, Mg, 0, etc"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002755_j.triboint.2004.12.003-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002755_j.triboint.2004.12.003-Figure4-1.png",
+        "caption": "Fig. 4. Evolution of pressure, distortion of the lip and thickness for",
+        "texts": [
+            "0 node becomes non-active when DR0 node becomes active End While residues (h, p)O3 (Newton-Raphson process) Computation of residues of equations (Reynolds and load balance) If first loop or rate of convergence too low: Computation and triangulation of the Jacobian matrix Resolution of obtained system Correction of p pressure and displacement parameters Calculation of elastic displacement hm Modification of the film thickness h End End Computation of Temperature, Viscosity and Young\u2019s modulus End Editing of results: pressure, thickness of the film, leakage, power loss,Temperature. roughness model (a, nyZ5, nxZ1), and for 2000 rpm. End of algorithm Results have been generated for typical data with the base parameters in Table 1. The roughness models of the lip are defined by Eqs. (14a)\u2013(14c). The calculated characteristics are: film thickness field, pressure field, power loss, leakage, and average lip temperature. To illustrate the results, Fig. 4 shows the evolution of the fields of pressure, lip distortion and thickness for one rotational frequency for two periods. Figs. 5 and 6 show the evolution of minimal and average thickness according to rotational frequency, for different mathematical roughness models. Whatever the model under study, the speed of rotation has only a slight influence on the thickness of the lubricant film. The modification of the number nx or ny of defect period within every model alters the thickness slightly differing from one model to another"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001191_0005-1098(93)90125-d-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001191_0005-1098(93)90125-d-Figure1-1.png",
+        "caption": "FIG. 1. Environment with a mobile robot and multiple moving obstacles.",
+        "texts": [
+            " A nominal trajectory is assumed to be known from off-line planning. The main idea is to change the velocity along the nominal trajectory so that collisions are avoided. A feedback control is developed and local asymptotic stability is proved if the velocity of the moving obstacle is bounded. Furthermore, a solution to the problem of inverse dynamics for the mobile robot is given. Simulation results verify the value of the proposed strategy. THE PROBLEM OF efficiently planning the motion of a mobile robot in an environment containing moving obstacles (Fig. 1) is difficult and computationally intensive. Although it has been stated as early as 1984 (Freund and Hoyer, 1984) ad hoc solutions were given (Liu et al. (1989); Tournassoud (1986)). Reif and Sharir (1985) gave an algorithmic solution to the problem but they were restricted to some categories of shapes of objects and their approach is not suitable for an on-line implementation. Search based approaches for solving the above problem have also been presented in Fujimura and Samet (1990) and Shih et al"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001074_la010751u-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001074_la010751u-Figure1-1.png",
+        "caption": "Figure 1. Film trapping apparatus. Basic scheme of the setup, allowing experiments with a freely moving air-water meniscus. A vertical glass capillary 1 is partially immersed in a vessel 2, containing water with dispersed colloidal particles. One can regulate the air pressure inside the capillary by means of a pressure control system in order to blow out the inner airwater meniscus. The gas-phase pressure control system consists of three-way stopcock 3, two syringes 4 (small and large), precise pressure sensor 5, and damping system 6, all connected with tubing. Micrometer screw 7 and spring 8 allow the precise pressure regulation by the smaller syringe. The capillary is supported by positioning device (not shown) mounted on a microscope stage 9. When the meniscus approaches the vessel\u2019s bottom at a distance smaller than the particle diameter, some particles remain sandwiched between the interface and the glass substrate (see the magnified part of the scheme). One observes the particles from below through the substrate by inverted microscope with objective 10.",
+        "texts": [
+            " The title of this section is \u201cPrinciples of Operation\u201d, because it is meant to provide the researchers information about what could be expected in experiments, depending on the properties of the system under study, and the way one can control their occurrence. In this section we present also several experimental results, which are compared with the theoretical predictions. As a demonstration of the new method, in Section 4, we have applied it for determination of the so-called \u201cdrop entry barrier\u201d (critical capillary pressure to drop entry). This is a quantity, which characterizes the ability of small drops to pierce through the air-water interface. The apparatus is shown schematically in Figure 1. A vertical glass capillary tube 1 (of diameter of a few millimeters) is held a small distance apart from the flat bottom of a glass vessel 2. The lower capillary end is immersed in the liquid in the vessel. A positioning device (not shown) supports the capillary. This device allows X, Y, Z movement. An additional device allows adjustment of the capillary tilt so that the capillary tip can be set parallel to the substrate. The liquid in the vessel includes dispersed colloidal particles (e.g., emulsion droplets, solid particles, or biological cells)",
+            " The upper end of the capillary is connected by a three-way stopcock 3 to a gas-phase pressure control system consisting of two syringes 4, a precise pressure sensor 5, and a buffer volume as a pressure damping system 6. The two syringes, large and small, are for rough and precise pressure control, respectively. Micrometer screw 7 with spring 8 ensures precise motion of the piston of the small syringe. The damping system reduces pressure fluctuations arising from irregular movement of the syringe pistons and pressure drifts due to temperature gradients along the system tubing. This system consists of a thermostatically isolated flask, 6, containing water (see Figure 1), which is in contact with gas in the rest of the system through a vertical tube immersed in the flask. Besides stabilization of pressure, the damping system ensures saturation of the internal air phase with water vapor. This minimizes evaporation from the air-water interface shown magnified at the side of Figure 1. The positioning device with attached capillary and the vessel are mounted on the stage, 9, of an inverted microscope. The stage is equipped with the standard microscope X, Y, Z translators, and has an opening for observation from below through the glass bottom of the vessel by an objective 10 (Figure 1). As mentioned in section 1, FTT-gentle allows one to trap particles at virtually zero capillary pressure, and consequently to precisely increase the pressure. This is achieved by making the interface flat before it touches the particles. (See also the explanations in section 3b.) One possible way to do this is to attach the interface at the edge of the capillary and to control its shape by changing the air pressure inside the capillary. The stable attachment of the air-water interface at the capillary edge, in the case of surfactant solutions, which improve the wettability of the capillary, is a difficult task"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001292_s0014-827x(03)00182-4-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001292_s0014-827x(03)00182-4-Figure1-1.png",
+        "caption": "Fig. 1. Schematic diagram of the electrochemical flow cell used in the amperometric measurements in flow injection system. (A) 1. Polyurethane resin block; 2. reference electrode (Ag/AgCl); 3. platinum electrode; 4. carbon paste electrode; 5. polyethylene tubing (flow). (B) Carbon paste packed into an electrode body.",
+        "texts": [
+            " In this paper, a FIA procedure with amperometric detection for the determination of dipyrone in pharmaceutical formulations is proposed, using a carbon paste electrode. The influence of several parameters (potential, pH and interference) besides the parameters of the flow system was studied. Cyclic voltammetric and amperometric measurements were carried out with an AUTOLAB PGSTAT-30 (Ecochemie) controlled by a personal computer using the GPES 4.8 software. The measurements were performed in a three-electrode flow cell configuration (Fig. 1) using a carbon paste electrode (CPE) as working, an Ag/AgCl as reference and a platinum auxiliary electrodes (f /3 mm disk). For cyclic voltammetry the potential was ranged from 0.0 to /1.3 V versus Ag/AgCl at a scan rate of 10 mV s 1, stationary solutions were used in such case. The current measurements were performed using the GPES software (Ecochemie) by chronoamperometry (constant potential). The body of the electrochemical flow cell (Fig. 1A) was fabricated with polyurethane resin from vegetable oil [14]. The effective volume of the flow cell was of 77 ml. All solutions were prepared using water from a Millipore Milli-Q system. All chemicals were of analytical reagent grade and were used without further purification. The supporting electrolyte used for all experiments was a 0.1 mol l 1 sodium acetate solution (pH 7.3). A 0.01 mol l 1 dipyrone stock solution was prepared daily by dissolving C13H16N3NaO4S.H2O (Merck) in 100 ml of the same sodium acetate solution and used to prepare dipyrone reference solutions in 0",
+            " The content of dipyrone in these samples was determined by the standard addition method and compared with the iodimetric standard procedure [4]. Carbon paste electrode was prepared by carefully mixing with 75% (m/m) of graphite powder (1 /2 mm particle size, Aldrich) and 25% (m/m) of mineral oil (Aldrich). This resulting mixture was submitted to magnetic stirring in a beaker (50 ml) containing 20 ml of hexane. The final paste was obtained by the solvent evaporation. The carbon paste was packed into an electrode body (see Fig. 1B), consisting of a polyethylene cylindrical tube (o.d. 7 mm, i.d. 4 mm) equipped with a stainless steel rod serving as an external electric contact. Appropriate packing was achieved by pressing the electrode surface (surface area of 0.126 cm2) against a filter paper. The electrochemical cell was inserted in a one-channel flow injection system schematically represented in Fig. 2. The system was assembled with a peristaltic pump (Ismatec, model 7618-40, Switzerland) and a manual injector made of Perspex\u2020 with two fixed sidebars and a sliding central bar [15]"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001768_b109326f-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001768_b109326f-Figure1-1.png",
+        "caption": "Fig. 1 Manifold for the determination of cyanide. PP, peristaltic pump; IV1 and IV2, injection valves; PM, pervaporation module; m, membrane; ISE, ion-selective electrode; RE, reference electrode; W1, W2 and W3, waste.",
+        "texts": [
+            "01 mol l21 NaOH. The sulfide solution was standardised by titration before use. All these standard solutions were stored at 4 \u00b0C in dark glass bottles. The solution used as the donor stream contained 0.3 mol l21 HNO3 and 0.1 mol l21 Pb(NO3)2 (Panreac). Sodium hydroxide solution (0.1 mol l21) was used as the acceptor stream. One four-channel Gilson Minipuls-3 peristaltic pump, two Rheodyne Model 5041 injection valves and polytetrafluoroethylene (PTFE) tubing of 0.8 mm id were utilised to build the manifold (Fig. 1). The photodissociation reactor consisted of a reaction coil (1.25 m 3 0.8 mm id) around a 20 W UV lamp (Philips, Eindhoven, The Netherlands). The cyanide-selective electrode (Model 6.0502.130, Metrohm, Hrisau, Switzerland) was fitted to the upper part of the pervaporation module facing the acceptor side of the gas-diffusion membrane. An Ag/AgCl reference electrode (Metrohm Model 6.0233.100) was located in a methacrylate flow cell made in the laboratory, which was placed in the loop of an auxiliary valve (IV2 in Fig. 1). A Model 692 pH/ion meter (Metrohm) was used for monitoring the potential. A pervaporation cell designed in our laboratory18 and PTFE membranes (47 mm diameter and 1.5 mm thickness) from Trace (Braunsweig, Germany) were also used for constructing the manifold. Proposed procedure for the determination of cyanide The injection of either the sample or the standard solution is realised by the injection valve IV1 (see Fig. 1) into a donor solution stream [0.3 mol l21 HNO3\u20130.1 mol l21 Pb(NO3)2] and is led through the 1.25 m photodissociation reactor for decomposition of stable cyanide complexes, thus obtaining free cyanide, which in the acidic medium of the donor solution forms hydrogen cyanide. This volatile species is led to the lower chamber of the pervaporation cell. The HCN evaporates to the air gap between the donor solution and the membrane and diffuses through the hydrophobic membrane to the upper chamber of the pervaporation cell, where it is collected",
+            " The upper manifold includes the acceptor chamber of the pervaporation cell, which is located in the loop of an auxiliary valve (IV2). This valve is filled with the acceptor solution, which contains 0.1 mol l21 NaOH. This acceptor stream is halted for 50 s by turning IV2 to the filling position, and the increase of the potential due to the accumulation of cyanide in the upper chamber of the pervaporation cell is registered by the cyanideselective electrode whose active surface faces the acceptor side of the membrane. The analyte signal obtained in an FI manifold such as that shown in Fig. 1 is affected by chemical (concentration of nitric acid and sodium hydroxide), flow injection (injection volume, length of the reaction coil and flow rate) and pervaporation variables. The optimisation of these variables was performed using the univariate method. A solution of 0.5 mg l21 cyanide prepared from the 100 mg l21stock standard solution by appropriate dilution with 0.01 mol l21 NaOH solution was used as the sample in the optimisation study. Table 1 shows the ranges over which each variable was studied and the optimum values found"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002408_jsvi.2001.3873-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002408_jsvi.2001.3873-Figure1-1.png",
+        "caption": "Figure 1. The tripod-ball sliding joint.",
+        "texts": [
+            "ects of clearance size and driving speed have also been investigated by these two means. Besides, the basal system and active system are de\"ned to obtain a set of consistent equations of motion for both free-#ight and followingmode, rather than two di!erent sets of 0022-460X/02/$35.00 2002 Elsevier Science Ltd. All rights reserved. equations in other publications. The agreement of numerical and experimental results shows that the analytical procedure presented in this paper is very e!ective. 2. THE TRIPOD-BALL SLIDING JOINT The TBS joint is shown diagrammatically in Figure 1. Shaft 1 is splined with tripod base 2, which has three pins on the circle of radius R equi-spaced in the plane A}A. Ball-rollers 3 are connected with pins through bearings 5, and in the guide sleeve 4 there are three inner cylindrical grooves which match with the three ball-rollers. Through rolling contact between ball-roller and cylindrical groove, the shaft 1 and the guide sleeve 4 can move relatively. Compared with other prismatic joints, the main advantage of the TBS joint is that the friction coe$cient is as small as 0)003",
+            "erent sizes were used to study the in#uence of the clearance size, while the driving speed can be easily changed over a large range by adjusting the motor voltage. The joints were very lightly oiled to minimize friction in the connections. The speed of crank was monitored with an optical code speedometer. The additional motions and , displacements of the joint elements around z- and x-axis were measured by three eddy current transducers (sensitivity 8 mV/ m). One was for recording and the other two signals were combined to obtain the #uctuation of . The acceleration yK in the direction of y-axis of shaft 1 (see Figure 1) was monitored to indicate the impact caused by the joint clearance. A BruK el andKjaer accelerometer, type 4366, and a charge ampli\"er, type 2635, sensitivity 44)6 Pc/g, were used here. The output cable of the charge ampli\"er was \"xed on the shaft to minimize the electromagnetic disturbance. Because the drive torque M of crank is equal to the output torque of the motor, it can be derived via the input power of motor and crank speed, considering the motor power factor at the same time. The input voltage and current of the motor were recorded",
+            " APPENDIX B: DATA FOR THE MECHANISM (see Table B1) TABLE B1 B m (kg) l (m) (m) J (kgm ) nk 0)2 0)03 0)017 1)43 10 k 0)2 0)15 0)046 6)6 10 er 1)05 * 0)105 5)07 10 ve 5)02 * * 6)69 10 APPENDIX C: NOMENCLATURE E Young's modulus (i\"1, 2) F contact force F y-component of force of joint O F the elastic contact force F the damping force F* generalized inertia force F generalized active force g gravitational constant J moment of inertia of body B (i\"1, 2, 3, 4) K the equivalent sti!ness of the spring k(e), m , some parameters obtained from the geometry for the contacting joint elements \u00b8, \u00b8* active and inertia moment l length of body B (i\"1, 2) m mass of body B (i\"1, 2, 3, 4) M the input torque of nominal mechanism M input torque q generalized co-ordinate r the clearance size r the actual displacement between each center point of group i of ball-roller and groove (i\"1, 2, 3) R the distance between the center of ball-roller and center of tripod base (in Figure 1) R, R* active and inertia force u generalized velocity < velocity of mass center C of body B (i\"1, 2, 3, 4) (xN , yN , zN ) unit vector of the absolute rectangular co-ordinates y , yK translational displacement and acceleration of body B in the direction of y-axis , K angular displacement and acceleration of body B about z-axis , G angular displacement and acceleration of body B about x-axis mode-change criterion ( ) the de#ection of the contact surface (of group i, i\"1, 2, 3) ( ) one-order derivative of the de#ection of the contact surface (of group i, i\"1, 2, 3) a value equal to 1203(i"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002725_zamm.19910710718-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002725_zamm.19910710718-Figure3-1.png",
+        "caption": "Fig. 3. Configuration of example 1 Fig. 4. Configuration of example 2",
+        "texts": [
+            " A soft-finger contact has, in addition, an angular spring with axis oriented along the normal on the object boundary and through the point of contact [5]. The flexibility of the springs are, for the normal F N N i = 1.5E - 6, the tangential FTTli = FTTzi = 6.OE - 6 and for the angular FTTmi = 1.OE - 5. The initial openings d N and dT are assumed to be equal to zero. In the approximation of the friction cone we use eight surfaces. As a first example let us consider the three-dimensional object which grasped with three fingers as shown in Fig. 3. For this example we consider three cases: i) Case 1: In this case we assume that finger Ng 1 is a frictionless and the two others are hard-fingers. Finger Nc 1 exerts a normal force rN1 = 1 on the object. For this force, and with friction coefficient p = 0.3, the normal and the tangential reactions of fingers 2 and 3, the corresponding slipping values and the rigid body displacements and rotations are given in Table 1. ii) Case 2: Here all the fingers are assumed to be hard-fingers. Finger 1 exerts on the object the forces rN1 = lo., rTll = 1. and rTZ1 = 1.. The friction coefficient is p = 0.3. In Table 2 the reactions and the corresponding slipping values of fingers 2 and 3, and the rigid body displacements and rotations are given. 264 Table 1. Example of Fig. 3, case 1 ZAMM . Z. angew. Math. Mech. 71 (1991) 7/8 fingers contact gaps tangential frictional slipping rigid body motion rigid body motion reactions components forces values components values 2 3 I 5.660E-01 0.000E+00 5.660E - 01 0.000E + 00 il I _. - 1.410E - 01 - 0.000E + 00 - 1.410E - 01 - 0.000E + 00 0.000E + 00 0.000E + 00 0.000E + 00 0.000E + 00 8.480E - 07 8.480E-07 0.000E + 00 0.000E + 00 0.000E + 00 0.000E + 00 I 1 I I I Table 2. Example of Fig. 3, case 2 1 I I I ~ 2 3 fingers 2 3 iii) Case 3: Now we assume that the fingers 2 and 3 are soft-fingers and finger 1 is a frictionless one. Finger 1 exerts a normal force rN1 = lo., also an external force (e.g. the object weight) P , = 1.9 is applied. The friction coefficient ,u = 0.3 and the torsional friction coefficient pm = 0.5. Here we must note that in cases 1 and 2 when the external force P , is applied the object can not be grasped. The reactions and the slipping values of fingers 2 and 3 are given in Table 3"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure3.8-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure3.8-1.png",
+        "caption": "Figure 3.8. A change of base point in a general dis placement of a rigid body.",
+        "texts": [
+            " Rotator Invariance Theorem. For a given displacement of a rigid body, the rotator is independent of the choice of base point; consequently, the axes of rotation corresponding to all base points are parallel and the angles of rotation about them are equal. Proof. Let P be any particle of the rigid body .IJ4; and, for the same dis placement of f1i, let us assume that T and T* are distinct rotators of f1i about lines through two base points 0 and 0* whose displacements are b and b*, respectively, as diagrammed in Fig. 3.8. Since the displacement of any particle of the rigid body, by definition, is the same for every choice of base point used Finite Rigid Body Displacements 193 in the decomposition described by (2.13), with the vectors defined in Fig. 3.8, we may write for both 0 and 0* d(P) = b + Tx = b* + T*x* = (b + Tr) + Tx *, (3.133) wherein x = r + x* has been used. But with 0 as the base point, it is seen that the term in parentheses is equal to b*. Therefore, (T*- T) x* = 0. Because P is an arbitrary particle, this equation must hold for all x*; hence, (T*- T) must be the zero tensor. It follows that the rotator is invariant with respect to the choice of base point: T* =T(O*, u*)=T(O, u). Moreover, it is now evident from (3.74) and either (3"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure3.5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure3.5-1.png",
+        "caption": "Figure 3.5. The position vector p representing both x and i, which are viewed in separate frames.",
+        "texts": [
+            " (Xt, X:2, X3) Spatial Frame I{J (x 1 ,x2,x3) Initial Position of P in Frame '{) Figure 3.4. Displacement of a particle P viewed in the spatial frame <p. Finite Rigid Body Displacements 185 displacement, though unchanged in the body frame cp', is identified differently by another observer in the spatial frame cp as the vector i having coordinate components {pd = {fd = (f1 , f 2 , f 3 ). Hence, referred to cp, the vector p= pkik = xkik. Notice that the numbers fk and xk are the same as those in ( 3.117 ). A plane example in Fig. 3.5 shows the relative rotation of the body frame cp' through an angle (} about the i 1 = i; axis in the spatial frame cp and the single position vector of the point P from 0 identified as x by the observer in cp' and as i by the observer in cp. We may ignore the observers, and note that in any case we may write (3.118) because the same vector always may be referred to any two bases in just this way in accordance with (3.93 ). This arrangement is special, because, by con struction, the component numbers in (3"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002408_jsvi.2001.3873-Figure13-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002408_jsvi.2001.3873-Figure13-1.png",
+        "caption": "Figure 13. The contact state in one cycle (r \"0)07 mm, \"75 r.p.m.).",
+        "texts": [
+            " Circumferential values represent the direction of the contact force relative to z-axis, and radial distances denote their amplitude. It is observable that the three contact forces, respectively, distribute in a certain limited region. It can be concluded that wear value must be much higher in these special regions of the TBS joint. Thus, some extra surface treatment should be carried out to enhance its abrasion resistance and prolong the life of the joint. Due to the clearance in the TBS joint, the elements stay in free-#ight mode or contact mode. Figure 13 shows the contact state of each group of joint elements in one cycle of crank rotation. The hatched regions indicate the separate mode (with frequent impact) and the rest is contact state. It can be found that there are at least two groups in contact at any angle of crank rotation, and the complete breakaway between body B and B never occurs. As a result, no large impact takes place. This agrees with the result in section 5.3. (In the above Figures 5}13, r \"0)07 mm, \"75 r.p.m.). Figure 14 shows the experimental results of the additional displacement and the driving torqueM at di"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003259_robot.2004.1307509-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003259_robot.2004.1307509-Figure6-1.png",
+        "caption": "Fig. 6 . Planned Pushing Operation",
+        "texts": [
+            " Planning of Sliding Operations Let us consider one-dimensional sliding of the cuboid on a horizontal plane. In this case, graspless manipulation as shown in Fig. 5 is generated; one force-controlled finger is located on the top of the object to press it down and another positioncontrolled finger is located behind the object to push it. It takes 533 CPU minutes for this planning with A*. When we do not use any heuristic functions, 1007 CPU minutes are required. When we use \u201cweaker\u201d robot fingers by setting f, = [ 5 , 5IT, different graspless manipulation is generated (Fig. 6); both fingers are position-controlled and push the object from behind. This corresponds to \u201cstable push\u201d [ 5 ] . The computation requires 203 CPU minutes (or 378 CPU minutes without heuristics). These results indicates that our algorithm generates graspless manipulation with large internal force like grasping for When additional obstacle exist by the side of the object, pinching the object is impossible. In this case, tumbling with regrasping is generated (Fig. 8). The computation time is 990 CPU minutes (or 1296 CPU minutes without heuristics)"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001530_s0263574700003003-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001530_s0263574700003003-Figure2-1.png",
+        "caption": "Fig. 2. An R3 \u2192 R2 example. (a) Standard cube in R3. (b) Resultant polytope in R2.",
+        "texts": [
+            "7112 20.3117 20.9958]T (26) s* = [1.1264 2.0000 2.0000 0.1421 0.6230 2.0000 0.8735 2.0000 1.8578 2.0000 1.3769]T (27) l* = 1.8618 (28) respectively. With these quantities we have the minimum infinity-norm solution of this example as x*\u221e = [20.0679 20.5371 0.5371 20.5371 0.4607 0.5371 0.2024 20.5371]T (29) which is exactly the same with the solution in Cadzow.2 Note that there were 50 solution candidates in this example. With the same notation of Sections 3, let\u2019s see an example of A : Q \u2192 P APR23 3 (Figure 2). Note that there are 8 vertices in the standard cube while there are only 6 vertices in the manipulability polytope (zonotope), i.e. two vertices of the zonotope are mapped internally in this example. The internally mapped vertices cause problems in determining the task-space directions where the best output performance is obtained or in determining a hyperplane made of vertices spanning minimum infinity-norm solutions.6 Let qi be a vertex of Q. Then what is of interest to us is if pi = Aqi is an internally mapped point or boundary point of the polytope of P"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002861_00423110500140013-Figure9-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002861_00423110500140013-Figure9-1.png",
+        "caption": "Figure 9. Transient response of the deformation of the stretched-string model to step changes in side-slip and turn slip.",
+        "texts": [
+            " [5] and Jansen et al. [6] presented at the conference and published in this volume for more information on some of these and subsequent models. In figure 8 the deflected one-dimensional brush model is depicted, which is subjected to a combination of side-slip and turn slip. The lower diagram refers to the equivalent case of combined side-slip and camber. For transient phenomena the stretched-string-based model is more suitable albeit that entering the nonlinear range poses an almost insurmountable difficulty. Figure 9 shows the development of the string deformation after step changes in side-slip and turn slip. The initial development of the lateral deformation which is uniform in the case of side-slip and angular in the case of turning explains the slow start of the moment and the side-force generation in the respective cases. D ow nl oa de d by [ U ni ve rs ity o f N ew ca st le , A us tr al ia ] at 1 7: 21 0 2 Ja nu ar y 20 15 The predicted force and moment responses are very similar to the measured values in figure 7 except for the moment response to turn slip"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002168_s0039-9140(03)00075-4-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002168_s0039-9140(03)00075-4-Figure3-1.png",
+        "caption": "Fig. 3. (A) Scheme of an alternative flow cell for 1808 illumination. (B) Scheme of a flow cell for 908 illumination.",
+        "texts": [
+            " When glucose solutions are injected in FIA mode (discrete sample volume) two opposite effects take place: (1) the increase in fluorescence intensity due to the enzymatic reaction; and (2) the decrease in intensity due to dilution of glucose and regeneration of the enzyme. These opposite effects give a FIA-like peak in which the analytical parameters described in Section 2.6, change with glucose concentration (Fig. 2B). Prior to the system shown in Fig. 1, two other flow cell systems were designed. Firstly, a system (Fig. 3A) consisting of a methacrylate piece (a; 7.7 /5 /0.4 cm) with a central hollow (b; 1.1 / 0.5 /0.5 cm; 275 ml volume) and two lateral orifices (c and d; 0.5 mm diameter) for sample inlet and outlet. Two Mylar films (e, f) fixed with silicone closed the central hollow; the rear film (e) contained the polyacrylamide-GOx-FS sensor film (g). Finally, a reflecting mirror (h) was fixed to the back part of the system to increase the optical path-length. With this system similar signals to those with the above-described system were obtained and so the system can be used as an alternative. However, the system has two main drawbacks: (1) operative problems arise due to the frequent formation of bubbles on the sensor film which perturb the signals (this can be avoided if a second pump is connected to the outlet tube); (2) as the sensor is composed of a large number of films, the system has to be tested frequently for liquid leakage. The second system designed is shown in Fig. 3B. A plastic cuvette (4 /1 /1 cm) is divided into two sections; the upper section is discarded. In the diagonal of the lower part (which is showed in the figure, 1.5 /1 /1 cm), a polyester film (a), in which the GOx-FS sensor (b) has been fixed, is located. The back part (c) is filled with silicone and the front part is provided with two orifices for sample inlet (d) and outlet (e). Finally, the system is closed with a methacrylate cover (f). This flow cell is located in the sample compartment of the luminometer"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003554_13552540510601309-Figure18-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003554_13552540510601309-Figure18-1.png",
+        "caption": "Figure 18 First-order check approximating the surface as a part of a sphere might fail to recognize a horizontal sharp edge",
+        "texts": [
+            " The algorithm as explained in Appendix 2 can be carried out so that the cusp volumes associated with the two patches come within user defined limit. Needless to say, the incorporation of an extra cutter trajectory in an intermediate slice would require some follow up action that is not discussed here. As a second example, a horizontal sharp edge \u2013 a thin fin for example (Figure 17) \u2013 can also be missed as the first-order check (de Jager, 1996; Faux and Pratt, 1979) would approximate the surface as part of a sphere and thereby fail to recognize the fin (Figure 18). This would result in the loss of this feature in the prototype. In case of cusp volume check \u2013 this would result in a number of successive cusps in a layer displaying high volumes. In such a case, it would be observed that mere introduction of an extra cutter trajectory line (as in the previous case) would not solve the problem. In such a case, the algorithm (Appendix 2) should be such as to introduce another slice in the layer concerned. The vertical position of this slice should be iteratively decided such that all the related cusp volumes are within limit (Figure 19)"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003217_tmag.1985.1064247-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003217_tmag.1985.1064247-Figure4-1.png",
+        "caption": "Fig. 4. Flux distribution of the machine at full- load in the preferred direction of rotation.",
+        "texts": [
+            " This value is easily computed from the total flux per slot pitch obtained by a Simpson's rule integration over each slot p i tch and interpolating the radial component of f lux density a t each point from nodal values using the shape functions of the elements. FLUX DENSITY AND .TORQUE CALCULATIONS SYNCHRONOUS MOTOR FOR A HIGH FIELD PERMANENT-MAGNET Figure 3 shows the transverse cross-section o f a high field 4 pole permanent-magnet synchronous machine. The configuration shown with non-radial rare-earth permanent-magnets has many advantages, particularly that the rotor flux per pole exceeds the flux passins through any one magnet. This is il lustrated by the distribution of f lux shown in Fig. 4 , which has been computed using the mesh shown in Fig. 5. Figure 6 shows the radial flux density a t the bore measured using a search coil with the machine on full load. Figures 7 and 8 show the computed flux densities for the same load condition using the two and three dimensional analyses respectively. It must be remembered"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure4.22-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure4.22-1.png",
+        "caption": "Figure 4.22. Motion of a speed control governor referred to a spherical reference frame.",
+        "texts": [
+            "p +UP+ 2iiJ -lri 2 sin {J cos {J) e0 . Let the student examine the following exercise. (4.74a) (4.74b) Exercise 4.4. Notice that x(A, t) = l(t) e, in t/t and recall (4.40a). Deter mine rof and rof referred to tft, and apply (4.46) and (4.48) to derive (4.74a) and (4.74b). When ri=0.5 radjsec, how does the result (4.74a) compare with ( 4.17d) found earlier for these conditions? D Example 4.13. The ball governor of a certain speed control device con sists of an arm OA hinged at 0 to a vertical shaft OZ as shown in Fig. 4.22. The shaft rotates with constant angular speed w 1 = 3n radjsec in the machine frame 0, and simultaneously the arm OA is elevated at the constant rate w2 = n radjsec in the shaft frame 1. The control ball B is attached to a light spring, but otherwise it may slide freely on the arm OA in frame 2. The designed shutoff position for the ball is set at 6 in. from 0 when e = 45\u00b0 and the ball is stationary on OA. To design a proper spring it is essential to know the maximum, absolute acceleration of B for the above conditions",
+            " The tube is held at a fixed angle 0 in a centrifuge which is spinning with a constant angular velocity ro, as shown. Find the total velocity and acceleration of P at a distance a along the tube, referred to the frame t/J = { F; ik} fixed in the tube. Problem 4.75. 4.76. Recall the data given for the shutoff position of the ball B of the speed con trol device described in Example 4.13. Determine the absolute velocity and acceleration of B referred to frame 1 = { 0; i, j, K} fixed in the vertical shaft, as noted in Fig. 4.22. 340 Chapter 4 4.77. A bead B slides as shown on a thin, circular hoop of radius 20 em. The bead moves with a constant speed of 40 em/sec relative to the hoop which spins about its vertical diameter with a constant angular speed w = 10 radjsec. Use two methods, one based upon the application of spherical coordinates, to determine the absolute velocity and acceleration of B at the position shown. Problem 4.77. 4.78. A telescopic rod OA shown in the figure has a ball and socket fitting, called a ball joint, at each end"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure2.3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure2.3-1.png",
+        "caption": "Figure 2.3. Tangential and normal displacement vectors associated with the displacement due to a rotation about an axis.",
+        "texts": [
+            "3), noting that a\u00b7a= 1, and recalling the expan sion rule for the vector triple product (see (A.14) in Appendix A), we obtain p~ =ax (x x a), P1 =ax x. (2.6) Finally, substitution of (2.6) into (2.4) yields the desired relation for the dis placement d(P) of a particle P of a rigid body in its right-handed rotation through an angle 0 about an axis a fixed in the body: d(P) = x- x =ax x sin 0 + ( 1- cos O)a x (ax x), (2.7) wherein x = x(P) and x = x(P) are the initial and final position vectors of P from 0 in cf>= {O;ek}\u00b7 The result (2.7) may be visualized graphically. It is seen in Fig. 2.3a, and it is also evident from (2.6 ), that the vector ax x is tangent to the circular path of Pat x, and the vector ax (ax x) is directed from Pat x to the center of the circle at A. We thus see in Fig. 2.3b that the rotational displacement dis the vector sum of a tangential displacement a x x sin 0 and a normal dis placement (1- cos O)a x (ax x). Kinematics of Rigid Body Motion 89 For future use and simplicity, it ts convenient to rewrite (2.7) in the abbreviated form d=x-x =Tx, (2.8) where T, which ts named the rotator, is presently identified as the vector operator T =: a X [ ] sin 8 + ( 1 - COS 8 )a X (a X [ ] ). (2.9) Equation (2.8) shows that the rotator transforms the initial position vector of a particle into its displacement vector due to a finite ri,gid rotation about a fixed line"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000986_20.877649-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000986_20.877649-Figure1-1.png",
+        "caption": "Fig. 1. Hysteron operators.",
+        "texts": [
+            " Shimasaki are with the Graduate School of Engineering, Kyoto University, Kyoto, 606-8501, Japan (e-mail: {tmatsuo; simasaki}@kuee.kyoto-u.ac.jp). Y. Osaka is with the Graduate School of Energy Science, Kyoto University, Kyoto, 606-8501, Japan. Publisher Item Identifier S 0018-9464(00)06838-2. where is the number of hysteron operators, is the play hysteron operator, and is a single-valued function. The play hysteron operator is given by (2) where is the value of at the previous time-point, and is a constant. The characteristics of operator are illustrated in Fig. 1(a). The play hysteron model, described by (1) and (2), can be less cumbersome in numerical implementations than the Preisach model, and it can describe hysteretic characteristics equivalently to the scalar static Preisach model [10], [7]. The hysteretic characteristics given by the scalar stop hysteron model are written as (3) (4) where is a single-valued function, 0018\u20139464/00$10.00 \u00a9 2000 IEEE is the stop hysteron, are the values at the previous time-point, and is a constant. The characteristics of operator are illustrated in Fig. 1(b). While this model is as simple as the play hysteron model, it is suitable for calculating from because the stop operator makes clockwise hysteresis loops, as in Fig. 1(b). If becomes a single-valued function when ( : saturation magnetic flux density), and should be restricted within and , respectively. Since the derivatives of functions (2) and (4) are easily obtained, both play and stop hysteron models can be used effectively together with the Newton method. III. VECTOR HYSTERESIS MODELS A. Vector Hysteresis Model by Play Hysterons Mayergoyz [2] has proposed a 2-D vector hysteresis model as a superposition of scalar models. (5) where is a scalar hysteretic function for the -direction, is the unit vector in the -direction, is the number of angular divisions, and "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001041_robot.2002.1014761-Figure11-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001041_robot.2002.1014761-Figure11-1.png",
+        "caption": "Fig. 11.",
+        "texts": [
+            ", 6 The results of the simulation axe presented in Fig. 9 and the phase portrait in Fig. 10. Test 3. A fuzzy controller associated with a conventional PD controller is proposed for a motion of a desired position defined by 3lr 8 7 \u2019 q d ( s i ) = - - si . E . i = 1,2, ..., 6 (47) The control law is determined by F* = U P D + U* where UPD is given by the relation (22) and UF is generated by a fuzzy controller (condition (34), Table 1 and the membership functions from Fig. 5 ) . The result of the simulation is presented in Fig. 11 and the phase portrait is plotted in Fig. 12. We notice the good evolution of the system and error convergence to zero. VI. CONCLUSIONS The paper treats the control problem of a tentacle manipulator. In order to avoid the difficulties generated by the complexity of the nonlinear integraldifferential equations that define the dynamic model of this system, the control problem is avoided by using a very basic energy relationship of this dynamic model. The energy relationships of a tentacle manipulator are inferred"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001896_ajpa.1330900406-Figure15-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001896_ajpa.1330900406-Figure15-1.png",
+        "caption": "Fig. 15. Circle of radius R generating the cycloidal curve of radius r, by the rotation of the angle 0. This eccentric cycloidal curve provides a model closer to the vertical movement of the body center of mass in the adult human than a sinusoidal curve (see text for explanations).",
+        "texts": [
+            " The vertical movement z( t ) , while periodic (with a period equal to 112 of the lateral movement), is not symmetric: from our data, the movement [ y ( t ) sagittal, z ( t ) vertical] of the center of mass is better described by a cycloidal curve than by a sinusoidal curve, being narrower in its upper part than in the lower part (Fig. 7, bottom panel). The movement of the center of mass in the vertical plane can be described in parametric coordinates, as the movement of a point tied to a small circle of radius r fixed on a rolling circle of radius R (Fig. 15). This can be expressed mathematically as a function of the rolling angle 8 ( t ) = 2d(TI2) = 47~t/T y(8) = R8 + r sin 8 z(0) = zo - (R + r cos 8). y (0 ) = 0 z(0) = zo - (R + r), i.e., the lowest position of the center of mass below the reference level z,,. R can be directly found from T by the length of the step L, which corresponds to the developed length of a circle of radius R: 2rR = L = V(T/2), or R = VT14-n From our measurements, we find the average saggital speed (V) of the CM: V = 152 cdsec , hence R = 12"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001925_84.388115-Figure10-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001925_84.388115-Figure10-1.png",
+        "caption": "Fig. 10. lubricant for micro-rotating bearing. Photograph of the experimental conditions to study the effects of",
+        "texts": [
+            " DISCUSSION The car ran at a maximum speed of 100 \"/sec, which does not seem fast, but it may be too fast for a 1/1OOOth scale car. Therefore, wear of the rotating parts could be quite severe. Fig. 9 shows the condition of the rotating shaft near the bearing after approximately one-half hour of operation. The contact point of the shaft is damaged because of the wear of the bearing. Lubrication, bearings, and other means of reducing the friction are difficult to apply to micro-systems. To study the effect of lubricant for micro-rotating wheel bearings, an experiment was conducted using a high speed video camera. Fig. 10 shows the experimental setup. Lubricant was supplied to the bearing while the wheels were rotating. The amount of the lubricant was approximately 0.1 pg. TESHIGAHARA et al.: PERFORMANCE OF A 7-MM MICROFABRICATED CAR 79 Because of the viscosity of the lubricant, the wheels stopped rotating. The viscous resistance is given by [lo] S dx d dt F = p - - where p is the viscosity of the lubrication medium, s is the contact surface area of the bearing, d is a clearance, and d x / d t is the relative velocity between the shaft and the bearing"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003657_j.cma.2005.02.033-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003657_j.cma.2005.02.033-Figure5-1.png",
+        "caption": "Fig. 5. Linear graph of 2-link manipulator; the branches shown in bold (m1 m2 and r3 r6) correspond to an absolute coordinate tree.",
+        "texts": [
+            " the virtual work principle) may be employed, especially when flexible bodies are included in the system model [12]. By selecting all rigid bodies into the tree, the branch coordinates take the form of absolute coordinates. The tree is completed by selecting all arm elements as branches; in fact, the arm elements are always selected into the tree since they contribute no unknown variables to the set of branch coordinates. For the 2-link manipulator, the absolute coordinates qa result from selecting edges m1 m2 and r3 r6 into the tree shown as bold edges in Fig. 5. The kinematic constraint equations are obtained by projecting the branch transformation equations for cotree joints h7 and h8 onto their reaction spaces. From the incidence matrix representation of the linear graph [11], the branch transformation equations are easily generated: r7 \u00bc r1 \u00fe r3 \u00f014\u00de r8 \u00bc r2 \u00fe r5 r1 r4; \u00f015\u00de where ri is the translational displacement vector of edge i, e.g. r1 \u00bc x1\u0302\u0131\u00fe y1|\u0302 is the displacement of m1 (\u0302\u0131 and |\u0302 are unit vectors parallel to X and Y, respectively) and r4 \u00bc l4\u00f0cos h1\u0302\u0131\u00fe sin h1 |\u0302\u00de is the displacement of body-fixed arm element r4, which depends upon the orientation of m1",
+            " One tree is used to generate translational equations and the other to generate rotational equations. By selecting joints into the tree for translation and rigid bodies into the tree for rotation, the branch coordinates take the form of absolute angular coordinates qh. Once again, all arm elements are selected into both trees. For the 2-link manipulator, the translational tree consists of the arm elements plus joints h7 and h8, as shown by the bold edges in Fig. 6. The rotational tree consists of arm elements plus bodies m1 and m2, as shown in Fig. 5. Since there are no translations associated with revolute joints, the only unknown tree displacements appearing in the branch coordinates are h1 and h2, the absolute angular coordinates. Even though there are revolute joints in the rotational cotree, their rotational branch transformations are orthogonal to the reaction space \u00f0\u0302\u0131; |\u0302\u00de of these joints. Thus, a null set of kinematic constraint equations is obtained for these independent coordinates. The transformation to joint coordinates is obtained by projecting the rotational branch transformations for the revolute joints onto their motion spaces\u2014the scalar form of Eq"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001615_0263-8223(93)90220-k-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001615_0263-8223(93)90220-k-Figure1-1.png",
+        "caption": "Fig. 1. Stress and strain signal.",
+        "texts": [
+            " 3-6 Their values are determined separately for the tension and compression phases of loading, thus enabling a very exact analysis of the behaviour of the material. In addition, the damping factor is calculated from the stored energy and the energy loss, for both linear and non-linear viscoelastic behaviour. 2 PROPERTIES -- DEFINITION AND DERIVATION During dynamic testing, the investigated materials are subjected to sinusoidal loading. The damping of a material causes a phase shift between stress and strain signal (Fig. 1). In a stress-strain diagram these two signals form a hysteresis loop on which four different characteristic quantities can be defined: stresses, strains, elastic moduli and mechanical energies. The maximum and minimum stress and strain can be directly read from the diagram (Fig. 2(a)). The upper part of the hysteresis loop, from e I to eu, is denoted by the upper curve, auc(e), and the lower part is denoted by the lower curve, ale (e). In addition the mid-curve is given by: Omc(e) =\u00b0uc(e)+\u00b0lc(e) (1) 2 The intersection of the mean value of stress o m is: ou+ol Om=-- T - (2) with the mid-curve defining the origin of the relative coordinate system"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure4.24-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure4.24-1.png",
+        "caption": "Figure 4.24. A fluid particle motion within a centrifugal pump, referred to the intrinsic frame.",
+        "texts": [
+            " Some problems that involve rigid bodies in Motion Referred to a Moving Reference Frame and Relative Motion 283 motion relative to one another will be solved. To emphasize that (4.46) and ( 4.48) are not restricted to an isolated material point nor to a point of a rigid body, but also are applicable to a deformable solid or fluid continuum, the first problem concerns the motion of a fluid particle referred to the intrinsic frame. Example 4.15. Motion of a Fluid Particle in a Centrifugal Pump. A fluid particle P shown in Fig. 4.24 moves outward along the impeller blade of a centrifugal pump with speed v and tangential acceleration a relative to the blade. The impeller rotates with a constant, clockwise angular speed w relative to the pump casing. (a) Determine the absolute velocity and acceleration of P referred to the intrinsic frame J1. = { P; tk }. (b) In particular, let r = R =2ft and w = 600 rpm; and suppose that v = 200 ftjsec and a= 100 ft/sec 2 at the instant when the fluid particle reaches the tip T of the blade. Evaluate the absolute velocity and acceleration of P at T. The pump geometry is shown in Fig. 4.24a. Solution. Part (a). Since the data are expressed in terms of intrinsic variables, it is natural to employ an intrinsic reference system at the fluid par ticle P, which is in motion relative to a rotating reference frame cp = { 0; ik} fixed in the impeller. Therefore, we shall apply ( 4.46) and ( 4.48) in which the preferred frame f/J is fixed in the pump casing. The intrinsic velocity and acceleration of P relative to the impeller frame cp but referred to the intrinsic frame 11 are given by use of ( 1. 70) and ( 1. 71 ). Thus, for the assigned parameters, ox Tt=vt, (4.77a) With reference to Fig. 4.24a, we have ror = wk = -wb, ror=O, x = R sin 1/J t - (1 - cos 1/J) n, ( 4. 77b) 284 Chapter 4 in which 1/J is the angular placement of P on the blade. The point 0 is fixed in the pump frame 1/>, so v 0 = a 0 = 0. Hence, with the aid of ( 4.77b ), the rigid body velocity and acceleration of P in 1/> are given by v0 +(1)1 xx= -Rwsint/Jn-Rw(l-cost/J)t, (4.77c) a0 +(I)! X ((I)! X x) + w1 x X= -Rw2 sin 1/J t +Rw2(1- cos 1/J) n. (4.77d) The relations (4.77c) and (4.77d) are the velocity and acceleration that P would have if it were fixed to the blade"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003335_j.engfailanal.2006.03.002-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003335_j.engfailanal.2006.03.002-Figure1-1.png",
+        "caption": "Fig. 1. Spiral bevel gear [1].",
+        "texts": [
+            " The calculated contact stress was higher than the allowable contact stress which is emphasized in literature. 2006 Elsevier Ltd. All rights reserved. Keywords: Pitting; Fracture; Failure analysis; Spiral bevel gear Differential drives are packaged units used for a wide range of power-transmission applications. The spiral bevel gears are beginning to supersede straight-bevel gears in differential drives. They have curved oblique teeth that contact each other gradually and smoothly from one end of the tooth to the other, meshing with a rolling contact similar to helical gears (Fig. 1). They have the advantage of ensuring evenly distributed tooth loads and carry more loads without surface fatigue. Thrust loading depends on the direction of rotation and whether the spiral angle of the teeth is positive or negative [1,2]. The investigated spiral bevel gears are made of two different case hardening steel. The case hardening steel (20MnCr5, EN10084) has a low carbon\u2013chromium and the other steel (17NiCrMo6-4, EN10084) has a low nickel\u2013chromium\u2013molybdenum with medium hardenability, generally supplied in the as rolled condition with a maximum brinell hardness of 280 (30 HRC)"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003066_095965180421800502-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003066_095965180421800502-Figure4-1.png",
+        "caption": "Fig. 4 Schematic showing variables of the model applied to the drill bit with respect to the stapes footplate",
+        "texts": [
+            " The dividing lines between these are: dxh dt = dx0 dt \u2212 d dtAFxk B (3) (a) the start of drilling; (b) the start of drill bit cutting across the full diameter Furthermore, the variables h1 and h2 give the angles of the drill bit; subtended from the axial centre of the burr tip on the (c) the start of equilibrium drilling; drill axis to the intersection of the orthogonal plane of (d) the start of breakthrough; the tissue interfaces on each side of the stapes footplate, (e) the completion of breakthrough. as shown in Fig. 4. An equivalent analysis for constant feed force ratherDepending on the compliance, the drilled material thickthan constant feed velocity is given byness and the cutting conditions, (b) and (d) may occur in the reverse order and (c) might not occur at all. dxh dt =F xA2vcpR B 1 2(h2\u2212h1)+sin 2h2\u2212sin 2h1 (4)The start of breakthrough and its identification are key to controlling the drilling process. The start of breakthrough determines the location of the far surface of the The drill torque equation (2) and the relationship given by equation (3) also apply"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003991_acc.2006.1656484-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003991_acc.2006.1656484-Figure1-1.png",
+        "caption": "Fig. 1. Double Pendulum System",
+        "texts": [
+            " The method relies on time-scale separation between the system dynamics and the controller dynamics. The control signal is sought as solution of fast dynamics, which is shown to satisfy the sufficient conditions of Tikhonov\u2019s theorem from singular perturbations theory. The paper is organized as follows. In Section II, we describe the dynamics and give the problem formulation. Section III details the control design, which is further analyzed in Section IV. Simulation results are given in Section V. II. PROBLEM STATEMENT Consider the two degree-of-freedom double pendulum in Figure 1. The two rods may rotate in the vertical plane. Research is supported by AFOSR under Contract No. FA9550-05-10157. A. Young, C. Cao and N. Hovakimyan are with Virginia Polytechnic Institute and State University, Blacksburg, VA, 24061-0203, e-mail: {ayoung83, chengyu, nhovakim}@vt.edu E. Lavretsky is with The Boeing Company - Phantom Works, Huntington Beach, CA 92647-2099, email: eugene.lavretsky@boeing.com Torque control is applied at the two connecting joints. The rods are treated as rigid bodies, and all frictional forces are ignored"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002091_s0141-6359(99)00027-6-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002091_s0141-6359(99)00027-6-Figure2-1.png",
+        "caption": "Fig. 2. Spindle error measurement with a spherical master artifact (a) and with a master axis (b). This configuration is representative of how rotating sensitive direction error motions are measured with radial capacitance gauges spaced 90\u00b0 apart [6].",
+        "texts": [
+            " Bryan has proposed a method of measuring spindle error motions with a master ball while machining. This approach may be suitable for some classes of machine tools [3]. However, a general purpose method of measuring error motions as a function of spindle load (cutting forces) and as a function of spindle speed is necessary to evaluate a broader range of machine tools. The master axis method of characterizing axes of rotation has been proposed as a suitable method of testing spindles under load [5,6]. Fig. 2 shows a spindle under test with an artifact (lapped master ball) and the master axis. A three-capacitance probe nest is shown to illustrate the gauging locations. As shown in the figure, the master axis method is based on the replacement of a lapped master artifact with a master axis of rotation, in this case, an air- bearing spindle. The rotor of the master axis is rigidly attached to the rotor of the spindle under test. Capacitance gauges are rigidly fixed to the machine tool or test stand structure in a position that includes the desired portion of the structural loop",
+            " To understand the sources of error motion best, the spindle can be removed from the measurement loop by relocating the capacitance gauges to target the * Corresponding author. Tel.: 1814-865-5242; fax: 1814-865-2986. E-mail address: emarsh@psu.edu (E. Marsh). 0141-6359/00/$ \u2013 see front matter \u00a9 2000 Elsevier Science Inc. All rights reserved. PII: S0141-6459(99)00027-6 quill or spindle housing. Implementation of the proposed approach requires that the master axis stator does not rotate. A simple restraint is shown in Fig. 2b to prevent rotation without constraining the remaining five degrees of freedom. A suitable contact, such as a diamond tip on a lapped gauge block, can be used in precision applications [6]. The motion of the master axis stator will reflect the x and y tilt, x and y radial, and axial error motions of the spindle and structure under test. If the gauging (datum) surfaces of the master axis are sufficiently smooth and otherwise ideal conditions are present, a master axis will provide the same error motion measurements as a master artifact"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003347_s10329-004-0100-1-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003347_s10329-004-0100-1-Figure2-1.png",
+        "caption": "Fig. 2 Joint and trunk inclination angles. h1 Ankle joint angle, h2 knee joint angle, h3 hip joint angle, W trunk inclination angle. P1\u2013",
+        "texts": [
+            " The threedimensional coordinates of the points were calculated by the software based on a direct linear transformation method (Nigg and Herzog 1999). The mean errors accompanying each of eight measured positions equally distributed in the calibrated space were less than 4 mm. The calculated change in each of the coordinates over time was smoothed using a second-order, zero-phaseshift digital low-pass filter (Bryant et al. 1984), with the cut-off frequency of 12 Hz. Two-dimensional, sagittally projected joint angles (hip, knee, and ankle) and inertial angle of the trunk segment, definitions of which are illustrated in Fig. 2, were then calculated. A total of nine gait cycles (from initial ground contact to the next ground contact of the same foot) were edited for further analysis. Stride length and duration were obtained from the videotapes. The speed of each gait cycle was calculated by dividing stride length by stride duration. Control experiment For comparisons, bipedal locomotions of two performing monkeys, Kampei and Kojiro, were measured in the same manner; instead of the platform, here the monkeys walked on a treadmill, with a piece of reflective tape attached to each of the landmarks on their bodies"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002688_0301-679x(89)90151-5-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002688_0301-679x(89)90151-5-Figure1-1.png",
+        "caption": "Fig 1 Two-aMal groove journal bearing configuration",
+        "texts": [
+            "(1 - le) /tj~) = ufl, + /q( l -- le) I e, the ratio of actual length occupied by the lubricant to the total bearing length, is unity in the lubrication (positive-pressure) region and is obtained from the con- TRIBOLOGY international tinuity of flow in the cavitation region: % < ct <~ 350 \u00b0 f;;; I le = (~ ~) d2 dfl ~i ~ d5 dfl (9) t\u00a2 2 l0 \u00b0 < ~ < 170 \u00b0 l e -- - =10 o (The subscript te refers to trailing edge.) The Fourier heat conduction equation in the non-dimensional cylindrical coordinates gives the temperature distribution in the bush and the housing, both of which are assumed to be cylindrical and possess the same thermal properties in the present investigation (see Fig 1). This equation is written as a~2 + ~ ~ + ~ + # a=-- ~- = o (10) The journal temperature is established by considering the journal in thermal equilibrium, which requires that the total heat flows to and from the journal are equal. The amount of heat received by the journal is given by [l~i kr R T, _ kf~/i c3~, ~ = ~ d a d fl ( l l ) The free convection hypothesis at the two ends of the journal gives q~o 2h, R k, A~ [1,o-kfR T~- k s kf R 2 ( L - T.) (12) For thermal equilibrium of the journal ~/si = ~]so (13) The fluid-bush interface distortion Jr in Eq (1) is computed by solving the three-dimensional elasticity equa- 349 tion",
+            " In fact, the results from the present analysis are even better than the published theoretical results 3. The authenticity of the IHD and EHD analysis is well established 13 15. in the present work, the bearing characteristics based on THD and TEHD analyses for a cylindrical bore journal bearing case were obtained by using the operating conditions of Table 1 and the viscosity temperature pressure relation defined in the analysis. Provision for two axial grooves, each of 20' arc length, was made at the horizontal split (Fig 1). The IHD and EHD results are, however, general and are applicable to any combination of ~)j, #o, c/R, E and th/R giving the value of C' d as 0.05. The performance characteristics studied in this paper include journal temperature, eccentricity ratio, attitude angle, minimum fluid film thickness, side flow and stability margins in terms of threshold speed and whirl frequency ratio. These characteristics are shown in F'igs 3 6 as functions of non-dimensional load (H;). To illustrate the effect of bearing clearance, the THD results for two values of c/R (0"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000780_ac001369+-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000780_ac001369+-Figure1-1.png",
+        "caption": "Figure 1. Schematic representation of the scanning capillary microscope used in this study: 1, sample electrode; 2, x translation stage; 3, electrochemical glass cell; 4, inner capillary; 5, outer capillary; 6, pressure chamber; 7a and 7b, T-junctions; 8, auxiliary fluid beaker; 9, auxiliary capillary; 10, pressure regulator; 11, z translation stage; 12, pressure chamber cover; 13, rubber seal; 14, steel rod; and 15, transfer line to the ESI-MS. Insert: Schematic representation of the miniature flow cell formed at the bottom of the coaxial capillary setup. F1 is the feed through the annulus of the coaxial capillary set up; F0 is the product stream to the MS.",
+        "texts": [
+            " The configuration of the miniature scanning flow cell of the scanning capillary microscopy mass spectrometer (SCM-MS) is described in the Experimental Section. To understand the role of the many controllable variables in this device, we describe a simple mathematical model for the SCM-MS in the theory section. The electrochemical oxidation of dimethyl-p-phenylenediamine (DPD) is used as a probe reaction, and its primary products and intermediates are described. Detailed account of the identification of the byproducts of DPD oxidation will be presented in a subsequent paper.38 Finally, SCM-MS images of model electrodes are presented. Figure 1 shows a schematic representation of the experimental set up. It comprised a three-compartment electrochemical cell placed in a pressure chamber, a coaxial capillary set, a 2-dimensional micropositioning device, and an electrospray ionization (ESI) mass spectrometer. The sample electrode (1) was placed horizontally on the x stage (2). The bottom opening of the electrochemical cell (3) was pressed to the sample electrode by a set of steel springs. A rubber gasket seal of GC septum (Thermolite septa, Restek, Bellenfonte, PA) was placed between the sample and the cell",
+            " A coaxial capillary set (4,5) was used to deliver the reagent solution to the specified location and to transfer the product stream to the interface of the mass spectrometer through the inner capillary. A syringe pump was used to deliver the feed stream to a T-junction (7a) located outside the pressure chamber (6), from which the stream was directed through the annulus between the two capillaries to the examined location. The cross section of the outlet/inlet head of the coaxial capillary set is also shown in the insert in Figure 1. Polishing of the capillary\u2019s end was accomplished using a flat 3-cm-height mandrel that had a through hole of 0.45 mm diameter drilled perpendicularly to its flat surface. (17) Hassel, A. W.; Lohrengel, M. M. Electrochim Acta 1997, 42, 3327-3333. (18) Bittins-Cattaneu, B.; Cattaneo, E.; Konigshoven, P.; Vielstich, W. In Elec- troanalytical Chemistry; Bard, A. J., Ed.; Marcel Dekker: New York, 1991. (19) Hambitzer, G.; Heitbaum, J.; Stassen, I. Electroanal. Chem. 1998, 447, 117- 124. (20) Hambitzer, G",
+            " 17, September 1, 2001 aqueous electrolyte feed containing 10 mM DPD was used. The capillary head was placed approximately 10 \u00b5m above the surface of the flat Pt electrode, and the applied pressure drop was P ) 2.6 105 Pa. The measurements were performed under open circuit conditions; therefore, no chemical transformation of DPD was observed. This curve was used to find the conditions for which the flow through the electrochemical flow cell (F0) originates exclusively from the feed stream that comes through the outer capillary (F1 of Figure 1). Under these conditions, the influence of the composition of the bulk electrolyte can be neglected. The flow rate in the inner capillary was set to F0 ) 0.7 \u00b5L min-1 by pressure regulation. The liquid in the cell and in the feed stream was aqueous 0.1 M trichloroacetic acid. Two nearly linear sections of the DPD concentration-feed flow rate curve are observed in Figure 4. For F1 < 0.5 \u00b5L min-1, almost all of the flow from the annulus is drawn into the flow cell and to the transfer line. A supplementary flow (F0 - F1) originates from the bulk of the electrochemical cell"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000715_978-94-015-9064-8_33-Figure9-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000715_978-94-015-9064-8_33-Figure9-1.png",
+        "caption": "Figure 9. A platform manipulator driven three planar motors.",
+        "texts": [],
+        "surrounding_texts": [
+            "Figure 3 shows a six-dof parallel manipulator developed by (Tsai and Tah masebi, 1993). This manipulator is made up of a moving platform, a fixed base, and three inextensible limbs, AiBi for i = 1 to 3. The upper end of each limb is connected to the moving platform by a revolute joint while the lower end is connected to a planar two-dof driver by a spherical joint. The three revolute joints lie on the BIB2B3 plane. The manipulator motion is obtained by moving the planar motors on the fixed base. As shown in Fig. 3, two Cartesian coordinate systems, (x, y, z) and (u, v, w), are attached to the fixed base and moving platform, respectively. The origin of the (u, v, w) frame is located at the centroid P of the moving platform with the u and v axes lying on the BIB2B3 plane. In the equiva lent limb, the spherical joint is replaced by three non-coplanar intersecting revolute joints, $A3,i, $4,i, and $S,i' The axis of $3,i is aligned with the x axis; the axis of $S,i is aligned with the longitudinal axis of the limb; and the axis of $4,i is perpendicular to both $3,i and $S,i' Overall, there are six joint screws associated with each limb. The first two are actuated prismatic joints while the remaining four are passive revolute joints. To facilitate the analysis, we define an instantaneous reference frame, (x' , y', z'), with its origin is located at point P and the x', y' and z' axes parallel to the x, y and z axes of the fixed frame. Then, we express all the joint screws with respect to this instantaneous reference frame as follows: $l,i = [ S~'i ], $3,i = [ (hi - ~') X S3,i ], $S,i = [ hi ~'~S'i ] , $2,i = [ S~'i ], $4,i = [ (hi - ~~') X S4,i ], $6,i = [ hi ~'~6,i ] , where Sl,i = S3,i = [1,0, oV, S2,i = [0, 1,OV, hi = PBi, di = AiBi, SS,i = di/d;\" and S4,i = SS,i X S3,i\u00b7 We now consider each limb as an open-loop chain and express the in stantaneous twist, $p, of the moving platform in terms of the joint screws of the ith limb. (8) where Vx,i and Vy,i denote the linear velocities the planar motor along the x and y directions, respectively, and iJ3,i,\u00b7\u00b7\u00b7, iJ6,i denote the rotation rates about the passive joint axes. Since there is a spherical joint at the lower end and a revolute joint at the upper end of each limb, all screws that are reciprocal to the unactuated joint screws form a planar pencil. These reciprocal screws pass through point Ai and lie on a plane Hi which contains point Ai and the axis of $6,i. Let ni = [nx,i, ny,i, nZ,iV be a unit vector defined by the cross product of SS,i and S6,i: ni = SS,i x S6,i. (9) Then, a screw that is reciprocal to all screws except for $l,i is obtained by an intersection of the Hi plane and the plane which contains Ai and is parallel to the x - z plane: $A [ Srl,i ] rl i = , , (hi - d i ) x Srl,i [nz i \u00b0 -nx iV where Srl i = 'V '. , 1-n2 . y,' (10) Similarly, a screw that is reciprocal to all screws except for $2,i is obtained by an intersection of the Hi plane and the plane which contains Ai and is parallel to the y - z plane: [0 n . - n .]T where S . = z,' y,' r2\" V 2 1-n . X,, $A [ Sr2,i ] r2i = , , (hi - d i ) x Sr2,i (11) Taking the orthogonal products of both sides of Eq. (8) with (10) and (11), we obtain: [ ((h~ - d~) x Srl,~)~ S9,i 1 [ wp ] = [ ((h, - d,) x Sr2,t) sr2,i vp \u00b0 ] nz,i y'l-n~,i [ vx,~ ] . Vy,t (12) Writing Eqs. (12) three times, once for each limb, we obtain: (13) where x = [Wpx,Wpy,Wpz, vpx , v py , vpz]T, q = [vx,I,Vy,I,Vx,2,Vy,2,Vx,3,Vy,3]T, and \u00abbl - dl) x srl,dT T SrI I \u00abb l - d l ) x Sr2,I)T T' Sr21 \u00abb2 - d 2) x Srl,2)T T' Jx = SrI 2 \u00abb2 - d 2) x Sr2,2)T T' Sr22 \u00abb3 - d3) x Srl,3)T T' SrI 3 \u00abb3 - d3) x Sr2,3)T T' Sr2,3 nz,l 0 0 0 0 0 ,,/1-n~,l 0 nzil 0 0 0 0 \\/1-n~,l 0 0 nz,2 0 0 0 Jq = JI-n~,2 n z,2 0 0 0 Jl-n~,2 0 0 0 0 0 0 nz,a 0 Jl-n~,a 0 0 0 0 0 nz,a Jl-n~,a An inverse kinematic singularity occurs when nz,i = 0 for i = 1 or 2 or 3. Hence, when one of the limbs points in the z direction, the manipulator loses two degrees of freedom. If two or three limbs simultaneously point in the z direction, four or six degrees of freedom will be lost. A forward kinematic singularity occurs when nx,i = ny,i = 0 for all three limbs. Under such condition, the sixth column of Jx becomes zero identically and the manipulator gains one degree of freedom. Physically, this corresponds to the configuration when the moving platform and the three limbs lie on the x - y plane. Another forward kinematic singularity occurs when the following three conditions are simultaneously satisfied: (1) b.BIB2B3 is an equilateral triangle; (2) the three limbs are of equal length; and (3) AI, A2 , and A3 are placed directly under the centroid of the moving platform. When the above conditions are met, the manipulator gains three rotational degrees of freedom. A third direct kinematic singularity occurs when nz,i = 0 for i = 1,2 and 3. Under this condition, the fourth and fifth columns of Jx are both equal to zero, and the moving platform can make an infinitesimal translation along any direction which is parallel to the x - y plane. In fact, this is a combined singularity since the manipulator is also under the inverse kinematic singulairy. 5. Summary First, the definitions of a screw and its reciprocal screws are reviewed. Then, reciprocal screw systems associated with some frequently used kinematic pairs and chains are developed. Using these reciprocal screw systems, it is shown that the Jacobian of a parallel manipulator can be systematically derived. To illustrate the methodology, the Jacobian of a six-dof parallel manipulator is analyzed and its singular conditions are discussed. 6. References Baker, J.E. (1980) On Relative Freedom Between Links in Kinematic Chains with Cross-Jointing, Mechanism and Machine Theory, Vol. 15, pp. 397-413. Ball, R,S. (1900) A Treatise On the Theory of Screws, Cambridge Univer sity Press, Cambridge. Davies, T.H., 1981, \"Kirchhoff's Circulation Law Applied to Multi-Loop Kinematic Chains,\" Mechanism and Machine Theory, Vol. 16, pp. 171- 183. Hunt, KH. (1978) Kinematic Geometry of Mechanisms, Clarendon Press, Oxford. Mohamed, M.G., Sanger, J., and Duffy, J. (1983) Instantaneous Kinemat ics of Fully Parallel Devices, Sixth IFToMM Congress on Theory of Machines and Mechanisms, New Delhi. Mohamed, M.G. and Duffy, J. (1985) A Direct Determination of the In stantaneous Kinematics of Fully Parallel Robot Manipulators, ASME Journal of Mechanisms, Transmissions, and Automation in Design, Vol. 107, No.2, pp. 226-229. Roth, B. (1984) Screws, Motors, and Wrenches That Cannot Be Bought in a Hardware Store, Journal of Robotics Research, 679-693. Sugimoto, K (1987) Kinematic and Dynamic Analysis of Parallel Manip ulators by Means of Motor Algebra, AS ME Journal of Mechanisms, Transmissions, and Automation in Design, Vol. 109, No.1, pp. 3-5. Tsai, L.W. and Tahmasebi, F. (1993) Synthesis and Analysis of a New Class of Six-DOF Parallel Mini-manipulators, Journal of Robotic Sys tems, Vol. 10, No.5, pp. 561-580. Waldron, KJ. (1966) The Constraint Analysis of Mechanisms, Journal of Mechanisms, Vol. 2, pp. 101-114. Waldron, KJ. (1969) The Mobility of Linkages, Ph.D. dissertation, Stan ford University, Stanford, CA."
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0001941_eurbot.1997.633569-Figure7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001941_eurbot.1997.633569-Figure7-1.png",
+        "caption": "Figure 7: combination of VIPER and SPIKE",
+        "texts": [
+            " Taking into account the velocity of the platform's legs of about wb = 50 y, the velocities for the karthesian coordinates can be calculated: Every leg needs At = smaav;sman = 3s for a complete stretch. This results in a stroke of length in z-direction of 2Az = 200mm, whereas the velocity in z-direction can be calculated as w, = 6 6 7 . The calculations for the values w,, wy, w j , wp, wr can be performed similarly 4 Combination of StewartPlatform and Mobile Robots To compensate the acceleration and the shocks acting on an object the Stewart Platform with 6 degrees of freedom is electively installed on MORTIMER (figure 6) or on VIPER (figure 7) so that abrupt vehicle movements and accelerations affect the object in a smooth way. Figure 6 shows an arrangement for the experiments. A jar containing a liquid is situated on the upper platform. The platform has to equalize the accelerations, calculated by the data of the basic motor controller. On the left side, the whole system is moving with a constant velocity v 2 0. The upper platform is parallel to the bottom, because no acceleration is effecting the liquid. On the right side, the system increases in speed, so the platform has to compensate this movement by an inclination of the upper platform"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001121_physreve.65.011701-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001121_physreve.65.011701-Figure1-1.png",
+        "caption": "FIG. 1. Block structure of the TGBC phase.",
+        "texts": [
+            " Experimental results obtained in several compounds bearing Sm-C*, Sm-A , TGBC , TGBA , and N* phases are reported and analyzed; the block structure and the block size clearly influences the dielectric properties of the TGB phases. The anchoring strength at the grain boundaries, and its variations according to temperature are deduced from experimental results. The rotational viscosities close to the Sm-C*-TGBA and Sm-C*\u2013TGBC phases transitions are analyzed. In the following, we will only consider one block of the TGB structure; other blocks have the same features. Figure 1 \u00a92001 The American Physical Society01-1 shows the structure of the j th block, which is turned by an angle C j5 j(2p/p)lb around the helical axis with respect to a reference block ( j50); p represents the helical pitch and lb the block width. Two reference systems, (OXY jZ j) and (Ox jY jz j), are used to describe the TGB structure. The first one is connected with the grain boundary (Y jZ j) planes and the helical axis OX . The second one is connected with the smectic layer (x jY j) planes and the layer normal (Oz j)"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003465_00423110600871533-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003465_00423110600871533-Figure3-1.png",
+        "caption": "Figure 3. Interpolation between two lateral wheel positions (a) and two cross-sections (b).",
+        "texts": [
+            " A frog, or generally speaking a turnout, is taken into account by regarding it as a set of varying profiles along the track. In the railway dynamics context, as there is some lateral play between the wheelset and the rails, contact properties in each strip are the function of the wheelset lateral displacement, relatively to the rail. Prior to the simulation, these properties are tabulated for a given set of lateral positions. To take into account, a varying rail profile along the track, a dimension has been simply added to the contact tables by considering a given set of profiles. Between the two profiles (figure 3(b)), as it is the case between two given lateral positions (see figure 3(a)), contact properties are interpolated. A difficulty arises as semi-Hertzian data tables, are not derived on line. The latter solution is believed to be too computationally expensive. But, interpolating data tables is not exactly the same as building tables from interpolated profiles. Caution must then be exercised when defining the strip discretization in order to avoid unintended results because of the interpolation process. Furthermore, it is necessary to keep some continuity between strips: from figure 3(b), it is obvious that if strip j is on the tread in cross-section i, and on the flange in cross-section i + 1, the interpolated strip will be twisted leading to uncertain results. Apart from the gap between the wing rail and the frog toe (see figure 1), transitions between strips should be smooth, and the best strategy for avoiding poor results because of meshing consists of having the same strip following the wheel path in a given position, say the centred position. For the other strips, twisted transitions should be prohibited"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001804_s0167-6911(96)00081-3-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001804_s0167-6911(96)00081-3-Figure1-1.png",
+        "caption": "Fig. 1. \"Boost\" converter circuit.",
+        "texts": [
+            " In Section 2 we consider DC-to-DC \"boos t\" converters. First, we present the circuit and its (averaged) model as well as the passivity-based and feedback linearization controllers reported in [14] and [13], respectively. Then, we prove some of the disturbance attenuation properties of these schemes. In Section 3 we carry out this ~2-gain analysis for rigid robots. We wrap up the paper with some concluding remarks. 2 . D C - t o - D C c o n v e r t e r s We consider the switch-regulated \"boos t\" converter circuit of Fig. 1. The differential equations describing the circuit are given by 1 E + c o -~1 = --(1 -- /)) ~X 2 ~- T ' 1 1 22- - (1 - v ) ~ X I -- ~--~X2, where xl and x2 represent, respectively, the input inductor current and the output capacitor voltage variables; E > 0 represents the nominal constant value of the external voltage source and co is an unknown disturbance, which satisfies ]cot < E; v, which takes values in the discrete set {0, 1}, denotes the switch position function, and acts as a control input"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003974_tia.2005.863911-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003974_tia.2005.863911-Figure2-1.png",
+        "caption": "Fig. 2. Flux detection system.",
+        "texts": [
+            " (28) The amplitudes V2 and V4 can be calculated from output signals as V2 = \u221a [V2 cos(2\u03c9t \u2212 \u03c6)]2 + [V2 sin(2\u03c9t \u2212 \u03c6)]2 (29) V4 = \u221a (V4 cos 2\u03c9t)2 + (V4 sin 2\u03c9t)2. (30) Next, cos \u03c6 and sin \u03c6 are calculated as cos \u03c6 = cos(2\u03c9t \u2212 \u03c6) cos 2\u03c9t + sin(2\u03c9t \u2212 \u03c6) sin 2\u03c9t (31) sin \u03c6 = cos(2\u03c9t \u2212 \u03c6) sin 2\u03c9t \u2212 sin(2\u03c9t \u2212 \u03c6) cos 2\u03c9t. (32) Substituting (27) and (28) into (12) and (13), radial forces F\u03b1 and F\u03b2 are written as F\u03b1 = kV2V4 cos \u03c6 (33) F\u03b2 = kV2V4(\u2212 sin \u03c6) (34) where k = Sa 2\u00b50 ( 1 2\u03c0NStG )2 ( 27 4 ) kw4kw2. (35) Fig. 2 shows search coil arrangement and voltage calculation. A total of six search coils are wound in the stator core. The output voltages of search coils are integrated. Then, the outputs of the integrators are added for motor flux detection. On the contrary, the outputs of the integrators are subtracted for radial force flux detection at 180\u25e6 and 270\u25e6. Coefficients of (1/2), (\u22121/2), and (1/ \u221a 3) are adjustment factors to compensate MMF space harmonics based on (23)\u2013(26). Note that V2 and V4 denote the signals proportional to the radial force and motor fluxes, respectively. The terms cos 2\u03c9t and sin 2\u03c9t indicate orthogonal components in two perpendicular axes. The four signals are used in the radial force detection block. Fig. 3 shows an algorithm block of radial force calculation. The outputs of Fig. 2 are given to the formula block of Fig. 3 as inputs. Then, (29)\u2013(35) are processed in a digital signal processor (DSP) to obtain radial forces F\u0302\u03b1 and F\u0302\u03b2 . Fig. 4 shows a simplified block diagram for the conventional \u03b2-axis magnetic suspension. The dotted box indicates the mechanical system. Note that m indicates the shaft weight. Two integrators convert acceleration, speed, and then radial shaft position. The attractive force, which is proportional to the radial shaft position, is generated. This unstable radial force is canceled by feedback radial force originated from a proportional\u2013integral\u2013derivative (PID) controller",
+            " If the time delay \u03c4 is zero, then the phase margin and low-frequency gain are increased. The frequency characteristics of H = 1 and H = 10 show that improvements are better with high gain in H . One can see that if H is more than 10, the phase margin is about the same as that in the case of \u03c4 = 0. Fig. 7 shows the system blocks of integrated bearingless ac motor drive with radial force feedback loops. Based on the search coil voltages, motor and radial force flux components are detected as previously shown in Fig. 2. As in conventional system, motor flux components V4 cos 2\u03c9t and V4 sin 2\u03c9t are given in the modulation block of Fig. 7. In the modulation block, radial force winding current commands are generated based on the radial force commands F \u2217 \u03b1 and F \u2217 \u03b2 , which are obtained from the PID controllers. In the proposed system, the radial force detection block, as shown in Fig. 3, is added in Fig. 7. The radial forces F\u0302\u03b1 and F\u0302\u03b2 are calculated in the radial force detection block. These signals are amplified by a constant H , and subtracted from (1 + H)F \u2217 \u03b1 and (1 + H)F \u2217 \u03b2 "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002285_s0020-7683(00)00153-0-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002285_s0020-7683(00)00153-0-Figure1-1.png",
+        "caption": "Fig. 1. TPJB with conventional and hybrid lubrication through multiple ori\u00aeces in the pads (Santos and Russo, 1998).",
+        "texts": [
+            " All rights reserved. PII: S00 2 0-7 6 83 (0 0 )0 01 5 3- 0 1990; Brockwell and Dmochowski, 1992; Fillon and Khonsari, 1996). However, all investigations were done taking into account conventional lubrication mechanisms. The main contribution of this theoretical work is the application of a THD theory to investigate the thermal e ects in the oil \u00afow, when di erent bore arrangements in the pads are used in the hybrid TPJB. The TPJB lubricated through multiple bores is composed of four tilting shoes (Fig. 1). Each shoe is built of two complementary parts, attached to each other by screws, forming a reservoir, which is \u00aelled with lubricant and connected to servovalves. Bores regularly displaced on the surface of the shoes are machined, allowing the \u00afuid \u00afow between the reservoir and bearing gap. The operational principle of such a lubrication is explained in detail in the work of Santos and Russo (1998). A test rig has already been built, and experimental results will be presented in future works (Santos and Scalabrin, 2000)",
+            " A new distribution oil viscosity over the pads is calculated after the convergence of the temperature distributions over the pads reaches a tolerance of 0.1\u00b0C. A \u00afowchart of the numerical procedure can be seen in Fig. 2 and the bearing characteristics are listed in Table 1. In order to investigate the in\u00afuence of di erent arrangements of bores on the \u00afuid \u00afow and thermal e ects of the hybrid bearing, a rotor angular velocity of 50 Hz was set, while the rotor is subjected to an external load of 400 N in the vertical direction (towards pad number 4 \u00b1 see Fig. 1). Six di erent arrangements of bores on pads were tested. Basically, two types of bores were used, with diameters of 5 and 2.8 mm. The number of bores in each pad was chosen in order to have a constant total area of bores in all arrangements (5 bores of 5 mm or 15 bores of 2.8 mm). The six arrangements are shown in Fig. 3. When an external load is applied to the rotor, the rotor remains in a position which is not the center of the bearing and can be measured as the eccentricity ratio (ratio between the rotor displacement YR and the bearing assembled clearance h0)"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002271_robot.1988.12256-Figure7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002271_robot.1988.12256-Figure7-1.png",
+        "caption": "Fig. 7 Advantage of Redundant Actuator System: Static Equilibrium Against Exerting Force",
+        "texts": [
+            " Suppose that passive joint 8, of the same closed link mechanism as shown in Fig.5 (a) has been replaced with an actuated joint as indicated in Fig.6. That is, 92= 8'j (33) Accordingly, q2 is represented as a function of q1 in two different ways: q2'=f j5 = - n - e 2 + e 3 (34) q22=e5 = - ~ - e 4 (35) Matrix W(al , a2) is obtained from Eqs.(24), (26), (34), and (35): 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 -al a, -a2 Now, suppose that the robot finger has to maintain static equilibrium against a force exerted on the end link as shown in Fig.7, where we neglect the effect of gravity to simplify the discussion. In this case, the joint torques of the corresponding open link tree structural mechanism become: z = ( 0 0 0.64 Nm 0.89 Nm 0.89 Nm )T (37) From Eqs.(6), (31), and (37), the joint torques of the closed link mechanism with the non-redundant actuator system are computed: z l C = ( 0 0 0.64 Nm)T (38) From Eqs.(6), (36), and (37), the joint torques of the closed link mechanism with the redundant actuator system become: z~~ = (0 -0.89alNm 0"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001856_rob.4620110607-Figure20-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001856_rob.4620110607-Figure20-1.png",
+        "caption": "Figure 20. Definition of the end-effector frames. Figure 21. Definition of the VAL transformations.",
+        "texts": [
+            " T,, is the vector that contains the coordinates of the origin of C, in 2,. here some features of this language, which are relevant for our implementation process. In VAL, the position of a frame C with respect to a given reference frame C, is described by the Cartesian coordinates X , Y, Z of the origin of C in 2,. The orientation of C is described by three angles denoted as 0, A, T. There exists a relationship between these angles and the Z-X-Z Euler angles a, p, y , as follows: x represents the cross product operator. Figure 20 shows C, and C, (attached to the sensor and the tool, respectively) as they are defined in our application. Once C is defined, it is possible to make the robot's tool frame C,, coincide with 2. To define this motion, there exist two types of so-called transformations in VAL language (Fig. 21). The first transformation, called absolute transformation, defines the position and the orientation of C with respect to a fixed refer5.3, The VAL II language Our UNIMATE controller uses the VAL I1 software as a robot programming language"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003764_bf02953383-Figure17-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003764_bf02953383-Figure17-1.png",
+        "caption": "Fig. 17 Surface grinding of conical membrane.",
+        "texts": [],
+        "surrounding_texts": [
+            "86 R. Snoeys and F. AI-Bender\nTheoretically, Kf(w) was determined by solving the time dependent Reynold's equation for a fixed conical gap geome try, by a predictor-corrector method.\nThe results obtained from the theoretical model were experimentally verified by means of a test set-up as shown in Fig.14. Figure 15 shows a good agreement between the two (Plessers and Snoeys, 1985b).\nSince the stability of air bearing performance is dependent on this F.R.F.(the imaginary part of which representing the damping), the influence of the basic bearing parameters on it was investigated with the aid of the theoretical model. The general results of this investigation are presented in Table 2\n4. DYNAMIC STABILITY OF BEARINGS\n4.1 Dynamic Identification of the Bearing Film The dynamic behaviour of the air gap was investigated theoretically and experimentally by considering the fre quency response function (F.R.F.) of the air film as a mechanical component. This F.R.F. is expressed as the dynamic stiffness Kf(w) of the air film :\nPneumatic hammering is a kind of self-excited vibration generated in the bearing gap due to the compressibility of the gaseous lubricant.\n3.4 Frictional Characteristics of Air Bearings Friction forces were determined at various low rotational speeds of spindles mounted on radial air bearing pads.\nThe friction moment increases linearly with the rotational speed(March, 1976). Typical results, expressed as coefficient of friction ttf with respect to the relative sliding speed of the bearing surface, were; ttf = 45 X 10-6 at speed of lm/s, increasing at the rate of 36 x 10-6m/ s.\n3.3 Sensitivity to Tolerance Deviations To evaluate the influence of shaft/bearing tolerances, a number of bearing characteristics have been measured for various spindle-bearing combinations(shaft diameter differ ence from +0.5 to - O. 5 mm with respect to the nominal diameter of the bearing gap). Some results of those investiga tions are summarized in Fig.13 for three different pad types. In this figure the specific load (load/active bearing surface) and mass flow associated with a bearing gap of 10 ttm are plotted versus the difference between shaft diameter and nominal diameter.\nPads with a convergent gap turn out to be considerably less critical to shaft tolerance deviations compared to pads with parallel gaps. To obtain the same thrust force as for a bearing with parallel gap and nominal diameter, a difference of even 0.5mm can be tolerated. The shaft diameter may be slightly(lOO -150ttm) smaller than the nominal pad diame ter; this would result in a somewhat smaller air consump tion without changing too much the load-carrying capacity.",
+            "DEVELOPMENT OIF IMPROVED EXTERNALLy\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7 87\n10-r--------------------,\nWorking condition\n- - -2- _\n30\n5-r-----------------,\n4.3 Aerodynamic Effects It is often desirable to use aerostatic bearings in a wide speed range. The aerostatic assumption for bearing design remains valid when the relative sliding speed of the two bearing surfaces is small in comparison with the average speed of air through the gap \\50 m/s). When this is not so, however, a significant aerodynamic effect is introduced, affecting the bearing performance characteristics. Work is being carried out to investigate this aspect both theoretically and experimentally.\nFig. 16 Geometry of circular disc supported on three bearing pads.\n5. MANUFACTURING T:ECHNIQUES\nmoment of inertia approached Ie ; the frequency of these vibration was very close to that which had been predicted theoretically.\nIn [Plessers, 1985,(pp.6-43)], a scheme is suggested to control the stability of aerostatic bearings in mechanical structures.\nexperimental theoretical - - - --\n0 0 500 1000\nFrequency 1Hz)\nro =.03024m\n-1O-l-~_~--_r_~-_-~~-_-~___J\no 500 1000 Frequencv (Hz)\nr 1 =.25mm ho(10'm) Ps(MP.) Pl(MP.)\n1 9.4 .7 .447 2 13.2 .7 .390 3 16.4 .5 .319\n,.. ~E :> --. CTZ ~'\"-5'1 o\nFig. 15 Comparison between measured & calculated freq. Response function of an air gap. Some rather simple and consequently cheap construction techniques may be applied to obtain the desired convergent bearing gaps.\n5.1 Compliant Bearing Surfaces Pads with a compliant bearing surface of a desired conicity may be obtained by deflecting the membrane(with the pressure of a f1uidum or with a screw). In this deformed situation, a machining operation(Fig.l7) or some kind of epoxy casting operation(Fig.18) produces again a perfect fIat membrane surface. When reducing the applied pressure(or the force applied with a screw) the membrane will elastically deflect back to its original unloaded position creating the conical shape of the bearing surface.\n(Plessers and Snoeys, 1985b). Some recent research shows that it is possible to improve the efficiency and accuracy of the theoretical model, yielding useful design guidelines for unconditionally stable bearings.\n4.2 Air Bearings in Mechanical Systems Based on the now readily available dynamic characteris tics of the air film, stability criteria for mechanical systems containing more than one air bearing could be worked out systematically using the Nyquist criterion. This resulted in some rules of thumb which may be quite useful for the design of bearing systems (Plessers and Snoeys, 1985b) : pneumatic hammering may be eliminated by a proper selection of bearing and/or structure parameters.\nAs an example, a test was carried out in whid. a rigid disc was mounted on three aerostatic pads as shown in Fig.16, being loaded on top by three identical masses placed symmetrically around its central vertical axis.\nThus, by shifting these masses away from the centre, the total mass remains the same while the moments of inertia are changed. The dynamic characteristics of the air gaps, and of the system as a whole, had been predetermined. From those, a critical mass me and a critical(diametral) moment of ineria Ie were established (exceeding which the system should be unstable in the translation and tilt modes, respec tively). The test showed that there was no instability in the axial direction, since the mass was well below me, but that tilt vibrations would commence as soon as the diametral",
+            "88 R. Snoeys and F. AI-Bender\n5.2 Non-Deformable Bearing Surfaces Bearing pads with a non-deformable wall may be manufactured with a similar casting technique as indicated in Fig.l8; however, the casting has to be carried out now with respect to an appropriate negative shape. This casting model for a radial bearing pad may by obtained as illus trated in Fig.19. The molding cylinder is provided with a membrane.\nCylinder and membrane are accurately machined at the nominal diameter of the bearing pad. The membrane may be deflected radially corresponding to the desired amount of the convergency of the gap. The same technique can be used for axial bearing pads, the bearing pad itself may also be made directly by diamond-tool turning on a precision lathe.\n6. CONCLUSIONS\n(1) A significantly larger carrying capacity may be obtained by using convergent gap shapes. The resulting bearing stiffness is increased, the airconsumption is reduced and problems of static stability are eliminated.\n(2) Deformable bearing surfaces yield quite some interest ing bearing load characteristics, to the point of obtaining infinite or negative bearing stiffness.\n(3) Bearings with convergent gaps are considerably less affected by bearing surfaces irregularities. Very low friction in air-bearings still remains, of course, an important advan tage in comparison with other bearing types.\n(4) The above mentioned bearings show better static\nstabiliy. Their dynamic instability in mechanical systems may be accurately predicted and avoided by a proper selec tion of working and design parameters.\n(5) The bearing geometry necessary to obtain optimum bearing characteristics can easily and cheaply be manufactured by a surface grinding operation or an epoxy resin casting technique.\nREFERENCES\nBlondeel, E., 1975, \"Ae'rostatische Largers Met Lastaf hankelijke Spleetkonfiguratie\", Ph.D. Thesis, K.U. Leuven.\nBlondeel, E., Snoeys,R., and Devrieze, L., 1976a, \"Aeros tatic Bearngs with infinite Stiffness\", Annals of the CIRP, Vol. 25/1.\nBlondeel,E., Snoeys, R., and Devrieze, L., 1976b, \"Exter\u00b7 nally Pressurized Bearings with Variable Gap Geometries\", 7th. International Gas Bearing Symposium, Cambridge, July 13-15.\nBlondeel E., Snoeys, R., and Devrieze, L.,1980, \"Dynamic Stability of Esternally Pressurized Gas Bearings\",ASME ]. of Lubrication Technology, Vol. 102.\nByant, M.R., Velinsky, S.A., Beachly, N.H., and Fronczak, F. ]., 1986, \"A Design Methodology for obtaining Infinite Stiffness in an Aerostatic Thrust Bearing\", ASME J. of Mechanisms, Transmissions, and Automation in Design.\nConstrantinescu,- V.N., 1959, \"Gas Lubrication\", The A.S. ME.\nDevrieze, L. and Snoeys, R., 1978, \"Low Cost Externally pressurized Air Bearings\", Proceedings of the 19th. M.T.D.R. Conference, Manchester, UMIST, pp.97-105.\nGross, W. A., 1962, \"Gas Film Lubrication\", Wiley, New york, London.\nLowe, I.R.G., 1974, \"Characteristics of Externally pressur ized Thrust Bearing with One Compliant Surface\", Paper A4, 6th international Gas Bearing Symposium, University of Southampton.\nMarch, H., 1976, \"Design for Minimum Total Power\", 7th. International Gas Bearing Symposium, July 13-15, Cam bridge.\nMori, H. and Ezuka, H., 1975. \"A Pseudo Shock Theory of Pressure Depression in Externally Pressurized Circular Thrust Gas Bearing\", International Lubrication Conference, Tokyo. Japan.\nPlessers, P. and Snoeys, R. 1985a, \"Dynamic Indentifica tion of Convergent Externally Pressurized Gas-Bearing Gaps\", Subj. for Publication in ASME ]. Tribology 1985.\nPlessers, P. and Snoeys, R., 1985b, \"Dynamic Stability of Mechanical Structures Containing Externally Pressurized Gas Lubricated Bearings\", Subj. for Publication in ASME ]. Tribology 1985.\nPlessers, P., 1985c, \"Dynamische instabiliteit Van Aeros tatische Gaslagers in Mechanische Systemen\", Ph, D. Thesis, K.U.Leven.\nSnoeys, R., Devrieze, L. and Vanherck, P., 1977, \"Self Aligning Aerostatic Shoe Bearings\", Annals of the CIRP. Vol. 25/1, pp.205-210."
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0002511_acs.678-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002511_acs.678-Figure1-1.png",
+        "caption": "Figure 1. Phase portrait of controlled and uncontrolled Van der Pol oscillator.",
+        "texts": [
+            " ], where , are arbitrary scalars, so that f (x)\"f (x)# 0 b 1 b [ ! , ! ,! ]F (x) \" 0 1 x (50) Now, with the proper choice of and , it follows from Corollary 2.1 that the adaptive feedback controller (26) with w (t),0 guarantees that x (t)P0 as tPR. Speci\"cally, here we Copyright 2002 John Wiley & Sons, Ltd. Int. J. Adapt. Control Signal Process. 2002; 16:151}172 choose \"!1, \"!2, and R\"2I , so that P satisfying (21) is given by P\" 3 1 1 1 (51) With \"1, \"1, \"2, b\"3,>\"I , and initial conditions x (0)\"[1, 1] and K (0)\"[0, 0, 0], Figure 1 shows the phase portrait of the controlled and uncontrolled system. Note that the adaptive controller is switched on at t\"15 s. Figure 2 shows the state trajectories versus time and the control signal versus time. Finally, Figure 3 shows the adaptive gain history versus time. Copyright 2002 John Wiley & Sons, Ltd. Int. J. Adapt. Control Signal Process. 2002; 16:151}172 Example 4.2 The following example considers the utility of the proposed adaptive stabilization framework for systems with time-varying dynamics"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002746_0278364905060149-Figure24-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002746_0278364905060149-Figure24-1.png",
+        "caption": "Fig. 24. Two coordinate systems defined using reference points on surface plate and base platform.",
+        "texts": [
+            " Consequently, the base platform\u2019s position and the orientation expressed in the coordinate system located on the surface plate are derived from the six distances among the reference points on both the joint supports and the surface plate, u1 \u2212 u6. In addition, if these nine displacements are measured by nine displacement sensors, variations in the base platform\u2019s dimensions, position, and orientation, which are caused by the thermal and elastic deformation of the frame, can be calculated by using the direct kinematics of a parallel manipulator called the triangular symmetric simplified manipulator (TSSM; Fichter 1986). Figure 24 depicts the two coordinate systems mentioned above, which are fixed on both the surface plate and the PKM\u2019s base platform or the TSSM\u2019s moving platform. Position vectors of the reference points, BPbi (i = 1, 2, 3), which are observed in the coordinate system fixed on the base platform, \u2211 B , are geometrically expressed by the three distances among the three reference points on the base platform, t1 \u2212 t3. Here, the origin of the coordinate system, \u2211 B , is located at the center of gravity of three points, bi "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001603_elan.1140071203-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001603_elan.1140071203-Figure2-1.png",
+        "caption": "Fig. 2. Schematic diagram of microdialysis systein with immobilized enzyme reactor: (A) Two-channel microsyringe pump; (B) microdialysih probe; (C) sample solution; (D) immobilized enzyme reactor; (E) amperometric detector [poly( 1,2-diaminobenzene)film-coated platinum electrode]; (F) potentiostat; (G) recorder. All the parts were connected with PTFE coil ( id. 0.1 mm).",
+        "texts": [
+            " The fiber was glued in the interior of the fused silica tube, leaving an active length of 3mm, and the fiber tip sealed with epoxy cement. Another two fused silica tubes (0.d. 150 pm, i.d. 75 pm) were also inserted as shown and served as the inlet and outlet. Two fused silica tubes were glued in the interior of the stainless steel tubes (0.d. 440 pm, i.d. 220 pm) and the upper end of the probe was sealed with epoxy cement. All the parts used for the construction of the probes were gifts from Eicom. The microdialysis system used in this work is outlined in Figure 2. The apparatus consisted of a two-channel microsyringe pump (Eicom EP-60), potentiostat (Yanagimoto VMD101A), and a strip chart recorder (Yanagimoto R3-201). Each of the immobilized enzyme reactors was positioned after a microdialysis probe and in front of a poly( 1,2-diaminobenzene)film-coated platinum electrode. All the parts were connected with PTFE coil (i.d. 0.1 mm). A constant potential (+0.6 V vs. Ag/AgCl) was applied to the polymer film-coated electrode and the current was recorded. The artificial physiological fluid (Ringer's solution), containing NaCl(l47 mM), KCl(4 mM), CaCI2 (1",
+            " The analyte in the dialysate from the probe was carried into the enzyme reactor and then produced enzymatically the hydrogen peroxide which could be detected selectively by a downstream poly( 1,2-diaminobenzene)film-coated platinum electrode. The steady-state current obtained was related to the analyte concentration in the sample solution. Experiments were first conducted to evaluate the effectiveness of enzymatic conversion of the reactor and permeability of the microdialysis probe, under a single channel flow condition without pump A\" (see Fig. 2). The glucose oxidase immobilized reactor was positioned in front of the flow cell. The 0.1 M phosphate buffer at pH 7.0, containing 1 mM sodium azide, was selected as a carrier solution. The probe was immersed in the same buffer containing 0.2 mM glucose and a steady-state current was recorded. In the system without a probe, the same carrier solution containing 0.2 mM glucose was pumped directly into the enzyme reactor. The results are shown at three different flow-rates (I, 2, and 3 PLmin-') in Table I ",
+            " When the flow-rate was increased, the permeability of glucose into the probe decreased. However, the conversion efficiency of P-u-glucose to hydrogen peroxide was ca. 100% at every flow-rate tested. The time required to reach steady-state response after the immersion of the probe in the sample solution was too long (ca. 11 -31 min). This delay time may be reduced by pumping the dialysate from the probe through the enzyme reactor and beyond the electrode. Therefore, a two-channel flow system (shown in Fig. 2) was examined in the subsequent experiments. When the flow rate of the buffer was increased, keeping that of the Ringer's solution constant (2 pLmin-'), the response 1,) L mln-' J with probe without probe [a ] _ ~ _ _ _ _ _ _ ___ ~ _ _ ~ _ _ ~ - - 1 82 36 1 22 7 31 4 2 69 677 10 2 17 8 3 62 942 6 6 10 6 [a] A 0 2 mM glucose solution (0 1M phosphate buffer dt pH 7 0 contdining 1 mM sodium dzide) was pumped directly to the system without a microdialysis probe [b] Calcuiated fiom the ratio of signal current for glucose obtained at the systems with dnd without probe - ~ ~ - _ _ - ",
+            " In later work, the Ringer's solution and buffer were pumped at flow rates of 2 and 4 pL min-' , respectively, because this provided good sensitivity and reasonable response times. Under the recommended flow conditions, a h e a r calibration plot for glucose assay was obtained over 2 x 10-h-10-2 M; the slope, the y intercept, and the linear correlation coefficient were 272 nA mM-', 0.93 nA, and 0.999. The lowest concentration that could be detected was 5 x M (based on signal-to-noise ratio of 3). In this work, the L-glutamate oxidase immobilized reactor was positioned in the line shown in Figure 2. As an optimum buffer, 0.1 M phosphate buffer at pH7.5 was selected [9] and pumped with pump A\" (Fig. 2). The effect of flow rate was first examined; the result is shown in Table 3. When the flow rate was increased, keeping the ratio (I : 2) of the flow rate of the Ringer's solution and the buffer constant, the permeability of glutam am ate into the probe was decreased in analogy with the glucose assay. However, the conversion efficiency of L-glutamate to hydrogen peroxide was ca. 100% at every flow-r.ate tested. A linear calibration plot for L-glutamate assay was obtained over 2 x 10-6-5 x M under the same flow conditions as the glucose assay; the slope, the y intercept, and the linear correlation coefficient were 181 nAmM-I",
+            " The detectable concentration was 1.5 x M ( S I N = 3). The poly( 1,2-diarninobenzene)-coated platinum electrode was used as an amperometric detector of hydrogen peroxide generated enzymatically in the enzyme reactors. This polymercoated electrode can detect hydrogen peroxide selectively without any interference from electroactive interferents (e.g., ascorbate and urate) and proteins in serum, as reported before [8]. The usefulness of this polymer-coated platinum electrode was evaluated in a continuous flow system (Fig. 2) with a microdialysis probe and glucose oxidase immobilized reactor. The signal currents for glucose were monitored continuously for 3 h after a microdialysis probe was immersed in a control serum. The stability of the signal current for glucose in control serum was good; even after 2 h, the signal current retained 98% of its original current. Also, in the system without the glucose oxidase immobilized reactor, the base-line current did not vary after the probe was immersed in serum and even in 0",
+            " The glucose concentration in the rat brain was calibrated from the glucose standard solutions. detection of the hydrogen peroxide generated in the enzyme reactor. Table 4 shows the analytical results for the in vitro monitoring of glucose in several control serums. These results agreed closely with the manufacturer's data. The coefficient of variation for the repeat measurements (n = 5) was less than 4% for all samples. In vivo monitoring of glucose in the rat brains was conducted by using the system shown in Figure 2 and implanting a microdialysis probe into the frontal lobe according to conventional procedures [lo]. The rat was allowed to recover overnight in a large plastic box with free access to food and water. The probe was then connected to a microsyringe pump through a swivel to allow the rat free movement. After 12 minutes the signal current increased up to a steady value, corresponding to glucose content in rat brain. When a 1 mL aliquot of 20% (w/v) glucose was injected into abdomen of the rat, the signal current increased and then decreased to the value before glucose injection, as shown in Figure 3"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001995_310-Figure9-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001995_310-Figure9-1.png",
+        "caption": "Figure 9. Schematic diagram of the displacement of the nozzle with the cut kerf (i.e. the overlap of the nozzle with the cut kerf).",
+        "texts": [
+            " Therefore, an increase in the inlet stagnation pressure enhances the ability to eject molten slag and improves the quality of the cut edge. Figure 8 shows the macrograph of the laser cut edge of 5 mm thick stainless steel under the conditions of this group of cutting parameters. The horizontal line on the surface of the cut edge is pushed down to near 3 mm and surface roughness of the cut edge at 1 mm above the cut edge bottom is decreased to Ra = 2.65 \u00b5m. When the displacement of the nozzle with the cut kerf is increased from 0.9 to 1.4 mm (i.e. the overlap of the gas jet with the cut kerf is increased to 1.4 mm as shown in figure 9) and other conditions remain unchanged, the flow field inside the cut kerf is improved greatly (shown in figure 10(a)) compared with the conditions in figure 1. Not only is the curved shock weakened from P2/P1 = 1.46 to 1.22 but the incident point also moves along the cutting front from 3.5 to 4.3 mm. The flow field distribution along the cutting front becomes smooth and the exit momentum thrust increases. Therefore, the ability to eject the molten slag increases greatly. However, when the displacement of the nozzle with the cut kerf decreases from 0"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003692_icmlc.2005.1527053-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003692_icmlc.2005.1527053-Figure4-1.png",
+        "caption": "Figure 4. Membership functions of torque |ET|, stator flux |E\u03a8| and angle \u03b7",
+        "texts": [
+            " According to fuzzy logic technique, when angle \u03b7 is estimated, required voltage space vector is obtained, and SVM is able to adapt to control the machine, instead of using hysteresis comparators and optimum voltage switching vector lookup table as in conventional DTC. In the fuzzy logic estimator, there are two input variables, which are absolute torque error|ET|, stator flux error |E\u03a8|, one output variable is the deflection angle \u03b7 of synthesized voltage vector. Each universe of discourse of the torque error, flux error, and deflection angle is divided into four fuzzy sets. Triangle membership functions have been used. All the membership functions (MF) are shown in Figure 4 respectively. There are total of 16 rules as listed in table 1. Each control rule can be described using the input variables |ET|,|E\u03a8| and control variable \u03b7 . The th rule i iR can be expressed as : Z P S P M || \u03a8E P B || E T \u03b7 Z P S P M P B P S P M P B P B Z P S P M P B Z Z P S P M Z Z Z Z The inference method used in this paper is Mamdani\u2019s procedure (inference) based on min-max decision. The firing strength (applied fuzzy operators) ,for ith rules is given by i\u03b1 min( (| |), (| |))i A T Bii E E\u03c8\u03b1 \u00b5 \u00b5= By fuzzy reasoning, Mamdani\u2019s mininum procedure (fuzzy inference) gives ' ( ) min( , ( ))V i Vi i \u00b5 \u03b7 \u03b1 \u00b5 \u03b7= Where A\u00b5 , B\u00b5 and V\u00b5 are membership functions of sets A, Band V of the variables |ET|, |E\u03a8| and \u03b7 , respectively"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001441_tmech.2003.816806-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001441_tmech.2003.816806-Figure3-1.png",
+        "caption": "Fig. 3. View cone of the camera.",
+        "texts": [
+            " The visibility constraint implies that there is no occlusion between the viewpoint and the entity to be inspected along the line of sight. In our vision-sensor-planning problem, the visibility is implied in the other three constraints, which will be discussed later. The field-of-view constraint requires that the interested entity be imaged to the active area of the image plane. A rectangular field of view is defined and it is characterized by a field-of-view angle , which is extended by the two side planes corresponding to the two shorter edges of the field-of-view rectangle (see Fig. 3). The resolution constraint ensures that a specified small-size entity with length be imaged to at least 1 pixel on the image plane. According to Cowan and Kovesi\u2019s work [8], the viewpoint region satisfying the resolution constraint for a given patch is the intersection of the resolution balls corresponding to each vertex on that patch. The radius of the resolution ball , and its height , are calculated as follows [8]: , , . Here, , are the height and width of 1 pixel on the image plane. The focus constraint guarantees that the entity of interest is sharply imaged",
+            " [13], the region that satisfies the focus constraint for a given patch is the band between the planes perpendicular to the viewing direction and at distances and from the farthest and nearest patch vertex, respectively. Here, [13] where is the back nodal point to image plane distance; is the focal length; is the entrance pupil diameter of the lens; is the signed offset between the front nodal point and the entrance pupil; is the limiting blur-circle diameter. Based on the above discussions, the view cone of the camera can be modeled as in Fig. 3, where the two parallel planes denote the two depth-of-field planes corresponding to and . is the field-of-view angle. As can be seen from the figure, is determined by and . can be calculated by and the width/length ratio of the camera. It is observed that most automotive parts share a common characteristic: they consist of several relatively flat patches that are joined by edges, or smooth transitional surfaces like fillets. Therefore, it is possible to partition the part surfaces into patches such that each patch has attributes desirable for the camera planning: there is not much geometry detail on the patch; the patch has low curvatures; the patch extends more in length and width direction than in depth direction"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001059_12.403696-Figure11-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001059_12.403696-Figure11-1.png",
+        "caption": "Figure 11. Deformation of the FEM-model of the compliant mechanism using the displacements qi as constraints",
+        "texts": [
+            " At a platform rotation of 10\u00b0 the work space reduces to 30x12 mm\u00b2, with an assumed maximal angular deflection of 20\u00b0 with the hinges. In order to investigate the influence of the kinematic deviations of the flexure hinges a simulation of the compliant mechanism is made in ANSYS. For a desired position and orientation of the tool center point (xTCP, yTCP, \u03d5TCP) the displacements qi of the drives are computed via the model of the inverse kinematics.15,16 These known values qi are then used as constraints for certain nodes representing the drives in the FEM-model (fig. 11). In figure 12 the deviation \u2206r of the compliant mechanism computed with FEM and the kinematic model of the parallel structure with conventional joints are shown. \u2206r is the amount of the differences between the two tool center points, TCPFEM and TCPkin. model. Proc. SPIE Vol. 4194 165 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/17/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx The maximum deviation is about 31\u00b5m at xTCP = 15 mm and yTCP = 4 mm. Neither a general tendency nor a functional relation between the height of deviation and the position of the TCP can be determined"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003686_tmag.2004.824549-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003686_tmag.2004.824549-Figure3-1.png",
+        "caption": "Fig. 3. One quarter of the cross-sectional geometry of the test motor.",
+        "texts": [
+            " The advantage of the impulse method is that, from one simulation, the forces and harmonics are reached for a wide whirling frequency range. The use of the impulse method to calculate the electromagnetic forces is verified by conventional calculations for a strongly saturated induction motor in [11] and is validated by measurements in [12]. The results of the verification and validation show very good agreement. III. RESULTS A four-pole 15-kW induction motor was chosen as a test motor. The main parameters of the motor are given in Table I and one quarter of the cross-sectional geometry of the motor is presented in Fig. 3. At first, the forces were computed as a function of whirling frequency at no load and supplied by the rated voltage 380 V. In order to compare the effects of saturation, the forces were also computed for a linearized motor in which the relative permeability of the iron was kept constant . Fig. 4 shows the calculated radial and tangential components of the force for both the normal and linearized motor. The whirling radius is 50 m. The results presented in Fig. 4 show that the effects of saturation on the forces are strongest near to the rotational speed 25 Hz. The forces are then studied as a function of supply voltage at whirling frequencies 5 and 25 Hz, again with whirling radius 50 m. Fig. 5 shows the radial and tangential components of the force as a function of the supply voltage at whirling frequencies 5 and 25 Hz. At no-load condition, the maximum force occurs at 25 Hz for the four-pole motor. Fig. 3 shows that the maximum force is reached close to 300 V and, for bigger values of supply voltages, the amplitude of the force is decreased. At a 5-Hz whirling frequency, the flux density harmonics are strongly damped by rotor currents and the radial component of the force behaves almost as in the linearized case. The ratio of the tangential and radial force components changes with the voltage. This means that the saturation also affects the direction of the force. Fig. 6 shows the behavior of the flux density harmonics of order as a function of supply voltage at whirling radius 50 m and whirling frequencies 5 and 25 Hz at no load condition"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000979_1.2802427-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000979_1.2802427-Figure5-1.png",
+        "caption": "Fig. 5 Measurement of Inertia tensor of first block",
+        "texts": [
+            " 6 Experimental Results To assess the accuracy of the proposed method, some tests were carried out in which the inertia tensor of simple rigid bodies was measured, thus allowing comparison between ana- Table 3 Comparison Conti and Bretl /\u201e% 0.5 /\u201e,% 3.0 4 % 18.0 with other identification methods Pandit and Hu 13.0 5.9 3.8 Proposed method 2\"\" test 5.9 1.3 2.2 lytical and experimental results. The smaller of the two working mechanisms, shown in Fig. 2, was used. In the first test a parallelepiped block of mass 1.649 kg was located on the plate with its sides parallel to the fixed axes (see Fig. 5) . The coordinates of the center of mass were x, = -0.95 mm y, = 2.2 mm z,, = 35 mm. Body axes xyz were not exactly the principal axes of inertia relative to point O, because small inertia products were caused by the offset of the center of mass from point O. Nineteen different orientations of the rotation axis were selected and the corresponding natural frequencies were measured. The identified values of the inertia tensor ele ments are listed in Table 1. The errors were lower than a, and hence were much smaller than the values of the inertia moments, but comparable to those of the inertia products"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002864_s0924-0136(03)00811-2-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002864_s0924-0136(03)00811-2-Figure6-1.png",
+        "caption": "Fig. 6. CAD model of test sample and the statistical results of accuracy test.",
+        "texts": [
+            " The parameters in sintering process affected the dimension and the precise shape of the prototype, and possibly led to the distortion of the prototype. As the dimensional change in the fabrication of the ceramic moulding shell was very small, the errors in precise casting process were mainly caused by solidification and shrinkage of the melting alloy. The solidification contraction coefficient of Al-based alloy was about 1.1%, but the shrinkage value changed with the actual casting condition such as the shape and thickness of the casting parts, the pouring temperature, and so on. The sample designed for accuracy test is shown in Fig. 6 (left). A series of samples of different size were measured. Statistical results of the measurement and analysis of dimensions are also shown in Fig. 6 (right). It shows that the error in sintering and casting process displays different characteristics. The dimensional changes in the process of SLS polymer prototype manufacturing has less dependency on the size and shape of the part, but is influenced more by the sintering equipment, material of the prototype and the sintering parameters. The range of the dimensional changes in the casting process is wide and the error is dependent on the size and the shape of parts. Through the experiment and analysis of the results, the rule of the dimensional change in the process of rapid manufacturing of metallic part could be summarized to feedback for the design of the CAD model"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003465_00423110600871533-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003465_00423110600871533-Figure4-1.png",
+        "caption": "Figure 4. Moveable frog strip discretization (a) and rolling trace on rail (b).",
+        "texts": [
+            " In other words, strips from one profile to another should have the same angle. Prior to the simulation, several static analyses are made on each profile for a set of relative wheel positions, supplying locations where contact is likely to occur. Strips are concentrated on these locations and follow the centred wheel trajectory. This has the double advantage of minimizing interpolation artefacts and increasing accuracy as only the potential contact areas are finely meshed. 4. Case study 4.1 Model Figure 4(a) shows a mesh of a moveable frog, derived from a CAD model, similar to the one shown in figure 1(b). Strips limits are longitudinal lines, and cross-sections, transversal ones. Perspective effects have been intentionally removed, as the tread is \u223c0.1 m wide and the view spans along 20 m. Strip widths vary between 0.04 and 2 mm. Cross-sections are selected according to two criteria: on one hand, they are associated to varying rail profiles and, on the other hand, to locations where contact will exhibit jumps and transitions. The latter type of cross-section is selected during the quoted static analyses performed prior to the simulation. In the present case, the mesh is concentrated on relatively thin zones, as theoretical profiles are concerned. In worn profiles, contact zones would be more spread over the rail surface. 4.2 Results Figure 4(b) shows a typical result from a dynamic simulation: the black area is the rolling trace of the wheel on the rail when the vehicle runs straightforward (figure 1(a)) on a tangent track without additional irregularities. The model has 250 strips per cross-section and 16 crosssections. The ratio between the computer time and the real time is about 10 on a 2.5 GHz processor PC. Figure 5 shows at the top the Q vertical force (expressed in kN) applied on the rail when the frog is crossed. Figure 5 shows at the bottom, the maximum contact pressure pmax (in MPa)"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure4.6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure4.6-1.png",
+        "caption": "Figure 4.6. Application of multiple reference frames to a motor-driven gear mounted on a spin ning platform.",
+        "texts": [
+            " Therein, the constant 244 Chapter 4 angular velocity of the gear relative to the platform is given as ro 1 = 1 Onh rad/sec; and ro1 = 20nk 1 rad/sec is the constant angular velocity of the platform relative to the ground. Determine the total angular velocity of the gear relative to the ground, but referred to a frame fixed in the platform. Label and identify carefully all references frames used. Solution. The problem statement suggests that three imbedded reference frames are relevant. The frames may be labeled in any convenient manner. We shall use the consecutive numerical scheme shown in Fig. 4.6. Thus, frame2={G;i 2 ,j 2 ,k 2 } is fixed in the gear G; frame l={O;i 1,j 1,kJ} is imbedded in the platform P; and frame 0 = { F; I, J, K} is in the ground F. Recalling the assigned data, we identify ro 21 = ro 1 = lOnh rad/sec as the constant angular velocity of frame 2 (the gear) relative to frame 1 (the plat form), and ro 10 = ro1 = 20nk 1 radjsec as the constant angular velocity of frame 1 relative to frame 0 (the ground). We note also that j2 = j 1 \u2022 Therefore, the total angular velocity of the gear frame 2 relative to the ground frame 0, but referred to the platform frame 1, is given by the kinematic chain rule ( 4",
+            " We thereby obtain the following composition rule for several angular acceleration vectors: ( 4.37) Finally and more generally, it may be seen from (4.22) and (4.21) that the time derivative of ro;k in any frame p is determined by ( 4.38) Clearly, when p = k, ( 4.38) yields ( 4.37 ). Henceforward, our use of the special notation will be restricted mainly to the first and last terms in (4.30), as appears in ( 4.34 )~( 4.37). Some examples will be presented next. Example 4.6. Let us return to Example 4.4 of the motor on the rotating platform shown in Fig. 4.6; and recall that the total angular velocity ro 20 of the gear relative to the ground is given by ( 4.26a ): Ref. ( 4.26a) Note that L belongs to the platform frame 1, and k 1 is fixed both in frame 1 and in the ground frame 0. Find the absolute angular acceleration of the gear referred to the platform frame. What is its time derivative in frame 0? Solution. Application of the composition rule ( 4.35) to the first equation in ( 4.26a) gives the total angular acceleration of the gear relative to the ground observer: ( 4",
+            " Motion Referred to a Moving Reference Frame and Relative Motion 255 Because the first equation in (4.39b) holds for all times, its derivative in frame 0 is given by (4.39c) in which (4.20a) was used with U=ro 21 and we have putj=j1 to reach iden tity with our earlier result ( 4. t 8b ). Note also that i being fixed in frame 1, di./dt = ro 10 xi, and hence ( 4.39c) may be derived from ( 4.39b) somewhat dif ferently, as described earlier in ( 4.8 ). D Example 4.7. Suppose that at the instant t 0 the gear in Fig. 4.6 has an angular speed of 3 rad/sec and an angular acceleration of 5 rad/sec2 relative to the platform, which has an angular speed of 7 rad/sec and is decelerating at the rate of 3 rad/sec2 relative to the ground. What is the angular acceleration of the gear relative to the ground at the time t0 , but referred to the platform frame? Solution. We are given ro 21 = 3j radjsec, bro2I \u2022 2 Tt = 5J rad/sec , ro 10 = 7k rad/sec, wherein we have put j = j 2 and k = k 1 \u2022 All vectors are referred to the platform frame"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001909_20.250667-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001909_20.250667-Figure4-1.png",
+        "caption": "Fig 4. Current distribution in the conductor^",
+        "texts": [
+            " This case is particulary favourable since there are only two different geometries of the end windings. The domain under investigation is represented in figure 3. We can see in the figure 3 one portion of the magnetic circuit and the conductors outside. The domain under investigation has been arbitrarily limited at a finite distance as is usually the case when solving partial differential equations. The computation proceeds along two steps. The first one consists of computing the current density at every point of the conductors using an electrokinetic formulation [ I l l ( fig 4 ). The second step consists of making a magnetostatic computation using the vector potential with Dirichlet boundary conditions on the boundary surfaces surrounding the machine. Once the vector potential has been computed, the end winding reactance is computed as previously described. In this special case, the only comparison was with the analytical formulae. An error of 3.7 % was found between the two results. This machine is interesting because its geometry is simple and it is possible to make many numerical experiments"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001121_physreve.65.011701-Figure26-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001121_physreve.65.011701-Figure26-1.png",
+        "caption": "FIG. 26. Top view of the TGBC j th block. ~a! At zero field, the director is oriented according to the intersection of the two cones related to the two successive blocks. ~b! Under an electric field, an induced tilt angle ensures the director continuity.",
+        "texts": [
+            " We can now ask the question of the physical origin of the anchoring coefficient b . Let us begin by the TGBC phase. We tempt to explain its behavior with the help of the TGBC phase description first given by Dozov @25# and backed up by optical reflectivity experimental studies @26#. In this model, the TGBC phase is not constituted by homogeneous Sm-C* blocks with director rotations localized in the grain boundaries; the rotation of the director is on the contrary uniformly distributed in all the block thanks to weak rotations easily realized on the smectic cone; Fig. 26~a! schematizes such a twisted structure in the absence of applied field: uSw0(X)52pX/p for 2lb/2,X,lb/2; at the grain boundary, the director is continuous and oriented along the intersection of the two smectic cones related to the two successive blocks. The electric field exerts a couple that tends to -13 turn the director on the first cone to the left side of the grain boundary and on the second cone to the right side of this grain boundary. If the spontaneous tilt angle of the cone is large ~far from TC for the compound n511, and in the whole existence domain of the TGBC phase for n512), these two movements would break the continuity of the director and would provoke a splay deformation of very large energy density. To ensure the continuity of the director, an additional tilt is then necessary @Fig. 26~b!#; its amplitude is about u i 5w0(lb/2)usw i . The associated energy density, localized near the grain boundary, is a(Tc2T)w0(lb/2) 2 us 2w i 2 . An additional torque, which is equal to 2a(Tc2T)w0(lb/2) 2 usw i , exists then near the grain boundary. The anchoring at the grain boundary can so be understood as a consequence of this torque induced by a tilt that must be added to the azimuthal rotation in order to ensure the director continuity. On the contrary, for the TGBA phase, the rotation of the director is probably not uniformly distributed in the whole block @because a large tilt like u0(X)5(2p/p)X would cost an energy density much larger than the energy cost of the azimuthal rotation usw0(X) in the TGBC phase#"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000704_a:1008228120608-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000704_a:1008228120608-Figure6-1.png",
+        "caption": "Figure 6. Plot of the full map with the parameter value Vdr = 0:0812. Thick lines indicate the permanent part of the map, thin lines the transient part. The numbers \u20181\u2019 and \u20182\u2019 distinguish between two attractors. The intervals B1 and B2 constitute the basin of attraction of the attractor \u20182\u2019 whereas the rest of the interval CA is attracted by the attractor \u20181\u2019.",
+        "texts": [
+            " The second property of the map was found in all the numerical examples that were taken into consideration. If the driving velocity is small the points lying on the line AC into the failure locus represent all the transient motions once the possible global slip phases have ceased [7]. The stretch length d may vary between 0:6764 and 0.6764 which correspond to the points C and A, respectively, of the failure locus of Figure 2. Choosing a grid of initial conditions on this line, it is possible to investigate the global dynamics of the system. Figure 6 is an illustration of the global dynamic behaviour of the system by means of the one-dimensional map. In Figure 6 the thin lines indicate the transient behaviour whereas the thick lines are composed by points belonging to the steady state behaviour of the system. There exist (at least) two attractors, indicated by the numbers \u20181\u2019 and \u20182\u2019, so that the interval CA, where the map is defined, is divided in two basins of attraction; the two sub-intervals B1 and B2 constitute the basin of the attractor \u20182\u2019, the other sub-intervals are the basin of attraction of the attractor \u20181\u2019. The one-dimensional map will be utilised to study the evolution of the attractor \u20182\u2019 as Vdr varies"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003477_cnm.913-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003477_cnm.913-Figure2-1.png",
+        "caption": "Figure 2. Symmetry groups associated with some symmetrical structures.",
+        "texts": [
+            " Based on the above definitions, the latter will be the principal axis of the structure. The symmetry centre of this grid is joint \u2018i\u2019. The concept of different kinds of symmetry planes can be recognized from the planar frames of Figure 1(b), and the three-dimensional frame of Figure 1(c). Symmetry operations of an object under the combination of transformation operations comprise a group, which is called a symmetry group. Symmetry groups are classified based on symmetry operations which make a group up. Figure 2 shows some symmetric structures and their symmetry groups. The symmetry group of a finite body is sometimes referred to as the point group. There are several methods for categorizing the point groups. In Figure 2, the point groups are named based on Scheonflies method, which is more conventional than the other approaches. The procedure of this method can be widely found in the literature [14, 15]. This method will be utilized in this paper. Copyright q 2006 John Wiley & Sons, Ltd. Commun. Numer. Meth. Engng 2007; 23:639\u2013664 DOI: 10.1002/cnm In an n-dimensional vector space V , with respect to a particular basis of the space, it is possible to show the effect of each symmetry operations on the basis vector of space with a square matrix"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002232_2.4711-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002232_2.4711-Figure1-1.png",
+        "caption": "Fig. 1 Airframe axes.",
+        "texts": [
+            " IV robuststabilityana-lysisof the closedloop system is considered. Conclusions follow in Sec. V. II. Preliminaries A. Missile Model Missile autopilots are usually designed using linear models of nonlinear equations of motion and aerodynamic forces and moments.15;18 The objective of this paper is robust design of a sideslip (yaw) velocity autopilot for a nonlinearmissile model. This model describes a reasonably realistic airframe of a tail-controlled tactical missile in the cruciform n con guration (see Fig. 1). The aerodynamicparameters in this model are derived from wind-tunnel measurements.10 The starting point for mathematical description of the missile is the following nonlinear model10;19 of the horizontal motion (on the x \u2013 y plane in Fig. 1): Pv D yv.M; \u00b8; \u00be /v \u00a1 Ur C y\u00b3 .M; \u00b8; \u00be /\u00b3 D 1 2 m\u00a11\u00bdV0S \u00a1 C yv v C V0C y\u00b3 \u00b3 \u00a2 \u00a1 Ur Pr D nv.M; \u00b8; \u00be /v C nr .M; \u00b8; \u00be /r C n\u00b3 .M; \u00b8; \u00be /\u00b3 D 1 2 I \u00a11 z \u00bdV0Sd \u00a1 1 2 dCnr r C Cnv v C V0Cn\u00b3 \u00b3 \u00a2 (1) where the variables are de ned in Fig. 1. Here, v is the sideslip velocity; r is the body rate; \u00b3 the rudder n de ections; yv and Cn\u00b3 Control moment s f Cy\u00b3 , where: s f D d\u00a11[2:6 \u00a1 .1:3 C m=500/] y\u00b3 semi-nondimensionalforce derivatives due to lateral and n angle; and nv; n\u00b3 , and nr semi-nondimensional moment derivatives due to sideslip velocity, n angle, and body rate. U is the longitudinal velocity. Furthermore, m D 125 kg is the missile mass, \u00bd D \u00bd0 \u00a1 0:094h air density (\u00bd0 D 1:23 kgm\u00a13 is the sea level air density and h the missile altitude in km), V0 the total velocity in m s\u00a11 , S D \u00bcd2=4 D 0:0314 m2 the reference area (d D 0:2 m is the referencediameter), and Iz D 67:5 kgm2 is the lateral inertia.For the coef cientsC yv ; Cy\u00b3 ; Cnr ; Cnv , and Cn\u00b3 only discretedata points are available,obtained from wind-tunnelexperiments.An interpolation formula for the Mach number M 2 [0:6; 6:0], roll angle \u00b8 2 [4:5, 45 deg] and total incidence \u00be 2 [3, 30 deg] has been derived with the results summarized in Table 1. The total velocityvectorV0 is the sum of the longitudinalvelocity vector U and the sideslip velocity vector v, that is, V0 D U C v, with all three vectors lying on the x \u2013 y plane (see Fig. 1). We assume that U \u00c0 v, so that the total incidence \u00be , or the angle between U and V0, can be taken as \u00be D v=V0 , as sin \u00be \u00bc \u00be for small \u00be . Thus, we have \u00be D v=V0 D v= p .v2 C U 2/, so that the total incidence is a nonlinear functionof the sideslipvelocity and longitudinalvelocity, \u00be D \u00be.v; U /. The Mach number is obviouslyde ned as M D V0=a, where a is the speed of sound. Because V0 D p .v2 C U 2/, the Mach number is also a nonlinear function of the sideslip velocity and longitudinal velocity, M D M"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002517_1.1515324-Figure24-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002517_1.1515324-Figure24-1.png",
+        "caption": "Fig. 24 Optimal trajectory solution at t1\u00c40.53 s and t2 \u00c40.09 s",
+        "texts": [
+            " In order to compare the optimal trajectory solution with human walking locomotion and examine the influence of the upper body mass on walking locomotion, we calculated the optimal trajectory solution under a full-actuated condition by using human body parameter values as shown in Table 2 @29#. The upper body is modeled as a concentrated mass at the hip. As illustrated in Section 3.5, the optimal step length is 0.3 m for the link parameter values in Table 1. Since the leg length values in Tables 1 and 2 are 0.8 m and 0.9 m, respectively, the step length of 0.33 m was used in this calculation by assuming that the step angle does not change in both cases. Figure 24 shows the most optimal trajectory solution that Transactions of the ASME 6 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F was obtained at t150.53 s and t250.09 s. We note that the walking pattern is very natural and similar to human walking locomotion. Figure 25 depicts the calculation results of the J value and the one step period in two cases with and without the upper body. In the case with the upper body, the optimal solution exists at t2 50.09 s (t150.53 s). It is notable that the one step walking periods in both cases are close to the adult\u2019s walking period of 0",
+            " From comparison of the walking pattern to the period and step length of the global optimal solution with those of an adult, it can be said that the walking gait of the global optimal solution is close to human walking locomotion. As seen in Fig. 25, the walking period is mainly determined by the leg parameter values, however the square integral of the input torque with upper body mass is about twice that without the upper body mass. Although not illustrated here, the walking pattern without upper body mass is very similar to that with upper body mass as shown in Fig. 24. Accordingly, it can be said that the upper body mass has little effect on walking pattern and step period, but increases square integral of input torque. Fig. 21 Walking period and average speed V\u0304 of optimal walking versus step length in full-actuated condition rom: http://dynamicsystems.asmedigitalcollection.asme.org/ on 01/28/201 In this paper, we numerically investigated the optimal walking locomotion with the least square input torque for a 3-dof model of a biped mechanism with a hip, knee, and ankle joints, using the optimal trajectory planning method"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003871_022-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003871_022-Figure1-1.png",
+        "caption": "Figure 1. The different separation points on the two sides of a spinning football lead to a deflected airstream.",
+        "texts": [
+            " Turbulent eddies form in a wake behind the ball and the kinetic energy in these eddies is derived from the slowing of the ball. With a spinning football, on the side of the ball moving with the flow the viscous force carries the air farther around the ball before the flow separates. On the side of the ball moving against the flow the air is slowed more quickly and separation occurs closer to the front of the ball. The result of this is that the air leaving the ball is deflected sideways as shown in figure 1. The sideways component of the airflow carries momentum in that direction, and since momentum is conserved, the ball must recoil with an equal but opposite momentum. This is the Magnus effect. The magnitude of the Magnus force can be written as FM = 1 2Cs\u03c1Aa\u03c9v (1) where \u03c1 is the density of air, A is the cross-sectional area of the ball, \u03c9 is the angular velocity, v is the velocity of the ball, a is its radius and Cs is an experimentally determined coefficient. 0957-0233/05/102056+10$30.00 \u00a9 2005 IOP Publishing Ltd Printed in the UK 2056 Alternatively, the Magnus force can be written in terms of a lift coefficient CL as FM = 1 2CL\u03c1Av2"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000627_10402000008982353-Figure12-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000627_10402000008982353-Figure12-1.png",
+        "caption": "Fig. 12-Schematic diagram of a step bearing.",
+        "texts": [],
+        "surrounding_texts": [
+            "N. WANG, C. HO AND K. CHA\nFig. 8(b)-Effect of elllptlclty ratio and orientation on minimum film thickness in en elllptlcal bearlng.\nEllipticity Ratio\nFlg. 9(a)--Search paths of maxlmlzlng film pressures In the lower and upper lobes of an elliptical bearlng.\nFig. 9(b)-Effect of elllpticlty ratlo and orientation on the normalized P21,msr + P22,max of an elliptlcal bearing.\nEllivtical Bearing Dbicctivc Fusction: p,,'- + p:_ W Desinn Varinblq : Ellipticity Ratio\nOricnlntion\nDiam. = 125 mm; Width = 95 mm Clcarnncc = 0.105 mm Ellipticity Rario = 0.805 Orientation = 59.7\" Sped= 1500rpm Load= 2.940 N pressure profile Effective Viscosity = 6.9 mPa-rec\no.m! . . ; . . *, . . , '. . , 0 PO 180 270 360\nCircumferential Location (deg.)\nFig. 9(c)-Pressure distribution along the centerline of the bearlng in the direction of sliding of an optimized elliptical bearing.\nFig. 9(d)-Pressure dlstribution of the optimized elliptical bearing for maximizing p2,m,x + P22,mar\nFor hydrodynamic bearings, the load-carrying capacity arises entirely from the pressure generated by the relative motion of thrust plate over the bearing pads. 'The magnitude of the pressure developed is a function of the profile of the film. In this section, two slider bearings (taper and step bearings) with no apparent side flow restrictions were optimized and the results are compared with those obtained from pocket-shaped bearing to determine the effect of side f ! ~ w restraint on load-carrying capacity.\nBoth finite element method and automatic mesh generation scheme were used in this study for effectively handling irregular film profile of pocket-shaped bearing. To simplify the analysis, the bearing length and width as well as the minimum film thick-\nD ow\nnl oa\nde d\nby [\nU ni\nve rs\nity o\nf Fl\nor id\na] a\nt 1 2:\n53 0\n1 O\nct ob\ner 2\n01 4",
+            "Engineering Optimum Design of Fluid-Film Lubricated Bearings\nCiumferential Location (deg.)\nFig. lO(a)-Comparison of film thickness and pressure distributions of two elliptlcal bearings.\nFlg. 10(b)-Lattlce search path of the optimized elliptical bearing for mlnlmizing frictlonal torque.\nness of the bearing were fixed to demonstrate the optimization procedure for finite slider bearings with several design parameters. In this study, golden section method for one variable and lattice search technique for multiple variables were employed to cany out the maximization procedure. In each calculation, a fixed film geometry was applied and the lubricant was considered to be incon~pressible and isoviscous (Eq. [2]). Finite element method (FEM) was used in this study to determine the pressure distribution of slider bearings. In contrast to finite difference method, FEM offers flexibility in handling step bearings where film profiles are discontinuous and for bearings with irregular shapes such as pocket-shaped bearings.\nIn this study a variation approach adopted for the two-dimensional lubrication problem was used. Two-dimensional, threenode triangular element was employed in the numerical scheme. Details of the assembly procedure, a bookkeeping procedure to form the fluidity matrix are given in Ref. (11) and will not be discussed here. In this example, the objective was to establish a numerical procedure to obtain the optimal film profiles for maximizing the load-carrying capacity of the slider bearings. The\nD ow\nnl oa\nde d\nby [\nU ni\nve rs\nity o\nf Fl\nor id\na] a\nt 1 2:\n53 0\n1 O\nct ob\ner 2\n01 4",
+            "N. WANG, C. HO AND K. CHA\nX-axis\nFig. 15--Normallzed mapped reglon of the optimal pocket-shaped slider bearing. A = (0.525,0.15), B = (0.725, 0.225), C = (0.775, 0.5), no. of elements = 640, no. of nodes = 349.\nl;\\l3l.lr 5-BlihRlNG GEOMETRY A N D LUBRICATION DATA USED IN THE\nSLIDER BEARING O~IMIZATION .\nMinimi1111 Film Thickness, ho --- Ltrbricnnt Viscosity, I( - Sliding Velocity. U . .-- 13cnring Lcngth, L - - -\nBcarine Widlh. B 50.8 rnrn 50.8 rnrn\nIn the analysis of pocket-shaped bearing, an automatic mesh generation neth hod was adopted to transform a rectangular region\nT~el.1: 6-NUMERICAL CONVERGENCE TESTS OF LOAD-CARRYING CAI>ACITY FOR 'I'HII POCKET-SHAPED BEARING SHOWN I FIG. 14\ninto a non-rectangular region by blending function method (12). For a pocket-shaped bearing, the square pad can be represented by two mapped regions, i.e. pocket recess and bearing land, with the same boundary points. In Fig. 14 three points, namely points A (%3,) = (0.25,0.2), B (%G) = (0.5,0.25), and C (73.Y,) = (0.6, 0.5), define the shape of the pocket. The number of the nodes and\nLOAD (N) 8,193 8,173 8,154 8,085 8,075\n. - - -\nNUMHIII< 01' NOI)I!S- ~\n127 163 189\n349 -- 447\nelements can be easily adjusted in the computer program that is essential to the optimization analysis. During the numerical calculations, the positions of points A, B, and C as well as the height of the step were adjusted independently using lattice search algo-\n- - - -- -\n~- N u M I ~ E R .. OF ELEMENTS . - - .- -- 22Op~- - -\n.- ~ 288 .- 336\n640 ~- 828\nrithm. Numerical convergence tests for the bearings with the same shape of pocket as shown in Fig. 14 were carried out by using FEM. The results are listed in Table 6. It can be seen from the calculated results, the bearing with 349-node and 640-element gives accurate estimation of load-carrying capacity. Based on this analysis, the number of the element of subsequent optimization analysis was chosen as 640 for pocket-shaped slider bearing.\nFor the taper bearing, the decision variable of the optimization problem was the slope of inclined surface of the slider, and golden section method was applied to calculate the optimal merit of load-carrying capacity. For the step bearing, the decision variables chosen were step height and the location of step. The decision variables for the pocket-shaped bearing analysis were step height, and the locations of three points defining the pocket shape. Lattice search was used to find the optimal geometry of the latter two bearings. The calculated load-carrying capacities for the optimal taper, step, and pocket-shaped bearings are 5,194 N, 5,586 N, and 9,222 N, respectively. The simulation results are summarized in Table 7.\nFor the optimal pocket-shaped bearing, the load-canying capacity is 1.65 times larger than that of optimal step bearing. Also, note that the optimal step height is increased from 0.019 mm in step bearing to 0.03 1 mm in optimal pocket-shaped bearing. The increased step height means the pocket-shaped bearing can sustain more start-stop operations. If the step is too small, the bearing will worn smooth and flat more quickly, and then eventually seized. The profile of the optimized pocket-shaped slider bearing is shown in Fig. 15.\nOPTIMIZATION OF AEROSTATIC BEARINGS\nIn this section, the air-bearing model and the solution scheme presented by Wang and Chang (13) was adopted to analyze the\nD ow\nnl oa\nde d\nby [\nU ni\nve rs\nity o\nf Fl\nor id\na] a\nt 1 2:\n53 0\n1 O\nct ob\ner 2\n01 4"
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0003219_iros.1992.594551-Figure13-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003219_iros.1992.594551-Figure13-1.png",
+        "caption": "Fig. 13. An undesirable intermediate configuration.",
+        "texts": [
+            " The advantage of this insight is that the simulated annealing method is faster by roughly a factor of three for our example. The space, however, is now small enough that it is possible to consider exhaustive search. It should be noted that this reduction of dimensionality is fortunate, since it is not always possible. D. How good is the planning? The method described above seeks the parameters of a dig that would optimize the payload at every dig. Attention to only local optimality, however, can cause problems in the long run. The configuration of the terrain shown in Fig. 13 illustrates this problem. Here, the excavator cannot fill its bucket because a small pile keeps it from getting close enough. A robot using the optimization scheme discussed above will continue to dig from the larger pile until the volume it can excavate is less than that it can obtain from the smaller pile. Such a scheme is bound to suffer in terms of overall efficiency. What we really want is to select actions that maximize the expected gain over a number of digs (ideally up to the end of the task) because some actions may produce low gain in the short term but are necessary to set the stage for greater gain in the future. Somewhat surprisingly, the local plans produced by the proposed method have shown quite good results. In simulation we have obtained over 90% efficiency, for the loading task that has been described a\u2019bove. That is, on the average,the excavator is able to fill its bucket to over 90% of its capacity. A close examination of the proposed method provides some clues as to why the efficiency is as high as we have seen. Configurations as the one shown in Fig. 13 are common as the excavator progresses in removing the soil from the pile. However, for the link dimensions and the joint limits of the excavators we have experimented with, the kinematic constraints reduce the action space such that before long the small pile is the only feasible dig remaining. Some caveats are in order. The simulation we have used does not model uncertainty in actuation. That is, the optimal dig selected is carried out perfectly, and the amount of soil obtained is exactly as expected"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003657_j.cma.2005.02.033-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003657_j.cma.2005.02.033-Figure1-1.png",
+        "caption": "Fig. 1. 2-link manipulator: absolute coordinates.",
+        "texts": [
+            " In this section, a quick review is given of coordinates that are suitable for implementation in a multibody formulation, i.e. an automated approach to equation generation with no manual intervention by a user. Note that the \u2018\u2018natural\u2019\u2019 coordinates used by Garc\u0131\u0301a de Jalo\u0301n and Bayo [7] and the closely-related \u2018\u2018point coordinates\u2019\u2019 of Nikravesh and Affifi [8] are beyond the scope of the current paper. Absolute coordinates represent the position and orientation of each body in the system relative to a global reference frame. To demonstrate, consider the planar 2-link serial manipulator shown in Fig. 1. A body-fixed reference frame is attached to each body i, often at the center of mass Ci. The position of the frame is given by the Cartesian coordinates (xi, yi) of its origin, while the angle hi defines the frame orientation. Thus, for the 2-link manipulator, the set of 6 absolute coordinates would be: qa \u00bc \u00bdx1; y1; h1; x2; y2; h2 T. \u00f01\u00de A disadvantage of absolute coordinates is that they are generally much larger in number than the degrees of freedom (DOF) of the system, especially for spatial problems when six coordinates (at least) are needed for each body"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003630_chem.200600304-Figure11-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003630_chem.200600304-Figure11-1.png",
+        "caption": "Figure 11. Plot of the apparent flat-band potential (Vfb) as a function of pH conditions for Zn ACHTUNGTRENNUNG(ImPPh)/Zn ACHTUNGTRENNUNG(ImPR)/ITO (R = PO3 (*), -Ac2 (^), and -S2 (~)).",
+        "texts": [
+            " [13] Depending on the pH, the surface states of ntype semiconductor electrodes are strongly affected by the potential drop across the bulk medium in the Helmholtz layer.[13,39] Comparison of the pH dependences for the anchoring groups implies that the surface state strongly depends on the surface anchoring group. Chem. Eur. J. 2006, 12, 8123 \u2013 8135 H 2006 Wiley-VCH Verlag GmbH&Co. KGaA, Weinheim www.chemeurj.org 8129 FULL PAPERPorphyrin Assemblies on ITO Anodes The apparent Vfb for the porphyrin-modified ITO was evaluated from the zero-current intercept in the I\u2013V plots (Figures 8, 9, and 10). Apparent Vfb is plotted as a function of pH in Figure 11. At alkaline pH, the apparent Vfb is shifted to more cathodic potentials. As the pH increases, the band-edge potentials are therefore assumed to rise and provide higher Schottky barriers, suppressing backward electron transfer from the CB to the porphyrin radical cation (Scheme 1a\u2013c). Since the slope in the Vfb\u2013pH plot exceeds the Nernstian slope of H2Q ( 59 mV(pH) 1),[40] the efficiency of anodic photocurrent generation is determined not only by the redox potential of H2Q, but also by the ITO surface state. The Vfb value of intrinsic n-type semiconductors normally changes linearly as a function of pH.[39] Thus, a relatively linear pH dependence of Vfb for ZnACHTUNGTRENNUNG(ImPPh)/ZnACHTUNGTRENNUNG(ImPPO3)/ITO supports the assumption that the conduction band of the ITO electrode and porphyrin are strongly coupled via the phosphonate group (Figure 11). On the other hand, the existence of inflection points may be attributed to a protonation\u2013deprotonation equilibrium of the physisorbed species. This may imply that the surface charge of ITO affects the band-edge potentials.[41] However, the detailed mechanism underpinning this phenomenon requires further study. The apparent Vfb value could be tuned by varying the anchoring porphyrin. The apparent Vfb values for ZnACHTUNGTRENNUNG(ImPPh)/ ZnACHTUNGTRENNUNG(ImPS2)/ITO were more anodic than those for ZnACHTUNGTRENNUNG(ImPPh)/Zn ACHTUNGTRENNUNG(ImPPO3)/ITO and ZnACHTUNGTRENNUNG(ImPPh)/Zn ACHTUNGTRENNUNG(ImPAc2)/ ITO"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002440_jp026799d-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002440_jp026799d-Figure4-1.png",
+        "caption": "Figure 4. Cyclic voltammograms of cell 1 with 4 \u00d7 10-4 M ferricytochrome c in the aqueous phase, (a) in the presence of, and (b) in the absence of, 1 \u00d7 10-4 M dimethylferricenium ion in the organic phase. Scan rate employed in both cases is 0.05 V s-1.",
+        "texts": [
+            "1 V, in the absence of any aqueous phase electron acceptor, Figure 3. This process is attributed to the transfer of the electro-generated dimethylferricenium ion from DCE to water: Randles-Sevc\u030cik analysis21 of the ion transfer data gave a diffusion coefficient value of 2.8 \u00d7 10-6 cm2 s-1 in agreement with the value reported for this species in DCE.26 Introduction of oxidized cytochrome c to the aqueous phase of cell 1, in the presence of preoxidized DMFeCp2 (1 \u00d7 10-4 M), gave the voltammetric response shown in Figure 4a. Comparison of the cyclic voltammogram with that obtained with no dimethylferricenium cation initially present (Figure 4b) shows that the two chargetransfer processes have merged into a single voltammetric feature, with an enhanced current. This observation suggests that there may be a coupling between the ion and electrontransfer processes, as found in biological systems.26,27 Finally, comparison of the midpoint potential, for the electron transfer observed at the ITIES between DMFeCp2 and cytochrome c, and the corresponding value reported for DMFeCp2 and ferricyanide ions26 reveals that the former is ca. 0.08 V positive of the latter"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000963_j.1460-2687.2001.00069.pp.x-Figure7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000963_j.1460-2687.2001.00069.pp.x-Figure7-1.png",
+        "caption": "Figure 7 Experimental arrangement used to measure the ACOR along the major axis.",
+        "texts": [
+            " This effect was not studied in detail, but estimates of the magnitude of this effect are consistent with a shift of 20 mm in the expected location of the COP. Of more direct signi\u00aecance is the possible shift in the COP resulting from the much larger force on the handle that would be exerted by the hand, as described by Hatze (1998). This effect warrants further careful experimental investigation. However, it is not easy to locate the COP precisely, since motion of the handle in this impact region is dominated by effects due to vibration of the handle (Cross 1998a; 1998b) The arrangement used to measure the ACOR is shown in Fig. 7. The racket was suspended horizontally, with the string bed in a vertical plane, using two lengths of string tied to the racket, one at the butt end of the handle and the other at the 3 o'clock point on the frame. A tennis ball was mounted, as a pendulum bob, at the apex of a V-shaped string support, so that it could impact the strings horizontally, at right angles to the string plane and at selected points along the major axis. This arrangement provided good reproducibility as well as a simple and accurate means of controlling 10 Sports Engineering (2001) 4, 1\u00b114 \u00b7 \u00d3 2001 Blackwell Science Ltd the impact point"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001508_978-1-4615-2135-8_1-Figure1.1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001508_978-1-4615-2135-8_1-Figure1.1-1.png",
+        "caption": "Figure 1.1 Diagrammatic representation of the dragflow moving material (nut) along a screw (bolt).",
+        "texts": [
+            " High-shear screw extruders are used to make pet foods, puffed snack foods and breakfast cereals. The discussion of extruders in this book will be limited to the most frequently used styles of screw extruders. Single:'screw extruders rely on drag flow to move material down the barrel and develop pressure at the die. To be pushed forward, dough should not rotate with the turning screw. This can be compared to a bolt being turned while the nut turns with it; it will not be tightened. When the nut is held fast it moves forward when the bolt is rotated (see Figure 1.1). A single-screw extruder is not like a positive displacement pump. It is a drag flow device, i.e. material is dragged down the barrel. To be pushed forward, material should not rotate with the screw. The only force that can keep the material from turning with the screw and, therefore, make it advance along the barrel, is its drag or friction against the barrel wall. The more friction, the less rotation and the more forward motion. Most N. D. Frame (ed.), The Technology of Extrusion Cooking \u00a9 Springer Science+Business Media Dordrecht 1994 single-screw extruders have grooves cut into the barrel in order to promote adhesion to the barrel wall"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000726_s0043-1648(96)07463-7-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000726_s0043-1648(96)07463-7-Figure3-1.png",
+        "caption": "Fig. 3. Schematic diagram of sealing zone with ingested meniscus.",
+        "texts": [
+            " the pressure-driven flow and the reverse pumping, are equal, and there is no net leakage. This defines the steady state operating point of the seal. As the shaft speed is increased, reverse pumping is increased and the meniscus moves closer to the edge of the sealing zone (l m decreases). Eventually, a critical shaft speed is reached, such that the meniscus is right at the edge of the sealing zone (l m s0). If the shaft speed is increased further, then the meniscus moves into the sealing zone and is said to be \u2018ingested\u2019. This situation is shown in Fig. 3, where the meniscus location is denoted by y m . Once again, themeniscus assumes a location such that the net leakage is zero, so defining the operating point of the seal. Analysis of the flow field in the sealing zone is a problem in elastohydrodynamics, because the fluid mechanics of the film are closely coupled with the elastic deformation (both normal and shear) of the lip. The film thickness distribution is taken to be of the form U U U U Uh sh q$[cos 2p(x yd )][1ycos(2pNy )] (1)0 where the first term represents the average film thickness, and is an initially unknown function of the axial location yU ",
+            "0q (I ) (P yP ) R Dy /h (3)0 i 1 ik avg contact k 18 ks1 n U U U U U(d ) s (I ) (t ) R Dy /l (4)i 2 ik avg k8 ks1 where the shear stress is given by U U U Ut s(V /h )(1/h ) (5)1 The average film thickness at each axial location depends on the difference between the fluid filmpressure and the static contact pressure at all locations, while the circumferential displacement of the lip surface depends on the shear stress in the film at all axial locations. The influence coefficients and the static contact pressure distribution are found from a finite element structural analysis and modelling of the lip. h and U 0 dU are computed over the entire sealing zone, even when the meniscus is ingested. When the meniscus is ingested, it is assumed that, in the portion of the sealing zone occupied by air (to the left of the meniscus in Fig. 3), the pressure is atmospheric and the shear stress is negligible. Thus, the pressure and shear stress in the air region do not contribute to the lip deformation. However, the pressure and shear stress in the liquid region produce deformations in the air region. Such deformations are necessary to prevent collapse of the film in the air region. The dimensionless leakage rate is found by numerically integrating, so we have 1 EfU U U U 3Q sV h dx (6)| U Emy0 Positive values of QU indicate leakage from the liquid side to the air side of the seal, while negative values indicate reverse pumping from the air side to the liquid side"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001441_tmech.2003.816806-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001441_tmech.2003.816806-Figure4-1.png",
+        "caption": "Fig. 4. Example compound surfaces and the initial FPAG.",
+        "texts": [
+            " Here, the merging operator is defined as follows: (3) \u2022 Replace node , and edge with node . \u2022 Recalculate the weight of all affected edges. In (3), is calculated after the new average normal is obtained. According to the above definitions, the FPAG has the following properties: 1) an FPAG is a connected graph; 2) when a FPAG undergoes a merging, it is still a FPAG; and 3) each merging reduces the number of nodes in FPAG by 1. The example compound surfaces and the corresponding initial FPAG are shown in Fig. 4. The merging algorithm is as follows. In the FPAG, find a pair of adjacent flat patches with the closest normals and test if the merged patch is a flat patch. If yes, update the FPAG. Otherwise, keep the two flat patches and assign a big value to the weight of the edge between them to keep them away from competing in the following iterations if neither of the two flat patches is changed. Then, the whole process is repeated on the updated FPAG. When updating the FPAG, the edge with big value weight will be recalculated if either of its corresponding flat patches is merged with other flat patches"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001113_ac025836u-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001113_ac025836u-Figure1-1.png",
+        "caption": "Figure 1. (a) Vial electrode, (b) injection capillary incorporating reference/counter electrodes, and (c) measurement system.",
+        "texts": [
+            "35-37 In this paper, we propose a new development of a picoliterscale vial, which includes an integrated (fixed) working microelectrode. This method of fabricating a vial electrode is based on the modification of a composite microelectrode. In brief, devices are fabricated by electrochemical etching of gold embedded in a glass capillary. The resultant cavity, formed in the end of the capillary, is utilized as an ultralow-volume vial into which either single cells or reagents can be readily placed using micromanipulators; see Figure 1. By varying the time of electrochemical etching and the radius of the gold wire, different geometries of electrodes can be readily fabricated with different measurement volumes. To prevent evaporation, the cavity of the vial electrode can be sealed with a layer of mineral oil to make a closed system as described below. Notably, the use of bulk metal (rather than evaporated thin films) as the electrode structure leads to a robust and simple device that is readily cleaned prior to reuse. In contrast to studies using recessed electrodes, referred to above,22-33 this method also has the advantage of not requiring the use of infrastructurally demanding equipment such as photolithography or screen-printing to fabricate devices suitable for the studies described below",
+            " As in other studies,46,47 enzyme-linked electrochemical assays provide a convenient route to quantitatively determine metabolic flux of specific species from cells. Reagents. Potassium ferrocyanide, L-ascorbic acid (AA), ferrocenemethanol (FcOH), hydrogen peroxide (30%), horseradish peroxidase (HRP), catalase, ascorbate oxidase (AOx), sodium dodecyl sulfate (SDS), and mineral oil were purchased from Sigma and used without further purification. All the solutions were prepared from distilled and deionized water obtained from Aquarius GS-200 (Advantec) or Milli-Q Jr. (Millipore) systems. Fabrication of Vial Electrodes. Picoliter-sized vial electrodes (Figure 1a) were fabricated from microdisk electrodes constructed as described in previous publications.48,49 The microelectrodes comprising embedded gold wire (radius 25 \u00b5m) were first heated 5 mm from the top of the tip using a platinum wire heating loop, and the softened glass formed a bend of \u223c90\u00b0 in the glass capillary. The gold tip was etched electrochemically (300 Hz, ac voltage with 5-10 V peak-to-peak) for 10-20 min in a saturated aqueous solution of NaNO3. Controlling the etching time and intensity of voltage varied the depth of the cavity (Figure 2). Fabrication of an Injection Capillary. The composite reference/counter electrode was constructed within an injection capillary; see Figure 1b. A \u03b8-type (conjoined double-capillary) glass tube (World Precision Instruments, Tokyo, Japan) was pulled using a capillary puller (model PD-5, Narishige, Tokyo, Japan) to make a capillary with two openings, each of 0.05-\u00b5m radius. An aperture was made in one of the two joined capillaries, a Ag/ AgCl wire was inserted, and the tube was filled with a saturated KCl solution. The Ag/AgCl wire was held in place using epoxy and was used as a reference/counter electrode. This composite electrode assembly was connected to a microinjector (IM300, Narishige), thereby allowing the nonreference electrode opening to be used to inject precise picoliter-scale quantities of solution into the analytical chamber",
+            " Measurement System. All measurements were performed using an inverted microscope (MSL2PL, Meiji Techno, Saitama, Japan), a multipotentiostat (HA-1512\u00b5M8, Hokuto Denko, Tokyo, Japan), a CCD video camera (STC-630A, Kenko, Tokyo, Japan), a micromanipulator (MM-200, Narishige), a tilt stage (TS-201, Chuo Precision Industrial, Tokyo, Japan), an X stage (LS-612, Chuo Precision Industrial), a YZ stage (LM-612, Chuo Precision Industrial), and an XYZ stage (C7214-9015, Suruga Seiki Co., Ltd., Shizuoka, Japan) (Figure 1c). The precise position of the vial electrode and microelectrode tip was determined by imaging both the chamber and the injection system with a CCD video camera. Control of electrode potential and data acquisition were performed with a notebook computer equipped with a 16-bit AD/DA board (AZI-3506, Interface, Hiroshima, Japan). The analytical chamberelectrode assembly was mounted on the XYZ stage, and the composite reference/counter electrode and injection port was attached to separate micromanipulators"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003734_ip-b:19830027-Figure9-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003734_ip-b:19830027-Figure9-1.png",
+        "caption": "Fig. 9 Thrust T and drag force D of linear and rotary armatures, respectively, at same value of winding current density in both armatures",
+        "texts": [
+            " The test and theoretical results are shown in Fig. 7. Since the rotor length is 2.0 m only, it was difficult to obtain higher linear speeds than 1 m/s. To illustrate the influence of end effects on RLIM performance, the torque and linear forces have been calculated at different values of linear speed. The results are shown in Fig. 8. It can be seen that the torque decreases at high linear speeds. There is a drag force developed by the rotary armature owing to the end effects. It increases strongly in the high-speed range. Fig. 9 shows the total thrust of the RLIM calculated, as the sum of thrust and drag force of the linear and the rotary armatures, respectively. The calculations of these forces were made with the same value of current density in the two armature windings. The results are compared with the results obtained for the RLIM without any end effects (L = \u00b0\u00b0). In the real operating conditions of the RLIM, a high value of linear speed is not expected and the end effects will not be significant. IX = 4.52,IZ = 1"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002722_proc.1987.13726-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002722_proc.1987.13726-Figure1-1.png",
+        "caption": "Fig. 1. View of magnetic actuator.",
+        "texts": [
+            " INTRODUCTION The analysis presented below is applicable to the actuators used in magnetic bearings [l] and torquers [2]. The effects of eddy currents on the impedance and power loss for sine-wave excitation of the above types of actuators have been discussed by many authors [3]-(51. More recently, numerical and analytical techniques [6]-[SI have been developed for the study of transient eddy currents. 1 1 . THE TOTAL FLUX IN THE MAGNETIC CIRCUIT AND ITS TRANSFER FUNCTION Consider the simple electromagnetic actuator shown in Fig. 1. It will be assumed that it is constructed from a solid core of linear ferromagnetic material having width 2a and height 26, where a >> b. The winding about the core is excited by a current source. The usual assumption, when considering eddy currents in conductors, of neglecting the displacement current is made. Since a >> b the actuator can be approximately analyzed using the semi-infinite plate shown in Fig. 2. Following Stoll [3, p. 101 it can be shown that the magnetic intensity Hz satisfies the diffusion equation where uand g (=wr) are the plate conductivity and permeability, respectively",
+            " It should be noted that in (6) a is a function of the Laplace transform variables, so the transfer function &(s)/i1(s) is a transcendental function of s. 1 1 1 . APPROXIMATE TRANSFER FUNCTION From [9, eq. 1.421(2)] it can be shown that (6) can be written as 8 &(s) = @(x)N - 1 ++s(y) 1 1 + + (T) + . . . ] (7) For transient disturbances the time response due to the first term in the infinite sum dominates the effect of all the higher order terms so that we can approximate (7) by 1 + - + - + - + . . . 1 1 1 9 25 49 I i1W J Again from [9, eq. 0.234(2)] it is easily seen that where Tl = 4u&'/*?. Iv. MAGNETIC A TUATOR FORCE TRANSFER FUNCTION In Fig. 1, assume for simplicity that that magnetic circuit has a uniform cross-sectional area A, and that fringing effects in the air gap can be neglected. We make two further assumptions to simplify the analysis. First, 0018-9219/87/02~259$01.00 1987 IEEE PROCEEDINGS OF THE IEEE, VOL. 75, NO. 2, FEBRUARY 1987 259 it will be assumed that the eddy current time constants are short compared with the mechanical system time response, so that changes in the magnetic force due to mechanical motion can be considered to be due to the steady-state air-gap flux changes only",
+            " It will be noted from (9) that if the current il(t) = io, a constant, then lim f(i,)(t) = io (11) t- OD and if (i(t)( i s small then 1 f (i)(t)( will also be small for all t. Considering small perturbations of the armature position and coil current about an operating point (xo, io), (10) can be written in functional form as &(xo + Ax, io + ail)(t) = @(xo + Ax)N f(io + Ai,)(t). (12) Recalling the assumption that the armature position is changing slowly compared with the response time of the eddy currents, and expanding (12) using Taylor\u2019s theorem we obtain &(xo + Ax, io + Ai,)(t) = S(x,JNio + - Nio]Ax(t) + [WXJM f (Ai,)(t). (1 3) For the magnetic actuator shown in Fig. 1 it can be shown using energy methods [lo] that the force acting on the armature is Substituting (13) into (14) we find + 2[6(xdNiJ[6(xdNl f(Aiq)(t) 3 hence the perturbation force AF(Ax, Ai,)A is AF(Ax, Ai,) = K,Ax(t) + Kif(Ail)(t) where K , = 26(xo) - N2ig& a m o ) ax and Ki = 2P2(xd N2id&. Taking the Laplace transform of (16) we find Thisequation shows thefunctional relationship between thearmature force AF(s), the armature displacement Ax(s ) , and the coil current Ai&). The effect of the eddy currents is to introduce a time lagintheapplicationoftheforceduetochangesinthecoilcurrent"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002386_ip-cta:20030017-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002386_ip-cta:20030017-Figure1-1.png",
+        "caption": "Fig. 1 Flexible joinr manipuluior configuration",
+        "texts": [
+            " To develop a systematic procedure, a T-S fuzzy modelling method, exact T-S fuzzy modelling, has recently heen developed. The basic idea of exact T-S fuzzy modelling for nonlinear systems was first discussed in [16]. Here, the word 'exact' means that the defuzzified output of the T-S fuzzy modelling for flexible IEE Proc.-ConIml Theoq Appl.. El. 150, No. 2, March 2003 constructed T-S fuzzy model is mathematically identical to that of the original nonlinear system. Consider the single link flexible joint manipulator shown in Fig. 1 whose dynamics can he written as x, =x, ~. MgL . k x2 = --smxI I - i ( ~ , -x3) x3 = x, (26) K 1 J 4, = + X I - x z ) + - u where I, J are, respectively, the link and the rotor inertia moments, M is the link mass, k is the joint elastic constant, L is the distance from the axis of rotation to the link centre of mass and g is the gravitational acceleration, respectively. The system (26) has a nonlinear term, sin(xl(t)). If this nonlinear term can he represented as a weighted linear sum of some linear functions, then the T-S fuzzy model of (26) can he Constructed"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003586_1.2164483-Figure8-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003586_1.2164483-Figure8-1.png",
+        "caption": "FIG. 8. Schematic representation of the vapor flow friction effect on the liquid wall.",
+        "texts": [
+            " Therefore we can consider that the modeling approach developed concerning the study of the vapor parameters outside the keyhole would be an interesting guide for optimization of the operating conditions during a laser welding process. For the second part of Sec. III, and as it was mentioned before, because of its importance in the determination of the weld seem geometry after solidification, we are interested in our study by the interaction of the vapor flow with the liquid wall through the friction effect leading to the induction of a movement in the melted bath. The main purpose of our modeling is thus to make evident the displacement process of the melted metal. The representation of the mechanism described is given in Fig. 8 shows that a flow is induced in the melted metal by the drag effect due to the vapor flow associated viscosity. Experimental studies on this phenomenon performed by Fabbro et al.,7,9 have allowed us to analyze the effect of the keyhole expelled vapor. By using twin or triple laser beams and high speed cameras, the melted bath surface evolution has been observed and the characteristics of the obtained hydrodynamic flow were interpreted as the demonstration of the vapor friction effect which can play a significant role in determining the weld joint pattern during resolidification"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000674_20.497338-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000674_20.497338-Figure1-1.png",
+        "caption": "Fig. 1. (a) Magnetic coupling with 8-8 poles bonded NdFeB magnets. 6) Magnetic coupling with 8-8 poles sintered NdFeB magnets.",
+        "texts": [
+            " EXPERIMENTAL ND THEORETICAL ANALYSES Two Merent commercially available magnetic materials, bonded NdFeB with (13Hmax) of 8.2 MGOe and sintered NdFeB with @Hmax) of 31.3 MGOe, were chosen for fabrication of magnetic gears for this study. The radial magnetic coupling device was constructed by using two cylindrical magnets which were magnetized with a multipole configuration along the radial direction. The magnetization profiles with 8, 10, and 12 poles were used to analyze the variation of magnetic coupling. For example, Fig. 1(a) shows an 8-8 poles magnetic coupling device made of the bonded NdFeB magnet, and Fig. l(b) shows an 8-8 poles magnetic coupling device made of the sintered NdFeB magnet. All bonded NdFeB samples have an outer radius of 00 18-9464/96$05 .OO @ 1996 IEEE 39 mm, inner radius of 33 mm and are 56 mm long. In case of the sintered NdFeB samples each pole was made of a piece of sintered NdFeB magnet with 2 mm thick dimensions of 4 x 6 x 30 mm3 which was attached to an iron yoke as shown in Fig. l(b). Therefore, the inner radii are 14"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002529_s0379-6779(02)00099-1-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002529_s0379-6779(02)00099-1-Figure4-1.png",
+        "caption": "Fig. 4. Cyclic voltammograms of PANI modified Ni (1) and Pt (2) electrodes in 0.5 M H2SO4 containing 5 mM Fe2\u00fe/Fe3\u00fe. Scan rate \u00bc 10 mV s 1.",
+        "texts": [
+            "5 M H2SO4 containing 50 mM of Fe2\u00fe=Fe3\u00fe. The voltammograms of the redox reaction (Fig. 3) resemble to those shown in Fig. 2 in shape as well as in magnitude of the peak currents and the peak potential values. These results suggest that the catalytic behavior of PANI deposited in presence and absence of redox ions is alike towards reaction (1). For the purpose of comparison, cyclic voltammograms of both Pt and PANI modified Ni electrodes were recorded in 0.5 M H2SO4 supporting electrolyte consisting of Fe2\u00fe=Fe3\u00fe (Fig. 4). Peak current of the PANI modified Ni electrode is higher than that of the Pt electrode. Similar observation is made at several concentrations of the redox couple and several sweep rates. The potential of a PANI modified Ni electrode was measured in 0.5 M H2SO4 consisting of Fe2\u00fe=Fe3\u00fe at several concentration ratios. A linear variation in potential (Fig. 5) suggests that the PANI modified electrode senses the concentration variation of the redox couple. The potential of a PANI modified Ni electrode was potentiostatically fixed at a know value on either side of the mid-potential (Er) of the voltammetric peaks and the current flowing through the electrode was measured as a function of concentration of one of the redox species by maintaining the concentration of the other species constant"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003477_cnm.913-Figure21-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003477_cnm.913-Figure21-1.png",
+        "caption": "Figure 21. Subsystems associated with subspaces of the problem: (a) basis vectors of subspaces; and (b) decomposed subsystems.",
+        "texts": [
+            " Therefore, it will be possible to form the vibration equation of each subspace and find the submatrices K( ) and M( ) of the subspace V ( ). In order to highlight the procedure, the simple example of part 4.2 is solved again with this technique. This method can easily be extended to more complex problems. The basis vectors of subspaces V (1) and V (2) found in Section 4.2 are as follows: V (1); (1) 1 = 1\u221a 2 (1, 1, 0)t, (1) 2 = (0, 0, 1)t and V (2); (2) 1 = 1\u221a 2 (1, \u22121, 0)t These basis vectors are depicted on the graph model of the structures in Figure 21(a). Based on the notation mentioned in Section 4.1, the mechanical interpretation of these subgraphs, are as shown in Figure 21(b). In this figure, it can be seen that for subspace V (1) there are two independent DOFs \u2018x1 and x2\u2019, and for subspace V (2) there is only one independent DOF \u2018x1\u2019. Copyright q 2006 John Wiley & Sons, Ltd. Commun. Numer. Meth. Engng 2007; 23:639\u2013664 DOI: 10.1002/cnm Free vibration equations of each subspace can now be written directly from Figure 21(b) as follows: Subspace V (1) : \u23a1 \u23a3 k2 \u2212\u221a 2k2 \u2212\u221a 2k2 \u221a 2k1 + 2 \u221a 2k2 \u23a4 \u23a6 { x1 x2 } + [ m2 0 0 m1 ]{ x\u03081 x\u03082 } = { 0 0 } Subspace V (2) : (k2 + 2k3) x1 + m2. x\u03081 = 0 which confirms the results provided in Section 4.2. Although the method described in this section is helpful for the hand calculation, in that there is no need to get involved in calculations dealing with super matrices\u2014especially in the large-scale problems\u2014the original step by step method that includes forming the full matrices of the system is more systematic and adaptable to automation"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002264_j.ijsolstr.2003.09.054-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002264_j.ijsolstr.2003.09.054-Figure2-1.png",
+        "caption": "Fig. 2. Geometry of a cylindrical helix.",
+        "texts": [
+            " (24) are the initial conditions given at t \u00bc 0. The elements of the column matrix B\u00f0s; z\u00de are Bi\u00f0s; z\u00de \u00bc 0 \u00f0i \u00bc 1; 2; . . . ; 6\u00de B6\u00fej\u00f0s; z\u00de \u00bc \u00f0 p\u00f0ex\u00dek \u00de qA zU 0 k \u00f0s; 0\u00de \u00fe oU 0 k \u00f0s; 0\u00de ot \u00f0j \u00bc 1; 2; 3\u00de B9\u00fej\u00f0s; z\u00de \u00bc \u00f0 m\u00f0ex\u00de k \u00de qIk zX0 k\u00f0s; 0\u00de \u00fe oX0 k\u00f0s; 0\u00de ot \u00f0k \u00bc 1; 2; 3\u00de \u00f025\u00de Note that the initial conditions present in Eqs. (24) are now included in the load vector B\u00f0s; z\u00de. The spatially curved system is taken as a special case of a helical bar. The parametric equation of a helix is given by Temel and C al\u0131m (2003) (see Fig. 2) x \u00bc a cos/; y \u00bc a sin/; z \u00bc h/ \u00f026\u00de where / is the horizontal angle of the helix. The infinitesimal length element of the helix is defined as c \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffi a2 \u00fe h2 p ; ds \u00bc cd/; cos a \u00bc a c ; sin a \u00bc h c \u00f027\u00de where a and a are pitch angle and centerline radius of the helix, respectively. The curvatures of a cylindrical helical spring are v \u00bc a c2 \u00bc constant; s \u00bc h c2 \u00bc constant \u00f028\u00de The relationship between the moving axis \u00f0t; n; b\u00de and the fixed reference frame \u00f0i; j; k\u00de are (Fig. 2) fV gTtnb \u00bc \u00bdB fV gTijk Vt Vn Vb 8< : 9= ; \u00bc \u00f0a=c\u00de sin/ \u00f0a=c\u00de cos/ \u00f0h=c\u00de cos/ sin/ 0 \u00f0h=c\u00de sin/ \u00f0h=c\u00de cos/ \u00f0a=c\u00de 2 4 3 5 Vi Vj Vk 8< : 9= ; \u00f029\u00de Non-dimensional parameters in Laplace domain are defined as Ui \u00bc 1 c U 0 i ; Xi \u00bc X0 i ; T i \u00bc c2 EIn T 0 i ; Mi \u00bc c EIn M0 i \u00f0i \u00bc t; n; b\u00de \u00f030\u00de Assuming that the centroid and the shear center of cross-section coincide, the n, b axes become the principal axes and the effect of warping of the cross-section is ignored. Now, equations obtained as a result of elimination of c0 and x0 between the transformed equations of compatibility (5) and the transformed constitutive equations (17) and (18) together with the transformed equations of motion (6) form the governing equations of the dynamic response of initially curved and twisted viscoelastic bars"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000747_10402009508983375-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000747_10402009508983375-Figure1-1.png",
+        "caption": "Fig. 1-Piston and connecting rod geometry.",
+        "texts": [
+            " THEORY 'This section begins with a brief discussion of the kinematics of the slider-crank mechanism. Surface parameters that numerically quantify the texture of the surface of the cylinder wall and piston ring are then discussed. Finally, this section outlines the models for the asperity contacts and the averaged Reynolds equation which are adopted for this research. Kinematics of the Slider-Crank Mechanism The slider-crank mechanism of a typical four stroke internal combustion engine is shown schematicaIly in Fig. 1. The piston displacement, s, and velocity CJ, for R small can be expressed as ( 9 ) : - R 0 where R = - and o = - 1 t The above equations are used to obtain the hydrodynamic forces as shown in a later section. Analytical Methods of Surface Topography Characterization A measured surface profile 6(x), representing a stationary random function may be comprehensively described by two probability functions ( l o ) , i.e., the statistical distribution function p(6) and the autocorrelation function R(A) "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure4.31-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure4.31-1.png",
+        "caption": "Figure 4.31. A particle motion relative to a frame fixed in the ea.rth's surface.",
+        "texts": [
+            "89) in (4.46) and (4.48), we obtain the relative velocity and acceleration of P in cp': (ix' v=Tt= Vp- (vc+O x x'), (4.90) wherein v c and a c. and v P and a P denote the total velocity and acceleration in frame cP of the origin point C in E and of the particle P, respectively. It is convenient in (4.90) to take Cat the geometrical center of the earth, but still be able to refer the motion to a reference frame cp fixed at a con vement site 0 in the earth's surface (or any other point in E), as shown in Fig. 4.31. Since the vector r of 0 from C is fixed in the earth, hence also in both cp and q/, we have br/bt = 0 and (i 2r/bt2 = 0. As a consequence, a shift to a reference frame cp at 0 in no way affects v and a in (4.90). Indeed, with x' = r + x, where x is the vector of P from 0 in cp, as shown in Fig. 4.31, we see that bx'/bt = bx/bt and b2x'/bt2 = b2xfbt2\u2022 Therefore, (4.90) also may be written as (4.91) When P moves on or near the earth's surface in the vicinity of 0 so that Motion Referred to a Moving Reference Frame and Relative Motion 299 lxl ~ lrl = 4000 miles, approximately, then x' = r, very nearly, and equations (4.90) or (4.91) may be replaced by bx V = Jr = V p- ( V c + fi X r ), (j2x a =w = ap- [ac+ n x (!! x r) +2!! x v]. (4.92) In equations (4.90)--(4.92), the terms preceded by the negative sign represent in each case the principal source of errors that would be committed by adopting the assumption that the earth is fixed in space relative to the dis tant stars, i"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001321_s1350-6307(99)00009-6-Figure9-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001321_s1350-6307(99)00009-6-Figure9-1.png",
+        "caption": "Fig. 9. Sketch of the CMB showing compressive stresses on the cage along the wear bands resulting in a fatigue crack. Location from where crack initiated is marked `origin'.",
+        "texts": [
+            " Most of the smeared material was iron containing Cr, probably coming from the outer race. Particles enriched in Al and Si were probably carried by the lubricant and got embedded on the silver coating along the band where the cage pressed against the outer race. A possible inference of the results of chemical analysis can be negligible wear and signi\u00aecant smearing. The deposition of material could be the reason for the decrease in the clearance. Fractography of the broken surfaces revealed that the mode of fracture was fatigue. Cracks initiated from location `O' in Fig. 3(b) and Fig. 9. The crack initiation sites matched in samples F, U and the cage retrieved from the accident which indicates that the weak region in the design is location `O'. No material defect could be traced at the possible initiation site in any of the above samples. Observations of the silver coating revealed cracks in the coatings near the initiation point. This was the lower inside edge where the balls remained in contact with the cage. Coating cracks were observed in those used cages which were replaced after completion of life as a usual maintenance procedure",
+            " In all the retrieved specimens, whether failed in accident or replaced after normal use, a band smeared with foreign material was observed; the region remained in contact with the outer race and contained Fe, Al and Si rich patches and particles. 4. The two consecutive quality check reports of the retrieved bearing showed a decrease in the cage\u00b1 outer race clearance within a short period. Normal use resulting in wear is expected to increase the clearance. The decrease in clearance in this case can either be due to smearing of a foreign layer or due to the outgrowth resulting from non-uniform radial stresses causing ovality of the cage. It is clear that cyclic stresses were operative on the cage surface along the band W in Fig. 9, where the deposited layer or the ovality in the cage reduced the clearance and the cage was pressed against the outer race [8]. The process enhanced ovality in the cage. In every cycle, stresses were generated on the rotating cage pressing against the stationary outer race. These stresses were compressive on the outer and tensile on the inner surfaces. The bearing operated at more than 11000 rpm and the cage, which was under a low stress high cycle fatigue regime, failed. The machining marks on the cage (Fig"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001835_s0301-679x(02)00024-5-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001835_s0301-679x(02)00024-5-Figure1-1.png",
+        "caption": "Fig. 1. Hydrostatic thrust bearing.",
+        "texts": [
+            "0 Mpa L\u0302 L /L0 power loss L\u0302Q LQ /L0 power loss due to leakage L\u0302T LT /L0 power loss due to friction L\u0304 L /ph0r2 2 ps power loss L\u0304Q LQ /ph0r2 2 ps power loss due to leakage L\u0304T LT /ph0r2 2 ps power loss due to friction M\u0304 M /psr3 2 load-carrying capacity of moment n rotative velocity of pad p\u0304 p /ps film pressure p\u0304p pp /ps pocket pressure p\u0304s ps /ps 1 supply pressure Q\u0304 Q /Cps leakage flow rate r2 outer radius of bearing r\u0304p rp /r2 ratio of pocket radius R\u0304L RL /r2 loading point from center of bearing T\u0304 T /ph0r2 2ps frictional torque u\u0304m mean radial velocity W\u0304 W /psr2 2 load-carrying capacity a\u0304 ar2 /h0 tilting angle of pad \u03b4e elastic deformation z 2Wlogr\u0304p /pr2 2(1 r\u03042 p)ps ratio of hydrostatic balance angle of rotation \u00b5o viscosity of oil \u00b5w viscosity of water \u03bdp Poisson\u2019s ratio of plastics \u03bds Poisson\u2019s ratio of stainless steel \u03c1o density of oil \u03c1w density of water \u03c6 azimuth of maximum tilting angle of pad w\u0304 w / angular velocity of pad psh2 0 /6mr2 2 representative angular velocity ings under the conditions of eccentric loading are clarified theoretically in this part. Fig. 1 shows the schematic of the disk-type hydrostatic thrust bearing modeling the bearing/seal parts of hydraulic pumps and motors. The pocket pad is made of stainless steel SUS420, and the disk pad, which is set on the stainless steel block, is made of SUS420 (JIS G 4303) and industrial thermoplastics PEEK 450FC30, PEEK EXL6, and AURUM JCL3030. An eccentric load F is produced at RL from the center of the bearing. The Reynolds equation of the cylindrical coordinates is written as \u2202 \u2202r\u0304 (rh\u03043 \u2202p\u0304 \u2202r\u0304 ) \u2202 \u2202q ( h\u03043 r\u0304 \u2202p\u0304 \u2202q ) w\u0304r\u0304 \u2202h\u0304 \u2202q h( r\u03042 2 \u2202h\u03043 \u2202r\u0304 r\u0304h\u03043) (1) h rh2 0w2 /10m is given here"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002478_s0167-6911(01)00185-2-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002478_s0167-6911(01)00185-2-Figure1-1.png",
+        "caption": "Fig. 1.",
+        "texts": [
+            " This system does not satisfy Brockett\u2019s condition so that a continuous stabilizing feedback does not exist. We consider the feedback law proposed by Canudas de Wit and SHrdalen [13;14]. They introduce the following functions: = x2 x1 ; x1 =0; !d(x1; x2) = { 2 arctan if (x1; x2) =(0; 0); 0 if (x1; x2) = (0; 0); where; if C is the circonference on the (x1; x2)-plane passing through the points (x1; x2) and (0; 0) and with centre on the x2-axis; !d is the angle between the line tangent to C in P and the x1-axis (see Fig. 1): (x1; x2; !) = !\u2212 !d \u2212 2 n(!\u2212 !d); where n : R\u2192 Z is such that belongs to (\u2212 ; ] for all (x1; x2; !)\u2208R3, b1(x1; x2; !) = cos ! ( !d \u2212 1 ) + sin ! ( !d 2 ( 1\u2212 1 2 ) + 1 ) ; =0; b2 = cos ! 2 (1 + 2)x1 \u2212 sin ! 2 (1 + 2)x1 ; x1 =0; a(x1; x2) =   x1 if x2 = 0; x21 + x22 x2 arctan x2 x1 if x2 =0; a can be seen as the arclength of the circonference C. Canudas de Wit and SHrdalen de@ne the feedback law u(x1; x2; !) =\u2212&b1(x1; x2; !)a(x1; x2); !(x1; x2; !) =\u2212b2(x1; x2; !)u(x1; x2; !)\u2212 k (x1; x2; !); where & and k are positive constants"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001294_(sici)1521-4109(199906)11:7<499::aid-elan499>3.0.co;2-8-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001294_(sici)1521-4109(199906)11:7<499::aid-elan499>3.0.co;2-8-Figure4-1.png",
+        "caption": "Fig. 4. Cyclic voltammograms of the microsensor based on Na\u00aeon and MV in a air-saturated (a) and deoxygenated (c) PBS solution, and a bare CFME in a air-saturated PBS solution (b) at a scan rate of 100 mVys.",
+        "texts": [
+            " However, it is not easy to realize electrocatalysis at a microelectrode because unlike to conventional electrodes, the product of the electrode reaction will diffuse rapidly away from the microelectrode surface, resulting in a low catalytic ef\u00aeciency of homogeneous oryand heterogeneous reactions. Therefore, in order to maximize the electrocatalysis at the electrochemical microsensor, an exceptionally high scan rate is employed or the Electroanalysis 1999, 11, No. 7 microsensor is based on a mediator or promoter \u00aexed to a polymer which is attached to the electrode. Figure 4 depicts cyclic voltammograms of the microsensor based on Na\u00aeon and MV in a air-saturated (a) and N2-saturated PBS solution (c) and an activated bare CFME in a air-saturated PBS solution (b). It can be clearly seen that the microsensor shows good catalytic activity for O2 reduction. MV2 yMV redox couple, which has a high electron-exchange rate as shown in Section 3.1., can facilitate the electron transfer between the microsensor and O2. Most importantly, MV , as electrode reaction intermediate, can also be entrapped in Na\u00aeon \u00aelm instead of diffusing rapidly away from the microsensor, thereby maximizing signal strength"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003377_joti.2001.0050-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003377_joti.2001.0050-Figure3-1.png",
+        "caption": "Fig. 3 Finite element models of the human body and the garment",
+        "texts": [
+            " According to the principle of virtual work, we have dWs dWI dWg dWb dWc \u00bc 0 \u00f017\u00de For the garment, the skin and the soft tissue, Equation (17) is represented as:Z tO t tsd t te dO\u00fe Z tO rtadu dO Z tO tqgdu dO Z tGc tqC1 dutNn 1 dS \u00bc 0 \u00f018\u00de where Nn 1 is the normal vector of contact boundary points n\u00bc 1, 2, 3. For the bone, the contact force tqc1 is regarded as an external force.Z tO tqgdu dO Z tGf tqb du dS Z tGc tqc1 du dS \u00bc 0 \u00f019\u00de In this paper, we developed a 3D finite element model of a female human body on the basis of a commercially available virtual human model. The finite element models of the human body and the garment are as shown in Fig. 3, where a quadrilateral shell element with four nodes is used in the finite element discretization. The garment is made from a stiff fabric-1 used in the waist and a soft fabric-2 used in the rest, as shown in Fig. 3(a). The human model is modeled with three layers of materials that have different properties representing the bone, the soft tissue and the skin respectively, as shown in Fig. 4. The total element number of the human body is 13 362 (7221 elements for the bone, 3145 for the soft tissue, 2996 for the skin), and 1585 for the garment. Considering a shell element with large displacements and large rotations, a local coordinate system x1 x2 x3 is estimated and attached to the shell element because the J"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003554_13552540510601309-Figure19-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003554_13552540510601309-Figure19-1.png",
+        "caption": "Figure 19 A cusp volume-based check could be more efficient in determining the appropriate slice height so that the sharp horizontal features are not missed",
+        "texts": [
+            " In case of cusp volume check \u2013 this would result in a number of successive cusps in a layer displaying high volumes. In such a case, it would be observed that mere introduction of an extra cutter trajectory line (as in the previous case) would not solve the problem. In such a case, the algorithm (Appendix 2) should be such as to introduce another slice in the layer concerned. The vertical position of this slice should be iteratively decided such that all the related cusp volumes are within limit (Figure 19). One way of determining the slice height is to calculate the cusp height errors and check whether they are within a userdefined limit (Kulkarni and Dutta, 1996; de Jager et al., 1997). However, cusp height error calculations may involve a number of approximations. These are: Volume deviation in direct slicing Chandan Kumar and A. Roy Choudhury Volume 11 \u00b7 Number 3 \u00b7 2005 \u00b7 174\u2013184 1 the surface is approximated as a part of a sphere for slice height calculations; and 2 the mid height normal is assumed to lie on the NVS of the lower contour point that may not necessarily be the case"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002704_0165-0270(87)90090-2-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002704_0165-0270(87)90090-2-Figure1-1.png",
+        "caption": "Fig. 1. Modification of a puller to make quartz micropipettes. A: photograph of the heating unit mounted in place of the original heater on a horizontal solenoid puller. B: axial section through the heating unit with the essential parts drawn to scale. The heating element (in black) is a flanged cylinder of graphite (refractory quality 2239PT, Le Carbone-Lorraine, Tour Manhattan-Cedex 21, F-92095 Paris La Defense 2, France) clamped between two aluminium endplates El, E 2 by threaded rods that have spring-loaded nuts and are insulated by ceramic tubes (Degussa AG, Postfach 2050, CH-8040 Ziirich, Switzerland). To prevent oxidation, the element is surrounded by a quartz cylinder Q within which the air is replaced by argon. Argon passes through the pressure regulator set at 20 mm Hg (not shown), and is delivered to the heating element through the tube T. Two holes (small arrows) allow the argon to pass into the axial hole and escape through the spaces round the pair of micropipettes M1, M 2. (The micropipettes are shown withdrawn from the heater.) Current is supplied through multistrand copper wires, diameter 6 mm, connected at W1, W z. Longitudinal spread of heat is reduced by two finned radiators (for electronic circuits) 10 cm by 7.5 cm (R 1, R:). The assembly is attached to the body of the puller by a bracket on E l. C: scale drawing of the graphite heating element, showing end view (left) and section through AA'. Dimensions in ram.",
+        "texts": [
+            " Coles, Universit6 de Gen~ve, Drparternent d'oto-neuro-ophtalmologie, Laboratoire d'ophtalmologie exp~rimentale, 22 rue Alcide-Jentzer, CH 1211 Geneve 4, Switzerland. The softening point of quartz (about 1665 \u00b0 C) is close to the melting point of plat inum (1772 \u00b0 C) 0165-0270/87/$03.50 \u00a9 1987 Elsevier Science Publishers B.V. (Biomedical Division) 58 A B R1 .......... - e i - - - - I , ! R2 r - - j..Je _. . M2 j E 2 \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ 5 cm f i 59 but below that of g raphi te ( > 3350 \u00b0 C). G r a p h i t e can therefore be used for a hea t ing e lement in a puller . Fig. 1 shows a tested design. Curren t passes longi tud ina l ly down the cyl indr ica l g raph i te elemen t shown in Fig. 1B, C. Ox ida t ion is p reven ted by ma in ta in ing an a tmosphe re of argon. The pressure regula tor (not shown) is set at 2.7 kPa above a tmospher ic and the f low is de t e rmined ma in ly b y the spaces th rough which the argon escapes, between the capi l la ry and the hea t ing element. I t is sufficient to turn on the flow immed ia t e ly be fore app ly ing power to the heat ing element . Long i tud i - na l spread of hea t is l imi ted by means of two large rad ia tors R 1, R 2. The power required is abou t 150 A at 6"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001896_ajpa.1330900406-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001896_ajpa.1330900406-Figure2-1.png",
+        "caption": "Fig. 2. Three-dimensional representation of a 20-node hexahedron showing the curve of each of the 12 edges by means of the presence of 12 \u201cmiddle nodes\u201d added to the 8 \u201ccorner nodes.\u201d (Reproduced from Zienkiewicz, 1977, with permission of the publisher.)",
+        "texts": [
+            " Each point is termed a \u201cnode\u201d of the \u201cmesh.\u201d However, such elements, whose edges are rectilinear, cannot be used satisfactorily to model volumes of complex shape, especially if they display curved surfaces. The principle of the method consists in distorting these basic elements, so as to obtain shapes which more accurately describe body volumes, by introducing a \u201cmiddle node\u201d between each corner node (Tardieu, 1987, pp. 35-36). Thus each side of the element becomes a curved surface; the hexahedron includes 20 nodes (Fig. 2) and the pentahedron 15 nodes. These are isoparametric elements of the second degree (Zienkiewicz, 1977, pp. 178-210). Each element is defined by the three-dimensional coordinates of the apices and midpoints of each edge. Eighteen volumetric elements for the whole body provide a mesh of 260 nodes (Fig. 1). Seventeen hexahedrons and one pentahedron are used. Head, neck, trunk (divided into thorax and abdomen), superior member (divided into arm, forearm), and inferior member (divided into thigh, leg) are considered"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001096_s0263-8231(00)00003-3-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001096_s0263-8231(00)00003-3-Figure1-1.png",
+        "caption": "Fig. 1. Undeformed and deformed geometry of frusta.",
+        "texts": [
+            " Several papers dealing with the theories of the collapse of tubes [1\u20137] and frusta [1\u20134] have appeared in literature. In frusta with * Corresponding author. Tel.: +91-11-659-1178; fax: +91-11-658-1119. E-mail address: nkgupta@am.iitd.ernet.in (N.K. Gupta). 0263-8231/00/$ - see front matter  2000 Elsevier Science Ltd. All rights reserved. PII: S 02 63 -8231( 00 )0 0003-3 Nomenclature a A parameter (a=0 for first fold; and a=1 for other folds) a Angle of taper of frustum B,B9,K Parameters dA Area of elemental ring D1,D2 End diameters of frustum (D1.D2) Di1,Di2,Di3 Diameters as shown in Fig. 1 e Strain in the elemental ring fy Yield stress of the material of frusta hi, h9i Size of upper and lower limbs of ith fold L Length of frustum Mp Plastic moment capacity Pi Average crushing load for ith fold P\u03b8i Crushing load for given q during the formation of ith fold t0 Thickness of frustum q,q9 Angles of rotation of limbs of a fold Wbi Energy dissipated in plastic bending in the formation of ith fold Wci,W9ci Energy dissipated in circumferential stretching of upper and lower limbs of ith fold Wei Total energy dissipated in the formation of ith fold Wbqi,Wcqi Energy dissipated in plastic bending and circumferential stretching for given q during the formation of ith fold xi Uncrushed length of frusta after the formation of ith fold z Crushing distance in the direction of the load low semi-apical angles, first few folds are observed in experiments to be of concertina type",
+            " Therefore, the energy absorption in flexure in the lower limb of the first fold is only at the junction of the two limbs of the fold. In the present study, this experimental observation has been incorporated by introducing a parameter \u2018a\u2019 which when taken as zero makes the model valid for first fold and for a=1 other folds can be considered. The parameter a=0 nullifies the flexural energy absorption in the lower hinge of the lower limb. For the analysis, we consider a thin frustum of thickness t0, length L and end diameters as D1 and D2 (D1.D2) as shown in Fig. 1(a). In the present work, complete crushing of the frustum has been assumed because the consideration of effective crushing distance [2] is coupled with the reduction in the energy dissipation. The axisymmetric crushing of the frustum, shown in Fig. 1(a), by the formation of straight total outside folding is depicted in Fig. 1(b). The size of upper and lower limbs of ith fold is denoted by hi and h9i respectively. The energy dissipation in flexure has been assumed to be localised at the hinges. The energy dissipated in plastic bending Wbi is in the form of rotation at lower, upper and intermediate plastic hinges and is given by Wbi5 E p/21a 0 MppDi1 dq1 E p/21a 0 MppDi3 dq1 E p/22a 0 MppDi3 dq91a E p/22a 0 MppDi2 dq9(1) (Upper Hinge) (Intermediate Hinge) (Lower Hinge) 5pMp[ E p/21a 0 (Di11Di3) dq1 E p/22a 0 (aDi21Di3) dq9] (2) During the formation of first fold lower hinge does not exist, therefore, a constant \u2018a\u2019 has been used in the above expression. Its value will be zero (i.e. a=0) for first and unity (i.e. a=1) for rest of the folds. Evaluating the integrals, Wbi is obtained as Wbi52pMpFH(11a) p 2 1(12a)aJDi12 2hi (1\u2212sin a) {a(p22a) sin a2cos a}G (3) where, a is the angle of taper of the frusta that can be written as a5tan\u22121SD1\u2212D2 2L D Di1, Di2, and Di3 are the diameters as shown in Fig. 1. These can be obtained from: Di15D122xi tan a (4) Di25Di122(K11)hi sin a5Di124hi sin a/(12sin a) (5) Di35Di112hi sin (q2a)5Di212Khi sin (q91a) (6) xi is the uncrushed length of frusta after the formation of ith fold that can be obtained from: xi5L2Oi j51 hj(11K) cos a (7) hi9, the size of lower limb of ith fold can be obtained from: hi95Khi (8) where, K5(11sin a)/(12sin a) (9) and q9 is related with q by the expression q95sin\u22121F1 KHsin (q2a)1 2sin a (1+sin a)JG2a (10) Employing Von-Mises criterion, Mp= 1 2\u221a3 fyt20, Eq. (3) reduces to Wbi5 p \u00ce3 fyt20FH(11a) p 2 1(12a)aJDi12 2hi (1\u2212sin a) {a(p22a)sin a2cos a}G (11) The energy dissipated in circumferential stretching Wci can be calculated as follows: Wci5 E p/21a 0 Sdwci dq D dq1 E p/22a 0 Sdw9ci dq9 D dq9 (12) where, wci and w9ci are the values of energy dissipated in circumferential stretching of upper and lower limbs of ith fold respectively. Considering an elemental ring of width dy in the upper limb at a distance y from the upper hinge (Fig. 1), the derivative of wci with respect to q can be calculated as given below dwci dq 5E hi 0 fyt0Sde dqD dA (13) where, dA is the area of the elemental ring dA5p[Di112y sin(q2a)] (14) the strain e in the elemental ring is written as e = phDi1+2ysin(q\u2212a)j\u2212p(Di1\u22122ysin a) p(Di1\u22122ysin a) or, e = 2y{sin(q\u2212a)+sin a} (Di1\u22122ysin a) (15) the derivative of strain e with respect to q is given by de dq 5 2ycos(q\u2212a) (Di1\u22122ysin a) (16) fy is the yield strength of material. Substitution of different values from Eqs. (14) and (16) into Eq. (13) and its integration gives dwci dq 52fyt0cos(q2a)E hi 0 yhDi1+2ysin(q\u2212a)j (di1\u22122ysin a) dy (17) dwci dq 5 pfyt0hi 2sin a [2(hi1B)sin 2(q2a)22Bsin a cos(q2a)] (18) where, B5 Di1 sin aF11 Di1 2hi sin a logeS12 2hisin a Di1 DG (19) Similarly, expression for the derivative of w9ci can be found by considering an elemental ring in the lower limb at a distance y from the lower hinge (Fig. 1) as follows dw9ci dq9 5 pfyt0Khi 2sin a [(Khi2B9) sin 2(q91a)12B9 sin a cos (q91a)] (20) where, B95 Di2 sin aF12 Di2 2Khi sin a loge S11 2Khi sin a Di2 DG (21) Using Eqs. (18) and (20), Wci can be calculated from Eq. (12) as follows: Wci5 pfyt0hi 2sin aF(1+cos 2a 2 h2(B1KB9)1hi(K21)j22sin ah(B2KB9)1(B (22) 1KB9)sin ajG Assuming that the energy dissipation in the axisymmetric axial crushing of frusta takes place in the form of flexural and circumferential deformations, therefore, the external work done can be equated to the energy absorbed in bending and circumferential stretching"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003688_tcst.2004.833622-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003688_tcst.2004.833622-Figure2-1.png",
+        "caption": "Fig. 2. Relative velocity between missile and target.",
+        "texts": [
+            " From (1) to (4), the motion model of the missile can then be written as (5) (6) where and . B. Zero-Effort-Miss Phase Assume that both the missile and the target are moving only with constant gravitational acceleration, i.e., (7) Therefore, the relative position vector and the relative velocity vector at can be, respectively, expressed as (8) Thus, zero-effort-miss (ZEM) can be computed as (9) If the convergence of is fast enough, the relative velocity will soon almost be lined up with LOS (see Fig. 2) and, hence, . Apparently, from (9) one can then conclude that ZEM as , which is our ideal goal. III. GUIDANCE SYSTEM DESIGN The equations of relative motion in terms of the relative position and the relative velocity are as follows: and (10) where , , and the translation motion of a missile is defined as (1). To proceed, we first derive the equation of the relative motion perpendicular to the LOS ( ) as follows: (11) where and . Referring to (11), an adequate design of is the following: (12) where is a positive definite diagonal matrix, and is a switching function of the sliding mode control, which readily yields (13) Let be a Lyapunov function candidate, and evaluate the time derivative of along the trajectories of the system (13) as follows: (14) with (15) where we use the fact "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002163_027836499301200602-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002163_027836499301200602-Figure4-1.png",
+        "caption": "Fig. 4. Setup of the experiments.",
+        "texts": [
+            " Thus the motion planning problem for this simple example has boiled down to two questions: (i) Given a known linear and angular velocity for the two fingertips, what will the angular velocity, c~, of the card be and what will the forces and moments at the fingertips be? (ii) Given a desired angular velocity of the card, what should the linear and angular fingertip velocities be; equivalently, what should the force and moment applied at each fingertip be? 2. Experimental Setup Experiments were conducted to determine the accuracy of predicted values of the angular velocity of the card wand the fingertip forces and moments, f and m, for prescribed fingertip motions. The experimental setup is shown in Figure 4 and consists of two direct drive fingers, each with two degrees of freedom in the plane. Soft fingertips bear on a card, which slides on a mirrorfinish steel plate. Fingertip locations are measured with joint angle encoders, achieving an accuracy of ~0.1 mm or better over the workspace. The fingertip forces and moments in the plane are measured with three-axis force sensors and have an accuracy of approximately ~0.02 N and + 1 x 10-4 Nm, respectively. The fingers are driven by a Cartesian position controller"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003657_j.cma.2005.02.033-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003657_j.cma.2005.02.033-Figure2-1.png",
+        "caption": "Fig. 2. 2-link manipulator: joint coordinates.",
+        "texts": [
+            " Together, the algebraic kinematic equations (2) and differential dynamic equation (3) form the set of differential-algebraic equations (DAEs) that constitute the system model. A forward dynamic analysis is obtained by solving the set of n + m DAEs for qa(t) and k(t). As their name implies, joint (or relative) coordinates correspond directly to the joints in a multibody system. For the 2-link serial manipulator, each revolute joint would contribute 1 variable to the set of joint coordinates: qb \u00bc \u00bdb1; b2 T ; \u00f05\u00de where b1 and b2 measure the relative motion of the bodies connected by the corresponding joints, as shown in Fig. 2. As this simple example shows, an advantage of joint coordinates over absolute coordinates is that they are independent for open-loop systems such as serial robotic manipulators. For this reason, and the fact that the coordinates correspond directly to the actuators of a manipulator, joint coordinates are preferred by researchers in robotics. With independent variables, there are no kinematic constraint equations and the dynamic equations consist only of ordinary differential equations (ODEs): Mb\u20acqb \u00bc Qb"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002541_s0039-9140(03)00408-9-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002541_s0039-9140(03)00408-9-Figure1-1.png",
+        "caption": "Fig. 1. Flow cell prototype I: (a) general view of the flow cell and the four removable all-solid-state ISEs; (b) cross section of the flow cell; (c) construction of the all-solid-state ISE.",
+        "texts": [
+            " In the following, solution-cast PEDOT(PSS) will be referred to as \u201cBaytron P\u201d. Poly(ethylene-co-propylene-co-5-methylene2-norbornene) (ethylene/propylene/diene terpolymer, EPD, 70% (w/w) ethylene, 4% (w/w) 5-methylene-2-norbornene) was obtained from Aldrich. Graphite (fine powder, extra pure) having a particle size <50 m (\u226599.5%) was obtained from Merck. All other chemicals were of analytical-reagent grade. ELGA ultrapure water (resistivity 18.2 M cm) was used to prepare all solutions. The flow cell prototype I containing four all-solid-state ISEs is illustrated in Fig. 1. The removable ISEs are radially distributed in the same plane (in parallel) in the flow cell that was made of PVC. The flow-channel (1 mm inner diameter) was drilled in the center perpendicularly to the plane of the electrodes (Fig. 1a and b). The cell dimensions were 10 mm (outer diameter) and 15 mm (flow-channel length) resulting in a cell volume of ca. 17 l. The construction of the ISE is shown in Fig. 1c. A gold wire (1 mm diameter) was inserted and fixed to the PVC body with a glue (13% (w/w) of PVC in cyclohexanone). The gold wire worked simultaneously as electrode substrate and electrical contact to the mV-meter. 2.2.2. Fabrication of the all-solid-state K+-ISEs Electrochemical synthesis of poly(3,4-ethylenedioxythiophene) was carried out by using an Autolab General Purpose System (AUT20.FRA2-Autolab, Eco Chemie, B.V., The Netherlands) connected to a conventional one-compartment three-electrode electrochemical cell. The working electrode was the bare gold electrode (area: 0.008 cm2) mentioned above (Fig. 1c). A GC rod was used as the auxiliary electrode and the reference electrode was a Ag|AgCl|KCl (3 M) electrode. Prior to polymerization, the Au working electrode was polished with a fine polishing paper and 0.3 m alumina, rinsed with water and cleaned ultrasonically for at least 15 min. PEDOT was deposited on the Au working surface by galvanostatic electrochemical polymerization from a deaerated aqueous solution containing 0.01 M EDOT and 0.1 M NaPSS as the supporting electrolyte. To produce a polymerization charge of 1.2 mC, a constant current of 0.0017 mA (0.2 mA cm\u22122) was applied for 714 s. In the following, electrochemically synthesized PEDOT doped with PSS will be called \u201cPEDOT\u201d. The resulting Au/PEDOT electrodes were conditioned in 0.1 M KCl solution for at least 1 day. Then a total volume of 8\u201310 l of the ion-selective membrane (ISM) cocktail was applied on top of the Au/PEDOT electrodes, covering completely the conducting polymer layer (Fig. 1b and c). The all-solid-state K+-ISEs for the flow cell prototype I can thus be described as follows: Au/PEDOT/ISM. The composition of the ion-selective membranes are shown in Table 1. To avoid weighting of small quantities, stock solutions of the ionophore valinomycin and the lipophilic salt KTpClPB were prepared in cyclohexanone. Then, aliquots of the stock solution and the other membrane components were dissolved in THF at a total concentration of ca. 16% (w/w). The resulting all-solid-state K+-ISEs (Fig. 1c) were conditioned in 0.1 M KCl solution for at a Membrane cocktails were prepared by dissolving the membrane components in cyclohexanone and THF. The dry fraction of the membrane cocktails were ca. 16\u201318% (w/w). b The molar ratio of KTpClPB versus ionophore is equal to 0.6. least 1 day prior to measurements in the flow cell prototype I (Fig. 1). The electrodes were conditioned in 0.1 M KCl between measurements. A carbon composite material was obtained by mixing graphite with ethylene/propylene/diene terpolymer [15]. The composite was studied as a moldable substrate material that is needed for the construction of the flow cell prototype II, described below. The carbon composite (CC) paste was prepared by manual mixing of graphite with a solution of EPD (1255 mg l\u22121) in cyclohexane to get a final concentration of 2% in EPD after evaporation of cyclohexane",
+            " The measurements were performed in 0.1 M KCl solution at room temperature (23 \u00b1 2 \u25e6C). The aim of the present work was the construction of a flow cell for miniaturized all-solid-state ISEs for potential use in clinical analysis. Radial distribution of the electrodes in the flow cell was considered crucial in order to minimize the cell volume. The performance of two different flow cell prototypes was tested for all-solid-state K+-selective electrodes. In the flow cell prototype I, the four all-solid-state ISEs were removable (Fig. 1). Thus, each electrode could be replaced by another electrode when necessary. Electrochemically synthesized PEDOT was used as the ion-to-electron transducer in these all-solid-state K+-selective electrodes [12]. Miniaturization of the macroscopic electrodes using electropolymerized PEDOT as solid contact material [12,13] was rather straightforward. An example of calibration plots for all-solid-sate K+-ISEs (prototype I) is shown in Fig. 3. The calibration plot was recorded from 10\u22121 to 10\u22125 M and then back to 10\u22121 M KCl"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001416_10402000308982622-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001416_10402000308982622-Figure1-1.png",
+        "caption": "Fig. 1-Schemallc vlew 01 s double-row tapered roller bearing In DBarrangement.",
+        "texts": [],
+        "surrounding_texts": [
+            "Analysis o f Double-Row Tapered Roller Bearings: Part I-Model\nQ Q,. Qc QE f l\n= semi-major axis of the roller end-flange contact, m = Hertzian contact area, In2 = semi-minor axis of the roller end-flange contact, m = drag coefficient = large-end diameter of roller, m = mean diameter of roller, m = distance between row roller frames (X ,, Y,,, Z,+,m), m = axial location of the friction force balance center, m = Young's modulus of bodies I and 2. respectively, ~1n-1~ = equivalent Young's modulus:\nE' = 2/[(1 - v:)/E, + (1 - u,2)/E2], ~ / m ~ = friction force due to asperity contact, N = lubricant drag force, N = hydrodynamic pressure force, N = rolling friction force, N = sliding friction force, N = roller centrifugal force, N = axial applied load, N = radial applied load, N = shear modulus of lubricant, ~ / m ~ = non-dimensional material parameter: a,E' = minimum lubricant film thickness, m = heat generation, W = moment of inertia of roller about its own axis (X,-axis),\n= load-deflection factor; ~lm~'-for point contact, and ~/m\"'-for line contact = active length of line contact, In = nominal roller length, m = fatigue life associated with 90% reliability, hrs = fluid drag moment about the roller axis, N.m = roller gyroscopic moment, N.m = moment of spin, N.m = bearing rotational speed, rpm = pressure, ~ / m ~ = maximum Hertzian pressure, ~ l m ~ = load per unit length, N/m = contact normal load, N = roller cage pocket normal force, N = basic dynamic capacity, N = race equivalent load, N = pitch radius of the bearing, m = equivalent radius of curvature in the Yw- direction, m = Reynolds number = curvature radius of the roller large end surface, m = inlet lubricant temperature, C = contact moment, Nm = average entraining velocity, m/s = non-dimensional parameter of speed: q,V/EIR = roller displacement. rn = surface velocity in moving direction, m/s = sliding velocity, m/s = non-dimensional parameter of load: QIE'IR-for line contact\nand Q/EIR-for point contact = total number of rollers per row = outer raceway semi-cone angle, rad = pressure-viscosity coefficient = inner raceway semi-cone angle, rad = fraction of initial axial compression, % = contact compression, m\n6: = inner ring displacement along the X , Y and Z-axis, respectively, m\n= initial axial compression, m = roller semi-cone angle: (u-p)/2, rad = thermal reduction factor for the lubricant film thickness = radial misalignment angle of roller, rad = misalignment angle around the Y and Z-axis, respectively,\nrad = mean contact angle: (a+p)/2, rad = lubricant shear rate, s i = lubricant dynamic viscosity, Pa-s = half angular extend of spherical roller end, rad = lubricant film parameter: h,Ju = coefficient of friction (traction) = Poisson's ratio of bodies I and 2, respectively = kinematic viscosity of the lubricant = rotational speed, rad/s = azimuth angle of roller, rad = composite surface roughness (RMS), m = lubricant shear stress, Pa = characteristic lubricant shear stress (Eyring stress), Pa = opening angle of the inner ring flange, md =density of the lubricant-gas mixture, ~ ~ / m ~\nMatrix and Vector Notations\n= vector cross product = colurnr~ vector expressed by elements = transposed column vector = matrix expressed by elements =transposed matrix = transformation matrix from roller to inertial frame = initial positions of raceway and roller, respectively, that\ncome into contact (vectors locating in the inertial frame)\n= final positions of raceway and roller, respectively, that come into contact (vectors locating in the inertial frame) = inner ring vector = inner ring displacement vector = roller vector = unit vector normal to the raceway surface = roller displacement vector\n!?I 0 t H' r Y Z EHD IVR PVE PVR DRTRB SRTRB = row number 1 of bearing = row number 2 of bearing = asperity-to-asperity contact = cage = guiding flange = inner raceway = roller orbital position = raceway: inner (k = i); outer (k = o) and flange (k = f) =bearing row: row I (m = I) and row 2 (m = 2) = outer raceway = t-th slice of line contact = roller = direction parallel to X-axis = direction parallel to Y-axis = direction parallel to Z-axis = elastohydrodynamic = isoviscous-rigid = piezoviscous-elastic = piezoviscous-rigid = Double Row Tapered Roller Bearing = Single Row Tapered Roller Bearing D ow\nnl oa\nde d\nby [\nU ni\nve rs\nity o\nf B\nat h]\na t 0\n3: 02\n0 6\nO ct\nob er\n2 01\n4",
+            "A~lv:~ltced Dyn:nntir.\\ O f R<,lliny Illenaeril\\ - lo nht:lin 2 iuII\n~fynatnic siti~t~l;bli#~n. in real-linle. ior \\.;lriotl< l!pc.i 01' h:lrinps. i ~ l r l ~ ~ d i n g the 1:tpcrcd rnllcr hc;tring one, Since IIB;II <vnrk, III;~II~\nrailling k ~ n n g ;lnalysc\\ presented in t l i r l i ~ c m ~ u r c llavc usctl IOIFlewtoninn tlt~icl nlixlels lolv:triou.i lr.lr*l i n cslimate [he traclion\nfrn1n.e.: ;lnd ~nton~cnls due l u luhncant hltcartn:. ah inr crnniple the work a l NEli:ts. el ;!I. (.?.?I nnd 1 3 1 on higlt-rpccrl roller hcarln$r\nand h;dl l\\enring%. rc\\pcclively. The! :we :I methml 111 ~dcnt i fy !he contrilrulion o f c:xcIt lnlcr:tclic>n lkt\\c.ret~ hcitring clcn1r.111~ lo tltc\nlolal ellerg). dih>ip;ltnl. 11 *Itot~Itl he e~np l~ ;~s i~u t l th;~t lhc rhcolr>gical models used In clcscrihc lhc Ilui<l khav iu r ;IVC senti-e~ltpirical\nnr they nccd tlnla deduced frnm expcrimcnl:$l 1r;lcliolt cuWc\\. In a diil'crent ot;tnllcr 7hoa ;~nd Hwpriclt 1-12, hnvc prnpa\\rd s neu nlrlll,xl 10 estimole llle friction torque o i l:~pcrc<l rullcr hr:~ring\\.\nI1;tsr.J vn t t ~ i r e ~ l - l i l l L luhriusticvn \\\\ill1 n contrihuliail o i dr) cnn1:lr.l~ hct\\~ecn aspcritic, In llte ovcr;lIl l i ~ c l ~ n n fnrce. Such a mcxlel should hc used \\\\,Iten lllc luhrlcanl l i lm Ihickncw is Iorv in ~OII-\nparison l o lhr \\arf;trr roughness, i.e. inr i o u \\peed ;tpplications. hlnrc recently Wan& ct :ti. IJII ihwe presenled i t mclhod l o prrdict ihc iorqoc and Iimt grn rc~ l ion in l i l ~ r c d roller hr:lrlngr ir,illt f l l l ly-r~r p:~rti:tlly-~arn~ited rcdlcrs. In Illis I;N work. the contncl kt tueen lllc rc~l l rr ; ;~nd 111c r:auc\\\\.:i!,.; is .t.;sunted dry luhric;~lcd\n\\%hen l l ~ u len~{xr;~Iurc cacerrl\\ I'JII'(. iarltl lhe lrsrtion k l l i t v i ~ ~ r IS wrnply tlcrcrihcd hy :I il-iclig,tt 'w l l ic i rnr v:t?lng wit11 lhc 4iili11g\nvc l~~c i ly .\nThe st;ll~c. qt~:~\\i-sI:~lic. ~~ l~: l \\ i - t l ! !~ i~ !~ l ic itncl full dgn:trn!r ;x~i:~Iy-\nscs hcrc ith,>\\,c-ntctilionutl u.crc pcrf<rrn~ccl lilr \\~tt~le-n,rv rolling\nhmrinps. a i l h linrilcd Ionrl c a n i n g capacity in cnntp:$rizon to doithlc-rmv rnlliltg hcarlngq. U'ltcn the 1n;al i~ vcn. high in both ;t\\i;ll ;lnd radi:tl ilircctions ~ 1 1 ~ 1 \\\\Iicn IIIC ;~v:l~l:thli. '~pacc ib 100 r n ~ ; ~ l l i t r I\\VU \\ ingk n,a rollinc lk.;iril,g*. I l ~ e use o f ~h,t~hlc.-rt~\\v\nI:t~(.red ruIIer hl:ilri,lp\\ I D R T R I ~ J rcprc\\r,nlr the IW<I prsc1ic:tl\n\\ t~ l l~ t inn. Allhntl$li thc IIRTRR is tl*e<l in nian! ;~plrlic:~lionq I w < h\n3. ul iccl lxaring'. rnacltinc i<x,l\\. lhrlicopwr and ;~~~lnnto l ive gr;irh3ws ctr.) the allention I,, ~l!n:tr~iic ~ in i t~ l i i t i on l l l r !hi\\ ~ y p e o i\nIheartng h;a k e n \\nlnll c<>rnpnrc<l u.ilh 111;t on other rollill: k : i r - lrtp 1ypc.5.\nThc f ~ r ~ . ~ f l i I r p ;I I n i c I I I I ior\nKlRTRR ;11Iowi11g CVIC I,, prsclicl I lwir p c ~ f ~ ~ n t ~ i ~ n ~ e ~ :ins1 10 pcr-\nfr,rtlr ~o r l l c p;tr;tmetric \\toclic\\. Ralb L.onlacl clci~~nttaliunc nnd q~~a\"i-I?l~antic cc j t~ i l ih r~t tn~ etls;tllnnc :#re cxpr \\ \\c< l h? IS\\III~ vec-\ntor and nt i~lr ih noti~tionk. The tr;tcli<~n iorccs ~ i r c < l c ~ l in ihc <I~II;IIIIic cqoilihnum 11:1re h.rn uh1;tined ering :I Nr>n-Nrxlol~iian rltroloeical rnnrlcl. 'Thc cffc-c~ o f rurl:tce nr~ghne*\\ II;I~ hren included in the prcdicrio~t ot'rr;ir~inn force-.\nDESIGN CONSIDERATIONS\nI ln~ lh le- rou i;!pcrcd iollcr kar ings IDRTRHI In:,? 11;trc roller\nrows in barh-~o-h;~ck (~lcsigt~;\\l ion d l i r 1)131 or III fi~cc-to-face Ideigtlarion \\ulli.\\ DF) :~rr:,l,~rincnl. IZI I R-.irr;tngrarttl, l l t r Io;l(l lines n i IIIC h c i ~ r i ~ ~ g divcrgc Io\\var(l\\ the I x a r i ~ ~ g ;ixi\\ wltilc\nlltc load lines ior DF~;~n ;~ny rn~cn l co vcrgc !n!v:~rd~ llte hci~ring auk. The i n m ~ c r clcs~gn provi<lr< ruh\\lantiill rcsi\\t;~ncc l o ntwnent\nlo;l<ling tlh:ll 1s. lhigb sliiI'!tcs.;l, u.hereas lltc lattcr pn,vidc\\ gw;ller ;~I>lli!? tn :~cct r~n~nn~ls le miv.tlign~ttent ircl:aive l lcxihil iryl\nI\\ r i~~ tp l i f i e t l cmxs-scclinn '11 n DRTKLl ( i n Dl<-:~rmngcrnent~\nrlih\\r,ing lhc csscnt~;~l hr;tr~ng c~~n~pc~ncn ts ii ncr ring or ,.rrrrr. otjler ring or , $ d p :i!ttl gtjiding xhouI(lcr or.fl~dtt,e<fl to$clIler $viIlt sotnc gcnmctric;ll ~ l c l i n i ~ i ~ i n s i\\ given in Fig. I. Tile drlinit inn 01' each syrnhol i s g i vm in the nnrnmcl;tl~~rc.\nl h c coninrl mrew:tr *r!rlnrcr o f lhc ronc ;and rtrp have a cmn-\nIIIIII~ 31 p<,i111 A , t iur rou I ) ;III~ A ? l in r row 21 :IS i l l t~stra~ed in Fig. I. Whilxl thc ;iprx coincidu\\ with IIIC ccntt'r-litic o f [he I rar iny il ir p ~ s \\ ~ h l c 113 dclcnttinc lllu nt;lin $co~t~ctrie:~l parante!err I S . thr roller r:tdiur :tnd lltc k l r i n p ;angle*:\npitcli raditt.: in r dividing ra<lils\\l lhc ha:tring\nMECHANICAL INTERACTIONS (OUASI-STATIC MODEL)\nA con lp re l~c l~~ i rc q o n ~ i - ~ l ; ~ l l r l l l ~ r l e l l o nhl;l!n tlic. In;1<1 Jislrihillinn :lrnc,ltg roller\\. 1I1c Ik>i$d i\\trihuli(,lt i~l<ltt$ lhc roller length.\nand tltr rcl;~ti\\.c movcrnrnl t~liqrl;~cemcnt :m<l i.ul;tlionl lrctwcun ring, is presenlcd lhcrc. 'Illis first nlndcl IS ;in inlcrnteili;!lr step ill lltc ~lcvclopmcnl of ;I ~ l ! ~ i $ s ~ - t l ? ~ ~ i ~ n u ~ rn~~t lc l . In order 111 cirnplif) Ihe ;an;ilysts. the t , l l o u i ! ~ ~ :tr*l$ml>llr,n< have h.cn rnadc:\n.The fnIlowi11: 111a1n courdirt:~tc \\~\\I~GII, II;!VC I>CCII inlrn~luccd Ir,r c~~nr.r l l i rncc: the i1icni:ll rcl'ercllrr c<>nr<lin;tlc ry\\lcol (XI. Y,. Z I i lihuJ 11, llic 0111rr riny ;<nJ with ilr nrtgin in IIK tniddlc cn , s~ -\nD ow\nnl oa\nde d\nby [\nU ni\nve rs\nity o\nf B\nat h]\na t 0\n3: 02\n0 6\nO ct\nob er\n2 01\n4",
+            ",\\BI:II!\\I\\ DI)LI~IC-RO\\L. Tapcrctl Roller Re:~rings: i'nrl l--Mmlcl\nFlg. 2--Cogrdtnate systems and external looding trnnnmlltcd tram tha shan to the bearing.\nsection ~1 111c hc;mnc. thc co l~e ct>ordtn;~lc C?\\IUIII IX,,,. Y,,,. I , , , ) and lhu roller cnordin:~lu sy\\le!n r X BG,8,,. Y %\" .,,, ). '111~ s~th\\criplr m denalc5 the Iw*.:ning yo\\\\: l h tn m = I rcfcr.; I<> r<rn I ;tnd 111 = 2 rcPrs 11) rn%r 2.\nTllc h a r i n g i\\ <~ j l> iec~e~ l h c :tctim, o l~ lac l ' ~ > l I ~ ~ v i r ~ g cs!cn~:~l\nl\";l,ls:\nI. F i r s ;in :$xial preloadinc tl; ) cxprc.isccl i n vn~n of 1\\11. ioi-\nII;~ lernl axial cornpres\\ion 1.1 I.\n2. Seconil :in eslen1;rl loitding wit11 live comlmnents:\n- the ;lri:ll iorcc. F:, = Fs, which aclr in the po%ilivr\n, l i rccl io~~ o l t11c XI -. :1\\i5. IWO r;liliol ~OICCS. Fn = I:, 2nd I:,, = F, wh~c l i olrne ihr YI - itxis and Ihc %, - ;$.xis. r ~ s p ~ ~ l i v r l ! . . t u o l i l l lnp morncntr. hl, :tnil \\,I,. \\r l~ i c i l acl arnolld IIIL. YI\ns I l l e - ; r r lc , rcspl.div?ly.\nA l l <,nnponrn~\\ 01' lhc a~tcrnn l o:lding nhovu-nlrnli<)ncd are :~pplied t r r l thc >linlt ;it rllc 111i11dlc croic-ccclian ol' ~ h c Ik;lring. They an. prescntcrl as u.cll as Ihc coorcIin:~tc sy\\ti'nl\\ ill i:i$. 2. X gc:lcr:il calcr~i ;~l lo;ldin!, prwluce\\ nlcehnni~;~l inler;\\c!ion, ;I!\nthe r i~ l l e r l raceu ;~~ : nd n,llcr/goi~ling 1l;tngc conl;lct\\ !hat dii i?r f<,r L.:I~I ror, :~nd e;uh roller. Cr,n%eqt~snlly. lllr hc;!rinp cnmp~~nr t i l *\n(inner ring? ;lntl rollcrsl i11.c Ir:~nxl:~t~d ;m'l mt:~lcd frnnl l l lcir ini. ti;ll porililm.;. Wilh rcspccl In lhr connll!l:tlc cy.sI~.m IX,. Y,,,. %,,,I. 1l1c cquilihriclrn po?itinlls o i ihc Inner ring* arc dc\\crihcil by lllr\nfollowing d i ~ p l : ~ c c ~ l ~ c n l and rillallon vcctni~:\n:~nd ,I' is lhc 1nl;Il i n ~ l i l l t%Yi: t l c o ~ n p r c ~ ~ i u ~ l l o f I?e;triog, b,. b,, bx, ,, HI^ y, arc 111e linc;~r :111d iillguI:lr d i s p l : ~ ~ ~ n ~ e ~ i t s ill lhe shaft )' men\\oretl u.ilh respect 11, l h r incr~i :~l ihlme. Ihc ltppzr sign rcfcrr 10 rou. I (111 = 1 I and llle l o u r r qign refers to rnw 2 l m = 21.\n\\\\'ill1 rcspccl l o llle roller coor(linu1e ryslcnls I S -,,,,. Y %,,.\nZ*,,,,). m = m. the e q o i l i h r i , ~ ~ ~ ~ posiltnn o l tlir rol len i b rlc*crihed\nby tllc k~ l low ing vecton:\n'rhr ~llspnilltdc o i l he rcclor uon~pnncnt> ill F.q,. /4:1l :~nrl IJbl\nclrpcnds nn ils ;tngtrlilr p s i l i o n lariml!lIi :~llglc qll . The lolal clastic defomlation krr e;sch Hcn~i: tn conlac1 IS exprcs.;ed in lcrm% of the k i u i n p internal genmelry m d thr di.iplnccrnc~~l ;lad rnlatinn vectors hove-dclirtctl.\nNornlnal Pos l t i on Vectors\nTIIc. clih~;uncc I'~OIII lhc Xh< ->tsi\\ o i lhc rnllcr 10 l lw in11cr :III<I outer r:sca.;!y\\ i< clciined hy:\nu l ~ c r c Y 0 s x s I I i\\ 1 1 1 ~ ;ni:bI c~n~r~ l in :~!c long the rtnllcr :tnd c 15 IIIC norninol cle:~rxnrc.\nOn inner and outer r;urea;ly surfnrcs: I'or ;an : ~ r h ~ ~ r a r ? ngular ccx?nlin;tlc *I,, the no t l l i n~ l posilion vei.ror RI II, = 1.01 inr n w i n 1 on lhc r:~cca-:ly o i tile conc or cup is cxpre\\*rd u.illl reqxc l to Ihc co-nrtlinatc ~ys lc l l l I S ,,,. Y,,,. %,,,I I,!:\nD ow\nnl oa\nde d\nby [\nU ni\nve rs\nity o\nf B\nat h]\na t 0\n3: 02\n0 6\nO ct\nob er\n2 01\n4"
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0003244_icsmc.2004.1398398-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003244_icsmc.2004.1398398-Figure2-1.png",
+        "caption": "Figure 2: Two-link model of a leg.",
+        "texts": [
+            " Recorded position of each marker was traced by a motion analysis software (Move-tr/2D, LIBRARY), and the positions, the angles and the angular velocity of each joint were determined. The speed data were smoothed by a six-order low-pass Butterworth Iter with a cutoff frequency of 5 Hz. 2.2 Numerical experiments In this section, the method used in this study to obtain the leg swing trajectory minimizing energy consumption is introduced. 2.2.1 A dynamical model of a leg It was assumed that a leg is a simple two-link system with two joints at a hip and a knee (Fig.2), and the trunk moves horizontally at a constant speed. Vertical movement of the trunk was ignored (Fig.3). The dynamical equation of a leg in swing phase is given as follows TI = (II + I2 + 2A&L1S2 cosSz + Af2L:)& -A4zL1S2(201 + & ) & ~ i n 8 ~ +g(A;r,Sl + A.lr,L,) sin81 +(I2 + A4zLiS2 C O S ~ ' Z ) & +gA42Sz sin(& + 8 2 ) (1) + A ~ ~ L ~ s ~ ~ ~ ~ sin 02 +gAGSz sin(& + 02) (2) T* = ( I 2 +A;12L1S~cosOz)& +12B2 where TI and r2 are a hip and a knee joint torque, respectively, and 81 and B2 are angles of a hip and a knee joint, respectively(Fig.2). I,, Mi, Li and Si represent the inertia moment around center of mass, the mass, the leg length and the center of mass of each link, respectively, and the subscript i=l indicates the thigh and i=2 indicates the leg. g represents the acceleration of gravity. The viscous term on each joint was ignored. The parameters to determine the dynamics of a leg were referred to Winter (1990) based on the leg length and the weight ofthe subject TK, and were de ne d as shown in Table 1. 2.2.2 Estimation of energy consumption It is dif cu It to estimate the energy consumption in muscles to realize a target trajectory of a leg because the kmd and number of activated muscular bers could change at every moment"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001841_irds.2002.1044053-Figure9-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001841_irds.2002.1044053-Figure9-1.png",
+        "caption": "Figure 9: Walking on a Pillar and Deformation of Limbs",
+        "texts": [
+            " After changing the limbs into soft-deformable state, the robot deforms the fore ones by pressing them against the ball, while it deforms hind ones by pressing them against the floor. Fig.8 shows the contact rates between the limbs and the ball with radius 120[mm] in grasping it. The left one shows when the limbs are straight and the right one show when they are deformed to be fit. In these graphs 5 means the positions of the limbs shown in Fig.4-bottom and contact rate means contact areal l i rnb width. We can see from the graphs, this deformation makes the contact areas larger and the robot grasps it using larger lengths of the limbs. 3.4 Walking on a Pillar Fig.9-top shows the robot walking on a pillar. The robot deforms the limbs to be fit to the outline of the pillar in walking on it, while they are straight when it walks on the floor. It is reported that the Hugging Walk[ll] can improves the robustness of the limbed robot in walking on the pillar because an external force can be supported by multiple contact points. For the robot in this paper, however, it is difficult to do the hugging walk because it has only two degrees of freedom in each limbs. Therefore it improves its robustness by deforming the limbs and making the contact areas of them larger",
+            "4 shows the walking speed on the pillar and the lateral load capacity when the robot grapes it using four limbs with straight shapes and with deformed ones. In this table a [degree] means how much the robot moves their limbs forward in the cycle of walking that is i) move forelimbs forward, ii) move hind limbs forward, iii) move body. The walking speed does not depend on the shape of the limbs, however, the lateral load capacity with deformed limbs is twice as large as the one with undeformed limbs. This means that the deformation of limbs improves the stability of the robot in walking on the pillar. Fig.9-bottom shows the deformation of the limbs. The deformation (i)-(iii) is similar to that of grasping a block. In (iv) the robot moves and pushes the limbs against the pillar to deform them fit to the outline of the pillar. 3.5 Climbing a Ladder Fig. 11 shows the robot climbing a ladder with the deformed limbs which keeps it from falling in front and in back. There are two types of deformation shown in Fig.12- (i),(ii). The robot deforms the limbs into these shapes by moving and pushing them against the rundles"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002374_naecon.1994.332886-Figure8-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002374_naecon.1994.332886-Figure8-1.png",
+        "caption": "Figure 8",
+        "texts": [
+            " A Central Interface Unit (CIU) i s included in the aircraft conversion to provide for maintenance data collection from each actuation package individually and provide a single maintenance interface. In addition, the CIU monitors spoiler position to greatly diminish the possibility of aircraft asymmetry. The overall aircraft electric actuation system provides system operational status and i s controlled through the existing aircraft's pilot interface. A photograph of the actuation package is shown in Figure 8. . Efficiency upgrade through elimination of hydraulic pump control servo loop and incorporation of electrically driven pump servo control Adaptation to 270 VDC power for use in future aircraft incorporating 270 VDC power generation. microcircuitry development Incorporation of extensive Fly-By-Light experience into the lAPTM control systems to adapt with future aircraft ARINC 629 or MIL-STD-1773 information networks. Weight/Size reduction through ECU These design improvements are part of ongoing and planned development programs at Lucas to improve the IAPTM"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003286_0167-2789(86)90076-x-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003286_0167-2789(86)90076-x-Figure4-1.png",
+        "caption": "Fig. 4. Bifurcations of f~. a) Case A; nk odd. b) Case B; n~ even.",
+        "texts": [
+            " To see this, we argue as follows. Let Jc -- [a, b] c I denote a small subinterval containing the critical point c, which is itself k-periodic for/ t =/~'k. Then in case A, since an odd number of points on the orbit of c falls to the right of c, fkl[a, c)reverses orientation for /t near #~, while in case B an even number of points lie to the fight of c and fkl[a, c) preserves orientation. In other words, in case A we have f~ (c ) < f~(a) , f~ (b) and in case a f ~ ( c ) > f f ( a ) , f~(b) , see fig. 4. Finally, the words w~, w k corresponding to \"y~ and \"/k are derived from ~'k and ~k * + - respectively as described before proposition 2.2, above. Period doubling: Let Pk = U~ * + -- be a *-factorizable 2k-periodic, admissible kneading invariant and let /~'k be the first parameter value at which v(/~) = u k. Then, by the arguments above, corresponding to ~'k we have a k-periodic orbit \"Yk with word w k containing an odd number of y ' s . As # increases, p(/~) takes its next admissible value v k * + -\" (at, s a y / ~ ' ); corresponding to which we have a 2k-periodic orbit \"/2k with word w2k containing an odd number of y ' s . There is evidently an intermediate parameter value /~' ~ (/~ 'k, /~\") at which \"Yk undergoes a period-doubling bifurcation and \"Y2k appears (initially with the same itinerary as ~'k). Again there are two subcases (fig. 4): Case A: The itinerary (~kj(e)}~= 0 corresponding to 1, k contains an odd number n k of y ' s in the first k entries. Then, as # passes #~\", each periodic block W2k of \"Y2k loses a y. Case B: ( qJj(e)}~_ 0 corresponding to Pk contains an even number n k of y ' s in the first 2k entries. Then as/~ p a s s e s / ~ \" , each periodic block Wzk of 3'2k gains a y. We summarize: Ph. Holmes / Knotted periodic orbits in suspensions of Smale's horseshoe 15 Proposition 2.3(a). Let l, k be an admissible, k-periodic kneading invariant which does not factor as vk = v~ * + - for any admissible v~,",
+            " Using the results of this section, we will show that the Beiersdorfer formula is correct for horseshoe 2-cablings o n l y for case B (n o even) orbits. Ph. Holmes/Knotted periodic orbits in suspensions of Smale's horseshoe 25 From (4.6) we have ( ) (2J 2,J) yj 2 J Y 0 - ( - 1 ) \"\u00b0 2 J - ( - 1 ) j = 2 J ( Y b + ( _ l ) n 0 ) _ ( _ l ) , O = 3 3 ' (4.12) where we note that in case A a y is lost as the base orbit moves over the critical point, so Yo =Yb - - 1 , while in case B the reverse occurs and Y0 = Yb + 1 (cf. fig. 4). Rearranging (4.12), we obtain y ( j ) = [(3y b + 2 ( - 1 ) \" \u00b0 ) 2 , + ( - 1)\"\u00b0+J]/3, (4.13) which agrees with (4.11) if and only if n o is even. Since embeddings of the horseshoe are prevalent in nonlinear oscillators and other three-dimensional dynamical systems (Guckenheimer and Holmes [18]), the general situation is evidently more complicated than Beiersdorfer et al.'s conjecture suggests. In this respect our work shows that, once a suspension has been chosen, the sequence of type numbers bj, along with the yj and crossing numbers cj, are completely determined by the word of the base orbit "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001438_s0094-114x(98)00003-2-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001438_s0094-114x(98)00003-2-Figure1-1.png",
+        "caption": "Fig. 1. Coordinate system.",
+        "texts": [
+            " The environment model is given in Section 5. In Section 6, three kinds of force constraints that need to be considered in the multiple robot cooperative manipulation are discussed. Finally, in Section 7, the modelling procedure is illustrated by an example. The problem addressed in this article is the synthesis of a mathematical model of multiple non-redundant rigid robot manipulators performing cooperative work on a single dynamical object the motion of which is constrained by a dynamical environment (Fig. 1). So, the whole system consists of k non-redundant robots with rigid joints, a dynamical tool or object, and a constraint dynamical environment. The coordinated robots have to simultaneously carry out the following main tasks: (i) move the object along a predetermined known trajectory on the constraint environment; (ii) exert a prespeci\u00aeed contact force on the environment, and (iii) regulate the internal force in the object. The manipulator dynamics, the object dynamics and the environment dynamics are taken into consideration, together with the material constraints imposed on the system (contact conditions between robots and object and between object and environment), and program constraints (speci\u00aeed internal forces, contact forces, object motion)"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002291_robot.1994.351239-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002291_robot.1994.351239-Figure1-1.png",
+        "caption": "Figure 1: Human/Robot Teachine Device The human demonstrates the task with the teaching device, and the data is used to generate the robot program. The magnetic position sensor records the 6D position and orientation, and the pressure sensor detects when the gripper is opened and closed.",
+        "texts": [
+            " However, for many elementary tasks the manipulation skill itself may not be difficult, but the programming may nonetheless be burdensome and discourage short term applications. Programming by Human Demonstration (PHD) is an intuitive method of robot programming. The programmer demonstrates how the task is performed using a humadrobot teaching device that measures the human's forces and positions, and the data gathered from the human is used to generate the robot program. The interface device used in our experiments is shown in Figure 1; it is essentially a six dimensional mouse and force sensor. For a six dimensional position sensor that allows relatively unencumbered motion we use either a magnetic sensor that is a product of Ascension Technologies, or an ultrasonic sensor that is a product of Logitech Corp. Pressure sensors mounted on the gripper detect when the gripper is closed and measure the gripping force. The applications addressed in this article are pick and place tasks, for which the force information is not utilized"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001929_952470-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001929_952470-Figure6-1.png",
+        "caption": "Fig. 6 Liner segment and ring segment J! - 1 ~ s ( i n m m ) .",
+        "texts": [
+            " The front surfaces of the windows were lapped after installation. The intent of the two probe locations was to observed whether the film thickness was uniform along the ring. The apparatus was not under temperature colntrol and was ran at the ambient temperature. A thermocouple, however, was mounted between the two window locations to measure the liner temperature during the experiment. Load Cell 0 RING AND LINER SAMPLES The ring and liner samples were from a production engine (Ford 4.6 L Engine) provided by Ford Motor Co. The dimensions are shown in Fig. 6. The liner was made of cast-iron with the inner surface polished and honed. The surface finish was -2.5pm. The liner segment was cut using electrical discharge machining to minimize distortion from the cutting process. The back of the liner sample was machined to provide a flat mounting surface. The top ring was used in these experiments. It had a barrel shaped contact surface which was chromium coated. It had a thickness of 1.47 mm and a width of 4.09 mm. The radius of curvature of the barrel surface was -1"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003217_tmag.1985.1064247-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003217_tmag.1985.1064247-Figure3-1.png",
+        "caption": "Fig. 3. Configuration of a high-field self-starting motor.",
+        "texts": [
+            " 2431 As an efficient alternative to this, the azimuthal force on the conductor (and hence the torque) can be determined using Fe = Br 1, I (8) Tests have shown that the average value of radial flux density over one slot p i tch on a surface lying midway between the rotor radius and the stator bore (surface S in Fig. 2) gives a satisfactory value for 8,. This value is easily computed from the total flux per slot pitch obtained by a Simpson's rule integration over each slot p i tch and interpolating the radial component of f lux density a t each point from nodal values using the shape functions of the elements. FLUX DENSITY AND .TORQUE CALCULATIONS SYNCHRONOUS MOTOR FOR A HIGH FIELD PERMANENT-MAGNET Figure 3 shows the transverse cross-section o f a high field 4 pole permanent-magnet synchronous machine. The configuration shown with non-radial rare-earth permanent-magnets has many advantages, particularly that the rotor flux per pole exceeds the flux passins through any one magnet. This is il lustrated by the distribution of f lux shown in Fig. 4 , which has been computed using the mesh shown in Fig. 5. Figure 6 shows the radial flux density a t the bore measured using a search coil with the machine on full load"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002417_0278364903022002001-Figure7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002417_0278364903022002001-Figure7-1.png",
+        "caption": "Fig. 7. (a) Model of the eel as a planar, serial chain, and (b) forces and torques on link i. Forces can be expressed in a frame oriented with the link (Fi\u2016, Fi\u22a5), or in a frame oriented with a fixed frame (Fix, Fij ).",
+        "texts": [],
+        "surrounding_texts": [
+            "In our model, locomotion is generated through the drag force terms. To simulate the forces in the water, we adopt a simple fluid mechanical model (Ekeberg 1993). We assume that the Reynolds number is high enough that inertial forces dominate over viscous effects\u2014a reasonable approximation for smooth bodies in an inviscid fluid. We also assume that the fluid is stationary, so the force of the fluid on a given link is due only to the motion of that link. The pressure differential created by an object moving in a fluid causes a drag force opposing the motion. Under the assumptions above, the drag force developed takes the form F \u221d \u00b5wv 2. Here, v is the forward speed of the link and \u00b5w is a drag coefficient for the water, determined by the formula \u00b5w = \u03c1AC/2, where A is the effective area of the object, \u03c1 is the density of water, and C is a shape coefficient. This statement of quadratic drag is an approximate, lumped-parameter model which is often made in the literature on swimming organisms (Ekeberg 1993; Blake 1983; Videlos 1993). It is based on the pressure drag acting on a blunt object in steady flow for Reynolds numbers in the range 400 < Re < 4 \u00d7 105. For the discrete eel model adopted in this work, a typical value for the Reynolds number, based on a characteristic dimension (link diameter) of 5 cm and a velocity of 10 cm s\u22121, is Re \u2248 5 \u00d7 103, which is well within the valid range. The drag model is typically described as \u201csemiempirical\u201d (Videlos 1993), and is usually justified through arguments based on Bernoulli\u2019s principle. at UCSF LIBRARY & CKM on April 9, 2015ijr.sagepub.comDownloaded from We assume that pressure differentials in the directions parallel to the moving body are decoupled from pressure differentials perpendicular to the body, to yield F \u22a5 i \u221d \u2212\u00b5wsgn(v\u22a5 i ) \u00b7 (v\u22a5 i )2, where v\u22a5 i is the projection of the vector (x\u0307i, y\u0307i) along a direction perpendicular to the link. We exclude drag forces parallel to the link. Due to the streamlined nature of the body of the eel, the drag coefficient in the perpendicular direction is much higher than in the parallel direction (Ekeberg 1993). The same observation has also been made for land snakes (Hirose 1993). The discontinuity in sgn(v) means that this expression is not tractable for use in analysis. Therefore, in our analytical derivations we use an approximation to this function that is linear in v Fapprox = \u2212\u00b5vv \u22a5, (11) where \u00b5v is defined by a least-squares fit over a small range around v = 0. This model is also consistent with the tradition in studies of oscillatory mechanical systems with friction, in which linear friction approximations can be used, provided the linear and non-linear friction models dissipate an equivalent amount of energy over one cycle (Hartog 1931). Finally, we note that this force model can be interpreted as a viscous damping model, as might be encountered with a snake moving over soft sand. Since the approximate linear drag model is only valid over a small range of velocities, care must be taken in the selection of \u00b5v. In both friction models, the link force and link velocities are defined in the same coordinate system, so that the frictional force always opposes the motion of the link. To find an expression for the momentum equation, we begin as usual with a formulation of the Lagrangian for the system L = 1 2 q\u0307TM(q)q\u0307, where M(q) is a positive-definite, shape-dependent mass matrix. Exploiting the invariance of the Lagrangian with respect to position\u2014see McIsaac and Ostrowski (2003) for a thorough derivation\u2014we find the following form for the momentum equation p\u0307 = r\u0307 T \u03b1r\u0307 + pT \u03b2r\u0307 + pT p + \u03c4g(p, r, r\u0307), where \u03c4g(p, r, r\u0307) captures the effects of the fluid drag forces in the directions defined by the generalized momenta. Using the linear force approximation given in eq. (11), we can express the vector of drag forces, \u03c4g, by( \u03c4g ) i = \u03b1(r) j i pj + \u03b7(r)ij r\u0307 j . (12) The determination of the \u03b1 and \u03b7 tensors in eq. (12) is complex, and is presented in detail in McIsaac and Ostrowski (2003). These tensors do not have any easy intuitive interpretation, except that \u03b1 = \u2202\u03c4 \u2202p and \u03b7 = \u2202\u03c4 \u2202r\u0307 , however, their form will prove crucial in determining the motion of the system."
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0001845_robot.1988.12305-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001845_robot.1988.12305-Figure2-1.png",
+        "caption": "Figure 2.",
+        "texts": [
+            " Checking t h a t conditions (1) and (2) are satisfied is straightforward. W e can choose an acceleration within t h e range, and then compute t h e velocity of t h e next C-point from t h e current values of velocity and acceleration, and the distance between t h e current and next C-points. As for condition (3), t h e following formulation is used for estimating t h e centrifugal force. W e assume t h a t the robot negotiates a curve having a curvature which depends on t h e angle formed by the t w o lines meeting a t t h e C-point (e.g., point C in Figure 2). W e consider a small distance (constant for all curves) between a C-point and the points where t h e robot begins t o deviate from a trajectory which would have taken it t o the C-point. We denote this distance by d (Figure 2). T h e n t h e radius r is r =d x t a n ( Y ) , 2 where a is t h e angle made by two line segments t h a t meet a t t h e G p o i n t . W e assume d to be sufficiently small in comparison with t h e distance between the t w o C-points. T h e n A path (dashed line) is approximated by two line segments AC and BC. 1664 requirement (3) can be expressed as - < Constan t , muZ r where v is t h e cur ren t velocity and m is t h e mass of the robot. T h i s means t h a t on each curve we are required t o satisfy t h e inequality <G V 2 t a n ( Y ) 2 for some cons tan t G "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001043_s1474-6670(17)46798-x-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001043_s1474-6670(17)46798-x-Figure2-1.png",
+        "caption": "Fig. 2. The robot workspace",
+        "texts": [
+            " The main theoretical result re lated to stability guarantees for the FL + MPC scheme can be stated as follows (a detailed expla nation of this result was given in (Nevistic, 1994)): Assume that the nonlinear plant is input/output feedback linearized and subject to input con straints; that the previously described \"iterative procedure\" together with an infinite output hori zon or a finite horizon with terminal constraint is used ; that the control horizon is sufficiently large to insure feasibility of the on-line optimization. Then the following results hold: \u2022 If the system is open loop stable, then the closed loop system is globally asymptotically stable, \u2022 If the system is open loop unstable, then the closed loop system is locally asymptotically stable 5. Examples 5.1. Example 1 (Benchmark Robot) Robot Dynamics. The benchmark robot is a sim ple two link manipulator . The workspace of the robot is shown in Figure 2. Model of the System: (J + mr2)cp + 2mrr<j/ pmr - pmrtj;2 where : m mass of the cart J the joint moment of inertia (11) (12) <p(t) position of the robot arm <p E [0\u00b0 . .. 270\u00b0] r(t) position of the cart rE[O.27m .. . lm] Tl ,2(t) the torque of the arm and the cart, respectively q(t) The state vector [<p rJ' Equations (11) and (12) can be rewritten as: M(q) . if + C(q , q) . q = T (13) where the definitions of the matrices M(q) and C(q, q) follow directly from these equations . The states of the system are: the position q(t) , the velocity q(t) and the acceleration ij(t) of the arm and the cart"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000869_ja964102u-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000869_ja964102u-Figure1-1.png",
+        "caption": "Figure 1. Cyclic voltammograms in aqueous 0.05 M bpy/bpyH+ buffer at pH 4.5 containing 0.1 M NaBF4 at a carbon electrode (scan rate 20 mV s-1) (A) of a 2 mM solution of [Mn2III,IVO2(bpy)4]3+ (1), (B) after oxidation at 1.25 V of (A), and (C) of a 2 mM solution of [Mn(bpy)3]2+ (2).",
+        "texts": [
+            " Furthermore, we report an original electrochemical method to prepare selectively high-valent polynuclear oxomanganese such as 1 and the linear tetranuclear [Mn4IVO6(bpy)6]4+ 10 (3) complexes from the mononuclear one (2) in this specific medium. We have also investigated associated back-transformations. At a suitably polished vitreous carbon electrode,11a the shape of the cyclic voltammogram of 1 (2 mM) in bpy buffer11b is in close correspondence to that obtained in CH3CN with a quasireversible oxidation wave at E1/2 ) 1.16 V (\u2206Ep ) 90 mV) and an irreversible reduction peak at Epc ) 0.40 V Vs Ag/AgCl (Figure 1A). To characterize the respective final products issued from the oxidation and the reduction of this complex, exhaustive electrolyses have been carried out. An exhaustive oxidation of the solution at 1.25 V leads to a pronounced color change (green to red-brown), accompanied by the disappearance of the quasireversible system at E1/2 ) 1.16 V while the irreversible peak at 0.40 V persists (Figure 1B). Unlike the electrochemical behavior of this complex in CH3CN,5a the oxidized [Mn2IV,IVO2(bpy)4]4+ species is not stable on the time scale of the electrolysis, indicating that a chemical reaction is coupled to the electron transfer. This oxidized species has been identified as the tetranuclear cluster 3, with a linear [Mn4O6]4+ core previously prepared chemically from MnIII(bpy)Cl3(H2O) by Girerd et al.10 In this case, formation of this tetranuclear cluster probably results from the association of two [Mn2IV,IVO2(bpy)3]4+ units issued from the decoordination of one bpy ligand of the initially electrochemically formed [Mn2IV,IVO2(bpy)4]4+ species",
+            "10 Moreover, this electrogenerated tetranuclear complex can be precipitated by addition of a large excess of NaBF4 (2 M) to the oxidized solution. After filtration, the resulting brown powder (yield 55%) exhibits the same characteristics as a chemically prepared authentic sample of 3.13 It should be noted that theoretically the oxidation involves 1 electron per molecule of binuclear complex 1. In practice, after approximately 2-3 electrons have been consumed (depending on the experimental conditions), about 5% of the initial complex remains in solution (Figure 1B). Additional consumption of electrons does not produce the total disappearance of this complex. That the observed excess of coulometry is due to a slow, competitive oxidation of the electrolyte at this potential has been established by a separate experiment conducted in the absence of 1. On the other hand, exhaustive reduction of a solution of 1 at 0.20 V consumes 3 electrons per molecule of 1 and produces quantitatively the mononuclear 2, following reaction 2a. The shape of the voltammogram of the resulting solution is identical to that of a solution of 2 (see below). This result is in accordance with previous studies on the chemical reduction of 1 in the same medium with reducing agents, e.g., ascorbate, hydroquinone, HSO3 -, and NO2 -.4,14 A solution of the mononuclear 2 complex in 0.05 M bpy/ bpyH+-0.1 M NaBF4 shows an irreversible broad oxidation peak around 0.86 V on the cyclic voltammogram, corresponding to the metal oxidation process Mn(II)/Mn(III) (Figure 1C). This oxidation leads, by releasing bpy ligands, as in CH3CN, to the formation of the binuclear manganese(III,IV) complex, following reaction 2b. The formation of this complex on the time scale of the cyclic voltammogram is evidenced by the presence of the quasi-reversible wave at E1/2 ) 1.16 V, typical of its oxidation, and by the irreversible cathodic peak at Epc ) 0.40 V, corresponding to its reduction on the reverse scan. A careful, controlled-potential oxidation carried out at the foot of the anodic peak (E ) 0"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001852_icpr.2002.1047389-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001852_icpr.2002.1047389-Figure3-1.png",
+        "caption": "Figure 3. F117 Stealth Fighter model.",
+        "texts": [
+            " If dense correspondences would allow a dense reconstruction, the usual correlation method used in 2-view stereo will generally not work since the two mirror views correspond to viewing directions far apart. Also note that any deviations of the camera from the pinhole model (e.g. radial distortion) can be corrected during the initial calibration process, without invalidating the described reconstruction method. 5.2. Stealth fighter model Our first example is a toy F-117 Stealth fighter. The input image and synthesized symmetric view are presented in figure 3a with their epipolar pencils. The internal parameters of the digital camera used were determined using Photomodeler\u2019s calibration tool. After specifying a minimum number of point correspondences between the two images, the software was able to perform a full calibration of both camera positions and to infer the 3-D position of the object points. Adding more point and line correspondences allowed to obtain a 3-D wireframe model of the object presented in figure 3b. Note that the recovered object is mirror symmetric, and that the recovered cameras are actually symmetrical in location and orientation with respect to the object\u2019s symmetry plane, properties that are not used at any point in Photomodeler\u2019s reconstruction algorithms (the symmetry property is only used to synthesize the symmetric view). Once the 3-D inference is performed, a 3-D surface model can be produced (figure 3c) and the texture can be extracted from the images (figure 3d). The construction of this 3-D textured model took only a few minutes to a novice Photomodeler user. Incorporating symmetry derived constraints in the workflow and in the interface would greatly facilitate the process and reduce the time needed to build a model, while also helping in improving the accuracy of the manual input. - a. Input image (left) of a (toy) F117 and inverted image (right), with overlaid epipolar pencils. 5.3. Face model The technique clearly applies beautifully to perfectly symmetric objects"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000909_027836499901800506-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000909_027836499901800506-Figure1-1.png",
+        "caption": "Fig. 1. A generalized disturbance force (a) and a generalized disturbance torque (b).",
+        "texts": [
+            " As in previous papers (Mangialardi, Mantriota, and Trentadue 1993, 1995, 1996), reference is made to a generalized disturbance force and torque, and the object geometry is normalized so that the maximum distance between the object\u2019s geometric center and its edges is a unit value. In a 2-D problem, the generalized disturbance force is defined as a force that is applied in the geometric center (C) of the object and has a unit value and a generic direction. In other words, if i, j , and k indicate the unit vectors of the reference system (C, x, y, z) of Figure 1a, then Fd = uF i + vF j (N), u2 F + v2 F = 1(N). (1) Similarly, the generalized disturbance torque is defined as a torque having a unit value and generic direction which, in the special case of a 2-D problem, is parallel to the z-axis; namely (Fig. 1b) Td = k (Nm) or Td = \u2212k (Nm). (2) Let us consider frictional contact for each finger and a given configuration of the n contact points as a grasp model. If a disturbance force (Fh) and a torque (Th) of a unit value directed along the axes of the reference system were to be exerted in turn on the object, the forces at the contact points would have to verify the following relations to ensure equilibrium: Fh + n\u2211 p=1 ( ap,hvN(p) + bp,hvT(p) ) = 0, (3.1) Th + n\u2211 p=1 (P(p) \u2212 C)3 ( ap,hvN(p) + bp,hvT(p) ) = 0, (3"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002163_027836499301200602-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002163_027836499301200602-Figure1-1.png",
+        "caption": "Fig. 1. Free body diagram of the card under sliding manipulation.",
+        "texts": [
+            " If the card is thin, the reaction forces between the card and the supporting surface will be concentrated beneath the fingers. The card moves slowly, so that the equations of static equilibrium apply: where fi are the tangential forces applied by the fingertips to the card, Is are the tangential forces between the supporting surface and the card, mi are the friction moments between the soft fingertips and the card, and ms2 are the friccion moments between the supporting surface and the card at each contact (Fig. 1). We note that while at Freie Universitaet Berlin on May 8, 2015ijr.sagepub.comDownloaded from 530 the friction between the smooth supporting surface and the card is smaller than the friction between the fingertips and the card, its effects may be noticeable. In the case of symmetric grasps, ri = r2, f = f2, Is = fs&dquo; mi = rn2, and m,s, = mS2; hence the subscript i can be dropped. The Coulomb friction model establishes constraints among the normal force and the tangential force and moment at each contact area",
+            " Without specifying the ratio of rigid to nonrigid motion, a unique solution is not obtained. Therefore, we will remove an additional degree of freedom from the example by requiring that the two fingertips be identical and move symmetrically in the x direction. In this case, it can easily be shown that the only possible motion of the card (i.e., the only motion that would not violate the equations of equilibrium) is a pure rotation with respect to a stationary reference frame in the plane; i.e., v = 0. Thus the velocity compatibility equations for Figure 1 reduce to for both fingertips, where v is the fingertip velocity in the ~ direction, r is distance between the centroid of the contact and the center of rotation (COR) located at the origin as shown in Figure 1, h is the (clockwise) angular velocity of the card and vslip is the sliding velocity of the card with respect to the fingertips. Combining equations (4) and (7) we obtain: where f and m are constrained by the equilibrium equation (2): m + ms - r( f - fs) = 0, for a symmetric grasp. Thus the motion planning problem for this simple example has boiled down to two questions: (i) Given a known linear and angular velocity for the two fingertips, what will the angular velocity, c~, of the card be and what will the forces and moments at the fingertips be"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002563_robot.1996.506892-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002563_robot.1996.506892-Figure1-1.png",
+        "caption": "Figure 1: Contact Point in Force Sensor Coordinate Frame",
+        "texts": [
+            " In this paper, we consider practical issues of contact localization for the robotic fingers in our laboratory. Each of these fingers measures a size of approximately 1.5 meters in a fully extended configuration, and has six degrees of freedom. Interfacing the last joint and the custorn-made fingertip is a Lord FT335x force/torque sensor. The fingertip consists of a cylin- 0-7803-2988-4196 $4.00 0 1996 IEEE 1339 der of radius 35\" and length 161mm, and a hemisphere at the distal end of the cylinder as is shown in Figure 1. The total mass of the fingertip is 0.62 kg, which gives rise to a gravity force of comparable magnitude with that of typical contact forces, and can lead to substantially biased outputs. This bias, however, depends only on the pose of the fingertip and can be properly compensated for. An outline of the paper is as follows: In Section 2, we present the mathematical formulation of contact localization for point contact with friction, along the lines of [l], together with a precise proof for uniqueness of solutions",
+            " In Section 5 we show some experiment results obtained, and conclude the paper in Section 6. 2 Problem Formulation In this section, we present the mathematical model for localization of contact modeled as point contact with friction ([5]), along the lines of [l]. We show how to use measurement data from the force/torque sensor and CAD model of the fingertip to obtain a system of nonlinear equations from which contact location can be solved for. We give precise conditions under which local uniqueness of the solution, if it exists, can be guaranteed. Consider Figure 1. Let fc E R3 be some contact force applied to the fingertip through contact with an object, a t some unknown location rc E R3. For frictional point contact, no moment can be transmitted through the contact. If the finger is massless, then the readings of force, fs E R3 and torque, r, E R3, from the force/torque sensor are related to the contact force fc and contact location r, by f s = fc, (1) r.3 = rc x fc, The problem of contact Eocalizatzon amounts to that of finding the contact location, rc E R3, using measurement data, (fs, rs) E R6"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001314_s0169-4332(96)00648-4-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001314_s0169-4332(96)00648-4-Figure1-1.png",
+        "caption": "Fig. 1. Schematic presentation of laser surface melt-hardening in the direction of x-axis.",
+        "texts": [
+            " In the experiments we used a laser beam power of Ps450 W, with the beam radius on the workpiece surface r s0.633 mm at 10 mmb defocus so that the achieved energy density was 35700 Wrcm2. The laser light absorptivity of the workpiece surface with a wave length of 10.6 mm was increased by treating the workpiece surface in a Zn-phosphate bath. The laser light absorption coefficient was chosen according to recommendations in the literature as a constant value and was As80% w x1 . The laser beam speeds with respect to the workpiece were chosen in a wide range from 2 to 42 mmrs in increments of 2 mmrs. Fig. 1 illustrates this procedure graphically. In laser surface melt-hardening tests, the modified trace was spherical consisting of the remelted and hardened zone. The remelted zone had an austenite\u2013 ledeburite microstructure whereas the hardened zone had a martensite microstructure with graphite flakes in the gray iron and martensite\u2013ferrite microstructure with graphite nodules in the nodular iron. The graphite nodules in the ferrite surrounding of the nodular iron are in the hardened zone surrounded with a hard martensite shell which had also been w xanalyzed, the results being presented in 7 "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002320_bf03222493-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002320_bf03222493-Figure1-1.png",
+        "caption": "Figure 1. An overall diagram of a selective laser sintering (SLS) system.",
+        "texts": [
+            " Use of SFF in large-vol ume production, by reducing the tool making time and cost, would make it possible to accommodate any modifica tionin the mold! die design without sub sequently incurring lengthy time delays and high costs. Selective laser sintering (SLS) is an SFF approach invented at the University of Texas at Austin and commercialized by DTM Corporation of Austin. It is a rapid prototyping! manufacturing tech nology and its importance has been well documented in the literature during the past few years.I-7 The SLS process is shown in Figure 1. A computer solid model of the part is created and appropriately sliced to pro vide data layerwise to the laser and ras ter scanner. A thin layer of powder is deposited under controlled temperature and atmosphere using a powder level ing drum. The layer thickness ranges between 75 /lm and 250 /lm. The first layer of the object is traced with a laser coupled to the computer-controlled scan ning system. The laser beam diameter is on the order of 05 mm, and output power ranges between 5 Wand 50 W. A proto type system that uses a 1"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002417_0278364903022002001-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002417_0278364903022002001-Figure4-1.png",
+        "caption": "Fig. 4. (a) The simplified model of the Snakeboard (top) along with (b) a demo prototype.",
+        "texts": [
+            " Unfortunately, cases will arise when more than one approximation is suitable (indeed, we present one such case, that of the eel-like swimmer, in Section 5). At present, the choice of the \u201cbest\u201d approximation in these cases is necessarily heuristic, and we cannot present rigorous criteria for selecting one approximation over another. We are working on ways to automate this process using results from optimal control (McIsaac 2001). The Snakeboard is a commercial variant of the skateboard that allows for independent rotation of the wheel trucks. The simplified model of the Snakeboard (referred to as the snakeboard model) is shown in Figure 4, along with a robotic version that was constructed in order to verify theoretical simulations. Full treatment of the control of the snakeboard is beyond the scope of this paper\u2014interested readers are referred to Ostrowski et al. (1994) and Ostrowski, Desai, and Kumar (2000) for more information\u2014however we include in this paper all the dynamic analysis necessary to demonstrate the application of our control algorithm. The basic premise of the snakeboard is that by properly coupling the rotating flywheel (modeling the swinging of a human torso) with the turning of the wheels, we can generate a variety of motions, including a forward serpentine-like gait reminiscent of a snake"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000496_a:1022548914291-Figure9-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000496_a:1022548914291-Figure9-1.png",
+        "caption": "Fig. 9. Standard rods in two inertial frames.",
+        "texts": [
+            ", Asa = AS), then the spatial length between them must also be equal, and the length measured by rods in k and K between A and B are equal. Similar arguments can be made for acceleration in the rod lengthwise direction, as well as for gravitational body forces induced by a massive body. Hence the surrogate rods postulate is merely a restatement of the proper spacetime path length invariance postulate for the special case where A(time) = 0 for both observers (which it is for zero relative velocity and time orthogonal frames). Figs. 9 and 10 reveal what this means in the context of non-time-orthogonal reference frames. Fig. 9 depicts two inertial reference frames, K and K1, in relative motion, and serves as a review of the cause of the Lorentz contraction effect. A rod fixed in K1 has length L1= L as seen from K1. The endpoints (and all points between) of L1 move with velocity v relative to K along world lines parallel to the K1 time axis. Lorentz contraction arises because the observer in K sees rod endpoint events as A and C, whereas the observer in K1 sees them as A and B. L1, the distance between A and C is less than L, the distance between A and B, by the Lorentz contraction factor",
+            " Though it is beside the point we are in the process of making, the Lorentz contraction effect is thus seen to be little more than an optical illusion fostered on us by lack of agreement in simultaneity. No Lorentz contracted object ever feels compressed. That is, even though L1 and lk have the same velocity as seen from K, they do not have the same spatial length as seen from K. Prior researchers have almost universally assumed they do. That L1 looks contracted as seen from k can be corroborated by superimposing the k frame of Fig. 10 with the K1 frame of Fig. 9. Hence, two rods with the same velocity, one in a time orthogonal frame and one in a non-time-orthogonal frame do not have equal lengths. We conclude that the surrogate rods postulate is only valid for time orthogonal frames. Several researchers [13,18] have considered the limiting case of very large radius, small angular velocity, with large circumferential velocity v=wr. In this case acceleration v/r2 approaches zero, and it is argued there is no way to discern between such a frame and an inertial frame",
+            " But in taking the limit described, v remains constant, and hence so does the slope of the time axis. Therefore, all of the non-Lorentzian phenomena heretofore described for rotating frames are unmitigated in passing to the limit. (See also Sec. 6.) Contrary to what many claim, an observer on this limiting case frame can determine she is rotating. In fact, three experiments can reveal this. The first is the Sagnac experiment. The second is Non-Time-Orthogonal Reference Frames 433 In contrast with Fig. 9, Fig. 10 shows the rotating coordinate frame k at radius r superimposed with the non-rotating inertial frame K. In Fig. 10 we show two circumferentially aligned standard rods, one designated by lk which rides with the disk and the other, L, fixed in K. When both rods are at rest in the same inertial system, they have equal length, i.e., lk = L, When the disk is spinning they also have equal length, as seen by both k and K observers, since, as discussed earlier, the same endpoint events (D and E) of both rods are seen as simultaneous in both frames. Yet, due to the special nature of the non-time-orthogonal frame k at r, the lk rod has a non-zero velocity relative to the L rod. Every point on the lk rod in Fig. 10 moves with the same velocity as every point on the L1 rod in Fig. 9. Yet L1 looks contracted from K, whereas lk does not, i.e., described in Section 6.2 below. The third involves measuring the mass of a known entity such as an electron which varies relativistically with the potential energy, i.e., as a function of v alone as in Eq. (26), and hence one can readily determine v. 6. THE NEW THEORY AND EXPERIMENT Given the speed of our planet around its sun, and the speed of our solar system around its galactic center, one might ask why measurements on our planet (which could be considered as part of a frame rotating about the center of each of these systems) do not seem to exhibit the aforementioned non-Lorentzian properties",
+            " Gr0n, 0., \"Relativistic description of a rotating disk\". Am. J. of Phys. 43(10), 869-876 (1975). 27. There is a little subtlety here. Calculation of the Lorentz contraction actually involves rod endpoints which appear to be different events to different observers. The example assumes the same two events are measured by both observers. However, the conclusion remains valid. If the endpoint events look simultaneous to two different observers, then the rod length measured must be the same for each. See Fig. 9 and the concomitant discussion in Sec. 5.2. 28. Arzelies, H., Relativistic Kinematics (Pergamon, New York 1966), Chap. IX. Arzelies was not convinced that tension arises in the disk, but references others who were. 29. Franklin, P., \"The meaning of rotation in the special theory of relativity,\" Proc. Nat. Acad. Sci. USA 8(9), 265-268 (1922). 30. Trocheries, M. G., \"Electrodynamics in a rotating frame of reference,\" Phil. Mag. 40(310), 1143-1154 (1949). 31.Takeno, H., \"On relativistic theory of rotating disk,\" Prog"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003942_tec.2005.847953-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003942_tec.2005.847953-Figure2-1.png",
+        "caption": "Fig. 2. Vector diagram of the conventional LCI-based induction motor drive.",
+        "texts": [
+            " The LCI can control only the fundamental frequency of the motor currents by selecting the gating instances of thyristors. For successful commutation of thyristors in the LCI, the output current of the LCI must lead the corresponding motor phase voltage . Since the motor currents in induction motors always lag the corresponding motor phase voltages, the leading power factor for the commutation is obtained by the output capacitor and the dc-commutation circuit. The output capacitors in parallel with the induction motor provide a phase shift of the motor current to produce a leading power factor, as shown in Fig. 2. In Fig. 2, the leading angle of the LCI and the lagging angle of the induction motor are depicted by and , respectively. This leading power factor obtained by the output capacitor enables soft switching of the LCI at a limited upper speed range of the induction motor. For speeds lower than the lower limit of the operating range, such as the startup and the low-speed region, these capacitors cannot make enough leading angle because the capacitor currents are too small due to high impedance of the capacitors"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002864_s0924-0136(03)00811-2-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002864_s0924-0136(03)00811-2-Figure4-1.png",
+        "caption": "Fig. 4. The technical curve of VDPC.",
+        "texts": [
+            " Its characteristics are as follows: (1) the shells are cleaned externally and internally after baking; (2) the geometries and the surface roughness of the shells are identical to those of the SLS prototype; (3) the shells have no cracks and no distortions, the accuracy of the shells depends only on the SLS prototypes. In order to obtain high quality metallic parts and fine shaping, an equipment known as the VDPC was used for casting of the shell mould. Fig. 3 is a schematic diagram showing the principle of the VDPC. In the VDPC, the shell mould is put in the upper chamber, the liquid metal in the lower chamber. The technical curve of the process is shown in Fig. 4. The air in the mould is removed with the counter-pressure reduction (A\u2013C), then the pressure raised in the lower chamber for mould filling (C\u2013D). After mould filling, it is necessary to have a holding pressure period (E\u2013F) to enhance the casting solidification under the pressure and to obtain highly sound metallic castings. The alloy for the moulding shell casting was Al-alloy (6\u20138% Si, 0.45% Mg, 0.21% Fe). After pouring and cleaning, the desired metallic parts were obtained. Fig. 5 shows the CAD model and the metallic parts manufactured using this process"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001397_70.897776-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001397_70.897776-Figure1-1.png",
+        "caption": "Fig. 1. A Stewart\u2013Gough platform manipulator.",
+        "texts": [
+            " INTRODUCTION PARALLEL manipulators consist of two main bodies coupled via legs. One body is arbitrarily designated as fixed, while the other is regarded as movable, and hence, are respectively called the base and the end-effector (EE) of the manipulator. These manipulators are referred to as Stewart\u2013Gough platforms, when the leg architecture is restricted to an actuated prismatic joint connected to the EE through a passive spherical joint and to the base via a passive universal joint, as shown in Fig. 1. The direct kinematics (DK) problem pertains to the determination of the actual pose\u2014i.e., the position and orientation\u2014of the EE relative to the base from a set of joint-position readouts. Kinematic decoupling refers to the separation of the kinematic relations into two parts: the first part involves only the translational or the rotational motion of the EE, and the second part involves both motions. The first part simplifies tremendously the problem because it leads to a linear algebraic system",
+            " Baron is with the Department of Mechanical Engineering, \u00c9cole Polytechnique de Montr\u00e9al, Montr\u00e9al, PQ H3C 3A7, Canada. J. Angeles is with the Department of Mechanical Engineering and the Centre for Intelligent Machines, McGill University, Montreal, PQ H3A 2K6, Canada. Publisher Item Identifier S 1042-296X(00)11644-1. concept of isotropic decoupling is discussed, together with the singularity analysis of the proposed procedure. In order to describe the motion of the EE relative to the base, let us attach frame to the base and frame to the EE, as shown in Fig. 1. The pose of the EE relative to the base is thus determined by , the position vector of the origin of in , and , the rotation matrix representing the orientation of in . Alternatively, the said orientation can be represented by , the nine-dimensional array constructed from the three rows of the proper orthogonal matrix such that (1) with (2) Each leg of a parallel manipulator defines a kinematic loop passing through the origins of frames and , and through the ankle- and hip-attachment points and , respectively"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000658_j.2042-3306.1996.tb03089.x-FigureI-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000658_j.2042-3306.1996.tb03089.x-FigureI-1.png",
+        "caption": "Fig I : Positions of reference markers and description of angles. p p and /IT depict the segment angle of the pastern, metatarsus an tibia, respectively. eF and eT define the fetlock joint and the tarsal joint, respectively. VH and Vv depict the positive direcrion of the horizontal and vertical hoof velocities, respectively.",
+        "texts": [],
+        "surrounding_texts": [
+            "Angles of the fetlock joint and tarsus are as defined in Figure 1. Angles are negative in extension and positive in flexion."
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0002477_011-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002477_011-Figure3-1.png",
+        "caption": "Figure 3. Junction depth versus annealing time for HgMnTe, p = 1.6 x 10l6 cmp3, T = 180 \"C.",
+        "texts": [],
+        "surrounding_texts": [
+            "The junction depth for short anneal times increases exponentially with temperature, but the maximum depth is achieved for shorter times if the anneal temperature is higher. The conversion process depends on the native acceptor concentration in all of the semiconductors studied. The junction depth decreases with increasing concentration. Comparing depth versus time curves for various semiconductors one can see that the conversion rate at the same temperature decreases in the order, HgCdTe > HgMnTe > HgZnTe. As table 1 shows the measured photoconductor lifetimes are comparable to those obtained on high-quality samples converted by the conventional anneal in mercury vapour."
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0002271_robot.1988.12256-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002271_robot.1988.12256-Figure3-1.png",
+        "caption": "Fig. 3 Finger Structure of UCSB HAND: Five Bar Closed Link Mechanism",
+        "texts": [
+            "2 shows the UCSB HAND developed in the Center for Robotic Systems in Microelectronics, University of California Santa Barbara. The robot hand has three 3 DOF fingers driven by nine DC servo motors. This hand was developed to research coordinative manipulation by multiple robotic mechanisms [8]. Since precise force control of each finger is required, simple gear reduction and transmission system were adopted. The reduction ratio of each motor is only sixteen. By using the five bar closed link mechanism and a special transmission, the finger structure was simplified as shown in Fig.3, and all the motors were located in the wrist portion. The transmission is shown in Fig.4. The dynamics of the closed link finger mechanism was computed using the computational scheme proposed in section 2. The coordinate frames and the corresponding open link tree structural mechanism are shown in FigS. The coordinate frames were defined according to the Denavit-Hartenberg notation [9]. O i indicates the rotational angle along the z axis of the (i-1)-th coordinate frame. e,, e,, and O3 axes are the actuated joints"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000704_a:1008228120608-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000704_a:1008228120608-Figure2-1.png",
+        "caption": "Figure 2. The failure locus in the plane X1\u2013X2. Global stick phases are represented as straight lines parallel to the bisection line of the first quadrant. A slip phase starts when a trajectory reaches the failure locus.",
+        "texts": [
+            " The dynamics of the mechanical system of Figure 1 are described through the time histories of positions and velocities of the blocks which have been defined in a non-dimensionalised form [7]: X1 and X2 are the displacements of the first and the second block, respectively, relative to the configuration where the three springs are simultaneously unstretched, V1 and V2 are the velocities of the first and the second block. The limit conditions that indicate the passage from the stick-motion to the slip-motion and vice versa are given by the equations: X1 + (X1 X2) = 1; (3a) X2 + (X2 X1) = : (3b) Equations (3) define the failure locus in the plane of the variables (X1;X2) (Figure 2). When the blocks are pulled by the belt their velocity is constantly equal to that of the belt; when the blocks slip their motion is described by the equations: X1 +X1 + (X1 X2) = 1=(1 + jV1 Vdrj); (4a) X2 +X2 + (X2 X1) = =(1 + jV2 Vdrj): (4b) In Equations (3) and (4) is the ratio between the stiffness of the coupling spring and the stiffness of the two other springs, is the ratio between the maximum static friction force acting on the second block and the same force acting on the first block, is the shape coefficient of the dynamic friction law, Vdr is the (non-dimensionalised) velocity of the belt, which is constant",
+            " The dynamics of the stick-slip system generate a one-dimensional map of the variable d [4], the so-called event map, that is the main object of this paper and will be indicated by f ; Figures 4 and 5 show two important features of the one-dimensional map: its graphical representation is in general much simpler than that of the global motion and it is a single valued function. The second property of the map was found in all the numerical examples that were taken into consideration. If the driving velocity is small the points lying on the line AC into the failure locus represent all the transient motions once the possible global slip phases have ceased [7]. The stretch length d may vary between 0:6764 and 0.6764 which correspond to the points C and A, respectively, of the failure locus of Figure 2. Choosing a grid of initial conditions on this line, it is possible to investigate the global dynamics of the system. Figure 6 is an illustration of the global dynamic behaviour of the system by means of the one-dimensional map. In Figure 6 the thin lines indicate the transient behaviour whereas the thick lines are composed by points belonging to the steady state behaviour of the system. There exist (at least) two attractors, indicated by the numbers \u20181\u2019 and \u20182\u2019, so that the interval CA, where the map is defined, is divided in two basins of attraction; the two sub-intervals B1 and B2 constitute the basin of the attractor \u20182\u2019, the other sub-intervals are the basin of attraction of the attractor \u20181\u2019"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002148_rob.4620110104-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002148_rob.4620110104-Figure3-1.png",
+        "caption": "Figure 3. Deformation by comparing B and %.",
+        "texts": [
+            " This is done by defining a deformation vector field A from the intrusion vector field. We can write * where h is the homeomorphism from S\"-' to R and 0 is the deformation vector field transforming B into 8. The function a is a normalizing function ensuring that E is still an imbedding of Sn-'. Figure 2 summarizes these different concepts for the 2-D world. The interaction component 8 can be chosen as a deadband value for the information boundary 8. In this case, E is deformed if and only if the information boundary manifold B is \"smaller\" than E (Fig. 3). Thus, the normalizing function a works as a trigger. From relations (2) and (3), the formal expression of Q can be written: = 0 otherwise (4) We have to note that possible discontinuities of the information boundary are finite and thus can be easily deleted. For instance, such is the case of the central observation of a polygonal room (Fig. 4). 2.4. Control loop The first cause of the interaction component deformation is the information intrusion due to the prox- imity of moving obstacles. The second cause is the internal control El, = p ( r ) of the robot for compensating this intrusion"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003231_491596-Figure7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003231_491596-Figure7-1.png",
+        "caption": "Fig. 7.\u2014Diagram of the twisted disk model showing the relevant parameters. The disk is viewed at elevation obs \u00bc 0 . Inset: The same disk viewed at obs \u00bc 90 , showing the disk twist angle tw.",
+        "texts": [
+            " We seek to test this possibility by comparing the observed hard- and soft-pulse profiles to a relatively simple model, in which a warped, twisted inner accretion disk is illuminated by a rotating X-ray pulsar beam. 5.1. Illuminated Disk Model Our model does not describe the entire disk but only the region close to the magnetosphere where the bright reprocessed component must be emitted. The disk model consists of a series of concentric circles with varying tilt and twist relative to each other with distance from the center (see Fig. 7). A similar shape has been inferred for the large-scale structure of the disk in Her X-1 from changes in the pulse profiles with superorbital phase (Scott et al. 2000; Leahy 2002). Warped and twisted structures have also resulted from numerical simulations of warped disks (Wijers & Pringle 1999) and of gas-magnetosphere interaction (Romanova et al. 2003). In our calculations we place this surface (we refer to it simply as the \u2018\u2018disk\u2019\u2019) at roughly the location of the magnetosphere ( 108 cm) and test if precession of such a surface around the disk axis can create changing soft-component profiles similar to those observed"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002927_fuzzy.1992.258722-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002927_fuzzy.1992.258722-Figure4-1.png",
+        "caption": "Figure 4: Nonlinearity of the output function of FCMAC suppresses noise. Three fuzzy weights Wi(i = 1 ,2 ,3 ) are used to generate the response fuzzy set. Suppose pw;(y + e ) = pw,(y) for some e > 0. Because of the nonlinearity of the defuzzification, the new fuzzy centroid will be less than B + e .",
+        "texts": [
+            " Note especially that f ( x ) of CMAC is a linear function of weights; however, f(x) of FCMAC is a nonlinear function of fuzzy weights. Linear functions make computation and analysis comparatively easy. But linear functions do not suppress noise, and thus they are not robust. Noise due to mapping collisions, producing an undesirable generalization between distant inputs, will be suppressed by the defuzzification process. Nonlinearity of f ( x ) increases FCMAC's computational richness and makes it robust in the case of mapping collisions (see Figure 4). The cost of nonlinearity is the extra computational burden in defuzzification process. In particular, computing the fuzzy centroid in the centroid defuzzification scheme requires division. Since FCMAC extends CMAC by including fuzziness in the system architecture and the mathematical data, the following question is naturally raised: Can a FCMAC module be reduced to a CMAC module? The answer is yes, as presented by the following theorem. Theorem: For a FCMAC module, if all sensors of S are crisp and all weights are nonfuzzy singletons3, then the FCMAC module functions as a CMAC module"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002310_1.2831616-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002310_1.2831616-Figure1-1.png",
+        "caption": "Fig. 1 Apparatus",
+        "texts": [
+            " The purpose of this study is to design and make an apparatus that can measure the surface separation and normal force accu rately and to measure fluid lubrication film thicknesses less than 10 nm using the new apparatus. Results of experiments are compared with the conventional lubrication theory considering the van der Waals force and the meniscus force. Contributed by tlie Triboiogy Division for publication in the JOURNAL OF TRIBOLOQY. Manuscript received by the Triboiogy Division May 4, 1995; revised manuscript received October 17, 1995. Associate Technical Editor: C. Cusano, Apparatus and Specimens A new apparatus that the authors developed is shown sche matically in Fig. 1. Lubricated surfaces are in a crossed cylinder configuration, which is geometrically equivalent to the configu ration between a sphere and a plane (Israelachvili, 1992). Opti cally polished glass lenses are used as the two cylindrical sur faces, and one of the lenses is supported by a rigid arm, the other by a flexible double cantilever spring. When certain forces act between these surfaces, the cylindrical surface supported by the cantilever spring is displaced, then the normal displacement is measured by a high resolution non-contact capacitive dis placement sensor",
+            "35 mPa-s\" d:(Hom and Israelachvih, 1981), e:(Israelachvili, 1992), ** denotes the measured value. Experimental Procedure Square sheets of mica with a size of 10 X 10 mm are cleaved to a thickness of 10~30 jim and then glued on the cylindrical optical lenses with cyanoacrylate paste. Curvature radius, R, of the cylindrical surface is measured by a surface roughness tester (R = 10.15 \u00b1 0.15 mm). Mass of the cylindrical lens and plates, which are attached to the end of the double cantilever spring (see Fig. 1), is measured by a electric balance. The two cylindri cal surfaces are then set to the apparatus. The free vibration frequency of the resulting spring-mass system is measured by FFT analyzer, and the spring constant, fcj, of the double cantile ver spring is calculated from the measured natural frequency of the spring and the mass by a one-degree-of-freedom lumpedmass/spring model (ks = 132.5 \u00b1 2.5 N/m). Parallel sliding of the elastic stage 1 is ensured to less than 7 nm (perpendicular to the sliding direction)/100 fxm (sliding distance)"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003927_1.1828069-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003927_1.1828069-Figure3-1.png",
+        "caption": "Fig. 3 Schematic diagram of the friction measurement rig",
+        "texts": [
+            " The Rq parameter for this artificial roughness was 71 nm. For the isotropic rough surface tests, a rough AISI 52100 steel ball, manufactured by early withdrawal from the ball-finishing process, was used, with roughness parameter Rq579 nm. A 3D plot of the surface of the rough steel ball obtained with an interference microscope is shown in Fig. 2. 2.2 Friction Measurement. Friction measurements were carried out using a minitraction machine ~MTM!. A schematic diagram of the testing rig is shown in Fig. 3. A lubricated contact is formed between a steel ball and a steel disk, which are driven independently by electric motors at any desired combination of 224 \u00d5 Vol. 127, JANUARY 2005 rom: http://tribology.asmedigitalcollection.asme.org/pdfaccess.ashx?url= sliding and rolling. A load cell connected to the ball shaft enables the friction force to be monitored continuously. For each entrainment speed, the friction force is measured with the disk moving faster than the ball and vice versa at the same entrainment speed and slide roll ratio"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003217_tmag.1985.1064247-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003217_tmag.1985.1064247-Figure2-1.png",
+        "caption": "Fig. 2. Determination of the electromagnetic torque in the machine.",
+        "texts": [
+            " For example, between nodes d and e, the constant value of radial f lux density is given by The nodal value for node e is then given by a weighted average o f the radial components on either side of the node, thus Br(ee) = b e - e f ) Br(de) + (8d - e,) Br(ef) ( 6 ) ed - ef With a reasonable discretisation, the degree o f accuracy by both methods is approximately equal, and, hence, results presented later in this paper have used the simpler second method for economy. CALCULATION OF TORQUE The conventional method of determining instantaneous torque in an electrical machine is to compute the force on individua1:stator conductors by a Maxwell stress integration F- = 4 B.H ds f (7) about an arbitrarily defined contour enclosing the conductors in each slot, for instance contour C shown i n Fig. 2. This has two disadvantages: f i rst the l ine integral calculation when performed for a machine with many slots over a range of operating conditions will require a considerable amount of central processor time and, secondly, for accurate results a fine discretisation along the contour is required, since the values o f B and H are both derivatives of the solution potential. 2431 As an efficient alternative to this, the azimuthal force on the conductor (and hence the torque) can be determined using Fe = Br 1, I (8) Tests have shown that the average value of radial flux density over one slot p i tch on a surface lying midway between the rotor radius and the stator bore (surface S in Fig. 2) gives a satisfactory value for 8,. This value is easily computed from the total flux per slot pitch obtained by a Simpson's rule integration over each slot p i tch and interpolating the radial component of f lux density a t each point from nodal values using the shape functions of the elements. FLUX DENSITY AND .TORQUE CALCULATIONS SYNCHRONOUS MOTOR FOR A HIGH FIELD PERMANENT-MAGNET Figure 3 shows the transverse cross-section o f a high field 4 pole permanent-magnet synchronous machine. The configuration shown with non-radial rare-earth permanent-magnets has many advantages, particularly that the rotor flux per pole exceeds the flux passins through any one magnet"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000595_1.2828771-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000595_1.2828771-Figure1-1.png",
+        "caption": "Fig. 1 A scliematic drawing of 6-axis CNC hobbing machines",
+        "texts": [
+            " The general gear mathematical model can also be applied to the design and manufacturing of spur, helical, worm gears and noncircular gears. Results shown in this study also provide the industry an important software for design, analysis, and manufacturing of various types of gears. A 6-axis CNC hobbing machine can be used to manufacture different types of gears owing to the movement of its axes with multi-degree of freedom. The generation process of gears by applying a CNC hobbing machine is quite complex. Figure 1 presents a schematic drawing of a 6-axis CNC hobbing machine, where axes X, Y and Z are the radial axis, the tangential axis, and the axial axis, respectively; axes A, B and C are the hob swivel axis, the hob spindle axis and the work table axis, respec tively. However, in today's CNC hobbing machines, axes A and Y are for set-up only and rotational ratio between axes B and C is a constant. Some machines allow an interrelationship between axes X and Z; therefore, today's CNC hobbing machines are 3- axis machines"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003564_05698190490500743-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003564_05698190490500743-Figure5-1.png",
+        "caption": "Fig. 5\u2014Face with single-row spiral grooves.",
+        "texts": [
+            "0 \u00b5m, and p3 = 2.02 MPa. That means, with the sealing-oil pressure disturbance, this seal can keep the radius r\u2217 of the interface between oil and gas nearly unchanged by means of adjusting the oil-film thickness and peak pressure. Therefore, this double-row spiral groove seal is very stable under oil-pressure disturbance. Wang, et al. (7) present another kind of noncontacting, zeroleakage face seals with single-row spiral grooves. The face with single-row spiral grooves and two annular dams is shown in Fig. 5. The pressure distribution of oil film over the interface and the axial force balance of the primary ring are shown in Fig. 6. Now the theoretical analyses aimed at Fig. 6 are carried out, in which the D ow nl oa de d by [ U ni ve rs ity o f C al if or ni a Sa nt a C ru z] a t 2 1: 31 1 0 O ct ob er 2 01 4 Fig. 6\u2014Pressure distribution of oil film over the interface and axial force balance of primary ring. assumptions are the same as those for the face seals with doublerow spiral grooves in a splay pattern"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003802_chicc.2006.280612-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003802_chicc.2006.280612-Figure1-1.png",
+        "caption": "Fig. 1 Quarter-car model for active suspension control design. The motion equations of the system are",
+        "texts": [
+            "ey Words: Active suspension, Quarter-car model, LQR, Backstepping suspension analysis and design. The simplified quarter-car model is depicted in Fig. 1. Suspension system is a complex dynamic system. To improve the performance of suspension system is the main way to dissipate the road disturbance and improve the ride and safety. Passive suspension system being used prevalently in traditional cars can only store and receive outside energy but not be able to adapt the variance of the road condition and outside stimulating, so the improvement of the car performance is restricted greatly. Since Dr. Federspiel-labrosse brought forward the idea of active suspension firstly in 1955, a long list of research papers were published in this area"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001423_s1350-4533(99)00095-8-Figure7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001423_s1350-4533(99)00095-8-Figure7-1.png",
+        "caption": "Fig. 7. The model of the common insertion (white ellipse) of the lumbrical (LUM) and radial interosseous (rIOSS) on the EDL hood (gray shell) is illustrated. A portion of the proximal phalanx is omitted for clarity. The instantaneous location of the insertion is approximated as the sum of",
+        "texts": [
+            " Point p \u2192 lat,union gives coordinates of the union of the lateral bands on the terminal extensor slip with respect to coordinate-system-3. Flexion of the distal joint qDIP is assumed to translate this point along the middle phalanx in the direction of x \u2192 3. coordinates of lumbrical origin (p \u2192 LUMo,straight) may be estimated with respect to the metacarpal bone (coordinate-system-0). Flexion of the finger joints {qMCPf, qPIP, qDIP} allows excursion of the tendon as determined previously (Fig. 4). This excursion is assumed to translate the lumbrical origin proximally by (Dp \u2192 LUMo). the EDL (Fig. 7). For simplicity, the kinematics of the extensor hood are initially calculated with respect to the first phalanx, coordinate-system-2. In this frame of reference, it is reasonable to assume the portion of the EDL central slip in contact with the first phalanx does not translate due to flexion or abduction of the MCP joint. When the finger is straight, a point on the extensor hood is given by ( 2p \u2192 hood,straight). Flexion of the PIP and the DIP joints can drag this point distally along the proximal phalanx"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001031_oceans.2003.178583-FigureI-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001031_oceans.2003.178583-FigureI-1.png",
+        "caption": "Fig. I . Foimation configuration",
+        "texts": [
+            " Horizontal following 4. Dive to the source 5. Marking the source Additionally several other discrete states are defined for the maneuver. These are fault condition or malfunction (in one, various vehicles or in the formation control); intermediate formation establishment (necessary to redefine the formation ) and return to survey. This last state corresponds to the return to the survey either after the 1. Survey 50 The state of the formation in three phases of the mission is depicted in the next figure. In the initial Survey state, the ASV executes a \u201csweeping\u201d pattem. The 3 AUVs follow the surface vehicle at a small fixed depth and maintain the vertical projection of the boat at the middle of the triangle formed by them. Upon the trace detection of the phenomenon by one of the A W s , this AUV reduces velocity and changes direction to a perpendicular to its previous movement. If the plume is confirmed the formation distortion introduced by the detecting vehicle is perceived by the others. This change of formation can also be reflected in the increase of acoustic pings since the navigation system adapts itself to the global dynamics (with the previous very steady state movements there is no need for faster update rates)"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002293_an9962101489-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002293_an9962101489-Figure1-1.png",
+        "caption": "Fig. 1 Optical arrangement for measurements with the flow-through cell: D, detector; FC. flow-through cell; MI, mirror; MC, monochromator; SM, sensor membrane consisting of the polymer support and the nitrite sensitive coating; S, sample solution.",
+        "texts": [
+            " Apparatus Fluorescence excitation and emission spectra a s well as response curves of the sensing membranes were measured on an Aminco (Rochester, NY, USA) SPF 500 spectrofluorimeter equipped with a 250 W tungsten halogen lamp as a light source and linked to an HP 98 15A desk calculator (Hewlett-Packard, Avondale, PA, USA) and a red sensitive detector. Response curves were recorded by placing the membranes in a flowthrough cell to form one wall of the cell. Excitation light hit the sensor membrane from outside (after passing the glass wall of the flow cell and the polyester support), and fluorescence was detected at an angle of 55\" relative to the incident light beam (Fig. 1). Buffer solutions and buffered sample solutions were pumped through the cell at a flow rate of I .S ml min-1. When studying the response of the sensing membranes, excitation and emission wavelengths were set to 550 and 590 nm, respectively. The absorption spectra of the sensor membranes were measured on a Shimadzu (Kyoto, Japan) UV-2 10 1 -PC photometer. All experiments were performed at 22 f 2 \"C. The sensing scheme used in this work is based on the use of lipophilic derivatives of rhodamine B which dissolve very well in polymeric matrices because of their high solubility in organic Table 1 Composition of anion seiisor membranes MI-M5 Metnbrane Dye Polymer BPP Plasticizer M1 KBOE PVC 200 mol% NPOE M2 RBOE PVC 100 mol% NPOE M3 RBOE PVC 40inol% NPOE M4 RBOE PVC 40mol% DOS MS KBOE PVC-Co 40tnol% NPOE solvents, plasticizers, and plasticized polymers"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001429_robot.1989.100102-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001429_robot.1989.100102-Figure2-1.png",
+        "caption": "Figure 2. Graphical Simulation Model for the DIGITS System (Version 1).",
+        "texts": [
+            " I11 EXAMPLE MECHANISM In order to demonstrate the significance of the Compact-Dual LP method, in this section, the Original LP, Compact-Primal LP, and Compact-Dual LP methods are applied to solve the force distribution problem of the DIGITS System. A brief description of the DIGITS System will be presented first, followed by the approach taken to obtaining the known components of the equations of the force distribution problem. Simulation results and computation times for each of the three L P methods will be highlighted and compared at the end of this section. A. The DIGITS System As shown in Fig. 2, the DIGITS System (Version 1) has 4 fingers, each with 3 degrees of freedom as is slightly larger than the human hand. All of the joints are revolute with each driven by a brushless DC motor and belt-drive system, which is under development at OSU. This system is targeted for loads of a few pounds. The maximum joint torque limits of each finger are approximately: (32) (33) (34) -0.9 nt-m 5 5 0.9 nt-m, -1.8 nt-m 5 r2 5 1.8 nt-m, -1.8 nt-m 5 r3 5 1.8 nt-m. For simplicity of presentation only two fingers are first used to manipulate a very dense 2 lb"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002581_robot.1996.503837-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002581_robot.1996.503837-Figure1-1.png",
+        "caption": "Figure 1: An experimental planar five-link walking biped.",
+        "texts": [
+            " Kajita and his coworkers [6, 71 built a series of bipedal robots with control algorithms that minimize excursions of the robots\u2019 bodies, but their goal was to simplify the dynamics of the system, rather than create a smooth walk. Blajer and Schiehlen [8] have examined impact-free walking of a complex biped from a theoretical point of view. None of the foregoing studies have aimed a t the the development of smooth walking over uneven ground. 0-7803-2988-4/96 $4.00 0 1996 IEEE 578 2 Experimental hardware We believe that experimental verification of our cont,rol strategies is essential, and consequently, we have constructed a planar bipedal robot to serve as the test bed for our research. Figure 1 shows the machine's basic structure, which consists of a pair of legs joined to a body. Each leg pivots on a rotary hip joint at the body and contains a prismatic lower leg joint which acts to change the leg length. Pneumatic cylinders drive the extension and retraction of the lower legs. We selected pneumatic cylinders for this application because of their favorable force to weight ratio. Unfortunately, continuous control of pneumatic syskms is notoriously difficult (see [9], for example), and we found it necessary to implement a nonlinear observer-based cont,rol scheme to obtain reasonable performance under walking conditions"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000497_a:1008966218715-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000497_a:1008966218715-Figure6-1.png",
+        "caption": "Figure 6. Determination of the local map.",
+        "texts": [
+            " Each obstacle region Mk is included in the present local map, if the following condition is satisfied: |pc \u2212 m\u0304k | < dc + \u03bbd , where pc is the center position of the mobile robot, \u03bbd =  \u03bb\u03041k cos1\u03b8 if 1\u03b8 < tan\u22121 \u03bb\u03042k \u03bb\u03041k \u03bb\u03042k sin1\u03b8 otherwise , and 1\u03b8 = |\u03b8\u0304k \u2212 6 (mk \u2212 pc)|. \u03bbd here represents the span of the obstacle region from m\u0304k along the direction of the vector pc \u2212 m\u0304k and 1\u03b8 represents the orientation difference between the major axis of Mk and the vector pc\u2212m\u0304k . Consequently, if1\u03b8 is zero degree, then the obstacle region is completely aligned with the vector pc\u2212 m\u0304k and \u03bbd becomes equal to \u03bb\u03041k . On the other hand, if 1\u03b8 is 90\u25e6, then \u03bbd becomes equal to \u03bb\u03042k . As shown in Fig. 6, if the above condition is satisfied, then all or part of the obstacles included in Mk may be located inside the active circle. Then, each obstacle region in the local map is put to the test in Step 3 to determine which of Mk\u2019s are associated with the present clustered regions. Whereas the clustered regions are newly defined every sampling time, the obstacle regions are created, updated or deleted depending on whether each obstacle region is associated with any of the clustered regions. Consequently, Step 3 determines which obstacle regions are associated with the current clustered regions and update their parameters accordingly"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000895_(sici)1097-4563(199603)13:3<177::aid-rob5>3.0.co;2-p-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000895_(sici)1097-4563(199603)13:3<177::aid-rob5>3.0.co;2-p-Figure1-1.png",
+        "caption": "Figure 1. Configuration of a 4-link planar mechanism in singular posture (dead point), in this case dI2 = 0.",
+        "texts": [
+            " In the example of a 3-DOF planar RRR manipulator, there exist three virtual 2- DOF manipulators. The determinates of each virtual 2-DOF manipulator Jacobian matrix are given by where For 3-DOF manipulator, where the manipulator end-effector position is given, 1-DOF of redundancy will change arm configuration through self-motion (homogeneous part of solution), just as with a 1-DOF 4-link planar mechanism. For a 4-link planar mechanism there exists a singular posture depending upon each link length. The singular posture, called Dead point, occurs at the arm configuration shown in Figure 1. In the case of dead point of the arm configuration, one of the dI2, d23, d,, must be zero. The 1-DOF of redundancy in the 3-DOF manipulator is lost in this case, thus the minimization of joint torques cannot be performed through self-motion, and only the manipulator end-effector demand will be guaranteed. Velocity-minimization can be executed even in this singular posture to guarantee the manipulator end-effector demand. Thus, in the case of no extra DOF in the redundant manipulator, the weighting 300 $ 200 100 0 - I \u2018 0 "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003893_0301-679x(83)90004-x-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003893_0301-679x(83)90004-x-Figure3-1.png",
+        "caption": "Fig 3 Testing set-up for (a) fiat and (b) spherical laminates. 1-rollers; 2-cage; 3-hardened steel plate; 4-spherical laminate; 5-double-convex adapter; 6-concave supporting plates",
+        "texts": [
+            " Standard extensometer amplifiers were used with the testing machines to give resolutions of 0.25/am actual displacement per mm on graph paper. Signals from two transducers (Fig 2Co)) were averaged to reduce the adverse influence of machining errors and of the asymmetry of motion of the left and right driving screws of the testing machines. The shear stiffness of the flat samples were measured under variable compression. To alleviate friction effects, a standard set of rollers in a cage and hardened and ground end plates (Fig 3(a)) were used to apply compression force Pz. In measuring shear ka and torsional k~/stiffness of the spherical samples, two identical samples with intermediate solid double-convex lens-shaped block were used for a similar purpose (Fig 3(b)). Compression load on the spherical samples was applied through solid concave lens-shaped blocks. When the double-sample set was used, as in Fig 3, the measured value of compression stiffness was kz]2, and of shear and torsional stiffness, 2k= and 2k7, respectively. Experimental results Compression stiffness Compression stiffness versus specific compression load Pz = Pz]A, where A is the surface area of the sample, is shown in Fig 4 in a double4ogarithmic scale. Compression stiffness is expressed in terms of differential (local) = Hardness was measured on standard cylindrical samples (2.54 cm diameter, 1.27cm high) made from a given rubber"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003927_1.1828069-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003927_1.1828069-Figure1-1.png",
+        "caption": "Fig. 1 Map of model rough ball surface measured with an optical profiler",
+        "texts": [
+            " In the SLIM method a similar disk was used, but with a much thinner silica layer, of thickness 130 nm. For the smooth surface tests, two types of ball were studied. The majority of tests employed highly polished AISI 52100 steel ball, with root mean square roughness, Rq of 12 nm, but a smooth steel ball coated with chromium was also studied, having similar roughness. The thickness of the chromium layer was 1\u20132 mm. Model rough surfaces were prepared by sputtering a series of parallel, chromium ridges on the surface of a smooth steel ball. The ridges, shown in Fig. 1, were of approximately sinusoidal shape, about 165 nm high, had a wavelength of 60 mm, and were oriented transverse to the rolling direction. The Rq parameter for this artificial roughness was 71 nm. For the isotropic rough surface tests, a rough AISI 52100 steel ball, manufactured by early withdrawal from the ball-finishing process, was used, with roughness parameter Rq579 nm. A 3D plot of the surface of the rough steel ball obtained with an interference microscope is shown in Fig. 2. 2.2 Friction Measurement"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001925_84.388115-Figure9-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001925_84.388115-Figure9-1.png",
+        "caption": "Fig. 9. one-half hour of operation. Photograph of the rotating shaft near the bearing after approximately",
+        "texts": [
+            " The vibration resulted form the asymmetry of the stator and the clearance between the wheel shaft and the chassis and it generated an elliptical movement. Fig. 8 shows the track of the wheel contact point that was measured by a noncontact, 2-dimensional displacement meter. The short diameter (5 pm) of the elliptical track was equivalent to the bearing clearance. This elliptical movement moved the microcar in one direction. IV. DISCUSSION The car ran at a maximum speed of 100 \"/sec, which does not seem fast, but it may be too fast for a 1/1OOOth scale car. Therefore, wear of the rotating parts could be quite severe. Fig. 9 shows the condition of the rotating shaft near the bearing after approximately one-half hour of operation. The contact point of the shaft is damaged because of the wear of the bearing. Lubrication, bearings, and other means of reducing the friction are difficult to apply to micro-systems. To study the effect of lubricant for micro-rotating wheel bearings, an experiment was conducted using a high speed video camera. Fig. 10 shows the experimental setup. Lubricant was supplied to the bearing while the wheels were rotating"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003067_bf00126072-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003067_bf00126072-Figure1-1.png",
+        "caption": "Fig. 1. Start Circular path with vertical forces.",
+        "texts": [
+            " It should be pointed out that any torques and forces to be realized at the gripper modify only the Ci (s)-terms, which for free trajectories contain only gravitational forces and, for force or torque controlled trajectories, contain additional contact forces or torques. ~1 76 I ~r Q 0 ~ (D 0 C ~ ,0 0 .2 0 .4 0 .6 0 .8 1 ,0 ~ .2 ;, 4 Sq ua re o f pa th v el oc it y (~ 2) ~0 0 .2 0~ 4 0~ 6 0 .8 l. O 1 ,~ 1 .4 0 .2 0 .4 0 .6 0 .8 1 .0 1 .2 1 .4 -n i! i 2 9 > r, > > Z Z The path planning optimization as presented above has been applied to various cases with forces at the gripper. Figure 1 gives an example for a circular path parallel to the y - z plane, being tracked by a manipulator with five revolute joints. Figure 2 shows the results of the time-optimization applying the method of [9]. The zero force case (F = 0) includes three critical points (saddle points). The maximum velocity curve as well as the time optimal curve are symmetrical with respect to the s = 0.5 point. Applying a negative force, which means pushing down the gripper (Figure 1), results in the manipulator starting very slowly due to the load of the additional force ( - F). Only one critical point remains, and the deceleration is performed as slowly as the acceleration. On the other hand, lifting the gripper with ( + F ) (Figure 1) allows for a large acceleration and deceleration because a positive force aids a steep slope at the start of the trajectory by partly compensating the gravity forces. But such a force in the upward direction brings down the velocity at the highest path point for s = 0.5. Figure 3 gives an illustration of the joint torques necessary to realize the timeoptimal trajectories of Figure 2. Each block of six diagrams contains the torques of the five joints in the first five diagrams and the time-minimum solution of Figure 2 in the sixth diagram"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003926_1.338581-Figure30-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003926_1.338581-Figure30-1.png",
+        "caption": "FIGo 30 First-order transition curveso",
+        "texts": [],
+        "surrounding_texts": [
+            "Numerical Methods Dan Bloomberg, Chairperson\nThe Preisach model and hysteretic energy losses I. D. Mayergoyz and G. Friedman Electrical Engineering Department and Institute for Advanced Computer Studies. University of Maryland. College Park, Maryland 20742\nUsing Preisach's model, general expressions for hysteretic energy losses are derived. These expressions are valid for arbitrary (not necessarily periodic) variations of magnetic field. Moreover, these expressions are given in terms of Preisach's function as well as in terms of experimentally measured \"first-order transition curves.\" A formula is also found which relates the hysteretic energy losses for arbitrary field variations to the losses ocurring for certain periodic variations of magnetic field. This formula allows for easy measurement of hysteretic losses occurring for arbitrary field variations.\nINTRODUCTION\nA hysteresis phenomenon is associated with some ener gy dissipation which is often referred to as hysteretic energy losses. The problem of determining hysteretic energy losses is a classical one. The solution to this problem has long been known for the case of periodic (cyclic) variations of magnet ic field. In that case, the hysteretic energy losses are equal to the area enclosed by a hysteresis loop resulting from a peri odic field variation. However, energy dissipation is a contin uous process, and it occurs for arbitrary (not necessarily periodic) variations of magnetic field. The problem of com puting hysteretic energy losses for the above general case has remained unsolved. A solution to this problem would be of both theoretical and practical importance. From the theo retical point of view, the solution of the above problem will allow for the calculation of internal entropy production, I which is a key point in the development of irreversible ther modynamics of hysteretic media. 2 It will also lead to the expression for the energy stored in the magnetic field which eventually may help to find electromagnetic forces in hyster etic media. 3 From the practical viewpoint, the solution of the problem may bring new experimental techniques for the measurement of hysteretic energy losses occurring for arbi trary field variations.\nIt should not be surprising that the solution of the prob lem has been known only for the case of periodic variations of magnetic field. The reason is that for cyclic field variations the expression for energy losses is easily derived using only the energy conservation principle; no knowledge of actual hysteresis mechanisms is required. The situation is much more complicated when an arbitrary variation of magnetic field is considered. Here, the energy conservation principle alone is not sufficient and an adequate model of hysteresis should be employed in order to arrive at the solution of the problem. It turns out that Preisach's hysteresis model is very well suited for this purpose.\nIn this paper, Preisach's model is used to derive general expressions for hysteretic energy losses. These expressions are given in terms ofPreisach's function as well as in terms of experimentally measured \"first-order transition curves.\"\nFurthermore, a formula is found which relates the hysteretic energy losses occurring for an arbitrary field variation to the losses occurring for certain periodic field variations. This formul.a leads to a simple technique for the measurements of hysteretic losses occurring for arbitrary variations of mag netic field.\nIt has been emphasized before4-7 that Preisach's model is purely phenomenological and can be used for the math ematical description of hysteresis of any physical nature. For this reason, the expressions for hysteretic energy losses de rived in this paper are quite general and valid regardless of the physical nature of hysteresis. The only requirement is that such hysteresis can be described by Preisach's model.\nEXPRESSIONS FOR HYSTERETIC ENERGY LOSSES\nTo make the exposition more or less self-contained, the main facts concerning Preisach's model will be briefly re viewed. The detailed information on this subject can be found in Refs. 4--8. For the sake of generality, we shall de scribe Preisach's model in a purely mathematical form. In this form, any hysteresis nonlinearity can be characterized by an input u(t) and an output J(t). In magnetic applica tions u (t) is the magnetic field, while f( t) is the magnetiza tion.\nConsider an infinite set of operators r a{3 which are rep resented by rectangular loops on the input-output plane (Fig. 1). Along with these operators, consider a weight fune-\n3910 J. Appl. Phys. 61 (8),15 April 1987 0021-8979/87/083910-03$02.40 \u00ae 1987 American Institute of Physics 3910 [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:\n128.138.73.68 On: Tue, 23 Dec 2014 09:06:37",
+            "tiontt (a,p) which is often called Preisach's function. Then, Preisach's model is given by\nf(t) = J J fl (a,/J)r afJ u(t)dad{J. (1)\na>{3\nFor hysteresis nonlinearities with closed major loops the functiontt{a,p) has a finite support within some triangular area T on the a-{3 plane.\nThere is a one-to-one correspondence between opera tors YaP and points (a,/J) on the half-plane a>p. Using this fact, it can be found that, at any instant oHime, the triangle T is subdivided into two sets (Fig. 2): S + (t) and S - (t) con ~isting of points (a,/3) for which Yapu(t) = 1 and YaP u(t) = - 1, respectively. The interface L(t) between S + (I) andS - (t) isa staircase line the vertices of which have a and {3 coordinates coinciding with local maxima and mini ma of u (t) at previous instants of time. The final (attached to the line a = f3) link of L(t) is horizontal and moves up when the input increases, and it is vertical and moves from right to left when the input decreases. For any given hystere sis nonlinearity, Preisach's function tt(a,{3) can be found from the set of \"first-order transition (reversal) curves\" at tached to the limiting ascending branch (Fig. 3). The appro priate formulas are\nF(a,/J) = fa -laP' (2)\n( ,{3) - 1 a2F(a,fJ) fla ---\n2 8a8p (3)\nIt turns out (see Refs. 5 and 8) that the integral in Eq. (1) can be directly expressed in terms of F(a,/J) as follows:\n1 n\nlet) = -2F (ao,/3o) + k~l [F(ak,Pk_d - Fad 3k)]'\n(4)\nwhere {ak} and {Pk} are decreasing and increasing se quences of a and /3 coordinates of interface vertices, respec tively, and n is the number of horizontal links of L (t) .\nIt has been proved in Ref. 6 that two properties consti tute necessary and sufficient conditions for the representa tion of a hysteresis nonlinearity by Preisach's model. These properties are the \"wiping-out property\" and the \"con gruency property.\" For the discussion of those properties see Refs. 6 and 7. In the sequel, we shall assume that these prop erties are satisfied, and Preisach's model is valid.\nNow we are equipped to proceed to the derivation of expressions for hysteretic energy losses. We begin with the case when a hysteresis nonlinearity is represented by a rec-\n3911 Jo AppL Phys., Vol. 61. Noo 6, j 5 April 1967\ntangular loop shown in Fig. 1. If a periodic variation of input is such that the whole loop is traced, then the hysteretic energy loss for one cycle equals the area 2(a - [3), enclosed by the loop. It is dear that the horizontal links of the loop are fully reversible and, for this reason, no energy losses occur when these links are traced. Thus, it can be concluded that only \"switching-up\" and \"switching-down\" result in energy losses. It is apparent (on the physical grounds) that there is symmetry between these two \"switchings\" and, consequent ly, the same energy losses (equal to a - {3) occur for each of these switchings. The product f.i (a,/3) Ya/3 can be construed as a rectangular loop with output values equal to \u00b1 /-L (a,/3). For this reason, switchings up or down of such a loop win result in energy loss p(a,{3)(a - /3). According to Prei sach's model (1), any input variation is associated with swi tchings up or down of some rectangular loop f.i (a ,/3) Yap. Thus, the energy loss occurring for an arbitrary input vari ation is naturally equal to the sum of energy losses resulting from the switchings of rectangular loops during this input variation, Since we are dealing with a continuous ensemble of rectangular loops, the above summation should be re placed by integration. Thus, if n denotes the region of points (a,p) for which the corresponding rectangular loops were switched during some input variation, then the hysteretic energy loss Q for this input variation is given by\nQ = I f j.l(a,f3)(a - {3) da d[3. (5)\nII\nA typical shape of the region n is shown in Fig. 4. It is clear from this figure that n can be always subdivided into a trian gle and some trapezoids, The trapezoids, in turn, can be rep resented as differences of triangles. Thus, if the integral (5) can be evaluated for any triangular region, then this integral can be easily determined for any possible shape of fto It makes sense to compute the values of integral (5) over var-\nI. 00 Mayergoyz and G. Friedman 3911 [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:\n128.138.73.68 On: Tue, 23 Dec 2014 09:06:37",
+            "ious triangles. Using these values, hysteresis losses can be easily found for any variation ofinput. In the case when n is a triangle, the integral (5) can be easily evaluated in terms of F(a,{:J) , which is related to the \"first~order transition curves\" by formula (2). The derivation proceeds as follows: It can be verified that\n(j2 --[F(a,{:J) (a - {J) ] (ja8p\n= a 2F(a,p) (a _ (3) + aF(a,{:J) oa a/3 ap\n_aF~(:.....-a.:!....J3.:.-) . (6) da\nUsing Eqs. (3) and (6), we find\n2jt(a,/3) (a _ (3) = 8F(a.{3) _ aF(a,/J) 8P oa\n(j2 - -- [F(a.{3)(a - {3) ]. (7)\naa 8{3\nNow, consider a triangle T(u+,u_) swept (see Fig. 5) dur~ ing the input increase from u _ to u +. According to Eq. (5), such input variation is associated with the losses\nQ(IL,U+) = f f p,(a,/3)(a - (3)da d/3 T(,,+,u ,.)\n= i~+ ([ jt(a,{J)(a - /3) d/3 )da\n= iU ,+ (Lu + p(a,/3)(a -fJ)da )d/3. (8)\nSubstituting Eq. (7) into Eq. (8), performing the integra tion and taking into account that F(a,a) = 0, after simple transformations we find 1 rru , lU' Q(u_,u+) = - 2\" Uu_ F(a,u_ )da + \"_ F(u+.{3)d{3\n- (u+ - u_ )F(U+,U_\u00bb) . (9)\nIt can be shown that the derived expressions for hysteretic energy losses are consistent with the classical result: the hys teretic energy losses for any cyclic input variation equal the area enclosed by the loop resulting from the cyclic input\n3912 J. Appl. Phys., Vol. 61, No.8, 15 April 1987\nvariation. The proof is omitted. Consider a cyclic variation of input from u _ to u + and back to u _. During the monotonic increase of input from u_ to u+, the final horizontal link of L(t) sweeps the triangle T( u + ,u ._ ). On the other hand, during the monotonic de crease of input from u + to u _, the final vertical link of L (t) sweeps the same triangle. Thus, it can be concluded that, for any loop, the hysteretic losses occurring along ascending and descending branches are the same:\n(10)\nNext, we shall use expression (10) to find the formula which relates hysteretic energy loss occurring for an arbi trary monotonic input variation to certain cyclic hysteretic losses. Suppose that the input u(t) increases monotonically from some minimum value u_ and reaches successively some values uland U2, (u2>u I). We are concerned with the hysteretic loss Q( u I,U2 ) occurring during the input variation between U I and u2\u2022 For the above input variation, we have: n = T(u2,u_) - T(ul,u_). Consequently,\nQ(ul,UZ) = Q(U_,U2) - Q(u_,u 1). (11)\nUsing Eq. (10), losses Q(u_,u 2 ) and Q(u_,u 1 ) can be ex~ pressed in terms ofcycliclosses Q(u_,u l ) = ~Q(U_,Ul) and Q(U_,U2) = ~Q(U_,U2)' where Q(u_,u j ) and Q(u_,u2) are cyclic losses for periodic input variations between u_ and U 1, u_ and U z, respectively. Using this fact, from Eq. (11) we find\n(12)\nThe last formula can be useful from the experimental point of view because it is much easier to measure cyclic losses than losses occurring for nonperiodic input variations.\nACKNOWLEDGMENTS\nThe reported research was motivated by the question raised by Professor H. A. Haus during the talk given by the first author at MIT. This research is supported by the U.S. Department of Energy, Engineering Research Program (contract no. DE-AS05-84EH13145).\n11. Prigogine, Introduction to Thermodynamics of Irreversible Processes, 2nd edition (Wiley, New York, 1961). 2J. S. Cory and J. L. McNicols, J. Appl. Phys. 58, 3282 (1985). 'P. Penfield, Jr. and H. A. Haus, Electrodynamics of Moving Media (MIT, Cambridge, MA, 1967). 4M. Krasnoselskii and A. Pokrovskii, Systems with Hysteresis (Nauka, Moskow, 1983). 51. D. Mayergoyz, J. Appl. Phys. 57, 3903 (1985). \"T. Doong and I. D. Mayergoyz, IEEE Trans. Magn. MAG-21, 1853 (1985). 71. D. Mayergoyz, Phys. Rev. Lett. 56,1518 (1986). 81. D. Mayergoyz, IEEE Trans. Magn. MAG-22, 603 (1986). 9J. A. Barker, D. E. Schreiber, B. G. Huth, and D. H. Everett, Proc. R. Soc. London Ser. A 386,251 (1983).\nI. D. Mayergoyz and G. Friedman 3912 [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:\n128.138.73.68 On: Tue, 23 Dec 2014 09:06:37"
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0003019_ajassp.2005.626.632-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003019_ajassp.2005.626.632-Figure5-1.png",
+        "caption": "Fig. 5: Experimental Device Components, where; (1)",
+        "texts": [
+            " 4), is the resultant of vertical components of the elementary forces due to pressure, by integrating the normal force it gives: n max maxF p cos dp p r cos d 2p r sin \u03b3 \u03b3 \u2212\u03b3 \u2212\u03b3 = \u03a6 = \u03a6 \u03a6 = \u03b3 (3) Where, db rd / cos= \u03c6 \u03c6 and - is the half of the central angle of the deformed zone. Also from the same figure, we can obtain: 2 3 4 2 (D d )b sin 1 2r 16r \u2212 \u03b3 = = \u2212 (4) The friction force due to ring deformation at assembly is: Ff=\u00b5 D3Fn (5) Replacing equations (2,3,and 4) in equation number (5), we get the developed expression of the friction force: 2 3 4 3 4 3 2 D d (D d ) Ff 2 D rE 1 1 4r 16r \u2212 \u2212 = \u03c0 \u2212 \u2212 (6) The validity of expression 6 ( 2 3 4 3 4 3 2 D d (D d ) Ff 2 D rE 1 1 4r 16r \u2212 \u2212 = \u03c0 \u2212 \u2212 ) was tested with an experimental device (Fig. 5), which was used for obtaining the experimental results. The Ram has five different sizes of sockets or grooves to increase the possibility of testing different number of O-ring sizes (Fig. 5). Each groove is designed for a specific diameter, The ram and cylinder geometry is characterized by the values of the diameters, both diameters are clearly shown in Fig. 3 and 4, in our case the cylinder diameter D3 = 28.03 mm, the inside ram diameter d4 having five different sizes, in our case (d4 = 21.41, 21.45, 21.59, 21.74 and 22.10 mm), all of these sizes were tested and the obtained results are indicated in Fig. 7 (in absence of the pressure), in which each size has its proper value of friction, Fig"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003587_1.2125971-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003587_1.2125971-Figure1-1.png",
+        "caption": "Fig. 1 The TriVariant robot",
+        "texts": [
+            " As a result, all configurations can be found by solving the end polynomial equation 1\u20137 . The complexity of the polynomial approach depends upon the geometry of the object and proper choice of elimination techniques. The numerical approach can be used to find the solutions close to the initial estimate using root search algorithms or optimization techniques 8 . This paper deals with the forward position analysis of the 3-DOF parallel mechanism module which forms the main body of a newly invented hybrid robot named TriVariant Fig. 1 9 . The research interests will be focused on finding the number of its forward position solutions in comparison with the corresponding results of the Tricept 10\u201312 . As shown in Fig. 1, the module consists of a base and a mobile platform connected by three kinematic chains limbs . Two are identical UPS limbs and the other is a UP limb whose output link is fixed with the mobile platform. Here, U, P and S represent the universal, prismatic, and spherical joints respectively, and P denotes that the corresponding joint is active. The TriVariant can be considered as a simplified version of the Tricept robot, achieved by integrating one of the three active limbs into the passive one while keeping the required type and degrees of freedom"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002460_63.85913-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002460_63.85913-Figure5-1.png",
+        "caption": "Fig. 5. Current space vector\\ and control error stripe for phase R",
+        "texts": [
+            " Therefore one can only give a continuous power density spectrum for them which could be obtained by a Fourier transform of the auto correlation function. However, in this paper the analysis in the frequency domain is not persued further. Besides the mathematical advantages of the space vector representation a very clear description of the system behavior is made possible. E.g., the deadbands around the phase current reference values are transformed into stripes lying perpendicular to the respective phase axis (see Fig. 5 , there shown for phase R). The common area of these stripes (i.e., the control errors of all three phases are smaller than the deadband width) results in a hexagon being characteristic for three-phase ON-OFF controllers (see Figs. 7, 17). The tip of the reference value space vector lies in the center of the hexagon. Basically one could define arbitrary areas instead of the hexagon if the control concept is based on a space vector representation of the control error (e.g. , such as in [2]). Contrary to such areas only the hexagon guarantees the full use of the allowable phase current control error"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003979_s10035-005-0210-5-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003979_s10035-005-0210-5-Figure2-1.png",
+        "caption": "Fig. 2 Schematic view of a light ray consisting of numerous refractions propagating through the granular medium",
+        "texts": [
+            " The autocorrelation function is then given by [13,14]: gE(t1, t2) = \u221e\u2211 n=1 P(n) < exp(j ( n(t2) \u2212 n(t1))) > (16) where P(n) is the fraction of the total scattered intensity in the light paths involving n scattering events. This quantity is related to the geometry of the experiment. The quantity n(t2) \u2212 n(t1) is the phase difference of the scattered electric field between the time t1 and t2, associated with a given path involving n scattering events. The average < ... > is calculated over all the paths involving n scattering events. Figure 2 is a simplified geometrical view of the random walk of a photon across the different beads, composed of travels across beads, intersticial media, and refraction or reflection.Any displacement of matter will contribute to a variation of the optical length between t1 and t2. This could include not only the displacement of the centers r\u03bd of the spheres, but also rotations of nonspherical beads or deformations of the beads. For the sake of simplicity, we will ignore such effects in the following discussions, although they are not expected to be systematically negligible"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001376_s0967-0661(99)00084-2-Figure7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001376_s0967-0661(99)00084-2-Figure7-1.png",
+        "caption": "Fig. 7. The scheme of the developed gyrodine with 5-DOF electromagnetically suspensed rotor, the #exible gyroshell's preloaded ball bearings, a gear stepping drive and an electromagnetic damper on the gyrodine precession axis.",
+        "texts": [
+            " The mathematical model of manoeuvring spacecraft takes into account: f the controlled orbital motion of the spacecraft mass center; f the spatial angular motion of the spacecraft frame as a carrying rigid body; f movements of #exible solar array panels (P 1 , P 2 ) and receiving}transmitting antennas (A 1 , A 2 ), see Fig. 2, about the spacecraft body by means of 2-DOF suspension with the gear stepping drives; f movements of the moment dyrocomplex in the form of the `2-SPEEDa-type minimum-excessive scheme, see Fig. 5; moreover, the model of each gyrodine describes } the nonlinear dynamics of the control laws for current loops in the gyrorotor's 5-DOF electromagnetic suspension, see Fig. 7; } the proper gyrorotor rotation dynamics with regard to its static and dynamic unbalance; } the #exibility of gyroshell's preloaded ball bearings; } the #exibility, dead band and kinematic defects in the gear; } the dynamics of a stepping motor with a breaking up the step and an electromagnetic damper on the gyrodine precession axis that takes into account the dry friction torque; f the moment gyrocomplex \"xation on the spacecraft body by means of a vibration-absorbing frame; f external torques * aerodynamic, gravitational and magnetic; f the #exible-viscous \"xation of the optical telescope construction (in Ritchey}Chretien's optical scheme) on the spacecraft body, by means of a vibration-absorbing frame P, see Fig",
+            " Some results, obtained by the software system DYNAMICS, on the vibrational analysis of the image motion dp z (t) onto the light detector Pi, while being sub- jected to the rotation frequency of all four statically unbalanced gyrodine's rotors in ball bearings and without a vibro-absorbing frame for the moment gyrocomplex \"xation on the body of the spacecraft, are given in Fig. 9. The vibration amplitude on velocity dQ p z of this image at the gyrorotor's nominal rotation frequency is equal to &0.4 arcsec/s. The use of the gyrorotor's 5-DOF electromagnetic suspension (see Fig. 7) in each gyrodine and the placement of the moment gyrocomplex on the spacecraft body by means of a vibro-absorbing frame made it possible for a vibration amplitude of&0.005 arcsec/s to be attained at this rotation frequency for all gyrorotors. Let the spacecraft's spatial rotation manoeuver in an inertial reference frame be de\"ned by the vector of Euler}Krylov's angles a(t)\"Ma i (t)N\"Ma x (t), a y (t), a z (t)N in sequence M3-1-2N, in addition to the quaternion K(t). The concrete problems of the precise control of the spacecraft's spatial rotation manoeuver and control of the process of the opto-electronic observation are formulated as follows: f to transfer the attitude control system's state vector precisely along a program from the position ai\"a(t i ) (a quaternion Ki), xi and bi, which is given at initial time t i \"0: ai\"M"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003895_j.1749-6632.1985.tb18426.x-Figure8-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003895_j.1749-6632.1985.tb18426.x-Figure8-1.png",
+        "caption": "FIGURE 8. Anticipated mechanism of oxaloacetate-CO, exchange by coupling to the transport of Na' ions over the membrane.",
+        "texts": [
+            " One would expect, therefore, that the decarboxylases are reversible systems, as well, if the same principles of vectorial energy coupling were valid. Decarboxylation reactions are completely irreversible when catalyzed by the soluble en~ymes.~'.]' These systems, however, do not imitate in full the physiological situation where the decarboxylation is coupled to the transport. Since this coupling could be essential, we have studied the reversal of decarboxylation reactions with the decarboxylases reconstituted into proteoliposomes (unpublished results). A schematic view of this kind of system is shown in FIGURE 8. When oxaloacetate is decarboxylated to pyruvate and CO,, a Na' ion gradient is developed over the membrane which in the reverse reaction could drive the carboxylation of pyruvate to oxaloacetate. The carboxylation was demonstrated by the incorporation of I4CO, into oxaloacetate. This incorporation was strictly dependent upon the Na+ gradient since no [\"C] oxaloacetate was formed in the presence of the Na' ionophore monensin. Similar observations have also been made with methylmalonyl-CoA decarboxylase containing proteoliposomes which catalyzed the isotopic exchange between ''C0, and malonyl-CoA by mediation of a Na' gradient"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003151_j.triboint.2004.10.004-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003151_j.triboint.2004.10.004-Figure2-1.png",
+        "caption": "Fig. 2. Schematic of a journal bearing.",
+        "texts": [
+            " Consequently, the problem mentioned above can be summarized as the following optimization problem in discrete: Min: J\u00f0p\u00de Z 1 2 fpg\u00bdK fpgK fpgT\u00f0\u00bdB \u00f0fuagC fubg\u00de C \u00bdF flgK \u00bdW f _hgK fqg\u00deK fmgTfpg (11a) s:t: \u00bdC fpgK \u00bdM flgC fdgK fng Z 0 (11b) flgTfng Z 0; flgR0; fngR0 (11c) fmgTfpg Z 0; fpgR0; fmgR0 (11d) where {m} is the Lagrangian multiplier vector. Letting dJ(p)/dpZ0 in Eq. (11a) and making use of Eqs. (11b) and (11d), the following complementary problem is obtained: \u00bdK fpgK \u00f0\u00bdB \u00f0fuagC fubg\u00deC \u00bdF flgK \u00bdW f _hg K fqg\u00deK fmg Z 0 (12a) \u00bdC fpgK \u00bdM flgC fdgK fng Z 0 (12b) flg T fng Z 0; flgR0; fngR0 (12c) fmgTfpg Z 0; fpgR0; fmgR0 (12d) The problem described by Eqs. (12a) and (12d) can be solved by many methods. In the present paper, the Lemke method is used. A journal bearing rotating with velocity u is shown in Fig. 2, where qZx/R, cZR0KRi/R0ZR., 3Ze/c. The unit length load support in the x and y directions are: wy ZK \u00f0qout 0 pR cos w dw (13a) wx Z \u00f0qout 0 pR sin w dw (13b) The total film load support is: w Z ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi w2 x Cw2 y q (14) and the load support angle is: f Z tanK1 wx wy (15) . (a) T0aZT0bZ6; (b) T0aZT0bZ5; (c) T0aZT0bZ2; (d) T0aZT0bZ0.5; (e) In the present paper, we use the dimensionless parameters: PZpc2/(huR2), HZh/c, T0aZt0ac/(huR), TLaZ tLac/(huR), TaZtac/(huR), UaZua/U, KaZkaR/c, L\u00f0i\u00de a Zl\u00f0i\u00dea =U \u00f0iZ1; 2; aZa; b\u00de, TZtU/R, QZqs/(cU), where UZuaCub"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000595_1.2828771-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000595_1.2828771-Figure5-1.png",
+        "caption": "Fig. 5 Heiipoid gears' tooth surface",
+        "texts": [
+            " In equation (39), parameter p is the screw parameters of the worm. Parameters u determines the location of current point A (or A') on the generating line; where u = \\MA\\ (or M = | M ' A ' | for the generating line II) as shown in Fig. 4. By applying the general gear mathematical model developed here, the Helipoid gears' tooth surface can be specified. By substituting equations ( 3 7 ) - (40) into Eqs. ( 4 ) - ( 6 ) and Eqs. (28) and (29), the tooth surfaces of the Helipoid gear are obtained and shown in Fig. 5. Conclusion Hobbing machines are widely used in industry for manufac turing different types of gears. Developing of 6-axis CNC hob bing machines makes the manufacturing of gears more efficient and flexible. Besides, it allows for novel type of gears to be developed. In this paper, we have proposed a general gear math ematical model based on the cutting mechanism, geometry of worm-type hob cutter and the theory of gearing. The developed general gear mathematical model can be applied not only to the gears manufactured by the conventional hobbing machines, but also to the noncircular gears and new type of gears with new manufacturing processes"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002864_s0924-0136(03)00811-2-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002864_s0924-0136(03)00811-2-Figure5-1.png",
+        "caption": "Fig. 5. CAD models (1) and metallic parts (2).",
+        "texts": [
+            " The technical curve of the process is shown in Fig. 4. The air in the mould is removed with the counter-pressure reduction (A\u2013C), then the pressure raised in the lower chamber for mould filling (C\u2013D). After mould filling, it is necessary to have a holding pressure period (E\u2013F) to enhance the casting solidification under the pressure and to obtain highly sound metallic castings. The alloy for the moulding shell casting was Al-alloy (6\u20138% Si, 0.45% Mg, 0.21% Fe). After pouring and cleaning, the desired metallic parts were obtained. Fig. 5 shows the CAD model and the metallic parts manufactured using this process. Investigation and control of accuracy were necessary in the process of rapid manufacturing of metallic parts. The main errors of parts included error from CAD model to SLS prototype and the error from the SLS prototype to metallic parts. The sintering process of the SLS polymer prototype, which included developing CAD model and sintering polymer powder, was one of the main sources of errors. Data of computer-aided slicing of the CAD model and sintering software system caused some error between the CAD model and SLS prototype"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003153_146441905x63322-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003153_146441905x63322-Figure1-1.png",
+        "caption": "Fig. 1 Side view of a gantry crane",
+        "texts": [
+            "n this article, the development of a gantry crane operator-training simulator, including all the earlier mentioned components, is presented. The aim of this article is to present an example of methods used in the development of the separate areas of a training simulator. Keywords: gantry crane, real-time simulation, user training, motion platform, dynamic modelling Gantry cranes are used in a harbour environment to move containers between the pier and the ships. The crane (Fig. 1) consists of three main parts that move in relation to the pier and each other: the gantry moves along the rails in the direction of the pier and the trolley moves along the rails attached to the gantry perpendicular to the pier. The spreader, used to grab the containers, is attached to the trolley via cables and carries out the hoisting movement by winding and unwinding the cables. Traditionally, gantry crane operators are trained while operating actual cranes with real cargo in harbours. This might cause dangerous situations, decrease work efficiency, and even become very expensive if mistakes occur"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002315_iros.1996.570801-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002315_iros.1996.570801-Figure3-1.png",
+        "caption": "Figure 3. Modeling of the wheeled inverted pendulum.",
+        "texts": [
+            " It also has a rate gyroscope in the upper part of the body and a rotary encoder on the motor axis as sensors. The concept of cooperative transportation by Proc. TROS 96 0-7803-3213-X/96/ $5.00 0 1996 IEEE Figuye 1. The st icture of the wheeled inverted pendulum. move - Wheeled inverted pendulum two wheeled inverted pendulums is presented in Figure 2. In Figure 2, each inverted pendulum exerts a force on the object and, from the opposite point of view, it sustains the same magnitude of an external force. So' we consider a model of the wheeled inverted pendulum which is subjected to an external force (Figure 3). We assume that the external force is applied on the body of the wheeled inverted pendulum at the axle height horizontally for simplicity. The equations of motion of this model are as follows. 3. Control method -9, - 9 2 (32 -E- X = We assume 8, and e, are so small that we can approximate el2 = 0, sin 8, = e,, and cos 8, = 1, and linearize Equations (1) and ( 2 ) about the point of equilibrium. Assuming also that the dynamics of the applied external force is such that - 0 0 8 , , A = a, a2 - 0 we obtain the state equation and the output equation of the system as follows"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure3.6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure3.6-1.png",
+        "caption": "Figure 3.6. Finite rotation of an antenna panel.",
+        "texts": [
+            " Euler's theorem has shown that the components of the rotation tensor, hence also those of the rotator, may be found by construction of the basis transformation matrix A in (3.123b ). Thus, the angle and the axis of the equivalent Euler rotation may be obtained from (3.89) and (3.90) when the initial and final orientations of the body reference frame are known. This will be illustrated next. Example 3.9. A certain mechanism is to be designed to rotate an antenna panel of a spacecraft about a point 0 so that the side facing the i 1 direction in the initial configuration ultimately must face the initial i 3 direc tion in the terminal configuration shown in Fig. 3.6. Determine the equivalent Euler rotation required for the design. Solution. The spatial frame <p = { 0; ij} is chosen to coincide with the body frame q/ = { 0; i~} in its initial orientation. The orientation of the body frame in the terminal configuration of the panel is shown in Fig. 3.6. The diagram is used with (3.123b) to construct the rotation matrix 0 1 J -1 0 . 0 0 (3.126) Thus, trR= -1 and (3.89) yields cos8= -1. Hence, 8=n is the equivalent angle of rotation. The axis of rotation cannot be determined by (3.90) for this exceptional case; rather (3.77b) or (3.88) must be applied directly. Use of (3.87) in (3.77) yields a0a=MR+ 1). (3.127) With (3.126), the diagonal components in (3.127) yield the three equations IX~= 0, IX~= 1/2; (3.128) Finite Rigid Body Displacements and the single nonzero, nondiagonal element cc 1 cc 3 = 1/2 shows that cc 1 and cc 3 have the same sign",
+            "129) in the spatial frame <p. This axis lies in the plane of i 1 and i 3 at 45o from the i 1 aXIS. It may be helpful to show that the results flow also from (3.88). Use of (3.126) gives Therefore, tx 1 = tx 3 and tx 2 = 0. Since o. is a unit vector, we have also cci + cc~ + tx~ = 2txi = 1; that is, tx 1 = cc 3 = \u00b1Jl/2. Hence, the axis of the Euler rotation is given by (3.129), as before. D Example 3.10. In another rotational maneuver of the panel mechanism from its initial configuration shown in Fig. 3.6, the rotation matrix about the point 0 is given by [ 1/2 0 R= 0 1 y'3;2 0 -y'J/2] 0 . 1/2 (3.130) 190 Chapter 3 Find the equivalent Euler angle and axis of the rotation through 0. Sketch the final orientation of the panel, and use the diagram to confirm the basis transformation matrix associated with (3.130). Solution. With tr R = 2, (3.89) yields 8 =cos - 1(1/2) = 60\u00b0 for the rotation angle. The axis of rotation is determined by (3.90). Thus, with sin 8 = ./312 and use of (3.130), we find easily o = -i2 \u2022 Of course, a rotation of 300\u00b0 about the axis i2 is the same; but, recognizing this trivial equivalence, we have agreed earlier to restrict 8 E [0, n]"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001394_00207170010025258-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001394_00207170010025258-Figure1-1.png",
+        "caption": "Figure 1. Two inverted pendula on carts.",
+        "texts": [],
+        "surrounding_texts": [
+            "In this section, we illustrate the proposed decentralized output-feedback methodology by means of a practical example of inverted double pendula on carts. For this decentralized benchmark example, a solution was given in Shi and Singh (1992) to the problem of decentralized full-state feedback control. Decentralized adaptive state-feedback controllers were derived in Shi and Singh (1992) to achieve the global ultimate boundedness for all states. Apart from this state-feedback solution, we are not aware of any existing decentralized outputfeedback algorithm which can solve the adaptive stabilization problem. Particularly, when the angles are taken as the output, the decentralized system contains quadratic terms that depend on the unmeasured states _\u00b31 and _\u00b32, i.e. the angular velocities. We show how our decentralized adaptive stabilization algorithm can be modi\u00ae ed to accommodate this hard technical issue. Example 2 (Inverted double pendula on carts (Shi and Singh 1992)): Consider a decentralized system, depicted in \u00ae gure 1, which is composed of two inverted pendula on carts, connected via a moving spring. The motion of the dynamics is described by S1: \u00b31 \u02c6 g cl ka\u2026t\u2020\u2026a\u2026t\u2020 cl\u2020 cml2 \u00b3 \u00b4 \u00b31  1\u2026\u00b31\u2020 _\u00b32 1 \u2021 1 cml2 u1 ka\u2026t\u2020\u2026a\u2026t\u2020 cl\u2020 cml2 \u2026s1\u2026t\u2020 s2\u2026t\u2020\u2020 \u2021 ka\u2026t\u2020\u2026a\u2026t\u2020 cl\u2020 cml2 \u00b32 8 >>>>>>< >>>>>>: \u202660\u2020 S2: \u00b32 \u02c6 g cl ka\u2026t\u2020\u2026a\u2026t\u2020 cl\u2020 cml2 \u00b3 \u00b4 \u00b32  2\u2026\u00b32\u2020 _\u00b32 2 \u2021 1 cml2 u2 ka\u2026t\u2020\u2026a\u2026t\u2020 cl\u2020 cml2 \u2026s1\u2026t\u2020 s2\u2026t\u2020\u2020 \u2021 ka\u2026t\u2020\u2026a\u2026t\u2020 cl\u2020 cml2 \u00b31 8 >>>>>>>< >>>>>>>: \u202661\u2020 where u1 and u2 are the control torques applied to the pivot point of each pendulum, \u00b0 \u02c6 m=M ,  i\u2026\u00b3i\u2020 \u02c6 \u00b0 sin \u00b3i, l is the length of the pendulum, and k and g are spring and gravity constants. We assume that \u00b0 > 0 is exactly known and the angles \u00b31 and \u00b32 are the only measured states. It is further assumed that c, l and k are unknown constants. Unlike in Shi and Singh (1992) where s1\u2026t\u2020 and s2\u2026t\u2020 are assumed to be sinusoidal, we consider general time-varying and bounded horizontal displacements s1\u2026t\u2020 and s2\u2026t\u2020 which are unknown. The system (60) \u00b1 (61) is not in the form (11), mainly because the vector \u00ae elds depend non-linearly on the unmeasured states _\u00b31 and _\u00b32. Inspired by our recent work (Jiang and Kanellakopoulos 2000), non-linear transformations are needed to bring the system (60)\u00b1 (61) into a decentralized system that depends aYnely on the unmeasured states. (Such a transformation was implicitly used in Mazenc et al. (1994).) As stated in Remark 2, extension to the practical tracking case follows trivially from results in practical output regulation. D ow nl oa de d by [ G eo rg e M as on U ni ve rs ity ] at 2 2: 03 0 1 Ja nu ar y 20 15 Non-linear transformations : For each i \u02c6 1; 2, de\u00ae ne xi1 \u02c6 \u00b3i, yi \u02c6 xi1 and xi2 \u02c6 e \u00b0 cos \u00b3i _\u00b3i \u202662\u2020 As it can be directed checked, (60) and (61) were transformed into ~S1: _x11 \u02c6 e\u00b0 cos y1 x12 _x12 \u02c6 e \u00b0 cos y1 cml2 u1 \u2021 g cl e\u00b0 cos y1 y1 ka\u2026t\u2020\u2026a\u2026t\u2020 cl\u2020 cml2 e\u00b0 cos y1 \u00a3 \u2026s1\u2026t\u2020 s2\u2026t\u2020 \u2021 y1 y2\u2020 8 >>>>>< >>>>>: \u202663\u2020 ~S2: _x21 \u02c6 e\u00b0 cos y2 x22 _x22 \u02c6 e \u00b0 cos y2 cml2 u2 \u2021 g cl e\u00b0 cos y2 y2 ka\u2026t\u2020\u2026a\u2026t\u2020 cl\u2020 cml2 e\u00b0 cos y2 \u00a3 \u2026s1\u2026t\u2020 s2\u2026t\u2020 \u2021 y1 y2\u2020 8 >>>>>< >>>>>: \u202664\u2020 Notice that all non-linerities in ~S1 and ~S2 now depend only on the outputs y1 \u02c6 \u00b31 and y2 \u02c6 \u00b32. Observer design: For any L1; L2 > 0, introduce two new variables \u00b9i \u02c6 cml2\u2026xi2 Lixi1\u2020; for i \u02c6 1; 2 \u202665\u2020 and let \u00b9\u0302i be an estimate of \u00b9i which is given as _\u0302 \u00b9i \u02c6 Li e\u00b0 cos yi \u00b9\u0302i \u2021 e \u00b0 cos yi ui \u202666\u2020 Now, for each i \u02c6 1; 2; denote \u00b1i as the observation error \u00b1i \u02c6 \u00b9i \u00b9\u0302i \u202667\u2020 By direct computation, we have _\u00b1i \u02c6 Li e\u00b0 cos yi \u00b1i \u2021 \u00bfi\u2026t; y1; y2\u2020; for i \u02c6 1; 2 \u202668\u2020 where \u00bf1 and \u00bf2 are de\u00ae ned by \u00bf1 \u02c6 cml2L2 1 e\u00b0 cos y1 y1 \u2021 mgl e \u00b0 cos y1 y1 ka\u2026t\u2020\u2026a\u2026t\u2020 cl\u2020 e \u00b0 cos y1 \u2026s1\u2026t\u2020 s2\u2026t\u2020 \u2021 y1 y2\u2020 \u202669\u2020 \u00bf2 \u02c6 cml2L2 2 e\u00b0 cos y2 y2 \u2021 mgl e \u00b0 cos y2 y2 ka\u2026t\u2020\u2026a\u2026t\u2020 cl\u2020 e \u00b0 cos y2 \u2026s1\u2026t\u2020 s2\u2026t\u2020 \u2021 y1 y2\u2020 \u202670\u2020 Like in Shi and Singh (1992), assume that a\u2026t\u2020 is an unknown time-varying function. Then, it is easily veri\u00ae ed that there exists an unknown constant p\u00a4 > 0 such that j\u00bfij \u00b5 p\u00a4\u2026j\u2026y1; y2\u2020Tj \u2021 1\u2020; for i \u02c6 1; 2 \u202671\u2020 To facilitate the controller design, denote \u00b7\u00b1i \u02c6 \u00b1i=p\u00a4. It then follows that _\u00b7\u00b1 i \u02c6 Li e\u00b0 cos yi \u00b7\u00b1i \u2021 1 p\u00a4 \u00bfi\u2026t; y1; y2\u2020; for i \u02c6 1; 2 \u202672\u2020 On the other hand, both xi1 subsystems in (63) and (64) can be rewritten as _yi \u02c6 e\u00b0 cos yi cml2 \u00b9\u0302i \u2021 e\u00b0 cos yi cml2 p\u00a4 \u00b7\u00b1i \u2021 Li e\u00b0 cos yi yi \u202673\u2020 So, for the practical output regulator design, we obtain the decentralized systems (72), (73) and (66) with partialstate measurements (yi; \u00b9\u0302i). Also, notice that the unknown coe cient 1=\u2026cml2\u2020 appears in the front of \u00b9\u0302i. Fortunately, this situation can be handled as in Marino and Tomei (1995, } 7.3) or Krstic\u00c2 et al. (1995, Chapter 8). We also borrow ideas from Marino and Tomei (1995, } 7.3) to avoid overparametrization . Noting that e \u00b0 \u00b5 e\u00b0 cos yi \u00b5 e\u00b0 for all yi, a direct application of our decentralized adaptive scheme in } 5.1 gives decentralized dynamic output feedback control laws of the form _\u0302pi \u02c6 \u00b6i\u00bci p\u0302i \u2021 \u00b6i\u2026Li \u2021 L 1 i \u2020 e\u00b0 cos yi y2 i \u2021 \u00b6i e\u00b0 cos yi w2 i2 @#i1 @yi  \u2021 4 @#i1 @yi \u00b3 \u00b42 \u20210:5 @#i1 @yi \u00b3 \u00b44 \u00c1 ! \u202674\u2020 ui \u02c6 ci2wi2 \u2021 Li e\u00b0 cos yi #i1 \u2021 @#i1 @yi Li e\u00b0 cos yi yi \u2026Li \u2021 L 1 i \u2020yi e\u00b0 cos yi _\u0302pi p\u0302i e2\u00b0 cos yi wi2 @#i1 @yi  \u2021 4 @#i1 @yi \u00b3 \u00b42 \u20210:5 @#i1 @yi \u00b3 \u00b44 \u00c1 ! \u202675\u2020 where #i1 \u02c6 ci1yi L3 i yi L 1 i e 4\u00b0 cos yi yi p\u0302i\u2026Li \u2021 L 1 i \u2020yi, wi2 \u02c6 \u00b9\u0302i #i1, and c11 \u00b6 0:5 \u2021 L 1 2 e4\u00b0, c210:5 \u2021 L 1 1 e4\u00b0, ci2 \u00b6 0, \u00bci > 0 and \u00b6i > 0, 1 \u00b5 i, j \u00b5 2, are design parameters. For simulation uses, take \u00b0 \u02c6 0:01, m \u02c6 g \u02c6 l \u02c6 k \u02c6 1 and c \u02c6 2. Also, take \u00bci \u02c6 \u00b6i \u02c6 1, L1 \u02c6 1, ci1 \u02c6 10 and c2j \u02c6 1 for 1 \u00b5 i, j \u00b5 2. For comparisons, as in Shi and Singh (1992), we take a\u2026t\u2020 \u02c6 sin \u20265t\u2020, s1\u2026t\u2020 \u02c6 sin \u20262t\u2020 and s2\u2026t\u2020 \u02c6 2 \u2021 sin \u20263t\u2020. Figure 2 shows the time histories of the angles \u00b31 and \u00b32 and the torques u1 and u2."
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0001253_rnc.754-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001253_rnc.754-Figure1-1.png",
+        "caption": "Figure 1. Formation geometry of ith and \u00f0i 1\u00deth aircraft.",
+        "texts": [
+            " Furthermore, these results confirm that when the wing aircraft is properly positioned in the vortex of the lead aircraft, it experiences reduction in its required flight power. The organization of this paper is as follows. Section 2 presents the mathematical models of the UAVs. A design model of the UAV is described in Section 3. The robust formation control system and observers are designed in Section 4. Section 5 present a stability analysis of the closed-loop system. Control of two UAVs and simulation results are presented in Section 6. Let us consider close formation of \u00f0m\u00fe 1\u00de aircraft. The formation geometry of the \u00f0i 1\u00deth and ith aircraft is shown in Figure 1. It is assumed that the Earth is flat and not rotating. Oi is the center of mass of the ith aircraft, where \u00f0i \u00bc 0; 1; . . . ;m\u00de: OiOi 1 is the separation vector. In this study, the coordinate systems for the ith aircraft of interest are the following: the ground axes system \u00f0Sgi\u00de (not shown in the figure), the local horizontal system \u00f0Shi\u00de with its origin fixed on the aircraft (axes Xhi; Yhi; Zhi), the wind axes system Swi (axes #iwi; #jwi; #kwi) obtained from Shi by three successive rotations of heading angle (velocity yaw) \u00f0wi\u00de; flight path angle (velocity pitch) \u00f0gi\u00de; and bank angle (velocity roll) \u00f0mi\u00de; and the body axes system \u00f0Sbi\u00de (not shown in the figure) obtained from Swi by two rotations, the sideslip angle bi and the angle of attack ai: Readers may refer to Etkin [23] and Miele [24] for the notation and the matrix equations relating various system of axes"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002541_s0039-9140(03)00408-9-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002541_s0039-9140(03)00408-9-Figure2-1.png",
+        "caption": "Fig. 2. Flow cell prototype II: (a) general view of the flow cell; (b) cross-section of the flow cell showing the different cell components.",
+        "texts": [
+            " Finally, the Baytron P layer was coated with 100 l of the ion-selective membrane with the composition shown in Table 1. The resulting carbon composite all-solid-state K+-ISEs (area: 0.07 cm2) can thus be described as follows: SS/CC/Baytron P/ISM. The electrodes were conditioned in 0.1 M KCl for at least 1 day prior to measurements. The electrodes were kept in 0.1 M KCl conditioning solution between measurements. The flow cell prototype II containing four all-solid-state ISEs is illustrated in Fig. 2. In a piece of PMMA, four holes were drilled in the same plane for the in situ fabrication of the four electrodes. The flow-channel (2 mm inner diameter) was then drilled in the center perpendicularly to the electrode plane (Fig. 2a). Standard connections were used to connect the cell to the flow system. The cell dimensions were 15 mm (outer diameter) and 12 mm (flow-channel length), and the total cell volume was ca. 37 l. 2.4.2. In situ fabrication of the all-solid-state K+-ISEs K+-selective membranes (ISMs) were cast in each of the four drilled holes, as shown in Fig. 2. After drying (overnight) the ISM forms a membrane (diameter: ca. 0.8 mm) that separates the flow channel from the internal solid contact of the ISE (Fig. 2b). The composition of the ISM is shown in Table 1. The internal solid contact of the ISE was prepared by solution casting of the aqueous dispersion of PEDOT (Baytron P) (Fig. 2b). After drying, the Baytron P layer formed a film on the ISM. The internal contact was completed by inserting the carbon composite paste (described in Section 2.3) in contact with the Baytron P layer. The CC paste was compressed with the stainless steel screw, which was connected to the mV-meter (Fig. 2b). The resulting all-solid-sate K+-ISEs were kept dry between measurements. For comparison, also macroscopic electrodes (area: 0.03 cm2) were made in the same way. However, these were kept in 0.1 M KCl solution between measurements. These all-solid-sate K+-ISEs were of the same type as the macroscopic electrodes described in Section 2.3 (SS/CC/Baytron P/ISM) but the ISM and Baytron P layers were cast in reverse order. The potentiometric measurements were performed with a homemade multi-channel mV-meter connected to a PC for data acquisition",
+            " Nevertheless, the present all-solid-state K+-ISEs were still working after more than one month when kept in conditioning solutions between measurements (Fig. 3). Poor adhesion of Baytron P to substrates such as gold and glassy carbon (GC) disk electrodes prevented the use of the Baytron P dispersion in the construction of the electrodes for the flow cell prototype I. This resulted in the development of the flow cell prototype II, where the electrodes were prepared in situ, as described in Section 2 (Fig. 2). The cell volume of prototype II was ca. 37 l, which was limited mainly by technological factors in the construction of the flow cell at the laboratory workshop. Since the ISM is cast directly in the cell body, the electrodes are not removable, which has to be considered in the choice of materials. However, this feature together with the mechanical fixation of the solid contact by the screw prevents leakage and loose contacts between electrode parts, and ensures easy handling of the cell-electrode device",
+            " When the CC/Baytron P is covered by the ISM, the impedance plot is dominated by a large high-frequency semicircle due to the bulk resistance in parallel with the geometric capacitance of the plasticized PVC-based ion-selective membrane, as shown in Fig. 4c. The impedance features are typical for solid-contact ISEs with a well-defined ion-to-electron transduction mechanism [12]. The results indicate that the all-solid-state K+-ISEs work properly and that there is contact between the different electrode layers. However, the adhesion between CC and Baytron P was found to be relatively weak and was improved by mechanical fixation in the flow cell prototype II (Fig. 2). Calibration plots of the all-solid-sate K+-ISEs obtained in KCl solutions with 0.1 M NaCl constant background is shown in Fig. 5. The calibration plots were recorded from 10\u22121 to 10\u22125 M and then back to 10\u22121 M KCl. The slope of the linear part of the calibration curve for miniaturized electrodes (10\u22121 to 10\u22125 M) was 56.4 \u00b1 0.7 mV per decade (n = 2); and for the macroscopic electrodes (10\u22121 to 10\u22124 M) it was 55.3 \u00b1 0.9 mV per decade (n = 3). The wider linear ranges and better slopes for miniaturized all-solid-state K+-ISEs in comparison with macroscopic electrodes may in this experiment be due to different placements of the reference electrode"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003286_0167-2789(86)90076-x-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003286_0167-2789(86)90076-x-Figure5-1.png",
+        "caption": "Fig. 5. The subtemplate .La(V\u00b0o) c,Xe'H, a) Simple substrips. K6 can be on either edge. b) Case A, n, o odd. c) Case B, nko even. d) Flip right-hand (twisted strip to left). K6 can lie on either edge.",
+        "texts": [
+            " ako_ v S\u00b0(l,\u00b0o) cAe~ H is a strip bounded on one side by K~ and containing K 0 in its interior. Since w~ (resp. wOwO) and w 0 agree except in one letter, S\u00b0(1,\u00b0o) consists of k 0 - 1 ' s imple ' strips connected subintervals of I x and Iy and jo ined end to end, together with one ' spl i t t ing ' strip in which the loops of K~ and K o pass a round opposi te sides of ~ H - F r o m the discussion before propos i t ion 2.3, in case A K o goes to the left and K6 to the right, while the oppos i t e occurs in case B. See fig. 5. In this figure we also pe r fo rm a simple isotopy which reveals that Ph. Holmes/Knottedperiodic orbits in suspensions of Smale's horseshoe 17 Za(p\u00b0o) is merely a strangely embedded copy of O'~H, and therefore induces a map on its branch line, Jo, homeomorph ic to f~ itself. This reflects the fact that f f o l j \u00b0 repeats the bifurcation sequence of f~ll ' in miniature ' ; section 2.3. Note that, although we have moved the twisted strip of figs. 5b, c over to the left, the words of the knots on ",
+            " In fact w 1 = WOWS, as the reader can check, so that K1 is a 2k0-periodic orbit, as required. The subtemplate construction also makes it clear that K 1 is the boundary of a M~Sbius band centered on K o and thus is a cabling: fig. 7. Finally, the number of crossings of K 1 over K 0 is 2c 0, inherited from the 'extrinsic' self-crossings of \u00a3a(r\u00b0o/2) due to its strange embedding, plus one crossing for each 'intrinsic' twist of o . \u2022 . ~ ( 1 ) k / 2 ) . i.e. for each strand of K o on the right of Xe\" n (in case B this includes the crossing in the splitting piece, cf. fig. 5c). Thus l ( K 1, K0) = 2c 0 +Y0, as claimed. It 2 0 Ph. Holmes / Knotted periodic orbits in suspensions of Smale's horseshoe With a little more information on the kneading invariant corresponding to the 'mo the r ' knot K 0 we can go further: Theorem 4.3. Let v \u00b0 ko = v0 * + - be an admissible, *-factorizable, 2k0-periodic kneading invariant corresponding to a k0-periodic itinerary ~0 with an odd number Y0 of y ' s in each finite acyclic block w 0. Let the horseshoe knot K 0 corresponding to w 0 have crossing number c o and let the it inerary of the critical po in t cor responding to v o have n o y ' s in the first k o entries"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001033_robot.1995.525419-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001033_robot.1995.525419-Figure1-1.png",
+        "caption": "Figure 1 Arm-hand meclianisin.",
+        "texts": [
+            " Kliatib has poiiitecl oiit t,liiLt, t,lie iiiert,ia of tlic IEEE International Conference on Robotics and Automation 2 Basic Equation 2.1 Arm-Hand Mechanism Arm-hand niecliaiiisnis, discusscd iii t,liis p q m . coiisist. of ~ 1 1 1 s iLiid iiiidt,ifiiigerc:d haiids. assiiiiied to liavc six DOF. Tlic iiiiiltifiiigered 1i;~iids liave tlireo fiiigers. aiid each fiiigcr hits t,lir<:e joiiits t,o iiiitkc frictioiial poiiit, c:oiit,ac:t,. Tlic assiiiiiIhoiis oil tjlic liaiicts a rc sitiiie as iii [3]. Iii t,liis sec:t,ioii. basic cqn;ttioiis of i t r i i i -h id iiicdiaiiisiiis. sliowii iii Fig. 1. i ~ r o dc:scril)ccl. Tlic: iioiiieiiclatiires in t~liis p p c r tire as follows: The itrills CB : Base coordinitt,e fraiiic. the origin OB E.i : A r m (:oordiiiat~~. fraiiio. t,lir, origin 0.4 CH : Haiitl coordiiiat,e franic. tlic origin OH C, : Coiit,act, point, of %-t,li fii~gert~ip. i = I , 2. 3 pF, E R3 : Positioii of C , froiii OB \u201cI,,, E R 3 : Posit,ion of C, from Oa p F , E R 3 : Positioii of C , froni OH 11 E R3 : Positioii of OH froiii OB p 4 E R 3 : Posit~ion of 0 . ~ froiii OB H E R3 : Position of OH froiii 0"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-FigureA.2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-FigureA.2-1.png",
+        "caption": "Figure A.2. Scalar component representations of a vector v in a plane and in space.",
+        "texts": [
+            "L The sum and difference of two vectors and their parallelogram interpretation show ing the commutative property of addition. ticularly their geometrical interpretation in a parallelogram construction, are useful. These are shown in Fig. A.! for the reader's review. Any vector v can be identified uniquely by its three perpendicular, direc ted projections {vd = (v 1 , v2 , v3 ) upon the three mutually perpendicular axes x 1, x 2 , x 3 (or x, y, .:::) of a rectangular Cartesian coordinate system, as shown in Fig. A.2. The positive directions of these coordinate lines, which are assumed to be arranged in a right-hand sense as usual, are themselves vector lines identified by three unit vectors, say, e1 , e2 , e3 . The set { ed is called a basis, and the three orthogonal projections v~ are known as the scalar com ponents of the vector v referred to {ek}\u00b7 Thus, when vis referred to this basis, it has the unique representation 1 v = I vkek = v1 c 1 + v2e2 + v3 e3 , k~! (A.l) which is illustrated in Fig. A.2. This means that only vectors equal to v can have the same scalar components when referred to { ek }. That is, u = v if and The Elements of Vector Calculus 355 only if the corresponding scalar components uk and vk are equal when u and v are referred to { ek}: uk = vk fork= I, 2, 3. This rule for equality of two vectors u and v referred to the same basis vectors ek is used often in applications to determine unknown components in vector equations. The same vector v may be referred to any other basis { e~ }, say. Of course, its scalar components { vk} in this basis will be different from those in (A.l ), but its representation has the same form as (A.l ), namely, v = L~~,vkek. The foregoing geometrical description of the scalar components shown in Fig. A.2 implies that the magnitude of a vector v is equal to the square root of the sum of the squares of its scalar components: (A.2) A.l.l. The Dot Product The dot product of two vectors u, v is a scalar defined by u . v = uv cos< u, v > (A.3) where u= lui, v = lvl, and cos<u, v) is the cosine of the angle between the vec tors u and v. Hence, if neither u nor v is the zero vector, then u \u00b7 v = 0 implies that u is perpendicular to v. Since cos< v, u) = cos< u, v), it is clear that the dot product is commutative: u \u00b7 v = v \u00b7 u"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000295_physrev.42.108-Figure7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000295_physrev.42.108-Figure7-1.png",
+        "caption": "Fig. 7. The effect of strain on the intensity of magnetization of nickel in a demagnetizing field.",
+        "texts": [
+            " In one case when the nickel was in a state of compression the point P was at about 8 gauss. For fields less than 8 gauss an increase of compression caused a reversible increase of residual magnetism. (However, as P was approached there was a decided tendency for irreversible decreases of magnetism to oc cur when the excess compression was removed.) For demagnetizing fields greater than that at P an increase of compression always caused an irreversi ble decrease of / . On the basis of these results the dotted curve Af was drawn as in Fig. 7. It was found that in demagnetizing fields greater than that at P a de crease of compression produced an irreversible decrease of 2\". Hence the shaded area cannot be entered vertically starting from the dotted curve A'\\ any attempt to enter in this way results in a drop downwards. Very similar results were obtained with nickel when initially in a stretched condition, the curves B and B' being obtained. In one case the point Q was at about 10 gauss. 116 C. W. HEAPS If a nickel wire is subjected to a bending torque its magnetization curve shows remarkably large discontinuities",
+            " This in crease of length of the compressed section tends to increase the degree of com pression, since the wire will be assumed not to bend. Also, the tension of the stretched section is increased. The situation is similar to that found where a straight, bimetallic strip is used on a thermostat. As the temperature rises and the strip is not allowed to curve, one metal is increasingly compressed, the other increasingly stretched. It is easy to show that the magnetization of such a composite wire will be stable for demagnetizing fields less than those corresponding to points P or Q, Fig. 7. In demagnetizing fields greater than these, however, there is insta bility. For, consider a small increase, AH, occurring in a shaded region of Fig. 7, and assume outside forces applied so as to keep the tensions in the two parts of the composite wire constant during this change. We then get de creases, AIAl and AIB, respectively, in the magnetizations of the compressed and stretched segments. However, from Figs. 3 and 7 we conclude16 that AIB is much smaller than AIA. Also from Fig. 4 we see that AH in this region pro duces negligible length change in the stretched segment B, as compared with that in the compressed segment A. Since the composite wire is not allowed to curve, the increase of length of A would produce a compressive stress in A and a tension in B, were it not for the external forces assumed to be applied. These forces are a pull on A and a compressive stress on B. Now remove these outside forces. From Fig. 7 it appears that decreases of magnetization, 81A and dIBl result, the value of 5IB being much less than 81A. The effect of 31A is to introduce magnetostrictive expansion of A, so that if the wire does not curve there results a compressive stress in A and a tensile stress in B. These new stresses now produce further increments of decrease of / . 15 R. Forrer, reference 3; M. Kersten, reference 7. 16 The curves for compressed nickel are not given in Figs. 3,4, and 5. However, the differ ences between stretched and compressed nickel will be similar to the differences between stretched and unstretched nickel"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001279_0022-0728(93)80303-y-Figure8-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001279_0022-0728(93)80303-y-Figure8-1.png",
+        "caption": "Fig. 8. Cyclic voltammograms for the reduction of 0 2 and H202 at a pyrolytic graphite electrode on which 4.5 x 10-10 mol cm -2 of FeAC was adsorbed: (A) response from adsorbed FeAC in the absence of 02 or H202; (B) response in the presence of 1.3 mM H202; (C) response in the presence of 1.3 mM 02. Supporting electrolyte as in Fig. 2; scan rate, 10 mV s-1.",
+        "texts": [
+            " However, reduction of the adsorbed FenIAC complex at this pH can be observed only once because the resulting FenAc - complex dissociates very rapidly, the Fe 2\u00f7 is lost from the surface, and no anodic peak appears in the cyclic voltammogram. However, the AC ligand remains on the surface and can be used again to bind Fe 3+ to the surface, even from solutions at pH 1.3. Catalysis of the reduction of 02 and H202 by adsorbed FeAC The adsorbed FeAC complex is an effective electrocatalyst for the reduction of H 20 2 and 0 2. The cyclic voltammograms in Fig. 8 demonstrate that the catalytic reductions of both substrates commence near the potential where the reduction of the Fe 3+ center occurs. The larger peak current for the reduction of 0 2 reflects its reduction by more than two electrons because the catalyst is active for the reduction of H202 at the same potential. For a more quantitative assessment of the catalysis, the reductions were measured at rotating disk electrodes on which the FeAC complex had been irreversibly adsorbed. A representative set of current-potential curves for the reduction of 0 2 is shown in Fig"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003820_j.talanta.2005.08.058-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003820_j.talanta.2005.08.058-Figure3-1.png",
+        "caption": "Fig. 3. Dimensions and shape of the gas\u2013l",
+        "texts": [
+            "6 mol l\u22121 nitric acid and finally rinsed several times with Milli-Q water before using. 2.3. Sample preparation The coffee plant tissue samples (fruits and leaves) were dried in an oven at 70 \u25e6C and then powdered with an analytical mill. Plant tissue samples were treated by a hot 1 mol l\u22121 nitric acid extraction procedure of boron according to Al-Ammar et al. [ \u22121 n 1 a t fi m T t w a w f m 5 s F on set d on co zomethine-H and tygon orange/white tubing for delivery of uffer, and hydrolyzed solutions. Two home-made gas\u2013liquid eparators showed schematically in Fig. 3 were used. Two prorammable peristaltic pumps (GILSON Minipuls-3, 8-roller) ith the option of remote control were used for the propulsion f the reagents. The flows of reagents were regulated varying the ump head rotation speed and different internal diameter tygon ump tubing (Cole-Parmer). Home-made software (Windows latform, PC compatible) was developed to control the pumps nd valves and other necessary devices. An R232/RS485 card, ncorporated in a Pentium I processor PC, was used to interface he periphery devices",
+            " When the nitrogen flow was increased from 10 to 20 ml min\u22121, an increase in the signal was observed. The signal reached a plateau within the range 20\u201330 ml min\u22121. Thereafter, the signal notably decreased as the fl A o a 2 w p iquid 1 as fixed in 20 cm long, which is a relatively short length and epresents a reaction time of approximately 0.015 s. This conrms that the esterification reaction it is very fast and that the ster methyl borate is produced almost instantaneously. The gas\u2013liquid separator, GLS1, (Fig. 3a) was a device esigned and constructed in-house, four different sizes of it, amely, 3.0, 6.0, 9.0, and 12.0 ml, were tasted for methyl borated eparation. The drains from all these devices were pumped. ow rate increased, which could be due to excessive dilution. dditionally, very pour reproducibility (R.S.D.% of 20%) was bserved at higher flow rates, as consequence of inefficient sepration of the new bulk of phases in the GLS2. A flow rate of 5 ml min\u22121 was chosen as optimal. The effect of the flow rate and type of hydrolysis solution as investigated",
+            " However, the liquefaction of the methanol increases the volume of the liquid phase that reaches the GLS2. In order to avoid accumulation of analyte solution in the GLS2 the flow rate of the drains of it was fixed somewhat higher than buffer flow rate. Finally, the optimum flow rates values for buffer a b d o h f results and to minimize the time of the analysis a 110 cm long hydrolysis reaction coil was selected for further experiments. Finally, the liquid phase which contain the analyte was separated from the bulk phases in the gas\u2013liquid separator, GLS2, (Fig. 3b). The GLS2 was a device designed and constructed inhouse; the dimensions and shape of it were chosen accordingly to guarantee the appropriated separation without losses of analyte. 3.3. Effect of interferences The tolerance of the system to interferences was evaluated by investigating the effect of a number of possible interferents, both anionic and cationic: Li+, Na+, K+, NH4 +, Cu2+, Co2+, Ni2+, Cd2+, Pb2+, Hg2+, Zn2+, Mg2+, Ba2+, Sr2+, Ca2+, Fe3+, Al3+, V5+, NO3 \u2212, Cl\u2212, and F\u2212. The tolerance limits to the interferences, expressed as the maximum concentration of the interfering element added to a boron solution which differed less than 5% to the signal of a solution of boron alone (5 g ml\u22121) were determined"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure2.20-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure2.20-1.png",
+        "caption": "Figure 2.20. Slider block, hinge pin, and yoke assembly.",
+        "texts": [
+            "101) In the same manner described before, z and y may be expressed as functions of the time alone, and in this way we shall have the complete solution. The angular velocity and acceleration of the rod depend upon the con straints introduced to fasten the rod to the slider blocks. An ideally smooth ball joint is a simple useful model, but hinged joints often are used too. To see the effect that different types of joint models may have on the angular rates of the rod, let us suppose that the ball joint at B is replaced by a hinge pin and yoke assembly shown in Fig. 2.20. In this case, we see that the rod can rotate about the k axis along the guide shaft and about the axis ~ parallel to the hinge pin; but it cannot turn about the axis y = k x ~. which is perpendicular to these directions. Therefore, ro \u00b7y=O (2.102) defines the hinge constraint relation imposed at B on the rotations of the rod. The vectors y = k x ~ and ~ = k xI, which generally are not unit vectors, may be used to define the directions ~ and y in terms of k and /, which are more easily expressed in 1/>",
+            " The position vector of the top of the antenna from the station F is denoted by X. Another frame cp = { 0; ek} has the absolute velocity v0 =6e 1 -4e2 +7e3 ft/sec at an instant t0 when ek = lk. The angular velocity and angular acceleration of cp relative to tP at time t0 are given by ffi = 4e 1 + 2e2 - 3e3 rad/sec, Compute the first and second time rates of change of X as seen from cp at the instant of interest. Does v 0 affect the results? .w Problem 4.6. I, 320 Chapter 4 4.7. Consider the hinged joint and slider block shown in Fig. 2.20. Let frame 1 = { B; p, y, k} be fixed in the slider block B, as shown, and introduce another frame 2 = { B; a, p, A} fixed in the hinged yoke of the connecting rod AB so that A is parallel to!. (a) Determine as functions of y the angular velocity of the rod relative to B and the absolute angular velocity of B in the frame t:P = { F; ik} shown in Fig. 2.19. (b) What is the angular speed of the rod relative to the slider block? (c) What is the absolute angular velocity of the rod referred to frame 1"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure4.2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure4.2-1.png",
+        "caption": "Figure 4.2. A vector U (t) referred to a preferred and to a moving frame.",
+        "texts": [
+            " The terms \"preferred\" and \"moving\" will be used only in the simple relative sense described above; and, whenever it may be convenient, we may reverse our choice of labels for the two frames and achieve parallel results. We shall assume that all observers employ the same time reference, i.e., all observers use the same standard clock. Let the preferred frame be denoted by <P = { F; Ik} and the moving frame by cp = { 0; ik}. Suppose that the frame cp has angular velocity rof relative to the frame <P and translational velocity v0 , as shown in Fig. 4.2. Let U(t) be any vector-valued function of the time t. The scalar components of U(t) are Uk(t) when referred to the preferred frame <P and uk(t) when referred to the moving frame cp at timet. Thus,* U(t)= Uk(t)Ik is the representation at time t of the vector U(t) as seen by the observer F fixed in frame <P and referred to that frame, whereas the relation U(t) = uk(t) ik(t) is the representation of U(t) as seen by the same observer F but referred to the moving frame. Of course, the basis vectors ik have always the direction of the moving coordinate axes, so that apparent to an observer 0 in frame cp, the vector U(t) at time t has the same representation U = uk(t) ik; however, as indicated, the moving obser ver perceives no change in ik with time t"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001869_irds.2002.1043954-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001869_irds.2002.1043954-Figure4-1.png",
+        "caption": "Figure 4: h e - b o d y diagram of one strand",
+        "texts": [
+            " Define Zla = L, &a = L, Z1b = h, and IIFlaII l lFZa11 l l F l b I I Z2b = A ll&, and let Zn = e be the unit vec- tor along which the normal forces apply and Zt be the unit vector along which the frictiyn forces apply. When the knot is in equilibrium, F = 0, so FlaZia + F2aZ2a FlbZIb + F2b&b = 0. (1) This equation has two unknown variables, F1b and F26, which can be uniquely solved in general. The condition of impending motion can be obtained from the free-body diagram of one strand as shown in Figure 4. The impending motion occurs when (FIaZla + F&b> . Zt = P(fian -k flbn). (2) From (2), it is possible to obtain the general sliding condition, but it is quite complicated. Since the desired knot trajectory lies in the normal direction to the tissue, we shall only consider the symmetric shown in Figure 5. At the equilibrium, the force and moment equations about p and p' are c=e(P = PI = ,927 7 = 71 = 7 2 , F1a = F2a), as (4) (5) Coulomb\u2019s law states the sliding occurs when It can be further simplified to (7) 1 1 tanp tany > 2P, --- which results in the following sliding condition (8) tany 2p tany + 1 o < p < tan-\u2019( )"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002191_6.2002-1261-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002191_6.2002-1261-Figure2-1.png",
+        "caption": "Figure 2. Finite element model of a coiled tube.",
+        "texts": [
+            " Material Properties Both the coiled and Z-folded models are polyethylene tubes with a diameter of 3.82 inches and a thickness of 0.006 inches. The values of the tube's Young\u2019s modulus, Poisson's ratio, and density used are 25,000 psi, 0.25, and 0.033 lbm/in3, respectively. The inflation is air at 70o F with a molecular weight of 28.97 lbm/lbmole. The gas flows in at one end of the tube with an inflation mass flow rate ( )/ dtdm of t\u00d71.0 lbm/sec. The finite element model for the coiled tube packaged configuration is displayed in Figure 2. It consists of seven CVs and is created by employing a simple Archimedean spiral equation, 0 rar += \u03b8 . The symbol a represents a constant, \u03b8 is the sweep angle, and 0 r is the initial radius as shown in Figure 2. The nodes are created starting at 0=\u03b8 and 0 rr = and continue up to a user defined length. The unwinding of the coiled tube is shown in Figure 3. The volume and pressure as a function of time for each CV are shown in Figures 4 and 5, respectively. The tube is fully deployed at time 0.35 sec. The pressure is 8 psi, which induces a hoop strain of 10 %. The finite element model for the Z-folded tube packaged configuration is displayed in Figure 6. Inflated shapes of the Z-folded tube in various stages of deployment are shown in Figure 7"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003974_tia.2005.863911-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003974_tia.2005.863911-Figure1-1.png",
+        "caption": "Fig. 1. Flux densities in the air gap.",
+        "texts": [
+            " A block diagram to suppress time delay, caused by eddy current, sampling period, and current regulation is proposed. Radial force and speeds of the shaft are also estimated, and used as feedback signals. The effectiveness on improving response and damping of radial positioning is shown both theoretically and experimentally. In the analysis, three conditions are assumed. 1) Magnetic saturation can be neglected. The permeability in the iron is infinite. 2) Flux distribution in the air gap confronting a stator tooth is uniform and fringing flux is negligible. 3) The rotor surface is magnetically smooth. Fig. 1 shows definitions of coordinates \u03b1 and \u03b2, angular position \u03b8, and air-gap flux densities B24t(\u03b8) in the air-gap area confronting stator teeth. With flux density B24t(\u03b8) of each stator tooth as a function of an angular position \u03b8, radial forces F\u03b1 and F\u03b2 in the 0093-9994/$20.00 \u00a9 2006 IEEE perpendicular \u03b1- and \u03b2-axes are the sum of the difference of flux density squared, written as F\u03b1 = Sa 2\u00b50 180\u25e6\u2211 \u03b8=0\u25e6 [ B2 24t(\u03b8) \u2212 B2 24t(\u03b8 + 180\u25e6) ] cos \u03b8 (1) F\u03b2 = Sa 2\u00b50 180\u25e6\u2211 \u03b8=0\u25e6 [ B2 24t(\u03b8) \u2212 B2 24t(\u03b8 + 180\u25e6) ] (\u2212 sin \u03b8) (2) where \u00b50 is the permeability in free space"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003258_51.35577-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003258_51.35577-Figure1-1.png",
+        "caption": "Figure 1. Motion of a particle in a periodically excited two-well potential.",
+        "texts": [
+            " Several general examples wil l be briefly discussed in this section, wi th references listed that enable the reader to explore each of the examples in more detail. Examples that wil l be discussed are: a particle in a two-wel l potential, a conical pendulum, the population dynamics equation, and the Van der Pol oscillator. The subject of fractals wil l be introduced wi th a brief look at the Mandelbrot and Julia sets. Particle in a Two-well Potential. One of the simplest chaotic systems t o envision is a ball (or particle) in a two-wel l potential, as illustrated in Fig. 1. The ball can be in either of the t w o wells, each of which is an equilibrium state when the base is at rest. Now imagine that the base is vibrated wi th a certain period and wi th an amplitude sufficient t o cause the ball t o go from one well t o the other. It turns out that, under certain conditions, the ball wil l jump back and forth wi th a fixed period such as ABAB ..., or AABAAB ..., but for other conditions the pattern is chaotic, that is, there is no periodicity in the sequence of As and Bs"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002038_ls.3010080402-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002038_ls.3010080402-Figure1-1.png",
+        "caption": "Figure 1 Schematic representation of a contact between sliding surfaces",
+        "texts": [
+            " A system for wear prediction in lubricated sliding contacts should encompass all such cases and integrate them into one logical structure. THE MODEL All theories that predict wear rates start from the concept of a true area of contact that is determined by the plastic deformation of the highest asperities on the contacting surfaces. During relative motion of contacting surfaces there takes place a continuous process of making and breaking of the adhesive junctions resulting from the interactions between surface asperities. This is shown, schematically, in Figure 1. Adhesive wear in dry contacts Lubrication Science 8-4, July 1996. (8) 318 0954-0075 $10.00 + $4.00 31 9 T.A. Stolarski : A System for Wear Prediction in Lubricated Sliding Contacts The real area of contact is the instantaneous sum of the areas of all junctions. The central assumption of the model is that it is possible to relate the volume of material removed, V; in the sliding distance, L, to the real area of contact,A, Archard\u2019s model In the model proposed by Archard,\u2019 it is assumed that the junction consists of a circle of radius r, the corresponding area of contact being ma"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000569_s0045-7949(98)00004-2-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000569_s0045-7949(98)00004-2-Figure2-1.png",
+        "caption": "Fig. 2. The deformation of an in\u00aenitesimal element whose deformed con\u00aeguration is a rectangular parallelepiped.",
+        "texts": [
+            " Moreover, Pai and Palazotto [3] showed that the rigidly translated and rotated frame x1x2x3 can be located by requiring that @u @xn im @u @xm in 18 Substituting Equation (18) into Equation (17) yields dP V 0 JmndBmn dV 0 19 where Jmn 1 2 J\u0302mn J\u0302nm , J\u0302mn f m dxp dxq in, m 6 p 6 q 20 Bmn 1 2 @u @xm in @u @xn im @u @xn im @u @xm in Bnm 21 Here Jmn are the so-called Jaumann stresses and Bmn are the so-called Jaumann strains. We note that Equation (18) makes Jaumann strain and stress tensors symmetric. Cauchy stresses tmn and in\u00aenitesimal strains lmn Since Cauchy stresses are de\u00aened with respect to the deformed area, we need to consider an in\u00aenitesimal element whose deformed shape is cubic, as shown in Fig. 2. Here, the frame x1x2x3 is an orthogonal rectilinear inertial frame, the base vectors along the axes x1, x2 and x3 are j1, j2 and j3, re- spectively. The frame y1y2y3 represents the rigidly translated con\u00aeguration of the frame x1x2x3 and hence the base vectors along the axes y1, y2 and y3 are also j1, j2 and j3, respectively. Moreover, v denotes the absolute displacement vector of the point O and f\u00c4k are forces acting on the deformed surfaces. Using the fact that the elastic energy P of a structural system is due to relative displacements among material particles, one can obtain its variation dP as dP V ~f 1 jn d @v @y1 dy1 jn ~f 2 jn d @v @y2 dy2 jn ~f 3 jn d @v @y3 dy3 jn 22 where V denotes the deformed system volume",
+            " The Cauchy stresses tmn are de\u00aened as tmn ~f m dyp dyq jn ~f n dyr dys jm tnm, m 6 p 6 q, n 6 r 6 s 23 where the fact that tmn=tnm can be proved by using the moment equilibrium equations of the deformed element [2, 5]. The in\u00aenitesimal strains lmn are de\u00aened as lmn 1 2 @v @ym jn @v @yn jm 24 We note that both tmn and lmn are symmetric. Substituting Equations (23) and (24) into Equation (22) yields dP V tmndlmn dV 25 where dV= dy1 dy2 dy3. Equation (25) can be written as [2, 5] dP V 0 t\u0302mndlmn dV 0, t\u0302mn Ftmn 26 where F0 v[F]v = dV/dV0, [F] denotes the deformation gradient tensor, and t\u0302mn are the so-called Kirchho stresses. Almansi stresses Omn and Almansi strains Amn It can be seen from Fig. 2 that @ro @ym jm, @rO @ym 1 lm j ~m 27 where lm denotes the stretch of dym and jm\u00c4 denotes the unit vector along the undeformed direction of dym. Because ro=rO+v, we obtain that d @v @ym jn d @ro @ym jn \u00ff @rO @ym jn d dmn \u00ff 1 lm j ~m jn \u00ff d 1 lm j ~m jn 28 The surface traction force f\u00c4m can be represented in terms of Almansi stresses Omk and stretches lk as [2] ~f m Om1 1 l1 j ~1 Om2 1 l2 j ~2 Om3 1 l3 j ~3 dyp dyq, p 6 q 6 m 29 Substituting Equations (28) and (29) into Equation (22) yields dP V O11 1 l1 j ~1 O12 1 l2 j ~2 O13 1 l3 j ~3 jnd \u00ff 1 l1 j ~1 jn O21 1 l1 j ~1 O22 1 l2 j ~2 O23 1 l3 j ~3 jnd \u00ff 1 l2 j ~2 jn O31 1 l1 j ~1 O32 1 l2 j ~2 O33 1 l3 j ~3 jnd \u00ff 1 l3 j ~3 jn dy1 dy2 dy3 30 Almansi strains (or Eulerian strains) Amn are de\u00aened by using the change of the squared length of an in\u00aenitesimal line segment as 2Amn dym dyn dro dro \u00ff drO drO @ro @ym @ro @yn \u00ff @ rO @ym @ rO @yn dym dyn 31 Hence, Amn 1 2 @ ro @ym @ ro @yn \u00ff @rO @ym @rO @yn 1 2 jm jn \u00ff 1 lm j ~m 1 ln j ~n 1 2 dmn \u00ff 1 lm j ~m 1 ln j ~n 32 where repeated subindices do not imply summation",
+            " 3 that dy1 dx 1 cos y 35a and the displacement component v1 of the points o, a, and g are vo1 0, va1 dx 1 cos y\u00ff 1 , vg1 \u00ffdx 1 sin 2y 35b Using Equations (35a)\u00b1(b) and the de\u00aenitions of strains shown in Equations (4), (9) and (24), we obtain e\u030211 e11 @v1 @x 1 va1 \u00ff vo1 dx 1 cos y\u00ff 1 6 0 36a l11 @v1 @y1 va1 \u00ff vg1 dy1 1\u00ff cos y 6 0 36b Hence, displacement gradients e\u00c3ij, engineering strains eij and in\u00aenitesimal strains lij are non-objective measures. From Equation (32) one can see that, if there are only rigid-body motions, lk=1, jm\u00c4 jn\u00c4=dmn and Amn=0. Hence, Almansi strains are objective. However, rigid-body rotations may make the physical meaning of Almansi stresses very di erent from common de\u00aenitions of stresses. For example, if j1\u00c4 =j2 in Fig. 2, then it follows from Equation (29) that the Almansi stress O11 represents a shear stress (not a normal stress) on the deformed surface dy2dy3 along j2. It also indicates that, in the Almansi stress\u00b1strain equations, the material constants need to be functions of deformations even if it is a small-strain but large-rotation problem. The use of \u00aerst Piola\u00b1Kirchho and engineering stresses also su ers from the same problem. From Equation (14) one can see that, if there are only rigid-body motions, lk=1, ik\u00c3=ik and im\u00c3 in\u00c3=dmn",
+            " However, for curvilinear coordinate systems, @jk/@xm and @ik/@xm may be nontrivial and results in initial curvature-induced terms. Equations (4), (9) and (24) show that the directions of the displacement gradients, engineering strains and in\u00aenitesimal strains are along the undeformed coordinates, which causes the non-objectivity. Equation (14) and Fig. 1 show that the directions of Green\u00b1Lagrange strains are along the directions of im\u00c3 , which are not three perpendicular directions. Equation (32) and Fig. 2 show that Almansi strains are along the directions of jm\u00c4 , which are not three perpendicular directions. Equation (21) shows that the directions of Jaumann strains are de\u00aened with respect to the deformed coordinates and along three perpendicular directions. Such characteristics are convenient for the imposition of shear stress conditions on the bonding surface in deriving the shear warping functions of beams, plates and shells [23]. Equation (21) (Equation (20)) and Equation (9) (Equation (8)) show that Jaumann strains (Jaumann stresses) and engineering strains (engineering stresses) have the same vector form except that jm and v are replaced with im and u"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000844_1097-4636(200104)55:1<54::aid-jbm80>3.0.co;2-y-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000844_1097-4636(200104)55:1<54::aid-jbm80>3.0.co;2-y-Figure1-1.png",
+        "caption": "Figure 1. Schematic representation of the compression of SPHs. Radial (A) and axial (B) compression are shown. The compression of SPHs in the direction of the dotted arrows resulted in compressed SPHs in the shapes on the right.",
+        "texts": [
+            " For some experiments, the weight of the SPH was taken before and after placement in the humidity chamber to determine water uptake in the humidity chambers. Percent weight increase (I) was calculated from the dry weight, wd, and the plasticized weight, wp, according to Equation (1). I = [(wp \u2212 wd)/wd] 100% (1) The SPHs to be compressed were placed in a carver press and compressed with either a \u00bc-inch tablet punch and die or two stainless-steel plates. The tablet punch and die resulted in an axial compression, whereas two steel plates resulted in a radial compression. Figure 1 is a schematic representation of the compression process used. Two plates were used for the radial compression; a tablet punch and die were used for the axial compression. A laboratory Carver Press (Fred S. Carver Co., Menomonee, WI) was used for all of the compression experiments. The hand press was calibrated for pressures from 0 to 1000 lb. After removal from the press, the samples were immersed in absolute ethanol overnight. Samples were then dried in the food dehydrator and stored in a dessicator until use"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003766_biorob.2006.1639165-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003766_biorob.2006.1639165-Figure2-1.png",
+        "caption": "Fig. 2. Optical force sensor attached to the haptic interface. The left image shows the opened sensor with the fiber setup in the middle",
+        "texts": [
+            " Since optical sensors are completely magnetically inert, they have been widely used in the MR environment for the detection of displacement [5] [14] [23], force [24] [25] [26] and torque [24]. Optical fibers are able to transmit signals by a long distance without degeneration, so the circuitry part of the sensor could be put far away from the coil center to avoid interaction with the magnetic field. In particular, the optical force sensor of J. Fu\u0308glistaller is comprised by three optical fibers connected to a processing unit [25]. Two fibers measure the light intensities I1 and I2 emitted by one opposing fiber, see Fig. 2. Force applied to the sensor causes a small dislocation that changes the amount of light received by the two opposing fibers. To make the system less sensitive to diffused light and absorption within the fibers the force is determined by relative rather than absolute intensity changes. A possible problem is the varying transmission losses when the fibers are moved or bended during robot motion. Hence, bending or motion of the optical fiber should be limited. Other approaches of MR-compatible sensors are also possible"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001158_s0925-4005(00)00322-1-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001158_s0925-4005(00)00322-1-Figure1-1.png",
+        "caption": "Fig. 1. Illustration of the enzyme electrode.",
+        "texts": [
+            " It re-activates the enzyme by extracting phosphate pesticides. \u017dAChE EC 3.1.1.7, 1000 Urmg, from Electric eel, type . \u017dV\u2013S and COx EC 3.1.1.17, 10 Urmg, from Arthrobac.ter globiformis were purchased from Sigma. Glutaralde\u017d . \u017dhyde 70% solution, for biochemistry , albumin 10%, . \u017dfrom bovine serum , acetylcholine chloride analytical . \u017d .grade , DDVP standard 99% purity were obtained from \u017d .Wako. PAM 99% purity was purchased from Aldrich. The enzyme electrode was fabricated by the following procedures, illustrated in Fig. 1. About 14 U of AChE and 58.5 U of COx were dissolved in 100 ml of 0.05 M phosphate buffer solution. Five microliters of the enzyme solution was coated directly onto a 5-mmf Pt plate and dried. Then, 50 ml of the above solution was mixed with 10 ml of 10 wt.% albumin and 2 ml of 70 wt.% glutaraldehyde. Five microliters of this solution was coated onto the enzyme-coated Pt plate and dried to form a crosslinked enzyme layer. The enzymes in the inner layer possess each original activities. Further, it is expected that they maintain high activities even in the outer layer, since albumin is believed to immobilize enzymes with little deterioration"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003735_tpwrd.1986.4307990-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003735_tpwrd.1986.4307990-Figure6-1.png",
+        "caption": "Figure 6. Illustration of Hysteresis Effect.",
+        "texts": [
+            " The downside function is simply the upside The probability density function, f(x), can be selected such that h(x) matches any given hysteresis curve. The only constraints are: F(x) must approach or equJal 1 for large x. This means that the integral of f(x) for MMF ranging from 0 to infinity must be 1. h(x) must be asymptotic to the curve x-1. This means that the centroid or mean of f(x) must be at x=l. With these constraints, and by choosing an appropriate starting point, h(x) forms the right-, upward-moving side of the hysteresis curve. Imagine, as shown in Figure 6, that MMF had started at some large negative value, Xl, and steadily increased to X2 along path (a), taking out all the deadband so that the output, Y2, equals X2 minuis 0.5. At this point, let MMF reverse direction. function flipped over and path (b) will be traversed. Let MMF continue down to X3, and again reverse. Now only the smaller elements have traversed their entire deadband. The larger elements have traversed only part way through just as in the example on Figure 4. All those small elements that had completely unwound their deadband will have to go back through in the other direction as MMF steadily increases",
+            " Consequently, the incremental slope following a current reversal varies with the coordinate position. The model of this paper would predict a slope independent of position (within the unsaturated region) which has been noted elsewhere experimentally [21 and theoretically [31. The existing EMTP model also does not provide for the sudden change in slope when overtaking a previous reversal point. Other limitations have been mentioned by users [4]. Could the authors make further comments comparing the existing and proposed models? On the above topic, following Fig. 6, it is noted that a sudden change in slope could induce a (step) change in winding voltage. This may be true only when the remainder of the simulation network has a Thevenin impedance large compared to the magnetizing inductance, with current rather than voltage being maintained constant. This condition could be approximated in certain ferroresonance-type problems. The idea of representing hysteresis as the composition of deadbands is not new, being described in [21, [5], and probably earlier. However, the postulated connection between probability density functions and hysteresis is new to this discusser and would appear to deserve further development since h(x) needs to be supplied by the model user"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003495_004-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003495_004-Figure5-1.png",
+        "caption": "Figure 5. Experiments with a piece of a rubber band.",
+        "texts": [
+            " It can be, since while calculating the circulation of B, we in fact integrate its tangent component B \u00b7 dr2, and the latter remains finite in spite of the divergence of B. As mentioned in the introduction, Darwin grasped, on an intuitive level, the existence of the topological conservation law. To arrive at it, he performed a series of simple experiments. Let us repeat one of the experiments made by Darwin. Take by one end a straight piece of a rubber ribbon and wind it around a pencil observing at the same time the behaviour of the free end: it rotates. But, when the orientation of the other end of the ribbon is fixed, a twist will appear. See figure 5(a). The rigorous explanation of the experiment is as follows. Splice the ends of the initially flat rubber ribbon so that a loop without any twist is formed. The linking number of the borders of the ribbon loop is equal obviously to zero, and it will remain zero whatever we do to the loop. Now stretch a part of the loop and freeze the rest of it. (Making experiments with the stretched part is equivalent to making experiments with a flat piece of ribbon, whose ends are fixed.) In view of the equation Lk = Wr + T w, the sum of the writhe and twist will remain zero. To be rigorous, we should consider the conservation law in its full form: Lk(K,U) = Wr(K)+T w(K,U). This needs a precise indication of what K and K + \u03b5U are. The best choice is to consider one of the ribbon\u2019s borders as the K + \u03b5U and the middle line between the borders, as K. Examining figure 5(a) we can see that the latter remains straight in the twisted part of the ribbon. This makes our reasoning simpler and cleaner. When, as shown in figure 5(a), we wind a half of it into a helix, which introduces writhe into K, the other half must become twisted in the opposite direction and the number of twists will be equal to the number of the helix turns. How do we avoid it? It is obvious: we must wind the ribbon in such a manner that the writhe of K will remain equal to zero. This is achieved when the helical winding starts from both ends with opposite handedness. See figure 5(b). The total writhe Wr(K) will be equal to zero and so will be the twist T w(K,K + \u03b5U). The same happens to a tendril. We treat it as a piece of ribbon. After it has caught a support, both its ends become fixed. Thus, in our imagination we may treat it as a part of a loop, the rest of which is frozen. How it will behave is described above. Obviously Darwin\u2019s considerations could not be so rigorous, but he grasped the idea perfectly well. Here is his reasoning: We can now understand the meaning of the spires being invariably turned in opposite directions, in tendrils which from having caught some object are fixed at both ends"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001376_s0967-0661(99)00084-2-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001376_s0967-0661(99)00084-2-Figure6-1.png",
+        "caption": "Fig. 6. The envelope of the moment gyrocomplex angular momentum.",
+        "texts": [],
+        "surrounding_texts": [
+            "Conventionally, spacecraft attitude control system have been designed in the form of a multifunctional system of combined control, which includes two interconnected multidimensional loops, a closed loop as a basic programmed feedback control and an openloop as an additional disturbance-compensation control (Anshakov, Antonov, Butyrin, Makarov, Matrosov & Somov, 1995; Kozlov, Anshakov, Antonov, Makarov & Somov, 1998). Since it is necessary for the closed loop to operate in the `reference memorya mode for long periods, this is the decisive criterion of e$ciency. The principal meter for this loop has been represented by a Strapdown Inertial Navigation System (SINS). Various meters for spacecraft body attitude and angular rate measurements have been applied to this loop: \"ne gyrosensors (#oat, laser, \"bre-optic, dynamically adjusted, etc.), and opto-electronic sensors (an Earth orientation device in the form of an infra-red horizon sensor, a \"ne Sun sensor, and also \"ne \"xed-head star sensor with a wide \"eld of view), which are intended for the correction of the strapdown system. To provide for the desired quality of image, rather strong requirements are applied to the attitude control of the spacecraft. This has stimulated the search for new techniques for guiding optical telescopes onto observed targets, including direct techniques. The latter employ image motion sensors and precision image motion stabilization systems that are directly embedded in the optical telescope, see Figs. 2 and 3. As far as ultra-precision image motion stabilization system is concerned, the image, which is obtained with the main mirror (1) of the telescope in the light detector (4) has been precisely stabilized using two cascaded closed loops, comprising the o!-set \"ne image motion sensor (5) and micro-processors (6), (9) and (10). The movements of the optical compensators (the secondary mirror (11) and near-focal diagonal mirror (2) is implemented by digital electromechanical (12) and \"ne piezo-ceramic (7) microdrives, see Fig. 4. The group has wide experience in the application of strapdown inertial navigation systems based on a precision inertial gyroscopic assembly using precision #oat gyros, which are rate gyrosensors. In the latest designs, when long-term operation of an attitude control system in the `memorya mode is needed, a strapdown inertial navigation systems based on a 4-channel Russian inertial gyroscopic assembly with two spherical electrostatic gyroscopes is applied. Drift values derived in practice for this type of strapdown system are measured in units of arcsec/24 h. This allows the \"ne \"xed-head star sensor to be substantially simpli\"ed by reducing the necessary sensitivity down to bright stars, and by performing the astronomic correction procedure of the SINS only once in a few days. The group also has wide experience in the application of moment gyrocomplexes based on di!erent types of electromechanical executive devices (reaction wheels with ball-bearing suspension and electromagnetic suspension, as well as momentum wheels and control moment gyros with di!erent degrees of freedom (DOF) and with di!erent types of controlled gimbal suspensions) with moment gearless drives and gear stepping drives (Aref 'yev, Sorikin, Bashkeyev & Kondrat'yev, 1995). The moment gyrocomplexes based on gyrodines are the most e$cient executive devices for fast and frequent changes of a spacecraft's body orientation, achieving precise angular motion stabilization, and they are applied in the attitude control system on the remotesensing Russian spacecraft. The singularity problems (Tokar, 1978; Margulies & Aubrun, 1978) for di!erent moment gyrocomplex' schemes based on gyrodines are carefully investigated in this paper. The moment gyrocomplex with four gyrodines in the `2-SPEEDa-type minimum-excessive fault-tolerant scheme, see Figs. 5 and 6 (Crenshaw, 1973), stands out because of its many advantages when the modi\"ed exact distribution law (Somov, 1997b) of the normed angular momentum between the pairs of gyrodines is used. The large power consumption of the moment gyrocomplex is provided by large-scale solar array panels. Motion-control systems on the remote-sensing Russian spacecraft also have executive devices such as gas reaction thrusters for attitude control, a main reaction thruster in a 2-DOF suspension with the gear stepping drives for orbit control, the gear stepping drives for the angular guidance of solar array panels, as well as highly directive receiving}transmitting antennas, onboard thermal control system radiators, etc. The problem of unloading the moment gyrocomplex from the accumulated angular momentum is quite speci\"c for a low-orbital spacecraft since the aerodynamic disturbing torque is substantially larger than disturbances arising from the Earth's gravitational and magnetic \"elds. The open-loop control with respect to disturbances is intended for both regular compensation of the external disturbing torques, and for unloading the moment gyrocompelx."
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0003057_0141-0229(86)90134-1-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003057_0141-0229(86)90134-1-Figure2-1.png",
+        "caption": "Figure 2 Plot of the amount of glucose consumed versus the amount of ATP added",
+        "texts": [
+            " 3 nmol rain -~ ; 350 Enzyme Microb. Technol., 1986, vol. 8, June Enzyme electrode for A TP and creatine kinase: G. Davis et al. consequently on the time-scale of the experiment the enzyme electrode does not cause a significant change in the bulk glucose concentration.) Five aliquots (2 pmol) of ATP were then added and the decrease in the steady-state current measured after each addition. From the decrease in current at the precalibrated electrode the amount of glucose consumed was calculated. A plot, Figure 2, of ATP added versus glucose consumed showed that the reaction followed the expected 1:1 stoichiometry, equation (2), and indicated that the complete reaction sequence for assaying creatine kinase, comprising equations (1), (2), (6) and (7) could be tested. The steady-state current response of the glucose enzyme electrode in 1 ml buffer containing glucose (20raM), hexokinase (20 U), ADP (5 mM) and creatine phosphate (20 raM) was initially stable (Figure 3). The glucose concentration used is within the linear range of the enzyme electrode, 6 other reagent concentrations were chosen to ensure that a sufficient excess was present"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002648_bf02439374-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002648_bf02439374-Figure1-1.png",
+        "caption": "Fig. 1 Hencky problem Fig. 2 Circular membrane under",
+        "texts": [],
+        "surrounding_texts": [
+            "the concentrated force and its boundary conditions and Hencky transformation, the problem~ of nonlinear boundary condition were solved. The Hencky transformation wc~ extended and a exact solution of large deformation of circular membrane under the concentrated force has been obtained.\nKey words: circular membrane ; concentrated force ; large deformation; exact solution\nChinese Library Classification: 0344.3 Document code: A 2000 MR Subject Classification: 74B20; 74K35\n1 A x i s y m m e t r y L a r g e D e f o r m a t i o n o f C i r c u l a r M e m b r a n e\nThe problem of axisymmetry large deformation of circular membrane is one with practical\nsignificance. Hencky (1915) ~11 gave a solution of power series under the uniform force; Alekseev (1951) [~-] gave an analytic solution of circular membrane under the concentrated force, which is exact only when v = 1/3. Chien Wei-zang et al . (1981)[3] gave an analytic solution of the symmetrical circular membrane under the action of uniformly distributed loads in its central portion. As for the results or other authors [4-6] were approximate ones.\nthe concentrated force\nIn this paper, the Hencky transformation was extended and a exact solution of large\ndeformation of circular membrane under the concentrated force has been obtained and the solution is simple. The result given in this paper is useful, although the case for this solution is exceptive\n* Received date: 2001-08-28; Revised date: 2002-09-18\nBiography: CHEN Shan-lin ( 1 9 4 2 - ) , Professor\n28",
+            "one of Refs. [2] and [31 ; It is due to that the result is difficult to derive directly from the Refs. [21 and [31 .\n2 B a s i c E q u a t i o n a n d H e n c k y T r a n s f o r m a t i o n ' s E x t e n d i n g\nL e t ' s introduce the following dimensionless parameters:\nr'- E3(1- ~-)]lJ'-,o x - R 2 , Y = h '\nd y 7) --\ndx '\n- 6(1 - ,'-)R'-N~ S =\nEh:~\n[ 3 ( 1 - v2) ] 3 / 2 R 2 p 19 =\n27rEh 4\nwhere r---radial radius; R--circular membrane' s radius; h-- thickness; u---deflection; Nr--radial membrane force; E - - Y o u n g ' s modulus; v - -Po i s son ' s ratio; P--concentrated force.\nThen the basic equation of large deformation of\ncircular membrane under the concentrated force is [37 p = x s v , ( 1 ) Fig. 3 Circular membrane under the action\n( xs )\" = v ~- . of uniformly distributed loads in\nIn which ( ) ' = d / d x . Deleting v and letting z = x s , its central portion\nwe can obtain z\" = p 2 z - : . (2)\nAnd the boundary condition is\nx -- 1, 2z ' - (1 + v ) z = 0. (3)\nThe condition for that is x = 0 at the center of the circular membrance thanks to the concentrated force which induces N r with singularity\nl i m z ( x ) = 0 ( x ~ ) , even a < 1. (4) x~-I)\nThe problems of nonlinear boundary condition, ( 2 ) and ( 3 ) were solved under the condition ( 4 ) .\nIt is supposed that z~ ( x ) is another special solution of Eq. ( 2 ) , then we have a transform\nZ ( X ) ---- a k Z l ( \u2022 l ) , ~C 1 = t'/,~C q- b . ( 5 )\nSubstituting Eq. (5) into Eq. ( 2 ) , we have\na 4 + 3 k d2zl ~2192 (6)\nd x i zT\nSuppose a _= 1 and Eq. ( 6 ) is right forever. So it gives general solution of Eq. ( 2 ) from transform ( 5 ) , b is integral constant. It regards transform (5) as extending of Henky transform under the concentrated forces, because transform (5) is a Hencky transform when b = 0."
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0003286_0167-2789(86)90076-x-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003286_0167-2789(86)90076-x-Figure1-1.png",
+        "caption": "Fig. 1. The horseshoe, its suspension and its template, a) The suspension of F, b) the template (,,~e\" H, ~t).",
+        "texts": [
+            " Holmes / Knotted periodic orbits in suspensions of Smale's horseshoe 9 t-\", + oo. Applied to the orbits in 12, - collapses the flow along the strong stable manifolds, thus producing a semiflow g~ t on a branched two-manifold .Xe'c M 3. The knot-holder or template (J{, ~,) has the property that any (finite) set of periodic orbits of % corresponds via isotopy to that of ~t: the knots and links induced on X\" by ~, are isotopic to those of the original flow ~t on M 3. We illustrate the process for the horseshoe in fig. 1; the resulting template, (X'n, ~t) is the object of our study here. For more details on its derivation and relevance to nonlinear oscillations, see Holmes and Williams [2]. One can regard this 'reduction-by-one-dimension' procedure as providing a method complementary to the usual one of taking a two-dimensional cross section D c M 3 and defining an diffeomorphism F: D --, D; the Poincarb map (Guckenheimer and Holmes [18], chap. 1). In this connection, the equivalence relation can be viewed as follows",
+            " Since embeddings of the horseshoe are prevalent in nonlinear oscillators and other three-dimensional dynamical systems (Guckenheimer and Holmes [18]), the general situation is evidently more complicated than Beiersdorfer et al.'s conjecture suggests. In this respect our work shows that, once a suspension has been chosen, the sequence of type numbers bj, along with the yj and crossing numbers cj, are completely determined by the word of the base orbit .Thus the 'chaotic renormalization orbits' conjectured by Crawford and Omohundro [17] are not realized in any specific flow. However, clearly by modifying the suspension of fig. 1, introducing additional twists, etc., one can produce infinitely many different sequences for any given base word. See section 6. 5. P e r i o d m u l t i p l y i n g We start by reviewing the generic behavior of area-preserving diffeomorphisms in the neighborhood of an elliptic fixed point. This introduces the notion of period-multiplying sequences and provides a generalization of the doubling sequences of section 4. We also recall the construction of resonant torus knots of Holmes and Williams [2]"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure2.6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure2.6-1.png",
+        "caption": "Figure 2.6. Finite displacement of a rigid body.",
+        "texts": [
+            " For example, the three coordinates of any par ticle, or any base point, and any three independent angles that specify the orientation of the body frame relative to the spatial frame f/J may be selected. This natural choice is basic to the following description of the most general displacement of a rigid body. The mathematical description of the decomposition of the general dis placement of a rigid body into its translational and rotational parts will be outlined here. Let us imagine that the body shown in Fig. 2.6 undergoes an arbitrary motion in space that carries it from a given initial configuration into another configuration relative to an assigned spatial frame f/J = { F; Ik }. Con sider an imbedded frame q/ = { 0; i~} which is parallel to f/J when the body is in its initial configuration. The corresponding position vectors of a particle P Kinematics of Rigid Body Motion 93 are denoted by x in q/ and X in l/J. After the displacement of the body, P has a new spatial position X in l/J but it retains the same position with respect to the imbedded, body frame. The point 0 initially at B in frame l/J is displaced to 0' at B, as diagrammed in Fig. 2.6. Finally, let us consider in the terminal configuration another auxiliary frame cp = { 0'; ik} which is parallel to l/J, hence also to the imbedded frame cp' in the initial configuration. If x denotes the position vector of P from 0', relative to cp, then the displacement vector of the particle P is given by d(P) =X- X= b +X- X, (2.12) where b = d( 0) = B- B is the displacement of the base point 0. The foregoing description illustrates our discussion of reference frames in the previous section. Indeed, the angles between the ik and ilc vectors in the final configuration may be used to characterize the orientation of the body in its final state in l/J",
+            " A relation that describes an arbitrary rigid body rotation about a fixed base point in terms of the nine direction cosines relating the orientation of the body reference frame in its initial and its final configurations will be derived next. The connection of the result with a rotation about a fixed line will be studied in the following section. To start with, we recall that x is the displaced position vector of P in the spatial frame cp = { 0; ik}, and x is the position vector of P in the body frame cp' = { 0; i~ }, which was coincident with cp initially, as described in Fig. 2.6. Thus, when viewed in cp alone, we envision the same particle P identified by two vectors x = xkik and x = .Xkik separated by an angle 1/J, as shown in Fig. 3.4. This is the usual representation considered in (3.116) and in all of our earlier equations for the displacement vector in an assigned spatial frame cp. Hence, as usual, (3.116) may be written in the following familiar component form in cp: (3.117) However, the same situation may be viewed differently. In the body frame cp' in Fig. 2.6, the point P has always the same position vector p, say. Therefore, it appears always to an observer in cp' that P has the coordinate components {p/J={xd=(x1 ,x2,x3 ) so that p=pkik=xkik referred to frame cp'. Of course, these also are the initial coordinates of P in the spatial frame q>, because the frames coincides initially. But the same vector p after the Final Position of Pin'/! (Xt, X:2, X3) Spatial Frame I{J (x 1 ,x2,x3) Initial Position of P in Frame '{) Figure 3.4. Displacement of a particle P viewed in the spatial frame <p",
+            "87), (3.122), and (3.123) the relations T=Q-1, det T=O. (3.124a) (3.124b) (3.124c) Therefore, as remarked in Chapter 2, it follows from Euler's theorem and (2.12) that the general displacement of a rigid body is equivalent to a parallel 188 Chapter 3 translation b of the base point 0 together with a displacement Tx due to a rotation about a line through 0: d(P) = b+Tx [cf. (2.13)]. Another useful form of (2.13) may be obtained by aid of (3.87). Recalling the description of the vectors defined in Fig. 2.6, the reader may show that ( 2.13 ) yields X(P) = B(O) + Rx(P}, (3.125) wherein X(P) and B( 0) are the terminal position vectors of P and 0 in the spatial frame cfJ = { F; Id. Euler's theorem has shown that the components of the rotation tensor, hence also those of the rotator, may be found by construction of the basis transformation matrix A in (3.123b ). Thus, the angle and the axis of the equivalent Euler rotation may be obtained from (3.89) and (3.90) when the initial and final orientations of the body reference frame are known"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002857_j.snb.2005.02.024-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002857_j.snb.2005.02.024-Figure3-1.png",
+        "caption": "Fig. 3. Scheme of the electrochemical cell: reference electrode (a), working solution (typical volume = 200 L) (b) and MEA (c).",
+        "texts": [
+            " (g) Hardening of photoresist by heating the MEA up to 450 \u25e6C for 1 h, in order to improve the device\u2019s chemical resistance. 2.3. Electrochemical measurements Electrochemical studies were carried out by using a two-electrode configuration. The reference electrode was a Ag/AgCl (saturated KCl) electrode and the gold microelectrodes set was used as working electrode. A few droplets of the working solutions (typically 50\u2013200 L) were placed on the microelectrodes region, see Fig. 1a, and the reference electrode was positioned at the top of the droplet, see scheme shown in Fig. 3. All electrochemical measurements were performed using an Autolab PGSTAT 30 (Eco Chemie) bipotentiostat with data acquisition software made available by the manufacturer (GPES 4.8 Version). 3. Results and discussion 3.1. Electrochemical characterisation of the fabricated microelectrodes array In order to check the connection between each microelectrode and the electrical contact with the equipment, preliminary potentiostatic experiments were carried out at \u22121.5 V in a 1 mol L\u22121 H2SO4 solution. During this experiment, the microelectrode array surface was visually inspected by using a CCD camera connected to a microscope (SONY CCD-IRIS)"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002677_rob.4620070207-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002677_rob.4620070207-Figure1-1.png",
+        "caption": "Figure 1.",
+        "texts": [],
+        "surrounding_texts": [
+            "226 Journal of Robotic Systems - 1990\nTwo applications are now well known for the determination of the minimum inertial parameters: (1) the determination of the minimum set of inertial parameters of robots contributes at reducing the computational cost of the dynamic rnodel~,l-~ (2) the minimum inertial parameters constitute also the identifiable inertial parameters. Its determination simplifies the identification of the inertial parameters of robots and increases the robustness of the identification proC ~ S S . ~ - ' ~ These two applications are directly related to the implementation of control laws which are based on the dynamic model of the robot.''-'3\nRe~ent ly '~ . '~ we have presented a general method to determine the set of minimum inertial parameters of serial or tree structure robots. At the same time similar results concerning the special case of serial robots whose successive axes are perpendicular or parallel have been given by Mayeda et al.'6.'7 A numerical method to get the number of these parameters has been presented by Sheu and Walker.'* The aim of this article is to give a new presentation for the determination of the minimum inertial parameters of serial robots. Most of these parameters will be determined by the use of recursive relations. Some parameters belonging to the first translational links may need particular solutions. If the robot contains only rotational joints or if the first joints are either parallel or perpendicular, all the minimum parameters can be directly obtained.\nDESCRIPTION OF THE ROBOT\nThe system to be considered is an open loop mechanism of n + 1 links, link 0 is the base and link n is the terminal link. The description of the system will be carried out by the use of the modified Denavit-Hartenberg n~tat ion, '~ ,~ ' thanks to this description the closed form solution of regrouping the inertial parameters has been obtained. The coordinate frame j is assigned fixed with respect to link j. The zj axis is along the axis of joint j , and xi axis is along the common perpendicular of zj and zj+'. The frame j is defined with respect to frame j - 1 by the matrixi-'Tj which is function of the parameters (aj, di, e,, r j ) , Figure (l), such that:\nwhere:\nj-IAj defines the orientation of frame j with respect to frame j - 1, j-lPj defines the position of the origin of frame j with respect to frame\nj - 1.\nThe joint variable j is given as:",
+            "Khalil, Bennis, and Gautier: Minimum Inertial Parameters of Robots 227\nwhere q = 0 for j rotational, uj = 1 for j translational, and ej = (1 - uj),\nTHE MINIMUM INERTIAL PARAMETERS\nThe minimum inertial parameters can be obtained from the classical inertial parameters by eliminating those which have no effect on the dynamic model and by regrouping some parameters. In the following we will give the conditions by which we can calculate these parameters, the analysis is based on the energy of the links and on the Lagrangian model.\nThe Lagrangian Dynamic Model\nThe Lagrangian equation is given as:\nwhere:\nrj is the torque (or force) of actuator j , E is the kinetic energy, and U is the potential energy of the robot, to be\ncalculated\nn n\nU = V , = - 2 [gT(MjoPj + OAjIMSj)] ( 5 ) I = I j = 1",
+            "228 Journal of Robotic Systems - 1990\nwhere:\nthe kinetic energy of link j , the potential energy of link j , the mass of link j , the first moments vector of link j around the origin of frame j , the inertia tensor of link j around the origin of frame j , the velocity of the origin of the link j fixed frame, referred to frame j , the angular velocity of link j . referred to frame j , the acceleration of gravity, referred to frame 0.\njwj and 'Vj can be calculated by the following recursive equations:\nwhere: Zo=[O 0 1]T\nThe components of Jwj and JVj will be denoted as:\n'mj=[olj YJ w ~ J ] ~ and JV,=[Vl,j V Z j V3J]T\nParameters having no Effect on the Dynamic Model Defining the inertial parameters of link j by the vector Xi, denoted as:\nXj = [XXj X y j XZj Wj YZj ZZj MXj MYj MZj Mj]' (8)\nwhere: (XXj , . . . ,ZZj) are the elements of the upper triangle of jJj, ( MXj, M YT,, M Z j ) are the components of JMS,. From Eqs. (4)-(7) we deduce that E and U are linear in the inertial parameters. Thus:\nwhere: x k j is the kth inertial parameter of link j .\nFrom (3), (9), (lo), we see that if:"
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0003834_physreve.71.041703-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003834_physreve.71.041703-Figure4-1.png",
+        "caption": "FIG. 4. Anchoring geometry and disclination line. sa,bd The direction of the disclination l at the contact point depends on the angle j between the planar easy axis s and the lower cylinder axis x. When j=0 the director configuration on the plane p is purely splay bend, otherwise a twist distortion must be considered. scd Effect of a tilt of a few degrees on the homeotropic anchoring: l do not pass at the contact point. sdd Top view of sbd, showing the curvature-induced twist between the planar easy axis s of the lower cylinder sin-plane component along yd and the homeotropic easy axis of the upper cylinder scomponent along xd.",
+        "texts": [
+            " When D reaches the critical value Dc= uLh\u2212Lpu, the sample undergoes a confinement-induced anchoring transition to a uniform alignment along the easy axis of the strongest anchoring f3g. For D,Dc, no additional force is required to vary the thickness of the uniform slab. Hence, the energy EsDd reaches a plateau, corresponding to the energy required to align the weaker anchoring along the stronger easy axis sFig. 3d. Approaching the transition, the birefringence falls to zero for a uniform homeotropic alignment, or grows to the full value for a planar alignment. Figure 4 shows the anchoring geometry between two crossed cylinders of radius R inducing, respectively, a planar and a homeotropic anchoring, with infinite anchoring strengths. The ideal hybrid anchoring conditions, with a splay-bend director rotation of 90\u00b0 across the thickness, is found only at the contact point. However, since the sense of rotation is not determined here, this point should correspond to a defect. In fact, a disclination line is expected to pass at the contact point, along a direction determined by the angle j between the planar easy axis s and the cylinder axis fFigs"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001869_irds.2002.1043954-Figure10-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001869_irds.2002.1043954-Figure10-1.png",
+        "caption": "Figure 10: Base force/torque semoT",
+        "texts": [
+            " Strain gauge transducers have been widely used for force measurement, but it is undesirable in the minimally invasive surgical setting. The sensor is sensitive to the temperature variation, contact with tissues during surgeries may cause drift in the sensor output, and it must be sterilized in high temperature after each use. The disposal type of strain gauge sensors addresses sterilization but means high cost and time consuming calibration. In this research, the suture tension is measured through a force/torque sensor in the base of the surgical robot, as shown in Figure 10. This approach has the advantage that the sensor does not need to be sterilized and the force measurement (and hence control) is independent of the tools. The measured wrench at the base sensor can be expressed as sum of the following components: Fs = Fm + Fg + Fb (18) where F, is the motion-induced dynamic wrench, Fg is the gravity wrench, and Fb is the base wrench where Fb x Fs - Fg. 3.2 Explicit Force Control Scheme To achieve a smooth transition from low tension to required tension, damping is needed"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003134_02640410400021914-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003134_02640410400021914-Figure1-1.png",
+        "caption": "Figure 1. Typical flight paths for a topspin ball impacted with loose and tight strings. The high-tension strings produce a rebound that is approximately 28 closer to the normal to the racket face.",
+        "texts": [
+            " In laboratory tests, a clamped racket strung loosely, for example, can project the ball up to 38 closer to the normal to the racket face than a racket strung tightly (Bower & Sinclair, 1999; Goodwill & Haake, 2004; Knudson, 1997). This produces a ball path that is Correspondence: R. Bower, School of Leisure, Sport and Tourism, University of Technology Sydney, PO Box 222, Lindfield, NSW 2070, Australia. E-mail: r.bower@uts.edu.au ISSN 0264-0414 print/ISSN 1466-447X online \u00aa 2005 Taylor & Francis Group Ltd DOI: 10.1080/02640410400021914 D ow nl oa de d by [ U ni ve rs ity o f L et hb ri dg e] a t 0 6: 20 0 4 O ct ob er 2 01 4 approximately 28 higher when a topspin stroke is generated with a moving racket (Figure 1). For a ball struck at 20 m s71 with an angle of inclination of 148, a 28 increase would result in a 2.5-m increase in the range of the ball and a 0.36-m increase in the maximum height of its flight path. These variables must be accounted for if the performer is to maintain the ball within the projectile limits of the court. In Figure 1, the ball is projected at an angle further from the normal to the racket face at the lower string tension. This initially appears to be inconsistent with the laboratory results. The two sets of results involve different reference frames, however, and are not inconsistent (Figure 2). Consider the situation shown in Figure 2a, where a ball is incident horizontally at speed vin on a racket moving at speed vR at an angle to the horizontal. The same impact can be viewed in a racket reference frame where the racket is at rest, by subtracting the vR vector as shown in Figure 2b"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001854_cdc.2001.980101-Figure12-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001854_cdc.2001.980101-Figure12-1.png",
+        "caption": "Figure 12: Actuator part",
+        "texts": [
+            " Figure 9: AM:(z,y) 21 9 4.1 Experimental setup and model The general view of our experimental setup is shown in Fig. 10. The twin rotor helicopter model is mounted on a base as shown in Fig. 11. The arm AB can rotate around the center 0 freely, and a1 and a2 are the yaw and the IOU angles, respectively. The airframe CD can also rotate freely on the axis AB, and 6' is the pitch angle. Thus, the model has three degrees of freedom. The rotors are driven separately by two DC motors. The actuator part is illustrated in Fig. 12. The angle 4 produces the coupling property. By the way, 4 is zero in (41 and [7]. The maSS of each rotor is A/2, and the distance from the point B to the center of mass of each rotor is r. f1 and f2 represent the vectored forces of the two rotors, then the lifting force u1 and the rotary force uz for the air .force are represented by U1 = (fl +fz)cos$ (36) U2 = r(fz -f1)CW$ (37) z13 = (f*-fi)sin4 = E.UZ (38) where e := tan4/r. As shown in Fig. 13, the arm is composed of two parts A 0 and OB, and the masses and the distance from the point 0 to the center of mass are m,,mb,l, and l a , respectively"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003788_j.engfailanal.2004.04.003-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003788_j.engfailanal.2004.04.003-Figure1-1.png",
+        "caption": "Fig. 1. Transmission system of rotary tiller.",
+        "texts": [
+            " The Rotary tiller is attached to a tractor threepoint linkage system and driven by the tractor PTO. Power is transferred from the PTO to the first gearbox. The drive direction changes by 90 at the horizontal shaft to the second gearbox. The Rotor shaft is used as power and movement transmission from the gearbox to the spade knives. The output shaft is horizontal and is driven by the second gearbox. A Clutch safety system is placed between the universal joint and the first gearbox to prevent overload. The Transmission system is shown in Fig. 1 and the technical features are given in Table 3. The failed component is the rotor shaft gear in the second gearbox. The failure types are abrasion dam- age and plastic deformation (see Fig. 2). The rotor shaft gear has 31 teeth, the tooth module is 6, the addendum circle diameter is 200 mm, the pitch circle diameter is 185 mm, the face width is 38 mm, the tooth thickness is 12 mm, and the tooth height is 15 mm (see Table 4). The gear material is SAE1020 steel. The flow stress out is 230 MPa, the rupture stress is 360\u2013440 MPa, the surface hardness is 69"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003788_j.engfailanal.2004.04.003-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003788_j.engfailanal.2004.04.003-Figure2-1.png",
+        "caption": "Fig. 2. Failured gear.",
+        "texts": [
+            " The Rotor shaft is used as power and movement transmission from the gearbox to the spade knives. The output shaft is horizontal and is driven by the second gearbox. A Clutch safety system is placed between the universal joint and the first gearbox to prevent overload. The Transmission system is shown in Fig. 1 and the technical features are given in Table 3. The failed component is the rotor shaft gear in the second gearbox. The failure types are abrasion dam- age and plastic deformation (see Fig. 2). The rotor shaft gear has 31 teeth, the tooth module is 6, the addendum circle diameter is 200 mm, the pitch circle diameter is 185 mm, the face width is 38 mm, the tooth thickness is 12 mm, and the tooth height is 15 mm (see Table 4). The gear material is SAE1020 steel. The flow stress out is 230 MPa, the rupture stress is 360\u2013440 MPa, the surface hardness is 69.2 RB, the carbon amount is 0.105% (wt) and the silicon amount is 0.024% (wt) (Table 5). Failure reasons were determined as design errors and material faults"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002291_robot.1994.351239-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002291_robot.1994.351239-Figure6-1.png",
+        "caption": "Figure 6: Shortest rob ot tr a' jectory",
+        "texts": [
+            " An alternate method for identifying the shortest robot path is presented here that avoids the need for an exhaustive search. This method takes advantage of the fact that the obstacle free region is a single polygon in which both the starting and target points .are vertices of the polygon. The procedure for finding the shortest path is presented and then the proof is provided that the resulting path is indeed the shortest. The following steps present the algorithm for determining the shortest path within the polygon region RF, and an example is shown in Figure 6. Divide the polygon border into two at the starting and target points, defining a right and left side. Guess an initial direction of a straight line that departs the starting point in a direction that is interior to RF, as indicated by the jnterjor side of the vertex at the starting point. Find the first intersection of the proposed line with the either the right or left side. Identify another straight line from the starting position that intersects the boundary at the side other than the initial guess",
+            " Propose a new line direction, interior to RF, between the right and left lines, by dividing the angle between the lines into two. Find the intersection of the new line with the polygon boundary. Define a new right or left line depending on which side of the boundary the proposed line intersects first. Repeat the previous step until both the right and left lines converge, which is indicated when the angle between them is less than a threshold. The direction of the final line intersects both the right and left side and indicates the direction of the shortest path. Figure 6 shows the direction of the first segment of the shortest path. The length of the shortest path segment is selected so that it ends at whatever side of the polygon it intersects first (which will always be at a vertex of the polygon). Repeat the above steps starting from the second step, where the starting point of the new segment is the end of the previous straight line segment. The shortest path is completed when the target can be reached with an obstacle free straight line from the starting point of the previous segment",
+            " The direction of each segment of the shortest path is selected so that if it was extended within the obstacle free region, RF, it would intersect both the right and left side. All other directions are not locally the shortest. The proof that the preceding procedure identifies the shortest line is based on the fact that the shortest path must at all points also be locally the shortest. The shortest path is piecewise linear, and potential directions for the first segment are those interior to the vertex at the starting point. Consider a potential first segment that intersects the polygon boundary on the right side, represented by line A in Figure 6. Region RA is defined by line A and a section of the polygon boundary. The target is outside RA. Thus a path to the target that includes line A must exit region RA. Line A is not locally the shortest if there exists a potential starting segment that is interior to the polygon yet exterior to RA, and also intersects the polygon on the right side. An example of such a segment is line B in Figure 6, which defines region Rg. The boundaries of region Rg includes line A, line B, and a section of the polygon boundary. Since the target is also on the exterior of Rg, the path to the target that includes line A must enter region RB and then exit that region by intersecting line B. The only other way to reach the target would be to cross the polygon boundary and exit the obstacle free region, RF. Accordingly, the path to the target that includes line A is required to intersect line B. Such a path is not locally the shortest, since a shorter line to the intersection point with line B would be directly along line B"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003253_j.engfailanal.2004.12.035-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003253_j.engfailanal.2004.12.035-Figure1-1.png",
+        "caption": "Fig. 1. Lay-up process of the shafts.",
+        "texts": [
+            " A commercial finite element analysis package, NISA 8.0 v, is used in order to secure an objective evaluation of the golf shafts. As a means of obtaining the data for finite element analysis, the material properties of carbon fiber-reinforced plastics, which are usually used in current golf shafts, are measured through experiments. Ultimately, this study will become a basis for the enhancement of the capacity of golf shafts and also for the development of their economical manufacturing technologies. Fig. 1 shows the generic patterns of golf shafts which are comprised of a double bias layer followed by the prepreg of a straight layer on the internal mandrel. As shown in Fig. 2, after the completion of laying-up, wrapping is required to maintain the pressure upon the shaft. Polypropylene tape is usually used for wrapping and the line pressure of the shaft is about 30\u201340 kgf/mm. Fig. 3 shows the curing process of the shaft in a hot-air oven. The hardening time in this process depends on the types of resin but the shaft used in this experiment was kept in an oven at 125 C for 90 min"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002434_0022-4898(91)90017-z-Figure8-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002434_0022-4898(91)90017-z-Figure8-1.png",
+        "caption": "FIG. 8. Diagram of measurement system.",
+        "texts": [
+            " Strain (Cauchy's infinitesimal strain) in the triangular elements formed by the centers of three mutually adjacent markers was calculated in the same manner as in the finite element method. The displacements of the centers of the markers were automatically depicted using computer graphics [10-12]. (8) Measuring system. Data from all sensors was input to a multi-channel data logger (scanning speed 100 msec/CH) with an analogue-to-digital converter and then transferred to the computer via a GPIB. Mechanical quantities (1)-(7) were analysed and displayed graphically on the on-line computer system. The whole measuring system of the test apparatus is schematically depicted in Fig. 8. Measured curves for each of the basic mechanical quantities of the traveling performance at 16.22% slip are shown in Fig. 9 as an example. At slip within the range from 0 to 15% the drawbar pull increased monotonically to a stable value. With slip higher than 15% the drawbar pull increased to a peak value, decreased to a minimum value, and then recovered to a plateau with some oscillations. This phenomenon became more pronounced as slip increased. The use of the linear bearings, with a frictional resistance between +5% of the contact load in the tests enabled the contact load to be maintained constant"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001376_s0967-0661(99)00084-2-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001376_s0967-0661(99)00084-2-Figure2-1.png",
+        "caption": "Fig. 2. The dynamic scheme of a remote-sensing spacecraft with a large-scale optical telescope.",
+        "texts": [
+            " The problem of unloading the moment gyrocomplex from the accumulated angular momentum is quite speci\"c for a low-orbital spacecraft since the aerodynamic disturbing torque is substantially larger than disturbances arising from the Earth's gravitational and magnetic \"elds. The open-loop control with respect to disturbances is intended for both regular compensation of the external disturbing torques, and for unloading the moment gyrocompelx. The mathematical model of manoeuvring spacecraft takes into account: f the controlled orbital motion of the spacecraft mass center; f the spatial angular motion of the spacecraft frame as a carrying rigid body; f movements of #exible solar array panels (P 1 , P 2 ) and receiving}transmitting antennas (A 1 , A 2 ), see Fig. 2, about the spacecraft body by means of 2-DOF suspension with the gear stepping drives; f movements of the moment dyrocomplex in the form of the `2-SPEEDa-type minimum-excessive scheme, see Fig. 5; moreover, the model of each gyrodine describes } the nonlinear dynamics of the control laws for current loops in the gyrorotor's 5-DOF electromagnetic suspension, see Fig. 7; } the proper gyrorotor rotation dynamics with regard to its static and dynamic unbalance; } the #exibility of gyroshell's preloaded ball bearings; } the #exibility, dead band and kinematic defects in the gear; } the dynamics of a stepping motor with a breaking up the step and an electromagnetic damper on the gyrodine precession axis that takes into account the dry friction torque; f the moment gyrocomplex \"xation on the spacecraft body by means of a vibration-absorbing frame; f external torques * aerodynamic, gravitational and magnetic; f the #exible-viscous \"xation of the optical telescope construction (in Ritchey}Chretien's optical scheme) on the spacecraft body, by means of a vibration-absorbing frame P, see Fig. 2, taking into account: } the #exibility of the \"xation of the telescope's main mirror M 1 into its frame F 1 ; } the #exibility of the telescope's tube T with blend B; } the movements of optical compensators K 0 (a sec- ondary mirror M 2 with respect to its frame F 2 ) and K 1 (a near-focal diagonal mirror about the frame F 1 ); } the nonlinear dynamics of the digital electro-mechanical micro-drive (12) with a precision screw gear and the \"ne piezo-ceramic micro-drive (7) (Somov, 1974), see also Fig",
+            " 5, bg p \"b p , p\"1, 2 and bg p \"p#b p , p\"3, 4; the angular rate vector x\"Mu i N and the symbols )3 , \" and [x]] are conventional notations; q\"Mq j N is a coordinate vector of the yexible oscillations of the spacecraft construction; H p (bg p )\"h g h p with a constant modulus of the proper angular momentum h g for each gyrodine, where Dh p D\"1 and H(bg) are the gyrodine and the gyrocomplex angular momentum's vectors; G is the angular momentum's vector of the `spacecraft together gyrocomplexa-system, and Go is its main component; the inertia matrixes Jo, Aq, D q , Ag and D g are constants; Qo(x, qR , q), Qq j ( ) ), Qg p (bg p , bQ g p , x) and also the electromagnetic damper' torques Mg dp (kg d , bQ g p ) with gain kg d are nonlinear continuous functions; the torques Mg fp of the rolling friction forces in the bearings on the gyrodine's precession axes are nonlinear discontinuous functions versus x, bg p , bQ g p and also versus b$ g p for the extended dexnition of the gyrodine's motion under bQ g p \"0; Mo d is the vector of an environment's external torques; functions Mg cp are components of the control vector Mg c which are gener- ated by electric gear stepping drives on a gyrodine's precession axes according to the digital command order vector uc(t)\"uc k \"const \u2200t3[t k , t k #\u00b9 u ), k3N, [0, 1, 22), where \u00b9 u is the period of the onboard computer control for the moment gyrocomplex. A state vector x of the #exible spacecraft with the optical telescope under its motion a(t), for an example on the pitch channel (see Fig. 2), has the form x\"Ma, qp, qa, qtN with subvectors qp\"Mqpk, k\"1, 2N, qa\"Mqan, n\"1,2N, qt\"Mao, ym 1 , am 1 , qT, qB, yp, ys, ak 0 , ak 1 N, qpk\"Mqpk s , s\"1 : npk q N, qan\"Mqan s , s\"1 : nan q N, qT\"MqT s , s\"1 : nT q N, qB\"MqB s , s\"1 : nB q N, where qp, qa and qt are the state vectors of solar array panels, highly directive receiving}transmitting antennas, and telescope. The mathematical model of the loworbital space telescope for its small movements on this channel has the form Ax(\"BxR #Cx\"F, (2) where vector F and matrixes A, B and C have the structure F\"MQ 0z , 0; 0; 0, 0, 0, 0; 0; 0, 0, Qk 0 , Qk 1 N, A\"C Jo z ap aa at (ap)T I n p q 0 0 (aa)T 0T I n a q 0 (at)T 0T 0T AtD, B\"v0; vvlpk s Xpk s y , k\"1, 2y , vvlan s Xan s y , n\"1, 2y ; Bty , C\"v0; vv(Xpk s )2yk\"1, 2y ; vv(Xan s )2yn\"1, 2y ;Cty, Bt\"Mt )Vt, Ct\"Mt )Wt, At\"Mt#A3 t \"C ko a8 om y aJ oma a8 oT a8 oB a8 oP y a8 oS y a8 ok 0 a8 ok 1 a8 om y km y 0 0 0 0 0 0 0 a8 oma 0 kma 0 0 0 0 0 0 (aJ oT)T 0T 0T vkT s y a8 TB 0 0 a8 Tk 0 (aJ oB)T 0T 0T (a8 TB)T vkB s y 0 0 0 0 a8 oP y 0 0 0T 0T kP y 0 0 0 a8 oS y 0 0 0T 0T 0 kS y 0 0 a8 ok 0 0 0 (aJ Tk)T 0T 0 0 kk o 0 a8 ok 1 0 0 0T 0T 0 0 0 kk 1 D Mt\"vk0, km y , kma , vkT s y ; vkB s y ; kp y , ks y , kk 0 , kk 1 y , Wt\"v(Xo)2, (Xm y )2, (Xma )2, v(XT s )2y ; v(XB s )2y ; (XP)2, (Xs)2, (Xk 0 )2, (Xk 1 )2y , Vt\"vloXo, lm y Xm y , lmaXma , vlT s XT s y ; vlB s XB s y ; lpXp, lsXs, lk 0 Xk 0 , lk 1 Xk 1 y , with the notation v)y,diagM ) N. In Eq. (2) a generalized moment Q oz is represented by a sum of moment gyrocomplex's control and disturbance torques, including the vibration torque caused by the unbalanced gyrodine rotors, with respect to the spacecraft pitch channel. Functions Qk s , s\"0, 1, are generalized control torques of the electromechanical and \"ne piezo-ceramic micro-drives for the optical compensators K 0 and K 1 , respectively in the optical telescope, see Fig. 2. Image motions dp z (t) in the light detector Pi of the telescope, see Fig. 2, and ds z (t) in the o!-set \"ne image motion sensor S1 (or dQ s z (t) in the o!-set \"ne image velocity sensor Sv) are formed in angular measure as dp z \"d o # o p yp; ds z \"d o #o s ys; d o \"Sq o , xJ o T, where xJ o \"Ma, ao, ym 1 , am 1 , qT, ak 0 , ak 1 N, qT\"MqT s , s\"1 : nT q N, q o \"Moa, oa o , oy m1 , oa m1 , qT, ok 0 , ok 1 N, qT\"MoT s , s\"1 : nT q N and constant `opticala coe$cients o with di!erent superscripts and subscripts are calculated on the basis of the optical telescope's parameters"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003554_13552540510601309-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003554_13552540510601309-Figure2-1.png",
+        "caption": "Figure 2 NVS and corresponding points",
+        "texts": [
+            " The points on the intersection contour between CAD model and horizontal plane were obtained by the application of a surface-plane intersection (SPI) algorithm (Choi, 1991). The algorithm has been explained in detail in the above reference and is not discussed here. Corresponding points of upper and lower slice In case of zero-order approximation, the cutter trajectory is always vertical while it may be slanted in case of first-order approximation. In the present case, with first-order approximation, the cutter trajectory is slanted and is considered to be contained in the normal vertical section (NVS) of the lower contour point (Figure 2). The NVS is a vertical plane that contains the normal to the surface at the point of consideration. This trajectory orientation of the cutting/depositing head has been adopted by a number of researchers in LM (Hope et al., 1996, 1997a; Kumar and Roy Choudhury, 2002; Gupta et al., 2004). In this case, once the lower contour point has been determined, the corresponding point on the upper contour needs to be found out. An algorithm has been implemented for this purpose and appended in Appendix 1 at the end of the paper"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000715_978-94-015-9064-8_33-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000715_978-94-015-9064-8_33-Figure1-1.png",
+        "caption": "Figure 1. Reciprocal screw systems of two dyads.",
+        "texts": [],
+        "surrounding_texts": [
+            "The screws and reciprocal screws associated with some frequently used joints are listed below: Revolute Joint. The unit screw associated with a revolute joint is a screw of zero pitch pointing along the joint axis. The reciprocal screws form a five system and, in particular, those zero-pitch reciprocal screws lie on all planes containing the axis of the revolute joint. Prismatic Joint. The unit screw associated with a prismatic joint is a screw of infinite pitch pointing along the direction of the joint axis. The reciprocal screws form a five-system and, in particular, those zero-pitch reciprocal screws lie on all planes perpendicular to the axis of the prismatic joint. Spherical Joint. The unit screws associated with a spherical joint form a three-system of zero pitch passing through the center of the joint. The reciprocal screws also form a three-system of zero pitch passing through the center of the sphere. Universal Joint. The unit screws associated with a universal joint form a two-system of zero pitch. It is a planar pencil radiating from the center of the universal joint and lying on a plane which contains the two axes of revolution. The reciprocal screws form a four-system. In particular, all zero-pitch reciprocal screws pass through the center of the universal joint, and there exists a reciprocal screw of infinite pitch which passes through the center of the universal joint and is perpendicular to both joint axes."
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0001882_s0003-2670(02)00603-7-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001882_s0003-2670(02)00603-7-Figure1-1.png",
+        "caption": "Fig. 1. (A) Schematic of the miniature Spreeta sensor. (B) Cross-sectional view of the test cell used for combined SPR/electrochemistry experiments.",
+        "texts": [
+            " Polycationic redox polymer, poly(vinylpyridine Os(bis-bipyridine)2Cl-co-allylamine) (PVP-Os-AA) was synthesized according to the procedures described previously [9,15]. Silicon wafers coated with Cr (20 \u00c5) and Au (500 \u00c5) were purchased from Lance Goddard Associates (Foster City, CA). The Spreeta sensor, a miniature (approximately 7 g), fully integrated surface plasmon resonance device produced by Texas Instruments, was described in detail elsewhere [16,17]. Briefly, the sensor possesses a light-emitting diode with a wavelength of 825 nm, a polarizer, a thermistor, and two 128-pixel silicon photodiode arrays (EOC 1401). A schematic of the device is shown in Fig. 1A. All components are seated on a small printed circuit board and encapsulated with clear, optical epoxy (index of refraction of 1.52), molded to have optically flat surfaces. Because the system was fully encapsulated, no optical alignment is necessary. The molded epoxy is shaped in the form of the Kretschmann geometry prism to facilitate the excitation and detection of surface plasmon resonance. The surface plasmon resonance glass sensing side of the sensor was modified with 10\u201320 \u00c5 chromium adhesion layer evaporated onto the surface, followed by the evaporation of 500 \u00c5 of gold onto the chromium",
+            " A small flow cell was attached to the sensor to enable the delivery of solutions across the sensing surface. In the electrochemical experiments, the gold surface of the SPR substrate also serves as the working electrode. Electrical contact with the gold surface was realized by attaching a wire via conductive silver epoxy with the contact shielded from water. Additional Ag/AgCl reference and Pt counter electrodes were introduced at the top of the flow cell to create a three-electrode configuration (Fig. 1B). Each experiment was performed with a new Au surface. Before starting an experiment, the gold surface of the SPR substrate was thoroughly cleaned using a cotton tip, dipped in 0.1% Triton and followed by immersion in 0.12 N NaOH to remove organic residues on the Au surface. The flow cell was assembled and system was flushed first with ethanol, then with DI water, 0.1% Triton and 0.12 N NaOH solution followed by DI water again. For all experiments, the flow cell was equilibrated in running PBS buffer until a stable baseline SPR signal was obtained",
+            " This hypothesis is supported by FT-IR\u2013ERS (which has depth of penetration of several micrometers) experiments presented later in this manuscript, as well as results obtained by others [10,24], where proportional increase in the amount of enzyme with increasing number of composite layers was observed. In order to verify, in situ, analyte-dependent activity of the glucose oxidase\u2013redox polymer nanostructured films, the SPR test cell was modified with counter and reference electrodes while SPR sensing surface served as a working electrode (see Fig. 1B for details). Substrate calibration curves were then obtained by introducing varying concentrations of glucose into the SPR flow cell and measuring the amperometric response of the sensing films by means of the potentiostat. The sensor response was found to be linear for glucose concentrations ranging from 1 to 10 mM with sensitivity of 0.197 A/cm2/mM. These results compare favorably with amperometric responses observed in our previous studies of the similar sensing system [25]. SPR analysis was also employed to conduct structural stability studies of the assembled three-bilayer nanocomposite films"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002606_iros.1997.655141-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002606_iros.1997.655141-Figure4-1.png",
+        "caption": "Figure 4: interpretat ion plane",
+        "texts": [
+            " Expressing Qfj in the robot world coordinate frame will lead the unknown transformations X and T to appear in (11). We have : Rewriting (13) with the notations introduced in section 2.1 causes the rotational and translational parts of the homogeneous transformations to appear explicitly in the equations. Then we have : Substituting this into (12) we have : For each image and for each 3D point of the calibration target, we can define an interpretat ion plane -+ Q\u2018. 23 = [(RhRx) .nfj]. [Rt .Pj\u201d +Z - l i h .T, - T h ] (16) (see fig.4). Let\u2019s P; and Pj be two 3D points of the calibration object and pi and p j their projective projections. pi and p j belong to the image plane. The interpretat ion -+ where n:j are computed from the image points, Pj\u201d are the tetrahedron 3D points and Rh and T h are given by the robot encoders outputs for each position k. 1061 For one station of the gripper, we can write 20 equations of the form (16). Thus, we obtain a total of (20 x n = N ) equa.tions for a series of n stations. Solving for the transformations X and T is then equivalent to minimize the positive error function : with respect to 0 (a,, p,, 7,) Euler's angles of R,, e (U,, U,, w,) components of T, , 0 (at , Pt rt) Euler's angles of Et, 0 (u t , vt , wt) components of Tt "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001351_s0734-743x(97)00033-x-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001351_s0734-743x(97)00033-x-Figure1-1.png",
+        "caption": "Fig. 1.",
+        "texts": [
+            " Mech. Eng. Sci. 17 (1975) 71-81-1. The equation of motion in the plane of the trajectory at an instant for a sphere of mass M during its encounter and partial immersion in a stationary mass of water is My 2 d2/ds = L - Mg cos )~. (d2/ds, is the curvature of the projectile path). The first term on the left above is the centripetal force on the sphere, L is the impact lift force on the body and M g its gravitational weight. 2 is the inclination of the velocity of the sphere to the horizontal, see Fig. 1. In this analysis we assume a relatively high speed of ricochet for which the projectile weight may be neglected. Two assumptions among many others are made, all questionable; (i) The pressure p on a spherical surface element along its outward drawn normal is puZ/2; u is the forward speed of the sphere resolved along the normal. (ii) The pressure applies only to those parts of the sphere which are immersed below the undisturbed surface of the water. The effect of the splash on the sphere is considered not to contribute any pressure"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003904_analsci.22.35-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003904_analsci.22.35-Figure1-1.png",
+        "caption": "Fig. 1 Pictures of the proposed FIA/ECD device specifically designed for SPEs.",
+        "texts": [
+            " 472) was used for the carbohydrate separation. A Cu layer was electrochemically plated on a SPCE in 200 mg/L Cu(NO3)2 + 0.1 M HNO3 solution at \u20130.7 V vs. Ag/AgCl for 300 s under photo-illumination to prepare the Cu-SPCE, as per our perviously reported procedure.21 The SPCEs were first washed thoroughly with deionized water, and then dipped into working solution for electrochemical experiments. As to FIA, the SPCEs can simply slide into the holding trail and the device was locked as illustrated in Fig. 1. Note that the outlet system also serves as a counter electrode. More details about the design will be discussed in a later section. Fifteen blood samples were collected from laboratory volunteers for real sample analysis. The plasma sample was prepared as follows: 2 mL of the blood was centrifuged at 2000 rpm for \u223c10 min in room temperature and the upper solution was then used for analysis in FIA. Samples were diluted by 200 times with 0.1 M NaOH prior to the injection. Figure 1 sketches different structural views of the proposed button-and-lock-type assembly specifically designed for disposable SPEs in FIA. The device contains two major parts: (1) a tray-cavity arrangement to drag the working SPE inside the assembly and (2) a pre-drilled T-like assembly to hold the stainless-steel inlet, outlet, and reference electrode in position. An \u201cO ring\u201d is suitably fixed on the center to cover the SPE inside the working space. The wall-jet design through the center micro-hole can then guide the inlet portion to have a proper function on the SPE"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure1.4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure1.4-1.png",
+        "caption": "Figure 1.4. A quick return mechanism.",
+        "texts": [
+            "18) shows that even at the moment of coincidence the velocity and acceleration * The angular acceleration vector ro will be defined later on; in general, its magnitude is not equal to the magnitude of the simple angular acceleration. Kinematics of a Particle 13 relative to the two frames differ. We shall learn in Chapter 4 how the velocities and accelerations relative to different frames moving in space are related through the rates of change of direction of their rotating basis vectors. D Example 1.5. The mechanism shown in Fig. 1.4a consists of a drive crank AB that rotates at a constant angular speed a= w, while the arm OBP oscillates about the hinge pin at 0 at a varying angular rate !3. The slider block at B is attached to the crank ABby a hinge pin and it drives the arm OBP. A pinned pair of slider blocks at P allows the assembly to slide in the arm 0 BP and in a horizontal guide H P. As AB rotates around the circle BCD, a cutting tool (not shown) attached to P moves in the cutting stroke from its extreme right position to its extreme left position while B moves along the arc DTC",
+            " For this reason the device is called a quick return mechanism. Find the velocity and acceleration of the point P in c[J = { 0; ik}, and compare the time required for the return stroke to the time expended in the cutting stroke. Solution. Since P is constrained by the horizontal guide, its position vec tor in c[J is x(P, t) =xi+ 4aj. Hence, the velocity ( 1.11) and the acceleration (1.12) are given by v(P, t)=i:i, a(P, t)=xi. (1.19) 14 Chapter 1 We must now express x in terms of the angle ex whose variation is known, using the assigned geometry shown in Fig. 1.4b. By the property of similar triangles OEB and OHP, we see that x a sin y sin ex 4a 2a + a cos y 2 - cos ex' wherein y = n- ex is used. Hence, x(t) is expressed m terms of the angular position ex( t ): 4asinet:(t) x(t) = . 2- cos ex(t) ( 1.20) A little patience with the differentiation of ( 1.20) and use of ( 1.19) yields even tually 2 cos ex- 1 . v(P, t) = 4aw (2 )2 I, -cos ex (1.21a) ( ) __ 8 2 sin ex( 1 + cos ex) \u2022 a P, t - aw 2 )' I, ( -cos ex \u00b7 (1.21b) in which w = i denotes the known constant angular speed of the drive crank. We note from (1.21a) that Pis at its extreme positions when v(P, t)=O. This happens when cos ex= 1/2. Thus, in this design C and D are 60\u00b0 from the vertical line AG. This is also evident from the assigned geometry in Fig. 1.4. Since the 1200 arc from C to D through G is one-half as far from D to C through T, and because w is constant, it is easy to see that the time t, required for the return stroke is equal to one-half the time tc expended in the cutting stroke: t, = tc/2. This characterizes the quick return efficiency of this mechanism. A graph of the dimensionless cutter velocity v P ..;- ( 4aw) as a function of the drive crank angle ex is shown in Fig. 1.5. The quick change in the velocity Vp 2cosa-1 4aw = (2 -cos tx) 2 ' Kinematics of a Particle 15 during the return stroke CGD is evident; in fact, the tangent line to the curve at a= n/3 makes an angle of -37"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000385_s0045-7949(98)00165-5-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000385_s0045-7949(98)00165-5-Figure2-1.png",
+        "caption": "Fig. 2. Plane shell composite triangle.",
+        "texts": [
+            " (14) has been performed in this work using the standard Newmark algorithm [9]. The previous plate triangle can be extended to the case of laminated shells. First it is necessary to consider \u00aerst the kinematics of the element, which is de\u00aened with respect to a local cartesian axes system x 0, y 0, z 0. The local axes x 0 and y 0 de\u00aene the directions of the inplane displacements u 0, v 0, whereas z 0 de\u00aenes the normal displacement w 0. Once the sti ness matrix is obtained in this local system, it is transformed to global axes (Fig. 2) in the usual way. As in the plate's case it is possible to de\u00aene n analysis layers and n + 1 interfaces. The displacements u 0, v 0 in the element plane corresponding to the kth layer are interpolated by [1\u00b13]: u 0 v 0 X3 i 1 Ni x; Z u 0oi v 0oi Nk z u 0ki v 0ki Nk 1 z u 0k 1i v 0k 1i ( )24 35 X6 i 4 Ni x; Z ei\u00ff3 Nk z Dukti Nk 1 z Duk 1ti h i 16 where u 0oi v 0 oi n o are constant (rigid-body) in-plane displace- ments across the thickness of the laminate, u 0ki v 0k i n o are the in-plane displacements which are variable over the thickness and Dukti are the in-plane displacement increments in the midside nodes of the triangle in the directions de\u00aened by the tangent vectors ei \u00ff 3 (Fig",
+            " The local displacements a 0 are transformed to global axes by a 0 Ta 22a where a ak ak 1 a0 8<: 9=; 22b and ak h u k 1 ; v k 1 ;w k 1 ; u k 2 ; v k 2 ;w k 2 ; u k 3 ; v k 3 ;w k 3 ;Du k t4;Du k t5;Du k t6 iT a0 u01; v01;w01; u02; v02;w02; u03; v03;w03 T 22c where the transformation matrix is given by T T\u0302 0 0 0 T 0 0 0 T 0 264 375 with T\u0302 T\u0302 0 0 0 I3 \" # 23 where T\u00c3 is the I3 identity 3 3 matrix and T\u03020 T 0 T 0 T 24 35; T lx 0x lx 0y lx 0z ly 0x ly 0y ly 0z lz 0x lz 0y lz 0z 24 35 24 and lx 0x is the cosinus of the angle between axes x 0 and x etc. (Fig. 2). The global sti ness matrix for the kth layer is obtained by the standard transformation K e TT K 0 e T 25 where the local sti ness matrix is given by K 0 e A e BT DBdV 26 where B Bb Bs n o and D is the local constitutive matrix for orthotropic materials [1\u00b13]. A more detailed version of the local sti ness matrix K 0(e) is given in Appendix E. As in the case of multilaminated plates, it is necessary to de\u00aene a unique direction for the transverse shear over the common side of two adjacent elements"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003465_00423110600871533-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003465_00423110600871533-Figure2-1.png",
+        "caption": "Figure 2. Geometrical virtual interpenetration of a wheel in a rail in Hertzian (a) and non-Hertzian (b) conditions.",
+        "texts": [
+            " A method that made it possible to obtain non-elliptical patches without losing too much computation time was first proposed [6]. The semi-Hertzian method is affiliated to this method where rail profile is divided in narrow strips, each having constant curvatures. The normal contact problem is then solved by assigning to each strip a given stiffness, the normal load being counterbalanced by the summation of elastic forces on the loaded strips, which depends only on the (virtual) interpenetration of the wheel inside the rail. The geometrical interpenetration is shown in figure 2(a) in a Hertzian case: the intersection is then elliptical. Figure 2(b) shows the case of profiles exhibiting non-constant curvatures: the intersection is no more elliptical. The tangent problem may be solved either later by an alternate Fastsim algorithm extended to non-elliptical patches [3] or via an approximate analytical solution. This latter approach, the so-called Chopaya formula, through introducing some approximations, allows a direct solution of the whole contact problem inside the time integration loop, which is not possible with the iterative Fastsim algorithm"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002766_j.ijmecsci.2003.09.004-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002766_j.ijmecsci.2003.09.004-Figure3-1.png",
+        "caption": "Fig. 3. Model of the system assumed for calculations.",
+        "texts": [
+            " (3) and making use of the theorem of the function convolution, a function of rheological strain of the ground in the form of Duhamel\u2019s integral of the form was obtained: y(t) = H (t) \u222b t 0 Q(t) exp [ \u22121 (t \u2212 ) ] d ; (4) where H (t) is Heaviside function. Sample courses of the rheological strain of the ground\u2014=ne-grain sand of a density d=1:56 g=cm3, obtained from the experiments for a variable pressure force (v Lsr = 120 N=s), and from theoretical calculations are presented in Fig. 2 [2]. For the dynamic description of an excavator during the digging of the ground, a discrete physical model has been assumed as a spatial system of masses appropriately joined to one another [8]. In the model shown in Fig. 3, the following masses, constituting components of the excavator, have been identi=ed: m1\u2014 the chassis mass as a rigid solid resting with the caterpillars on a deformable soil foundation, m2\u2014 the body mass as a rigid solid joined to the chassis, capable of making rotational motion with respect to the chassis, m3\u2014 the excavator jib mass as a rigid element joined to the body by means of a cylindrical joint (point A in Fig. 3), m4\u2014 the excavator arm mass as a rigid element lying in the same plane as the jib and joined to it by means of a cylindrical joint (point B in Fig. 3), m5\u2014 the excavator shovel mass as a rigid element joined to the arm by means of a cylindrical joint and lying in the same plane as the jib and the arm (point C in Fig. 3). The excavator is resting on a deformable soil foundation, whose strain resulting from the pressure of rigid caterpillars on the ground has been described by a Kelvin\u2013Voight rheological model. Basing on the results of the experimental investigations, it has been assumed that the ground is an almost plastic material, which means that during the unloading of the deformed ground, the ground does not expand but remains in the deformed state. The dynamics of motion of the discrete excavator model was described by Lagrange equations of the second order, whose general form in the generalized coordinates is presented by the equation: d dt ( @T @q\u0307i ) \u2212 @T @qi + @D @q\u0307i = Qi \u2212 @V @qi (5) for i = 1; : : : ; 6",
+            "z1 ] T + [0 0 \u0307]T (17) the transformation matrices have the form: A1 =   cos\u20192 cos\u20193 \u2212sin\u20193 cos\u20192 sin\u20192 sin\u20193 cos\u20191 +cos\u20193 sin\u20192 sin\u20191 cos\u20193 cos\u20191 \u2212 sin\u20191 sin\u20192 sin\u20193 \u2212cos\u20192 sin\u20191 sin\u20191 sin\u20193 \u2212cos\u20193 cos\u20191 sin\u20192 cos\u20193 sin\u20191 +sin\u20193 cos\u20191 sin\u20192 cos\u20192 cos\u20191   ; (18) A2 =   cos \u2212sin 0 sin cos 0 0 0 1   : For small oscillation angles \u20191; \u20192; \u20193, the body energy is T2 = 1 2 m2[(vS2) 2 x0 + (vS2) 2 y0 + (vS2) 2 z0 ] + 1 2 Jx2 [(\u2019\u03071 + \u2019\u03072\u20193) cos + (\u2019\u03072 \u2212 \u2019\u03071\u20193) sin ]2 + 1 2 Jy2 [(\u2019\u03072 \u2212 \u2019\u03071\u20193) cos \u2212 (\u2019\u03071 + \u2019\u03072\u20193) sin ]2 + 1 2 Jz2 [(\u2019\u03073 + \u2019\u03071\u20192) + \u0307]2; (19) where components of the liner velocity of the centre of mass of a body S2 in the constant system of axes have the value: (vS2)x0 = x\u0307 + \u2019\u03072h2 + \u2019\u03073b2; (vS2)y0 = y\u0307 + \u2019\u03071\u20191b2 + \u2019\u03073\u20193b2 \u2212 \u2019\u03071h2; (vS2)z0 = z\u0307 \u2212 \u2019\u03071(b2 + \u20191h2) \u2212 \u2019\u03072(h2\u20192 + b2\u20193)h2 \u2212 \u2019\u03073\u20192b2: (20) It has been assumed that the excavator has a symmetry plane y1z1 (Fig. 3). In this plane the position of the centre of mass of the body with respect to the centre of mass of the chassis, in the horizontal direction\u2014b2 and in the vertical direction h2. The kinetic energy of a jib of a mass m3 is T3 = 1 2 [vT S3 m3vS3 + !T 3J3!3]; (21) where vS3 = vS2 + A1[A2[!2 \u00d7 rA]T]T + A1[A2[A3[!3 \u00d7 r3]T]T]T; !3 = AT 3 [!x2 !y2 !z2 ] T: (22) The transformation matrix has the form A3 =   1 0 0 0 cos 1 \u2212sin 1 0 sin 1 cos 1   : (23) By putting relationships (22) in the expression describing the kinetic energy of the jib (21) we obtained T3 = 1 2 m3[(vS3) 2 x0 + (vS3) 2 y0 + (vS3) 2 z0 ] + 1 2 Jx3",
+            "3 in the system of axes related to the jib have the value: (vS3)x0 = x\u0307 + \u2019\u03072w1 + \u2019\u03073b2 \u2212 (\u2019\u03073 + )w2 cos + (\u2019\u03073 + )\u20193w2 sin + \u2019\u03072\u20192w2 sin ; (vS3)y0 = y\u0307 + \u2019\u03071\u20191(b2 \u2212 w2 cos ) + \u2019\u03073\u20193b2 \u2212 (\u2019\u03073 + )\u20193w2 cos \u2212 \u2019\u03071w1 \u2212 \u2019\u03071\u20192w2 sin \u2212 (\u2019\u03073 + )w2 sin \u2212 \u2019\u03072\u20191w2 sin ; (vS3)z0 = z\u0307 \u2212 \u2019\u03071b2 \u2212 \u2019\u03071\u20191w1 \u2212 \u2019\u03072\u20192w1 \u2212 \u2019\u03072\u20193b2 \u2212 \u2019\u03073\u20192b2 + (\u2019\u03073 + )\u20192w2 cos \u2212 (\u2019\u03073 + )\u20191w2 sin + (\u2019\u03071 + \u2019\u03072\u20193)w2 cos + (\u2019\u03072 + \u2019\u03071\u20193)w2 sin ; (25) !x3 = (\u2019\u03071 + \u2019\u03072\u20193) cos + (\u2019\u03072 \u2212 \u2019\u03071\u20193) sin ; !y3 = [(\u2019\u03072 \u2212 \u2019\u03071\u20193) cos \u2212 (\u2019\u03071 + \u2019\u03072\u20193) sin ] cos 1 + [(\u2019\u03071\u20192 + \u2019\u03073) + \u0307] sin 1; !z3 = \u2212[(\u2019\u03072 \u2212 \u2019\u03071\u20193) cos \u2212 (\u2019\u03071 + \u2019\u03072\u20193) sin ] sin 1 + [(\u2019\u03071\u20192 + \u2019\u03073) + \u0307] cos 1; (26) w1 = h2 + h3 + h4 cos 1 + b4 sin 1; w2 = b3 \u2212 h4 sin 1 + b4 cos 1; (27) where b3 and h3 are coordinates, the horizontal and vertical, respectively, of the position of a joint A of the mounting of the jib to the body, with respect to the centre of mass of the body in the plane y2z2 (Fig. 3), while b4 and h4, are coordinates of the position of the centre of mass of the jib S3 with respect to joint A in the plane y3z3 (Fig. 3). The kinetic energy of the arm of a mass m4 is T4 = 1 2 [vT S4 m4vS4 + !T 4J4!4]; (28) where vS4 = vS2 + vA=S2 + vB=A + vS4=B; vA=S2 = A1[A2[!2 \u00d7 rA]T]T; vB=A = +A1[A2[A3[!3 \u00d7 rB]T]T]T; vS4=B = A1[A2[A3[A4[!4 \u00d7 r4]T]T]T]T; !4 = AT 4 [!x3 !y3 !z3 ] T: (29) The transformation matrix has the form: A4 =   1 0 0 0 cos 2 sin 2 0 \u2212sin 2 cos 2   : (30) Putting relationships (29) into the expression describing the kinetic energy of arm (28) we obtained T4 = 1 2 m4[(vS4) 2 x0 + (vS4) 2 y0 + (vS4) 2 z0 ] + 1 2 Jx4",
+            "z3 = \u2212[(\u2019\u03072 \u2212 \u2019\u03071\u20193) cos \u2212 (\u2019\u03071 + \u2019\u03072\u20193) sin ] sin( 1 \u2212 2) + [(\u2019\u03071\u20192 + \u2019\u03073)+ \u0307] cos( 1 \u2212 2); w3 = h2 + h3 + lw sin 1; w4 = b3 + lw cos 1; w5 = h5 cos 1 + b5 sin 1; w6 = h5 sin 1 \u2212 b5 cos 1; k1 = w3 + w5 cos 2 + w6 sin 2; k2 = (w4 \u2212 w6 cos 2 + w5 sin 2) cos ; k3 = (w4 \u2212 w6 cos 2 + w5 sin 2) sin ; k4 = (w5 cos 2 + w6 sin 2) sin ; k5 = (w5 cos 2 + w6 sin 2) cos ; k6 = w6 cos 2 \u2212 w5 sin 2; (33) where b5 and h5 are coordinates of the position of the centre of mass S4 with respect to joint B, in the plane y4z4 (Fig. 3), while lw is the distance of joint B of the mounting of the arm and the jib from joint A of the mounting of the jib on the body. The kinetic energy of a bucket of a mass m5 is T5 = 1 2 [vT S5 m5vS5 + !T 5J5!5]; (34) where vS5 = vS2 + vA=S2 + vB=A + vC=B + vS5=C ; vC=B = A1[A2[A3[A4[!4 \u00d7 rC]T]T]T]T; vS5=C = A1[A2[A3[A4[A5[!5 \u00d7 r5]T]T]T]T]T; !5 = AT 5 [!x4 !y4 !z4 ] T: (35) The transformation matrix has the form A5 =   1 0 0 0 cos 3 sin 3 0 \u2212sin 3 cos 3   : (36) Inserting relationships (35) in the expression describing the kinetic energy of bucket (34) we obtained T5 = 1 2 m5[(vS5) 2 x0 + (vS5) 2 y0 + (vS5) 2 z0 ] + 1 2 Jx5",
+            "z5 = [(\u2019\u03072 \u2212 \u2019\u03071\u20193) cos cos 1 \u2212 (\u2019\u03071 + \u2019\u03072\u20193) sin cos 1 + (\u2019\u03071\u20192 + \u2019\u03073 + \u0307) sin 1] \u00d7sin( 2 + 3) \u2212 [(\u2019\u03072 \u2212 \u2019\u03071\u20193) cos sin 1 \u2212 (\u2019\u03071 + \u2019\u03072\u20193) sin sin 1 \u2212 (\u2019\u03071\u20192 + \u2019\u03073 + \u0307) cos 1] cos( 2 + 3); (38) w7 = lr sin 1; w8 = lr cos 1; w9 = h6 cos 1 + b6 sin 1; w10 = h6 sin 1 \u2212 b6 cos 1; k7 = w3 \u2212 w8 sin 2 + w7 cos 2 + w9 cos( 2 + 3) + w10 sin( 2 + 3); k8 = w4 + w8 cos 2 + w7 sin 2 + w9 sin( 2 + 3) \u2212 w10 cos( 2 + 3); k9 = w8 sin 2 \u2212 w7 cos 2; k10 = w9 cos( 2 + 3) + w10 sin( 2 + 3); k11 = w7 sin 2 + w8 cos 2; k12 = w10 cos( 2 + 3) \u2212 w9 sin( 2 + 3); (39) where b6 and h6 are the coordinates of position of the centre of mass of the bucket S5 with respect to joint C, in the plane y5z5 (Fig. 3), while lr is the distance of joint B of the mounting of the arm and the jib, from the joint C of the mounting of the arm and the bucket. The total kinetic energy of the excavator model considered in a constant system of coordinate axes is T = T1 + T2 + T3 + T4 + T5: (40) The potential energy V (q) of the whole system is a sum of the potential energy of masses in the gravitational =eld Vg(q) and the potential energy of the viscoelastic strain of the soil foundation Vs(q): V (q) = Vg(q) + Vs(q): (41) According to the assumed constant system of coordinate axes xo; yo; zo, vectors of position of centres of gravity of individual masses, with a non-deformed soil foundation, were determined",
+            " Numerical data characterizing a single-bucket excavator on a caterpillar chassis of a bucket capacity of 1:10 m3 and soil foundation of mechanical properties corresponding to =ne-grained cohesive, consolidated soils of modulus of strain E = 10 MPa [4], were applied. \u2022 Basic numerical data are as follows: \u2022 The chassis mass m1 = 11 000 kg. \u2022 The body mass m2 = 6000 kg. \u2022 The jib mass m3 = 3500 kg. \u2022 The arm mass m4 = 1200 kg. \u2022 The bucket mass m5 = 900 kg. \u2022 The length of the jib (the distance AB between the joints mounting the jib with the body and the arm, Fig. 3) lw = 4:4 m. \u2022 The length of the arm (the distance between the joints BC Fig. 3) lr = 2:1 m. \u2022 The distance of the bucket edge K from the mounting joint C (Fig. 4) ll = 1:2 m. \u2022 The width of the caterpillars a = 0:5 m. \u2022 The length of the caterpillars b = 2:8 m. \u2022 The caterpillar track a1 = 2:0 m. \u2022 The equivalent rigidity of a soil foundation in the vertical direction cz = 9; 550; 000 (N=m2)=m. \u2022 The equivalent rigidity of a soil foundation in the horizontal direction cx = cy = 4; 000; 000 N=m. \u2022 The equivalent viscosity of a soil foundation Rx = Ry = Rz = 250 kNs=m. \u2022 The calculations were made for the process of getting a soil with a bucket and with an arm and a bucket"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000888_s1350-6307(98)00024-7-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000888_s1350-6307(98)00024-7-Figure1-1.png",
+        "caption": "Fig[ 1[ Sketch of the bearing assembly[",
+        "texts": [],
+        "surrounding_texts": [
+            "(a)\n(b) Fig[ 0[ \"a# The plane after the accident[ \"b# Bearing components on the compressor shaft after the accident[\nTable 0[ Chemical composition of the di}erent parts of the CMB\nComposition wt[) of components\nElement Cage Balls Inner race Outer race Bearing lock\nCr * 0[5629[01 0[6529[00 0[5229[91 0[9529[05 Mn 0[2229[01 9[3929[09 9[2629[96 9[1429[94 9[5929[96 Si * 9[1429[93 9[2929[98 9[2429[04 9[1729[95 C * 9[8129[90 0[9129[90 9[8729[90 9[2629[90 S * 9[990 9[992 9[990 9[991 Al 6[7129[01 * * * 9[3329[95 Cu Bal[ * * * * Fe 0[5129[96 Bal[ Bal[ Bal[ Bal[ Material QAl09!2!0[4$ AISI 41099 AISI 41099 AISI 41099 27 Cr Al$\n$ Closest standard[\n1[0[ After the accident\nExamination of the compressor region revealed that the cage was broken and signi_cantly deformed[ The inner and outer races were put together with the cage and the probable con_guration",
+            "of bearing components after mishap is shown in Fig[ 2a[ The compressor and then the CMB components were disassembled^ the latter were retrieved in a severely distressed condition[ The condition of the retrieved components was compared with ones which were in normal use in another engine[ The retrieved cage compared with a new one is shown in Fig[ 2b[ A detailed study of the retrieved components was conducted using stereo\\ optical and electron microscopes to establish the mechanism of damage[ Detailed views of the sections of interest of each component are discussed in the following with the help of the micrographs in Fig[ 3[\nThe worst condition was that of the cage^ Fig[ 3a!i[ Its outer surface is compared with that of another used cage[ During the accident the cage was fractured and the results of fractography are discussed in Section 2[ The inner surface of the cage\\ as evident from the crushed hole peripheries in Fig[ 3a!ii\\ had been severely deformed by the hard Cr!steel bearing balls[\nIn Fig[ 3b!i the inner surfaces of the retrieved outer races are shown where signi_cant deformation and smearing is visible[ The sections of the edges of a used and of a retrieved outer race are compared in Fig[ 3b!ii and b!iii[ The cross sections of the edges clearly show extensive deshaping indicating high stresses acting on them^ this is quite signi_cant on the left!hand side \"LHS# edge shown in Fig[ 3b!iv[\nThe photograph in Fig[ 3c!i shows delamination of surface layers of the steel inner race[ It can be seen\\ at a higher magni_cation in Figs 3c!ii and c!iii\\ that a layer of the cage material was smeared on the surface and the subsequent deformation was so severe that inner race material covered it up\\ sandwiching the cage material completely[\nThe view of the left and right edges in Fig[ 3c!iv was obtained following necessary sectioning of the component[ The degree of deformation is compared with the edges of another used inner race in Fig[ 3c!v[ A closer look at the edges in Fig[ 3c!vi shows serious deshaping of the edges[ It is noted that LHS edges of the inner and the outer races were much more deformed than the respective RHS edges[",
+            "The rolling elements\\ Cr!steel balls\\ also experienced severe deformation and wear^ see Fig[ 3d!i[ One of these balls\\ which was stressed to a relatively small extent was sectioned to study the locations where stresses were overbearing[ The etched sample in Fig[ 3d!ii shows a band of the stressed region which is \u00bd3 mm wide and generated while the ball was rolling[\nTo summarize the above observations\\ the inner and one of the outer races of the retrieved bearing were heavily deformed from one side[ The o}!center extensive deformation indicates high stresses operating in these areas prior to the failure[ The inner and outer races put together with the cage in Fig[ 2a show the probably con_guration in which the cage broke and was trapped between the balls and the races[ The balls shifted towards one side and severely deformed the races[ The function of the bearing was impaired resulting in the air crash[ The observations concerning the deformation and smearing of the components are sketched in Fig[ 3e to show the possible position and condition of the bearing components just before the accident[\n1[1[ Material of CMB components\nThe chemical analysis of di}erent parts of the bearing was carried out using energy dispersive X! ray analysis \"EDX#\\ atomic absorption spectroscopy \"AAS# and carbon:sulphur \"C:S# analyzer[\nThe cage is fabricated from a Cu\u00d0Al alloy^ its chemical composition is summarized in Table 0["
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure2.13-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure2.13-1.png",
+        "caption": "Figure 2.13. A cam-driven linkage mechanism design.",
+        "texts": [
+            " 0 Industrial design problems usually involve integration of several design concepts, technical analyses, and a variety of manufacturing procedures assembled to create some product or system; and it is customary that several parts of a product or a manufacturing system must be analyzed and designed at the same time to accommodate certain specified criteria. The simple mechanical design problem iiiustrated in the next example integrates an easy cam design analysis with the design of a link mechanism so that both parts satisfy specified design conditions for a particular set of system parameters. Example 2.4. The shuttle mechanism of a certain sewing machine described in Fig. 2.13 is driven by a cam that rotates with a constant angular velocity ro = wk, while a linkage arrangement moves the shuttle, slider block B, in a fixed vertical slot in the machine. The cam must be designed for the geometry shown in Fig. 2.13 so that the shuttle drive block A has a sinusoidal velocity v A = 6 sin 8 i cmjsec, and the length I of the link AB must be chosen so that the link has no angular acceleration at the instant ! 0 when the device is in the configuration where ,P = 30\u00b0 when 8 = 60\u00b0. Find the shape of the cam and the angular speed at which it must operate, and determine the link length l needed for the design specifications. Determine the velocity and the acceleration of B at the instant t0 . Assume that 8 = 0 initially"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002485_1.1902843-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002485_1.1902843-Figure1-1.png",
+        "caption": "Fig. 1 Flexible-link robot with its conventional link deflection model",
+        "texts": [
+            " Then a new dynamic Contributed by the Dynamic Systems, Measurement, and Control Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received June 24, 2003; final manuscript received December 12, 2003. Review conducted by: Yidirim Hurmuzlu. Paper number: DS-03-1178. Copyright \u00a9 20 rom: http://dynamicsystems.asmedigitalcollection.asme.org/ on 01/28/2016 model is derived and shown to describe the dynamic characteristics of a real flexible-link robot. Finally, in Sec. 4, the conclusions are drawn for this study. 2.1 Summary of Dynamic Modeling. Figure 1 shows the conventional coordinate system of a one-link flexible robot with its link deflection model, where x, u, wsx , td, and t are the position along the link of length l, joint angle, link deflection, and joint torque, respectively. X0Y0 and X1Y1 are the inertial and rotating frames, respectively. In this link deflection model, the link deflection wsx , td results in free link elongation. The links of a flexible-link robot are modeled as Euler\u2013 Bernoulli beams, and hence they have infinite number of natural modes of vibration, resulting in an infinite-dimensional dynamic model for the flexible-link robot",
+            " This infinite-dimensional dynamic model can be discretized to a finite-dimensional dynamic model of order n via the so-called assumed mode method f10g, for which the link deflection wsx , td is approximated as wsx,td = fsxdTdstd , s1d where t is the time; fsxd is the n31 shape function vector; dstd is the n31 modal displacement vector. Each element of fsxd is subject to geometric boundary conditions at the joint and dynamical boundary conditions at the free end f7\u20139g. The finite-dimensional dynamic model of a flexible-link robot can be derived following the Lagrangian approach. The first step is to find a position vector psu ,x ,wd in the inertial coordinates denoting the end point of the deflection vector wsx , td. From Fig. 1, psu,x,wd = scos ux \u2212 sin uwdi\u0304 + ssin ux + cos uwd j\u0304 , s2d where i\u0304 and j\u0304 are the base vectors of the inertial coordinates X0 and Y0, respectively. Then the square of the velocity at the end point of the deflection vector wsx , td is computed as p\u0307Tp\u0307 = sx2 + w2du\u03072 + w\u03072 + 2xw\u0307u\u0307 , s3d with which the Lagrangian L f10g is obtained as L = 1 2SJhu\u03072 +E 0 l rp\u0307Tp\u0307dx + Mpp\u0307l Tp\u0307l + Jpsu\u0307 + w\u0307l8d 2D \u2212 1 2E 0 l EIsw9d2dx , s4d where Jh, Mp, and Jp are the joint mass moment of inertia, payload mass, and payload mass moment of inertia, respectively; r is the mass per unit length of the link; E is the Young\u2019s modulus of link material; I is the area moment of inertia of link cross section"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001183_s0020-7683(00)00010-x-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001183_s0020-7683(00)00010-x-Figure1-1.png",
+        "caption": "Fig. 1. Loading and deformation of the viscoelastic column at (a) upper end and (b) middle section.",
+        "texts": [
+            " Although there is a standard test procedure to measure the shear modulus of rubber (ASTM, 1987), the properties of the rubber used in the bearings are somewhat di erent from the properties measured in the standard test due to di erent curing conditions and di erences in specimen size between the isolation bearings and the specimens of standard test. By means of the theoretical solution of viscoelastic columns, a procedure to identify the shear modulus and loss factor of the rubber from the cyclic shear tests of isolation bearings is proposed in this article. Through this identi\u00aecation procedure, the dependence of the material properties on the strain amplitude and input frequency can be explored. The deformation of a viscoelastic column of height h is shown in Fig. 1(a). The lower end of the column is \u00aexed against any displacement and rotation, whereas the upper end is allowed to move horizontally and vertically but is still constrained against rotation. The x-axis denotes the centroidal axis of the column with the origin located at the bottom of the column. When the upper end of the column is subjected to a constant compressive force P and a time-varied horizontal force, F t , it will induce the bending moment M x; t and shear force V x; t at the cross-section of the height x as shown in Fig. 1(b). The moment equilibrium leads to M x; t M0 t \u00ff Pu x; t \u00ff F t x; 1 where u x; t is the horizontal displacement and M0 t is the moment reaction at the lower end of the column. The equilibrium of horizontal forces gives V x; t F t cos w x; t P sin w x; t ; 2 where w x; t is the rotational angle of the cross-section. Considering the small magnitude of w, Eq. (2) can be approximated as V x; t : F t Pw x; t : 3 The shear deformation c x; t is the di erence between the rotation of the column axis ou=ox and the rotation of the cross-section w: c x; t ou x; t ox \u00ff w x; t : 4 When F t is a sinusoidal excitation of amplitude F0 and frequency x and the response of the column reaches a steady state, then the exciting force can be expressed in a complex form as F t F0eixt and the induced deformations also have complex forms as u x; t u x eixt; w x; t w x eixt; c x; t c x eixt; 5 where the superscript denotes the complex amplitude"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000561_a:1009888213333-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000561_a:1009888213333-Figure3-1.png",
+        "caption": "Figure 3. Two-degrees-of-freedom robot.",
+        "texts": [
+            " Otherwise, the algorithm recomputes the acceleration using the static friction force for the friction force opposing the applied force. The idea here is to use the same type of friction model for a robot with friction in the joints. In the robot case, however, the situation is more complex due to the interaction between the links. In the stick phase, the force/torque needed to maintain zero velocity becomes state-dependent and a simple representation such as in Equation (2) is inadequate. Consider the two-degrees-of-freedom robot shown in Figure 3. The angles \u03b81 and \u03b82 are the motor angles. Depending on the state of friction, one or both joints can be locked. To compute the friction torques in the motors, the first step consists in checking the motor velocities. If they are not zero, the standard Coulomb friction is used. For each motor having zero velocity, the acceleration is set to zero and the joint remains locked. Then, for each locked joint, the torque required to maintain zero acceleration is computed from the dynamic equations. In the event that the required friction torque is smaller than the static friction, the joint remains fixed",
+            " The dynamic model of an n degree of freedom is written as M(q)q\u0308+ g(q, q\u0307) = T\u2212 Ff , (3) with M(q) the inertia matrix, g the nonlinear vector, q the generalized coordinate vector, and T the input vector. For each joint i, Ffs,i is the maximum static friction force (for v = 0) and Ffk,i is the kinetic friction force (for v 6= 0). The nonlinear vector g includes viscous friction modeled as a term proportional to the relative velocity. According to this general formulation, the model for the two-degrees-offreedom robot shown in Figure 3 is[ m11 m12 m21 m22 ]{ q\u03081 q\u03082 } + { g1 g2 } = { T1 T2 } \u2212 { Ff,1 Ff,2 } . (4) Suppose that joint 1 is moving while joint 2 remains still. The friction in joint 1 can be well represented using a standard kinetic friction model while the friction in joint 2 is unknown. In order to maintain zero velocity, the friction in joint 2 must balance all the forces applied on the joint; the input torque, the gravity and inertial forces resulting from the motion of joint 1. In the model presented here, joint 2 is first assumed to remain locked up with the joint 2 acceleration set to zero, meaning that the constraint is applied at the acceleration level",
+            " The treshold velocity vmin,i is a factor that is usually determined experimentally, and \u03b1 is selected as a trade-off between minimizing the discontinuity at the treshold velocity and obtaining a reasonable damping speed. The selection of vmin and \u03b1 also depends on the fact that adding the damping factor bn,i corresponds to including a fast dynamic mode characterized by a mechanical time constant \u03c4 = mi,i/bn,i that should be maintained reasonably larger than the minimum integration step. The friction model presented herein has been validated using the two-degrees-offreedom robot moving in the vertical plane shown in Figure 3. Controlled free motions were obtained from setting initial angles on both motors, disconnected from their amplifiers to avoid the braking effect of the back electromotive force. The motor/reducer required characteristics shown in Table Ia were taken from the Harmonic Drive System data sheet. Harmonic Drive System provides the following equation for the determination of theoretical viscous damping: bv = Torque constant No load current \u2212 0.8 Starting current Rated output speed . (11) The static friction corresponds to the torque constant times the starting current"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003502_095440904322804439-Figure21-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003502_095440904322804439-Figure21-1.png",
+        "caption": "Fig. 21 Simpli\u00aeed model: scheme for calculation of the pressure distribution and press load",
+        "texts": [
+            " For the wheelsets analysed it was proved to give results very similar to those obtained by the FEM, with errors less than 2 per cent on the maximum press-\u00aet load. 4. The contact pressure distribution in each of the \u00aeve zones is obtained from Lame\u00c1 formulae, considering the zone to be composed of several in\u00aenitesimal cylindrical layers with an external radius r\u2026z\u2020, as Proc. Instn Mech. Engrs Vol. 218 Part F: J. Rail and Rapid Transit F01203 # IMechE 2004 at HOWARD UNIV UNDERGRAD LIBRARY on February 28, 2015pif.sagepub.comDownlo ded from shown in Fig. 21. Using the design interference i, the contact pressure acting on each cylinder is given by p\u2026z\u2020 \u02c6 iE R r2\u2026z\u2020 \u00a1 R2 4r2\u2026z\u2020 \u20265\u2020 where r\u2026z\u2020 \u02c6 RA \u2021 \u2026RB \u00a1 RA\u2020 z L \u20266\u2020 5. The friction resistant load was then calculated independently from the integral of the friction tangential stresses, which, using Coulomb\u2019s law, was found to be proportional to the local contact pressure. The press load is \u00aenally given by the sum of the friction-resistant loads acting on each of the \u00aeve jth zones: P \u02c6 X j \u2026Lj 0 f \u2026 p\u2026z\u2020\u2020 p\u2026z\u2020 2pR dz \u20267\u2020 where f\u2026 p\u2020 is given by equation (4)"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003206_iros.2004.1389402-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003206_iros.2004.1389402-Figure3-1.png",
+        "caption": "Fig. 3. Anglc helwern 1hc her and the Boor",
+        "texts": [],
+        "surrounding_texts": [
+            "Proceedings of 2004 IEEElRSl International Conference on Intelligent Robots end Systems September 28 - Oclober 2,2004, Sendai, Japan\nSafe Knee Landing of a Human-size Humanoid Robot while Falling Forward\nKiyoshi FUJIWARA, Fumio KANEHIRO, Shuuji W I T A and Hmhisa HIRUKAWA Intelligent Systems Institute, AlST\nTsukuba, JAPAN Email: k-fujiwara@aist.go.jp\nAbstract--This paper studies B falling motion control of a human-size humanoid robot when it falls forward. Safe knee landing of the mbot is realized as a first step l o minimize the damage of the falling over. The landing follows the detection of the falling, the decrease of the knee height after the detection, and the brake of landing speed. It is confirmed that lhhe proposed method can soften the landing impact significantly hy the proposed method.\nHumanoid robot, Fall over, UKEMI\n1. INTRO1)UCTION\nBiped humanoid robots have several advantages over wheeled mobile robots. They can step over obstacles and go up and down stairs. On the other hand, the robots have a major disadvantage. They may fall over and then damage severely. This is one of the crucial barriers for practical application of humanoid robots. Humanoid robots cannot be accepted for use in society unless this problem is overcome.\nCompared with quadruped walking robots or wheeled ones, the center of gravity of a biped-walking robot is located at a relatively high position and the size of the convex hull of the feet is smaller. A biped humanoid robot is essentially an unstable structure, and so little can be done to prevent the robot from falling over [I]. In addition, the robot may he damaged seriously enough to prevent it from walking thereafter, since the impact between the robot and the ground can be large. The bigger the humanoid robot, the more serious the damage can be. It is therefore important to address this problem.\nThe goal of our research is to prevent physical damage that would disable the locomotive ability of the robot, thus giving it a chance to stand up again. For this purpose, we proposed \u201dUKEMI\u201d strategy, a falling motion control to minimize damage to humanoid robots, in which we have shown how to control falling backward [21, [3].\nThe next challenge is how to control falling forward. In this paper, we investigate this problem. Specifically we focus on the first half part of the falling motion, that is, the touch down of the knee to the floor, and explore a method to realize a soft landing.\nThis paper is organized as follows. Section 2 overviews humanoid robot HRP-2P as the target robot, and describes how to find relative relationship between the floor and the robot. Section 3 presents the algorithm to soften the landing. Section 4 shows the results of the simulation and experiments. Section 5 concludes the paper.\n11. HUMANOID ROBOT HRP-ZP 4. Specifcadom of the mbor\nOur target humanoid robot, HRP-2P (Fig. 1) is fullbodied with 30 D.O.F., complete with cameras in the head for stereo vision [4], [ 5 ] . The specification of HRP-2P is summarized in Table 1.\nPig. I . Humanoid mho1 HKP-2P\n. It has a large shock absorptive stmcture on the hip in . It has a small shock absorptive smcture with limited falling are as follows. order to absorb the impact of falling over.\nabsorptive capacity on the knees and the elbows.\n0-780314636/041S20.00 @ZOO4 IEEE 503",
+            "The structures on the knees are small and limited because the legs have to be light to give priority to walking. The structure of the hip joint at which three axes cross is very complex, so strong impact should not he applied to the joint. We use the harmonic drive distinguished by its precision and high reduction ratio in joint structures. Though the harmonic drive has a hack drivahility, it might breakdown if large force exerted against driving power of the motor.\nB. Posirion esrirnarion <$the mbot to thefloor The relative positional relationship between the robot and the floor must be found to detect the beginning of the fall and the current state of the motion. We assume that . the floor is a flat horizontal plane, . the falling motion of the robot is on the sagittal plane,\nand the robot is always in contact with the floor. The joint angles of the robot can he sensed by encoders, and the posture of the torso to the floor can be found from the accelerometer and the gyroscope mounted on HRk-2P through Kalman filter. Therefore we can know the relative relationship between the robot and the floor in principle. The remaining mission is how to find the positional relationship between the landing pan of the robot and the touch down point on the floor.\nTo this end, the following conversion is applied to the geometry of the robot.\ns The convex hull of each link is taken. Each convex hull is simplified to make the minimum depth between vertices larger than 2Omm. . The vertices that have no chance to hit the flat floor when the links are connected are removed.\nThe vertices of the simplified model are illustrated in Fig.2, and the number of the vertices for each link is summarized in Table II.\napproximation of the convex hull of the lower link of the legs. Therefore, the control algorithm also must take this into account.\n111. ALGORITHM\nWe propose the following algorithm to soften the landing of the knees while falling forward. The algorithm consists of four stages.\nDetection of falling over: When the projection of the center of the gravity onto the floor is not included in the convex hull of the soles, it is judged that the robot has staned to fall down. Then the mode of the controller is switched into the falling control mode, and the relative relationshin between the robot and the floor is found by the method mentioned above. Knee bending: The goal of this phase is to make the height of the knees as low as possible before its landing, since it is expected that the potential energy of\nWhile we consider the touch down of the knees to the flat floor, the relative relationship between the robot and the floor can be specified by the angle between the line",
+            "the knee can be smaller which will be converted into kinetic energy. To this end, the knee joints are bended at the maximum angular velocity until 8 becomes smaller than a pre-determined threshold (Fig.4).\nFit. 4. Knee bending\nBraking of the landing speed: The hip pitch joint, waist pitch joint and shoulder pitch joint are moved such that 0 should be braked. Landing: The feedback gains of the joints control are made one-tenth to make the joints compliant to the impact of the landing.\nThe details of the braking of the landing speed are as follows. The angular momentum of the robot around the tip of the feet increases while falling forward as\n(1) C = P ( ~ ) x mg: where C is the angular momentum, pft) the position of the center of the gravity, and m the total mass. C can be represented by\nwhere IO is the moment of inertia. When the hip pitch joint, waist pitch joint and shoulder pitch joint are driven actively, the angular momentum of the robot around the tip of the feet should be kept constant since no extemal force is generated. See FigS. Let A0 be the deviation of 8 caused by the motions of the joints, then\n(3)\nc = loa, (2)\n0 = Ioai + I ,& + 1 2 8 2 + I3&,\nwhere 8,,i = 1,. . . , 3 is the joint angle of the hip pitch, waist pitch and shoulder pitch respectively and Ii the moment of the inertia for a,, i = 1 , . . . , 3 respectively. Taking the sum of both sides of Eqs.(Z) and (3), we obtain\n(4)\nwhich means that ),can be braked by controlling ai. From Eq.(3), the desired can be given from a desired ABre\u2019\nc = I0(S +A%) + I101 + 1 2 8 2 + 1383,\nby\nwhere,()? stands for the pseudo inverse of a matrix. Let 8, = 0 + A@, the braked angular velocity, then Eq.(S) can be rewritten by\nwhere\nK1 = y, 1<2 = -70,\nwhere sup() stands for the supremum. Here, the supremum is determined by taking several joint values, because the values do not vary much.\nWe chose y so that S y remains within actual speed limits. Note that K2 depends on 8, but it is,fixed to a constant value, and that the magnitude of (K10o + Kz) is clipped at a specified value.\nIv. EVALUATION OF THE ALGORITHM\nA. Sin~ularions We use the dynamics simulator of OpenHRP [6] to simulate the proposed method. The dynamics parameters and geometry of HRP-ZP are used in the simulations. The integration interval of the dynamics simulation is 1 msec, and the outputs of the controller are updated every 5 msec.\nThe initial posture of the robot is the standing with a slight bending of the knees(Fig.6). Then a forward force with 100[N] is applied to the torso of the robot for 1.0 sec. When the robot s t a s to fall forward, the mode of the controller is switched from balancing mode to falling mode (Fig. 7) and the knees start to bend immediately."
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0000917_s0003-2670(99)00158-0-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000917_s0003-2670(99)00158-0-Figure2-1.png",
+        "caption": "Fig. 2. Pervaporation cell. Hexagonal donor chamber depth 0.5 cm, length 1.5 cm, width 1.0 cm. Hexagonal acceptor chamber depth 0.1 cm, other dimensions as for donor chamber.",
+        "texts": [
+            " It was degassed with nitrogen for 15 min prior to use. The PFI system constructed for this work is shown in Fig. 1. This system can be used for the analysis of samples containing cyanide in the presence of sul\u00aede by introducing a solution of Pb(NO3)2 through the channel labeled `\u0300 reagent stream'' in Fig. 1. Two peristaltic pumps (Gilson Minipuls-2 and Minipuls-3), a type 50 injection valve (Rheodyne), and PTFE tubing (0.8 mm i.d.) were used to construct the FI-manifold. A home-made perspex pervaporation unit (Fig. 2), equipped with a 0.5 (Alltech), 2.0 or 5.0 (Gelman Sciences) mm pore PTFE \u00aelter membrane (47 mm diameter) and a PTFE membrane support, was used as the separation unit. The temperature of the donor stream was controlled by thermostating the supply reservoir of the donor stream and immersing the donor chamber of the pervaporation module in the water bath of the thermoregulator (RATEK Instruments, Australia). The current produced was continuously monitored at \u00ff50 or 0 mV using a \u00afow-through amperometric cell (Metrohm 656 Electrochemical Detector) consisting of a silver working electrode, an Ag/AgCl reference electrode and a platinum auxiliary electrode"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002189_s0963-8695(02)00026-9-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002189_s0963-8695(02)00026-9-Figure4-1.png",
+        "caption": "Fig. 4. Pre-determined positions on test-rig at which AE signatures were generated.",
+        "texts": [
+            " It is noted that the release of strain energy within such lead breaks is caused by the sudden recoil of the compressed atoms upon the surface of the metal when the pencil snaps and does not originate within the lead itself. The turbine rotor interrogated was a six stage lowpressure rotor of a 550 MW turbine unit, as shown in Figs. 2 and 3. The fifth stage blades were cropped. This rotor was undergoing an overhaul with the fifth stage blades being refurbished. The unit has a bearing diameter of 430 mm. The test initially involved generating AE events at various different positions on the shaft where seal rubbing could potentially occur, i.e. between the blades, as shown in Fig. 4. Due to the symmetry of the rotor, it was only necessary to examine seven shaft locations between the bearing and the rotor mid-span. In addition to these shaft tests, the validity of detecting blade-tip rubbing was examined by generating AE sources on blades across five stages of the rotor, as shown in Fig. 4 (\u2018B\u2019 positions). In each case, the lead fracture was undertaken at 75% of the blade\u2019s radius. Table 1 lists the distance of the AE receiving transducer from each blade and the distance from positions at which AE signatures were generated by the Nielson source, as shown in Fig. 4. The exact location of position P1 is not shown in Fig. 4; however, it was located adjacent the position P2 on the other side of the stage blades. Fig. 5 shows the position of the receiving sensor on the turbine, which was located in the region where the turbine would be supported by its bearings. The sensor was held in position with a magnetic clamp as shown in Fig. 5. It was also decided to investigate transmission from the varying positions across a second discontinuity to the receiving sensor, as shown in Fig. 6. These tests were intended to simulate the interface between the shaft and its bearings"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002374_naecon.1994.332886-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002374_naecon.1994.332886-Figure5-1.png",
+        "caption": "Figure 5",
+        "texts": [
+            " To reduce development costs and take advantage of proven, high reliability components, the system was constructed from Lucas's splayed axis piston pump technology previously used for Variable Exhaust Nozzle (VEN) actuation applications on fighter aircraft engines. The unit was a tandem system utilizing two independent channels. The control system was completely mechanical. An input bellcrank was used to command actuator position. This bellcrank acted upon a four bar linkage which received mechanical feedback of actuator position. This mechanism produced movement of a hydraulic shuttle valve, providing servo control. The system was subjected to limited bench testing. A photograph of the package i s shown in Figure 5. SYSTEM ADVANCES - Dual channel system provided redundancy. Used 115VAC 400Hz power. MODEL 91E03 (1983 - 1988) This demonstrator unit was designed to be used in a nose wheel steering power-by-wire demonstration system. While similar in design to the model 91E01 described above, the control system was modified to incorporate an electrical input and feedback signal. A simple electronic control circuit resolved these signals into a command voltage to a proportional solenoid. The solenoid input the \"error\" signal mechanically into a flow control servovalve"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001439_20.179574-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001439_20.179574-Figure1-1.png",
+        "caption": "Fig. 1. Definition of the reluctivity and of the coercive field",
+        "texts": [
+            " CONSITIWT\" LAWS usually, Classical constitutive laws, such as H =V B or H = v(B) B , are used that are both reversible and respectively linear and non-linear. In the case of ferromagnetic materials, these relations are not useful because they are not able to take irreversibility into account. This being so, our work is based on the definition of a more complete constitutive law for such materials : (4) The additional term & can be understood as the coercive ferromagnetic behaviour and depends on the past-history of the material. In another way, & can also be seen as the parameter determining on which hysteresis branch the as (Fig. 1) - H =v(B) B + a. field, it is the representation of the irreversible p m of the to a given of B. In view of the P h c u l x magnetic state is at, at time t. The reluctivity is then defined v(B) =I&@) -& I/B. (5) * '*?O ***** B It is always positive and finite in spite of the division by a possibly zero-induction. The non-linearity of ferromagnetic behaviour is described by the dependence on induction of that reluctivity. H Manuscript received February 17, 1992 Fig. 2. Regula Falsi method 0018-9464/92$03"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003580_elan.1140020703-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003580_elan.1140020703-Figure1-1.png",
+        "caption": "FIGURE 1. Schematic diagram of the flow-cell configuration.",
+        "texts": [
+            " All tissuemodified carbon paste electrodes were stored under the same conditions throughout the study. All solutions were prepared fresh daily with deionized water. The single-channel flow-injection analysis (FIA) system consisted of a Sage Model 341 B syringe pump (Orion Research, Boston, Massachusetts), a Rheodyne Model 7010 injection valve (Rainin Instrument, Cotati, California) with a 100 p L stainless steel sample loop (unless stated otherwise), and a laboratory-designed electrochemical flow detector. Figure 1 shows the configuration of the flow cell with a built-in 0.127 mm deep (channel thickness) and a flow channel volume o f 15 pL. A BAS Model 0'-1B cyclic voltammograph (Bioanalytical Systems, West Lafayette, Indiana) and a Keithley 169 multimeter (Keithley Instruments, Cleveland, Ohio) were used to control and monitor, respectively, the potential of the working electrode. A Heath strip-chart recorder was used to record the responses from the flow cell. The Ag/AgCl reference microelectrode (Model KE-1, Bioanalytical Systems) was held in a downstream chamber together with a stainless steel tube auxilliary electrode"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000715_978-94-015-9064-8_33-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000715_978-94-015-9064-8_33-Figure2-1.png",
+        "caption": "Figure 2. The ith limb of a parallel manipulator.",
+        "texts": [
+            " Specifically, all reciprocal screws pass through the center of the spherical joint and lie on a plane which is perpendicular to the axis of the prismatic joint as shown in Fig. l(b). 3. The Screw Based Jacobian A parallel manipulator typically consists of several limbs, say m. Each limb is made up of several links connected together by joints. Kinematically, we can replace a cylindrical joint by a revolute joint plus a coaxial pris matic joint, and a spherical joint by three non-coplanar intersecting revolute joints. Hence, we may consider each limb as an open-loop chain connecting the moving platform to the fixed base by i one-dof joints. Figure 2 shows a typical limb, where the first subscript denotes the joint number of a limb and the second subscript represents the limb number. This way, the in stantaneous twist, $p, of the moving platform can be expressed as a linear combination of i instantaneous twists (Mohamed and Duffy, 1985). l $p = E qj,i$j,il for i = 1,2, ... , m, (5) j=l where qj,i and $j,i denote the intensity and the unit screw associated with the jth joint of the ith limb. Equation (5) contains many unactuated joint rates which should be eliminated"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002923_acc.2005.1470620-Figure7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002923_acc.2005.1470620-Figure7-1.png",
+        "caption": "Fig. 7. Geometric representation of necessary and sufficient conditions for different radial locations of the ECAV.",
+        "texts": [
+            " To allow more flexibility on the initial conditions, the ECAV, the phantom point and the radar (OEP) are constrained to be inline only at the beginning of each time step of the algorithm at which point the direction and speed are set for both the phantom point and ECAV. This collinearity constraint requires ( ) sin sin ( ) r t V R t W (10) A Necessary condition for solutions for (10) to exist is, ( ) sin 1 ( ) r t V R t W (11) where ,V W are the ground speeds of the phantom and ECAV respectively. This necessary condition imposes a restriction on the feasible annular velocity sector of the phantom. The hatched area of the annular velocity sector of the phantom in Fig.7 represents this feasible velocity sector restricted through the necessary condition. Here, existence of solutions simply means the existence of a feasible trajectory for the ECAV. A sufficient condition for the existence of solutions for (10) is simply, cr where cr satisfies, 0 0 sin tan sin cos cr cr V tW t a r R V t where t is the time-step of the algorithm. In Fig.7, the area cross-hatched corresponds to this sufficient condition and is as expected a subset of the area corresponding to the necessary condition. The proposed algorithm implements this sufficient condition in place of the more difficult to implement necessary condition. It should be noted here that practical values of the bounds on the speeds make these annuli very narrow compared to their radii and hence the implementation of the sufficient condition in place of the necessary condition does not significantly reduce the freedom allowed for the phantom"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001338_0094-114x(95)00082-a-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001338_0094-114x(95)00082-a-Figure4-1.png",
+        "caption": "Fig. 4. Tip interference during disengagement.",
+        "texts": [
+            " To avoid the tooth tip interferences the following conditions are to be satisfied [3, 7]: In the case of tip interference during engagement: Angles 0 o and 0g are calculated as follows: cos_,(r~, + A 2 - r~,) _ 0 , = \\ 2At., / ' 00 = cos - ' ( r \u2022 ' - A 2 - r.~p) + ap \\ 2Ar~p ,] (6) (7) (8) where the subscripts g and p refer to the gear and pinion respectively and 'A' is the center distance between gear and pinion. Also, fl~ = inv \u2022 - inv ~tg (9) tip = inv ~tp - inv ~ (10) 478 R. Maiti and A. K. Roy Minimum tooth difference where, ars, alp are the corresponding addendum factors i.e. the ratio o f addendum (with respect to their s tandard pitch circles) to the module for the gear and the pinion. Figure 4 illustrates the disengagement interference o f internal gearing with ring gear as the driver. The disengagement interference is to be examined as follows to select the manufac tur ing tolerances in backlash free gearing: c o s - , / r 2g + A 2 - r2p.'~ - a (14) O, = \\ 2Ar,, ] ,-s 0 v = cos - l r,g 2---~rap \"] -- tip (15) tip ---- 7p -- (inv ~ttp -- inv ct) (16) fig = Ys + (inv ~ -- inv ~ts) (17) where 7p, 7, are the angular arc thicknesses o f pinion tooth and gear tooth at their respective pitch circles"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003734_ip-b:19830027-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003734_ip-b:19830027-Figure5-1.png",
+        "caption": "Fig. 5 Explanation of slip equations 12 and 18",
+        "texts": [
+            " 3, MA Y1983 187 Hence u>t n H (9) where a(t) is the angle between point P and the wavefront of the kith harmonic. Differentiating each side of eqn. 9, we obtain: CO + Vx+ Vz = Txk Tzl (10) where vx, vz are the rotary and linear rotor speeds, respectively, and dt is the angular speed of point P in relation to the kith field harmonic. Similarly, as in the theory of conventional induction motors, we can write Thus, from eqns. 10 and 11, we obtain eqn. 7. This equation can be also derived, using trigonometric transformations, in the following way: The rotor speed v can be divided in two components (Fig. 5) vn and vt. The vt component, which is parallel to the 188 wavefront, does not make any contribution to electromagnetic induction. Thus, the rotor slip in relation to kith field harmonic can be defined as follows: Ski = 1 - (12) where vn and vnM are the rotor and field velocities in the normal direction of the kith wavefront. Looking at the geometric relations of vn (Fig. 5), we have vn = z;cos|3 Since j3 = 7 \u2014 a, eqn. 13 takes the form vn = v cos 7 cos a + v sin 7 sin a Since vz = v cos a and vx = v sin a Hence vn - Vz cos 7 + vx sin 7 From Fig. 5, we have also Vnkl = Vzl COS 7 Inserting eqns. 15 and 16 into eqn. 12, we obtain vz + vx tan 7 (13) (14) Ski = 1 ~ (15) (16) (17) vzl Since tgy = vzl/vxk, eqn. 17 finally takes the form of eqn. 7. Eqn. 7 can also be obtained by starting with the following definition of the rotary-linear slip: s = 1 (18) where vki is the synchronous speed in the direction of the rotor motion (Fig. 5). Eqn. 7 indicates that the slip depends on two components of the rotor speed. If one of them is zero, then the slip takes the form well known in the theory of conventional motors. Considering the direction of the travelling rotating wave speed (Fig. 3), it is noticed that a change of the TX1 or TZ1 value causes a change of the direction of its movement. If we put Txi ->\u00b0\u00b0 in eqn. 6, we obtain a travelling wave, and if TZI ~*\"\u00b0\u00b0. w e n a v e a rotating wave. That means that the description of a helical movement is more general than that of a travelling or a rotating wave"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003735_tpwrd.1986.4307990-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003735_tpwrd.1986.4307990-Figure2-1.png",
+        "caption": "Figure 2. Composite Hysteresis-Saturation Curve. Multiple values of flux can be caused by a single value of MMF.",
+        "texts": [
+            " general, the model can accept any number of windings around the core. 0885-8977/86/0007-0174$01.00\u00a91986 IEEE 175 Each winding is modeled with resistance and self-leakage flux. For generality, mutual coupling outside the steel core is assumed between each pair of windings although only that component of flux linking the primary and secondary windings is shown. The steel core is characterized by a non-linear, history dependent hysteresis-saturation relationship between net MMF and the resulting flux as on Figure 2. Eddy-current effects are modeled by a short--circuited turn. Additional short--circuited turns having different values of resistance and leakage inductance can be included to represent eddy current effects more accurately. is very important, and one that distinguishes the model described in this paper. Completing the core model is a small component to represent the permeance of free-space. Functionally, it is in parallel with hysteresis and saturation. When 4v and 4s are combined to form 4m, it forms a flux that links all coils",
+            " / Core Model Modeling of a laminated steel transformer core involves an input--output relationship between net MMF driving the core and the resulting flux. There are four eVrfctcs that must be modeled; hysteresis, saturation, free-space flux and eddy-currents. From a modeling standpoint, they are each quite different. Eddy currents are induced in core laminations by transformer action and can be modeled simply as another winding or windings (14], similar to that done successfully to model eddy current effects in rotating machines [17). Hysteresis appears to be a multi-valued function of MMF. Given an MMF, Ml on Figure 2, several values of flux seem to be possible. However, given a history of where, (not when), MMF has been, flux is determinable. Saturation, on the other hand, is independent of history. The two effects are postulated to combine in series as illustrated on Figure 3; the input to the saturation function being the output of the hysteresis function. The relationship between these two effects effect forms 4,v. This model is referred to as Fl(MMF). b. Multiple deadband. A more complex mechanism might contain two parallel paths linking input and output, each path, A and B, having its' own deadband"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002285_s0020-7683(00)00153-0-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002285_s0020-7683(00)00153-0-Figure6-1.png",
+        "caption": "Fig. 6. Oil pressure distribution in the pad centerline for di erent arrangements \u00b1 Pinj 0:7 MPa.",
+        "texts": [
+            " If one considers the distribution of bore areas on the pad surface in relation to its center (Table 2), one observes that these are the arrangements with higher percentuals of bores near the pad edges, where the hydrodynamic pressures are lower (0:3 < d=Lz < 0:5). Thus, one can replace the rotor to the bearing center by using a di erence of injection pressures of only 0.25 MPa with a 5-5-5 pad, whereas pressures of 0.3, 0.32 and 0.4 MPa are necessary when using the 7-8, 21-2 and 15, 2-3 and 5 arrangements. Results presented in Table 2 were obtained summing the areas of the ori\u00aeces which were positioned in a given distance d to the pad center, and later calculating the percentuals within certain ranges (Fig. 5). Fig. 6 shows a comparison between arrangements 5-5-5, 2-3, 5 and conventional, of the pressure distribution in the pad centerline, in both y and z directions. One can see that one has an increase of pressure in areas where there is not high pressures in the conventional case. This is the cause of a better performance of pad 5-5-5 in centering the rotor, since this arrangement increases the pressure near the edges in both directions. In order to investigate the e ciency of di erent types of pads in cooling the oil \u00afow in he bearing gap, by injecting cooled oil through the bores, a di erence of injection pressures between pads 2 and 4 was used, within the range of 0"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002381_robot.2001.933052-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002381_robot.2001.933052-Figure1-1.png",
+        "caption": "Figure 1: Flexible manipulator",
+        "texts": [
+            " However, precise state estimation by this method becomes difficult when the virtual link division number is large, which is the case that the links have much more flexibility. In this paper, we propose a state estimation method based on discrete position information of flexible links by visual sensor. Some previous research [6] used visual sensors to control flexible manipulators, but the visual sensors were utilized just to measure the tip position of flexible link, not to estimate the state variables directly. 2 Flexible Manipulator We consider a flexible manipulator shown in Fig.1 in this paper. It is N d.0.f. plane manipulator which has serial N flexible links and N joints, and fixed on the inertial coordinate system Co. Each joint displacement is 8 = [&,&,... , Q N ] ~ . The length of link i ( i = 1 , 2 , . . . , N) without elastic deformation is I , , and the mass is m,. 0-7803-6475-9/01 /$I O.OO@ 2001 IEEE 2840 as natural frequencies, the minimum IC is constrained by the sampling theorem. The link i coordinate system E, is fixed on the center of joint i. Its 5, axis is along link i when it's not deformed, z , axis is along the displacement axis of joint i, and y2 axis is determined to compose the right hand coordinate system"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003554_13552540510601309-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003554_13552540510601309-Figure4-1.png",
+        "caption": "Figure 4 Volume Ve under surface with re-entrant sides",
+        "texts": [
+            " It can only be applied for surfaces bounded by iso-parametric curves. Also, the above integration is not valid for a surface that has more than one z coordinate value for a particular combination of x and y, i.e. a surface that folds over itself in z-space. In some literature, these surfaces are referred to as those with re-entrant sides (Gupta et al., 2004). However, in such cases, equation (3) may be employed that yields the volume engulfed by the surface and the vertical columnar volume beneath it extended up to the z \u00bc 0 plane (Figure 4). V e \u00bc ZZ z\u00f0u; v\u00deJ dudv \u00f03\u00de The Jacobian J corresponds to the vertical component of the normal to the surface given by ! nz \u00bc \u203ax \u203au \u203ay \u203av 2 \u203ax \u203av \u203ay \u203au \u00f04\u00de Thus, for surfaces with re-entrant sides, the Jacobian J would change sign with ! nz and hence application of equation (3) would yield the volume engulfed by the surface. Surface re-construction \u2013 Bezier surface fitting to CAD model surface patch The portion of the CAD model surface associated with the cusp volume is not necessarily an iso-parametric patch (i"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002220_s0045-7949(02)00003-2-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002220_s0045-7949(02)00003-2-Figure1-1.png",
+        "caption": "Fig. 1. Physical configuration of a partial journal bearing (transverse roughness).",
+        "texts": [
+            " Based upon the Christensen\u2019s stochastic model [12,13], the stochastic Reynolds-type equation is derived to take into account the presence of roughness on the bearing surfaces. The dynamic film pressure and force is solved and applied to derive the nonlinear motion equation of the journal. The dynamic squeeze-film characteristics (including the journal-center velocity, journal-center locus, and maximum eccentricity ratio) are then evaluated. To show the effects of surface roughness on the bearing operating under cyclic loads, the results are compared with the smooth-bearing case and presented for various values of roughness parameter and Sommerfeld number. Fig. 1 shows the pure squeeze-film configuration of a long partial journal bearing. The journal of radius R is approaching the bearing surface with a squeezing velocity ( ohT=ot). It is assumed that thin film lubrication theory is applicable and the flow in bearing is incompressible, isothermal and laminar. The Reynolds-type equation is given by o ox h3T op ox \u00bc 12l ohT ot \u00f01\u00de The local film geometry hT is treated as a stationary, ergodic, stochastic process with zero mean, and is considered to be made up of two parts: hT \u00bc h\u00f0x; t\u00de \u00fe d\u00f0x; z; n\u00de \u00f02\u00de where h\u00f0x; t\u00de represents the nominal smooth part of the film geometry depending upon the coordinates x and the squeezing time t"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure2.1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure2.1-1.png",
+        "caption": "Figure 2.1. Displacement of a particle and parallel translation of a rigid body.",
+        "texts": [
+            " Our immediate objective in this chapter will be to derive from the exact finite displacement vector equation special representations for the velocity and acceleration of the particles of a rigid body that separate and exhibit clearly the translational and rotational parts of the body's motion. Afterwards, several sample applications of these results will be presented. We shall con clude our study with discussion of some useful theorems related to instan taneous screw motions. Let us begin with a few definitions of terms needed in our study. Let a rigid body :11 undergo an arbitrary displacement in space relative to an assigned Cartesian frame cfJ = { 0; ek }, as shown in Fig. 2.1; and let X and X denote the respective position vectors of a particle P in its initial and final positions from 0. Then, regardless of the actual motion of P between these positions, the vector d(P) =X- X defines the finite displacement of P in cfJ. Hence, d(P) is named the displacement of P relative to cfJ. A motion of :11 in which every material point sustains the same dis placement d is called a parallel translation, or briefly, a translation. In this case, d(P) = d is the same vector for every particle P in :11. Therefore, any arbitrary motion that the body may have suffered in reaching its terminal state is the same as a motion in which its particles traverse parallel, straight line paths, as shown in Fig. 2.1, though the body need not move on that line at each instant. (See Problem 2.1.) Whenever the initial and final spatial position vectors of at most one point P are the same, then d(P) = 0 only for that one point. The arbitrary motion that the body may have experienced in achieving its end state is indistinguishable from any other having the same end state and for which P is Kinematics of Rigid Body Motion 87 assumed to be fixed in </>; hence, the displacement of !11 is described as a rotation about a fixed point"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003926_1.338581-Figure40-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003926_1.338581-Figure40-1.png",
+        "caption": "FIGo 40 A typical shape of the region O.",
+        "texts": [],
+        "surrounding_texts": [
+            "Numerical Methods Dan Bloomberg, Chairperson\nThe Preisach model and hysteretic energy losses I. D. Mayergoyz and G. Friedman Electrical Engineering Department and Institute for Advanced Computer Studies. University of Maryland. College Park, Maryland 20742\nUsing Preisach's model, general expressions for hysteretic energy losses are derived. These expressions are valid for arbitrary (not necessarily periodic) variations of magnetic field. Moreover, these expressions are given in terms of Preisach's function as well as in terms of experimentally measured \"first-order transition curves.\" A formula is also found which relates the hysteretic energy losses for arbitrary field variations to the losses ocurring for certain periodic variations of magnetic field. This formula allows for easy measurement of hysteretic losses occurring for arbitrary field variations.\nINTRODUCTION\nA hysteresis phenomenon is associated with some ener gy dissipation which is often referred to as hysteretic energy losses. The problem of determining hysteretic energy losses is a classical one. The solution to this problem has long been known for the case of periodic (cyclic) variations of magnet ic field. In that case, the hysteretic energy losses are equal to the area enclosed by a hysteresis loop resulting from a peri odic field variation. However, energy dissipation is a contin uous process, and it occurs for arbitrary (not necessarily periodic) variations of magnetic field. The problem of com puting hysteretic energy losses for the above general case has remained unsolved. A solution to this problem would be of both theoretical and practical importance. From the theo retical point of view, the solution of the above problem will allow for the calculation of internal entropy production, I which is a key point in the development of irreversible ther modynamics of hysteretic media. 2 It will also lead to the expression for the energy stored in the magnetic field which eventually may help to find electromagnetic forces in hyster etic media. 3 From the practical viewpoint, the solution of the problem may bring new experimental techniques for the measurement of hysteretic energy losses occurring for arbi trary field variations.\nIt should not be surprising that the solution of the prob lem has been known only for the case of periodic variations of magnetic field. The reason is that for cyclic field variations the expression for energy losses is easily derived using only the energy conservation principle; no knowledge of actual hysteresis mechanisms is required. The situation is much more complicated when an arbitrary variation of magnetic field is considered. Here, the energy conservation principle alone is not sufficient and an adequate model of hysteresis should be employed in order to arrive at the solution of the problem. It turns out that Preisach's hysteresis model is very well suited for this purpose.\nIn this paper, Preisach's model is used to derive general expressions for hysteretic energy losses. These expressions are given in terms ofPreisach's function as well as in terms of experimentally measured \"first-order transition curves.\"\nFurthermore, a formula is found which relates the hysteretic energy losses occurring for an arbitrary field variation to the losses occurring for certain periodic field variations. This formul.a leads to a simple technique for the measurements of hysteretic losses occurring for arbitrary variations of mag netic field.\nIt has been emphasized before4-7 that Preisach's model is purely phenomenological and can be used for the math ematical description of hysteresis of any physical nature. For this reason, the expressions for hysteretic energy losses de rived in this paper are quite general and valid regardless of the physical nature of hysteresis. The only requirement is that such hysteresis can be described by Preisach's model.\nEXPRESSIONS FOR HYSTERETIC ENERGY LOSSES\nTo make the exposition more or less self-contained, the main facts concerning Preisach's model will be briefly re viewed. The detailed information on this subject can be found in Refs. 4--8. For the sake of generality, we shall de scribe Preisach's model in a purely mathematical form. In this form, any hysteresis nonlinearity can be characterized by an input u(t) and an output J(t). In magnetic applica tions u (t) is the magnetic field, while f( t) is the magnetiza tion.\nConsider an infinite set of operators r a{3 which are rep resented by rectangular loops on the input-output plane (Fig. 1). Along with these operators, consider a weight fune-\n3910 J. Appl. Phys. 61 (8),15 April 1987 0021-8979/87/083910-03$02.40 \u00ae 1987 American Institute of Physics 3910 [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:\n128.138.73.68 On: Tue, 23 Dec 2014 09:06:37",
+            "tiontt (a,p) which is often called Preisach's function. Then, Preisach's model is given by\nf(t) = J J fl (a,/J)r afJ u(t)dad{J. (1)\na>{3\nFor hysteresis nonlinearities with closed major loops the functiontt{a,p) has a finite support within some triangular area T on the a-{3 plane.\nThere is a one-to-one correspondence between opera tors YaP and points (a,/J) on the half-plane a>p. Using this fact, it can be found that, at any instant oHime, the triangle T is subdivided into two sets (Fig. 2): S + (t) and S - (t) con ~isting of points (a,/3) for which Yapu(t) = 1 and YaP u(t) = - 1, respectively. The interface L(t) between S + (I) andS - (t) isa staircase line the vertices of which have a and {3 coordinates coinciding with local maxima and mini ma of u (t) at previous instants of time. The final (attached to the line a = f3) link of L(t) is horizontal and moves up when the input increases, and it is vertical and moves from right to left when the input decreases. For any given hystere sis nonlinearity, Preisach's function tt(a,{3) can be found from the set of \"first-order transition (reversal) curves\" at tached to the limiting ascending branch (Fig. 3). The appro priate formulas are\nF(a,/J) = fa -laP' (2)\n( ,{3) - 1 a2F(a,fJ) fla ---\n2 8a8p (3)\nIt turns out (see Refs. 5 and 8) that the integral in Eq. (1) can be directly expressed in terms of F(a,/J) as follows:\n1 n\nlet) = -2F (ao,/3o) + k~l [F(ak,Pk_d - Fad 3k)]'\n(4)\nwhere {ak} and {Pk} are decreasing and increasing se quences of a and /3 coordinates of interface vertices, respec tively, and n is the number of horizontal links of L (t) .\nIt has been proved in Ref. 6 that two properties consti tute necessary and sufficient conditions for the representa tion of a hysteresis nonlinearity by Preisach's model. These properties are the \"wiping-out property\" and the \"con gruency property.\" For the discussion of those properties see Refs. 6 and 7. In the sequel, we shall assume that these prop erties are satisfied, and Preisach's model is valid.\nNow we are equipped to proceed to the derivation of expressions for hysteretic energy losses. We begin with the case when a hysteresis nonlinearity is represented by a rec-\n3911 Jo AppL Phys., Vol. 61. Noo 6, j 5 April 1967\ntangular loop shown in Fig. 1. If a periodic variation of input is such that the whole loop is traced, then the hysteretic energy loss for one cycle equals the area 2(a - [3), enclosed by the loop. It is dear that the horizontal links of the loop are fully reversible and, for this reason, no energy losses occur when these links are traced. Thus, it can be concluded that only \"switching-up\" and \"switching-down\" result in energy losses. It is apparent (on the physical grounds) that there is symmetry between these two \"switchings\" and, consequent ly, the same energy losses (equal to a - {3) occur for each of these switchings. The product f.i (a,/3) Ya/3 can be construed as a rectangular loop with output values equal to \u00b1 /-L (a,/3). For this reason, switchings up or down of such a loop win result in energy loss p(a,{3)(a - /3). According to Prei sach's model (1), any input variation is associated with swi tchings up or down of some rectangular loop f.i (a ,/3) Yap. Thus, the energy loss occurring for an arbitrary input vari ation is naturally equal to the sum of energy losses resulting from the switchings of rectangular loops during this input variation, Since we are dealing with a continuous ensemble of rectangular loops, the above summation should be re placed by integration. Thus, if n denotes the region of points (a,p) for which the corresponding rectangular loops were switched during some input variation, then the hysteretic energy loss Q for this input variation is given by\nQ = I f j.l(a,f3)(a - {3) da d[3. (5)\nII\nA typical shape of the region n is shown in Fig. 4. It is clear from this figure that n can be always subdivided into a trian gle and some trapezoids, The trapezoids, in turn, can be rep resented as differences of triangles. Thus, if the integral (5) can be evaluated for any triangular region, then this integral can be easily determined for any possible shape of fto It makes sense to compute the values of integral (5) over var-\nI. 00 Mayergoyz and G. Friedman 3911 [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:\n128.138.73.68 On: Tue, 23 Dec 2014 09:06:37",
+            "ious triangles. Using these values, hysteresis losses can be easily found for any variation ofinput. In the case when n is a triangle, the integral (5) can be easily evaluated in terms of F(a,{:J) , which is related to the \"first~order transition curves\" by formula (2). The derivation proceeds as follows: It can be verified that\n(j2 --[F(a,{:J) (a - {J) ] (ja8p\n= a 2F(a,p) (a _ (3) + aF(a,{:J) oa a/3 ap\n_aF~(:.....-a.:!....J3.:.-) . (6) da\nUsing Eqs. (3) and (6), we find\n2jt(a,/3) (a _ (3) = 8F(a.{3) _ aF(a,/J) 8P oa\n(j2 - -- [F(a.{3)(a - {3) ]. (7)\naa 8{3\nNow, consider a triangle T(u+,u_) swept (see Fig. 5) dur~ ing the input increase from u _ to u +. According to Eq. (5), such input variation is associated with the losses\nQ(IL,U+) = f f p,(a,/3)(a - (3)da d/3 T(,,+,u ,.)\n= i~+ ([ jt(a,{J)(a - /3) d/3 )da\n= iU ,+ (Lu + p(a,/3)(a -fJ)da )d/3. (8)\nSubstituting Eq. (7) into Eq. (8), performing the integra tion and taking into account that F(a,a) = 0, after simple transformations we find 1 rru , lU' Q(u_,u+) = - 2\" Uu_ F(a,u_ )da + \"_ F(u+.{3)d{3\n- (u+ - u_ )F(U+,U_\u00bb) . (9)\nIt can be shown that the derived expressions for hysteretic energy losses are consistent with the classical result: the hys teretic energy losses for any cyclic input variation equal the area enclosed by the loop resulting from the cyclic input\n3912 J. Appl. Phys., Vol. 61, No.8, 15 April 1987\nvariation. The proof is omitted. Consider a cyclic variation of input from u _ to u + and back to u _. During the monotonic increase of input from u_ to u+, the final horizontal link of L(t) sweeps the triangle T( u + ,u ._ ). On the other hand, during the monotonic de crease of input from u + to u _, the final vertical link of L (t) sweeps the same triangle. Thus, it can be concluded that, for any loop, the hysteretic losses occurring along ascending and descending branches are the same:\n(10)\nNext, we shall use expression (10) to find the formula which relates hysteretic energy loss occurring for an arbi trary monotonic input variation to certain cyclic hysteretic losses. Suppose that the input u(t) increases monotonically from some minimum value u_ and reaches successively some values uland U2, (u2>u I). We are concerned with the hysteretic loss Q( u I,U2 ) occurring during the input variation between U I and u2\u2022 For the above input variation, we have: n = T(u2,u_) - T(ul,u_). Consequently,\nQ(ul,UZ) = Q(U_,U2) - Q(u_,u 1). (11)\nUsing Eq. (10), losses Q(u_,u 2 ) and Q(u_,u 1 ) can be ex~ pressed in terms ofcycliclosses Q(u_,u l ) = ~Q(U_,Ul) and Q(U_,U2) = ~Q(U_,U2)' where Q(u_,u j ) and Q(u_,u2) are cyclic losses for periodic input variations between u_ and U 1, u_ and U z, respectively. Using this fact, from Eq. (11) we find\n(12)\nThe last formula can be useful from the experimental point of view because it is much easier to measure cyclic losses than losses occurring for nonperiodic input variations.\nACKNOWLEDGMENTS\nThe reported research was motivated by the question raised by Professor H. A. Haus during the talk given by the first author at MIT. This research is supported by the U.S. Department of Energy, Engineering Research Program (contract no. DE-AS05-84EH13145).\n11. Prigogine, Introduction to Thermodynamics of Irreversible Processes, 2nd edition (Wiley, New York, 1961). 2J. S. Cory and J. L. McNicols, J. Appl. Phys. 58, 3282 (1985). 'P. Penfield, Jr. and H. A. Haus, Electrodynamics of Moving Media (MIT, Cambridge, MA, 1967). 4M. Krasnoselskii and A. Pokrovskii, Systems with Hysteresis (Nauka, Moskow, 1983). 51. D. Mayergoyz, J. Appl. Phys. 57, 3903 (1985). \"T. Doong and I. D. Mayergoyz, IEEE Trans. Magn. MAG-21, 1853 (1985). 71. D. Mayergoyz, Phys. Rev. Lett. 56,1518 (1986). 81. D. Mayergoyz, IEEE Trans. Magn. MAG-22, 603 (1986). 9J. A. Barker, D. E. Schreiber, B. G. Huth, and D. H. Everett, Proc. R. Soc. London Ser. A 386,251 (1983).\nI. D. Mayergoyz and G. Friedman 3912 [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:\n128.138.73.68 On: Tue, 23 Dec 2014 09:06:37"
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0002082_s1350-4533(01)00125-4-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002082_s1350-4533(01)00125-4-Figure2-1.png",
+        "caption": "Fig. 2. Inertial force and moment of link i and forces and moments applied to link i by its neighboring links, i 1 and i+1.",
+        "texts": [
+            " Applying the Newton\u2013Euler equations: Fi F\u2217 i 0 (1a) where F\u2217 i miv\u0307ci, (1b) And Ni N\u2217 i 0 (2a) where N\u2217 i (ciIiw\u0307i wi \u00d7 ciIw\u0307i), (2b) the inertial force and moment on link i were computed, where Fi and Ni represent the resultant force and moment, respectively, applied to each link, F\u2217 i is the inertial force acting at the center of the mass of link i, mi is the mass of link i, v\u0307ci is the acceleration vector of the center of mass of link i, N\u2217 i is the inertial moment acting at the center of mass of link i, ciIi is the inertial tensor of the link i with center of mass at the origin of the fixed link frame, and wi and w\u0307i are the angular velocity and angular acceleration vectors of link i. Force and moment equations were applied to calculate the external torques and forces associated with the accelerations. Based on a free body diagram of a typical link (Fig. 2), Eqs. (1a,b) and (2a,b) become: Fi fi ( ifi+1) (3) and Ni ni ( ini+1) ( iPc) \u00d7 fi (iPi+1 (4) iPc) \u00d7 ( ifi+1), where fi is the force exerted on link i by link i-1, measured in frame i, ni is the torque exerted on link i by link i-1, measured in frame i, ifi+1 is the force exerted on link i+1 by link i, measured in frame i, ini+1 is the torque exerted on link i+1 by link i, measured in frame i, iPc is the position vector of the center of mass of link i in frame i. Rewriting the Eqs. (3) and (4) in terms of a rotation matrix, R\u2217, the force and torque equations appear as iterative relationships from the higher-numbered neighbor to the lower-numbered neighbor: fi Fi i i+1R i+1fi+1, (5) and ni Ni i i+1R i+1ni+1 iPc \u00d7 Fi (6) iPi+1 \u00d7 i i+1R i+1fi+1, where i+1fi+1 is the force exerted on link i+1 by link i, measured in frame i+1 and i+1ni+1 is the torque exerted on link i+1 by link i, measured in frame i+1"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000704_a:1008228120608-Figure10-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000704_a:1008228120608-Figure10-1.png",
+        "caption": "Figure 10. Event maps corresponding to different values of Vdr showing the existence of a partition.",
+        "texts": [
+            " That is, there exist periodic points of any prime period (for the second iterate), and uncountably many orbits that are not even asymptotically periodic. Finally in some cases it seems possible to detect a partition of intervals a, b, and c on the interval of definition of the \u2018permanent\u2019 map, as suggested by Figures 10a and 10b, corresponding to the values Vdr = 0:0811 and Vdr = 0:0813. It is reasonable to hypothesise the existence of a map with a superstable period-4 orbit which was approximately found for Vdr = 0:0812 (Figure 10c). Such an orbit divides the interval of definition of the \u2018permanent\u2019 map in three sub-intervals a, b, c which are mapped in the following way: f(a) b; f(b) c; f(c) a [ b [ c: (6) The transition matrix A (or Markov graph) is constructed according to the rule: Aij = 1 if f(ai) aj and zero otherwise: A = 0 B@ 0 1 0 0 0 1 1 1 1 1 CA : (7) The construction of the transition matrix enables us to count the number of period-m orbits. If Nm denotes the number of fixed points of fm then: Nm = tr(Am): (8) Part of these Nm orbits are trivial, i"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002915_s00170-004-2449-0-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002915_s00170-004-2449-0-Figure2-1.png",
+        "caption": "Fig. 2. a Percentage values of failure frequency b Percentage values of downtime",
+        "texts": [
+            " It contained the following information: 9 Product name, model and size 9 Product code 9 Reported time and date of failure 9 Failure phenomena 9 Cause of failure 9 Repair process 9 Repair time 9 Downtime 9 Date of handover 9 Model, size and number of breakdown components 9 Number of service engineers or repair engineers 9 Site of machine tool As indicated earlier, a lathe has been classified broadly into having the subsystems of headstock, tailstock, carriage, feed mechanism, electrical and coolant. In this analysis, failure frequency and downtime have been taken into consideration for deciding critical subsystems in a lathe. Figure 2a and b show the percentage values of frequency of failures and breakdown for different subsystems, respectively. It can be seen from Fig. 2a that the maximum number subsystem, it was observed that the gear and bearing element form the most significant components. This study focused on the condition monitoring studies of spindle bearings (taper roller bearings). of failures took place in electrical and headstock subsystems. The headstock subsystem has observed more downtime than the electrical subsystem, as shown in Fig. 2b. The electrical subsystem has faced failures on fuses, connectors and switches that required less downtime. The headstock subsystem has faced failures in components like the gears, gearbox bearing, spindle bearing, spindle clutch and cross-slide jib. It was observed that the gear and bearing failures cause longer downtime. All failures in the lathe have been grouped into four-failure modes: component damage, burnt fuse, circuit fault and looseness. Figure 3 gives failure modes and their relative failure frequencies"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000470_s0043-1648(97)00232-9-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000470_s0043-1648(97)00232-9-Figure2-1.png",
+        "caption": "Fig. 2. t'-Z(; tesl machine I~1.",
+        "texts": [
+            " all tests were performed using the same oil type but different ADI gears. The wear and sculling resistance of each ADI gear is then established by comparison with results from other similar FZG tests. 3.2. Procedures The FZG A/8 .6 /90 test consists in imposing a sequenUal load to the tested working gear for periods of 15 rain (stages). When stage 12 is attained, contac! pressure at gear teeth surfaces reaches about 2 GPa. Gears are mounted inside a closed box (carter) bathed in the lubricating oil ( see Fig. 2). The oil temperature is raised and stabilized at 90\u00b0C before running each stage of the test. During each of these stages, an electric motor coupled Io the wheel axis imposes a constant angular speed of 1500 rpm. The test ends when teeth contact surfaces are considered as scuffed I when lhe lotal length damaged by adhesion scratches equals a tooth width). The test result is expressed by the number of stages gears managed to work until scuffing o c c u r s . 3.3. Data gathering Besides the number of stages a gear works until scuffing, other parameters are recorded along each lest stage"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003219_iros.1992.594551-Figure8-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003219_iros.1992.594551-Figure8-1.png",
+        "caption": "Fig. 8. The shaping constraint.",
+        "texts": [],
+        "surrounding_texts": [
+            "the robot may attain. Inadmissable regions (c-space \u201cobstacles\u201d) correspond to impossible configurations such as interpenetration of the robot and objects in the environment. Now, the start and goal configurations can be specified as points in the c-space and the navigation task is reduced to finding a path between these points while avoiding the c-space obstacles. Other researchers have extended these ideas to produce plans that transform the world from a start state to a goal state [ 121. Here a point in the c-space describes a configuration of the world rather than the robot. A path between two points in cspace can be found as before, only the path represents movement of the various parts of the world towards their final destination and thus provides a prescription for a robot.\nThere are two main stumbling blocks in using\u2018c-space methods. The lirst arises from the complexity of c-space obstacles. C-space obstacles are hard to describe analytically even in three dimensions. For low dimensions (fewer than 5), it is tractable to build a volumetric (as opposed to exact) model of the c-space obstacles, before the planning starts. The c-space is divided into voxels that are either occupied or free, and, the solution now proceeds by finding a path from start to goal [131. For higher dimensions, it is hopeless to attempt a volumetric representation because of the very large number of cells in the space. One solution is to skip the step of computing the c-space obstacles before the fact, and, proceed with navigation in the cspace using a good collision-checker [ 141 that keeps the gradient descent from running into obstacles.\nThe second stumbling block is that unless a globally exhaustive method is used, the search follows the local gradient and is not guaranteed to find the best path or to even get to the goal. A serious problem with gradient descent methods is that they are prone to getting stuck in local extremas. In the excavation domain, this would mean that the excavator had created a state from which it could not be able to readily proceed towards the goal without putting some soil back. Fortunately, this is a rare occurrence for most excavation tasks. The more common problem corresponds to moving along one side of a ridge in c-space, along which the rate of travel is slow. The smart thing to do would be to cross the ridge and proceed at a much faster rate, but this is not possible by gradient descent methods.\nThe main problem in using c-space methods for excavation is that the necessary representation would be so large that it would be intractable. This is because the c-space would necessarily have to encode all possible states of the terrain. Since soil is deformable, we would need a very large number of variables to represent the state of the terrain, in contrast to rigid bodies that can be represenred uniquely by a few parameters.\nSome researchers have used an operation space, an augmented c-space that includes essential action variables that uniquely specify task execution [151. For example, in the squeeze grasping domain where the robot is trying to grasp an object, the position and orientation of the object forms the cspace, while the operation space additionally includes separate dimensions for control variables like pushing direction. Construction of such a space allows the identification of actions that are guaranteed to succeed.\nSince it is not tractable to represent the state of the terrain\nexplicitly for the excavation task, we propose to formulate the task in an action space that is spanned only by the variables required to parameterize the task. The state of the terrain is implicit in this space; it is reflected by the imposed constraints. Instead of finding a trajectory in a high dimensional c-space, we will now look for a single point that optimizes a cost criterion in a lower dimensional action space. The cost of this simplification is that the selected point in the action space specifies only one dig and at most we can be sure that we have picked the best dig on a per dig basis but not necessarily the one that will provide the most gain over the entire task. Neither can we be certain that the search will escape local extrema. Hence, although we have avoided the issue of a very large search space with complex obstacles to avoid, the second issue of search remains.\n111. THE APPROACH\nIn order to provide an intuitive understanding of the proposed approach, let us consider an extended example in a twodimensional world. Fig. 3 Fig. 3 shows a terrain that must be excavated and Fig. 4 shows the conventional version of a mechanism that is to be used.\nThis sort of device is commonly called a \u201cbucket loader\u201d or a \u201cfront-end loader\u201d and can be automated. The loader is M completely excavate the pile, without intruding below the surface of the ground. In this example, we will show how geometrk and force constraints are imposed on the acuon space (a, d , h) from Fig. 2. Force constraints are refined through force feedback data obtained during experimentation. The constrained volume is then searched to select a dig that maximizes the amount of soil obtained. Finally, the selected dig is executed using control scheme that ensures robust excavation. A. Geometric Constraints\nLet us consider three types of geometric constraints that can be imposed on the action space: reachability, volume and shuping.",
+            "Reachability Constraint: This constraint separates the action space into digs that are kinematically feasible and those that are not. We will model the excavator as a P-R-R manipulator shown in Fig. 5.\nGiven a candidate dig, that is a trajectory for the bucket tip to follow, a standard inverse kinematics method is used to find the corresponding joint displacements (dl , 02, e3). A candidate dig may fail this constraint if it is required that the excavator reach outside its workspace (exceeds joint limits) or if in the course of the dig, one or more of the links are required to interpenetrate the terrain. The composite constraint surface due to the terrain in Fig. 3 and the excavator in Fig. 4, is shown in Fig. 6. The surface represents the boundary between the reachable and nonreachable digs- all points below the surface represent digs that meet the reachability constraint.\nVolume Constraint: Since the excavator bucket can only hold a volume Vmax, then an (a, d, h) triplet should not excavate more than this amount of soil. This gives us a further basis on which we can limit the set of feasible digs. This constraint is shown in Fig. 7.\nShaping Constraint: This constraint is given by the goal state of the terrain. In general this may be an arbitrary, stable, geometric specification of the earth. For our example, we will limit digs so that they do not intrude below the surface of the\nB. Force Constraints\nIf we assume that the robot excavator is infinitely strongthat it can muster any torque required, then the type of constraints discussed above are sufficient. More realistically, for robots with torque limits, we must consider the forces required to accomplish digging. Pushing on a section of soil results in failure along an internal rupture surface, also known as a failure surface. The force necessary to perform a particular dig is therefore partly dependent on the force necessary to fail the soil along the rupture surface, or, in other words to overcome the shear strength of the soil along that surface.\nCalculation of cutting resistance forces is not simple to estimate, because in general, the failure plane inside the soil is unknown. There is some research on the operation of earthmoving machinery [ 17][18] that explicitly addresses the issue of estimating forces necessary to overcome the shear strength of soil. Unfortunately, this work is mostly stated in empirical terms for specific types of machines. There is little attempt to work from first principles that use measures of well known soil properties. There has also been some work in the field of agricultural engineering that is directed at producing estimates of cutting resistance for tilling implements [19][20] using well understood physical principles. Unfortunately, the motions of the cutting surfaces analyzed for tilling are different enough",
+            "from those common in excavation, that a carryover of these formulations to the excavation domain is not immediately evident.\nThere are, however, some interesting ideas that can be gleaned from the tillage research. For example, McKyes claims that since an excavator bucket has side walls that cause soil to move inside the bucket, a two dimensional analysis can be used to estimate the cutting resistance. This is a useful insight since three dimensional analysis of a blade moving through soil is significantly more complex.\nIn lieu of a readily available model of soil-tool interaction, we will resort to a simple model that relies on well known principles in soil mechanics, so as to obtain order of magnitude estimates of cutting resistance. For our three parameter digs operating in dry uncompacted soil, there are two kinds of interactions between the bucket and the soil. The first is during the insertion phase, when the bucket edge is driven straight along the approach angle, into the soil. The maximum resistance experienced, till the bucket fills up, is at the deepest point of this phase. In the next phase, the bucket is lifted straight up. We might approximate the shear surface as being along the direction that edge of the bucket is going to lift through (Fig. 9).\nIn the second phase, the maximum resistance is encountered just as the blade starts to move up through the soil. At this point the force necessary to move the bucket is the sum of force necessary to overcome the weight of the soil in the bucket and the force necessary to fail the soil along the predicted shear surfacr. All (a, d, h) triplets for which the force required is greater than the maximum force available, will be ruled inadmissable. The force, F, necessary to excavate is given by:\nF = vy+fs (1)\nfs = 7 . A (2)\nwhere v is the volume of soil excavated, y is the density of soil, f, is the shear force necessary to fail the soil.f, is given by\nwhere 2 is the shear strength of the soil and A is the area of the failure plane- a product of the length of the failure plane and the width of the bucket. Since this is a two-dimensional analysis, the bucket will have unit width.\nThe basis of soil mechanical strength is ascribed to Coulomb (1776) who noted that there appeared to be two mechanical processes which determine the ultimate shearing strength of a material. One process (friction), he noted, is proportional to the pressure acting perpendicularly on the shearing surface. The other process (cohesion) seemed to be independent of normal pressure. The shear strength of a soil, T, is therefore modeled as\na sum of these two components:\nT = c+otan@ (3)\nwhere c is the cohesion, cr is the normal pressure acting on the internal shear surface' and tan @ is the coefficient of sliding friction. $ is also called the angle of internal friction and is directly visible as the angle of repose of a pile of dry, uncompacted granular material like sand and sugar.\nSo far, in this section we have said that if the soil properties (density, angle of internal friction, cohesion) are known, it is possible to get order of magnitude estimates of the resistance force encountered for the type of digging motions that have been proposed. The action space can now be further constrained based on whether or not it is possible for the robot to generate the required forces for perform a candidate dig. Lets say that the excavator in Fig. 4 can develop a maximum of 1000 units of force at the end effector. Also, lets assume that the soil properties are y= 20, @ = 30, c = 5. The constraint surface due to force limitation, given the terrain of Fig. 3, can be seen in Fig. 10.\nC. Search for an r r O p t i d Dig"
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0002766_j.ijmecsci.2003.09.004-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002766_j.ijmecsci.2003.09.004-Figure5-1.png",
+        "caption": "Fig. 5. Displacement of the excavator caterpillars.",
+        "texts": [
+            " The vectors of position of the centres of weight have the form: rS1 [0; 0; 0]; rS2 [0; \u2212b2; h2]; rS3 [ \u2212 YS3 sin ; (YS3 cos \u2212 b2); ZS3 ]; rS4 [ \u2212 YS4 sin ; (YS4 cos \u2212 b2); ZS4 ]; rS5 [ \u2212 YS5 sin ; (YS5 cos \u2212 b2); ZS5 ]; (43) where YS3 = b3 + b4 cos 1 \u2212 h4 sin 1; ZS3 = h3 + b4 sin 1 + h4 cos 1; YS4 = b3 + lw cos 1 + b5 cos( 2 \u2212 1) + h5 sin( 2 \u2212 1); ZS4 = h3 + lw sin 1 \u2212 b5 sin( 2 \u2212 1) + h5 cos( 2 \u2212 1); YS5 = b3 + lw cos 1 + lr cos( 2 \u2212 1) + b6 cos( 2 + 3 \u2212 1) + h5 sin( 2 + 3 \u2212 1); ZS5 = h3 + lw sin 1 \u2212 lr sin( 2 \u2212 1) \u2212 b6 sin( 2 + 3 \u2212 1) + h6 cos( 2 + 3 \u2212 1): The potential energy from the forces of gravity for the whole system with a non-deformed soil foundation is Vg(q) = (m1 + m2 + m3 + m4 + m5)g \u00b7 z + m2g(h2 \u2212 \u20191b2) +m3g(ZS3 + \u20191YS3 cos \u2212 \u20191b2 + \u20192YS3 sin ) +m4g(ZS4 + \u20191YS4 cos \u2212 \u20191b2 + \u20192YS4 sin ) +m5g(ZS5 + \u20191YS5 cos \u2212 \u20191b2 + \u20192YS5 sin ): (44) A soil foundation has been treated as a homogeneous body whose strain results from the pressures transferred by the caterpillars onto the foundation. It has been assumed that the caterpillar is supported in the chassis frame and during the pressure constitutes a rigid plate interacting with the foundation, as shown in Fig. 5. Denoting equivalent rigidities of a soil as super=cial ones in a vertical direction cz [(N=m2)=m], and linear ones in a horizontal direction cx and cy (N/m), the potential energy of the deformed soil foundation was determined. This energy is Vs(q) = cz \u00b7 a \u00b7 b[z2 + 1 12 \u2019 2 2(3a2 1 + a2) + z \u00b7 \u20191(b02 \u2212 b01) + 1 3 \u2019 2 1(b2 02 \u2212 b01b02 + b2 01)] +1 2 cx[2 \u00b7 x + \u20193(b01 + b02)]2 + 1 2 cy[2 \u00b7 y2 + 1 2 \u2019 2 3(a1 + a)2]: (45) It has been assumed that during the strain a soil foundation is subjected to energy dissipation, which is described by a Rayleigh dissipation function of the form: D(q; q\u0307) = 1 2 k\u2211 i=1 k\u2211 j=1 Rijq\u0307iq\u0307j: (46) Following the determination of rate of strain of the foundation resulting from displacements of the chassis with its caterpillars, the dissipation function of the system of the following form was determined: D(q\u0307) =Rza \u00b7 b[z\u03072 + 1 2 \u2019\u0307 2 2(3 \u00b7 a2 1 + a2) + z\u0307 \u00b7 \u2019\u03071(b02 \u2212 b01) + 1 3 \u2019\u0307 2 1(b2 02 \u2212 b01b02 + b2 01)] + 1 2 Rx[2 \u00b7 x\u0307 + \u2019\u03073(b01 + b02)]2 + 1 2 Ry[2 \u00b7 y\u0307 2 + 1 2 \u2019\u0307 2 3(a1 + a)2]: (47) Non-potential generalized forces result from cutting forces that are formed on the edge of the bucket during operation of an excavator"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003259_robot.2004.1307509-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003259_robot.2004.1307509-Figure1-1.png",
+        "caption": "Fig. 1. Gnspless Manipulation",
+        "texts": [],
+        "surrounding_texts": [
+            "I. INTRODUCTION\nManipulation without grasping is referred to as graspless manipulation [I] or nonprehensile manipulation [2]. In this paper, we study graspless manipulation where the manipulated object is supported not only by robot fingers but also by the environment; it includes pushing, sliding and tumbling (Fig. I). Graspless manipulation brings the following advantages to robots:\nManipulation without supporting all the weight of the\n. Manipulation with simple mechanisms Manipulation - when grasping is impossible object\nThus graspless manipulation is important as a complement of conventional pick-and-place to enhance the dexterity of robots.\nPlanning of robot motions to move an object from an initial configuration to a goal is a fundamental problem in robotic manipulation. However, robot motion planning for graspless manipulation is much more difficult than that for pick-and-place 131. In pick-and-place operation, once an object is grasped, the correspondence of its motion to the robot motion is trivial: therefore manipulation planning is reduced\nto a geometrical collision avoidance. On the other hand, the correspondence in graspless manipulation is nontrivial; thus manipulation planning requires mechanical analysis for consideration of the effect of gravity, contact forces, and so on. Moreover, graspless manipulation may be irreversible: For example, a robot can push an object but may not be able to pull it back. Therefore, most of related studies deal with planning of manipulation with a specific operation such as pushing (e.g.,\nThe authors proposed a planning method for general graspless manipulation by multiple robot fingerhps 131. However, the method can deal with only planar graspless manipulation. In this paper we extend our previous method. The main improvements are as follows: . Now it can deal with spatial graspless manipulation such\nas pushing and tumbling of a polyhedron by multiple robot fingertips. . Control modes of robot fingers (force controllposition control) are considered explicitly for realistic manipulation. . A new stability measure 16) is adopted in planning lo generate robuster graspless manipulation. . A* algorithm [7] is used to accelerate planning.\nThis paper is organized as follows: Section 11 introduces a model of graspless manipulation. Section U1 describes a method to determine appropriate finger control modes (force control or position control) at an instant in graspless manipulation based on 181. Section N proposes a method of motion planning of robot fingertips for graspless manipulation. In Section V, some examples of planned graspless manipulation including pushing and tumbling are presented. We also show an experimental result of execution of planned manipulation by a robot with a multi-fingered hand. Finally, this paper is concluded in Section VI.\n141,151).\n11. MODEL OF GRASPLESS MANIPULATION A. Assumptions\nfingertips, we make the following assumptions: In this paper, for graspless manipulation by multiple robot\nI ) The manipulated object, robot fingertips, and the environment are rigid.\n07803-8232-3/04/$17.00 @004 IEEE 2951",
+            "object motion is specified. We approximate each friction cone at contact point p by a polyhedral convex cone with unit edge vectors, cl(p), . . . , c.(p) E R3. For p,,,, E Csiide. let c'(penv,) E P3 be a unit edge vector of the friction cone at contact point p,,, , opposite to its sliding direction.\nThe set of possible contact force f E L3 at p,,, can be written as follows:\n{flf E sPan{cl(P,,\",),...,c,(P,,,)}} if P,\"\", E cstat .\n{flf E sPan{c'(P,\"\",)l} if P,, E Cslide,\n(1)\nwhere span{. . .} is a polyhedral convex cone spanned by its element vectors [9]. On the other hand, the set of possible finger force f at probl is: 2) Manipulation is quasi-static. 3) Coulomb friction exists between the object and the environment (or robot fingertips). The friction coefficient f { f l f E span{q(prob,), .. . , cs(prob,)}, ~.\nn ( ~ m b i ) ~ f If m a x i }\nif robot finger i is position-controlled, (2) {flf E span{cl(probi),...,cB(PTObi)}) 1 n(pr&()Tf f c o m i S ' f m a x i } .\non a contact surface is uniform. 4) Static and kinetic friction coefficients are equal. . ~ 5 ) All the contacts can be approximated by finite point\n6) Each of friction cones can be approximated by a poly-\n.\ncontacts [6] ;\nhedral convex cone [9]. I if robot fineer i is force-controlled, - 7) Each robot finger is modeled as a rigid sphere and- is where fm, , is the upper4imit of the normal component of\nin- onemint non-sliding contact with the 0bject;'we the finger force and f c o m i is the commanded force for .. robot finger i. . . consider only fingertips.\n8) Thenormal force of each robot finger has an upper limit. 9) Each robot fineer is either in Dosition-control mode or Then we define the following matrices: I\nin force-control mode. IO) Each of robot fingers in position-control mode'can apply\narbitraly force passively within its friction cone. -1 1). Each of robot fingers in force-control mode is in hybrid\npositionlforce control [10]:- the finger can apply commanded normal force actively and arbitrary ,tangential force passively within. its friction cone. 12) sliding and,rolling of robot fingers on object surfaces is not allowed. Regrasping is required to change the location of fingertips on the object.\nThe problem to be solved is to determine a sequence of fingertip positions and finger control modes to move an object from a given initial configuration to a given goal configuration by graspless manipulation. A sequence of desired normal forces is also to be obtained for forcesontrolled fingers.\n8. Mechanical Model\n-. ~~\n'\nI .\nConsider graspless manipulation of an object a s in Fig. 2. We set an object reference frame whose origin coincides with the center of mass of the object. Let pen, . . ,p,,, E @ be positions of contact points between .the object and the environment. ,Similarly, let probI, . .. ,probn, E? be positions of contact points between the object and the robot finger 1,. . . , n. We denote inward unit normal .vectors at contact point p by n(p) E @.\nLet us denote-the sets of positions of sliding and nonsliding contacts by Cslid& and CStat, respectively. We can identify whether p,,, E Cslide or penvi E CSw when the\nI if P,,,, E Cslide.\nCrab :=diag(C,,b1,...,Crobn) E %3\"xns\nCrobt := [cl(probl). . .Cs(Probt)l E pX' N m b := diag(n(P,bi), . . . I n(Probn)) E enxn,\nwhere I 3 is the 3 x 3 identity matrix, and p x 1 3 E P x 3 is a linear transformation equivalent to the cross product with p.\nWithout external disturbances, the equilibrium equation of the object can be expressed as:\nQknown + WenvCenvkenv + Wrobcrobkrob = 0, (3) where ken\"(> 0) and krob(> 0) are coefficient vectors to represent contact forces; Qknown E L6 is a known external (generalized) force applied to the object such as gravitational force. The upper limitation on the magnitude of normal finger forces can be written as:\nNTobCrobkrob 5 f,, (4)\nwhere f, := [ f m a x l , . . . , f m a x n l T E Ln."
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0001039_960485-Figure16-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001039_960485-Figure16-1.png",
+        "caption": "Fig. 16 : New hydraulic brake actuator under development",
+        "texts": [
+            " 15 shows the occurrence frequency of the steering wheel angular velocity for the pylon slalom condition mentioned above. The driver steered very quickly to keep the vehicle stable for the test without ASTC. However, ASTC reduces the driver's required steering reaction time to keep the vehicle stable. Pylon slalom test Vxo = 27.8 m/sec 5 10 Steering wheel angular velocity (rad/sec) Fig. 15 : Histogram of steering wheel operation (Experimental) NEW HYDRAULIC BRAKE ACTUATOR A drawing of a new hydraulic brake actuator under development as a future product is shown in fig. 16. This is smaller and 50 % lighter than a conventional hydraulic booster with ABS and traction control. This hydraulic brake actuator is not only applicable to ASTC but also to brake assist and adaptive cruise control, with minor modifications. SUMMARY (1) Vehicle directional stability in a transient steering maneuver has been studied. It was found that applying an active brake force to the front-outer wheel stabilizes the vehicle since an outward yaw moment is generated. (2) The effect of controlling the brake force response was evaluated by simulation and experiment to determine the brake actuator response criteria"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002867_s0094-5765(03)00194-2-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002867_s0094-5765(03)00194-2-Figure1-1.png",
+        "caption": "Fig. 1. Experimental spacecraft on-orbit conGguration.",
+        "texts": [
+            " The largest error quaternion vector components [ qerr1(t) qerr2(t) qerr3(t) ] are compared to its precomputed values at the halfway mark (qhalf ) to determine if the maneuver time reaches th: max i |qerri(t)| \u2212 qhalf = { \u00bf 0 \u2200t \u00a1 th ; \u00a1 0 \u2200t \u00bf th ; (25) where Iqerr =   qerr0 qerr1 qerr2 qerr3   =   qr0 qr1 qr2 qr3 \u2212qr1 qr0 qr3 \u2212qr2 \u2212qr2 \u2212qr3 qr0 qr1 \u2212qr3 qr2 \u2212qr1 qr0     q0 q1 q2 q3   ; (26) qhalf = maxi|qerri(0)| |sin( =2)| \u2223\u2223\u2223\u2223sin ( 4 )\u2223\u2223\u2223\u2223 : (27) In order to demonstrate the superiority of the proposed minimum-time SMC algorithm, we further adapt the eigenaxis quaternion regulator: * T = * M + Kqvec + D * !: (28) It has been shown in Ref. [2] that an eigenaxis rotation will occur when K = k diag( II) and D = d diag( II), where k and d are positive constants. A typical remote sensing spacecraft system is used as an example. Fig. 1 depicts the remote sensing spacecraft on orbit conGguration. The large angle maneuver of interest is speciGed in terms of Euler angles as shown in Table 1, with II = diag[ 182 329 336 ] kg m2. The maneuver on yaw is null for the most Earth-pointing remote sensing cases. The conGguration of reaction wheels in the simulated spacecraft has been deliberately arranged to accommodate the capability of fast attitude maneuver. According to the wheel conGguration, the maximum wheel torque Nsat = [ 0:56 0:52 0:24] N m, maximum wheel speed max = 5400 rpm, and MOI of wheel Iw = 0:041 kg m2 are used in the simulation"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001127_s0022112002002483-Figure10-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001127_s0022112002002483-Figure10-1.png",
+        "caption": "Figure 10. Four computed menisci (\u00a7 4.1), A1\u2013A4, between two curved plates, S1 and S2, for given normalized heights h1 = 1.5 and h2 = \u22121.0 of the triple points are shown. The plates are curved such that, at the triple (solid\u2013liquid\u2013vapour) points, the angle of the menisci with the vertical can take appropriate values necessary to form four different menisci, and yet satisfy the fixed contact angle with the solid. The outer menisci are computed by the procedure outlined in \u00a7 3.4. The interaction force between S1 and S2 (in (e)) is repulsive at all non-dimensional distance, x0, between the triple points. There are four solutions for the force originating from two bifurcation points B1 and B2. The points A1\u2013A4 correspond to the menisci shown in (a)\u2013(d ). The energy (hydrostatic and surface) as a function of x0 is shown in ( f ). A numerical derivative of the lowest energy with respect to x0 coincides with the corresponding force\u2013distance curve of (e) as expected.",
+        "texts": [
+            " Thus, A is the lowest or the highest point of the meniscus. Then, by (4.7), where y and h0 have opposite signs, \u03b8\u2032 6= 0 at any point on the meniscus. For the former family, let \u03b8\u2032 = 0 at B on the meniscus. Then, h(B) = 0 and \u03b8(B) 6= 1 2 \u03c0. At any point of the meniscus below the far-field liquid surface, \u03b8\u2032 < 0 and above the far-field liquid surface, \u03b8\u2032 > 0 (equation (4.1)). Thus, if there exists a point, A\u2032, on the meniscus where the tangent is horizontal, then the liquid is above A\u2032 (see e.g. figure 10). Thus, the two families are mutually exclusive. 4.5. Formation of clusters by floating plates: is there a critical size for sinking? Solids, floating on liquids, are known to agglomerate owing to interaction forces between them. The shape and size of a cluster formed by floating plates depend on the size and shape of the plates and their initial states. The weight of the cluster is the sum of the weights of the individual plates, but the perimeter of the cluster is less than the sum of the perimeters",
+            "3 that for a prescribed height, there are at most two possible menisci between the edge of a single plate and a liquid. Thus, for the meniscus between two plates (two edges are involved) there are at most four possible menisci for given prescribed heights of the triple points. However, the four solutions will result in four different horizontal gaps, x0, between the plates. Figures 10(a)\u201310(d ) show the four possible menisci formed between two solids, S1 with h1 = 1.5 and S2 with h2 = \u22121. The angle of the menisci at L1 with the vertical, \u03b81, is close to \u2212 1 2 \u03c0 (in figure 10(a), \u03b81 > \u2212 1 2 \u03c0, in 10(b), \u03b81 < \u2212 1 2 \u03c0). Thus, the menisci are close to the bifurcation point \u03b81 = \u2212 1 2 \u03c0. Note that the solids are curved at the edges so that they allow \u03b81 and \u03b82 to take required values to sustain the menisciL1L2 that maintain the fixed contact angle \u03c6 between the solid and the liquid. Figure 10(e) shows the four bifurcation branches of the solution for the repulsive interaction force between the two solids as a function of the horizontal gap, x0 (non-dimensional), between L1 and L2. The equal interaction force for the menisci A1 \u2212 A4 are shown by the ordinate of the line A1A4 in figure 10(e). Each pair of menisci, such as A1 and A2, originate from a bifurcation point such as B1 where \u03b81 = \u2212 1 2 \u03c0. The pair, A3 and A4, originate from B2 where \u03b82 = \u2212 1 2 \u03c0. Figure 10( f ) shows the energy associated with the four possible menisci as a function of x0. In calculating the hydrostatic part of the energy, the width of each of the plates in non-dimensional units is taken as 2w = 2. The energies corresponding to the four menisci A1\u2013A4 are represented by the filled circles A1\u2013A4 in figure 10( f ). The lowest energy curve is differentiated with respect to x0 numerically and the result is plotted on the force diagram. It matches the corresponding force curve as expected. Figures 11(a)\u201311(d ) show the four possible menisci between two solids S1 and S2 with h1 = 1 and h2 = 2, respectively. Note that h = 2 is the maximum allowable height (see (3.5) and the following paragraph) of the meniscus mR on the right-hand side of S2 with an angle \u03b8R = \u2212 1 2 \u03c0 at the triple point LR . Figure 11(e) shows the interaction force, Fx/\u03b3, which is attractive for all x0"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure3.11-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure3.11-1.png",
+        "caption": "Figure 3.11. The displacement due to a pure rotation about an axis at 0 is equal to the dis placement due to the same rotation about a parallel axis at 0* and a translation b* perpen dicular to the axis of rotation.",
+        "texts": [
+            "138) for a pure rotation about 0 can be accomplished by a translation b* perpen dicular to the axis a= k together with the same rotation about a parallel axis through 0*. Since T is the same as before, the rotational part of the dis placement of P about 0* is given as (3.139) 196 Chapter 3 Thus, use of (3.138) and (3.139) in (3.137) yields b* =d(P)-Tx*(P)= ( -i + j)- ( -2i + 2j) = (i- j) ft, which is certainly perpendicular to a. This is the required translational displacement of 0* in qJ. The reader may confirm that the translation b* obtained from (3.137b) yields the same result. The dis placement is illustrated in Fig. 3.11. Notice that b* is simply the chord dis placement of 0* on the circle of radius 00* due to a pure rotation about 0. A displacement of a rigid body .19 each of whose particles is displaced parallel to a given plane is called a plane displacement of !JI. Any plane cross section of !JI parallel to the assigned plane, which is named the displacement plane, may be chosen as the plane for discussion; it requires no special dis tinction. It follows that the axis of rotation must be perpendicular to the dis placement plane"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000569_s0045-7949(98)00004-2-Figure8-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000569_s0045-7949(98)00004-2-Figure8-1.png",
+        "caption": "Fig. 8. The undeformed and deformed con\u00aegurations of an in\u00aenitesimal reference surface of a general two-dimensional structure.",
+        "texts": [
+            " 7(b) that f ~f 1 ~f 2 ~f 3 danrjr trsjrjs danrtrsjs 59 It follows from Equations (57), (58a)\u00b1(c) and (59) that s\u0302 S F T J\u0302 T , t 1 F F s\u0302 60 Using Equations (3), (8), (20), (42a) and (60), we obtain the following relationships: S s\u0302 F \u00ffT F F \u00ff1 t F \u00ffT, J\u0302 s\u0302 T T S U , J 1 2 J\u0302 J\u0302 T 1 2 S U U S , s 1 2 s\u0302 s\u0302 T 61 These relationships are the same as those obtained in Atluri [1]. However, the presented derivations clearly show the directions of di erent stresses. For highly \u00afexible structures undergoing large displacements and rotations but small strains, Jaumann strain measure is the most appropriate one for use because Jaumann strains are shown to be objective geometric measures de\u00aened with respect to the rigidly rotated undeformed area. Next we show how to use Jaumann strains and stresses in the modeling of highly \u00afexible two- dimensional structures. Figure 8 shows the undeformed and deformed con\u00aegurations of an in\u00aenitesimal reference surface of a general two-dimensional structure. To simplify derivations and explanations, we adopt the Kirchho hypothesis and hence neglect transverse shear deformations and transverse normal strain in the following derivations. The system xyz corresponds to the system x1x2x3 in Figs 1\u00b17 and is an orthogonal curvilinear coordinate system with the curvilinear axes x and y being on the undeformed reference surface and the z-axis being a rectilinear axis",
+            " We also let i1\u00c3 and i2\u00c3 denote the unit vectors along the axes x\u03021 and x\u03022, respectively. Jaumann strains can be easily obtained by using the concept of local displacements [21, 24]. The local displacement vector u of an arbitrary point on the shell element has the form u ukik 62a where u1 x, y, z, t u01 x, y, t z y2 x, y, t \u00ff y02 x, y , u2 x, y, z, t u02 x, y, t \u00ff z y1 x, y, t \u00ff y01 x, y , u3 x, y, z, t u03 x, y, t 62b Here, uk 0 are the displacements (with respect to the frame x1x2x3) of the reference point A' in Fig. 8, y1 and y2 are the rotation angles of the observed shell element with respect to the axes x1 and x2, respectively, and y1 0 and y2 0 are the corresponding initial rotation angles. Because the frame x1x2x3 is a local coordinate system attached to the observed shell element, and the x1\u00b1x2 plane is tangent to the deformed reference surface, we have u01 u02 u03 y01 y02 y1 y2 @u03=@x @u03= @y 0 63 It follows from Fig. 8 that @u02 1 e1 @x sin g61, @u01 1 e2 @y sin g62 64a @u01 @x 1 e1 cos g61 \u00ff 1, @u02 @y 1 e2 cos g62 \u00ff 1 64b @y02 @x \u00ff @ j1 @x j3 k01, @y01 @y \u00ffk02, @y01 @x \u00ff k061, @y02 @y k062 64c @y2 @x \u00ff @ i1 @x i3 k1, @y1 @y \u00ffk2, @y1 @x \u00ff k61, @y2 @y k62 64d where kij are deformed curvatures and kij 0 are undeformed curvatures. Substituting Equations (62a)\u00b1 (b), (63), (64a) and (64b)\u00b1(d) into Equation (21) yields the Jaumann strains of a general shell struc- ture as B11 1 e1 cos g61 \u00ff 1 z k1 \u00ff k01 , B22 1 e2 cos g62 \u00ff 1 z k2 \u00ff k02 , B12 1 2 1 e1 sin g61 1 e2 sin g62 z k6 \u00ff k06 , B33 B13 B23 0 65 where k60k61+k62 and k6 00k61 0 +k62 0 "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001324_rsta.2002.1155-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001324_rsta.2002.1155-Figure1-1.png",
+        "caption": "Figure 1. The geometry of simple shear experiment with three principal orientations, labelled V , G and D, for the initial nematic director n aligned along the vorticity, gradient and displacement directions, respectively. The small-amplitude simple shear \" \u00bb ei!t is applied to the elastomer, and the measured stress \u00bc (!) provides the linear complex modulus in each of the three con\u00afgurations.",
+        "texts": [],
+        "surrounding_texts": [
+            "The dynamic equations are obtained from the classical variational principle applied to the proper Lagrangian density amended by the Rayleigh dissipation function, L \u00a1 T _s = 1 2 \u00bb (@tu)2 \u00a1 F (u; \u00a3) \u00a1 T _s( _u; _\u00a3). The elastic potential energy density in a nematic rubber takes the form (de Gennes 1980) F = C1(n \u00a2 \" \u00a2 n)2 + 2C2 Tr[~\"](n \u00a2 \" \u00a2 n) + C3(Tr[~\"])2 + 2C4[n \u00a3 \" \u00a3 n]2 + 4C5[n \u00a3 \" \u00a2 n]2 + 1 2 D1[n \u00a3 \u00a3]2 + D2n \u00a2 \" \u00a2 [n \u00a3 \u00a3]; (2.1) Phil. Trans. R. Soc. Lond. A (2003) with \"ik = ~\"ik \u00a1 1 3 Tr[~\"] \u00af ik, the traceless part of linear symmetric strain ~\"ik = 1 2 (@kui + @iuk). In the isotropic limit C1 = 2C4 = 2C5 ! \u00b7 \u00ba cxkBT (the rubber modulus, proportional to the crosslinking density cx) and the elastic energy density reduces to the classical Lam\u0301e expression \u00b7 \"ik\"ki + B\"2 kk . In the fully incompressible case one should omit the C2 and C3 \u00ba B terms in (2.1). Since rubber is a weak solid, its shear moduli are much smaller compared with those involving compression and we thus now ignore the e\u00acects of volume change. Neglecting the e\u00acects of heat convection, the total entropy production in a uniaxial anisotropic medium is expressed by the volume integral of the conjugate forces and \u00aeuxes. Let us rewrite the density of dissipation function in a form matching the elastic energy density (2.1) T _s = A1(n \u00a2 _\" \u00a2 n)2 + 2A4[n \u00a3 _\" \u00a3 n]2 +4A5([n \u00a3 _\" \u00a2 n])2 + 1 2 \u00ae 1N 2 + \u00ae 2n \u00a2 _\" \u00a2 N (2.2) in the incompressible case, where the Leslie{Ericksen notation reads N = [n \u00a3 _\u00a3]. Here the constants are linear combinations of the classical Leslie coe\u00af cients of a nematic elastomer medium: A1 = 1 2 ( \u00ac 1 + \u00ac 4 + \u00ac 5 + \u00ac 6); A4 = 1 4 \u00ac 4; A5 = 1 8 (2\u00ac 4 + \u00ac 5 + \u00ac 6): In the isotropic limit, one  nds A1 = 2A4 = 2A5 ! \u00b2 . By di\u00acerentiation of (2.2) by the symmetric strain rate _\"ij and by _\u00a3 i, respectively, one obtains a representation of the symmetric viscous stress tensor and the nematic molecular  eld, contributing to the local viscous torque (Terentjev & Warner 2001). Two important non-dimensional numbers control the regimes of \u00aeuid dynamics in nematic liquids: the Reynolds number Re and the Ericksen number Er. In elastomers and gels, one is much more concerned with the balance between \u00aeow-induced torques, scaling as \u00b9 \u00b2 rv, and those of the rubbery matrix, expressed by @F=@\u00a3 \u00b9 D1\u00a3. This yields a new dimensionless group of parameters characterized by the number Ne = \u00b2 v=(LD1), with L the characteristic length-scale. The assumed domination of rubber-elastic e\u00acects over the nematic Frank (curvature) elasticity essentially means that D1 \u00be K=L2, that is, Ne \u00bd Er. There is a clear parallel between the form of equilibrium potential energy density (2.1) and the dissipation function (2.2): Ai $ Ci and \u00ae 1;2 $ D1;2. This is not a surprise since the symmetry of an equilibrium elastic deformation at constant volume and of a slow viscous \u00aeow in a uniaxial continuum is the same. Equally, there is a direct correspondence in the dependence of the various coe\u00af cients on nematic order parameter Q. We can, therefore, represent the viscous coe\u00af cients of a nematic elastomer as products of the corresponding rubber-elastic constant and an appropriate relaxation time, that is Ai = Ci \u00bd R; \u00ae 1 = D1 \u00bd 1; \u00ae 2 = D2 \u00bd 2: (2.3) Relaxation times \u00bd R do not have to be equal for each pair of coe\u00af cients, however; one can expect them all be of the same order of magnitude|of the order of Rouse time for the corresponding polymer backbone (Edwards et al . 2000). Two orientational relaxation times, \u00bd 1;2, describe the dynamics of the nematic director. One expects, in many polymer systems, to  nd \u00bd R \u00b9 10\u00a15 s (Doi & Edwards 1986), while the nematic director relaxation time is \u00bd 1 \u00b9 10\u00a12 s from Sch onstein et al . (2001). The demand of Phil. Trans. R. Soc. Lond. A (2003) positive-de niteness of the entropy production imposes a constraint on the values of relaxation times: \u00bd 1 \u00bd R > D2 2 8C5D1 \u00bd 2 2 : (2.4) In the ideally soft nematic elastomer, with C5 = D2 2=8D1, this reduces simply to \u00bd 1 \u00bd R > \u00bd 2 2 . Neglecting in the  rst instance the e\u00acects of Frank elasticity on the director gradients, one obtains the set of dynamic equations \u00bb @2 t u = r \u00a2 \u00be s ym \u00b2 @k \u00b5 @F @[rku] \u00b6 + @k \u00b5 @T _s @[rk _u] \u00b6 ; (2.5) 0 = @F @\u00a3 + @T _s @ _\u00a3 : (2.6) Here the  rst equation describes the balance of forces per unit volume acting at a material point. We shall neglect the inertial term \u00bb u, relevant only in higherfrequency acoustic e\u00acects (Terentjev et al . 2002). The second equation represents the balance of torques, of elastic and viscous origin. The local moments of inertia are neglected in (2.6): at low frequencies and \u00aeow rates this is well justi ed in classical hydrodynamics, while, in the high-frequency regime, the polymer transition to the high-frequency glassy modulus would overwhelm the angular inertia. We have discarded the nematic Frank elasticity contribution: if it happens that the nematic rubber penetration length is not small, K=\u00b7 L2 \u00b9 1 (e.g. in highly diluted gels or very thin samples), then the torque balance will be controlled by the full molecular  eld. Equation (2.6) transforms to [n \u00a3 hfu ll] = 0, with the molecular  eld hfu ll \u00ba Kr2 \u00af n + D1\u00a3 + D2n \u00a2 \" + \u00ae 1 _\u00a3 + \u00ae 2n \u00a2 _\": (2.7) In the limit of isotropic rubber, Q ! 0, the only relevant equation is that for the symmetric stress, equation (2.5), which in this case reduces to \u00be = C4\" + A4 _\". This is the low-frequency limit of a general linear-response expression \u00bc (t) = Z G(t \u00a1 t0) _\"(t0) dt0: In the frequency domain, this limit of a general complex modulus G \u00a4 (!) ! Ci +i!Ai shows the initial rise in the loss modulus with frequency. The condition of zero net torque determines the rate of relative director variation _\u00a3 . In a  xed coordinate system, for instance with the initial director n along the z-axis, and assuming oscillatory solutions so that d=dt ) i!, this is straightforward: \u00b5 \u00a3 x \u00a3 y \u00b6 = D2 + i!\u00ae 2 D1 + i!\u00ae 1 \u00b5 \u00a1 \"yz \"xz \u00b6 : (2.8) Substituting it into the corresponding components of stress \u00be s ym , one obtains the e\u00acective viscoelastic response. This operation, known as the integration out of the internal degrees of freedom, is precisely what has been done (Golubovi\u0301c & Lubensky 1989; Olmsted 1994) in the analysis of equilibrium soft elasticity. Here it is complicated by the viscous terms, but the essence remains the same: the e\u00acective shear Phil. Trans. R. Soc. Lond. A (2003) modulus is renormalized to CR 5 (!) = C5 \u00a1 D2 2 8D1 (1 + i!\u00bd 2)2 (1 + i!\u00bd R)(1 + i!\u00bd 1) : (2.9) Clearly, at any non-zero frequency there will no longer be a complete `soft\u2019 cancellation leading to CR 5 = 0. However, a reduction of the e\u00acective elastic modulus will nevertheless occur. The three principal shear geometries of classical dynamic mechanical experiments are shown in  gure 1. The three cases are labelled according to the orientation of the initial uniformly aligned director n with respect to the shear direction. These three geometries are the same as in the classical setting for Miesovicz viscosity experiments (de Gennes & Prost 1993). The elastic free energy density, equation (2.1), takes the form, FG = (C5 + 1 8 [D1 \u00a1 2D2]) \"2 \u00a1 1 2 (D1 \u00a1 D2) \"\u00b3 + 1 2 D1 \u00b3 2; F D = (C5 + 1 8 [D1 + 2D2]) \"2 \u00a1 1 2 (D1 + D2) \"\u00b3 + 1 2 D1 \u00b3 2; FV = C4\"2; 9 >= >; (2.10) in the three cases of  gure 1, where the amplitude of the small change in director orientation, \u00af n, is taken equal to the angle \u00b3 . Clearly, one does not expect director rotation to occur in the `log-rolling\u2019 geometry V . The analysis (Terentjev & Warner 2001) gives the linear `nominal stress\u2019 at a given frequency of imposed simple shear strain, \u00bc (!) = G \u00a4 (!)\"(!), with the linear complex shear modulus G \u00a4 = G0 + iG00. The linear response in the two geometries involving n-rotation, G and D, is exactly the same despite the di\u00acerence in the rotation angles \u00b3 G; D . These storage and loss moduli have a single-relaxation time behaviour with a characteristic frequency !1 = D1=\u00ae 1 and can be written in a universal form: G0(!) = 2 \u00b5 C5 \u00a1 D2 2 8D1 \u00b6 + (!\u00bd 1)2 1 + (!\u00bd 1)2 D2 2 4D2 1 \u00b5 1 \u00a1 \u00bd 2 \u00bd 1 \u00b62 ; G00(!) = !\u00bd 1 1 + (!\u00bd 1)2 D2 2 4D2 1 \u00b5 1 \u00a1 \u00bd 2 \u00bd 1 \u00b62 + 2!\u00bd 1 \u00b5 D2 2 4D1 \u00b5 \u00bd 2 \u00bd 1 \u00b62 \u00a1 C5 \u00bd R \u00bd 1 \u00b6 : 9 >>>>= >>>>; (2.11) The `non-soft\u2019 V geometry returns a trivial sum of the elastic and viscous parts, G \u00a4 V(!) = 2C4 + 2i!A4 \u00b2 2C4(1 + i!\u00bd R); (2.12) which is simply the low-frequency limit of the classical isotropic polymer dynamics. Figure 2b shows the qualitative sketch of the storage modulus (the real part, G0) Phil. Trans. R. Soc. Lond. A (2003) of an ordinary polymer network. To make the simple conceptual point, this plot ignores more complicated e\u00acects, such as entanglements, and only expresses the role of Rouse dynamics. Thus, at ! ! 0 the isotropic modulus approaches the constant value G0 = 2C4 \u00b2 \u00b7 , which is of course the equilibrium rubber modulus. At !\u00bd R \u00b9 1 one  nds the dynamic glass transition (often called the \u00ac -transition). The shear modulus saturates at a very high (glass) value at high frequencies. The main content of the  gure 2 is given by the two plots ( gure 2a) which show the frequency dependence of G0 and G00, expressed by equations (2.11) in the two director-rotating geometries, G and D. One  nds the classical single-relaxation behaviour with the characteristic time-scale \u00bd 1 = \u00ae 1=D1. At !\u00bd 1 \u00be 1 (assuming this is still much lower than the dynamic glass transition), the storage modulus saturates at the constant level of the modi ed rubber plateau, given by equation (2.11), while the loss modulus begins its linear rise towards the glass transition peak. More interesting is the behaviour at !\u00bd 1 \u00bd 1. Here we see a substantial drop in the storage modulus due to the internal director relaxation: the e\u00acect of `dynamic soft elasticity\u2019. The family of curves G0(!) in  gure 2a is drawn for the increasing nematic order parameter Q, which enters into the elastic constants and the Leslie coe\u00af - cients: we see the increasing drop in G0 and also the rise of the new loss peak in G00 at !\u00bd 1 \u00b9 1. Phil. Trans. R. Soc. Lond. A (2003)"
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0001635_3.20858-Figure8-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001635_3.20858-Figure8-1.png",
+        "caption": "Fig. 8 Dimensions of the antenna.",
+        "texts": [],
+        "surrounding_texts": [
+            "To validate the theory, two different control designs are presented, i.e., a spring-mass-damper system and a shape and pointing control system for a space antenna. The active controller has been determined in both cases by means of a discrete linear suboptimal control technique,7 and the system response has then been evaluated via an exact nonlinear integration of the equations of motion, to take into account the presence of saturations and PWM actuators. Pulse-width modulated actuators are always assumed to be coupled and acting in opposite directions, the switching between the two being determined by the sign of the firing duration time 6. Example 1: Second-Order System The first test was carried out to demonstrate the effects of the firing delay r, the maximum input amplitude UM, and the D ow nl oa de d by C O R N E L L U N IV E R SI T Y o n Fe br ua ry 1 , 2 01 5 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .2 08 58 sampling time A on the transient and steady-state response of a system subjected to a control input and to a reference command by using the spring-mass-damper system shown in Fig. 2. The dynamics of the system having mass m, damping coefficient c, and elastic spring constant k is represented in the state-space form by *l r-2f\u00ab *H i -o>2 0 the input force (/) is given by (34) (35) where [r] is the desired set point. It can be noted that the feed-forward control, i.e., mu2[r], is capable of achieving the desired set point in case of perfect model knowledge. Thus the feedback terms are added to improve response performances and to take into account uncertainties in the model knowledge. The system parameters are m = 1, f = 0.1, and co = 6.28, i.e., an open-loop natural frequency of 1 Hz. With these system characteristics, a controller sampling time of 0.1 s appears appropriate. Specifications for the closed-loop system are established in terms of damping factor, to be as close as possible to 0.7, and a sufficiently low input requirement to prevent undesirable control saturations in PWM operational mode. To meet the dynamic performances, kv and ke are computed for a PAM control by minimizing the discrete quadratic performance index7: (36) c f Fig. 2 Second-order system. Spring-Mass-Damper System Sampling time 0.1 sec ; no input delay Sampling time 0.1 sec ; optimal input delay 0.0 0.0 0.0 1.0 2.0 3.0 0.0 1.0 2.0 3.0 Time (sec) Time (sec) Sampling time 0.05 sec ; no input delay Sampling time 0.05 sec ; optimal input delay 1.5 -| 1.0 2.0 3.0 0.0 1.0 2.0 3.0 Time (sec) Time (sec) \u2014\u2014PAM -o-4Jmax = 50 \u2014x-Umox = 200 Fig. 3 Displacement response of second-order system (PAM and PWM). where E {\u2022} indicates the expected value operator for a suitable set of stochastic disturbances and/or nonzero initial conditions, and [Qy] = (37a) (37b) (37c) which leads to kv = -2.67, ke = 24.2. Two different sampling times were then used to analyze the system response, namely A = 0.1 and 0.05 s. Shorter sampling times are not considered since this would mean operating almost as in continuous time, so that PWM control would not be applicable. The optimal firing delay T and the closed-loop eigenvalues are collected in Table 1, whereas the step responses to a unit reference command, either PAM or PWM, with different delays and maximum amplitudes, are reported in Figs. 3-5. In Fig. 5 the PAM input is plotted vs the left ordinate axis, whereas PWM inputs, i.e., duration, are plotted vs the right ordinate axis. Considering Table 1, it should be immediately remarked that, depending on A, the system eigenvalues are not constant. This is not surprising since, because of Eq. (30), both the state transition matrix [$] and input matrix [F] depend on A, whereas in this particular case [K] and [C] are held constant. For the purpose of the present example, this is not important, since the comparisons are done between PAM and PWM responses of analogous systems, with the sampling period as the distinctive parameter of the system configuration. D ow nl oa de d by C O R N E L L U N IV E R SI T Y o n Fe br ua ry 1 , 2 01 5 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .2 08 58 The analysis of the step responses is in good agreement with the theoretical analysis. A few considerations should be noted. As stated in Eq. (8), if the delay is not optimal, the error of the PWM controlled response relative to the \"desired\" response, i.e., the PAM controlled response, is proportional to the input amplitude UM, and this clearly appears from the steady-state biases in Figs. 3 and 4. Moreover, in this particular example, the value UM = 50 is quite close to the steady-state discrete input, which is precisely 39.48. Then it is obvious that the steady-state value of 5 will be quite close to A. This does not agree with the assumptions made to establish the relationship between PAM and PWM control and explains why the performances of the system subjected to a PAM input and to a PWM input with null delay are quite similar. In fact, from Eq. (4), it is seen that, for d = A, the equivalence between PAM and PWM control is obtained with r = 0. Figures 3 and 4 clearly point out the peculiar response of PWM controlled systems. Even at \"steady state,\" the system tends to oscillate around the average condition, due to the on/off input type, and the only reduction in amplitude is due to the integral action of the system dynamics. From Fig. 5 it can be seen that the PWM is always of the same sign. Thus the limit cycles are due only to the elastic action of the system and not to a change of sign of the control force. This fact also explains why the limit cycle amplitude is larger for the higher input level. In fact, since the pulse intensity is equivalent, the duration is shorter for the higher input, and thus it leaves more time for the elastic action to operate, causing a larger amplitude oscillation. The optimum firing delay r guarantees that the steady-state response of the PAM and PWM controlled systems are the same. The difference in the transient response depends on the input amplitude. Higher amplitudes mean smaller pulse firing durations 6, and so the approximation of Eq. (6) becomes indeed true, and Eq. (7) represents the real dynamic behavior of the system, so that the optimal firing delay effectively minimizes the response error. The same holds also for smaller sampling periods since, as shown by Eq. (5), d is also proportional to A. Considering that in discrete control the sampling time is usually limited by the control hardware and cannot therefore be made as small as possible, it can then be stated that it is advisable to select the optimal firing delay for PWM control and, compatible with actuator limits, operate with a sufficiently high input level. Example 2: Shuttle-Attached Antenna The second example shows an application of a mixed PAM/ PWM control to the shape and pointing control of a large space antenna. This system is clearly more complex than the preceding one, and since the antenna structural damping is neglected and the overall system is a free body, it is open-loop neutrally stable. Nevertheless, it will be shown that the equivalent PWM control can be successfully applied also to this kind of system. The antenna studied in the present work consists of a large dish connected to the Shuttle by an aluminum L-shaped flexible truss.8 Figures 6-8 depict the topology and dimensions of the antenna, along with its finite element representation consisting of 95 grid points. Three representative points are marked in Fig. 7, and their dynamic behavior will be used to assess the performance of the system, i.e., node 480 at the corner of the flexible truss, node 751 at the center of the dish, and node 920 on the dish boundary. The flexible truss is considered to be clamped to the Shuttle. All of the elements are supposed to be uniform tubular beams with a cross-sectional area of 200 mm2, Young's modulus equal to 72,520 D ow nl oa de d by C O R N E L L U N IV E R SI T Y o n Fe br ua ry 1 , 2 01 5 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .2 08 58 N/mm2, and density 3000 kg/mm3. The total mass of the antenna is 635 kg, and the total system mass is 102,788 kg. The system dynamics are governed by two sets of equations, one governing the average rigid body motion and another governing the small perturbations of the rigid motion and the elastic deformations. A detailed derivation of the equations of motion is found in the literature9'10 and will not be repeated here for the sake of conciseness. Instead, attention is focused on the small perturbed overall motion and on the elastic deformations as represented by the simplified system (38) in which only two coupling terms [A] and [\u00a3] are present. In Eq. (38), [V] is the matrix of the antenna branch modes, i.e., the modes of the antenna clamped to the still standing Shuttle; [70] and [m] are the inertia and mass matrices of the system in the undeformed condition; {/?) , {/3) , and {q} are, respectively, the perturbed displacement and orientation of the system center of gravity and the antenna branch modal coordinates. It is possible to reformulate Eq. (38) as a set of first-order linear differential equations, with state vector [ x ] , state matrix [A], input vector [u ) , and input matrix [B] given by (39a) V'QiV (39b) 0 J 0 0 0 0 0 0 0 0 X2 lx] + [Rift <?#i 0 q\\ To -MI A ] = [ Vf ] = m 0 F'A ' 0 Io V'T, 0 r > 1\u0302 J J AF E 'V I { u } = [F, (39d) The branch mode shapes corresponding to the lowest 10 eigenfrequencies were used to represent the antenna. This restricted choice of natural mode shapes is considered accurate enough since, as illustrated in Table 2, they are representative of a wide class of possible motions of the antenna. The analysis of the eigenvalues of the [A] matrix of Eq. (39), also reported in Table 2, shows that basically the coupling has the effect of modifying the flexible branch modes that nonetheless are enough to correctly represent the lowest vibration modes of the whole system since, due to the massive Shuttle, the last branch modes are practically the vibration modes. The control system consists of 23 actuators driven in a decentralized way from collocated sensors. Six of them exert forces and moments on all six degrees of freedom of the rigid Shuttle; eight thrusters are placed on the flexible truss: four on the truss corner acting in the X and Y directions and four at the end acting in the Y and Z directions. The corresponding sensors are local displacement and velocity sensors. The control of the dish is carried out by using three reaction wheels, acting along the three axes at the connection with the truss, driven by angle and angular rate sensors and by six piezoelectric layers on the dish's outer radial beams, marked in Fig. 7 as Pi-P6- The piezoelectric layers are supposed to work in couples, one acting as an actuator and one as a sensor, measuring local deformations. For the piezoelectric actuators a lead-lag network has also been devised to provide better performance. Let { u s } indicate the forces acting on the Shuttle, { u t } the PWM forces on the truss, \\ u d ] the moments applied at the dish center, and { u p } the forces exerted by the piezoelectric actuators; by partitioning the measurements vector accordingly, the decentralized feedback control law can be expressed as (40a) (40b) (40c) (40d) The most common performance indexes used for antennas are the nominal pointing error and the average shape error, whose definitions and limits for a large reflector are pointing error = V { t f c ) ' \\ & c } / 3 <0.02 deg shape error = V (za } ' [ za } /na < 5 mm (41a) (41b) where { d c } represents the three rotations at the center of the antenna, and {za } are the displacements of the na nodes of the dish perpendicular to the dish plane. These performance indexes are nonlinear and difficult to treat numerically, so a more simple linear quadratic function of a performance vector {x) is used to build a suitable quadratic cost function to be minimized 02 (42) (43) The matrices [Qx] and [Qu] are diagonal with unit weighting factors for the first two entries of the performance vector, 10 for the modal coordinates, 1/10 for the Shuttle actuators, 1/1000 for the truss actuators, and 1/10,000 for the piezoelectric actuators. A sampling rate of 2 samplings/s, i.e., 10 times the highest natural frequency considered, was chosen for the controller. Table 3 reports the optimal firing delays for each of the four pairs of thrusters located on the flexible truss. As predicted by Table 3 Actuator firing delay times of the Shuttle antenna system Actuator Delay r F.480 FZ15\\ 0.2497 0.2485 0.2495 0.2496 D ow nl oa de d by C O R N E L L U N IV E R SI T Y o n Fe br ua ry 1 , 2 01 5 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .2 08 58 Table 4 Gain parameters and lead and lag constants of the piezoelectric actuators Actuator Pi P2 P3 P4 PS ?6 Kp -314.4 151.9 -115.2 -219.6 161.5 -309.1 b 0.8095 1.276 0.0185 0.0226 1.125 0.2713 a 0.5396 0.7791 0.0084 0.2780 0.5446 0.3213 Shuttle Attached Antenna 5.00 - Fig. 9 Impulse response of the Shuttle-antenna system. Eq. (17), the optimal delays are quite close to half the sampling period. An analysis of the gain parameters, lead and lag constants of the piezoelectric actuators reported in Table 4, shows a nonsymmetric behavior of the control, in spite of the structural symmetry, due to the unsymmetry of the natural modes representative of the antenna. A mixture of integrating and derivative effects of the lead-lag networks can be seen, and it is remarked that this solution is the best one compatibly with the structure of the system, since the lead and lag constants were included as unknown parameters during the minimization process. The closed-loop response of the system to an impulse comparable to the effect of a lateral docking maneuver, producing a lateral velocity increment of the Shuttle of 1 cm/s in the Y direction, has been simulated considering PAM and PWM control of the truss. In the latter case all of the thrusters are supposed to have a unique thrust level of 10 kg. The time histories reported in Fig. 9 are in good agreement with the performances already discussed. The sampling time and the amplitude of the PWM inputs are well within the hypothesis at the base of the theory presented. No control saturations occur, and once more it is demonstrated that the application of PWM with an optimal delay is perfectly equivalent to PAM control. It is remarked that this system is open-loop neutrally stable, and despite this fact the response of the PWM controlled system shows no tendency to become unstable and no errors in the system displacements or discrete inputs. This holds both for points located near and far from the location of the pulsed thrusters. Just a slight intersample ripple appears in the velocity at the truss corner where the pulsed actuator is located. IV. Conclusions A method for the pulse-width application of a discrete pulse amplitude control law computed for a linear system has been proposed. This conversion technique maintains the dynamic performance of the PAM control and requires a simple equivalence of the total impulse applied during each sampling interval and the computation of the firing time delay. Since the latter depends only on system parameters, it can be computed separately from the control law. This fact is fairly attractive for practical applications in which a PWM control is required, since it allows computation of the control law for a PAM control system, using one of the many available software packages. The only further operation required to perform the conversion from PAM to PWM is one multiplication for each of the inputs and a constant firing delay which, under reasonable assumptions, does not cause unpredictable effects on the system performance. References franklin, G. F., and Powell, J. D., Digital Control of Dynamic Systems, Addison-Wesley, Reading, MA, 1980. 2Sutton, G. P., Rocket Propulsion Elements: An Introduction to the Engineering of Rockets, Wiley, New York, 1986. 3Anthony, T. C., Wie, B., and Carroll, S., \"Pulse Modulated Control Synthesis for a Flexible Spacecraft,\" Proceedings of the AIAA Guidance, Navigation, and Control Conference, AIAA, Washington, DC, 1989, pp. 65-76. 4Kubiak, E. T., Penchuk, A. N., and Hattis, P. D., \"A Frequency Domain Stability Analysis of a Phase Plane Control System,\" Journal of Guidance, Control, and Dynamics, Vol. 8, No. 1, 1985, pp. 50-55. 5Friedland, B., \"Modeling Linear Systems for Pulsewidth-Modulated Control,\" IEEE Transactions on Automatic Control, Vol. AC21, Oct. 1976, pp. 739-746. 6Friedland, B., Control System Design: An Introduction to StateSpace Methods, McGraw-Hill, New York, 1987. 7Bernelli-Zazzera, F., Mantegazza, P., and Ongaro, F., \"A Method to Design Structurally Constrained Discrete Suboptimal Control Laws for Actively Controlled Aircrafts,\" Aerotecnica Missili e Spazio, Vol. 67, No. 1-4, 1988, pp. 18-25. 8Wang, S. J., Lin, Y. H., and Ih, C. H. C., \"Dynamics and Control of a Shuttle Attached Antenna Experiment,\" Journal of Guidance, Control, and Dynamics, Vol. 8, No. 3, 1985, pp. 344-353. 9Quinn, R. D., and Meirovitch, L., \"Maneuver and Vibration Control of SCOLE,\" Journal of Guidance, Control, and Dynamics, Vol. 11, No. 6, 1988, pp. 542-553. 10Bernelli-Zazzera, F., Ercoli-Finzi, A., and Mantegazza, P., \"Mixed Discrete/Pulse-Width Control of a Shuttle Attached Antenna,\" Proceedings of the X Congresso Nazionale AIDAA, ETS Editrice, Pisa, Italy, Oct. 1989, pp. 469-476. D ow nl oa de d by C O R N E L L U N IV E R SI T Y o n Fe br ua ry 1 , 2 01 5 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .2 08 58"
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0000979_1.2802427-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000979_1.2802427-Figure1-1.png",
+        "caption": "Fig. 1 Diagram of spatiai mechanism for measuring inertia tensor",
+        "texts": [
+            " The first is a small device suitable for measuring of the inertia tensor of small specimens (maximum dimension 250 mm, maximum mass 6 kg). The second is larger (mass range 50 -\u0302 200 kg, maximum length about 2 m). This paper presents the kinematic and dynamic analyses of the spatial mechanism for measuring the inertia tensor, and describes the principle of identification and calibration proce dures. Some examples of inertia tensor identification are then given and discussed. 2 Kinematic Analysis Figure 1 shows the spatial mechanism for measuring the inertia tensor; Fig. 2 is a photograph of the smaller version of the prototype mechanism. A fixed coordinate system XYZ with origin at point O is introduced; axis Z is vertical, whereas axes X and Y lie in the horizontal plane. Plate 7r, which is used to mount the specimen, rotates around fixed point O, where there is a spherical pair. This pair is airlubricated in order to reduce friction torque. Disks Ci and C2 rotate around axes X and Y, respectively, by means of two revolute joints and are named \"adjustment disks"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003394_tmag.1985.1064226-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003394_tmag.1985.1064226-Figure6-1.png",
+        "caption": "Fig. 6. Equipotential plots of the motor",
+        "texts": [
+            " A finite element mesh of 2906 triangular elements of first order and a t o t a l of 1474 nodes to the entire cross section is shown in Fig.5. The sky-line storied technique is taken. There are 29 average elements per line. The rotor currents for slip s with frequence sf, may be modelled by modification of rotor condu.chvity where f , is the su.pply freqwncy. In the rotor, the equation is V V w Fig. 5 . Einite eiement mesh 2291 REFERENCE A = A,sinCswt + rp), so aiiAIht = jwasA = jwcr'A 6' is equivalent conductivity with 6' = sa. The solution has been performed for slip values from 0 to 1. The equipotential plots are shown in Fig.6 at slip s= 1, and computed exciting currents versus the slip in Fig. 7. ' CONCLUSION The matrix method which ombines field equations with circuit equations has been, developed for calculating the performances of electromagnetic devices with specified terminal voltages and external impedances of electric circuit. This approach takes into account eddy current effects and creates a symmetric system with respect to the ones mentioned in the literature. I t has been verified using a 4-pOle shaded-pole motor and a electromagnetic relay in which the exciting current is computed"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002571_cca.1996.558742-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002571_cca.1996.558742-Figure2-1.png",
+        "caption": "Figure 2: Rate of strain in a continuum",
+        "texts": [
+            " In addition, F can be written df d X F = - ( x , t ) 1 1 2 2 - -E+-s2 where E is the symmetric part of the deformation and 1(2 its skew-symmetric part. In continuum mechanics, E represents the rate of strain tensor and Jz is the rotation tensor [Aris, 19621. 3.1. Rate of strain tensor Since E is symmetric, it has n real eigenvalues and n orthogonal eigenvectors. The eigenvectors give the stretching directions of the continuum, and the corresponding real eigenvalues give the stretching velocities in these directions. This is illustrated in Figure 2, and motivates the following definition. Definition 1 Given the continuously differentiable system equations k = f(x, t ) , a region of the state space is called strictly contracting (expanding) i f F or E is uniformly negative (positive) definite in that region. Note that by a region we mean an open connected set, and by F uniformly negative definite we mean that 3 ,b > 0, VX, V t 2 0, F(x, t ) 5 -PI < 0 3.2. Rotation tensor The skew-symmetric tensor Cl can be regarded as a generalized crossproduct matrix [Fluegge, 19721, which means that any vector r multiplied with Cl is perpendicular to r"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000517_1616-8984(199607)1:1<1::aid-seup1>3.0.co;2-6-Figure1-13-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000517_1616-8984(199607)1:1<1::aid-seup1>3.0.co;2-6-Figure1-13-1.png",
+        "caption": "Figure 1-13. Grating coupler without mechanical parts using a CCD array (according to [77]).",
+        "texts": [
+            " Both input and output couplers are realized depending on whether radiation (incident) is coupled into the waveguide to be guided or leaves the waveguide in the grating region. The principle is shown schematically in Figure 1-12. A variety of set-ups have been developed [20]. Commercially available is a grating coupler system from Artificial Sensing Instruments (ASI) in Zurich, Switzerland. A further development is a set-up with a position sensitive CCD array which avoids mechanical angle scanning to find the optimum coupling angle [80] (see Figure 1-13). Another possibility is the bi-diffractive coupler. In Figure 1-14, the grating structure is shown schematically, representing a mixed grating with two grating constants [162], A second angle of outcoupling is achieved which differs from that of the normal reflection. By these means, the signal-to-noise ratio drastically increases and this set-up is simpler than the ASI instrumentation. 1.2 Principles of Optical Transduction 19 Using embossed polycarbonate gratings, even disposable chips can be considered"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000569_s0045-7949(98)00004-2-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000569_s0045-7949(98)00004-2-Figure1-1.png",
+        "caption": "Fig. 1. The deformation of an in\u00aenitesimal element whose undeformed con\u00aeguration is a rectangular parallelepiped.",
+        "texts": [
+            " We also illustrate the use of Jaumann stresses and strains and the new concepts of local displacements and orthogonal virtual rotations [21] in the development of a geometricallyexact theory for shells with arbitrary initial curvatures and show the correlation of energy and vector formulations. Moreover, we illustrate the use of corotated Cauchy stresses and corotated Eulerian strain rates in elastoplastic analysis. To derive the elastic energy of a structure, we consider an in\u00aenitesimal element whose undeformed shape is a cube, as shown in Fig. 1. Here, the frame x1x2x3 is an orthogonal rectilinear inertial frame, the base vectors along the axes x1, x2, and x3 are j1, j2, and j3, respectively. The frame x1x2x3 represents the rigidly translated and rotated con\u00aeguration of the frame x1x2x3, and the base vectors along the axes x1, x2, and x3 are i1, i2 and i3, respectively. Moreover, fk are forces acting on the deformed surfaces and v (=vkjk) denotes the absolute displacement vector of the point O and also the rigid-body translation of the frame x1x2x3",
+            " Engineering stresses smn and engineering strains emn If it is assumed that @v @xm jn @v @xn jm 6 then it follows from Equations (2) and (6) that dP V 0 smndemn dV 0 7 where smn 1 2 f m dxp dxq jn f n dxr dxs jm , m 6 p 6 q, n 6 r 6 s 8 emn 1 2 @v @xm jn @v @xn jm 9 Here smn and emn are called engineering stresses and engineering strains, respectively. Both smn and emn are symmetric. Because of the assumption, Equation (6), Equation (7) is not exact. Second Piola\u00b1Kirchho stresses Smn and Green\u00b1Lagrange strains Lmn Since @rO/@xm=jm in Fig. 1, d(@rO/ @xm jn) = d( jm jn) = 0. Moreover, the position vector ro of the point o is given by ro=rO+v and @ro/ @xm=lmim\u00c3 (no summation), where im\u00c3 denotes the unit vector along the deformed dxm and lm denotes the stretch along im\u00c3 , as shown in Fig. 1. Hence, d @v @xm jn d @ rO @xm jn @v @xm jn d @ ro @xm jn d lmim\u0302 jn 10 Washizu [2] showed that the surface traction force fm can be represented in terms of second Piola\u00b1 Kirchho stresses Smk and stretches lk as f m Sm1l1i1\u0302 Sm2l2i2\u0302 Sm3l3i3\u0302 dxp dxq, p 6 q 6 m 11 Substituting Equations (10) and (11) into Equation (2) yields dP V 0 S11l1i1\u0302 S12l2i2\u0302 S13l3i3\u0302 jnd l1i1\u0302 jn S21l1i1\u0302 S22l2i2\u0302 S23l3i3\u0302 jnd l2i2\u0302 jn S31l1i1\u0302 S32l2i2\u0302 S33l3i3\u0302 jnd l3i3\u0302 jn dx 1 dx 2 dx 3 12 Green\u00b1Lagrange strains (or Lagrangian strains) Lmn are de\u00aened by using the change of the squared length of an in\u00aenitesimal line segment as 2Lmn dxm dxn dro dro \u00ff drO drO @ ro @xm @ro @xn \u00ff @ rO @xm @rO @xn dxm dxn 13 Hence, Lmn 1 2 @ro @xm @ro @xn \u00ff @rO @xm @ rO @xn 1 2 lmim\u0302 lnin\u0302 \u00ff jm jn 1 2 lmim\u0302 lnin\u0302 \u00ff dmn 14 where repeated subindices do not imply summations and dmn denotes the Kronecker delta function. We note that Lmn=Lnm. Using the fact that d(dmn) = 0 and Smn=Snm [2], we obtain S12 l2i2\u0302 jn d l1i1\u0302 jn S21 l1i1\u0302 jn d l2i2\u0302 jn S12d l1i1\u0302 jn l2i2\u0302 jn S12d l1i1\u0302 l2i2\u0302 S12d 2L12 S12dL12 S21dL21 15 Hence, Equation (12) can be rewritten as dP V 0 SijdLij dV 0 16 which shows that Green\u00b1Lagrange strains are work-conjugate to the second Piola\u00b1Kirchho stresses. Jaumann stresses Jmn and Jaumann strains Bmn Since elastic energy is due to relative displacements among material points, it follows from Fig. 1 that the variation of elastic energy can be represented in terms of relative displacements as [3] dP V 0 f 1 in d @u @x 1 dx 1 in f 2 in d @u @x 2 dx 2 in f 3 in d @u @x 3 dx 3 in 17 where u (=0) is the local displacement vector of the point o with respect to the frame x1x2x3, as shown in Fig. 1. Moreover, Pai and Palazotto [3] showed that the rigidly translated and rotated frame x1x2x3 can be located by requiring that @u @xn im @u @xm in 18 Substituting Equation (18) into Equation (17) yields dP V 0 JmndBmn dV 0 19 where Jmn 1 2 J\u0302mn J\u0302nm , J\u0302mn f m dxp dxq in, m 6 p 6 q 20 Bmn 1 2 @u @xm in @u @xn im @u @xn im @u @xm in Bnm 21 Here Jmn are the so-called Jaumann stresses and Bmn are the so-called Jaumann strains. We note that Equation (18) makes Jaumann strain and stress tensors symmetric",
+            " The vector representations of strains shown in Equations (4), (9), (14), (21), (24) and (32) are valid for any orthogonal curvilinear or rectilinear coordinate systems. One can substitute v = vkjk or u= ukik into these equations to obtain strain\u00b1displacement relations. However, for curvilinear coordinate systems, @jk/@xm and @ik/@xm may be nontrivial and results in initial curvature-induced terms. Equations (4), (9) and (24) show that the directions of the displacement gradients, engineering strains and in\u00aenitesimal strains are along the undeformed coordinates, which causes the non-objectivity. Equation (14) and Fig. 1 show that the directions of Green\u00b1Lagrange strains are along the directions of im\u00c3 , which are not three perpendicular directions. Equation (32) and Fig. 2 show that Almansi strains are along the directions of jm\u00c4 , which are not three perpendicular directions. Equation (21) shows that the directions of Jaumann strains are de\u00aened with respect to the deformed coordinates and along three perpendicular directions. Such characteristics are convenient for the imposition of shear stress conditions on the bonding surface in deriving the shear warping functions of beams, plates and shells [23]",
+            " To derive the relationship of di erent stress measures, we consider an undeformed area dA with a unit outward normal N(=Nkjk) and its deformed area da with a unit outward normal n(=nkjk), as shown in Fig. 7(a). Because F= dV/dV0, dV0=dAN dx = dANk dxk, and dV= dan dy= danm dym=danmFmk dxk, we obtain F dANk danmFmk 57 It follows from Equation (3) and Fig. 7(a) that f f 1 f 2 f 3 dAN1j1 s\u03021sj1js dAN2j2 s\u03022sj2js dAN3j3 s\u03023sj3js dANrs\u0302rsjs 58a Second Piola\u00b1Kirchho stresses are measured with respect to the rigidly rotated undeformed area dANkik. Moreover, it follows from Fig. 1 that dx1j1 is deformed into l1 dx1i1\u00c3 and hence l1i1\u00c3 =Fs1js. Consequently, it follows from Equation (11) and Fig. 7(a) that f dAN1i1 S1klki1ik\u0302 dAN2i2 S2klki2ik\u0302 dAN3i3 S3klki3ik\u0302 dANrSrklkik\u0302 dANrSrkFskjs 58b Because Jaumann strains are measured with respect to the rigidly rotated undeformed area dANkik, it follows from Equation (20) and Fig. 7(a) that f dANrir J\u0302rkirik dANrJ\u0302rkik dANrJ\u0302rkTksjs 58c Next we consider the same undeformed and deformed areas as those in Fig. 7(a) but described in terms of Euler coordinates, as shown in Fig"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001045_a:1019555013391-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001045_a:1019555013391-Figure4-1.png",
+        "caption": "Figure 4. A system with a 2 dof joint.",
+        "texts": [],
+        "surrounding_texts": [
+            "In [7], recursive combination rules have been found in order to find such a minimal parameter set. Starting from the leaves of the tree-like structure, these rules determine the parameters that combine on a body, those that completely disappear from the equations, and those that are reported on the preceding body, depending on the nature (prismatic or revolute) of the joints. For example, Table I gives the combination rules that are to be applied for a revolute joint j . These rules have been demonstrated in the case of one dof joints. When joints have more than one dof, ROBOTRAN inserts fictitious massless bodies between two real bodies and apply the same rules. However, it can be shown that, for some MBS structures, the previous rules are not sufficient anymore, as shown in the following simple didactic example. EXAMPLE. 2 (orthogonal rotational) dof joint. Starting from body 3, we recursively apply the rules described in [7] and reproduced in the table, to our examplative structure: \u2022 Body 3 identifiable parameters: b3 x , b3 z , K3 xy , K3 xz, K 3 yz, K 3 yy , K3 d = (K3 zz \u2212 K3 xx)/2. \u2022 Body 2 reports from body 3: K\u22172 =  K3 s 0 0 0 0 0 0 0 K3 s  with K3 s = (K3 zz + K3 xx)/2 b\u22172 =  0 b3 y 0  identifiable parameters: b\u22172 y , K\u22172 zz , K2 d = (K\u22172 xx \u2212 K\u22172 yy )/2. \u2022 Body 1 reports from body 2: K\u22171 = K1 +  K2 s 0 0 0 K2 s 0 0 0 0  with K2 s = (K\u22172 xx +K\u22172 yy )/2 b\u22171 = b1 identifiable parameters: b\u22171 x , b\u22171 z , K\u22171 yy . If we examine the identifiable parameters on body 2, we have both K\u22172 zz = K3 s and K2 d = K3 s /2. This means that we end up with two parameters that are multiples of each others, so that only one of them should be kept. In order to detect these particular cases, two solutions are foreseeable: the first one is to try to register analytically all the possible cases where such a situation occurs: this presents the risk to forget some of them. The other solution takes advantage of symbolic manipulations, and is the only effort to cover all possible particular situations of this kind in an efficient way. We will not develop the combination rules here (for a detailed description, see [7]), but briefly expose the methodology we have followed in order to symbolically apply them in ROBOTRAN to any open MBS and to automatically generate its minimal parameterization: 1. All the possible combinations are symbolically performed on the pre-computed barycentric parameters using the above mentioned rules. Since, at each step, we have the symbolic expression of the previously determined identifiable parameters at our disposal, ROBOTRAN can symbolically check that any new parameter to be formed is not a multiple of a previous one. This provides us with all the possible combined parameters that can appear in the dynamical equations, together with their symbolic expression. We will call this set {p}. 2. The inverse dynamics equations are calculated using the recursive Newton\u2013 Euler technique described in Section 2. It must be noted that these equations are written with respect to the barycentric parameters. These do not correspond to parameter set {p} found in step 1. In fact, we can consider that {p} is forming a new set of barycentric parameters that is constructed from the real barycentric parameters in the following way: some of the barycentric parameters are themselves present in {p}: they remain unchanged; barycentric parameters that do not appear at all in {p} are removed; the remaining parameters of {p} can be introduced as components of the barycentric parameters according to some indications derived from the recursive combination rules of [7]. These indications are briefly explained in Appendix A. 3. These equations are then symbolically derived with respect to {p} using a recursive derivation routine developed within ROBOTRAN [10]. When computing the inverse dynamics of the MBS (Section 2), each recursive equation is assumed to depend, explicitly or not, on each variable of the set {p}. This a priori dependency provokes the systematic creation of a recursive auxiliary variable, being a partial derivative of the current equation, even if in the end it appears that the latter variable was useless: indeed, at the end of the recursion, an elimination process will detect it and remove the corresponding equation before printing. In this way, we obtain a matrix D with Dij = \u2202\u03c4 i/\u2202pj . 4. D may contain some columns that are identically equal to zero. These columns correspond to the parameters that do not appear in the equations. These parameters are removed from {p} and we finally end up with the minimal parameterization of the MBS."
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0001635_3.20858-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001635_3.20858-Figure6-1.png",
+        "caption": "Fig. 6 Topology of the Shuttle-attached antenna.",
+        "texts": [],
+        "surrounding_texts": [
+            "To validate the theory, two different control designs are presented, i.e., a spring-mass-damper system and a shape and pointing control system for a space antenna. The active controller has been determined in both cases by means of a discrete linear suboptimal control technique,7 and the system response has then been evaluated via an exact nonlinear integration of the equations of motion, to take into account the presence of saturations and PWM actuators. Pulse-width modulated actuators are always assumed to be coupled and acting in opposite directions, the switching between the two being determined by the sign of the firing duration time 6. Example 1: Second-Order System The first test was carried out to demonstrate the effects of the firing delay r, the maximum input amplitude UM, and the D ow nl oa de d by C O R N E L L U N IV E R SI T Y o n Fe br ua ry 1 , 2 01 5 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .2 08 58 sampling time A on the transient and steady-state response of a system subjected to a control input and to a reference command by using the spring-mass-damper system shown in Fig. 2. The dynamics of the system having mass m, damping coefficient c, and elastic spring constant k is represented in the state-space form by *l r-2f\u00ab *H i -o>2 0 the input force (/) is given by (34) (35) where [r] is the desired set point. It can be noted that the feed-forward control, i.e., mu2[r], is capable of achieving the desired set point in case of perfect model knowledge. Thus the feedback terms are added to improve response performances and to take into account uncertainties in the model knowledge. The system parameters are m = 1, f = 0.1, and co = 6.28, i.e., an open-loop natural frequency of 1 Hz. With these system characteristics, a controller sampling time of 0.1 s appears appropriate. Specifications for the closed-loop system are established in terms of damping factor, to be as close as possible to 0.7, and a sufficiently low input requirement to prevent undesirable control saturations in PWM operational mode. To meet the dynamic performances, kv and ke are computed for a PAM control by minimizing the discrete quadratic performance index7: (36) c f Fig. 2 Second-order system. Spring-Mass-Damper System Sampling time 0.1 sec ; no input delay Sampling time 0.1 sec ; optimal input delay 0.0 0.0 0.0 1.0 2.0 3.0 0.0 1.0 2.0 3.0 Time (sec) Time (sec) Sampling time 0.05 sec ; no input delay Sampling time 0.05 sec ; optimal input delay 1.5 -| 1.0 2.0 3.0 0.0 1.0 2.0 3.0 Time (sec) Time (sec) \u2014\u2014PAM -o-4Jmax = 50 \u2014x-Umox = 200 Fig. 3 Displacement response of second-order system (PAM and PWM). where E {\u2022} indicates the expected value operator for a suitable set of stochastic disturbances and/or nonzero initial conditions, and [Qy] = (37a) (37b) (37c) which leads to kv = -2.67, ke = 24.2. Two different sampling times were then used to analyze the system response, namely A = 0.1 and 0.05 s. Shorter sampling times are not considered since this would mean operating almost as in continuous time, so that PWM control would not be applicable. The optimal firing delay T and the closed-loop eigenvalues are collected in Table 1, whereas the step responses to a unit reference command, either PAM or PWM, with different delays and maximum amplitudes, are reported in Figs. 3-5. In Fig. 5 the PAM input is plotted vs the left ordinate axis, whereas PWM inputs, i.e., duration, are plotted vs the right ordinate axis. Considering Table 1, it should be immediately remarked that, depending on A, the system eigenvalues are not constant. This is not surprising since, because of Eq. (30), both the state transition matrix [$] and input matrix [F] depend on A, whereas in this particular case [K] and [C] are held constant. For the purpose of the present example, this is not important, since the comparisons are done between PAM and PWM responses of analogous systems, with the sampling period as the distinctive parameter of the system configuration. D ow nl oa de d by C O R N E L L U N IV E R SI T Y o n Fe br ua ry 1 , 2 01 5 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .2 08 58 The analysis of the step responses is in good agreement with the theoretical analysis. A few considerations should be noted. As stated in Eq. (8), if the delay is not optimal, the error of the PWM controlled response relative to the \"desired\" response, i.e., the PAM controlled response, is proportional to the input amplitude UM, and this clearly appears from the steady-state biases in Figs. 3 and 4. Moreover, in this particular example, the value UM = 50 is quite close to the steady-state discrete input, which is precisely 39.48. Then it is obvious that the steady-state value of 5 will be quite close to A. This does not agree with the assumptions made to establish the relationship between PAM and PWM control and explains why the performances of the system subjected to a PAM input and to a PWM input with null delay are quite similar. In fact, from Eq. (4), it is seen that, for d = A, the equivalence between PAM and PWM control is obtained with r = 0. Figures 3 and 4 clearly point out the peculiar response of PWM controlled systems. Even at \"steady state,\" the system tends to oscillate around the average condition, due to the on/off input type, and the only reduction in amplitude is due to the integral action of the system dynamics. From Fig. 5 it can be seen that the PWM is always of the same sign. Thus the limit cycles are due only to the elastic action of the system and not to a change of sign of the control force. This fact also explains why the limit cycle amplitude is larger for the higher input level. In fact, since the pulse intensity is equivalent, the duration is shorter for the higher input, and thus it leaves more time for the elastic action to operate, causing a larger amplitude oscillation. The optimum firing delay r guarantees that the steady-state response of the PAM and PWM controlled systems are the same. The difference in the transient response depends on the input amplitude. Higher amplitudes mean smaller pulse firing durations 6, and so the approximation of Eq. (6) becomes indeed true, and Eq. (7) represents the real dynamic behavior of the system, so that the optimal firing delay effectively minimizes the response error. The same holds also for smaller sampling periods since, as shown by Eq. (5), d is also proportional to A. Considering that in discrete control the sampling time is usually limited by the control hardware and cannot therefore be made as small as possible, it can then be stated that it is advisable to select the optimal firing delay for PWM control and, compatible with actuator limits, operate with a sufficiently high input level. Example 2: Shuttle-Attached Antenna The second example shows an application of a mixed PAM/ PWM control to the shape and pointing control of a large space antenna. This system is clearly more complex than the preceding one, and since the antenna structural damping is neglected and the overall system is a free body, it is open-loop neutrally stable. Nevertheless, it will be shown that the equivalent PWM control can be successfully applied also to this kind of system. The antenna studied in the present work consists of a large dish connected to the Shuttle by an aluminum L-shaped flexible truss.8 Figures 6-8 depict the topology and dimensions of the antenna, along with its finite element representation consisting of 95 grid points. Three representative points are marked in Fig. 7, and their dynamic behavior will be used to assess the performance of the system, i.e., node 480 at the corner of the flexible truss, node 751 at the center of the dish, and node 920 on the dish boundary. The flexible truss is considered to be clamped to the Shuttle. All of the elements are supposed to be uniform tubular beams with a cross-sectional area of 200 mm2, Young's modulus equal to 72,520 D ow nl oa de d by C O R N E L L U N IV E R SI T Y o n Fe br ua ry 1 , 2 01 5 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .2 08 58 N/mm2, and density 3000 kg/mm3. The total mass of the antenna is 635 kg, and the total system mass is 102,788 kg. The system dynamics are governed by two sets of equations, one governing the average rigid body motion and another governing the small perturbations of the rigid motion and the elastic deformations. A detailed derivation of the equations of motion is found in the literature9'10 and will not be repeated here for the sake of conciseness. Instead, attention is focused on the small perturbed overall motion and on the elastic deformations as represented by the simplified system (38) in which only two coupling terms [A] and [\u00a3] are present. In Eq. (38), [V] is the matrix of the antenna branch modes, i.e., the modes of the antenna clamped to the still standing Shuttle; [70] and [m] are the inertia and mass matrices of the system in the undeformed condition; {/?) , {/3) , and {q} are, respectively, the perturbed displacement and orientation of the system center of gravity and the antenna branch modal coordinates. It is possible to reformulate Eq. (38) as a set of first-order linear differential equations, with state vector [ x ] , state matrix [A], input vector [u ) , and input matrix [B] given by (39a) V'QiV (39b) 0 J 0 0 0 0 0 0 0 0 X2 lx] + [Rift <?#i 0 q\\ To -MI A ] = [ Vf ] = m 0 F'A ' 0 Io V'T, 0 r > 1\u0302 J J AF E 'V I { u } = [F, (39d) The branch mode shapes corresponding to the lowest 10 eigenfrequencies were used to represent the antenna. This restricted choice of natural mode shapes is considered accurate enough since, as illustrated in Table 2, they are representative of a wide class of possible motions of the antenna. The analysis of the eigenvalues of the [A] matrix of Eq. (39), also reported in Table 2, shows that basically the coupling has the effect of modifying the flexible branch modes that nonetheless are enough to correctly represent the lowest vibration modes of the whole system since, due to the massive Shuttle, the last branch modes are practically the vibration modes. The control system consists of 23 actuators driven in a decentralized way from collocated sensors. Six of them exert forces and moments on all six degrees of freedom of the rigid Shuttle; eight thrusters are placed on the flexible truss: four on the truss corner acting in the X and Y directions and four at the end acting in the Y and Z directions. The corresponding sensors are local displacement and velocity sensors. The control of the dish is carried out by using three reaction wheels, acting along the three axes at the connection with the truss, driven by angle and angular rate sensors and by six piezoelectric layers on the dish's outer radial beams, marked in Fig. 7 as Pi-P6- The piezoelectric layers are supposed to work in couples, one acting as an actuator and one as a sensor, measuring local deformations. For the piezoelectric actuators a lead-lag network has also been devised to provide better performance. Let { u s } indicate the forces acting on the Shuttle, { u t } the PWM forces on the truss, \\ u d ] the moments applied at the dish center, and { u p } the forces exerted by the piezoelectric actuators; by partitioning the measurements vector accordingly, the decentralized feedback control law can be expressed as (40a) (40b) (40c) (40d) The most common performance indexes used for antennas are the nominal pointing error and the average shape error, whose definitions and limits for a large reflector are pointing error = V { t f c ) ' \\ & c } / 3 <0.02 deg shape error = V (za } ' [ za } /na < 5 mm (41a) (41b) where { d c } represents the three rotations at the center of the antenna, and {za } are the displacements of the na nodes of the dish perpendicular to the dish plane. These performance indexes are nonlinear and difficult to treat numerically, so a more simple linear quadratic function of a performance vector {x) is used to build a suitable quadratic cost function to be minimized 02 (42) (43) The matrices [Qx] and [Qu] are diagonal with unit weighting factors for the first two entries of the performance vector, 10 for the modal coordinates, 1/10 for the Shuttle actuators, 1/1000 for the truss actuators, and 1/10,000 for the piezoelectric actuators. A sampling rate of 2 samplings/s, i.e., 10 times the highest natural frequency considered, was chosen for the controller. Table 3 reports the optimal firing delays for each of the four pairs of thrusters located on the flexible truss. As predicted by Table 3 Actuator firing delay times of the Shuttle antenna system Actuator Delay r F.480 FZ15\\ 0.2497 0.2485 0.2495 0.2496 D ow nl oa de d by C O R N E L L U N IV E R SI T Y o n Fe br ua ry 1 , 2 01 5 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .2 08 58 Table 4 Gain parameters and lead and lag constants of the piezoelectric actuators Actuator Pi P2 P3 P4 PS ?6 Kp -314.4 151.9 -115.2 -219.6 161.5 -309.1 b 0.8095 1.276 0.0185 0.0226 1.125 0.2713 a 0.5396 0.7791 0.0084 0.2780 0.5446 0.3213 Shuttle Attached Antenna 5.00 - Fig. 9 Impulse response of the Shuttle-antenna system. Eq. (17), the optimal delays are quite close to half the sampling period. An analysis of the gain parameters, lead and lag constants of the piezoelectric actuators reported in Table 4, shows a nonsymmetric behavior of the control, in spite of the structural symmetry, due to the unsymmetry of the natural modes representative of the antenna. A mixture of integrating and derivative effects of the lead-lag networks can be seen, and it is remarked that this solution is the best one compatibly with the structure of the system, since the lead and lag constants were included as unknown parameters during the minimization process. The closed-loop response of the system to an impulse comparable to the effect of a lateral docking maneuver, producing a lateral velocity increment of the Shuttle of 1 cm/s in the Y direction, has been simulated considering PAM and PWM control of the truss. In the latter case all of the thrusters are supposed to have a unique thrust level of 10 kg. The time histories reported in Fig. 9 are in good agreement with the performances already discussed. The sampling time and the amplitude of the PWM inputs are well within the hypothesis at the base of the theory presented. No control saturations occur, and once more it is demonstrated that the application of PWM with an optimal delay is perfectly equivalent to PAM control. It is remarked that this system is open-loop neutrally stable, and despite this fact the response of the PWM controlled system shows no tendency to become unstable and no errors in the system displacements or discrete inputs. This holds both for points located near and far from the location of the pulsed thrusters. Just a slight intersample ripple appears in the velocity at the truss corner where the pulsed actuator is located. IV. Conclusions A method for the pulse-width application of a discrete pulse amplitude control law computed for a linear system has been proposed. This conversion technique maintains the dynamic performance of the PAM control and requires a simple equivalence of the total impulse applied during each sampling interval and the computation of the firing time delay. Since the latter depends only on system parameters, it can be computed separately from the control law. This fact is fairly attractive for practical applications in which a PWM control is required, since it allows computation of the control law for a PAM control system, using one of the many available software packages. The only further operation required to perform the conversion from PAM to PWM is one multiplication for each of the inputs and a constant firing delay which, under reasonable assumptions, does not cause unpredictable effects on the system performance. References franklin, G. F., and Powell, J. D., Digital Control of Dynamic Systems, Addison-Wesley, Reading, MA, 1980. 2Sutton, G. P., Rocket Propulsion Elements: An Introduction to the Engineering of Rockets, Wiley, New York, 1986. 3Anthony, T. C., Wie, B., and Carroll, S., \"Pulse Modulated Control Synthesis for a Flexible Spacecraft,\" Proceedings of the AIAA Guidance, Navigation, and Control Conference, AIAA, Washington, DC, 1989, pp. 65-76. 4Kubiak, E. T., Penchuk, A. N., and Hattis, P. D., \"A Frequency Domain Stability Analysis of a Phase Plane Control System,\" Journal of Guidance, Control, and Dynamics, Vol. 8, No. 1, 1985, pp. 50-55. 5Friedland, B., \"Modeling Linear Systems for Pulsewidth-Modulated Control,\" IEEE Transactions on Automatic Control, Vol. AC21, Oct. 1976, pp. 739-746. 6Friedland, B., Control System Design: An Introduction to StateSpace Methods, McGraw-Hill, New York, 1987. 7Bernelli-Zazzera, F., Mantegazza, P., and Ongaro, F., \"A Method to Design Structurally Constrained Discrete Suboptimal Control Laws for Actively Controlled Aircrafts,\" Aerotecnica Missili e Spazio, Vol. 67, No. 1-4, 1988, pp. 18-25. 8Wang, S. J., Lin, Y. H., and Ih, C. H. C., \"Dynamics and Control of a Shuttle Attached Antenna Experiment,\" Journal of Guidance, Control, and Dynamics, Vol. 8, No. 3, 1985, pp. 344-353. 9Quinn, R. D., and Meirovitch, L., \"Maneuver and Vibration Control of SCOLE,\" Journal of Guidance, Control, and Dynamics, Vol. 11, No. 6, 1988, pp. 542-553. 10Bernelli-Zazzera, F., Ercoli-Finzi, A., and Mantegazza, P., \"Mixed Discrete/Pulse-Width Control of a Shuttle Attached Antenna,\" Proceedings of the X Congresso Nazionale AIDAA, ETS Editrice, Pisa, Italy, Oct. 1989, pp. 469-476. D ow nl oa de d by C O R N E L L U N IV E R SI T Y o n Fe br ua ry 1 , 2 01 5 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .2 08 58"
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0003477_cnm.913-Figure8-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003477_cnm.913-Figure8-1.png",
+        "caption": "Figure 8. Factors of the system with form III symmetry and its factors: (a) E; and (b) D.",
+        "texts": [
+            " Consider the determinant of matrix E as det(E) = \u2223\u2223\u2223\u2223\u2223 A + B P 2Pt R \u2223\u2223\u2223\u2223\u2223 From matrix algebra, if a row or column of this matrix is multiplied or divided by a scalar, the amount of the determinant will, respectively, be multiplied or divided by that scalar. Therefore, the second column of the matrix is multiplied by \u221a 2, leading to \u221a 2\u00d7 det(E) = \u2223\u2223\u2223\u2223\u2223 A + B \u221a 2\u00d7P 2Pt \u221a 2\u00d7R \u2223\u2223\u2223\u2223\u2223 2nd row\u00d7 \u221a 2 2\u2212\u2212\u2212\u2212\u2212\u2212\u2212\u2212\u2212\u2192 \u221a 2 2 \u00d7 \u221a 2 det(E) = det(E)= \u2223\u2223\u2223\u2223\u2223\u2223\u2223 A + B \u221a 2P \u221a 2 2 \u00d7 2Pt \u221a 2 2 \u00d7 \u221a 2R \u2223\u2223\u2223\u2223\u2223\u2223\u2223 = \u2223\u2223\u2223\u2223\u2223 A + B \u221a 2P \u221a 2Pt R \u2223\u2223\u2223\u2223\u2223 = det(L(2)) This shows that the determinants of the matrices L(2) and E are identical, and both matrices contain the same sets of eigenvalues. Figure 8 shows the factors of previous problem. A directed edge from i to j , represents a directed spring in the dynamic system. The main characteristic of such a spring is that the connection of this spring to masses is such that it does not take part in the stiffness of k j,i , but it affects ki, j [11]. As it was shown in Sections 3.1 and 3.2, the problems with two and three DOFs can be decoupled into two smaller problems; in the first example, each subproblem had one DOF, and in the second one, one- and two-dimensional subproblems were obtained"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002457_1.1536652-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002457_1.1536652-Figure1-1.png",
+        "caption": "FIG. 1. Experimental setup for one-step laser cladding by 6 kW high power diode laser: ~1! diode laser head; ~2! optical tube, focusing lens and protection glass; ~3! alignment system for powder nozzle; ~4! cyclone; and ~5! flat powder stream nozzle.",
+        "texts": [
+            " In the cyclone carrier gas and powder particles were separated whereupon powder particles fell gravitationally to the flat nozzle, where the powder stream was spread to a width of the larger dimension of the beam spot. The flat nozzle was positioned at an angle of 60\u00b0 to the work piece. The shielding gas ~Ar! shrouded the powder stream, protecting the hot powder particles from oxidation. Shroud gas also produced a relatively low divergence powder stream, which made it easier to focus the powder stream to a more or less line shape beam spot size. The tip of the flat nozzle was located 30 mm from the work piece. The experimental setup for one-step HPDL cladding is shown in Fig. 1. Machined rectangular sheets of unalloyed low carbon steel Fe52 with dimensions of 100 mm3100 mm and a thickness of 20 mm were used as substrate material. A nickel-based superalloy Inconel 625, which contains chromium and molybdenum as the main alloying elements, was selected as the coating material. The nominal composition of the Inconel 625 powder is 64.1 Ni, 21.5 Cr, 8.9 Mo, 3.8 Nb, 1.2 Fe, and 0.5 Si in wt %. The particle size of the powder was 53\u2013150 mm. The coating samples were prepared by moving the HPDL and powder feeding head fixed to a robot upon substrate materials"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003052_1.2121752-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003052_1.2121752-Figure1-1.png",
+        "caption": "Fig. 1. Geometry of a falling pencil. The bottom end of the pencil is free to slide forward or backward on the table.",
+        "texts": [
+            "3 Given that the center of mass pivots about one foot on the ground, a walking stride will change to a running stride when 2 /R g, where R is the height of the center of mass. For most adults, R is about 1 m so the maximum adult walking speed is about 3.1 ms\u22121. In this paper we consider only the case of a falling pencil because a pencil or pen will be within easy reach of all readers. However, the word \u201cpencil\u201d can be taken as a generic term for any elongated object, including a top-heavy human leg. The geometry is shown in Fig. 1 and the equations of motion are 26 Am. J. Phys. 74 1 , January 2006 http://aapt.org/ajp Downloaded 29 Sep 2012 to 136.159.235.223. Redistribution subject to AAPT F = Md x/dt 1a N \u2212 Mg = Md y/dt 1b and Icmd /dt = NH sin \u2212 FH cos , 2 where M is the pencil mass, x and y are the velocity components of the center of mass, H is the distance from the center of mass to the bottom end of the pencil, Icm is the moment of inertia about an axis through the center of mass, and =d /dt. We will focus our attention on the relatively simple case where x, y, and are all zero and where = 0 at t=0"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003512_j.mechatronics.2005.12.002-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003512_j.mechatronics.2005.12.002-Figure5-1.png",
+        "caption": "Fig. 5. Experimental setup.",
+        "texts": [
+            "1 Hz frequency. The physical linear motor application was driven such a way that the proposed velocity controller was implemented in Simulink to gain the desired force reference. The derived algorithm was transferred to C code for dSPACE \u2019s digital signal processor (DSP) to use in real-time. The force command, F*, was fed into the drive of the linear motor using a DS1103 I/O card. The computational time step for the velocity controller was 0.1 ms, while the current controller cycle was 31.25 ls. Fig. 5 shows a diagram of the real-time system. For the Kalman filter, introduced in the previous chapter, a linear state-space model of the mechanical system is derived. The friction and other nonlinearities are assumed to be system noise, which the Kalman filter handles as a random process. The estimated states of the system are velocity of the motor vM, velocity of the load vL, and spring force Fs, i.e. the state vector is x \u00bc x1 x2 x3 2 64 3 75 \u00bc vM vL F s 2 64 3 75. \u00f056\u00de le of PMLSM. The state matrix A, input matrix B and output matrix C in Eq"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003901_1.2159040-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003901_1.2159040-Figure1-1.png",
+        "caption": "Fig. 1 \u201ea\u2026 Schematic of a rotating ring on multiple ro",
+        "texts": [
+            " Assuming the spring stiffnesses to be small compared to the ring bending stiffness, the method of multiple scales is used to identify parametric instability conditions for different configurations. The significance of stiffening effects due to ring rotation and the occurrence or suppression of instabilities due to symmetry in spring placement are investigated. These analytical results are applied to investigate ring gear instabilities using example planetary gears with nonrotating and rotating ring gears. 2 Problem Formulation Figure 1 a shows a thin ring of uniform cross-section with mean radius r and center O subject to forces at its centroidal surface from M multiple spring-sets, j=1,2 , . . . ,M. Each springset consists of two springs of time-varying stiffness k1j t and k2j t oriented in mutually perpendicular directions with arbitrary orientation angle j 0 j /2 and arbitrary angular coordinate j 0 j 2 measured from fixed E1 at initial time t=0. All angles are measured positive counterclockwise. The springsets and ring rotate at constant angular speed sp and r, respectively",
+            " As the spring-sets rotate, the orientation angles j and relative angular spacing j \u2212 j\u22121 between adjacent spring-sets remain fixed. All spring stiffnesses vary independently with the same period Tm=2 / m, so that each stiffness function is expressed as the Fourier series APRIL 2006, Vol. 128 / 23106 by ASME 16 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F k1j t = k1j 0 + l=1 k1j l eil mt + k\u03041j l e\u2212il mt 1 k2j t = k2j 0 + l=1 k2j l eil mt + k\u03042j l e\u2212il mt Referring to Fig. 1 b , is the angular coordinate of any point on the ring in the inertial E1-E2 reference frame. Similarly, and are the angular coordinates of the same point in the ring-fixed e1 -e2 and spring-fixed e\u03021-e\u03022 reference frames, respectively. The angular coordinates of a material point on the ring are related by = + rt= + spt. The equations of motion are derived in the ring-fixed reference frame. Defining u\u0302 and w\u0302 as the tangential and radial displacements of the centroidal axis of the ring, the coupled equations of motion are 23 rA u\u0308\u0302 + 2 rw\u0307\u0302 \u2212 EA r u\u0302 + w\u0302 \u2212 EI r3 u\u0302 \u2212 w\u0302IV \u2212 rA r 2 u\u0302 + 2w\u0302 + j=1 M \u2212 relt \u2212 j k1j t u\u0302 cos2 j + k2j t u\u0302 sin2 j + k2j t \u2212 k1j t w\u0302 cos j sin j = 0 2 rA w\u0308\u0302 \u2212 2 ru\u0307\u0302 + EA r u\u0302 + w\u0302 \u2212 EI r3 u\u0302 \u2212 w\u0302IV + rA r 2 2u\u0302 \u2212 w\u0302 + j=1 M \u2212 relt \u2212 j k1j t w\u0302 cos2 j + k2j t w\u0302 sin2 j + k2j t \u2212 k1j t u\u0302 cos j sin j = 0 3 where E is Young\u2019s modulus, is density, and I is the area moment of inertia of the cross section"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001080_s0006-3495(93)81454-1-FigureI-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001080_s0006-3495(93)81454-1-FigureI-1.png",
+        "caption": "FIGURE I (a) Relationship between the torque (MM) generated by the flagellar motor of a tethered cell and the viscous drag (f E) from the medium, when rotation is driven by an electrical field torque MEP + MEO. See the text for details. (b) Schematic illustration of a tethered cell which is rotated by an electric field at WE as described in Principle.",
+        "texts": [],
+        "surrounding_texts": [
+            "INTRODUCTION E. coli has several helical flagella around its cell surface and possesses an ability to swim in aqueous medium by rotating its helical flagellar filaments as propellers. Each flagellum is rotated by a molecular rotary motor anchored in the cytoplasmic membrane (Silverman and Simon, 1974; Berg, 1974). The basal body ofa flagellum embedded in the membrane is thought to serve as a rotor ofthe motor complex, and the stator elements and other structural components are placed around the basal body in the membrane (for recent reviews, see Blair, 1990; Jones and Aizawa, 1991) . The energy source for these motors was found to be the electrochemical potential gradient of a specific ion across the membrane; this gradient is composed of the membrane electrical potential and the chemical gradient of the ion (Manson et al., 1977; Matsuura et al., 1977; Hirota and Imae, 1983). To understand the mechanism ofenergy transduction of the flagellar motor, one of the most effective methods is to investigate the mechanical properties of the motor itself. Specifically, the relationship between torque and rotation rate is a characteristic property of the motor itself, which is closely related to its mechanism. Manson et al. (1980) estimated torque at low speeds (about 10 Hz) in tethered cells of Streptococcus. Lowe et al. (1987) made measurements of torque at various bundle frequencies in swimming cells. Their results showed that in the case of swimming cells the torque of the motor linearly decreased with rotation rate from -50 Hz up to 100 Hz and that values oftorque ofswimming cells were smaller than those of tethered cells.\nIn this study we attempted to measure the relationship between rate ofrotation and torque ofthe flagellar motor\nAddress correspondence to Dr. Yasuo Imae, Department of Molecular Biology, School of Science, Nagoya University, Chikusa-ku, Nagoya, Japan 464-01.\nin tethered cells ofa smooth-swimming E. coli strain and determined the torque over the range 0-55 Hz speed by externally applying a rotating electric field to the cell. By this method, we were also able to extend the measurement to negative rotation (i.e., rotation in the reverse of the natural direction) up to about -20 Hz. Our measurements suggest that the torque of the flagellar motor decreases linearly with the rotation rate within the range observed. We also investigated the temperature effect on the torque versus rotation rate.\nPRINCIPLE\nThe torqueMM generated by the motor ofa tethered cell rotating at angular velocity wo is balanced by the hydrodynamic viscous drag acting on the cell body (Fig. 1 a). The viscous drag may be expressed asfc where f and w are the frictional coefficient of the rotation of the cell about the axis through the tethering position and the angular velocity of the tethered cell, respectively. Under an electric field, free cells migrate along the electric field by two mechanisms. One is the electrophoretic effect because the cells are carrying net charge. The other is a hydrodynamic effect due to the flow of medium driven by electroosmosis, which inevitably exists in a usual cell for the measurement ofthe electrophoresis (Bier, 1959). In contrast, when the same cells are tethered eccentrically on a slide glass by one oftheir flagella, the cells cannot migrate, but show a directional change around a tethered point by the force produced by the electrophoresis and electroosmosis.\nLet us now apply an electric field rotating with an angular velocity WEto an eccentrically tethered cell rotating with wO (#WE). Fig. 1 b illustrates a tethered cell rotating in the presence of an electric field at WE higher than its natural speed (wo < WE). Provided the electric field is sufficiently intense, the cell would be expected to rotate\nBiophys. J. Biophysical Society Volume 64 March 1993 925-933\n0006-3495/93/03/925/09 $2.000006-3495/93/03/925/09 925",
+            "MEO = g(r X (), (2)\nor in terms of scalars by\nMEO = grvo sin X, (vo = 11 v 11 ) (2')\nWAO WE\nMEO\nwhere g represents a geometrical factor including the size of the cell body. Thus, the torque MM, MEP, MEO, and the hydrodynamic viscous drag on the cell bodyfwE are related by the following equation.\nMM + MEP + MEO = f)E, (3) 1- where WE is the axial vector ofthe angular velocity ofthe\nrotating electric field. The electroosmosis is proportional W to the electric field applied as described in Materials and\nMethods and v may be put as\nv = aE. (4)\nEq. 3 equally applies to the cases ofdecreased speed (O < WE < WO) and reverse rotation (WE < 0).\nLet us now gradually decrease the amplitude of the rotating electric field EO without altering the rate WE. The angle X will correspondingly increase toward 900 in compensation for the decline ofthe electric field in order to supply a constant torque, and the tethered cell will continue to rotate at the same angular velocity WE as the electric field. When X just exceeds 90\u00b0, the synchronization is broken and rotation ofthe cell returns to its natural angular velocity w0. From Eqs. 1', 2', 3, and 4 we get the equation\nwith WE, in which X, the angle between the direction of the electric field and the long axis ofthe cell remains less than 90. The torque exerted on the cell body by the electropho-\nresis is given in terms of vectors by\nMEp=q(rXE),(1\nor in terms of scalars by\nMEP = qrEO sin X, (EO = IIEII) ( 1)\nwhere E is the rotating electric field, r is the distance from the tethering axis to the center ofthe cell body and q is the effective charge on the cell. In addition, a torque MEO is exerted on the same cell body by the electroosmotic flow. Let us denote the velocity of the flow as v, the direction of which may be parallel to the electric field. Then, the torque may be expressed in terms ofvectors by\nMM =fwE - (q + ga)rE9, (5)\nwhere El is the threshold amplitude ofthe rotating electric field at the moment of desynchronization. According to Eq. 5, the torque ofthe flagellar motor at WEcan be estimated from El'and factorsf, q, g, r, and a. However, ifwe use a constant-voltage mode for applying the electric field, the real values ofEO are difficult to estimate on account of the polarization at the boundary between the electrodes and the sample solution. Instead, we use the constant-current mode. Let us denote IO as the current that passes through the sample to establish EO in the medium. Then, the relation between EOand IO is written as follows:\nEo= kIo/a, (6)\nwhere k is a geometrical factor ofthe electrode cell and a\nis the specific conductance ofthe sample medium. Then, substituting Eq. 6 into Eq. 5 yields\nMM =fwE - (k/lo)(q + ga)rI9. (7)\nThus, torque ofthe motor is represented as a linear function of both angular velocity WE and the threshold current PO. When the relationship between JO\u00b0 and WE has been obtained experimentally, the torque ofthe mo-\n926 Biophysical Journal Volume 64 March 1993\nTorqu e\n(b)\n(a)\nBiophysical Journal Volume 64 March 1993",
+            "torMM can be expressed as a function of WE using Eq. 7, if the factors, f, k, q, g, r, a, and a are known.\nMATERIALS AND METHODS\nSample preparation A smooth-swimming Escherichia coli strain RP4979 (Ache Y), whose flagellar rotation is fixed in the counterclockwise direction, was used in this study. Cells were grown to early or late logarithmic phase at 300C with shaking in 1% tryptone (Difco Laboratories, Detroit, Michigan), 0.5% NaCl, and 0.5% glycerol (wt/vol). The cells grown in early log phase were used for observation ofreverse (clockwise) rotation oftethered cells by the application of an electric field rotating in the reverse direction, because these large cells were found to be more suitable for such observations. They were harvested by centrifugation at 8,000g for 5 min at room temperature and washed with motility medium containing 5 mM potassium phosphate buffer (pH 7), 0.1 mM EDTA, and 0.5% glycerol, and stored on ice until use.\nThe viscosity of the medium was changed by addition of Ficoll 400 (Pharmacia LKB, Uppsala, Sweden) into sample medium (Manson et al., 1980). A 10% wt/vol stock solution of Ficoll 400 was prepared in motility medium. Solutions of lower Ficoll concentrations were made by dilution. Viscosity was measured in Ostwald and Ubbelohde viscometers at 25.0\u00b0C. For exchange ofthe motility medium, we used a modified version of the flow chamber described by Berg and Block ( 1984). A 3-8 min operation of a peristaltic pump type P-I (Pharmacia Fine Chemicals, Sweden) set at a flow rate of 100-250 ml/h was sufficient for complete exchange of the content of the flow chamber. For preparation of tethered cells, cells were sheared by passage through a Pasteur pipet (7095-5X, Coming Inc., New York) about 200 times per 1 ml medium and attached with antiflagellin antibody to an electrode cell (see below) or the bottom window of the flow chamber. Then a cover glass stored in ethanol before use was wiped with tissue and put onto the electrode cell, or the upper window of the flow chamber cleaned with ethanol and screwed into the flow chamber. These cells were allowed to incubate at room temperature for about 1 h before observation.\nMeasurement system The rotation ofthe tethered bacterial cells was detected by an apparatus schematically shown in Fig. 2. The sample was illuminated in darkfield mode of a microscope (Nikon Co. model L equipped with 20x objective and 15X eyepiece, Tokyo, Japan) with Xenon lamp (UXL300D, Ushio Electric Inc., Osaka, Japan). An image of the cell was focused on a linear graded filter, so that the rotation of the cell was monitored as a light signal, whose intensity was sinusoidally modulated (Kobayasi et al., 1977). The light was detected by a photomultiplier in photon counting mode with a discriminator (R649 and C 1050, Hamamatsu Photonics K.K., Hamamatsu, Japan). The output ofthe discriminator per unit time was counted by a photon counter. Finally, these data were displayed on a personal computer (Apple II plus; Apple Computer Inc., Cupertino, California) and written on a dot printer (SP-500; Seiko Epson Co., Suwa, Japan). The rotation rates of the tethered cells were calculated from the time interval required for an integral number of cycles of the rotation. The size and shape ofthe cell body and the tethering position in the cell were measured by the same microscope in phase-contrast mode at the end of each measurement. For swimming speed measurement, unsheared bacteria diluted to a suitable concentration for observation were placed in the flow chamber and observed in dark-field mode. Swimming speed was measured by analyzing the lengths of the track ofthe cells in the photographs (Imae et al., 1986). To change the temperature of the medium, we placed the flow chamber filled with the sample medium on a temperature-regulated microscope stage controlled by circulation of water from a water-bath\nequipped with a thermostat. The temperature ofthe medium was measured by attaching a chromel-constantan thermocouple (0.1 mm diam.) to the frame ofthe flow chamber. For the calculation oftorque, the temperature dependence of the viscosity of the medium was taken into account. The electrode cell for applying a rotating electric field to tethered cells was made of a slide glass (inset of Fig. 2). Two pairs of pieces of thin platinum foil were attached around a shallow circular well (4 mm diam., 0.2 mm depth) made of epoxy resin on the glass. Sinusoidal current pulses Io(t) cos wEt and Io(t) sin wEt were then supplied to these two pairs ofelectrodes, where Io(t) is the amplitude ofthe current which was gradually decreased with time. These amplitude-modulated sinusoidal currents were generated in a home-made sine/cosine function generator and high voltage amplifier (Output max. \u00b1 280 V). To apply the pulses in constant-current mode, resistors of 50 kg or 210 kQ were connected in series between the outputs ofthe high voltage amplifier and the electrode cell, such that the resistance between the electrodes and the sample medium was negligible. To test that the sum of the effects of the electrophoresis and electroosmosis is proportional to the magnitude of the applied electric field, we measured the distances ofthe movement ofthe cells by applying rectangular current pulses with a fixed duration through one pair of the electrodes ofthe electrode cell. Then, these distances were found to be proportional to the amplitude of the pulses in the range used in the experiments with rotating electric fields as shown in Fig. 3. Measurement were performed at 25\u00b0C unless otherwise stated.\nCalculation of frictional coefficient and torque In order to estimate the frictional coefficient ofrotating tethered cell we treated the cell body as a prolate ellipsoid and used the formula: f =\nIwazawa~~ eta.Tru td fBctra lgla oolwazawa et al. Torque Study of Bacteria] Flagellar Motor 927"
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0001441_tmech.2003.816806-Figure7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001441_tmech.2003.816806-Figure7-1.png",
+        "caption": "Fig. 7. Visibility for a flat patch.",
+        "texts": [
+            " However, due to the high computational cost in calculating the intersection of resolution balls, the following indirect method is used: discretize the search space formed by the line of sight, the field-of-view and the in-focus region; test each discrete point to see if the distances between this point and the centers of the resolution balls are all less than the resolution ball radius . The visibility of the patch is guaranteed by the bounding box and the flatness constraint of the patch as long as the flatness constraint threshold satisfies . This condition is illustrated in Fig. 7. Any position in the intersection of the line of sight and the three constraint regions is an admissible look-from position. In practice, we choose the lowest solution position to obtain a larger image. A recursive algorithm is used to determine all the viewpoints for a flat patch. If the intersection of the line of sight and all the constraint regions of the current patch is null, which means no viewpoint exists that satisfies all constraints, we split the patch into two subpatches using the center plane of the bounding box along the length direction"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002455_j.precisioneng.2004.03.003-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002455_j.precisioneng.2004.03.003-Figure5-1.png",
+        "caption": "Fig. 5. Method of generating location of balls.",
+        "texts": [
+            " Let the number of balls be Z, then the total number, N, of location patterns of balls is expressed as follows. N = (Z! \u2212 1) 2 (7) Table 2 shows the data of the number of balls, number of patterns and elapsed time of calculation. The CPU of the computer used for the calculation is a Pentium 4 (1.8 GHz). For Z = 3, N = 1. In contrast, for Z = 10, N = 181440. There is a greater increase in N for a large number of Z. In addition, the elapsed time of the fc component for 72 patterns is approximately one second. The generation method for the location patterns of balls is shown in Fig. 5. Considering a polygon whose vertices are the centers of the balls, we can create a new location pattern of balls nontautologically inserting a new ball into the edge connecting the existing two balls. In the case of Z = 3, there is only one pattern. Therefore, if the fourth ball is inserted into one of the three edges (Z = 3, triangle), three location patterns of balls can be generated. The process to obtain the expected value of the fc component is as follows. (1) Let the balls be numbered virtually"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001066_1350650011541738-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001066_1350650011541738-Figure1-1.png",
+        "caption": "Fig. 1 Geometry and coordinates of the journal bearing",
+        "texts": [
+            " The basic equations governing the motion of an incompressible coupled stress fluid, in the absence of body forces and body couples, derived by Stokes are =:V \u02c6 0 (4) r DV Dt \u02c6 \u00a1= p \u2021 \u00ed =2V \u00a1 \u00e8 =4V (5) The ratio \u00e8=\u00ed has the dimensions of length square and, hence, characterizes the material length of the fluid. Proc Instn Mech Engrs Vol 215 Part J J03400 # IMechE 2001 at UNIV OF PITTSBURGH on December 19, 2014pij.sagepub.comDownloaded from A schematic diagram of the problem under study is shown in Fig. 1. The non-porous journal of radius R is approaching the homogeneous and isotropic porous bearing surface with a given velocity dh=dt at any circumferential section \u00f5. The lubricant between the journal and porous bearing is a Stokes coupled stress fluid and the body forces and body couples are assumed to be absent. However, the fluid in the porous matrix of the bearing is assumed to be purely viscous. This assumption is made to model the flow situation in which the polymer additives present in lubricant do not percolate into the porous matrix, i"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003091_b:jint.0000015344.84152.dd-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003091_b:jint.0000015344.84152.dd-Figure1-1.png",
+        "caption": "Figure 1. Single-link flexible joint manipulator configuration.",
+        "texts": [
+            " \u2737 Consequently, since the stability condition is expressed in terms of parametric uncertainties and design parameters, we can choose the design parameters of controller which guarantee the stability of the system with the given parametric uncertainties Ai and Bi (i = 1, 2, . . . , n). In this section, the validity and effectiveness of the proposed controller are examined through the control simulation for a single-link flexible joint manipulator. In the simulation, we examine the effects of parametric variation on behaviors of the closed-loop systems with the proposed control scheme. In order to apply the suggested controller, we need a Takagi\u2013Sugeno fuzzy model representation of the manipulator. Consider the single-link flexible joint manipulator shown in Figure 1 whose dynamics can be written as x\u03071 = x2, x\u03072 = \u2212MgL I sin x1 \u2212 k I (x1 \u2212 x3), (4.1) x\u03073 = x4, x\u03074 = K J (x1 \u2212 x3) + 1 J u, where I = 1 kg m2, J = 1 kg m2 are, respectively, the link and the rotor inertia moments, M = 1 kg is the link mass, k = 1 N/m is the joint elastic constant, L = 1 m is the distance from the axis of the rotation to the link center of mass and g = 9.8 m/s2 is the gravitational acceleration, respectively. We first transform the nonlinear system to the normal form [15] with z1 = x1 as z\u03071 = z2, z\u03072 = z3, z\u03073 = z4, z\u03074 = a(z) + b(z)u, (4"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002368_910530-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002368_910530-Figure2-1.png",
+        "caption": "Figure 2 -- Sealing tip manufacturing methods",
+        "texts": [
+            " Instant gross leakage ensues if extreme changes occur, such as reversing seal geometry by installing the seal backwards. Researchers also agree that all properly functioning seal designs will pump oil from the air side across the contact band into the oil sump (14). This pumping action must be maintained over the life of the seal to ensure reliability and long life. In some cases, projections are molded on the air side of the report describes studies that linkseal reliability and pumping ability to asperity formation. WEAR MECHANISM The sealing tips of radial lip seals can be manufactured in two ways (Figure 2). The old method trims the rubber cap from the oil side, leaving a molded surface on the air side and a trimmed surface on the oil side. The modern method accurately forms the seal tip with molded surfaces on both air and oil sides. The benefits of molded lip seals and deficiencies of trimmed lip seals have been previously described (1 5). Both methods of sealing tip manufacture yield the same result when the seal is installed on a shaft. The molded surface of the air side of both molded and trimmed tip seals contacts the shaft (Figure 3)"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000888_s1350-6307(98)00024-7-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000888_s1350-6307(98)00024-7-Figure3-1.png",
+        "caption": "Fig[ 3[ \"a\u00d0d# Deformation in the components just before the accident[ \"e# Hypothetical sketch based on observations in Figs 3a\u00d0d[",
+        "texts": [
+            "i# where it seemed that material was removed due to impact\\ a high concentration of Fe\\ Cr\\ Si\\ Al and Cu was detected[ It seems that the material of the cage was smeared probably at the inner race _rst and then extensive compressive:shear stresses between the ball and the outer race resulted in chipping or shearing of the ball material[ Smearing on the outer race is accompanied by deformation\\ as is evident from the deformation bands near the surface in Fig[ 5[ Three di}erent regions were analyzed and the results are summarized in Table 1a^ the _rst two regions were big enough to permit analysis at a couple of locations[ In all the locations cage material was smeared[ Region I contained a signi_cant amount of Ag showing that the cage got smeared when the coating was intact[ Analysis at Region III\\ on the other hand\\ did not show the presence of an Ag coating\\ indicating that the cage had already been distressed to the level that its coating was completely stripped o} before smearing at Region III[ Micrographs in Fig[ 3c show the condition of smearing on the inner race[ The LHS was quite deformed and damaged[ Figure 3c!i shows the seat of the race where extensive smearing and deformation is clearly visible[ Four di}erent locations\\ marked in Figs 3c!vi and c!vii\\ were analyzed and they indicate the presence of smeared cage material at Regions II and IV^ see Table 1b for the analysis report[ At Region II\\ Ag is also present indicating that when the cage got smeared here the coating was at least partially intact[ No bearing component was found to contain Cr\\ Si\\ Al and Mg in the amounts detected in Region III of the inner race[ Particles rich in Si and Al and containing Mg were retrieved from the lubricating oil and could be transported to the inner race from some other source through the lubricant[ The material protruding from the RHS of the race \"Fig[ 3c"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000385_s0045-7949(98)00165-5-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000385_s0045-7949(98)00165-5-Figure3-1.png",
+        "caption": "Fig. 3. Simply supported square laminated plate (\u00aeve graphite-epoxy laminates) geometry and material properties.",
+        "texts": [
+            " The integration across the thickness is performed explicitly, whereas the integration over the surface of every interface is made by means of a three-point Gauss quadrature. Again it is possible to use the condensation technique across the thickness in order to reduce the number of calculations. The procedure consists now in eliminating the global displacements of the lower interlaminar surface ak for every layer k as a function of a k + 1 and a0 by means of an expression similar to Eq. (11). Further details can be found in [12]. The \u00aerst example studied is a graphite\u00b1epoxy simply supported plate. The geometry and material properties are shown in Fig. 3. We consider \u00aeve laminates with orientations 08/908/08/908/08 and thickness h 6 = h 4 = h 6 = h 4 = h 6 : The distributed load over the plate is given by q= q0 sin px/a sin py/a. For symmetry reasons only a quarter of plate was analyzed. The discretization is shown in Fig. 3. The number of analysis layers was taken the same as the number of laminates. Table 1 shows some results for the vertical displacement at the center of the plate and the stresses in some characteristic points, for di erent side length/thickness ratios (a/h). In order to show the accuracy of the results, they are compared with the solution obtained by Stavsky [18] by means of the Classical Theory of Laminated Plates (CLPT) which is based on Kirchho 's hypothesis. Note the di erence of the results when the thickness increases"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002472_j.jsv.2004.04.037-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002472_j.jsv.2004.04.037-Figure1-1.png",
+        "caption": "Fig. 1. Coordinate systems of a gear pair at the pressure line.",
+        "texts": [
+            " In this paper a general method is presented for obtaining the unbalance response orbit based on the finite element approach of a gear-coupled two-shaft rotor-bearing system, where the shafts rotate at their different respective speeds. Specifically, analytical solutions of the maximum and minimum radii of the orbit are proposed. The method is then applied to the unbalance response analysis of a 600 kW turbo-chiller rotor-bearing system, having a bull-pinion speed increasing gear. In addition, the validity of the proposed analytical solutions of the orbit radii is tested against those obtained fully numerically. A displacement vector of a gear pair can be defined from the pressure line coordinate system as shown in Fig. 1 by qG0 \u00bc uG0 1 vG0 1 yG0 X1 yG0 Y1 uG0 2 vG0 2 yG0 X2 yG0 Y2 yG0 Z1 yG0 Z2 j kT ; (1) where u; v; yX and yY are the translational and rotary degrees of freedom and yZ the torsional degree of freedom, and the subscripts 1 and 2 indicate the driving and driven gears. From the equilibria of the generalized forces for each gear, the coupled equation of motion of a gear pair can be expressed by (a detailed derivation can be found from [3]) MG0 \u20acqG0 \u00fe CG0 \u00fe GG0 _qG0 \u00fe KG0 qG0 \u00bc QG0 ; (2) where MG0 ; CG0 ; GG0 and KG0 are the inertia, damping, gyroscopic and stiffness matrices and they are given in Appendix A by Eqs"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002222_1.533555-Figure10-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002222_1.533555-Figure10-1.png",
+        "caption": "Fig. 10 Simulation reference frames",
+        "texts": [
+            "1 Main Symbols DRatio 5 decimal ratio Mctb 5 work machine center to back Offset 5 work offset N\u0304 5 tooth flank unit normal vector V\u0304r 5 relative velocity vector ac 5 cutter angular position a3 5 work roll angle t 5 cutter tilt angle k 5 cutter swivel angle A.2 Simulation of Tooth Manufacturing. Both the generating process and operation of gear sets are based on the same basic concept, that of meshing elements. In the manufacturing process, meshing takes place between a cutter blade, whose rotation represents the shape of one tooth of a crown gear, and the work itself ~see Fig. 10!; in operation, meshing occurs between the contacting teeth of the pinion and gear. The fundamental equation of meshing is N\u0304\u2022V\u0304r50 (A1) which states that the relative velocity vector V\u0304r between contacting surfaces must be in a plane tangent to the meshing surfaces at any contact point. Equation ~A1! yields the equation of the generated surface in general reference frame Z. The surface equation is a function of three variables ac , a3 , and Sr , respectively the cutter angular position, the work roll angle, and the position of a point along the cutter blade edge: S5 f ~ac ,a3"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001553_s0045-7825(99)00329-1-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001553_s0045-7825(99)00329-1-Figure5-1.png",
+        "caption": "Fig. 5. Transmission functions (a and b) and parabolic function of transmission errors (c).",
+        "texts": [
+            " The above described methods of worm pro\u00aele crowning of the worm yield that worm thread surface Rw and worm-gear tooth surface R2 are in point contact at every instant and the bearing contact is localized. However, meshing of Rw and R2 is accompanied by large transmission errors of undesirable shape that are caused by errors of alignment. The purpose of worm longitudinal crowning is to provide a predesigned parabolic function of transmission errors that is able to absorb transmission errors caused by errors of alignment. Fig. 5(a) shows that transmission function /2 /w of a misaligned gear drive is a piecewise discontinuous function. The theoretical transmission function of an ideal gear drive is a continuous linear function. The function of transmission errors determined for each cycle of meshing /w 2p=Nw is represented as D/2 /w /2 /w \u00ff Nw N2 /w; 15 where Nw is the number of worm threads and N2 is the number of gear teeth. The goal of longitudinal crowning of the worm is to obtain for each cycle of meshing such a transmission function /2 /w (Fig. 5(b)) that will cause a parabolic function of transmission errors (Fig. 5(c)) determined as D/2 /w \u00ffa/2 w; 16 where a is the parabola coef\u00aecient. It is important to recognize that the worm-gear lags with respect to the worm, if the transmission function is of the shape shown in Fig. 5(b). Then, the transfer of meshing from one pair of teeth to the neighboring one is accompanied with elastic deformation of contacting teeth and the contact ratio is larger than one. In case of a misaligned gear drive with imaginary rigid teeth, the contact ratio due to misalignment is one only. The desired parabolic function of transmission errors is obtained by plunging of the disk that generates the pro\u00aele crowned worm surface R 1 w . Thus, the worm thread surface will be crowned in the longitudinal direction also"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001321_s1350-6307(99)00009-6-Figure7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001321_s1350-6307(99)00009-6-Figure7-1.png",
+        "caption": "Fig. 7. Cracks in the cage U.",
+        "texts": [
+            " Cases of previous cage failures were reviewed. It was found that on-site reports of bearing failures indicated cracks in CMB cages but the matter was not pursued to check the failure mode. One such bearing from a similar used engine was obtained, which had undergone more than 300 h of operation before the cage was inspected and removed. The cage, designated as sample U, was subjected to laboratory investigations. Visual and stereographic examination of the bearing in the laboratory showed cracks in the cage (Fig. 7). Wear marks were visible on the contact surface of the cage and the outer race, see Fig. 8(a) and a higher magni\u00aecation micrograph of the worn band in Fig. 8(b). The chemical analysis of the regions which had undergone smearing is summarized in Table 4. In none of the cases was the Cu peak more dominant than the Ag peak, indicating that the coating was intact. The analysis of the region in general showed signi\u00aecant smearing of Fe on the surface. Most of the smeared material was iron containing Cr, probably coming from the outer race"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002514_135065003765714863-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002514_135065003765714863-Figure1-1.png",
+        "caption": "Fig. 1 Effective spread E of a DRTRB (DB) (left) and a DRTRB (DF) (right)",
+        "texts": [
+            " This is due to the bearing\u2019s ability to support large combined loads for a given envelope and mass. DRTRBs are used for their high load-carrying capacity, load in both axial directions being permitted, and also since the bearing width is smaller than in the case of a set of two single-row tapered roller bearings (TRBs). The load lines of a DRTRB (DB) diverge towards the bearing axis. Therefore such bearing arrangements are relatively stiff and can accommodate tilting moments, while the load lines of a DRTRB (DF) converge towards the bearing axis (Fig. 1), giving it more ability to rotate under moment loading. The effective spread E is a function of the bearing arrangement and contact angle. A wider effective spread usually acts to reduce the load on rolling element. However, under certain loading conditions such as high bending moment the rolling element load may increase with increasing effective spread. When looking for a high stiffness, it is necessary to take into account both rolling bearing stiffness and shaft bending. The system is statically indeterminate and the static equilibrium equations are insuf\u00aecient to solve the bearing reactions",
+            " In this case the distance between supporting bearings was chosen to be equal to l \u02c6 354mm. It can be observed that, when the axial compression dp exceeds the value of 0.04 mm, the shaft de\u00afection remains approximately constant for both the TRB in the DB arrangement and the TRB in the DF arrangement. From Figs 4 and 5 it can be observed that the DB or DF con\u00aeguration affects the amount of shaft de\u00afection. This is due to different abilities of the DB and DF arrangements [the effective spreads E for DB and DF arrangements are different (see Fig. 1) and therefore have different in\u00afuences on the bearing stiffness] to support the bending moments generated by the external radial load. The angular stiffness (due to the moment load) of the DB arrangement with larger spread E is higher than that of the DF arrangement with smaller spread. This result is consistent with ball bearing arrangement behaviour, where the `O\u2019-type assembly is known to be stiffer than the `X\u2019-type assembly (in terms of angular stiffness due to the moment load). Comparative results concerning the axial and radial bearing loads generated by the external loading applied to the shaft in straddle design for DRTRBs (DB) and DRTRBs (DF) are listed in Table 3"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure1.6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure1.6-1.png",
+        "caption": "Figure 1.6. Path of a particle having the motion",
+        "texts": [
+            " Thus, x(P, t) = x0 + 2t3i + 2t2k. With x0 = x(P, 0) = -2i ft, we have, finally, the motion of P: x(P, t) = 2(t3 - 1) i + 2t2k ft. (1.31) We observe that the motion of P always is in the xz plane. To determine the path of P, we use ( 1.6) and ( 1.31) to obtain the follow ing time-parametric equations: x(t) = 2(t 3 -1 ), y(t) = 0, z(t) = 2t2 ( 1.32) Then elimination of the time parameter t yields the standard equation for the path of Pin the xz plane: ( X )2/3 z=z(x)=2 ~+1 . ( 1.33) Its graph is shown in Fig. 1.6. It remains to compute the distance traveled in one second. Using the for- x(P, 1) = 2(13 - I) i + 212k. 18 Chapter 1 mula provided for v(P, t), we find that the speed of P is given by v(t) = 2t( 4 + 9t2 ) '12 in accordance with ( 1.13 ). Then ( 1.25) becomes Hence, the distance traveled by P in the time t is ( 1.34) In particular, we see from ( 1.32) and ( 1.34) that after one second the particle is at the place x = 0, y = 0, z =2ft shown in Fig. 1.6, and it has traveled the distance s(l) = ; 7 [13 312 - 8] = 2.88 ft. We notice in closing that with the help of the path equation (1.32), the dis tance traveled in ( 1.34) also may be expressed as a function of z: 2 [( 9 )3/2 J s=s(z)= 27 4+ 2z -8 . D Example 1.7. An electron E is at rest at the position x0 = 2i + 3j- k m initially. Subsequently, it is observed that the electron has an acceleration a(\u00a3, t) = 12t2i- 6tj + lOk m/sec2\u2022 What are the position, velocity, and acceleration of E after 2 sec"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001941_eurbot.1997.633569-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001941_eurbot.1997.633569-Figure6-1.png",
+        "caption": "Figure 6: combination of MORTIMER and SPIKE",
+        "texts": [
+            " Taking into account the velocity of the platform's legs of about wb = 50 y, the velocities for the karthesian coordinates can be calculated: Every leg needs At = smaav;sman = 3s for a complete stretch. This results in a stroke of length in z-direction of 2Az = 200mm, whereas the velocity in z-direction can be calculated as w, = 6 6 7 . The calculations for the values w,, wy, w j , wp, wr can be performed similarly 4 Combination of StewartPlatform and Mobile Robots To compensate the acceleration and the shocks acting on an object the Stewart Platform with 6 degrees of freedom is electively installed on MORTIMER (figure 6) or on VIPER (figure 7) so that abrupt vehicle movements and accelerations affect the object in a smooth way. Figure 6 shows an arrangement for the experiments. A jar containing a liquid is situated on the upper platform. The platform has to equalize the accelerations, calculated by the data of the basic motor controller. On the left side, the whole system is moving with a constant velocity v 2 0. The upper platform is parallel to the bottom, because no acceleration is effecting the liquid. On the right side, the system increases in speed, so the platform has to compensate this movement by an inclination of the upper platform"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001419_robot.1991.131938-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001419_robot.1991.131938-Figure6-1.png",
+        "caption": "Fig. 6: Second Method to Select a Support Trajectory of Circling Gaits.",
+        "texts": [
+            " I t is possible that the selected support trajectory of leg 4 is outside the workspace of leg 4 or that the straight line M ~ M I and the circular path of leg 4 do not intersect. Under these circumstances, the turning gait is considered to be unstable. Similarly, we can select the support trajectories of leg 2 and leg 3. This strategy can be also applied to +y type, - z type and --y type wave-circling gaits. In the second strategy, the two support trajectories with larger available leg angular strokes do not necessarily pass through their workspace centers. Referring to Fig. 6 , the available leg angular stroke 91 is less than the largest leg angular stroke 9 4 . The support trajectory of leg 1 is also first selected. The points Q and Q\u2019 represent the two intersections of the straight line oM1 with boundaries of the workspace of leg 4. These two points may locate a t any two of the four boundaries, depending on the location 21 10 of turning center. Since the support trajectory of leg 4 is divided into three identical pieces, segment QQ\u2019 is accordingly split into three equal small segments by points M4 and Mi"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003173_b:tril.0000015200.37141.f5-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003173_b:tril.0000015200.37141.f5-Figure1-1.png",
+        "caption": "Figure 1. Photographs of the specimens made of SiC (a) Cylinder (b) Disk.",
+        "texts": [
+            " To whom correspondence should be addressed. E-mail: xlwang@tribo.mech.tohoku.ac.jp 1023-8883/04/0500\u20130253/0 # 2004 Plenum Publishing Corporation The specimens were made of stainless steel, bronze and silicon carbide (sintered without pressurization). Purified water, paraffin oil P60 and P60 with oiliness additive, i.e., 0.5% stearic acid, were used as lubricants. The properties of the oil are listed in table 1. Sliding tests were performed between the flat surfaces of a cylinder and a disk by rotating the cylinder. Figure 1 shows a pair of specimens made of SiC. The upper specimen is in the shape of a cylinder, which has a hole in center and two grooves \u00f04 0:5mm\u00de on the flat surface so as to supply lubricant to this surface. The Lower specimen is in the shape of a disk. The metal specimens have the same shape as that of the SiC shown in figure 1. The combinations of the specimens and lubricant are listed in table 2. In order to increase the load-carrying capacity of SiC in water, the flat surface of the disk was textured withmicropits arranged in a square array as shown in figure 2. Reactive ion etching (RIE) was used to produce micro-pits on the flat surface of the disk. RIE is a widely used method for the processing of MEMS and ICs. It ionizes a reactive gas by electric discharge, then accelerates these ions to sputter and react with the target"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001042_robot.1994.350911-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001042_robot.1994.350911-Figure3-1.png",
+        "caption": "Figure 3 - Planar Bodies in Contact",
+        "texts": [
+            " The bodies are modeled as rigid, except for the allowable local deformations, and thus respond to applied wrenches like a rigid body. Frictionless contacts can be thought of as a special case in which kt = 0. Rigid body contact forces can be found from looking at the results in the limit as kn and kt approach infinity. If the fingers and the body have stiffnesses k n l , ktl and kn2, kt2, respectively, then the composite stiffnesses, in the normal and tangential direction, are: k, - kl11klt2 k, - k,lk,2 knl + k n 2 k,, + kt2 3.1 Planar Kinematics Consider a body, B, in point contact with a finger, A, (see Figure 3a). Let the constants KA and KB be the signed curvature (the inverse of the radius of curvature) of the undeformed finger and body, respectively, at the point of contact such that the curvature is positive for convex surfaces. We wish to examine the stability of the grasp under small displacements of body B. To do this, we let uA be the arc length along the surface of object A (measured in the direction of xA) , with a corresponding definition for uB. W i t h t h i s p a r a m e t e r i z a t i o n , we g e t = 1, LA = -KA, 6 = 1 and LE = - K , ",
+            " Note further that Ax, and Ay, refer to the contact frame, but they can be related to other reference frames through appropriate transformations. We use a fixed frame 0 at an arbitrary point. If we let 'K, be the stiffness matrix from either Equation (1 1) or (17) (whichever is applicable), and (ldB Idy) be the coordinates of 0 as seen from loc, then the change in the wrench referred to the coordinate system at 0 for any infinitesimal rotation or displacement, due to contact i , is given by: where: . . Aw0= iTT 'K, iT Axo (18) cos '@ -sin'@ and l @ is the angle of rotation of the frame 0 with respect to the contact frame ioc (see Figure 3 for definition of a). 4.2 Constant External Forces Consider the gravitational force on body B acting through the center of gravity. We define a coordinate system, oCg, fixed in space and coinciding with the center of gravity, where the axes are aligned such that gravity acts in the ycg direction. A rigid body motion of body B will not change the gravitational force, but will result in changes in the moment about the origin of ocg, given by: 0 0 0 AxXca [ :Ica =[ ;g ; ;Ica[\";,] Or Awcg =% Axcg (19) where m is the mass of body B and g is the gravitational force",
+            " When the force displacement relations are added together and the results analyzed, we find that all equilibrium frictional two-contact point grasps are stable. A grasp with only one frictional contact does not have this property, however, and the following lemmas address these cases: Lemma 5: An equilibrium grasp with one frictional contact opposing a gravitational .force is stable (unstable) if ( K A + K,)r+cos@ is negative (positive). Here r is us defined in Lemma 2, and 0 is the angle of rotation of contact frame 2 with respect to contactframe 1 (see Fig. 3) . J.emma 6; An equilibrium grasp with one frictionless point contact and one .frictional point confucf (without gravity) is (positive), where the frictionless contact is contact 2, r is as defined in Lemma 1, and 0 is us defined in Lemma 5. 5.0 Discussion In this paper, we categorize all planar equilibrium grasps, and establish results which can be used to determine the stability of virtually all planar grasps (including indeterminate grasps) by examining the eigenvalues of the combined stiffness matrix"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001799_s0168-874x(02)00056-2-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001799_s0168-874x(02)00056-2-Figure3-1.png",
+        "caption": "Fig. 3. Schematic illustration of the conic surface of the rocker and the spiral surface of the workpiece at plane r = r0.",
+        "texts": [
+            " It can be expressed as M (r; ; z) = z \u2212 S 2 ; (8) where S is the feed per revolution. Thus, the outline of the contact zone is a cross line of the curved surface (Eq. (7)) and the curved surface (Eq. (8)). Its equation is z2(1\u2212 tg2 )\u2212 r2 sin2 tg2 + 2rz cos tg = 0; z \u2212 S 2 = 0: (9) A new method to numerically calculate the contour boundary of the contact zone for FEM is established according to the fact that the slope in the exit end of the contact zone is equal to that of the spiral feed, as shown in Fig. 3. As shown in Fig. 3, the curve equation of the conic surface of the rocker at plane r = r0 is g( ; z) = z2(1\u2212 tg2 )\u2212 r0 sin2 tg2 + 2r0z cos tg : (10) The slope at any point of the above curve is \u2212 @g=@ @g=@z = r20 sin cos tg 2 + r0z sin tg z(1\u2212 tg2 ) + r0 cos tg : (11) The slope of the spiral line at plane r = r0 of the workpiece is k =\u2212 S 2 r0 : (12) According to the fact that the slope at point A of the conic surface (Eq. (11)) equals to that of the spiral line of the workpiece (Eq. (12)) at r = r0, the following equation is established as r20 sin cos tg 2 + r0z sin tg z(1\u2212 tg2 ) + r0 cos tg =\u2212 S 2 r0 (13) then, we have z = kr0 cos tg \u2212 r20 sin cos tg 2 r0 sin tg \u2212 k(1\u2212 tg2 ) : (14) Substitution of Eq"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002163_027836499301200602-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002163_027836499301200602-Figure2-1.png",
+        "caption": "Fig. 2. Elliptical limit surface of a soft fingertip. The states of the two experiments discussed in Section 3 are indicated.",
+        "texts": [
+            "comDownloaded from 530 the friction between the smooth supporting surface and the card is smaller than the friction between the fingertips and the card, its effects may be noticeable. In the case of symmetric grasps, ri = r2, f = f2, Is = fs&dquo; mi = rn2, and m,s, = mS2; hence the subscript i can be dropped. The Coulomb friction model establishes constraints among the normal force and the tangential force and moment at each contact area. The limits on the tangential force and moment are described by a limit surface (Goyal et al. 1991), which can be approximated by an ellipsoid plotted in force/moment space (Kao 1990), as shown in Figure 2. Let us define as the ratio of the maximum moment, mmax. that the contact can sustain when the tangential force is zero to the maximum tangential force, p fn, that the contact can sustain when no moment is applied. In the limiting case, as the contact area becomes very small, the frictional moment approaches zero (A = 0) and the friction limit is simply ft < ~ fn, which corresponds to the familiar case of a point contact with Coulomb friction. It can be shown (Goyal et al. 1991) that for a given frictional force, f, and moment, m, on the limit surface, the orientation of the corresponding surface normal is related to the relative magnitudes of the linear and angular sliding velocities",
+            "38 N and 2.47 x 10-3 Nm, respectively. Therefore, A = 6.5 mm. The experimental results are compared with predicted values of (2\u2019 (using equation (8)) for the two cases in Table 1. In the first case, the fingertips are close together and they slide considerably with respect to the card; in the second case, the card pivots between the fingertips almost as though they were point contacts with friction. The two cases result in different ratios of tangential force and moment at the fingertips as shown in Figure 2, with correspondingly different ratios of translational-torotational sliding velocity. As another check on the limit-surface accuracy, the measured card velocity and fingertip velocities can be used directly to compute A cot o = vs,;~/c.vS,;F, without using force information (Kao 1990). This gives A cot ~b = 7.8 mm and 1.53 mm, for r = 15 mm and 75 mm, respectively. Then, using equation (8), one obtains predicted values of h of 0.156 rad/sec and 0.0446 rad/sec for the two cases. 3.1. Discussion The experimental and predicted angular velocities are very close for both sets of experiments",
+            "5%, and the difference in w obtained by using the measured fingertip and card velocities directly is 2.6%. In the case of r = 75 mm, the differences are 1.7% and 0.5%, respectively. Comparing the two cases, we observe that when the fingers are farther apart, the contribution of the term (A cot ~) to the angular velocity is less significant. Hence, the errors u1 h are less sensitive to the inaccuracy in A cot ~ or to the ratio of force and moment. In such cases, the location of ( f , m) on the limit surface is closer to the vertical (moment) axis, as shown in Figure 2. Table 1. Comparison of the Experimental Results of Sliding Manipulation at Freie Universitaet Berlin on May 8, 2015ijr.sagepub.comDownloaded from 533 As the plots show, the force measurements are noisier than position information, because small stick-slip vibrations were present. The sliding excited a 60-Hz vibration in the manipulator fingers. However, this vibration was well above the 12-Hz closed-loop bandwidth of the device. If one low-pass filters the force and moment information at 10 Hz, one can see that average forces and moments agree closely with those predicted by the equation of the limit surface",
+            "&dquo; As these &dquo;fingertips&dquo; are attached to the stationary supporting surface, the sliding velocity of the card with respect to them is simply the absolute velocity of the card. Consequently, it is not necessary to measure the force and moment at these contacts or to use limit surfaces to obtain their sliding velocities. In other words, the forces between the card and the supporting surface are experienced indirectly when solving for LD; their effect is to alter the forces and moments at the moving fingertips, shifting them to different locations on their respective limit surfaces (see Figure 2), with different ratios of translational-to-rotational sliding velocity. As a result, only the three-axis force sensor mounted at each moving fingertip is needed to provide the force and moment information for analyzing the motion. 4. Conclusions Quasistatic sliding analysis has been promoted in the literature as an approximate tool for predicting and planning sliding motions. The results of the (admittedly carefully controlled) experiments described in this article suggest that it can also provide accurate quantitative results provided that the main assumptions of the method (low average speeds and accurate knowledge of the average coefficient of friction and normal force) are met"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000617_s1526-6125(00)70021-1-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000617_s1526-6125(00)70021-1-Figure2-1.png",
+        "caption": "Figure 2 Three Typical Types of Five-Axis Machine Tool Configurations",
+        "texts": [],
+        "surrounding_texts": [
+            "Owing to the increasing requirement of enhancing a product\u2019s esthetics and performance, free-form surfaces, which can be defined as surfaces with variable curvature by higher-degree polynomials, are conventionally used in automotive, naval, and aeronautic industries, as well as in turbine blades, impellers, and plastic injection dies/molds. With the advent of commercial CAD/CAM systems and CNC machines, free-form surfaces can be machined with three- or five-axis machine tools through the tool path generation by software packages. To reduce preliminary work and increase cutting efficiency as well as workpiece accuracy, employing five-axis machining is increasingly prominent as compared to conventional three-axis machining, owing to the application of adding two rotational degrees of freedom such that spindle orientation with respect to workpiece may be varied while machining. However, industries frequently encounter difficulties in interfacing the CAM system with the machine control system. The interface is a software program known as the postprocessor, which converts the cutter location (CL) data created by CAM systems into the machine control data or \u201cG\u201d codes. Figure 1 illustrates that the postprocessor acts as the bridge between the CAM system and the machine tool. The CL data not only include the physical locations of the cutter, composed of cutter tip position and the tool orientation, but also the information regarding a machine tool\u2019s operation, such as tool change, feed rate, and coolant on/off. Because individual controls manufacturers do not adhere to an international standard, such as ISO 6983, the machine operation information processed by the postprocessor may be different according to various machine tool controllers; that is, different manufacturers may use different codes to define the same function. Consequently, the more variety of NC units and machine configurations used, the greater the number of postprocessors. The postprocessor plays a crucial role in a modern machine shop. Owing to the lack of standardization of code format for various machine tool builders, the postprocessor presented here concerns only the transformation from the cutter\u2019s physical locations to the desired machine tool\u2019s motions, including linear motions and rotary motions, which is the main part of NC programs. Methods to develop postprocessors for NC machine tools can generally be divided into two categories: three-axis and multi-axis. From the perspective of the three-axis postprocessor, the processing technology is straightforward and no coordinate transformation technique is required because the orientation of the cutter remains unchanged. Further details regarding the three-axis postprocessor can be found in Bedi and Vickers1 and Lin and Chu.2 From the perspective of the multi-axis (four- and fiveaxis) postprocessor, because of the varying cutter\u2019s orientation with respect to the workpiece, the coordinate transformation matrix must be introduced to obtain the desired equations for NC code; refer to Suh and Lee,3 especially for five-axis machining. On the other hand, with the two additional rotary degrees of freedom in the tool motion, various combinations may be synthesized to yield five-axis machine tool configurations. Consequently, the postprocessor for a five-axis machine tool is inevitably developed individually.4 For instance, Takeuchi and Watanabe4 presented the postprocessor method on two five-axis configurations. Warkentin, Bedi, and Ismail5 developed the technique of machining spherical surfaces and derived the five-axis NC code for one configuration. Moreover, Sakamoto and Inasaki6 classified the configurations of five-axis machine tools into three typical types. Recently, Lee and She7 presented the method for deriving the complete analytical NC code expressions for the above three kinds of fiveaxis machine tool configurations. Worth mentioning is binary cutter location (BCL), which is another approach used as an input to the NC controller with postprocessor function.8 R\u00fcegg9 proposed a generalized kinematics model for three to five-axis machine tools and implemented in a CNC controller. However, due to the high cost investment on the controller and the BCL data format not being widely accepted by users and machine tool builders,10 this concept is not popularly used for universal five-axis machine tools. The purpose of this paper is to extend the previous research proposed by Lee and She7 and develop the generalized postprocessor for effectively dealing with the universal five-axis machine tool\u2019s configuration. By adding four rotational degrees of freedom where two of them are applied to the fixture table and the other two are applied to the spindle, the generalized kinematics model of general five-axis machines can be established and the corresponding form-shaping function matrix can then be determined through the homogeneous coordinate transformation matrix. In addition, the desired analytical equations for NC data are obtained by equating the known CL data matrix and the form-shaping function matrix. Furthermore, the validity of this methodology is confirmed by implementing a trial cut on the five-axis machining center and verifying on the coordinate measurement machine (CMM) according to the proposed algorithms. 132 Journal of Manufacturing Processes Vol. 2/No. 2 2000"
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0002672_j.sysconle.2004.11.014-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002672_j.sysconle.2004.11.014-Figure5-1.png",
+        "caption": "Fig. 5. Situation in Theorem 3.3.",
+        "texts": [
+            " If the set A enclosed by this curve has finite measure , it is absurd, just as in the previous proof. So, the question we must answer is if S \u2208 A\u0304. But if it was the case, S would be the -limit of the bold trajectories and then S could not attract almost all the initial conditions of the original system. In order to see this, consider again the closed path constructed with the negative trajectory of z, the positive trajectory of y0 and a piece of the transversal section through z. We draw again the picture in Fig. 5. Then all the trajectories started outside this closed path must enter it to reach S and these can be done only through the piece of transversal section, which can be made arbitrarily small because of the dense assumption on the set of initial conditions attracted by the north pole N to the past. The counter-reciprocal version of the previous theorem is very interesting. Corollary 3.3.1. Consider the nonlinear system x\u0307 = f (x) with f \u2208 C1(R2,R2). Assume that the set f \u22121({0}) is finite in R2 and that there is a monotone Borel measure bounded at infinity"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003253_j.engfailanal.2004.12.035-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003253_j.engfailanal.2004.12.035-Figure4-1.png",
+        "caption": "Fig. 4. Shafts polishing process.",
+        "texts": [
+            " 1 shows the generic patterns of golf shafts which are comprised of a double bias layer followed by the prepreg of a straight layer on the internal mandrel. As shown in Fig. 2, after the completion of laying-up, wrapping is required to maintain the pressure upon the shaft. Polypropylene tape is usually used for wrapping and the line pressure of the shaft is about 30\u201340 kgf/mm. Fig. 3 shows the curing process of the shaft in a hot-air oven. The hardening time in this process depends on the types of resin but the shaft used in this experiment was kept in an oven at 125 C for 90 min. Fig. 4 illustrates the shaft polishing process, which removes its coating and optimizes its delicate surface and size. The characteristics of a golf shaft can be investigated using four different mechanical parameter tests [3]. These four tests are as follows. The frequency of the golf shaft can be defined by its cycles per minute (CPM) when a mass of 205 g iron is hung at its tip, with its butt fixed as shown in Fig. 5. In general, the frequency, which is often used as a means of quality evaluation for golf shafts following manufacture, is related to the deflection or flex of the shaft"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003515_j.jmmm.2004.04.084-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003515_j.jmmm.2004.04.084-Figure1-1.png",
+        "caption": "Fig. 1. Cross section of (a) IPM and (b) SPM motors.",
+        "texts": [
+            "jmmm.2004.04.084 believed to either directly or indirectly affect motor performance and can be quite dangerous to the motor. Therefore, it is necessary to investigate the effects of rotor eccentricity in permanent magnet synchronous motors. PM synchronous motors generally have two classifications: the popularly used surface permanent magnet (SPM) motor where magnets are mounted on the rotor surface, and the buried or interior permanent magnet (IPM) motor where magnets are mounted inside the rotor (Fig. 1). In this paper, a finite element-based study with and without rotor eccentricity for IPM and SPM synchronous motors is presented. The results including air gap flux density, EMF, cogging torque and average torque are computed from the finite element model. d. Fig. 1 shows three-phase, 6-pole, Y-connected, 8-hp and 36-slot IPM and SPM motors used in the study. Both motors have the same specifications except for different magnet configurations. A twodimensional (2D) cross-section of the motor is modeled using the well-established 2D time-stepping vector potential formulation [7]. The model includes the effects of magnetic saturation, circuit coupling, an external power system, slotting effects and rotor motion. At each time step, the model computes magnetic quantities like magnetic field distribution within the motor and mechanical quantities like position and torque"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002254_3.46181-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002254_3.46181-Figure2-1.png",
+        "caption": "Fig. 2 Aeroelastic model layout-spars, actuators, and hinge attachments.",
+        "texts": [
+            " The wing box consisted of nine aluminum-reinforced balsa sections, and the leading- and trailing-edge control surfaces each consisted of nine aluminum-reinforced balsa sections. The wing sections were attached to a wing box spar and control surface sections were attached to four separate control surface spars. Springs, simulating both actuators and hinges, were used to attach each of the control surface spars to the wing box sections. Each of the balsa sections was mass balanced so that mass, static unbalance, and mass moment of inertia properties corresponded to full-scale values. Figure 2 shows the section layout of the scaled aeroelastic model. Model geometry was scaled to be identical to the full-scale preliminary design. Full-span wing aspect ratio was 3.75, the taper ratio based on tip and fuselage centerline chords, 0.218, and the thickness to chord ratio, 3.8%. The leading-edge sweep was 34.3 deg aft and the trailing-edge was unswept. Airfoil selection was based on full-scale specifications, but was modified to simplify both model fabrication and model trim in the tunnel. A symmetric, 3",
+            " For a swept elastic axis, the pitching moment causes some wing bending, which shifts the effective elastic axis forward, as shown in Fig. 3. The set of influence coefficients was generated using the full-scale NASTRAN finite element model. Bending (El) and torsional (GJ) stiffnesses were determined using the cantilever beam equations. Figure 4 shows the scaled stiffness distributions along the wing box determined from the finite element model. The kinked beam spar design, shown in the layout in Fig. 2, was selected to model the wing box stiffness. NASTRAN analyses indicated that this spar design deformed with deflection and bend/twist characteristics that approximate the influence coefficient description. More precision in matching the influence coefficient description might have been attained through design of a more complicated and costly structure. However, past experiences in the construction of low-speed aeroelastic models has shown that the simulation of actual aircraft structures by beams located on the elastic axis will give acceptable results",
+            " Actuator and Hinge Modeling Full-scale actuator stiffness values were simulated by springs in the form of aluminum brackets that connected the control surface spars to the wing box. Four actuators connected the inboard leading-edge surface. The outboard surface was connected with one leading-edge actuator and two hinge points. Because the leading- and trailing-edge surfaces were segmented, a trailing-edge outboard actuator was added to the outboard flaperon. In addition to this actuator, the outboard trailing-edge control surface was connected at two hinge points. The inboard trailing-edge surface was connected by one actuator and three hinges. Figure 2 depicts the master layout containing the location of all the spars, actuators, and hinges. Hinges were constructed of springs with low rotational stiffness to reduce the damping normally encountered with ball D ow nl oa de d by U N IV E R SI T Y O F O K L A H O M A o n Ja nu ar y 25 , 2 01 5 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .4 61 81 bearing hinges. Each hinge consisted of a 1.5-in. piece of angled beryllium copper, which was connected to three small steel attachment fittings"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003153_146441905x63322-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003153_146441905x63322-Figure3-1.png",
+        "caption": "Fig. 3 Coordinate systems of the dynamic model of the gantry crane",
+        "texts": [
+            " The trolley moves along the rails attached to the gantry perpendicular to the pier, so it basically has one DOF. Nevertheless, owing to the structural flexibility of the gantry, the operator senses vertical accelerations while hoisting or lowering the container, therefore another DOF is required to model this direction of motion. The spreader is attached to the trolley via cables and has all six DOFs. The bodies of the dynamic model of the gantry crane and the coordinate systems attached to the bodies are presented in Fig. 3. The model has a total of nine DOFs. Owing to possible singularities during numerical solutions, a more stable behaviour can be achieved using more than three rotational coordinates. In this case, four Euler parameters were selected. As the four parameters increase the DOFs, normalization constraint of the coordinates is required [1\u20134]. The generalized coordinates q that fully describe the DOFs of the system can be expressed as q\u00bc\u00bdZg Xt Yt Xc Yc Zc u0c u1c u2c u3c T\u00bc\u00bdRTuT T (1) where R\u00bc \u00bdZg Xt Yt Xc Yc Zc T and u\u00bc \u00bdu0c u1c u2c u3c T (2) The normalization constraint equation of the Euler parameters is C(q)\u00bc uTu 1\u00bc 0 (3) Using Lagrange\u2019s method, it is possible to model the connecting joints between separate bodies by using constraint equations that describe joints between bodies"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001508_978-1-4615-2135-8_1-Figure1.4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001508_978-1-4615-2135-8_1-Figure1.4-1.png",
+        "caption": "Figure 1.4 The centre line distance (Cd governs the maximum power transmittable from the motor to the shafts and the screw conveying volume.",
+        "texts": [
+            " The main disadvantage of the piston type is in the valve and ball arrangement where any solid matter, either as a foreign body or natural in the feed stock, will prevent the ball seating in the valve. This drastically reduces the positive nature of the pump and although it may be apparent that the pump is functioning well under atmospheric pressure, any back pressure caused by partial blockage in the feed pipe will be disastrous. The degree of intermeshing is determined by the shaft centre line distance (CL , Figure 1.4) and the desired screw to screw clearance, with zero clear ance being fully intermeshing. Many manufacturers of extruders claim machines which are self-wiping but this implies zero clearance which would give severe mechanical wear from metal to metal contact. In reality a compromise is found and screws are made as fully intermeshed as pos sible. The volume of material that screws can convey and the power they can transfer in pumping and heat generation is a design optimisation which is made to suit different products"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002381_robot.2001.933052-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002381_robot.2001.933052-Figure4-1.png",
+        "caption": "Figure 4: Construction of virtual joint model (n = 3)",
+        "texts": [
+            " az( t ) = {(\")T(\")}-'(\")T(\") (7) 4 Virtual Joint Model In this section, we describe ii model construction of flexible manipulators based on the virtual joint model by Yoshikawa e t al. [4] 4.1 Model Constructioin In the virtual joint model, which is one of the lumped parameter models, each flexible link is divided into some virtual rigid links connected by virtual passive joints. The link flexibility is represented by virtual springs and dampers attached to the virtual passive joints. As shown in Fig.4, each of\u2019 N flexible links is divided by n virtual passive joints. The divided virtual rigid links are numbered link :io, i l , \u201d \u2018 , in from the manipulator base (Fig.4 is an example of n = 3 ) . l i j is the length, 1,ij is the center of mass, mzj is the mass, Iij is the inertia moment around the center of mass of link i j ( j = 0,1, . . . , n). The virtual passive joint attached to the base of link ij ( j = 1 , 2 : . . . ,n) is called joint ij. The displacement of the virtual passive joints on link i is +i(t) = [4il, 4i2, . . . , & I T . The damping coefficient and spring constant of joint ij are respectively Di,?, Kij . 4.2 Dynamics The equations of motion of a flexible manipulator based on the virtual joint model are given by M11($)8 + M12($)4 + h l ( w i J ) = 7- (8) M21($)8 + M22($)4 + hz(yj, 4) + D 4 + K 4 = 0 Mll, M12, M21, M22 are the inertia matrices, hl, h2 are the vectors containing centrifugal, Coriolis, gravity and other nonlinear force, D = diag[Dll ,D12,"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003922_bf02844162-Figure7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003922_bf02844162-Figure7-1.png",
+        "caption": "Figure 7 A schematic of the rigid body Newtonian oblique impact model.",
+        "texts": [
+            " In order to achieve this logical combination, a Newtonian impact model was considered. Daish (1974) first proposed the applicability of a Newtonian impact model for cricket and his work was later developed by Carr\u00e9 et al. (2000). Essentially, the Newtonian impact model allows for no deformation of either the surface or the ball and calculates the ball rebound dynamics using a combination of friction and restitution measurements. Whilst it is inaccurate to describe the cricket ball and pitch as rigid bodies, the model provides some useful insights. Fig. 7 shows a schematic of the rigid body model. The cricket ball arrives with a spin rate, \u03c9in (positive = topspin, negative = backspin), a horizontal velocity, Vxin, and a vertical velocity, Vyin. Two forces act on the ball during impact, a normal reaction force, F, and a frictional force equal to the product of the coefficient of friction and the normal reaction force, \u00b5F. After impact, the ball rebounds with the velocities of Vxout and Vyout and a spin rate of \u03c9out. The ball\u2019s radius is denoted by r and its mass is m"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001325_jsvi.2000.3040-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001325_jsvi.2000.3040-Figure5-1.png",
+        "caption": "Figure 5. Response of the axially moving string under a sinusoidal point load and controlled by the &&simulation'' control forces of Figure 3.",
+        "texts": [
+            " The latter is suitably termed &&simulation'' because it can be achieved only in simulations but not in real time control. The &&real time'' and &&simulation'' control forces for this example are plotted in Figures 2 and 3. The corresponding responses of the controlled system are shown in Figures 4 and 5. In Figure 4, it is seen that the controlled vibration does not go to zero as a result of nonzero motions at the boundaries when the control forces are applied at t c . However, the controlled amplitude is much smaller than the uncontrolled one. In Figure 5, as predicted by the control laws, the vibration is suppressed to zero in x)a 1 and x*a 2 . Comparing Figures 4 and 5, it is seen that the control is still e!ective in the presence of non-zero initial conditions at non-\"xed boundaries. For this type of feedforward control, disturbances in the uncontrolled regions and boundary excitations can be attenuated by feedback control [36]. Numerical results show that similar control e!ects are obtained when di!erent types of boundary conditions are considered and when a random excitation force is applied"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002333_a:1025991618087-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002333_a:1025991618087-Figure3-1.png",
+        "caption": "Figure 3. The open-constraint coordinates and the constraint reactions.",
+        "texts": [
+            " , m7,m7, JC7) is the constant generalized mass matrix related to p, mi and JCi are the masses and mass moments of inertia with respect to Ci of the segments, h = [(h(1))T . . . (h(7))T ]T contains the generalized applied forces on the bodies due to the gravitational forces, reactions from the trampoline (for segment 4) and control torques (as an example, for the said segment 4, we have h(4) = [\u2212Rx m4g\u2212Ry MA+\u03c43]T ), C(p) is the 12\u00d721-dimensional matrix of constraints due to the kinematical joints, and the Lagrange multipliers \u03bb = [\u03bb1 . . . \u03bb12]T are the reaction forces in the joints, shown in Figure 3. The 21 absolute coordinates p are dependent because of the joints in the system, modeled by 12 kinematic constraints on the bodies. Physically, the constraints express the prohibited relative translations in the joints. By introducing 12 local coordinates z = [z1 . . . z12]T to describe these prohibited relative motions, say open-constraint coordinates, the constraints on the bodies are z = 0. Since z can be expressed in terms of p, the constraint equations at position and velocity levels, given in implicit forms [13], are: z = (p) = 0, (2) z\u0308 = C(p)p\u0307 = 0, (3) where C = \u2202 /\u2202p is the constraint matrix used in Equation (1)"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000417_a:1008980606521-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000417_a:1008980606521-Figure1-1.png",
+        "caption": "Figure 1. Schematic drawings of the TUM walking machine and the Indian stick insect, Carausius morosus, upon which it is modeled, showing the body-centered coordinate system, the joint axes, and the joint angle designations. The machine lacks the long abdomen of the insect and, for economy in fabrication, all legs have the same dimensions, but it shares the scaling of the three leg segments as well as the inclinations of the axes of the basal joints.",
+        "texts": [
+            "eywords: hexapod, walking machine, neural net, cybernetics, Carausius morosus Walking is one of many behaviors where machines still lag notably behind the performance of animals, so it is natural to examine walking in animals for hints to improve the performance of machines. The animal discussed here is the stick insect (Fig. 1(a)) or walking stick\u2014a slow, long-legged hexapod adapted for locomotion on complex substrates consisting of branches and leaves. Like most other insects the stick insect can walk with all different orientations to gravity; it can walk upright on flat or uneven surfaces, climb or descend vertical surfaces, and walk inverted hanging from \u2217Present address: BGES/Cleveland State University, 2399 Euclid Avenue, Cleveland, OH 44115-2406. branches or leaves (e.g., Cruse, 1976a). Natural surfaces provide more-or-less rigid mechanical coupling among the legs in contact with the substrate, but the stick insect can also walk with good coordination on mercury or other slippery surfaces where the legs are mechanically uncoupled (Cruse and Graham, 1981)",
+            " In contrast to the bottom-up description just given, a top-down analysis beginning with the global task naturally leads to the choice of control principles that explicitly ensure adequate global performance, in other words, control mechanisms incorporating some form of global optimization. This in turn suggests the need for a single central controller to supervise the global optimization. This central instance would need information on the state of all six legs, that is, information on the current step phase and the angles, velocities, and torques at all the joints. Results in the stick insect and in the modeling work do not support the need for an architecture based on a central controller. Each leg of the stick insect (Fig. 1(c)) has three major joints and three major segments, which lie approximately in a plane. The two distal joints, the coxatrochanter joint and the femur-tibia joint, essentially are hinge joints providing one degree of freedom each; they are primarily responsible for leg elevation and leg extension, respectively. The subcoxal joint, the proximal joint linking the leg to the body, has a more complex structure providing two degrees of freedom. The primary movement is that of a hinge joint with its axis tilted from the vertical: this degree of freedom is primarily responsible for the forward and backward movement of the leg",
+            " For example, if the joint angle changes a lot in one time interval, the controller attempts to make it change a lot in the next. The low-pass characteristic provides an upper limit to velocity, such as would be imposed by the inertia and the biomechanical limits of a skeletal muscular system. The role of the physical interaction via the substrate is to cause a change at any single joint to impose physically realistic changes on all the other joints. Imagine a hexapod standing motionless in a configuration similar to that of Fig. 1(a) but with all six legs on the ground. Then let the femur-tibia joint of the left front leg begin an active flexion, pulling the animal forward. The mechanical coupling acting on the elastic skeletal muscular system will cause changes in the other 17 joints, although the net effect of their own controllers will reduce movement amplitudes, including that originally commanded for the femur-tibia joint of the front leg. The mechanical interaction ensures that the whole system changes in a consistent and physically realistic manner, that is, all the connections between segments and between tarsi and substrate are maintained"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002746_0278364905060149-Figure29-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002746_0278364905060149-Figure29-1.png",
+        "caption": "Fig. 29. Arrangement of measurement device for frame deformation in another configuration.",
+        "texts": [
+            " If the distances between the surface plate and the joint supports, u1 \u2212 u6, are considerably long, some non-contact displacement sensor systems (e.g., a laser interferometer system) are utilized as shown in Figure 27. The combination of the sensor and the rod also measures the distance changes among the three joint supports, t1 \u2212 t3. In the PKM shown in Figure 2, the mechanism is suspended from the frame. This compensation system can be successfully utilized even if other configurations of the PKM are adopted. For example, a PKM can be held in the inverted position as shown in Figure 28. Figure 29 shows another configuration of a PKM that is manipulating the workpiece. The compensation device for the frame deformation, described in Section 4, was installed in an experimental CMM (Oiwa 1997, 2000) as shown in Figure 8. This CMM uses a parallel manipulator with three degrees of freedom, which is shown in Figure 2(b). A triangular-prism-shaped aluminum truss frame supports the manipulator through three spherical joints. A surface plate made of low-expansion cast iron at UNIVERSITY OF BRIGHTON on July 11, 2014ijr"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002991_sis.2003.1202253-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002991_sis.2003.1202253-Figure2-1.png",
+        "caption": "Figure 2. Relative sensory range limitatinnS.",
+        "texts": [
+            " However, if there is no information from the current state, the higher behavior layer of the architecture will inhibit and subsume the lower layer(s) as required by the subsumption scheme. The tight coupling between the sensordstate and behaviors is responsible for the UAVs' reactive maneuvers. The architecture is divided into three main subcomponents: sensors, actions, and behaviors. 4. SENSORS The sensors are the \"eyes\" and \"ears\" of the UAV. A UAV's behavior is greatly dependant on its sensors. Nonetheless, the UAV's sensing capacity bas limits as depicted in Figure 2. We assume that the target emits a detectable signal that can be sensed by a UAV at a relatively long range, The detection range (the larger circle in Figure 2) is a parameter that is dependant on the effectiveness of the UAV's target sensor. As the UAV detects the target signal, it is capable of determining the relative distance and direction to the target. The ranges for local-communication and viaion, for simplicity, are presumed to be the same (the smaller circle in Figure 2). The vision range is the distance at which the UAV can visually sense obstacles. The simulation assumes the imaging technology is able to determine the relative distances and directions of obstacles so the UAV can take evasive action. The local-communication range is the distance at which the UAV can receive or broadcast short-range messages from or to its neighbors. Normally the detection range is greater than the local-communication or vision range. 5 . ACTIONS The output of the architecture is a vector composed of two motor mechanisms: rotational and forward velocity"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002793_j.jsv.2005.03.024-Figure9-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002793_j.jsv.2005.03.024-Figure9-1.png",
+        "caption": "Fig. 9. Edge excited plate strip.",
+        "texts": [
+            " Nevertheless this modification will have no effect on the static stiffness\u2019 discussed in the previous section, only on the characteristics above the first side-wall resonance. The example here will only include one wavetype and the shear waves generated by the belt circumferential or longitudinal motion are chosen, being the most simple, described by a secondorder differential equation. It will be shown that the effects depend upon the relative sizes of the side-wall (or plate), free wavenumber and the excitation wavenumber from the belt at the boundary. Fig. 9 shows an infinite orthogonal plate strip of width ly, representing the side-wall. The wavenumber ky, across a strip of width ly, is very similar to that of the one-dimensional system of the same length, considered previously. However, for the strip, the wavenumber ky has a larger attenuation part due to the extra distance actually travelled between boundaries by the nonnormal wave front. Two methods of finding this damped wavenumber in the y direction are obtained by considering the in-plane response of the strip to an inexorable x displacement U0 exp\u00f0 ikxx\u00de, travelling in the x direction at the boundary y \u00bc 0",
+            " (37a) This is now an equation for one-dimensional waves in the y direction; the complex wavenumber is the same as before but now with extra attenuation dependent upon the angle of incidence to the boundary y k\u0302y \u00bc k\u0304y ik0x cot y. (37b) For normal incidence there is no extra attenuation, while for grazing incidence the attention becomes infinite because of the increased path, i.e. lx becomes infinite. a\u0302y is the attenuation and phase change as the wave between the boundaries separated by distance ly a\u0302y \u00bc exp\u00f0 ik\u0302yly\u00de. (37c) The complex wavenumber k\u0302y can actually be found much more directly, but without physical interpretation from the vector summation of wavenumbers seen in Fig. 9 k\u0302y \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k\u0304 2 k2 x q ; k\u0304 2 \u00bc k\u0304 2 x \u00fe k\u0304 2 y. (38a,b) The real and complex wavenumbers are defined in Eq. (35). It is to be noted that the purely real wavenumber kx imposed on the boundary is used in Eq. (38a). If the loss factor Z, in directions x and y are the same, then Eq. (38b) becomes k\u0304 2 \u00bc k2 x \u00fe k2 y 1\u00fe iZ . (38c) By making this substitution into Eq. (38a) the modified wavenumber in the y direction is k\u0302y \u00bc kyffiffiffiffiffiffiffiffiffiffiffiffiffi 1\u00fe Z2 p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 \u00f0Z cot y\u00de2 iZ\u00f01\u00fe cot y\u00de2 q ; cot y \u00bc kx ky "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002571_cca.1996.558742-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002571_cca.1996.558742-Figure3-1.png",
+        "caption": "Figure 3: Variation of length in a flow field",
+        "texts": [
+            " 2Recall that a virtual displacement is an infinitesimal displacement at fixed time. a n-dimensional space. That means there is only 2- dimensional space left in which the velocity vectors have to lie. Thus it can always be represented as a rotation in a 2-dimensional plane. It is also well known that all the eigenvalues of 0 are imaginary and correspond to n orthogonal eigenvectors. 4. Contracting regions Consider two neighboring Lagrange particles in the flow field, and the line vector ds between them (Figure 3). The squared distance between these two Lagrange particles can be written [Fluegge, 19721 ( d S ) 2 = (6x)2 The rate of change of any length in the flow field is 3For non-Cartesian coordinates length is defined in tensor analysis as 6x,glJ6x3, where gzJ represents the metric tensor and thus the metric of the system. thus of the form d - ( S X ) ~ = 2 6xTF(x, t)Sx = 6xTE(x, t)Sx ( 2 ) dt since O(x,t) is skew-symmetric. The rate of strain tensor E, which is symmetric, can in turn be written\u2019 E ( x , t ) = V T ( x , t ) A ( x , t ) V ( x , t ) (3) where V ( x , t ) is a matrix of eigenvectors and V T ( x , t ) V ( x , t ) = I, and A(x , t ) is a diagonal matrix containing the real eigenvalues of E(x , t ) "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001852_icpr.2002.1047389-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001852_icpr.2002.1047389-Figure1-1.png",
+        "caption": "Figure 1. Symmetrical points seen from symmetrical cameras",
+        "texts": [],
+        "surrounding_texts": [
+            "1. Introduction\nSymmetry is a rich source of information in images. Mirror symmetry (also called bilateral symmetry) is a property shared by many natural and man-made objects. A 3-D object exhibits mirror symmetry if there exists a plane that separates the object into two (identical) chiral parts. The plane is called symmetryplane. For each point of such an object, there exists an identical symmetric point that also belongs to the object. A line joining two symmetric points is called a symmetry line. All symmetry lines are perpendicular to the symmetry plane, which by construction contains all symmetry pair midpoints.\nMethods to exploit symmetry and infer constraints on the 3D reconstructed shape of the objectlscene have a long history in Computer Vision. Based on the assumption that \u201ca skew symmetry depicts a real symmetry viewed from some unknown angle\u201d (Kanade [5]), a large number of approaches rely on the analysis of skewed symmetries in images to infer constraints on the 3-D geometry of\ndepicted objects. In most cases, (scaled) orthographic projection is assumed (see e.g. [7][2]). A more limited number of studies deal with symmetry observed under perspective projection. Some (e.g. [11][6]) use the vanishing point of symmetry lines, whose computation is unstable unless the perspective distortion is severe. Different studies make use of the epipolar geometry arising from the bilateral symmetry of a scene in a single perspective view (see e.g. [9][12][10][4]).\nWe establish more general epipolar projective properties of single views of mirror symmetric scenes, and apply them in a different context: we perform Euclidean 3-D reconstruction of mirror symmetric objects from a single perspective view using traditional 2-view stereo geometry. This is allowed by the mirror-stereo theorem. Theorem: One perspective view of a mirror symmetric scene, taken with an arbitrary projective camera, is geometrically equivalent to two perspective views of the scene\nthe unknown 3-0 symmetry plane. We show how to extract the epipolar geometry relating the two views from the single input image. Classical 2- view stereo results can then be applied (see e.g. [ 1) or [3]), and the concepts of fundamentaVessentia1 matrix, epipolar geometry, rectification and disparity hold. If the camera is calibrated, we show how to synthesize the image generated by the original camera placed symmetrically, in order to be able to use traditional 2-view stereo tools to obtain an Euclidean reconstruction of the scene.\nThis paper is organized as follows. In section 2 and section 3, we establish two lemmas used in the proof of the mirror-stereo theorem, given in section 4. In section 5, we show in the case of a calibrated pinhole camera, how to build a virtual view taken by the same camera placed symmetrically in location and orientation. Examples of Euclidean 3-D reconstructions obtained from such pairs with an off-the-shelf stereo package are presented. A summary of the contribution concludes the paper in section 6 .\nThroughout the paper, the approach and notation used are consistent with that of [3].\nfrom h v o projective cameras symmetrical with respect to\n1051-465U02 $17.00 Q 2002 IEEE 12",
+            "2. Virtual view respect to the (R, y , z ) plane is x = Z X , where\nLemma 1: The image of a scene that is symmetric with respect to an unknown plane, formed by an arbitrary projective camera, is identical to the image of the scene formed by the (virtual) projective camera symmetric of the Jirst one with respect to the scene's 3-0 (unknown) symmetry plane.\nWithout loss of generality, we place the origin R of the world Euclidean, orthogonal, right-handed coordinate system ( R , x , y , z ) on the symmetry plane, which we also define as the (R, y , z ) plane. The setting is illustrated in figure I . Let X denote a world point represented by the\nhomogeneous 4-vector 1 . Let x denote the cor-\nresponding image point represented by a homogeneous 3- vector [U v 4 T . A general projective camera is defined\nby a 3x4 projection matrix P = M[II - C'] , where M is a\n3x3 matrix, and C denotes the inhomogeneous 3-vector of the camera center coordinates in the world coordinate system. X is mapped to x according to the relation\n[ I'\nx = M[II - C ] X . By construction, the world point symmetric to X with\n10 0 0 11 L \" I\nThus the image point X of the world point x seen by camera C is:\nP = M[II - C ] X = M[II - C ] Z X\nConsider now the virtual camera c, symmetrical of camera C with respect to the object's symmetry plane. By construction, its center is c = ZC , and it projects a world point X into the image point x' such that:\nx' = M[II - ? ] X , where fi = M Z Replacing symmetric elements by their expression, we\nget:\nx' = MZ[II - Z C ] X = M[II - QZX = X and\nX' = M.z[II - ZC]ZX = M[II - CIZZX = x It follows that the image of a pair of symmetric points viewed by the real camera is identical to the image of the same symmetric pair viewed by the virtual symmetric camera, the actual image points of the symmetric points being reversed in the real and virtual view. Q.E.D.\n3. Through the looking glass\nLemma 2: In stereo pair of images of a mirror symmetric scene, taken by cameras whose centers are symmetrical with respect to the scene k symmetry plane, the epipolar lines are images of symmetry lines, and reverseb symmetry lines project into epipolar lines.\nSymmetry lines are 3-D lines perpendicular to the symmetry plane. With the notations defined above (see figure\nI), for any world point X, the lines X?i and C c are parallel by construction. It follows that the epipolar plane con-\ntaining a point X also contains the symmetric point ?i, and consequently the corresponding symmetry line Xi. In other words, all symmetry lines lie in an epipolar plane. It results that the epipolar line defined by the epipolar plane in each image is also the projection of all symmetry lines contained in this plane. Reversely, any symmetry line projects into the epipolar line defined by the epipolar plane containing the symmetry line. Q.E.D.",
+            "4. Mirror-stereo theorem\nPer Lemma 2, the symmetry lines in a single perspective view of a mirror symmetric scene, taken by an arbitrary projective camera, are also the epipolar lines of the stereo pair consisting of the given image and the image formed by any projective camera located symmetrically, and thus completely characterize the epipolar geometry between such a view and the original view. Per Lemma 1, one such view, specifically the one taken by the virtual camera symmetrical to the real one with respect to the scene's symmetry plane, is actually the same image as the original. In those two (identical) images, the image points of a world point and its (world) symmetrical point are reversed. It results that the original image is geometrically equivalent to two views from two different positions, related by a computable epipolar geometry. Q.E.D.\nGiven the epipolar pencil and a set of point correspondences in the one real image, it is possible, using classical epipolar geometry results, to compute the fundamental matrix relating the two views, the camera matrices (up to a projective transformation), and for each point correspondence, the 3-D point that projects to those points (up to a projective transformation). Note that additional constraints derived from the mirror symmetry property can be used to make those computations simpler than in the general case, as computations can be done in a single image.\n5. Application\nWe developed our novel formulation to use existing 2- view stereo tools to perform 3-D reconstruction of mirror symmetric objects from a single, real perspective image. Such systems take as input two images, taken by the same physical camera from different positions, and sometimes require the images to be rectified. If the rectification poses no theoretical problem given the availability of epipolar pencils, the synthesis of a virtual symmetric view taken by a physical camera requires more work. We show how to build such an image in the case of a calibrated pinhole camera, in order to allow Euclidean reconstruction of the scene. We then present one example of the results obtained by processing image pairs made of one real perspective image of a mirror symmetric object, and one synthetic symmetric view, in an off-the-shelf commercial package, Eos Systems' PhotoModeler Pro 4.0 [SI.\n5.1. Calibrated pinhole camera case Suppose the camera used to take the available picture is a pinhole camera. It projects the world point into the image point according to the formula:\nx = K R [ / I ( - c ) ] X\nThe 3x3 matrix K is the camera calibration matrix. R is the 3x3 transform matrix from the world coordinate system to the camera coordinate system, in this case a rota-\ntion, defined by R = e T eT eT , where ( e l , e2, e 3 ) is\nthe orthonormal basis of the Euclidean coordinate system associated with the camera.\nLet (el ' , e2', e 3 ' ) be the orthonormal basis of the\nEuclidean coordinate system associated with the virtual\nsymmetrical camera. By construction, e.' = e - = Z e - . Because of the symmetry, this coordinate system's orientation is reversed compared to that of ( e l , e2, e 3 ) (i.e. if one\nis right-handed, the other is left-handed). The virtual camera projects the world point X into the\nimage point x' according to:\n[ I 2 J T\n- J J J\nThe image point of the same world point seen by the\nand with principal axis direc- physical camera placed in\ntion e3 IS: - T .\nx\" = KR\"[/J-F] .Y\nand (e, \", e2\") is an orthonormal basis of the principal\nplane such that (el\", e2\", e 3 ) has the same orientation as\n( e l , e2, e 3 ) (both are either right or left-handed). Such a\nbasis is obtained by applying an arbitrary rotation to the\nbasis (e l , e 2 ) in the plane it defines, and inverting the\ndirection of one of the axes. The rotation of the coordinate system corresponds to a rotation of the physical camera around its optical axis. The simplest analytic form naturally corresponds to no rotation, i.e. to the cases where the real camera coordinate system axes are aligned with that of the virtual (symmetric) ones, the direction of one of the axes being reversed to preserve the coordinate system's orientation. The two corresponding cases are shown in figure 2. For sake of clarity and simplicity, without loss of generality, we only consider an inversion of the x-axis. It follows that if the camera is calibrated, then the symmetric view of the virtual stereo pair can be obtained by simply performing a horizontal mirror of the original image with respect to a vertical axis going through the principal point.\n-\n- -"
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0003384_s0022-0728(83)80266-6-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003384_s0022-0728(83)80266-6-Figure4-1.png",
+        "caption": "Fig. 4. Cyclic voltammogram of ferricytochrome c at a MVM gold electrode. Electrode area = 0.25 cm 2, potential scan rate = 10 mV s i. (A) 42.5 ffM ferricytochrome c in 0.1 M phosphate buffer, 0.1 M NaC1, pH 7.0; (B) electrolyte alone.",
+        "texts": [
+            " This slow electrode charging behavior observed in the metalloprotein studies is suggestive of a more involved reaction occurring at the electrode interface, than that taking place in the ferri/ferrocyanide direct electron-transfer events. Cyclic voltammetry studies of myoglobin and cytochrome c in quiescent solutions were also conducted in an attempt to characterize further the charge-transfer mechanisms of these two metalloproteins at MVM gold surfaces. Cyclic voltammograms of oxidized myoglobin samples at various potential scan rates yielded nondescript current responses. Ferricytochrome c, on the other hand, exhibited a scanrate-dependent cathodic peak. No apparent oxidation peak was observed on scan reversal (see Fig. 4). The magnitude of the cathodic peak current was directly proportional to the square root of scan rate for potential sweep rates no faster than 50 mV s -~. Upon completion of the CV experiments, the electrodes were rinsed in distilled water and then immersed in a phosphate buffer/NaC1 solution. Figure 5 shows a representative cyclic voltammogram obtained under these conditions. The ap- pearance of a voltammetric response at ca. 0.35 V was reproducible in both the myoglobin and cytochrome c experiments"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001941_eurbot.1997.633569-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001941_eurbot.1997.633569-Figure2-1.png",
+        "caption": "Figure 2: VIPER",
+        "texts": [
+            " 2 The mobile robots As test vehicle for the Stewart platform we use different autonomous mobile robots which have been build at our institute or in cooperation with industrial partners. All include a very efficient navigation system which allows orientation in complex, dynamic surroundings. The sensor system of each vehicle includes a laser scanner for position detection, a ring of ultrasonic sensors for collision avoidance and a camera for object recognition. Two of the mobile robots are presented in detail in this paper as they are of particularly interest for our applications: MORTIMERl (see figure 1) and VIPER2 (see figure 2). 2.1 MORTIMER MORTIMER has an octagonal shape with a diameter of 720\". The height of the loading platform is 450\" and the height of the control tower is 1150\". The robot has been developed and built in 'Mobile robot for transport and indoor room service in 'Four wheeled vehicle of the Institute for Real-Time hotels Computer Systems and Robotics 0-8186-8174-8/97 $10.00 0 1997 IEEE cooperation with a hotel in Karlsruhe where it will be used for transport of luggage and room service. MORTIMER is based on a two wheel kinematic which is explained in detail in [JLC92] "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001553_s0045-7825(99)00329-1-Figure8-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001553_s0045-7825(99)00329-1-Figure8-1.png",
+        "caption": "Fig. 8. Cross-section of an involute worm.",
+        "texts": [
+            " (21) and determination of initial set P 0 of parameters, the computations are based on Newton\u00b1Raphson method and computerized [3]. Determination of functions (22) enables to accomplish the process of simulation of meshing of misaligned gear drive. It becomes possible to obtain [7]: (i) The path of contact on R2 determined as r2 ut /w ;wh /w : 26 (ii) Function of transmission errors determined as D/2 /w /2 /w \u00ff Nw N2 /w: 27 The term ``involute'' means that the hob is provided with an involute screw surface (Fig. 8). Such a surface may be traced out by a straight line performing a screw motion and being tangent to the helix on base cylinder. Hob surfaces R i h i I; II) and the unit normals to R i h are represented for both sides I and II of the thread by the following equations: r i h u i h ; h i h r i bh sin h i oh h i h u i h cos k i bh cos h i oh h i h \u00ffr i bh cos h i oh h i h \u00ff u i h cos k i bh sin h i oh h i h u i h sin k i bh phh i h 266664 377775 i I; II ; 28 n i h h i h N i h N i h sin k i bh cos h i oh h i h sin k i bh sin h i oh h i h cos k i bh 266664 377775 i I; II ; 29 where h i oh p 2N1 \u00ff inv a i o : 30 In both cases the upper and the lower signs refer to surface sides I and II, respectively"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003001_10402008908981893-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003001_10402008908981893-Figure1-1.png",
+        "caption": "Fig. 1-Nomenclature for rolling bearing thermal study",
+        "texts": [],
+        "surrounding_texts": [
+            "Estimate of Surface Temperatures During Rolling Contact@\nJ. W. KANNEL and S. A. BARBER (Member, STLE) Battelle Columbus Division\nColumbus. Ohio 4320 1-2693\nTetnperature has been shown to be a key factor i n the peformance\nof rolling and sliding contacb. I n normal bearing operation, contact areas 071 the bearing ball (or roller) and race are briefly heated due\nto ball or roller slip then cooled from convection to the surrounding medium. After numerous repetitive heating and cooling cycles, the bearing elemenb attain a steady state temperature that is dependent upon the heat input and the surrounding convective conditions.\nThis paper examines the temperature profile i n a rolling element using two approaches. The first approach involves a discrete stepby-step computation of the heating and cooling that occurs during a. typical cycle under various conditions of heat input and convectiot~\nconditions. Steady-state conditions are predicted by extending this repetitive process over many cycles. The second approach assumes that the heating and cooling occurs over the entire ball or roller\ntrack area after steady state is achieved. The resulb of both approaches are compared.\nPresented at the 43rd Annual Meeting In Cleveland, Ohio\nMay 9-1 2, 1988 Final manuscript approved January 11, 1988\na = Half length o f Hertz conlac1 (axial direction) A = Constant A, = Contact area A, = Circumferential surface area b = Half' width of contact (rolling direction) c = specific heat D = Friction Force 5; = Elliptical integral h, = surface heat-transfer coefficient\n7\nHeat = Ball race heating k = Diffusivity (Wpc) K = Conductivity L = Ball-race load\nThe tmhnique was used to exatnine probable temperatures i n a liquid hrbricated, liquid-cooled turbine engine bearing and in a hypothetical solid-lubricated, air-cooled turbine engrne bearing.\nINTRODUCTION\nTemperature has been shown to be a key factor in galling o r scuffing of critical machine elements. Presumably when the temperature at an interface, such as between meshing gear teeth, reaches a critical level, a boundary lubricant fill11 thermally degrades and surface transfer occurs from one tooth to the other. Leech and Kelley's ( I ) development of the critical temperature theory was based on Blok's (2) flash temperature equation. In essence, flash temperature implies the rise in temperature from a single mesh of the gears. I n many instances, however, temperature increases over a finite time interval and eventually this temperature reaches a level where surface damage can occur.\nT h e problem d u e to gradual temperature rise can occur in many components such as poorly lubricated and/or cooled ball o r roller bearings. T h e problem can also occur with traction drives o r even with high-pressure spool valves where repeated sliding motions can generate high frictional heat-\nM = Ball spin moment n = rotational speed\nrR = ball or roller radius s = Laplace transform variable t = time V = velocity x = coordinate variable y = coordinate variable - y = y / d G\na = h ~ d G p = density p = coefficient of friction WR = angular velocity\nD ow\nnl oa\nde d\nby [\nN ew\nY or\nk U\nni ve\nrs ity\n] at\n0 3:\n39 0\n9 Fe\nbr ua\nry 2\n01 5",
+            "306 J . W . K A N N E L and S. A. BARBER\nk g . 'l'lic purpose of this paper is to develop a simple model l i ~ r accumulative temperature rise in a tribological system. Co~~ccntratccl ontact temperature analyses have been pursuccl by a few researchers (3)-(8) including a recent work I)y Kasliicl :uicl Scrieg (8). T h e research has usually been focusccl on the computation of temperature for a single contacl. 'l'l~cse single contact analyses are very complicated 11111 have proclucecl some interesting temperature predictiot~s Ibr rolling contact, especially lubricated rolling contact, situations.\n'I'ltc thcory presented herein is based on classical thermal :~n;~lyscs techniques is an extension of the theory used to ~wocli~ce Blok's Ilash temperature theory. The model consists ol' a one-climensional tr:unsient heat flow analysis. In the case ol' a rollcr o r ball in a bearing, the model is used to track t lie temperature of a point on the surface of the roller o r I ~ c a r i ~ ~ g ball. 'The point is heated as it passes through the r;tcc contact. After contact, the point is cooled by conduction ittto the rollcr ancl convection at the surface. After a revolution (or a half revolution if both inner and outer races arc consiclcrecl) the point is reheated in the contact region. - I his process of heating and cooling can continue for a periocl ol'timc. Under these conditions of heating and cooling, tltc corttact surlitcc eventually reaches a steady-state tem1)c\";ttiwc clclinecl by the convective heat transfer conditions ;IIICI the licat i t~pu t .\n'l'llc 1);11)cr clcscc'-)es two approaches for surface tempera t i ~ r c cotnl)utations Ibr a bearing I~all o r roller. T h e first :11)l)ro;tc11 ir~volvcs a step-by-step computation of heating ;t t tc l cooling. 'fhe seconcl approach involves the use of an :tssurnl)tion that the contact zone heating occurs over the c t~t i rc roller circuml'ercnce. This assumption appears to be rc ;~so~~al) lc lijr computing long-term temperature rise.\nT h e boundary and initial conditions will be\nT(y,O) = 0 T(a , t ) = 0 and\naT K - = - Q + h , T a t y = O\na y\nwhere:\nQ is the frictional heating Q = Q(t) h, is the heat transfer coefficient (assumed to be constant\naround the circumference).\nLaplace Transforms\nT h e Laplace transforms for Eqs. [ I ] and [2] can be written\nand\nwhere:\nANALYSIS FOR SURFACE TEMPERATURES\nBasic Equation\n'I'lic I);tsic system to be analyzed is shown in Fig. I. A point on the rollcr surl'nce will be in contact with the inner rittg over ;I cIist;~~~cc of 2b. T h e point will be out of inner ring contact over a span of appl-oximately 2.rrrK. During contact the point will be heated by slippage between roller ;IIICI r;tce. 1;igilrc 1 coillcl also represent an angular contact I ~ c a r i ~ ~ g ill which heating would be due to ball spin and slip. For tile analysis it will be assumed that the roller can be trcatccl as a semi-infinite half space with surface heating :~t~cl/or cooling. 'flrc heat transler equation can be written (scc I;igilrc 2)\nr . 1 is tcml~cr-aturc t is time K is t1icrm:tl concluctivity p is clc~rsity c is sl~ecilic heat\n8 is the transform of T q is the transform of Q.\nSolution to Transformed Equation\nT h e solution of Eq. [3] can be written\n0 = A e x p (- Ey)\nD ow\nnl oa\nde d\nby [\nN ew\nY or\nk U\nni ve\nrs ity\n] at\n0 3:\n39 0\n9 Fe\nbr ua\nry 2\n01 5",
+            "Estimate of Surface Temperatures During Rolling Contact 307\nUsing Eq. [4]\n- - A = - q + h,A [GI h, rn h: (t - t') ATi = Q [ erfc exp Kpc hs . [I 11\nT h e transformed surface temperature then is\nInversion of Eq. [8]\nEq. [8] can be written\nwhere:\n' Q dt ' ~ = l , ~ ~ - a [ Q e \" P\n[as(t- t')] erfc ( a m) dt'\nwhere\nNote Eq. [I I] can be solved for numerous time steps where\n[71 Q is different at each step. For example, during contact ti < t' < (ti + At), Q could\nbe a large number. Conversely, during no contact (ti + At) < t < ti+ 1 , Q could be zero. For this situation\nwhere:\nD is the friction force\n[91 V is surface velocity A, is contact area\nIf Q is assumed to be spread out over the entire circumference (call this heating QA) rather than just the contact zone\nQA = DVIA, for all time. [ 131\nHere A, is the circumferential surface area. Equation [I I ] can be solved for a given time interval to yield\nas t - (large 11,)\nIf Q is a constant over some time increment, such as ti to ti Temperatures computed, using Eqs. [I I], [I41 and [I51 + At, then the temperature rise over that increment, ATi, for the conditions given in Table I , are given in Table 2. can be written There is reasonable agreement between the temperature\nD ow\nnl oa\nde d\nby [\nN ew\nY or\nk U\nni ve\nrs ity\n] at\n0 3:\n39 0\n9 Fe\nbr ua\nry 2\n01 5"
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0002606_iros.1997.655141-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002606_iros.1997.655141-Figure1-1.png",
+        "caption": "Figure 1: Coordinate systems definitions",
+        "texts": [
+            " So, L estimation might be (7) R1 3 L = ( o 1 ) According to the figure 2, it is obvious that AX = X 3 (8) (3) 0 T : homogeneous transformation matrix from Fm where A and B are known and X represents the handeye calibration transformation that is to be estimated. t.o Fm - I ' _ _ At least three different robot motions are necessary to solve the system [3]. In practice, a set of n positions ( n 2 3) is selected and the system is overdetermined. T represents the location of the calibration object in the robot world coordinate sytem. There is a lot of possibilities to solve for (AiX = X B i ) i E [l..n] (9) (4) Rt Tt T = ( 0 1 ) 0 X : homogeneous transformation matrix from Fe to Fh is the unknown hand-eye transformation. (5) Figure 1 explains the relationships between the different frames and the various homogeneous matrices. 2.2 Classical Approach Let's consider two different positions i and j of the gripper inside the robot workspace (see fig.2). Then, matrices H and L have to be indexed by i and j corresponding to these two different stations of the gripper. Matrix X doesn't have any index since the camera is rigidly mounted on one of the robot links. As H, and H j are known, it is possible to estimate the transformation A that gives the location of the second gripper position relative to the first position"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001553_s0045-7825(99)00329-1-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001553_s0045-7825(99)00329-1-Figure1-1.png",
+        "caption": "Fig. 1. Face worm-gear drive.",
+        "texts": [
+            " . . ; 5) fij 0 equation of meshing during the process of generation of worm (i w; j c), hob (i h; j t) and worm-gear (i 2; j h) F2h 0 equation of singularities * Corresponding author. Tel.: +1-312-996-2866; fax: +1-312-413-0447. E-mail address: \u00afitvin@uic.edu (F.L. Litvin). 0045-7825/00/$ - see front matter \u00d3 2000 Elsevier Science S.A. All rights reserved. PII: S 0 0 4 5 - 7 8 2 5 ( 9 9 ) 0 0 3 2 9 - 1 A face worm-gear drive is formed by a worm and a worm-gear with a special location of teeth (Fig. 1) that is di erent from the location of teeth of a conventional worm-gear. In addition to the term ``face worm-gear drive'' there are two other terms applied in the literature: (i) helicon gear drive, related with the patent and invention proposed by Saari [10], and (ii) hybrid gear drive, related with the patent and invention proposed by Litvin et al. [9]. Saari's invention was proposed as a gear drive alternative for a hypoid drive. The helicon gear drive is designated for transformation of rotation between crossed axes and is provided with the following features: (1) The worm is of Archimedes' type (with straight axial pro\u00aele of thread)"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001811_s0956-5663(98)00010-4-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001811_s0956-5663(98)00010-4-Figure1-1.png",
+        "caption": "Fig. 1. Construction of the ring electrode. Illustrations of (a) and (b) are the side view and the surface of the electrode, respectively. 1: copper covered wire, 0.5 mm diameter; 2: polyolefin heat shrinkable material tube; 3: copper bare wire, 0.05 mm diameter; 4: carbon paste; 5: TTF-TCNQ carbon paste mixture. (c) A microscope photograph of the TTF-TCNQ band on the ring electrode surface.",
+        "texts": [
+            " After mixing the two solutions, the mixture was kept with stirring at room temperature to be cooled down overnight. The mixture was filtered to collect black crystals under vacuum. The crystals were then washed with 5 ml acetonitrile followed by diethyl ether until the wash became colorless. The crystals obtained were dried under vacuum at room temperature to give | 1.6 g of fine black crystals. Details of this procedure can be found elsewhere (Bartlett, 1990). The structure of a ring electrode of diameter approximately 1.5 mm, and a band width of 10\u201320 mm is illustrated in Fig. 1. The method of \u2018fabrication\u2019 was crude and adopted with the intent of an initial investigation of the possible improvement in the signal/noise ratio which could be achieved through the use of a \u2018band\u2019 electrode. Such electrodes show intermediate behavior between spherical and linear diffusion. As far as the fabication of such an electrode is concerned, the dimensions are more important than the preparation method which is reported here and a more sophisticated development is recommended for further work",
+            " The tip of the rod, where the carbon paste had been packed, was then sliced making a new surface of a ring electrode. Finally, excess carbon paste was removed by wiping with a piece of clean paper and TTFTCNQ carbon paste, which had been prepared by mixing 50 mg of TTF-TCNQ salt, and 50 mg of graphite carbon powder and 50 mg of silicon oil were packed on the band of the ring electrode by smearing on a glass slide. The excess TTF-TCNQ carbon paste was also removed by wiping with a piece of clean paper. The electrode surface is shown in Fig. 1(c). The TTF- TCNQ band width of the ring electrode is 10\u201320 mm and therefore the surface area is | 0.10\u20130.19 mm2. The electrode is reusable, when the surface is renewed by slicing. In the case of preparing a lactulose sensor, FDH and b-gal were dissolved with 50 mM citrate buffer solution (pH 4.5) to make the concentrations 90 mU/ml and 600 mU/ml, respectively. 10 mL of the enzyme solution was dropped on the surface of the TTF-TCNQ ring electrode, and then the electrode surface was covered with a dialysis membrane and was secured with a rubber Oring"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003477_cnm.913-Figure20-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003477_cnm.913-Figure20-1.png",
+        "caption": "Figure 20. Further decomposition of factors DC and CD (subspaces V (51) and V (52)): (a) DDC and DCD ; and (b) EDC and ECD .",
+        "texts": [
+            " The factors of this structure are shown in Figure 19. It can be observed that the factors resulted by both group-theoretical and algebraic method, are identical. Considering the factor of the subspace V (51) and its graph model, as shown in Figure 19(d), it can be seen that this factor has a vertical plan of symmetry, which suggests the point group C1v . In the other words, this factor is of canonical form III symmetry and can be further decomposed. The result of decomposition of this factor is shown in Figure 20. Copyright q 2006 John Wiley & Sons, Ltd. Commun. Numer. Meth. Engng 2007; 23:639\u2013664 DOI: 10.1002/cnm As it is seen, factors DDC and DCD are exactly the same as factors DCC and DDD , shown in Figure 19(b), and do not have to be solved. Thus, instead of solving a problem with 16 DOFs only a number of small problems are being solved: a one-dimensional problem and three problems of dimension three. This can some how highlight the efficiency of the proposed method. The procedure introduced in this paper consists of forming the graph model of a mass\u2013spring system, recognizing the symmetry operators and symmetry group of the graph, selecting the positional functions of the nodes of the graph as the basis vectors of the vector space of the problem"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002913_tmag.2003.810552-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002913_tmag.2003.810552-Figure1-1.png",
+        "caption": "Fig. 1. Magnetic field inside the induction machine for rotor position = 20 .",
+        "texts": [
+            " This comparison allows us to estimate the influence of rotor slot wedges on the stator current harmonic content and stator vibration spectrum. During steady-state operation, all electromagnetic and mechanical phenomena occur at various fixed frequencies. It is therefore possible to perform a frequency domain analysis based upon a set of samples taken from the time domain and computed using a transient finite element analysis. For every time step of the transient analysis, the instantaneous magnetic field is used to postprocess the reluctance forces acting on the stator teeth. Fig. 1 shows the flux pattern for one pole of the four-pole induction machine for a certain rotor position. Fig. 2 shows the corresponding reluctance forces acting on the entire stator. The magnetic forces (both Lorentz forces and reluctance forces) are obtained using [4]: (1) where represents the magnetic energy and represents the displacement or deformation. The deformation is considered in 0018-9464/03$17.00 \u00a9 2003 IEEE the entire model. represents the magnetic finite element system: is magnetic stiffness matrix, is the vector of nodal values of magnetic vector potential, and is the source term representing the current excitation"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000497_a:1008966218715-Figure7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000497_a:1008966218715-Figure7-1.png",
+        "caption": "Figure 7. Example of associated case.",
+        "texts": [
+            " The difference between the orientations of the major axes of Ri and Mk is smaller than some uncertainty bound 2. The mean vector mi of Ri is located within the distance \u03bb\u03042k from the major axis of Mk 3. Ri is located within the distance \u03bb\u03041k from the mean vector m\u0304k of Mk Condition (1) checks if the angle difference between the major axes of Mk and Ri is sufficiently small. If the difference is larger than the uncertainty bound \u03c3\u03b8 , then some obstacles that used to be in Mk may have been moved outside of Mk . \u03c3\u03b8 here is defined as \u03c3\u03b8 = tan\u22121 \u03bb\u03042k \u03bb\u03041k . As shown in Fig. 7, \u03c3\u03b8 represent the upper limit of the angle variation of the major axis of Mk assuming that the obstacles are fixed. Condition (1) is then equivalent to |\u03b8\u0304k\u2212\u03b8i | < \u03c3\u03b8 . Condition (2) checks whether Mk and Ri are closely located by examining the distance from the mean position of Ri to the major axis of Mk . Once the condition (1) is satisfied and if the distance is smaller than \u03bb\u03042k , then Mk and Ri are aligned and closely located with each other. If we define m\u0304k as the mean vector of Mk and \u03c6\u0304k as (cos \u03b8\u0304k, sin \u03b8\u0304k), then any point p on the major axis of Mk can be formulated as \u03c6\u0304k \u00b7Q1 \u00b7 (p\u2212 m\u0304k) T = 0, where Q1 = [ 0 \u22121 1 0 ] ",
+            " The distance di from the major axis of Mk to the mean vector mi of Ri is then computed as di = |\u03c6\u0304k \u00b7Q1 \u00b7\u2206mT |, where \u2206m = mi \u2212 m\u0304k . Condition (2) is then equivalent to di < \u03bb\u03042k , where the minor eigenvalue \u03bb\u03042k is used as an uncertainty bound of Mk along the direction of its minor eigenvector. On the other hand, condition (3) checks whether the associated Ri is roughly overlapped with Mk . It is then equivalent to |\u03c6\u0304k \u00b71mT | < \u03bb\u03041k + \u03bb1i where |\u03c6\u0304k \u00b71mT | is the projection if1mT on the major axis of Mk and \u03bb\u03041k is used here as an uncertainty bound of Mk along the direction of its major eigenvector. As shown in Fig. 7, if conditions (1), (2) and (3) hold, then Ri is associated with Mk and vice versa. Now, condition (3) is further divided according to whether the obstacles in Mk are fixed or moved. If all of the obstacles are static and fixed, then |\u03c6\u0304k \u00b71mT | will be close to zero and the obstacles previously identified as Mk may be detected again as Ri with small disturbances in its parameters. However, if the obstacles in Mk is moved to another location or some obstacles are added to Mk or subtracted from it, then the parameters of Mk are changed"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001341_s1359-6462(98)00437-0-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001341_s1359-6462(98)00437-0-Figure1-1.png",
+        "caption": "Figure 1. Illustration of the geometrical relationships between specimen, and incident & beams for measurements of the (a) tensile extension and (b) Poisson contraction.",
+        "texts": [
+            "17\u00b0 on the incident and diffracted beams respectively. Square-sectioned 5 by 5mm testpieces of gauge length 70mm were used for the in-situ neutron diffraction studies. These were machined from Waspaloy stock material, the chemical composition of which is given in Table 1. A servo-hydraulic universal testing system was used with the samples orientated such that the scattering vector lay either along the direction of the load or perpendicular to it, thus allowing measurements of either the tensile extension or the Poisson contraction, see Figure 1. The whole of the gauge length of the specimens was immersed in the neutron beam so that the counting statistics were optimised. Additionally, an extensometer was attached to the sample, which permitted measurement of the total engineering strain accumulated and hence also the determination of the true stress at each load. For the measurements in the longitudinal direction, the nominal stress on the sample was increased in ;100 MPa increments to 1000 MPa before unloading; further load cycles were applied subsequently which had a peak nominal stress of 1200 MPa"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002731_j.ijmachtools.2004.03.005-Figure8-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002731_j.ijmachtools.2004.03.005-Figure8-1.png",
+        "caption": "Fig. 8. Contact between angle with probe; (c) surface normal n perpendicular to probe; (d) rigid force feedback; and (e) soft force feedback.",
+        "texts": [
+            " When a collision is detected between the part and the stylus or the body, a force is fed back to the user via the haptic device and an alarm is sent to the user visually. When only collision between the probe tip and the part occurs the coordinates of the tip is recorded and a force is feedback to the user. In order to have a more realistic force feedback, a mechanics model is proposed. When a probe tip comes into contact with a part, the direction and the magnitude of collision force depend on the probe contact angle h between the probe and the normal of touched surface of the part as shown in Fig. 8. Different contact angle h gives a different felt force as the elasticity of the stylus is different in different directions. The following equations provide an estimate about the difference in spring constant in two extreme conditions as shown in Fig. 8(a),(c). In the case of Fig. 8(a), the displacement d can be calculated as d \u00bc FL EA F \u00bc kad where ka \u00bc EA=L, E is the modulus of elasticity, L is the length of the stylus and ka is the spring constant. And in Fig. 8(c), the displacement d is calculated by d \u00bc 5FL3 48EAr2 or F \u00bc kpd where kp \u00bc \u00f048EA=5L\u00deC2 and C \u00bc r=L, r is the radius of the stylus and kp is the spring constant. Based on the above equations, for a typical stylus of r \u00bc 2 mm and L \u00bc 100 mm, C \u00bc 2=100 \u00bc 0:02, the ratio between the two spring constants ka and kp is about 260. That is, the spring constant of ka is normally much bigger than kp. So, different forces could be felt by the user when the contact angle h is different. When ka is used, the felt force is instant and big as shown in Fig. 8(d) while kp gives a much smaller contact force. There is a transition in-between ka and kp. The duration of the transition is dependent on the contact angle hi as shown in Fig. 8(e). When collisions as shown in Fig. 5(b)\u2013(d) occur, a crispy force corresponding to a solid collision is output. This force indicates that the contact is invalid, and the stylus must be repositioned to select a surface point so that only the stylus tip is in contact with an object. The above mechanics model provides a kind of fidelity as if the user is operating on a real CMM. Measuring points are selected according to the tolerance type and its requirement and the shape and size of the part. Taking the measurement of the parallelism between planes A and B of a flange shown in Fig"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001277_s0997-7538(00)00139-x-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001277_s0997-7538(00)00139-x-Figure2-1.png",
+        "caption": "Figure 2. Fluid-film linear model.",
+        "texts": [
+            " (20) The dimensionless dynamic transmissibility, which compares the hydrodynamic force generated during nonlinear transient motion to the force due solely to unbalance, is important in the kind of this investigation. In equation form this is written as FD = \u221a F 2 x + F 2 y Meb\u03c92 . (21) Under the assumption of small displacements of the journal centre, the fluid-film force components in the vertical and horizontal directions, Fx and Fy , may be linearized around the static equilibrium position Oj0 (figure 2) to obtain: { Fx = Fx0 + axxx + axyy + bxxx\u0307 + bxyy\u0307, Fy = Fy0 + ayxx + ayyy + byxx\u0307 + byyy\u0307, (22) where Fx0 and Fy0 are the fluid-film force components under the static conditions, and aij and bij the stiffness and damping coefficients expressed as: aij =\u2212 ( \u2202Fi \u2202xj ) Oj0 , bij =\u2212 ( \u2202Fi \u2202x\u0307j ) Oj0 , (i, j)= (x, y). (23) At the threshold of instability (Lund, 1986), the dimensionless critical mass Mc and the corresponding whirl frequency ratio \u03b3c are expressed as: Mc = As \u03b3 2 c , (24) \u03b3 2 c = ( \u03bdc \u03c9 )2 = (Axx \u2212As)(Ayy \u2212As)AxyAyx BxxByy \u2212BxyByx , (25) where: As = AxxByy +AyyBxx \u2212AxyByx \u2212AyxBxy Bxx +Byy , Aij = aij C W0 , Bij = bij C\u03c9 W0 , (i, j)= (x, y) and Mc = McC\u03c9 2 W0 "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002874_j.aca.2005.02.040-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002874_j.aca.2005.02.040-Figure2-1.png",
+        "caption": "Fig. 2. The structures of hydrochlorothiazide (a) and furosemide (b).",
+        "texts": [
+            " In athletic sports, because diuretic could increase urine flow, some athletes utilize it to achieve two aims shown as blow: one is diluting the urine to conceal the other doping agents; another is reducing the body weight at short notice to participate in the lower weight category. Since 1988, diuretic has been banned by the Medical Commission of the International Olympic Committee [7,8]. Hydrochlorothiazide (6-chloro-3,4-dihydro-2H-1,2,4-benzothiadiazine-7-sulphonamide-1,1-dioxide) and furosemide (5-(aminosulfonyl)-4-chloro-2-[(2-furanyl-methyl)amino]benzoic acid) are two representative diuretics, and their structures are shown in Fig. 2. Some methods based on various analytical techniques have been reported for the determination of the two diuretics, such as coulometric titration [9], electrochemical detection [10,11], spectrophotometry [12\u201315], fluorescent detection [16], electrogener- 003-2670/$ \u2013 see front matter \u00a9 2005 Elsevier B.V. All rights reserved. oi:10.1016/j.aca.2005.02.040 ated chemiluminescence detection [17] and chemiluminescence detection [8,18]. In this paper, it was found that both hydrochlorothiazide and furosemide could enhance the chemiluminescence emission intensity of RuBPS\u2013Ce(IV) system"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure4.28-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure4.28-1.png",
+        "caption": "Figure 4.28. The gear train geometry.",
+        "texts": [
+            " However, since the reference frames are fixed in the ge:ars, their material points have no motion relative to these frames. Hence, the basic equations (4.46) and (4.48) reduce for each gear to the rigid body formulas (2.27) and (2.30) referred to frames whose angular velocities in the machine frame are ID 10 , ID 20 , and ro 30 , as noted before. Thus, for the point Ron the fixed gear A, the contact point at R on C must satisfy V R = V c + ID20 X r = 0, (4.85b) in which r is the position vector of R from C, as shown in Fig. 4.28. Of course, point C belongs also to the extension of the power gear B for which v B = 0; hence, with r = -q, as shown, we find with ( 4.85b) the absolute velocity of point C: Vc = ro 20 X Q = ro 10 X b, (4.85c) 292 Chapter 4 in which q is the position vector of Q from C and b is the position vector of C from B. Use of (4.85a) in (4.85c) yields (1)21 X q = ro 10 X (b- q). (4.85d) Using the geometry of Fig. 4.28 and the rule (4.84), we find from (4.85d) the relative angular velocity component W 21 = -w[sin 8 + (b/q) sin (r/J + 8)] = -w(sin 8 +cot r/J cos 8). But the last term may be written as the ratio cos(\u00a2>- 8)/sin \u00a2>; hence, with the use of ( 4.84 ), the angular velocity of the epicyclic gear C relative to the power gear B may be expressed as . sin 38. ro21 = w2Ilz = -w cos 281z. (4.85e) Part (b). The total angular velocity of the epicyclic gear in the machine frame may be derived by substitution of (4",
+            "85e), we obtain the angular acceleration of the epicyclic gear in the machine frame, but referred to the power gear frame 1: \u2022 2 sin 38 cos 8 . Olzo = -w cos 28 \u20223\u00b7 (4.86b) Motion Referred to a Moving Reference Frame and Relative Motion 293 The reader also may confirm this result by differentiation of ( 4.86a ). Part (c). It remains to determine the angular velocity of the output gear D. Since the rolling contact point Q belongs to both C and D, and v D = 0, we have V Q = (!) 30 X X = V C + (!) 20 X q, (4.87a) wherein x is the position vector of Q from D, as shown in Fig. 4.28. Therefore, use of (4.85c) in (4.87a) yields ID 30 X X= 2ID20 X q = 2ID 10 X b. (4.87b) Q = 2w(b/d) sin(Q? +e). (4.87c) Further, with the aid of the rule ( 4.84) and the triangle relations b/c =cot tP and c/sin tP = djsin e, it follows from ( 4.87c) that the angular speed of the out put gear Dis Q = 4w cos2 e. (4.87d) This completes the solution of the problem. It may be seen from ( 4.84) that 0 < e < n/4. It thus follows from ( 4.87d) that the ratio of the output angular speed to the input angular speed decreases with increasing e so that QjwE (4, 2); and according to (4"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002410_1475921703036049-Figure7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002410_1475921703036049-Figure7-1.png",
+        "caption": "Figure 7 The AMRL gear test rig.",
+        "texts": [
+            " It is worthwhile to notice that, in cases where the structural resonant frequency is not significantly separated from the major meshing harmonics (usually the 1st and 2nd meshing harmonics), the CWT could be less effective in detecting localized changes. at NIPISSING UNIVERSITY LIBRARY on October 6, 2014shm.sagepub.comDownloaded from In this section, we present the analysis results using existing data collected in a tooth-crack propagation test [29]. The test procedures were designed to simulate the natural development of gear tooth cracking. The test rig is shown in Figure 7. The test gear was the input pinion manufactured under AGMA Class 13 standard (aircraft quality). It had 27 teeth; a tooth width of 10mm, a rated power of 24.5 kW and it was operated at a constant shaft speed of 40Hz. The gear was spark-eroded at the root fillet of a tooth, across the middle of the tooth width. The eroded notch (length width depth\u00bc 2 0.1 1 mm) was designed to simulate the crack initiation. Figure 8(a) shows the SA acquired at 164% rated load and 5-h 36.8-min into a total of 8-h test, where we can easily see the dominance of gear meshing harmonics and the amplitude modulation waveform with a period of about two cycles per revolution (2nd shaft order)"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure3.12-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure3.12-1.png",
+        "caption": "Figure 3.12. Schematic for Chasles' screw displacement theorem.",
+        "texts": [
+            " Let the displacement of a base point 0 and the Euler rotation of the rigid body be assigned; then the general displacement of any particle P at x from 0 is provided by (3.134a). We wish to prove that there exists a base point 0*, say, whose displacement b* is parallel to the axis of the Euler 198 Chapter 3 rotation; hence, with 0* as the base point, the result follows. Therefore, we shall need to determine the new parallel translation b* and the location r of 0* from 0. We may always write b = b\" + ba in terms of the component vectors b\" and ba normal and parallel, respectively, to the axis of rotation, as shown in Fig. 3.12. Hence, (3.134a) may be written d(P) = ba + [b\" + Tx(P) ]. (3.140) However, in accordance with the parallel axis theorem, the displacement terms consisting of a rotation about a line and a translation perpendicular to the line is equivalent to a pure rotation about a parallel axis through a base point at 0*, say. Thus, the term in the brackets in (3.140) may be replaced by the pure Euler rotation Tx*(P) to yield d(P) = b, + Tx*(P) ( 3.141 a) with bn= -Tr, (3.14lb) where r = x- x* is the position vector of 0* from 0, as shown in Fig. 3.12. But (3.141a) states that the assigned displacement d(P) is equal to the same Euler rotation about an axis at 0* and a new translation b* = b, parallel to that axis, and Chasles' theorem follows. This displacement (3.141) is recognized as a typical screw displacement, from which the theorem derives its name. The axis of the Euler rotation at 0* is called the screw axis.* The pitch of the screw, defined by p = (b \u00b7a )/8, is identified as the ratio of the screw translational displacement to the angle of rotation"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002489_j.talanta.2004.06.048-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002489_j.talanta.2004.06.048-Figure4-1.png",
+        "caption": "Fig. 4. Cyclic voltammograms of platinum electrodes (\u00d8 = 5 mm): (a) bare, (b) modified with copolymer poly(pyrrole\u2013biotin, pyrrrolelactitobionamide), (c) modified with biotinylated polypyrrole in the presence of 1 mM catechol, 0.1 M LiClO4 in water (pH 7). Polymer films were electrodeposited by controlled potential electrolysis at 0.8 V (charge: 1 mC). Scan rate at 100 mV s\u22121.",
+        "texts": [
+            " In order to imobilize CT on the electrode surfaces by affinity interactions ia the formation of avidin\u2013biotin bridges, a novel biotinyated copolymer (poly(pyrrole\u2013biotin), poly(pyrrole lactoionamide)) was used as the initial anchoring layer. This ew polymerized film was designed to improve the transuction sensitivity of the enzymatic reactions based on the mperometric detection of the enzyme products at the unerlying electrode surface. Catechol was used as an elecrochemical probe to illustrate the difference of permeabilty between the biotinylated copolymer and the previously sed poly(pyrrole\u2013biotin). Fig. 4 shows a series of cyclic oltammograms collected at 100 mV s\u22121 for a bare electrode, poly(pyrrole\u2013biotin) and a copolymer modified electrodes. For the poly(pyrrole\u2013biotin) electrode, the electrochemial activity of the redox probe was markedly blocked by the resence of the polymer film. As expected, the oxidation peak ecreased drastically while the peak separation increased inicating the low permeability of poly(pyrrole\u2013biotin) film. n contrast, the copolymer appeared much more permeable ince the catechol electroactivity remained almost identical"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002056_s0379-6779(00)00450-1-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002056_s0379-6779(00)00450-1-Figure3-1.png",
+        "caption": "Fig. 3. Dependence of first oxidation peak current of PAN/PAn composite on sulfuric acid concentration.",
+        "texts": [],
+        "surrounding_texts": [
+            "Electrochemical polymerization was carried out in a simple cell chamber of 200 ml capacity using a threeelectrode system, i.e. a disc-type Pt working electrode (diameter, 1 cm) coated with 2.0 mm thick PAN \u00aelm, a plate-type Pt counter electrode (1 cm 1 cm), and an aqueous sodium chloride saturated calomel electrode (SSCE) as the reference electrode.The electrolyte solution consists of 0.1 M aniline and 0.1 M sulfuric acid in 50:50 (volume ratio) mixture of acetonitrile and water. The potential range for electrochemical polymerization and scanning rate are \u00ff0.2 to 1.0 V (versus SSCE) and 50 mV/s, respectively. Unless otherwise stated all data are for above-mentioned experimental conditions. The details of the experimental technique are reported in an earlier paper [16]."
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0002434_0022-4898(91)90017-z-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002434_0022-4898(91)90017-z-Figure4-1.png",
+        "caption": "FIG. 4. Forces acting on the wheel system.",
+        "texts": [
+            " Measured quantities and sensors (1) Resultant soil reaction. The resultant soil reaction and its line of action were calculated according to the following equations. The value of the contact load was corrected by subtracting the small vertical force due to the bearing friction detected by a pair of L-shaped sensors [7] in the right and left sides from the net weight of the wheel system. The magnitude F and the direction 0 of the resultant soil reaction F, and the minimum distance R from the center of the wheel to F (see Fig. 4) were 362 Y. NOHSE et al. calculated f rom the moments of the L-shaped sensors using the equations: f = V ' { ( M 2 - M1)/ l l} 2 + {(M3 - M4)//14 + W} 2 (1) 0 = COS -1 {M2 - M1)/(Fl l )} (2) R = {M1 + W ( l + l 3 + 14)}/{F - Lcos (o l - 0)} (3) where W is the net weight of the wheel system, M1, M2, M3, M4 are the moments measured by the strain gauges 1, 2, 3, and 4, respectively in the L-shaped sensors, I 1, 12, 13, 14, are the distances between the gauges and l is the horizontal distance between the position of gauge 4 and the center of gravity of the net weight of the wheel system"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002517_1.1515324-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002517_1.1515324-Figure1-1.png",
+        "caption": "Fig. 1 Biped walking mechanism",
+        "texts": [
+            " In order to compare with the human walking locomotion, human body parameters are adopted to calculate the optimal trajectory solution, and the influence of the upper body mass on a walking locomotion is discussed. Finally, in Section 4, we summarize the main results of this study. 2.1 Model of a Biped Mechanism and Walking Locomotion. As the first step to solving minimum input walking trajec- rom: http://dynamicsystems.asmedigitalcollection.asme.org/ on 01/28/201 tory by the optimal trajectory planning method, we deal with a planar biped walking mechanism which has thighs, shanks and small feet as shown in Fig. 1. We disregard the upper body because it has little effect on walking locomotion. It will be confirmed in Section 3.7. Thus, two legs are assumed to be directly connected to each other through an actuator. We assume that both knee and ankle joints can be driven by individual actuators, and the knee joint of the stance leg is passively locked by means of a stopper mechanism or an actuator to prevent the mechanism from collapsing. The ankle of the stance leg is modeled as a rotating joint fixed to the ground, while the foot of the swing leg is neglected",
+            "325 m and 0.35 m are similar to the pattern with the step length of 0.3 m as shown in Fig. 7b . Figure 21 shows the step periods t11t2 and the average speeds V\u0304 of the optimal solutions for the step length values of 0.25 ;0.35 m. We note that the period and the step length increases gently with an increase in the step length. 3.6 Forward Dynamic Simulation. One of our aims in this study is to obtain the optimal feed forward control torque at all joints for the biped walking mechanism as shown in Fig. 1 by the optimal trajectory planning method. Therefore, there remains a question whether the same motion as the trajectory solution can be generated by using the solved joint input torque. Particularly when u150, u1 shows a large undulation in Figs. 11b \u2013 d although the constraint Eq. ~21! is satisfied. It needs to be confirmed whether the same motion as Fig. 10 can be obtained by forward dynamic simulation if we put u150 and use the solutions of u2 and u3 as shown in Fig. 11. We first simulated the walking motion for the full-actuated system by using the solutions of u1 , u2 , and u3 as shown in Figs"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002129_09500830210128074-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002129_09500830210128074-Figure2-1.png",
+        "caption": "Figure 2. Applying a magnetic \u00aeeld to an ordered ferro\u00afuid foam can result in a change in the structure. (a) The transition from 2\u00b11\u00b11 to 2\u00b12\u00b10 was induced by a local oscillating magnetic \u00aeeld gradient (frequency, 2 Hz; strength, 450 G mm 1). The bubbles (diameter, 6.2 mm) move upwards in the tube at a rate of 30 bubbles per minute. (b) The same oscillating \u00aeeld gradient resulted in a transition from 2\u00b11\u00b11 to bamboo. Here the bubbles (diameter, 6.2 mm) move upwards at a rate of 20 bubbles per minute. Such structural transitions can also be induced using a static permanent magnet.",
+        "texts": [],
+        "surrounding_texts": [
+            "The most primitive structure is a regular train of \u00afat \u00aelms: this is the bamboo or 1\u00b11\u00b10 structure (\u00aegure 1). Apart from this case the structures belong to a sequence of spiral arrangements with only hexagonal cells at the surface. They are indexed with the standard notation of phyllotaxis (Jean 1994), as in the nomenclature of carbon nanotubes. Examples are the structures 2\u00b11\u00b11, 2\u00b12\u00b10 and 4\u00b12\u00b12, as shown in \u00aegure 1.\nThe imposition of a local magnetic \u00aeeld by means of a small permanent magnet dramatically a\u0152ects these moving structures. The \u00aeeld can, for example, induce transitions from one structure to another or twist them through 90 or 180\u00b0. Some of these e\u0152ects are shown in \u00aegures 2 and 3 (and in digital video clips of cylindrical ferro\u00afuid foams, available at the present authors\u2019 websitey). The bubbles are very robust; we do not observe rupture of the \u00aelms that separate them, even during rapid changes of the kind shown here.\nThis use of a magnetic \u00aeeld provides precise local control over structural changes which have in the past been promoted by forced drainage (Hutzler et al. 1997, Boltenhagen and Pittet 1998) or mechanical compression\u00b1dilation (Boltenhagen et al. 1998), applied to the whole system. Moreover we have observed that the size of generated bubbles, of crucial importance in determining the cylindrical structure, may also be adjusted by a magnetic \u00aeeld.\nThe action of the magnetic \u00aeeld appears to be based on two e\u0152ects, both arising from the attraction of ferro\u00afuid to the region of maximum \u00aeeld. Firstly, the foam develops a higher liquid fraction, which is enough in itself to provoke a morphological change (Hutzler et al. 1997, Boltenhagen and Pittet 1998). Secondly, since most \u00afuid resides in the Plateau borders (the channels which are formed between bubbles in a foam of low liquid fraction), the borders are pulled towards the region of high \u00aeeld, resulting in a net torque. Together these two mechanisms o\u0152er many possibilities for propulsion and control of the bubble stream.\nThe present con\u00aeguration is vertical, but it should be possible to generate and propagate structures horizontally, again using magnetic \u00aeelds to control the liquid\ny http://www.tcd.ie/Physics/Foams/ferro.html",
+            "fraction. One may envisage networks of channels through which bubbles travel in bamboo and 2\u00b11\u00b11 structures, separating, coming together or being selectively switched at junctions by application of local magnetic \u00aeelds. Such a scenario may have implications for micro\u00afuidics, a technology of great current interest. The present technique would have considerable advantages in its ability to maintain and process localized samples by simple variations of magnetic \u00aeelds. Moreover, identical properties should be available with emulsion systems, that is a liquid\u00b1liquid foam. In either case a small sample injected into a channel as one of the bubbles will not be smeared out by Poiseuille \u00afow, which is otherwise a serious problem in micro\u00afuidics (Whitesides and Stroock 2001).\nAs an example of the kind of operation that is clearly possible at this stage see \u00aegure 4. For suitable dimensions a 2\u00b11\u00b11 stream of bubbles splits into two bamboo sequences at a bifurcation. The introduction of a twist induced by a magnetic \u00aeeld interchanges the two streams, as indicated.\nFluidic networks based on the above techniques could \u00aend applications in the area of biotechnology, where one could \u00aell individual gas bubbles (or droplets in a ferro\u00afuidic emulsion) with di\u0152erent samples or compositions. The bubbles could then be transported to their destination as part of a moving cylindrical foam structure, to be monitored by spectroscopic methods or combined with reagents by the rupturing of the thin \u00aelms that separate bubbles. The possibilities of elaboration of this methodology seem rich indeed.\nThanks are due to Jean-Claude Bacri and to Nicolas Rivier for stimulating discussions and Valerie Cabuil for providing the ferro\u00afuid.\nBacri, J.-C., Perzynski, R., Salin, D., Cabuil V., and Massart, R., 1989, J. Colloid Interface Sci., 132, 43. Boltenhagen, P., and Pittet, N., 1998, Europhys. Lett., 41, 571. Boltenhagen, P., Pittet, N., and Rivier, N., 1998, Europhys. Lett., 43, 690. Elias, F., Flament, C., Bacri, J.-C., Cardioso, O., and Graner, F., 1997, Phys. Rev. E, 56, 3310. Harris, W. F., 1970, Phil. Mag., 22, 949."
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0001338_0094-114x(95)00082-a-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001338_0094-114x(95)00082-a-Figure6-1.png",
+        "caption": "Fig. 6. Tip interference for elliptical cam.",
+        "texts": [
+            " the wave generator) the basic approach is that the original pitch circle of the pinion is deformed, to give the double contacts, such that the distance between the pitch points at two contacts becomes equal to the summation of pitch circle diameter of the pinion and double the center distance. Or in other words it is equal to the pitch circle diameter of the ring gear. This means that the pitch curve of pinion is a profile which has constant-difference (i.e. point to point parallel shift) to the cam ellipse. The amount of shift (a,m, see Fig. 6) depends upon the required rim thickness and the type of bearing used. MMT31/4--I 484 R. Maiti and A. K. Roy Figure 6 illustrates the condition when tip interference just exists in the case of an elliptically deformed pinion. Tip interference is avoided if the tip of the pinion tooth, which is now in contact, does not reach at T before the corresponding gear tooth tip. Or in other words, the tip interference is avoided if 0p > ?, (31) where 0p and 7 are derived as follows: Referring to Fig. 6, let the line MP be on the radius (of curvature) vector of the inner ellipse of the rim at point P of co-ordinate (x~, y~) and T on the extension of MP. Now the co-ordinate (xc, x\u00a2) of the center of curvature can be expressed as [8]: /a a - b2\\ \"1 w ) /b 2 _ a2\\ (32) where a is the semi-major axis and b is the semi-minor axis of the elliptical cam profile. The co-ordinate of the point M (x2, Y2) is expressed as: y =0 ; _ x151 x2 x~ + (Y2-Y~)/x~ (33) \\Yc - - Y l , / J Angle ~b is given by: ~b = tan-~( y2- YJ~",
+            " (35) (36) Now to calculate the angle 0p at the critical condition of tip interference r 2 must be equal to rag, i.e. O1 T (= r) must be expressed as: r = N/(x2 + rlx - A)2 ..1_ r21y. (37) The angles 0p and 08 are then calculated as: Op= cos -1 ra~ 2~r + fp (38) 0g -- cos -1 r,g + - & - fig. (39) 2Ar Now, if the internal gear is given a rotation of angle 0g the corresponding rotation of the circular pinion would have been (ZJZp)Og. The corresponding rotation ? of the elliptical pinion can be obtained from the condition that the arc length of the circle with radius equal to (a - A) and center at Oi (see Fig. 6) over the angle (Zs/Zp)Og is equal to the length of the arc on the elliptical cam Minimum tooth difference 485 from the common starting point on the cam. If the final co-ordinate on the contour of the ellipse after the rotation is (x, y), then: ~, = t a n - ' ( x _ - - ~ ) + tip. (40) Numerical calculations using the above formulae show that with rim deflection the tooth difference can be lowered to 2 avoiding tooth interference, without tooth truncation for any practical number of gear teeth for all standard pressure angles"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000569_s0045-7949(98)00004-2-Figure7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000569_s0045-7949(98)00004-2-Figure7-1.png",
+        "caption": "Fig. 7. The deformation of an in\u00aenitesimal tetrahedron: (a) Lagrangian description and (b) Eulerian description.",
+        "texts": [
+            " If one does not know that [R] = [T]T in Equation (38), an iteration method can be used to obtain the six unknowns g42, g43, g51, g53, g61 and g62 that locate the system x1x2x3, as shown in Appendix A. This iteration method may not be more e cient than the direct method shown in Equations (52)\u00b1(54), but it reveals the geometric im- plication of polar decomposition and the identity [R] = [T]T. To derive the relationship of di erent stress measures, we consider an undeformed area dA with a unit outward normal N(=Nkjk) and its deformed area da with a unit outward normal n(=nkjk), as shown in Fig. 7(a). Because F= dV/dV0, dV0=dAN dx = dANk dxk, and dV= dan dy= danm dym=danmFmk dxk, we obtain F dANk danmFmk 57 It follows from Equation (3) and Fig. 7(a) that f f 1 f 2 f 3 dAN1j1 s\u03021sj1js dAN2j2 s\u03022sj2js dAN3j3 s\u03023sj3js dANrs\u0302rsjs 58a Second Piola\u00b1Kirchho stresses are measured with respect to the rigidly rotated undeformed area dANkik. Moreover, it follows from Fig. 1 that dx1j1 is deformed into l1 dx1i1\u00c3 and hence l1i1\u00c3 =Fs1js. Consequently, it follows from Equation (11) and Fig. 7(a) that f dAN1i1 S1klki1ik\u0302 dAN2i2 S2klki2ik\u0302 dAN3i3 S3klki3ik\u0302 dANrSrklkik\u0302 dANrSrkFskjs 58b Because Jaumann strains are measured with respect to the rigidly rotated undeformed area dANkik, it follows from Equation (20) and Fig. 7(a) that f dANrir J\u0302rkirik dANrJ\u0302rkik dANrJ\u0302rkTksjs 58c Next we consider the same undeformed and deformed areas as those in Fig. 7(a) but described in terms of Euler coordinates, as shown in Fig. 7(b). It follows from Equation (23) and Fig. 7(b) that f ~f 1 ~f 2 ~f 3 danrjr trsjrjs danrtrsjs 59 It follows from Equations (57), (58a)\u00b1(c) and (59) that s\u0302 S F T J\u0302 T , t 1 F F s\u0302 60 Using Equations (3), (8), (20), (42a) and (60), we obtain the following relationships: S s\u0302 F \u00ffT F F \u00ff1 t F \u00ffT, J\u0302 s\u0302 T T S U , J 1 2 J\u0302 J\u0302 T 1 2 S U U S , s 1 2 s\u0302 s\u0302 T 61 These relationships are the same as those obtained in Atluri [1]. However, the presented derivations clearly show the directions of di erent stresses. For highly \u00afexible structures undergoing large displacements and rotations but small strains, Jaumann strain measure is the most appropriate one for use because Jaumann strains are shown to be objective geometric measures de\u00aened with respect to the rigidly rotated undeformed area"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001244_rspa.1998.0297-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001244_rspa.1998.0297-Figure2-1.png",
+        "caption": "Figure 2. Solutions of the dispersion relation for \u03c32 as a function of n with increasing values of \u03b3S = 0.2267, 0.2675, 0.2687, 0.2695. \u0393 = 3 4 , \u03c6 = 1 10 , N = 5.",
+        "texts": [
+            " (a) Linear analysis The fundamental mode solutions to the variational equations (2.18 a) are of the form \u00b5(1) n = \u03bene\u03c3nt+i\u03b4(ns/N), (5.2) where \u03ben \u2208 C6 and n denotes the mode number which, due to the choice of boundary conditions, is an integer between 1 and N . The explicit form of the linear operator LE as a function of the curvature, torsion, twist and tension is given in Goriely & Tabor (1997c) and from this the dispersion relations, \u2206(\u03c3, n; \u03b3H) = 0, can be obtained in the usual way. A typical plot of them is shown in figure 2 for increasing values of \u03b3H. The neutral curve is determined from \u2206(0, n; \u03b3H) = 0, where \u2206(0, n; \u03b3H) = (\u0393 \u2212 1)(\u0393 \u2212 2)\u03c42 F + 2\u0393 (\u0393 \u2212 2)\u03b3H\u03c4F + \u0393 2\u03b32 H + \u03b42(1\u2212 n2/N2). (5.3) For given n, one can then read off the value of \u03b3H at which the instability occurs. In general, different modes of n can become unstable; however, within the family of helices parametrized by \u03b3S, the mode n = 1 is always the first unstable mode as the control parameter is increased. It is this case that corresponds to our \u2018secondary\u2019 bifurcation"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003477_cnm.913-Figure19-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003477_cnm.913-Figure19-1.png",
+        "caption": "Figure 19. Factors of the symmetric system of Example 3: (a) subspace V (1)\u2014factor ECC ; (b) subspaces V (2) and V (3)\u2014factors DCC and DDD ; (c) subspace V (4)\u2014factor EDD ; and (d) subspaces V (51) and V (52)\u2014factors DC and CD .",
+        "texts": [
+            "1002/cnm form II stiffness and mass matrices, the blocks of which are in symmetry form II in turn. K= \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a3 A1 B1 A2 B2 B1 A1 B2 A2 A2 B2 A1 B1 B2 A2 B1 A1 \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a6 8\u00d78 3 4 8 7 1 2 6 5 k1 k1 k1 k1k2 k2 k3 k3 k2 k2 k6 k6 A system with 16 DOFs is studied. Figure 18 shows this system and its graph model. In this model, we have m1 =m2 =m5 =m6 =m9 =m10 =m13 =m14 =m, m3 =m7 =m11 =m15 =m\u2032 and m4 =m8 =m12 =m14 =m\u2032\u2032 Symmetry operations of this graph comprise of the symmetry group C4v . The factors of this structure are shown in Figure 19. It can be observed that the factors resulted by both group-theoretical and algebraic method, are identical. Considering the factor of the subspace V (51) and its graph model, as shown in Figure 19(d), it can be seen that this factor has a vertical plan of symmetry, which suggests the point group C1v . In the other words, this factor is of canonical form III symmetry and can be further decomposed. The result of decomposition of this factor is shown in Figure 20. Copyright q 2006 John Wiley & Sons, Ltd. Commun. Numer. Meth. Engng 2007; 23:639\u2013664 DOI: 10.1002/cnm As it is seen, factors DDC and DCD are exactly the same as factors DCC and DDD , shown in Figure 19(b), and do not have to be solved. Thus, instead of solving a problem with 16 DOFs only a number of small problems are being solved: a one-dimensional problem and three problems of dimension three. This can some how highlight the efficiency of the proposed method. The procedure introduced in this paper consists of forming the graph model of a mass\u2013spring system, recognizing the symmetry operators and symmetry group of the graph, selecting the positional functions of the nodes of the graph as the basis vectors of the vector space of the problem"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003438_j.talanta.2005.01.036-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003438_j.talanta.2005.01.036-Figure2-1.png",
+        "caption": "Fig. 2. Schematic representation of the thin-layer radial flow microsensor: glass-based screen-sputtered Au ring-disk electrode (left), plastic cover with micro-flow injection system and conventional electrodes (right).",
+        "texts": [
+            " PBS was used both as solvent for preparing lucose and H2O2 stock solutions and as background olution for electrochemical analytical measurement. The queous solutions of GOx, HRP and AOx in 2 units l\u22121 ere prepared using doubly distilled water. The aqueous olution of 2 mM K3Fe(CN)6 and 0.1 M KNO3 served or cyclic voltammetric investigation. Ruthenium complex u3( 3-O)(AcO)6(Py)3(ClO4) (Ru-Py) was used as received rom other research group. .2. Fabrication of microsensor A thin-layer radial flow ring-disk microsensor (Fig. 2), onsisting of the glass base and the plastic cover, was deigned for the conventional three-electrode electrochemcal analysis. A screen-printed Au ring-disk electrode disk \u03c6 = 3 mm, S= 7.06 mm2; ring inner \u03c6 = 4 mm, ring idth=1 mm, S= 15.7 mm2) was applied as base. The disk part was coated with ascorbate oxidase in order to pre-oxidize the ascorbic acid. The ring part was modified by GOx and the mediator as the working electrode. On the cover, there were the micro cell (about 10 l with the suitable diameter to the ring-disk electrode), a Ag/AgCl wire (0"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002646_acc.1991.4791487-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002646_acc.1991.4791487-Figure2-1.png",
+        "caption": "Fig. 2. Advaned Technology Wing wind-usnl model.",
+        "texts": [
+            " Aerodynamic cotwl is provide by fourconrl surfces on ech Wing: leading edge outod (LO), ledig edge inbord (L), trailing edge outboard (TO), and tailing edg ibord T) surfaces. Loading on the Wing exists in re fm: tosion momnt, bending m t, d hinge moment in this paper we consider only control of the torsion m ts The n mo s are meaured by strin gauge at the wing midpan and root, which correspond to the ouboad torsion manent and the inboard torsion moment, respeively. A diagram of the ATW identifying the cotrl swfm and tors moment locations is shown in Figure 2. The task of the roll controller is to detamine the a iat control swrfc tions hat will ahieve a comanded rol rait as well as satfy pre bed torsion ent constaints. Aldtough te are eight control sfaces availk on te ATW, the contributio to the roll maneuver from the left and right laing edge ibxd surfacs is negligible. hIerefore, for our purpose they are excluded as usable actaos. In what follows, we will use t symbio to denote srface deflection and\u00b6 to&nc*e torsion mn e.. Subsc sland t denot leading and tiling edge; sipts i and o denote inboard and outboard; and subscripts r and I denote right and left"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000979_1.2802427-Figure7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000979_1.2802427-Figure7-1.png",
+        "caption": "Fig. 7 Mechanism for measuring inertia tensor of large mechanical systems",
+        "texts": [
+            " Journal of Dynamic Systems, Measurement, and Control MARCH 1999, Vol. 121 / 115 Downloaded From: http://dynamicsystems.asmedigitalcollection.asme.org/ on 05/17/2015 Terms of Use: http://asme.org/terms hence CTI and errors increased. As in the first test, the dimensions of the inertia ellipsoid were identified with good accuracy. Table 3 compares the accuracy of the proposed method with those of other methods (Conti and Bretl, 1989; Pandit and Hu, 1994) and shows lower errors for the proposed method. The second mechanism is shown in Fig. 7. It was developed with the aim of measuring the inertia tensor of large mechanical systems (mass range: 50-200 kg, maximum dimension about 2 m), like the equipment installed in satellites. The inertia tensors of several pieces of equipment were identi fied with good accuracy, because the ratio between residual root mean square a^ and the smaller principal moment of inertia was about 2.5 percent. 7 Conclusions The proposed method for identifying of the inertia tensor of rigid bodies is quite fast, because it requires only one accurate positioning of the specimen and allows the inertia tensor of large bodies to be determined"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002310_1.2831616-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002310_1.2831616-Figure4-1.png",
+        "caption": "Fig. 4 Procedure of experiment, (a) Free; (b) liquid bridge; (c) return to initial position by elastic stage 2; (d) the offset force, Foi (e) generation of lubrication film by sliding.",
+        "texts": [
+            " 3, but the output can be approximated by a straight line which passes through the origin of the coordinate axes. The change of load caused by the inclination during the sliding is less than 2 /uN. Journal of Tribology OCTOBER 1996, Vol. 1 1 8 / 8 3 3 Downloaded From: http://tribology.asmedigitalcollection.asme.org/ on 02/21/2018 Terms of Use: http://www.asme.org/about-asme/terms-of-use I / / It I Fo (a) Free (d) The Offset Force, Fo Next, the balance of forces is considered carefully. After ensuring parallelism, the two mica surfaces are separated by a small distance (Fig. 4(a)) and a small amount (0.1 ~0.2 cc) of OMCTS is carefully dropped between the mica surfaces by a syringe. The mica surfaces approach each other by an attractive meniscus force (Fig. 4(b)) . The mica surface supported by the double cantilever spring is moved to an initial position in order to remove the deflection of the double cantilever spring using the elastic stage 2 (Fig. 4(c) ) . Under this condition, two sur faces are attracted to each other by the meniscus force, F\u201e, and the van der Waals force, F\u0302 ^w and repulsed by the compressive Hertz pressure. Then a pulling force, Fo is applied by using the double cantilever spring (Fig. 4(d)) in order to cancel F\u201e be cause Fm is very large compared with F^^w Note that Fo must be smaller than F,\u201e in order to avoid the surface separation. When the surfaces are slid by the elastic stage 1, the two sur faces separate from each other with film thickness h because fluid force is generated between the surfaces (Fig. 4(e)) . The fluid force is generated by the wedge effect (Cameron, 1966) between mica surfaces and this force is the predominant one in a lubricating film where the lubricant film thickness is relatively large, e.g., larger than 10 nm. The counterbalance of forces is written as: F - F^ciw + Fm - (Fo - Fj) (1) where F is the fluid force and FQ \u2014 F, is pulling force applied by the double cantilever spring and F, = k^h, where h is the minimum film thickness. An example of film thickness measurement (output data from the displacement sensor during sliding) is shown in Fig"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002968_j.conengprac.2003.12.013-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002968_j.conengprac.2003.12.013-Figure2-1.png",
+        "caption": "Fig. 2. Simplified launcher representation.",
+        "texts": [
+            " * Control the destabilizing bending modes: the aim is to attenuate these modes under a gain limit (XdBo0) except for the first one which can be controlled in phase with a sufficient delay margin (at least one sample period Ts). * Time domain specifications: * Limit the angle of attack i in case of wind disturbance (a typical wind profile will be given in Fig. 12). * Limit the angle of deflection b and its velocity \u2019b: * The consumption C must be limited to Cmax where C \u00bc XTend k\u00bcTinit b\u00f0k \u00fe 1\u00de b\u00f0k\u00dej j: \u00f01\u00de * Robustness * All these objectives have to be robust against uncertainties (which affect rigid and bending modes). A simplified launcher scheme is given in Fig. 2 where the angle of attack between the launcher axis and the relative speed VR is noted i; the attitude c; the angle of deflection b (control input) and the wind velocity W (disturbance). The ARTICLE IN PRESS B. Clement et al. / Control Engineering Practice 13 (2005) 333\u2013347 335 sensors allow measuring the attitude and its velocity whereas the actuators allow controlling the angle of deflection for the thrusters. The challenge of such a control issue is to minimize the angle of attack i which in addition cannot be measured"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001047_iros.1994.407656-Figure8-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001047_iros.1994.407656-Figure8-1.png",
+        "caption": "Figure 8. Orientation of Group Pattern",
+        "texts": [
+            " The limitation of this algorithm is that it cannot be used in cases when some requirement on the goal orientation has to be met. 3.3.2 Object's Orientation Changes as Specified In many object transportation tasks, not only the goal location is specified but also its orientation. We propose the following algorithm to coordinate the motion of the followers in order to meet this performance requirement. To describe the position and orientation of the group pattern, we assume that there is a local coordinate system attached to the group leader as shown in Figure 8. The orientation of the group pattern can then be described by %t) as shown in Figure 8. In Figure 8, we let the origin of the local coordinate system be at the center of the leader. Suppose that the sensory and communication devices on each follower allow the follower to determine the leader's location and its own location with respect to the world coordinate system. After the robots have formed a specified pattern, each robot computes its relative position with respect to the leader, which is equivalent to its location in the local coordinate system. Let (a(i),b(i)) represent the location of the i-th follower in the local coordinate system as shown in Figure 8, where i = 1, 2, ..., N. In order to maintain the group pattern, each follower should remain steady with respect to the local coordinate system as the group moves. 3.3.1 Object's Orientation Remains Unchanged Upon receiving (v(t)$(t)), which is the leader's speed This \"leader following\" strategy requires minimum computation to be conducted by each follower. In applying this method, the followers move at a same speed and direction with the leader at all the times. Upon receiving the leader's broadcast information (v(t)$(t)), each follower calculates its desirable position at t+At as: xi(t+At) = xi(t) + v(t) At cos@(t)) yi(t+At) = yi(t) + v(t) At sin(p(t)) and steering angle, each follower computes its desirable location at t+At with respect to the world coordinate system individually"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003477_cnm.913-Figure9-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003477_cnm.913-Figure9-1.png",
+        "caption": "Figure 9. A symmetric dynamic system with three DOFs and its graph model.",
+        "texts": [
+            " As it was observed, the decomposition is resulted only by the aid of symmetrical properties of the system. The symmetry of systems studied in the previous examples was almost simple, consisting of one symmetry operation only, however the power and efficiency of the group-theoretical method become more apparent when a system contains more symmetrical properties, establishing point groups of higher orders. Copyright q 2006 John Wiley & Sons, Ltd. Commun. Numer. Meth. Engng 2007; 23:639\u2013664 DOI: 10.1002/cnm As a simple example, which possesses rather more complex symmetry, the system shown in Figure 9 is considered. Although this system does not seem symmetric, its symmetry operations become apparent when its graph model is studied. This system has three translational DOFs, which result in a 3\u00d7 3 stiffness matrix as follows: K= \u23a1 \u23a2\u23a3 k1 + 2k2 \u2212k2 \u2212k2 \u2212k2 k1 + 2k2 \u2212k2 \u2212k2 \u2212k2 k1 + 2k2 \u23a4 \u23a5\u23a6 Having a C3 as its principal axis and three vertical planes of symmetry, this system belongs to the symmetry group C3v , with set of operations as: {e,C3,C \u22121 3 , 1, 2, 3}. Referring to the character table of this group [15]"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001500_978-1-4899-1465-1-Figure7.4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001500_978-1-4899-1465-1-Figure7.4-1.png",
+        "caption": "Figure 7.4. Equivalent circuit of de motor.",
+        "texts": [
+            " Process lines requiring that tension be maintained on material being processed can save energy by replacing mechanical brakes with regenerative, adjustable-speed drives. Because of the potentials for energy savings that exist with vari able speed, a discussion of several of the most common methods of achieving variable speed is presented in the following sections. 7.2. de Drives Direct current drives date back to the 1930s when the Ward Leonard system was patented by H. Ward-Leonard. They have un dergone many evolutionary changes over the years, but today the de drive remains one of the most versatile and widely used methods of speed control. Figure 7.4 shows the equivalent circuit of a dc motor. 122 Chapter 7 The flux is established by the field current If and the armature rotating through this flux generates a counter emf, Ec. The armature has some finite value of resistance shown as RA in the figure. The equations relating these quantities are (7.4) (7.5) where Kf = constant of proportionality between field current and flux, Ke = constant of proportionality between (speed X flux) and armature counter emf, and n = rotational speed of armature"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000569_s0045-7949(98)00004-2-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000569_s0045-7949(98)00004-2-Figure4-1.png",
+        "caption": "Fig. 4. The deformation of an in\u00aenitesimal element whose undeformed and deformed con\u00aegurations are rectangular parallelepipeds.",
+        "texts": [
+            " Geometric interpretation of polar decomposition The above discussions reveal that the Jaumann strain measure is the most appropriate one for problems involving large rotations but small strains. Jaumann strains are de\u00aened by using the polar decomposition theory [2, 5], which decomposes the deformation gradient tensor [F] into a symmetric tensor [U] and an asymmetric tensor [R] as F R U 38 where [U] is the so-called right stretch tensor and [R] accounts for rigid-body rotations. The Jaumann strain tensor is de\u00aened as B U \u00ff I 39 where [I] is a 3 3 unit matrix. To understand Jaumann strains Bmn, we consider the deformation of an in\u00aenitesimal parallelepiped, as shown in Fig. 4. Here the frames x1x2x3 and x\u00cf1x\u00cf2x\u00cf3 are two inertial orthogonal frames and the frames x1x2x3 and x1 x2 x3 represent the rigidly translated and rotated con\u00aegurations of x1x2x3 and x\u00cf1x\u00cf2x\u00cf3, respectively. The movement of the in\u00aenitesimal parallelepiped consists of a rigid-body translation which moves the point A to the point a, a rigid-body rotation which rotates the frame x1x2x3 (x\u00cf1x\u00cf2x\u00cf3) to the frame x1x2x3 ( x1 x2 x3), and pure stretches along the axes x1, x2 and x3. The coordinate systems are related as fi123g T fj123g, 40a fi 1 2 3g C Tfi123g, 40b fj 1 2 3g C Tfj123g 40c where {j123}0{j1, j2, j3} T, {j1\u00cf 2\u00cf 3\u00cf }0{j1\u00cf , j2\u00cf , j3\u00cf } T, {i123}0{i1, i2, i3} T, {i1\u00cf 2\u00cf 3\u00cf }0{i1\u00cf , i2\u00cf , i3\u00cf } T, jk are base vectors of the system x1x2x3, jk\u00cf are base vectors of the system x\u00cf1x\u00cf2x\u00cf3, ik are base vectors of the system x1x2x3, and ik\u00cf are base vectors of the system x1 x2 x3",
+            " If g61$g62, the rotation of the frame x1x2 is not equal to the average of the rotations of the axes x\u03021 and x\u03022. This fact may not be important in geometrically nonlinear analysis but it is important in elastoplastic analysis because vg61\u00ffg62v can be large due to e1>>e2 or e1<<e2. To show how to locate the local orthogonal system x1x2x3 from the convected system x\u03021x\u03022x\u03023 in a three-dimensional case, we consider Fig. 6, where OA=dx1, OB=dx2 and OC=dx3 because the system x1x2x3 represents the rigidly translated and rotated con\u00aeguration of the undeformed system x1x2x3 (see Fig. 4). It follows from Fig. 6 that the base vectors along the convected axes x\u03021, x\u03022, and x\u03023 are i1\u0302 cos g1i1 sin g61i2 sin g51i3, i 2\u0302 sin g62i1 cos g2i2 sin g42i3, i3\u0302 sin g53i1 sin g43i2 cos g3i3 49 Moreover, the ij\u00c3 can be represented in terms of the global displacement components vj and their deriva- tives ([F] is assumed to be known from numerical analyses) as i1\u0302 1 1 e1 1 @v1 @x 1 j1 @v2 @x 1 j2 @v3 @x 1 j3 , i 2\u0302 1 1 e2 @v1 @x 2 j1 1 @v2 @x 2 j2 @v3 @x 2 j3 , i3 1 1 e3 @v1 @x 3 j1 @v2 @x 3 j2 1 @v3 @x 3 j3 50 where jk are the base vectors of the undeformed sys- tem x1x2x3 and e1 1 @v1 @x 1 2 @v2 @x 1 2 @v3 @x 1 2 s \u00ff 1, e2 @v1 @x 2 2 1 @v2 @x 2 2 @v3 @x 2 2 s \u00ff 1, e3 @v1 @x 3 2 @v2 @x 3 2 1 @v3 @x 3 2 s \u00ff 1 51 It follows from Equations (40a), (49) and (50) that cos g1 sin g61 sin g51 sin g62 cos g2 sin g42 sin g53 sin g43 cos g3 264 375 1 1 e1 0 0 0 1 1 e2 0 0 0 1 1 e3 266666664 377777775 F T T T 52 To obtain [T], if one knows the geometric meanings of [R] and [T] = [R]T, one can use the following direct method to perform polar decomposition to obtain [T]"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001397_70.897776-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001397_70.897776-Figure2-1.png",
+        "caption": "Fig. 2. Geometric interpretation of the 3-D decoupling equation.",
+        "texts": [
+            " Under a general combination of 3-D, 2-D, 1-D, and 0-D measurements of the position of the hip-attachment points, the decoupling equation is given as (10a) where (10b) (10c) Proof: See the Appendix. When all the leg-attachment points of the manipulator are under 3-D measurement, we have (11) the closer equation (7) becomes identical to (3) and Theorem 1 reduces to the following corollary. Corollary 1: Let , , and be the mean values of the sets , , and , respectively. Under a 3-D measurement of the position of the leg hip-attachment points, the decoupling equation is given as (12a) where (12b) Proof: See the Appendix. For 3-D measurements, we refer to Fig. 2, showing the centroids of the leg-attachment points as joined by vector . If now the origins of frames and are chosen at the centroids of the foregoing points, and , then , and the 3-D decoupling equation reduces to (13) where does not appear any more. In this case, can be solved for independent of , meaning that we have obtained a complete decoupling of the DK problem. Now, we reduce the DK problem to an orientation problem by eliminating the position with the decoupling equation. For 3-D measurements, the position elimination is equivalent to locating the centroid of at the centroid of plus the mean \u201cleg-vector\u201d , while the orientation problem corresponds to rotating the EE around the centroid of "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002255_70.97870-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002255_70.97870-Figure1-1.png",
+        "caption": "Fig. 1. (a) A two-arm chain consisting of a two-link planar arm and a three-link planar arm. (b) S , for the two-arm chain, S , = ( ( T T ~ ; ) ~ I ~ , E S , , , 7 b ~ S r b ) . (c) S,forthetwo-armchainat q = ( ( 7 / 3 ) , ( 5 n / 3 ) ) .",
+        "texts": [],
+        "surrounding_texts": [
+            "LI et al.: DYNAMIC WORKSPACE ANALYSIS OF ROBOT ARMS 593\n1) Compute the mapping (J;l>?J&. 2) Compute the images of the vertices of S , under\n3 ) Form the convex hull of the image points obtained in\n4) Solve for the intersection of a vector in the direction of\n128.68\u201d, and 0 3 , = 25.66\u201d. These values are obtained from the relation 8 = O(q). After we obtain the analytic forms of J,(q) and J, (q) , we can plug the value of q into them to obtain ( JL>+ Je. (2) to obtain S , in I;.\na and the boundary of S,.\n- v 5 3 JL(? 3 \u2019 \u201d) 3 = [ ? 71 -9.4651 1 0 -8.465 18.93 It can be seen that all the above steps involve only analytic\ncomputations. Therefore, the procedure proposed here to J& - , - = 0 1 -7.100 14.20 6 100 \u2019 solve the dynamic workspace analysis problem for multiple (3 \u20193\u201d) [ cooperating robot arms is computationally rather simple. We ignore the gravity terms and assume that the robot\nThe joint-driving torques that produce the maximum chain is at a steady state. Then we have force/torque F can be easily computed by plugging the value of F into (2). Pseudo inverse of JA is then necessary in the S , = { T I - 1 0 N . M . S T ~ , T ~ , T ~ , , T ~ , I l O N . M . ,\nv\ncomputations. Consideration can be made in choosing this -5 N.M. I T-,, C: 5 N.M.} pseudoinverse to accommodate constraints such as different robot arms\u2019 capabilities.\nIn some applications, it is necessary to find the maximum magnitude of the force that m robot arms can jointly apply while keeping magnitude of the torque applied at a predetermined value. Solution of this problem can be achieved based on the solution of the dynamic workspace analysis problem. Given the directions of the force and torque vectors to be applied, a force/torque vector F can be found that has the maximum magnitude for both the force and the torque subvectors. The force/torque vector F\u2019 that contains a force subvector of maximum magnitude and a torque subvector of given magnitude can be obtained by simply scaling down the magnitude of the torque subvector in F to the specified value. This is possible since the maximum F requires full potential of the arms, whereas scaling down the torque subvector only reduces the utilization of the arms\u2019 capabilities. Therefore, we have, if F = (fxfyfit,tytz)\u2019, then F = ( fxfyfzct ,c t ,c tz)\u2019 can be found such that c . 1 ( t x t y f z ) \u2019 1 equals the specified value. The corresponding joint driving torques to produce F can again be easily found by plugging F\u2018 into (2).\nWe conclude this section by an example that illustrates the application of the above method to a simple two-arm closed chain.\nExample 1: We consider a two-arm closed chain consisting of a two-link planar arm and a three-link planar arm rigidly connected together at the end point of their last links, as shown in Fig. l(a). The parameters of the two robots are given as - 10 N.M. I r 1 I 10 N.M., - 10 N.M. I T, I 10 N.M., and 1, = I, = l m for the first arm and - 10 N.M. i\nr 3 , I 5 N.M. and I,. = 12, = l m , 13, = 0.5m for the second arm. The distance between the center points of the bases of the two arms is d = 2m. We present here only numeric results because of space limits. We choose generalized variables q to be q = (q,q2)\u2019 = (O,O,)\u2019. That is, they are the joint variables of the two-link arm. The origin of the compliance frame C is assumed to be at the connection point of the two arms, and its axes are chosen to be parallel to those of the world frame. Based on these choices and the given data, we have, at q = ((7r/3),(57r/3))\u2019, O , , = 25.66\u201d, 0 2 , =\nT ~ , I10 N.M, -10 N.M. IT^, I 1 0 N.M., -5 N.M. I\nwhich is a five-dimensional rectangular parallelpiped. The image S , of S , under JL(( K /3), (57r /3))- J&(( ?r / 3 ) , (5n/3)) is a convex decagon. The graphs of S , and S, are shown in Fig. l(b) and l(c). The mapping between S , and S , is such that point ( A L ) is mapped to P,, (BL) to P 2 , ( B I ) to P3, ( B J ) to P4, ( B F ) to Ps, (CF) to P6, ( D F ) to P,, ( D G ) to P,, ( D H ) to P9, and ( D L ) to Plo . Given a direction in the compliance frame C in which we wish to apply a force as large as possible, we can immediately find an F vector in this direction on the boundary of S,. For example, the maximum load this robot chain can lift is the maximum force it can apply along the fy axis. This is given by the vector F, in Fig. l(c), which has a length of 170.83 N.\nThe solution procedure presented here for Problem 1 is modified in the next section to apply to the dynamic workspace analysis of multiple cooperating robot arms with internal force/torque constraints.\nIV. DYNAMIC WORKSPACE ANALYSIS OF MULTIPLE COOPERATING ROBOT ARMS WITH INTERNAL\nFORCE/TORQUE CONSTRAINT When the internal force/torque constraint is present, the optimization problem associated with the dynamic workspace analysis problem for multiple cooperating robot arms is the same as Problem 1 except for the additional constraint given by (5) and (6). We restate the problem here as follows:\nMaximize I F 1 with respect to Fnet, Subject to\nF = l F l a m\n1 Fi=O, i = I\nI Fil I F,,, J;lF = Jljrnet, i = l ; . . , m\n, n, , where Fi, i = 1; * . , m, are as defined in Section II-B.\ni = l ; . . , m j = 1,. -\nBecause of the presence of the additional constraint, solu-\nT T -,- -\nscription prices!",
+            "594 IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION, VOL. 7, NO. 5, OCTOBER 1991\ntion of the above problem is not as straightforward as for Problem 1. We define the following notations in our discus-\n1 r j r n,}, i = I ; . . , m\nsion of maximizing F while limiting the magnitude of internal force/torque. s;= { P = (~~)(~~)~rLet l rLet\u20acS~}, i = l ; . - , m .\nDefining CE,Sb = { C L I F ' I F i e $ , i = l; . . , m}, it is easy to see that S, = Xy!,lSk. That is, the polygon S, can be found by obtaining Sh's first and then adding them together.\nThus the optimization problem associated with the dynamic workspace analysis of multiple cooperating robot arms with internal force constraints can be written as",
+            "LI et al.: DYNAMIC WORKSPACE ANALYSIS OF ROBOT ARMS\nt 'y\n595\n-40 k\nObviously, the above procedure provides only a guideline to find the maximum force/torque that m cooperating robot arms can apply to the environment in a given direction without violating the internal force/torque constraints. Efficient computation algorithms are to be developed to speed up the computation. The following simple example illustrates the above approach.\nExample 2: We consider a two-arm closed chain consisting of two identical two-link robot arms configured as in Fig. 2(a). We find the maximum weight this two-arm chain can lift (maximum force applied in the fy direction) under the internal force constraint 1 Fi I I Fcm, where the internal force direction is given as parallel to the f, direction. The\n(b) I arms. (b) Maximum force parallelograms for the two-link planar arms.\nparameters of the two-arm chain are as follows: I, = I, = 11, = 12, = 1 m, 17; 1 5 10 N * M., i = 1,2, l', 2'. The configuration of the two arms are given as 8 = (a /2), 8, = - (a /6), 8 = (a /2), 0 2 , = (n /6). Given these parameters and the configuration of the two-arm chain we obtain the maximum force parallelegrams Sb and S i as shown in Fig. 2@).\nThe maximum weight that this two-arm chain can lift is obtained by adding up the components of F 1 in S i and F2 in Sg in the direction of f,, while maintaining the components of F' and F2 in the f, direction to be of the same magnitude but with opposite direction. It can be seen that, under these requirements, the maximum weight this two-arm chain can lift remains at 20 N as long as 1 0 6 N CC F,, 5 40 + 1 0 6 N. The maximum weight it can lift becomes smaller if Fcm < 1 0 6 N.\nV. CONCLUSIONS\nThe problem of finding the maximum force/torque in a compliance frame that multiple cooperating robot arms can apply is discussed in this paper. The solutions of these problems provide basis for the task planning for force control of multiple cooperating robot arms. We formulated these problems as optimization problems under the constraints of the dynamic equation of the robots and their joint-driving torque limits. We also took into consideration the constraints on the maximum internal force/torque that the object the robot arms are in contact with can withstand, whereas the cooperating robots are modeled by a closed mechanical chain. Conceptually simple procedures are developed to solve these optimization problems. These procedures also provide deep\nT -,- - scription prices!"
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0003364_0020-7403(88)90076-8-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003364_0020-7403(88)90076-8-Figure5-1.png",
+        "caption": "FIG. 5. Sl id ing con tac t , # = 1.0. (a) v = 0.3; (b) v = 0.5.",
+        "texts": [
+            " This is in contrast with some earlier solutions in which an approximate integral equation formulation approach was adopted, but where the kernel was itself expressed as an integral; these solutions demand a separate treatment if the material is incompressible [10, 11-]. Full slip The treatment above can be extended to cover the case where full slip takes place, i.e. where one roller is sliding with respect to the other. In this case the shear traction is simply proportional to the normal pressure, so that equation (13) becomes: 4(1 - - v 2 ) 2B s - 1 2 D R A 2 2meA 2 m 2 A 2 P , E I A ( n - - m ) + b t l a ( n - - m ) ] -- _ _ + - - $2 rrE Z n = - ( S - 1 ) a aS m = - S . . . . . S. (15) The equations are then solved as before. Sample results are shown in Fig. 5 obtained with S = 10. Once again the appropriate halfplane solutions are recovered for large tyre thicknesses. For v ~ 0.5 the appropriate solution is that for the sliding of dissimilar elastic half-planes, since the thick tyre approximates an elastic half-plane in contact with a rigid cylinder. Solutions are given by Buffer [12] and Hills and Sackfield [13]; they agree well with the numerical results obtained here for large tyre thicknesses. Figure 5(a) demonstrates the coupling present between shear and normal tractions which leads to the asymmetric distribution, together with a non-zero value for e. This effect is largest for thick tyres and diminishes as the thickness is decreased and the layer becomes less compliant. The case of an incompressible tyre (v = 0.5) leads to different results, as illustrated in Fig. 5(b). This value of v eliminates the coupling present in the half-plane solution so that a Hertzian distribution of pressure is appropriate. Coupling is now introduced as the tyre thickness is reduced, and it should be noted that this is opposite in sign to that caused by the elastic mismatch for v = 0.3 (i.e. the peak pressure occurs on the entry side of the contact for v = 0.3 and on the exit side for v = 0.5). Full adhesion The next case to be considered is that of adhesive rolling, where the two rollers are adhered over the entire contact patch"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003502_095440904322804439-Figure20-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003502_095440904322804439-Figure20-1.png",
+        "caption": "Fig. 20 Schematization of the wheel and subdivision in \u00aeve truncated-cone zones for the analytical calculation with the simpli\u00aeed model",
+        "texts": [
+            " The height of each rectangle in the \u00aegure represents the load range corresponding to the design interference range. The simpli\u00aeed model is based on the following hypotheses: 1. The material behaviour was considered to be linear elastic. 2. The wheel and the axle were considered to be axisymmetric bodies. This means that the in\u00afuence of the tangential actions due to friction on the stress and strain state of these components has been neglected. 3. The wheel was schematized in \u00aeve truncated-cone zones, as shown in Fig. 20, whose dimensions depend on the actual wheelset geometry. This equivalent wheel geometry has been de\u00aened on the basis of the previously described FEM analyses. For the wheelsets analysed it was proved to give results very similar to those obtained by the FEM, with errors less than 2 per cent on the maximum press-\u00aet load. 4. The contact pressure distribution in each of the \u00aeve zones is obtained from Lame\u00c1 formulae, considering the zone to be composed of several in\u00aenitesimal cylindrical layers with an external radius r\u2026z\u2020, as Proc"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure1.13-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure1.13-1.png",
+        "caption": "Figure 1.13. Description of the intrinsic reference frame and the intrinsic velocity and acceleration vectors in the osculating plane.",
+        "texts": [
+            "71) wherein s = ds/dt is called the tangential acceleration component and 1d2 is named the normal acceleration component. Since the normal component is directed toward the center of curvature, it also is known as the centripetal acceleration component. The result ( 1. 71) shows that the acceleration vector of P lies always in the osculating plane tangent to its path and containing the cen ter of curvature. The foregoing description of the intrinsic frame t/1 = { P; tk} and the intrinsic velocity and acceleration vectors in the osculating plane at P are illustrated in Fig. 1.13. 32 Chapter 1 The curvature K, or the radius of curvature R, is given by K=~= 1:1 =~~~I\u00b7 (1.72) in which (} is the angle between the tangent vector t and an arbitrary fixed line in the osculating plane. Two easyapplications of (1.72) deserve special men tion. (i) Rectilinear Motion. A motion on a straight path is known as a rec tilinear motion. The tangent vector on a straight path obviously is a constant vector; hence, by ( 1. 72 ), we have K = 1/ R = 0. That is, a straight line path has zero curvature, hence an infinite radius of curvature",
+            "74) Finally, it is easy to verify that the tangential and normal components of the intrinsic acceleration of a particle and the curvature of the path can be computed from the relations a\u00b7v a,=s=-, v \u00b72 Ia xvl an::Ks =--, v (1.75a) (1.75b) (1.75c) Kinematics of a Particle 33 in which v = s i= 0. The construction of these results is left as an exercise for the student. It should be observed that whereas s= lvl, in general si= lal. Rather, by (1.71) (1.76) We have learned that equations (1.70) and (1.71) are the representations of the velocity and acceleration expressed in terms of a basis that is moving relative to an assigned Cartesian frame l/J = { 0; ik }, as shown in Fig. 1.13. They must not be confused as the velocity and acceleration relative to the intrinsic frame, for it is clear that the particle has no motion relative to an observer situated at the origin of that frame. Rather, the relations (1.70) and ( 1. 71) are representations of the velocity and acceleration of a particle relative to the assigned rectangular Cartesian frame l/J but referred to the moving, intrinsic frame 1/J. Said differently, the intrinsic velocity and acceleration com ponents are the instantaneous projections upon the moving, intrinsic frame 1/J of the velocity and acceleration as seen by an observer stationed at 0 in frame l/J",
+            " Kinematics of a Particle 41 The speed of the particle is the time rate of change of the distance s(t) traveled along its path: [ cf. ( 1.13 )]. The velocity and acceleration relative to cp have an especially simple and useful representation when referred to the intrinsic reference frame I{!= { P; tk} that follows the particle: v = st, [ cf. ( 1. 70 )-( 1.71 )]. The velocity vector is in the direction t tangent to the path. The acceleration, if it is not zero, is in the osculating plane and directed toward the concave side of the path, as shown in Fig. 1.13. Among all planes at the point P on the path, the osculating plane lies nearest to the curve at P; it is determined by t and the principal normal vector n directed from P toward the center of cur vature. The curvature K, or its reciprocal, the radius of curvature R, is a measure of the rate of turning of the tangent line along the path: K=~= ~~;~ = ~~~~ [cf. (1.72)], wherein e is the angle that the tangent vector makes with a fixed line in the osculating plane. All of these properties are independent of the coordinate system used in the spatial frame"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002883_robot.2004.1302491-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002883_robot.2004.1302491-Figure1-1.png",
+        "caption": "Fig. 1 Structure of the Microrobot",
+        "texts": [
+            " This paper describes the new structure and motion mechanism of an underwater microrobot using ICPF actuator, and discusses the swimming possibility of the microrobot in water. Characteristic of the underwater microrobot is measured by changing the frequency (from 0.1Hz to 5Hz) and the amplitude (from 0.5V to 1OV) of input voltage. The experimental results indicate that the swimming speed and the buoyancy of the underwater microrobot can be controlled by changing the frequency and the amplitude of voltage. II. STRUCTURE OF THE MICROROBOT A. Total Structure of the Microrobot Fig.1 shows the basic structure of the developed underwater microrobot using ICPF actuator. This microrobot consists of the body made of wood material shaped as a fish (A), a pair of tail with a fin driven by ICPF actuator respectively (B), the lead wires for supplying electric energy to ICPF actuators (C) and a pair of fins are installed in parallel structure for generating a large propulsive force. The fins are driven independently. The buoyancy adjuster under of the microrobot body is also driven by the same ICPF actuator",
+            " Displacement of the ICPF is proportional to the electrical voltage in put on its surface as the swelling of polymer gels. The other characteristic of the ICPF actuator is that when the frequency of the applied voltage is low less than 0.3Hz, water around the ICPF surface is electrolysed, so water bleb on both side of the ICPF surface is generated. In result of the change of body volume, and buoyancy of the microrobot can be controlled. ICPF actuator (0 .2~3~15mm) is cut in a strip to drive a fin for propulsion, and ICPF actuator (0.2~4~6mm) is used for buoyancy adjuster as shown in Fig.1. 0-7803-8232-3/04/$17.00 02004 IEEE 4881 Body Solenoid Pennanmt magnet Fig2 sture (b) DOF (c) Underwater Micro Biped Robot with 1 DOF Fig.3 View of the Developed Microrobot III. MOTION MECHANISM OF MICROROBOT The developed microrobot has two tails with a fin driven by the ICPF actuator respectively as shown in Fig.1. A pair of fins is offset in the distance d, and driven by electric voltage of fl and f2 frequency independently as shown in Fig.4. A motion of a fin is described by combination of two kinds of motion, feathering and heaving . When proper phase difference appears between heaving and feathering, the fin generates an effective force as shown in Fig.5. The propulsive force is the sum of drag force vectors to the moving direction in equation (1). It can be realized by changing frequency fl, E2 of the electric voltage applied on the ICPF actuators that the moving motion in the directions (forward, right turn and left turn) as shown in Table"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000704_a:1008228120608-Figure9-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000704_a:1008228120608-Figure9-1.png",
+        "caption": "Figure 9. (a) Permanent event map generated with Vdr = 0:082377. There is no fixed point, the interval \u2018a\u2019 is mapped into \u2018b\u2019 and vice versa; (b) the f 2 map shows the existence of a homoclinic orbit.",
+        "texts": [
+            " Figure 7 shows the bifurcation diagram of the attractor \u20182\u2019 in a portion of the range of small driving velocities; starting from Vdr = 0:0846 the attractor undergoes a period-doubling cascade giving birth to an apparently chaotic attractor which suddenly disappears for Vdr 0:08058. A sequence of one-dimensional maps in the non-periodic region can be seen in Figure 8; the shape of those maps constitutes evidence of the chaotic nature of the system. For values of the driving velocity close to Vdr = 0:082377 (see bottom right of Figure 8) and above, the steady state part of the one-dimensional iterated mapping is composed of two (or more) separated branches; see also Figure 9a. This separation into two branches clearly rules out the existence of odd periodic orbits since f(a) :! b, f(b) :! a, and a \\ b = ;, where a and b are the two intervals where the permanent portion of the map is defined. The only exception is a fixed point in between the two branches (not shown). The map is, however, still continuous as the transient part of the map shows (not shown on Figures 8 and 9). Considering Figure 9b and the illustrative trajectories shown, it is evident that the map possesses a so-called snap-back repeller, or in more traditional terms a homoclinic orbit to the unstable fixed point; the fixed point is, of course, a fixed point for the second iterate of f , and in reality is a prime period-2 orbit. The fixed point for the second iterate is located at approximately d = 0:1624. The snap-back repeller is sufficient for the existence of chaos [11, 18]. That is, there exist periodic points of any prime period (for the second iterate), and uncountably many orbits that are not even asymptotically periodic"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003395_bf01022266-Figure7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003395_bf01022266-Figure7-1.png",
+        "caption": "Fig. 7. Double channel electrode cell.",
+        "texts": [
+            "7cm, Vr = 10 -3, 10 2, 10-t and 1 c m 3 s - I , D = 10 -5 cm 2 s -~, d = 0.6 cm and b -= 0. t cm), heterogeneous rate constants in the range 10-1 _ 10- 5 cm s - ~ may be measured. The general observat ion to be made is that slower flow rates favour the measuremen t of slow rate constants. 3. Experimental details 3.1. The flow cell and flow system The flow cell and flow system have previously been described [13, 15], and so only a br ief description will be given here. Exper iments were carried out using the cell shown in Fig. 7, which was fabr icated in Perspex. The channel is 40 m m long, 6 m m wide and approx imate ly 1 m m deep. A precise value for the latter pa rame te r was found f rom the slope of a Levich plot ( t ransport - l imited current vs (flow rate ~/3) [20], obta ined f rom an electroactive species o f known diffusion coefficient. A cover plate bore the substrate - in this case a piece of cot ton cloth - onto which were cemented to the electrodes. The electrodes consisted of strips cut f rom pla t inum foil, 0 . 0 2 5 m m thick (99.95%, Goodfet lows, Cambr idge , U K ) . The upstream electrode was located 3-4 mm downstream of the upstream edge of the cloth, and the upstream region of the substrate was masked from the solution with thin PTFE tape, as shown in Fig. 7. The edges of the substrate and electrodes were treated in the same manner, as illustrated, so that the width of the exposed substrate and electrodes was approximately 4mm. This arrangement ensured that flow over the reactive interface was of a plug nature with respect to the z direction; edge effects (in which v x deviates from the expression given in Equation 3), occur over distance ~ b/2 [15]. In general, the lengths of the upstream and downstream electrodes were of the order of 2 and 4 ram, respectively, with a gap of l m m ",
+            " Connections between the PTFE tubing, the cell and the counter electrode were formed with silicone rubber tubing. Deoxygenated electrolyte was gravity fed from the reservoir via one of several calibrated glass capillaries, which gave a total flow rate range of 10-4-3 \u2022 10-~ cm 3 s-~. Adjustment of the rate of flow with each capillary was achieved by varying the height between the reservoir and the tip of the capillary, where the electrolyte ran to waste. Electrical contact to the two working electrodes was facilitated by extending the foils beyond the edge of the coverplate as illustrated in Fig. 7. Locating the cell and about 1 m of the preceeding tubing within an air thermostat allowed temperature control to 25 _+ 0.1~ 3.2. Materials Solution were made up using triply distilled deionized water (resistivity > 107 s cm). Ferricyanide solutions constituted approximately 5 x 10 .3 M potassium ferricyanide in 0.1 M sodium hydroxide and 1 M potassium chloride to serve as background electrolyte. Bromide solutions were approximately 10 -3 M in sodium bromide, 0.5 M sulphuric acid acting as background electrolyte"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000813_bf01209025-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000813_bf01209025-Figure1-1.png",
+        "caption": "Fig. 1. Kinematic variables and axes.",
+        "texts": [
+            " We are going to explore the case when the ball and the surface 50 have only one point in common during all motion, so the curvature of the meridian of 50 (i.e., an intersection of 5 ~ and a vertical plane containing the line Z) is smaller than 1/a. In that case, the set S of all possible positions of the center of the ball is also a smooth surface of revolution with the same axis Z [4]. The position of the ball's center O can be described by geographical coordinates 0 and 9. The latitude O is an angle between the inner normal vector to S and the plane orthogonal to the line Z (see Fig. 1). The longitude 9 is the angle between the fixed plane containing the line Z and the mobile plane that goes through the line Z and the point O. Introduce a moving orthogonal basis eleze3. The vector el is a tangent vector to a meridian of S at O (i.e., an intersection of S and a vertical plane containing the line Z and the point O), e3 is the inner normal vector to S at O, and e2 is equal to e3 \u2022 e l . Let us denote the velocity of the ball's center by v and the angular velocities of the ball and the basis ele2e3 by co and ~ respectively"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001045_a:1019555013391-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001045_a:1019555013391-Figure1-1.png",
+        "caption": "Figure 1. Definition of the MBS structure.",
+        "texts": [
+            " We assume here that the structure is a topological tree, excluding the presence of any closed loops in the system. The dynamical model of the MBS is characterized by a set of inertial parameters describing the mass distribution of the bodies. These parameters could be considered individually for each body, but it is well-known that some of them combine together [3] to form the so-called barycentric parameters. These combinations can be performed a priori from the description of the topological structure (Figure 1): m\u0304i = \u2211 j :i\u2264j mj , (1) bi = \u2211 j :i\u2264j mj dij = [X\u0302i]t  bi1 bi2 bi3  , (2) Ki = Ii \u2212 \u2211 j :i\u2264j mj d\u0303ij d\u0303ij = [X\u0302i]t  Ki 11 Ki 12 Ki 13 Ki 12 Ki 22 Ki 23 Ki 13 Ki 23 Ki 33  [X\u0302i]. (3) where \u2022 i \u2264 j means that body i is an ancestor of body j in the tree structure; \u2022 dij (i \u2264 j) is the vector contribution of body i to the absolute position vector of joint j . We also define dij z as dij + zi; \u2022 x\u0303 stands for the skew-symmetric tensor associated with the cross-product by a vector x; \u2022 mj , djj and Ij are the mass, position vector of the center of mass and inertia tensor of body j ",
+            " The vector bi is the moment vector locating the mass centre of this augmented body and the tensor Ki is its inertia tensor with respect to its attachment point O \u2032i . In our formalism, the reference point for computing the resultant joint force Fi and pure torque Li (for joint i) being chosen as the point Oi (located on the parent body h), the following augmented parameters are also introduced: bi z = m\u0304izi + bi = \u2211 j :i\u2264j mj dij z ; Ki z = Ii \u2212 \u2211 j :i\u2264j mj d\u0303ij z d\u0303ij z (4) defined with respect to point Oi (Figure 1). The kinematic formulation is of course similar to the one used for the classical recursive Newton\u2013Euler scheme. We shall briefly recall these equations for our case. In Figure 2, the various kinematical elements are represented and in the following equations, \u03d5i and \u03c8 i represent unit vectors aligned with joint i axis, respectively for a revolute and a prismatic joint. For body i, one can write: \u2022 Absolute position vector: pi = ph + dhi z , for the attachment point Oi on body h. (5) \u2022 Absolute velocities: \u2013 angular: \u03c9i = \u03c9h + \u03d5i q\u0307i; (6) \u2013 linear: p\u0307i = p\u0307h + \u03c9\u0303h "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002725_zamm.19910710718-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002725_zamm.19910710718-Figure1-1.png",
+        "caption": "Fig. 1. a) Rigid object in an elastic frictional multifingered gripper. b) Hard finger-contact. c) Soft finger-contact",
+        "texts": [
+            " The numerical treatment of the resulting LCP by an appropriate algorithm gives normal reaction, tangential forces (friction forces), the slipping when it occurs and the corresponding rigid body displacement. In this paper a variant of LEMKE\u2019S algorithm (c.f. [14], 1151) is used to solve the problem. Numerical examples illustrate the theory. It is also shown by means of a numerical example that an object which is grasped with soft-fingers cannot be grasped with hard-fingers for the same external forces. 2. Problem formulation Let us consider in the orthogonal Cartesian coordinate system a rigid object which is grasped by a multifingered gripper with n frictional elastic fingers (Fig. 1 a). The contact between the object and the fingertips is modeled either as a hard-finger contact (Fig. 1 b) or as a soft-finger contact (Fig. 1c). The hard-finger contact can prevent displacements of the object in the normal and the tangential directions with respect to the object boundary, whereas the soft-finger contact can prevent in addition rotations of the object about the normal to the boundary axis passing through the contact point, up to a certain value of torque which depends on the normal contact force through Coulomb-type static friction. Under the above assumptions the relations which govern the frictional contact problem are the following: i) The g loba l equi l ibr ium equat ions where GN is the m x n equilibrium matrix corresponding to the normal contact reactions, C T is the m x 2n (m x 3n for the soft-finger case) equilibrium matrix corresponding to the friction forces (plus the frictional torques in the soft-finger case), rN = {r,,, rN2, "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003646_robot.2006.1642337-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003646_robot.2006.1642337-Figure1-1.png",
+        "caption": "Fig. 1. Stereographic projection for 1-D.",
+        "texts": [
+            " To make a projection, a line is drawn from the north pole to each point on the sphere and the intersection of this line with the projection plane constitutes the stereographic projection. For simplicity, we will illustrate the equivalence between stereographic projections and conformal geometric algebra in R 1. We will be working in R 2,1 with the basis vectors {e1, e4, e5} having the usual properties. The projection plane will be the x-axis and the sphere will be a circle centered at the origin with unitary radius. Given a scalar xe representing a point on the x-axis, we wish to find the point xc lying on the circle that projects to it (see Figure 1). The equation of the line passing through the north pole and xe is given by f(x) = \u2212 1 xe x + 1 and the equation of the circle x2 +f(x)2 = 1 . Substituting the equation of the line on the circle, we get the point of intersection xc xc = ( 2 xe x2 e + 1 , x2 e \u2212 1 x2 e + 1 ) , (5) which can be represented in homogeneous coordinates as the vector xc = 2 xe x2 e + 1 e1 + x2 e \u2212 1 x2 e + 1 e4 + e5. (6) From (6) we can infer the coordinates on the circle for the point at infinity as e\u221e = lim xe\u2192\u221e {xc} = e4 + e5, (7) eo = 1 2 lim xe\u21920 {xc} = 1 2 (\u2212e4 + e5), (8) Note that (6) can be rewritten to xc = xe + 1 2 x2 ee\u221e + eo, (9) B"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002495_12.497801-Figure10-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002495_12.497801-Figure10-1.png",
+        "caption": "Fig. 10 Comparison ofgas pressure distribution on specimen surface in Ar and He gas.",
+        "texts": [
+            " Cross sections, X-ray inspection results and X-ray transmission observation results are summarized in Fig. 9. The penetration depth increases with a decrease in the pressure both in CO2 and YAG laser welding. Also, bubble and porosity formation was suppressed, and no porosity was formed under high vacuum although the bottom part of a keyhole was swollen. It was moreover revealed that the thin vapor plume upwards was induced, and the melt flow in vacuum was opposite to that in coaxial shielding gas. Fig. 10. The negative pressure was produced. Moreover, the negative pressure was more noticeable in Ar than in He because ofhigher gas density. The nozzle was first used in CO2 laser welding. The results are shown in Fig. 11. As the negative pressure increases, porosity is smaller and the number is reduced. The action of Ar is higher. Porosity is reduced remarkably at a low speed. It was confirmed that this nozzle was effective to the reduction in porosity at low speeds in both CO2 and YAG laser welding ofan aluminum alloy A5083"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002469_1.1468870-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002469_1.1468870-Figure1-1.png",
+        "caption": "Fig. 1 The different shapes of helical springs \u201ea\u2026 cylindrical \u201eb\u2026 barrel \u201ec\u2026 conical \u201ed\u2026 hyperboloidal",
+        "texts": [
+            " The results are given with six digits in order to enable comparison by other methods. As shown in Figs. 3 and 4, the mode shapes are presented in the global and the local coordinate systems as can be seen. All the mode shapes are coupled. In addition, the symmetrical and asymmetrical modes can be identified from the plots. Example 2: Noncylindrical \u201eHyperboloidal\u2026 Helical Spring In order to show the excellent performance of the dynamic stiffness analysis, the results are compared to finite element analysis results for a hyperboloidal type spring ~Fig. 1! fixed at both ends. It is clearly seen from Table 2 that the results obtained by the suggested method are the converged results of the finite element analysis. In Figs. 5 and 6, the first six mode shapes are presented. JULY 2002, Vol. 124 \u00d5 405 016 Terms of Use: http://www.asme.org/about-asme/terms-of-use 4 Downloaded Fr Here too the symmetrical and asymmetrical mode shapes are obvious in the mode shapes. Example 3: Noncylindrical \u201eBarrel\u2026 Helical Spring. For the second noncylindrical example, a barrel type spring ~Fig. 1! is considered. This problem has been studied by Nagaya et al. @8# using the Myklestad method. They have taken into account only the axial deformation, and neglected the rotary inertia. They have solved this problem by dividing every coil into 12 segments. Their results were obtained theoretically and experimentally. A close agreement between the results computed in the present study which are given in Table 3 and some of their results is demonstrated. It is also observed that the results of the present study are very close to those of Yildirim @9#"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003692_icmlc.2005.1527053-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003692_icmlc.2005.1527053-Figure2-1.png",
+        "caption": "Figure 2. Space voltage vector and stator flux vector in stationary reference frame",
+        "texts": [],
+        "surrounding_texts": [
+            "For three phase voltage source inverter, there are six non-zero active voltage switching space vectors (V 621, VV ) and two zero space vectors (V 70 ,V ). Six non-zero switching space vectors of three phase inverter are evenly distributed at 60\u00b0intervals with the length of 2Vdc/3 and form a hexagon (two zero space vectors are located at the center of the hexagon in the complex plane) as shown in Figure 1. Generally, in direct torque control of induction machine drives, there are ripples of torque and flux since none of the eight vector is able to generate the exact stator voltage required to produce the desired changes in torque and flux in the most of the sampling period. So, SVM is introduced in DTC for IM to reduce the torque and flux ripples. The voltage reference vector can be synthesized by two adjacent effective vectors (V andV *V i 1+i ) and two zero vectors on the basis of volt-second balance as in Figure 1, that is dtVdtVdtVdtV ss T TT TT T i T i T \u222b\u222b\u222b\u222b + + + ++= 21 21 1 1 0100 * (5) If *V is dynamically obtained on the control of IM, that is its amplitude and space position are adjustable, the ripples of torque and flux are expected to be decreased. As shown in Figure (2), in stationary reference frame, the stator flux variation can be resolved in two perpendicular components sf\u03c8\u2206 and st\u03c8\u2206 , where sf\u03c8\u2206 affects the stator flux magnitude, and st\u03c8\u2206 influences on torque magnitude. Synthesized space voltage vector *V is in the direction of s\u03c8\u2206 , and affects on both sf\u03c8\u2206 and st\u03c8\u2206 . In this paper, the magnitude of required voltage space vector is simplified as a constant, angle of *\u03b8 *V is the controlled variable. Since space position of stator flux can be calculated, the space angle of is able to be determined by predicting the angle of and stator flux, i.e. *V *V \u03b7\u03b8\u03b8 += s * (6) In formula (6), s\u03b8 is the angle between stator flux vector and d axis, which stand for actual position of stator flux. \u03b7 is called deflection angle, and obtained by torque error and stator flux error using fuzzy inference method in the paper. As described previously, DTC is direct control of flux and torque within the limits of flux and torque hysteresis bands by selection of optimum inverter switching vectors. predictive control method in DTC presented in this paper means the deflection angle of required voltage vectors is dynamically regulated, so that, more precise voltage vectors can be applied to the machine to reduce the ripples of torque and flux. Since the angle \u03b7 is function of torque error and flux error, a novel fuzzy logic DTC using SVM of IM is presented and shown in Figure 3. According to fuzzy logic technique, when angle \u03b7 is estimated, required voltage space vector is obtained, and SVM is able to adapt to control the machine, instead of using hysteresis comparators and optimum voltage switching vector lookup table as in conventional DTC. In the fuzzy logic estimator, there are two input variables, which are absolute torque error|ET|, stator flux error |E\u03a8|, one output variable is the deflection angle \u03b7 of synthesized voltage vector. Each universe of discourse of the torque error, flux error, and deflection angle is divided into four fuzzy sets. Triangle membership functions have been used. All the membership functions (MF) are shown in Figure 4 respectively. There are total of 16 rules as listed in table 1. Each control rule can be described using the input variables |ET|,|E\u03a8| and control variable \u03b7 . The th rule i iR can be expressed as : Z P S P M || \u03a8E P B || E T \u03b7 Z P S P M P B P S P M P B P B Z P S P M P B Z Z P S P M Z Z Z Z The inference method used in this paper is Mamdani\u2019s procedure (inference) based on min-max decision. The firing strength (applied fuzzy operators) ,for ith rules is given by i\u03b1 min( (| |), (| |))i A T Bii E E\u03c8\u03b1 \u00b5 \u00b5= By fuzzy reasoning, Mamdani\u2019s mininum procedure (fuzzy inference) gives ' ( ) min( , ( ))V i Vi i \u00b5 \u03b7 \u03b1 \u00b5 \u03b7= Where A\u00b5 , B\u00b5 and V\u00b5 are membership functions of sets A, Band V of the variables |ET|, |E\u03a8| and \u03b7 , respectively. Thus, the membership function V\u00b5 of the output \u03b7 is given by 16 ' 1 ( ) max( ( ))V Vii \u00b5 \u03b7 \u00b5 \u03b7 = = The Maximum criterion method is used for defuzzification, and the final single-valued output is obtained by this method. As stated above, in the case that both torque error and flux error are positive, the angle \u03b7 is obtained by the fuzzy logic estimator. In the other three cases, deflect angle can be derived simply as follows: If 0\u2265TE and 0\u2264\u03c8E , then \u03b7\u03c0\u03b7 \u2212= ; If TE <0 and \u03c8E <0, then \u03b7\u03c0\u03b7 += ; If TE <0 and 0\u2265\u03c8E , then \u03b7\u03c0\u03b7 \u2212= 2 Finally, the space angle of required space voltage vector is able to be calculated by formula (6)."
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure2.22-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure2.22-1.png",
+        "caption": "Figure 2.22. A change of base point in a general motion of a rigid body.",
+        "texts": [
+            "28) shows that their vec tor sum is equivalent to a single angular velocity vector about a single instan taneous axis through the same base point. On the other hand, we may ask: What change, if any, occurs in co if the base point is shifted arbitrarily to another place in fJI? To answer this question, we let P be any point of fJI; and, for the same motion of fJI, we assume that at the same instant co and co* are distinct angular velocities of fJI about lines through distinct base points at 0 and 0*, respectively, as shown in Fig. 2.22. Since the velocity of any particle P, by its definition ( 1.8 ), is the same for every base point used in application of (2.27), using the vectors defined in Fig. 2.22, we may write for both 0 and 0* =v 0 .+co*xx* =(v 0 +coxr)+coxx*, (2.114a) (2.114b) (2.114c) wherein x = r + x*. However, with 0 as base point, it is clear that the term in parentheses in (2.114c) is equal to v a\u2022. Consequently, we have ( ro* - ro) x x * = 0. Since P is an arbitrary particle, this relation must hold for all x*; therefore, ro* = ro follows. In sum: The angular velocity vector is the same for every choice of base point associated with a rigid body. Let us recall, for example, the description in Fig",
+            " As a consequence of this invariant property of ro, (2.114) becomes =v 0 .+roxx*. (2.115a) (2.115b) The result shows that a motion of a rigid body due to a translation v 0 and a rotation ro about a base point 0 is equivalent to a rotation ro about any other base point 0* together with a new translation v0 \u2022 given by v0 \u2022 = v0 +ro x r, (2.116) where r = x- x* is the vector of 0* from 0. Thus, a change of base point cer tainly results in a change of velocity for the new base point, but the angular velocity of the body remains the same. (See Fig. 2.22.) Two additional easy theorems follow readily from (2.115). Their proof is left for the reader in Problem 2.70. (i) Invariant Projection Theorem. The projections upon the instantaneous axis of rotation of the velocities of all points of a rigid body are the same; that is, for all points P v P \u2022 a = v 0 \u2022 a, or v P \u2022 ro = v 0 \u2022 ro, (2.117) where a= ro/lrol is the instantaneous axis of rotation and 0 is any assigned base point. (ii) Parallel Axis Theorem. The velocity of a particle P due to a pure rotation with angular velocity ro about on axis a is equivalent to a rotation with Kinematics of Rigid Body Motion 125 the same angular velocity about\" a parallel axis together with a translational velocity perpendicular to that line, and conversely",
+            " Therefore, we may choose 0* to be at the shortest distance from 0 between the parallel lines so that r\u00b7ro=O (2.121) must hold. Then we form the vector product of (2.120) with ro, expand the result, and use (2.121) to obtain in terms of the originally assigned base point data the unique location r of the point 0* on the new parallel axis: (2.122) Thus, shifting the base point to 0* by using (2.118) in (2.1115) yields v P =pro+ ro x x*, (2.123) in which x* = x- r is the position vector of P from 0* on the new parallel axis. (See Fig. 2.22.) The equation (2.123) is the content of Chasles' theorem. It shows that the velocity of any particle P of a rigid body may be simply and uniquely charac terized by a rotation with angular velocity ro about a parallel line through a base point O* at the unique place r from 0 given by (2.122) together with a translational velocity (2.118) along that line. This is the motion typical of a nut moved along a threaded screw; it is reminiscent of the helical motion of a particle studied in Chapter 1. In fact, such a motion is known as an instan taneous screw motion; and the axis of rotation is named the screw axis"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000597_ac0006831-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000597_ac0006831-Figure1-1.png",
+        "caption": "Figure 1. Simplified diagrams showing (A) a disposable card-type flow cell detectors and (B) a disposable ion sensor. Key: (a) Perspex holder, (b) Ag/AgCl reference electrode for the organic phase, (c) Ag/AgCl reference electrode for the aqueous phase, (d) Aqueous electrolyte gel reference for the organic phase, (e) 2.8% (w/w) PVCNPOE organic gel layer, (f) Micro-photoablated 23-\u00b5m PET film containing PVC-NPOE gel in microholes, (g) plastic support, and (h) PET film.",
+        "texts": [
+            " The 2.8% (w/w) PVCNPOE gel was cast hot on the perforated PET film of the side exposing the smaller diameter. The gel filled the conical holes so that an array of microdisk interfaces could be obtained with a diameter of 22 \u00b5m exposed to the flowing aqueous solution The ionode was operated in a two-electrode mode using a pair of reference/counter electrodes.22 Flow System and Electrochemical Measurements. For experiments with flow conditions, a disposable card type of flow cell detector shown in Figure 1 was used. The easily removable disposable sensor shown in Figure 1B was produced by attaching the perforated PET film (23 \u00b5m thick) onto the plastic support and exposing to the analyte the smaller diameter of the hole array. The reference/counter electrode for the organic phase consisted of a tetrabutylammonium ion selective electrode (TBA+ISE) comprising an aqueous solution of TBACl gelified with 20% (m/ m) hydroxyethyl cellulose and a Ag/AgCl reference electrode. A TBA+ISE aqueous gel was added to the top of the composite polymer membrane having a total thickness of \u223c50 mm and covered with paraffin films, preventing the evaporation of water from the gel"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001575_1097-4628(20001121)78:8<1566::aid-app140>3.0.co;2-i-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001575_1097-4628(20001121)78:8<1566::aid-app140>3.0.co;2-i-Figure2-1.png",
+        "caption": "Figure 2 Coordinate system of tire.",
+        "texts": [
+            " Kamoulakos and Kao2 studied the transient dynamic responses of a tire rolling on a spinning drum with cleat. In the following section, we also show a finite element model of tire and cornering simulation of tire using implicit FEA code (ABAQUS/Standard) and explicit FEA code (ABAQUS/Explicit). Figure 1 shows a structure of the typical passenger car\u2019s radial tire. The tire is made of both rubber components such as cap tread and sidewall, and fiber-reinforced rubber components such as steel belt and textile carcass. Figure 2 shows an axis system for this simulation. A slip angle is an angle between direction of wheel travel and direction of wheel heading. A cornering force and a self-aligning torque characterize cornering ability of a tire. Direction of the cornering force is normal to direction of wheel travel. The self-aligning torque is moment around the axis in the direction of normal to road surface. Figure 3 shows an axisymmetric FE tire model, which is a passenger car\u2019s radial tire of 235/ 45ZR17. Rubber components are modeled by the continuous elements with hyperelastic material of Mooney\u2013Rivlin form"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003460_09544100g03204-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003460_09544100g03204-Figure1-1.png",
+        "caption": "Fig. 1 Missile airframe and dynamic variables",
+        "texts": [
+            " The design procedure for pitch-axis controller of tailcontrolled missile is presented in this section. The model employed in this analysis is based on the theoretical tail-controlled missile used as a base line for pervious non-linear control design [4, 26]. The missile model assumes constant mass, no roll rate, zero roll angle, no sideslip, and no yaw rate. Under these assumptions, the longitudinal non-linear equation of motion is reduced to two forces and one moment. Using body axis components (Fig. 1) these equations are Fx \u00bc QSCD (5) Fz \u00bc QSCN (6) My \u00bc QSdCM (7) The dynamic pressure is defined as Q \u00bc 1 2 rV 2 m \u00bc 0:7P0M 2 (8) Note that missile velocity and air density are not assumed to be constant or slow-varying, but a standard atmospheric model is assumed in simulations based on previously reported data [35]. Aerodynamic polynomials are given as CD \u00bc 0:3 (9) CN(a, d, M) \u00bc b1Na 3 \u00fe b2Najaj \u00fe b3N 2 M 3 a\u00fe dnd \u00bc cn(a, M)\u00fe dnd (10) CM (a, d, M) \u00bc b1Ma 3 \u00fe b2Majaj \u00fe b3M 7\u00fe 8M 3 a\u00fe dmd \u00bc cm(a, M)\u00fe dmd (11) The numerical values of the earlier equations are given in Table 1"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001127_s0022112002002483-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001127_s0022112002002483-Figure4-1.png",
+        "caption": "Figure 4. Two possible menisci between a solid and a liquid for a prescribed height of the triple point. Here, h0 > 0, and the initial angle of the meniscus with the vertical is \u03b80 and \u2212\u03c0\u2212 \u03b80, both satisfying (3.5). The two menisci merge when \u03b80 = \u2212 1 2 \u03c0, i.e. h0 = 2. The bent plates are introduced to illustrate the multiplicity of menisci for a given height of the triple point. The profiles of the menisci are computed based on the procedure outlined in \u00a7 3.4.",
+        "texts": [
+            " For example, a thin plate attached to an actuator in air can form the meniscus preventing the liquid from wetting the actuator, whereas the probe attached to the plate may be inundated (figure 3). 3.3. Uniqueness of the solution for the meniscus Proposition. For a prescribed admissible height, h0, of the triple point, there may be only two possible menisci. Proof. Let the prescribed non-dimensional height of the triple point L be h0 > 0 (i.e. only the positive solution in (3.5) is considered). Then \u03b80 < 1 2 \u03c0. Now, if \u2212 1 2 \u03c0 6 \u03b801 < 1 2 \u03c0 satisfies (3.5) then so does \u03b802 = \u2212\u03c0\u2212 \u03b801 (figure 4). Thus, the menisci, m01 or m02, starting with \u03b80 = \u03b801 or \u03b80 = \u03b802 increase \u03b8 from \u03b80 to 1 2 \u03c0 with increasing s. There are other angles < \u2212 3 2 \u03c0, such as \u03b803 = \u22122\u03c0 + \u03b801 that also satisfy (3.5), but a meniscus starting with \u03b80 = \u03b803 increases \u03b8 to \u03b8 = \u2212 3 2 \u03c0 as s \u2192 \u221e which results in a meniscus m03 identical to m01. Similarly, the meniscus with \u03b80 = \u22122\u03c0\u2212 \u03b801 coincides with m02. Thus, for a given h0 there are two distinct menisci. They merge into one when \u03b80 = \u2212 1 2 \u03c0 or h0 = 2 by (3.5), and we can view the two menisci as the two bifurcation branches with \u03b80 = \u2212 1 2 \u03c0 as the bifurcation point",
+            " The corresponding change in energy owing to the change of interfacial area at the edges is negligible compared to the change in the hydrostatic or the liquid\u2013vapour interface energies. We will thus evaluate the hydrostatic energy, EH , and the surface energy, ES , contributed by the liquid\u2013vapour interface only. Furthermore, the change in energy from the reference configuration where the meniscus height is zero is of interest. Thus, in what follows, EH and ES indicate the changes in energies per unit length of the plates from the reference configurations. If the plates are bent (e.g. figure 4) or thick, then the change in the solid\u2013liquid interface energy may not be negligible depending on the geometry and shape of the edges of the plates, and can be evaluated from the specific geometry. Here, for simplicity, we assume that such a change in the interfacial energy for the bent plates considered later is small compared to ES and EH , and hence the analysis, when applied to the bent plates, is restricted to geometries where the solid\u2013liquid interface energy change is small. The bent plates are introduced only to illustrate a bifurcation phenomenon in menisci"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003183_3.20488-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003183_3.20488-Figure1-1.png",
+        "caption": "Fig. 1 A multibody structure.",
+        "texts": [
+            " The first section describes the system configuration and geometry organization. In the second section a description of the modeling of a flexible body and detailed derivation of the kinematics are presented. The equations of motion derived via Kane's equations are given in Sec. III. In Sec. IV a simulation of a space robotic system is presented. The conclusion forms the last section. II. System Description The system is composed of rigid and flexible bodies forming a treelike structure as shown in Fig. 1. The bodies are interconnected by joints that have three rotational and three translational degrees of freedom. The flexible bodies in the system are modeled by beams undergoing small deformations in all directions. The beam may have variable cross-sectional area along its length with the restriction that the principal axes at each cross-section are parallel. For simplicity the shear center is assumed to coincide with the centroidal axis. In the formulation of the equations of motion, all bodies will be considered flexible",
+            " (A10) in Appendix A, and assuming small rotations due to deformation, it can be expressed as where and (is) ( 19) where vjm and ^m are the partial angular velocity arrays associated with c5^ and qp9 respectively. In Eqs. (18) and (19), Bk and Ck are Boolean matrices used for describing the indices of cbk in c5r and r\\k in f/r, respectively, defined as In a more compact form, Eq. (17) can be written as where (20) (21) The partial angular velocity arrays are functions of displacements only and need to be generated for each element i in body A:. Consider an element / in B4 in Fig. 1. Let each body have c modal coordinates. The angular velocity of n 4| is (22) In the subsequent analysis the angular velocity of nk with respect to 11\u00b0 and the angular velocity of iik* with respect to 0, denoted as cok and o**, respectively, are also needed. The cok can be obtained by subtracting nk\u00bbki from Eq. (13) (23) where fik m is obtained by setting the last term in Eq. (19) to zero. Similarly, cok* can be obtained by subtracting from cok. This yields con (24) Similarly, from Eq. (7) the angular velocity of the element i relative to nk can be written as (15) Substituting Eqs"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001127_s0022112002002483-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001127_s0022112002002483-Figure2-1.png",
+        "caption": "Figure 2. (a) A family of menisci formed between a hydrophilic solid plate and a liquid is shown for different prescribed heights of the plate. The contact angle \u03c6 between the tangent to the solid surface and the menisci is constant, but the angle, \u03b80, of the meniscus with the vertical at the triple point, L, changes as L moves from the bottom surface of the plate towards the top with the displacement of the plate towards the liquid. The local normal, n\u0304, to the plate surface rotates from vertical down to vertical up. Among all the members of the family, m2 offers the maximum capillary force \u03b3 (per unit length of triple line) vertically downward. When the plate is lowered into the liquid, m5 is the highest possible meniscus attainable prior to collapse that offers an upward vertical force \u03b3 sin\u03c6, a fraction of \u03b3. (b) Similar menisci for a hydrophobic solid. (c) The coordinate system used to define the meniscus. All the profiles of the meniscus shown in (a)\u2013(c) are computed based on the procedure outlined in \u00a7 3.4.",
+        "texts": [
+            " (ii) All interfaces are smooth and the local asperities are ignored. Similarly, no local pinning point occurs as the line L advances along a solid surface. (iii) The solid plates are long normal to the paper, but they have a finite width. The heights of the meniscus at all points along its length are equal. Thus, the problem is one-dimensional and the meniscus has only one non-zero principal curvature. Consider a long thin rigid strip of a hydrophilic solid (\u03c6 < 1 2 \u03c0) on the surface of a liquid. Its cross-section at the edge is shown in figure 2(a). For illustration, the plate is assumed symmetric about its vertical axis, and its edge is represented by a semicircle. The outward normal at any point of the boundary is n\u0304. When brought into contact with the liquid surface, the liquid spreads over the entire bottom of the plate and forms a meniscus. That such a spreading cannot be partial, at least for a circular disk, is shown mathematically by Vogel (1982). If the plate is moved upward, away from the liquid surface, the meniscus takes a form such as shown by m1 which forms an angle \u03b80 with the vertical (positive downward) at L",
+            " In the latter case, symmetry in the meniscus breaking forces will be restored. Thus, in the absence of hysteresis, \u03c6 < 1 2 \u03c0 and geometric constraint (horizontal top) give rise to asymmetry. The presence of hysteresis can only reduce the asymmetry (reduce the difference in the meniscus breaking forces), but cannot alone explain the asymmetry. In the rest of the paper, contact angle hysteresis is assumed negligible. The sequence of menisci for a hydrophobic plate (\u03c6 > 1 2 \u03c0) for its various heights is shown in figure 2(b). Here, no meniscus is formed when the plate is moved away from the liquid surface. In order to estimate the force prior to collapse in the experiment of figure 1, we estimate from the micrographs the average angle of the meniscus at the triple points with the vertical as \u03b80 = 24\u25e6 and 130\u25e6 corresponding to removal and submersion. Then, with \u03b3 = 0.072 J m\u22122 for water, and with a perimeter of 240 \u00b5m, the forces for removal and submersion are found to be 15.8 \u00b5N and 11.1 \u00b5N, respectively. The corresponding experimental values are 12",
+            " In other words, a small enough solid plate, hydrophilic or hydrophobic, no matter how dense it is, can float in any gravitational field, as long as the radius of curvature of the solid surface is larger than rc, the radius of the core region of the triple point. It is, however, worth noting that circular thin plates are difficult to fabricate when micro mechanical systems are formed by deep etching (such as deep silicon etching) or by filling a mould. A mathematical model is provided next. 3.2. Mathematical modelling We start by setting up the coordinates shown in figure 2(c). The triple point, L, is the origin, Y denotes the vertical axis (positive downward), S is the coordinate along the liquid\u2013vapour interface, \u03b8(S) is the angle that the tangent to the interface makes with the vertical at S . For the one-dimensional meniscus, the Young\u2013Laplace equation (equation (2.2)) can be represented as d\u03b8 ds = h0 \u2212 y with \u03b8(s = 0) = \u03b80, (3.3) which has been non-dimensionalized by the capillary length l0 = \u221a \u03b3/\u03c1g. Here, in reference to (2.2), 1/R1 = d\u03b8/dS , 1/R2 = 0, \u2206p = \u03c1g(H0\u2212Y ), the hydrostatic pressure assuming that the atmospheric pressure does not change with the small height of the meniscus, \u03c1 is the density of the liquid, and S = sl0, H0 = l0h0 and Y = l0y",
+            "5) where \u03b20 = 1 4 \u03c0 \u2212 1 2 \u03b80. h0 is positive when \u2212 3 2 \u03c0 6 \u03b80 6 1 2 \u03c0 or 0 6 \u03b20 6 \u03c0, and h0 is negative when 1 2 \u03c0 6 \u03b80 6 5 2 \u03c0 or \u2212\u03c0 6 \u03b20 6 0, i.e. the sign of sin \u03b20 is similar to that of h0, which is the reason for introducing the angle \u03b20. Equation (3.5) implies that h0 = H0/l0 can vary between \u22122 and +2 for all solids (hydrophilic and hydrophobic) and liquids under any gravity. For a given \u03c6, the geometry of the edge determines the possible range of \u03b80 and hence h0. For the flat plate of figure 2(a, b), \u03b80 can vary from \u2212( 1 2 \u03c0 \u2212 \u03c6) to ( 1 2 \u03c0 + \u03c6). If the edge is circular then the range increases, although the contact angle (\u03c6) remains the same. Thus, a hydrophilic or a hydrophobic solid can be designed to contact a liquid surface and move into the liquid without submerging itself, which offers micro actuators considerable flexibility for manipulating objects in liquids with a probe. For example, a thin plate attached to an actuator in air can form the meniscus preventing the liquid from wetting the actuator, whereas the probe attached to the plate may be inundated (figure 3)",
+            " Here, for simplicity, we assume that such a change in the interfacial energy for the bent plates considered later is small compared to ES and EH , and hence the analysis, when applied to the bent plates, is restricted to geometries where the solid\u2013liquid interface energy change is small. The bent plates are introduced only to illustrate a bifurcation phenomenon in menisci. 5.1. Energy for the meniscus formed by a single plate Consider a small element of the meniscus (liquid\u2013vapour interface) of length dS at an angle \u03b8 with the vertical (figure 2c). Its horizontal projection is dX = dS sin \u03b8. Then the liquid\u2013vapour interface energy of the element before and after formation of the meniscus is \u03b3dX and \u03b3dS , respectively. The elementary change in energy, dES = \u03b3(dS \u2212 dX) = \u03b3l0(1\u2212 dx/ds)(d\u03b8/\u03b8\u2032), and ES E0 = 2 \u222b \u03c0/2 \u03b80 (1\u2212 sin \u03b8) d\u03b8 \u03b8\u2032 = 2 \u222b 0 \u03c0/4\u2212\u03b80/2 \u22122 sin \u03b2 d\u03b2 = 4(1\u2212 cos \u03b20), (5.1) where \u03b2 = 1 4 \u03c0\u2212 1 2 \u03b8, \u03b20 = 1 4 \u03c0\u2212 1 2 \u03b80, E0 = l0\u03b3, the factor 2 outside the integral accounts for the two menisci on either side of the plate, and \u03b8\u2032 is defined by (3",
+            " It is contributed by the liquid column under the plate and the column of the liquid under the liquid\u2013vapour interface. The former gives an energy EH1 = \u03c1gH2 0W = \u03c1gl30h 2 0w = E0h 2 0w where H0 is the height of the column under the solids surface, 2W is the width of the plate, w = W/l0 and h0 = H0/l0. The contribution of the liquid column under the liquid\u2013vapour interface can be evaluated by considering a small segment of the interface dS with column height H(S). The energy due to the elementary column is dEH2 = 1 2 \u03c1gH(S)2dX, where dX is the horizontal projection of dS (figure 2c). From (3.3), \u03b3(d\u03b8/dS ) = \u03c1gH(S) giving H(S) = l20(d\u03b8/dS ) = l20(d\u03b8/l0ds) = l0\u03b8 \u2032. Thus, EH2 = 2\u03c1g \u222b \u221e 0 1 2 H2 dX = \u03c1g \u222b \u03c0/2 \u03b80 l30\u03b8 \u2032 sin \u03b8d\u03b8 = 2E0[\u2212 2 3 + cos \u03b20 \u2212 1 3 cos(3\u03b20)], (5.2) where the upper limit \u03b8 = 1 2 \u03c0 is arrived at as s \u2192 \u221e. Note that EH2 accounts for the hydrostatic energy of the meniscus on both sides of the plate. The total energy, E = ES + EH1 + EH2, normalized by E0, is given by E E0 = 8 3 + wh2 0 \u2212 2 cos \u03b20 \u2212 2 3 cos(3\u03b20). (5.3) Note that E = 0 when \u03b80 = 1 2 \u03c0 and H0 = 0, i"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000796_s0947-3580(01)70939-9-FigureI-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000796_s0947-3580(01)70939-9-FigureI-1.png",
+        "caption": "Fig. I. Geometry of scale model autonomous helicopter.",
+        "texts": [],
+        "surrounding_texts": [
+            "Consider Fig. 1. LetI = {Ex, Ey , Ez} denote a right hand inertial frame. Let the vector ~ = (x,y,z) denote the position of the centre of mass of the helicopter relative to the frame I. Let A = {EY,E2,E3} be a (right-hand) body fixed frame for the helicopter. The orientation of the helicopter is given by a rota tion R : A ----t I, where R E SO(3) is an orthogonal rotation matrix. The angular velocity of airframe with respect to the body fixed frame is denoted n while the angular velocity of the rotor blades around axis Adaptive Compensation of Aerodynamic Effects 45 of rotation is denoted 'W. Note that the position of the rotor blades is irrelevant and only the angular velocity of the blades is considered. Let m E lR denote the mass of the helicopter and I E lR3x3 denote the constant inertia matrix around the centre ofmass (with respect to the body fixed frame A). The dynamics of the helicopter airframe are modelled as rigid body motion [2,22,24] where sk(n) is the skew symmetric matrix associated with the vector product n x u = sk(n)u. The vector FE I combines the principal non-conservative forces applied to the helicopter airframe including main rotor thrust Tand drag terms associated with the rotor wake on the airframe (cf. Eq. (10\u00bb. The term ~ denotes the modelling error in the linear force input and r denotes the external torque applied to the airframe. Some brief comments on the nature of these terms are given below. For a detailed discussion of helicopter aero dynamics the reader is referred to any standard text on helicopter design (cf. for example [22]). Torque inputs r: Control input for the attitude dynamics is obtained via the tail rotor collective pitch and cyclic pitch input to the main rotor. Cyclic pitch inputs lead to a tilting of the rotor disk relative to the airframe and hence an inclination of the principal thrust component of the lift that, due to the offset between the rotor hub and centre of mass of the air frame, results in a torque input to the airframe attitude dynamics. The aerodynamic balance of the rotor disk is highly susceptible to local wind conditions and its tilting motion is strongly influenced by wind gusts and deformation of the rotor wake. Stabilisation of the attitude dynamics of a scale model autonomous heli copter (or indeed any helicopter) is a difficult problem. This is especially true when the helicopter enters the ground effect zone in which the rotor wake interacts with the earth's surface causing random wind gusts, the formation of vortices I and dynamic inflow reso nance effects [4,20]. These complex aerodynamic dis turbances tend to affect the roll and pitch stability of the helicopter first and lead to significant perturbation of the linear dynamics only if the motion of the heli copter tends towards instability. The stabilisation of ~ = v, mv = F + mge3 + ~, R= Rsk(n), H1= -n x In+r, (1) (2) (3) (4) the attitude dynamics is not the subject of this paper and we assume that a suitable low level robust stabilis ing control is implemented that satisfactorily regulates the torque inputs r. The torque input Ta used in the control design may be thought of as time-varying set point for the fast dynamics of the low level control. In the theoretical development we assume that r = Ta in order to focus on the adaptive control algorithm. In Section 4 the robustness of the proposed algorithm is simulated with a noise-like disturbance added to the actual torque inputs r = Ta + v(t). The disturbance v is chosen to model the types of input disturbances that may be encountered due to the complex aerodynamic effects mentioned above. Perturbation to the linear force input: Apart from some negligible noise effects the perturbation ~ incorpo rates an important dynamic coupling between the alti tude and linear dynamics. The expression used in Section 4 (Eq. (59\u00bb to model ~ for the robustness simulation corresponds to the form used in contem porary works [10,12,29]. The coupling leads to weakly non-minimum phase zero dynamics [10] that are qua litatively similar to those encountered for the original investigation of the VTOL [6]. Unlike the VTOL [17] the system is not differentially flat [12,15,29]. As a con sequence (to the best of the authors knowledge) there is no control design available that deals with the full non linear dynamics of the accepted model. The approach taken in prior control algorithms [2,3,16,25,26,31] is to design a robust controller for the system where ~ == 0 and analyse the robustness of the closed loop system with respect to the perturbation ~. We take an analo gous approach in the present paper. The focus of the present investigation, however, is on robustness and adaptation with respect to inaccuracies in modelling the force F; a different problem to that of robustness with respect to ~, and not one that has been considered in previous works. For this reason, and in the interest of a less complicated presentation, we analyse only the dynamic model Eqs (1)-(4) where ~ == 0 in detail and leave further discussion of the dynamic perturba tion ~ until Section 4. The dynamics of the main rotor disk around its axis of rotation is a decoupled system independent of its tilting motion. The torque exerted by the helicopter engine Te is transmitted via a flexible coupling to the rotor blades. The engine torque is opposed by an aerodynamic drag QM. The dynamic of the angular velocity of the disk is (5) I A discussion of this effect is given in Prouty [22, p. 138] for the case of forward flight. Local wind and uneven ground can generate this situation in hover conditions. where I M is the moment of inertia of the rotor disk around its axis. Lead-Iag motion of the rotor blades is negligible in this analysis. 46 R. Mahony and T. Hamel The lift and drag generated by the main rotor is directly affected by two input controls: The collective pitch that is the angle of the rotor blades with respect to the plane of the rotor disk, controlled by regulating the elevation of the swash plate, and the velocity of the rotor blades, controlled by regulating the throttle to the engine. As a first approximation the total thrust Tmay be approximated as [22, p. 15] the principal control input for the thrust T. Fix () to be a constant value such that the thrust generated at the nominal operating condition supports the helicop ter in hover. Dividing through Eq. (8) by w 2 and com pleting the square for vT/w one obtains (9) where VM 4> ~ tan(4)) =-, wrM (10) where b > 0 is an unknown parametric error. An important observation is that the sign of the constant b is known. Recalling the discussion following the model Eqs (1)-(4) the aerodynamic torque inputs applied to the airframe using the cyclic and tail rotor control inputs are r ~ - (Tt 2 3) ~ Ta - a,Ta,Ta \u00b7 Air resistance on both the rotors generate anti-torques applied to the airframe acting through the hub of the respective rotor (independent of the orientation of the actual rotor disk). With the collective pitch fixed to a constant value the air resistance on the main rotor blades is proportional to the square of the angular velocity of rotation of the rotor blades. Thus, one may write (cf. Eq. (5)) where dM , dT are unknown constants. The tail rotor and main rotor are mechanically coupled in all scale model autonomous helicopters resulting in the direct dependence of the tail rotor drag on w 2. The final tor que contribution to the airframe dynamics comes from the reactive torque exerted on the airframe by the motor. This torque is equal and opposite to the engine torque applied to the main rotor dynamics. may be thought of as an unknown parametric input uncertainty. The total force applied to the airframe in direction E'3 is (to a first approximation) F= (T-D M )E'3, where DM = CDMPV~ [22, p. 7] is the drag due to the rotor wake on the helicopter airframe (CDM is the drag coefficient of the exposed airframe times its surface area). The drag is proportional to the thrust T due to the quadratic dependence on the down-flow velocity VM (Eq. (7)); thus (noting that E} = Re3 one may write) (7) (6) where a small angle approximation is used for 'tan' vM is the down-flow velocity at the main rotor while wrM is the effective forward velocity of the rotor tip in the plane of the rotor disk. For hover condition in the absence of the ground effect the down-flow velocity"
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0000595_1.2828771-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000595_1.2828771-Figure3-1.png",
+        "caption": "Fig. 3 The instantaneous screw axis",
+        "texts": [
+            " How ever, low contact ratio and load capacity limit the application and working life of crossed helical-gears. In the theory of gear ing, two meshing surfaces in crossed axes are hyperboloids and the contact line is a screw axis (Litvin, 1989). In order to increase the contact ratio and load capacity of the crossed heli cal-gear, a novel type named Helipoid gears is proposed based on the concept of two meshing hyperbolids. Consider that the equations of the instantaneous screw axis MN, as shown in Fig. 3, are known. The axis of screw motion may be represented by the following equations: (32) Journal of Mechanical Design MARCH 1997, Vol. 1 1 9 / 1 1 1 Downloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/30/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use where b = \\OfM\\ and \u20ac = \\MN\\. The matrix representation of the hyperbolid represented in coordinate system Sf( Xf, Yf, Zf) is expressed by cos ifi sin (f 0 -sin ifi 0 cos ip 0 0 1 (33) Because the path of the hob cutter is parallel to the axial section of the hyperbolid, angle y can be obtained by considering Eqs"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001477_6.2001-4160-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001477_6.2001-4160-Figure2-1.png",
+        "caption": "Figure 2. Missile Coordinate System",
+        "texts": [
+            " Sample engagement scenarios with a nonmaneuvering target will be given to illustrate integrated guidance-control system performance. 2. Missile Model A six degree-of-freedom nonlinear dynamic model of an air-to-air homing missile is employed in the present research. The missile is controlled using four tail-mounted fins, and includes the logic to distribute the pitch, yaw, and roll commands to the appropriate fins. The missile equations of motion are expressed in the body coordinate system XB? YB, ZB illustrated in Figure 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 A ug us t 3 , 2 01 3 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /6 .2 00 1- 41 60 Successful operation of the missile requires it to approach the target as close and as parallel as possible, while maintaining a specific roll orientation with respect to the target. The equations of motion used in the present research are: p= \u2014 q=M ^~ /zV I* ' Iy Iy I _ _ \\ Nr = \u2014 - u = xci x\u2014\u2014\u2014 m \u00ab yci vi?v = \u2014 \u2014\u2014\u2014 \u2014-ur + wp, m zg \u2014 m -vp + uq In the above equations, u, v and w are the velocity components measured in the missile body axis system"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001833_1.2916914-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001833_1.2916914-Figure6-1.png",
+        "caption": "Fig. 6 Impact of a slider-crank mechanism with a free-block",
+        "texts": [
+            "C( Y) ,C(Z),0,0,0, - C(X), - C( Y), - C ( Z ) ,0 ,0 ,0] , where ciX), C(Y)> and c(Z) are the components of c in the XYZ reference frame. Different coefficients of restitution were con sidered to represent the energy loss in the collision of the two spheres as the system experienced multiple impacts. The motion of pendulum 1 is shown in Fig. 5 for a restitution coefficient of 0.5. As a second example, the impact between the slider of a slider-crank mechanism and another sliding block is considered [6]. A schematic representation of the system is shown in Fig. 6. Physical data for this example are provided in the Appendix. If a set of Cartesian coordinates is employed to describe the configuration of the system, then the system is kinematically constrained. The constraint equations correspond to the pris matic and the pin joints connecting different components. The slider-crank is driven by a restoring torque such that the crank maintains almost a constant angular velocity. At some instant, the slider impacts a free block which is inertially driven to the left at a constant speed"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002608_physreve.67.011710-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002608_physreve.67.011710-Figure1-1.png",
+        "caption": "FIG. 1. Illustration showing bookshelf vFLC smectic layers, the orientation of the FLC dipoles P, and the director/index ellipsoid axis c.",
+        "texts": [
+            "com 1063-651X/2003/67~1!/011710~12!/$20.00 67 0117 stiffened, yet the strength of the electrostatic effect is not so large that surfaces can be neglected. To account for this, simple models for surface anchoring forces have been added to the electrostatic model. The resulting dynamical equation has been used to numerically simulate vFLC switching and the result is compared to the dynamic response of a high-PS smectic-C* FLC cell. The computed vFLC switching time constant was found to be close to the measured value. Figure 1 is an illustration of the surface stabilized smectic-C* bookshelf structure ~suppressed helix!, in which the FLC molecules organize themselves into sheets ~smectic layers!. The FLC molecules\u2019 electric dipoles are confined to rotate within the smectic planes, while the molecule\u2019s long axes (; the director! are constrained to tilt away from the layer normal by a fixed angle u . This is also the direction of the optical index ellipsoid\u2019s extraordinary axis. As the director rotates through the angle f around the layer normal \u00a92003 The American Physical Society10-1 ~driven by an applied electric field E), the projection of the index ellipsoid onto the cell face changes, causing the cell\u2019s optic axis to rotate",
+            " The retardation G of the wave plate is a function of the index ellipsoid\u2019s ordinary and extraordinary indices of refraction no and ne , and of the angle c which denotes the degree to which the index ellipsoid\u2019s c axis tilts out of the plane of the cell @16#: G~c!5 2p@ne~c!2n0#L l , ~29! 1 ne 2~c! 5 sin2c n0 2 1 cos2c ne 2 . 0-8 The angles Q and c are related to the dipole orientation and FLC tilt angle u through the following relations: tan Q57tan u sin f , sin2c5cos2f sin2u . ~30! The (2) sign applies if the c director is clockwise from P as illustrated in Fig. 1, the (1) sign applies if it\u2019s counterclockwise. The standard configuration for viewing V-shaped switching is to place the vFLC cell between crossed polarizers such that the cell\u2019s z axis is parallel to the polarization state of incident light. The intensity of light transmitted by this assembly is I5I0sin2@G~c!/2#sin2~2Q!. ~31! In order to compare the models to a test cell, we need to know the FLC\u2019s values of PS , h , and \u00abF , and we need to know the cell\u2019s values for tA , \u00abA , and tF . The test cell\u2019s alignment layer was nylon-6 with tA51962 nm ~profilometer measurement",
+            " The ratio of Debye screening length to jP might be at least a crude measure of how 011710 important ions are. That ratio is estimated to be around 10 for the cell studied here, suggesting that ions might have had only a small effect. However, a better analysis is needed. This work was funded by the DARPA Liquid Crystal Agile Beam Steering program under Contract No. DAAH01-97C-0139 with the Rockwell Scientific Company. The author thanks Noel Clark, Mark Handschy, Michael Meadows, and Michael Wand for helpful discussions. Figure 1 is based on an illustration provided by Noel Clark. The FLC cells were built by Chris Walker who also measured alignment layer thicknesses. The FLC was supplied by Michael Wand. With the inclusion of dielectric anisotropy the torque equation @Eq. ~3!# becomes @19# h df dt 5EFPScos f~12a sin f!, ~A1! a[ D\u00abEF PS sin2u . This is the same as Eq. ~3! except for the term proportional to D\u00ab . Next substitute Eq. ~2! for EF into the expression for a: a52 D\u00ab \u00abF~f! V/VS1sin f 11 \u00abA \u00abF~f! tF 2tA sin2u . ~A2"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002580_robot.2003.1241777-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002580_robot.2003.1241777-Figure1-1.png",
+        "caption": "Figure 1 : HRP-2L",
+        "texts": [
+            " For running pattern generation, we introduce a new method nsing precise physical parameters of a robot. Aft,er discussing a hopping pattern for less power consumption, we show a realistic running under the consideration of the actuator limits. 2 Humanoid Model To build a running humanoid with conventional actuators, we must makei t as light as possible. However, there is a physical and technical limitation for weight saving. Therefore we decided to set the model parameter based on the specification of an existing humanoid robot. 0-7803-7736-2/03/$17.00 02003 IEEE 1336 2.1 HRP-2L HRP-ZL(Figure 1) is a biped robot that was developed in the Humanoid Robotics Project(HRP) of t,he Ministry of Economy, Trade and Industry of Japan[lO]. Table 1 shows the specification of HRP2L, and Table 2 shows the specification of leg actuators. HRP-2L has batteries and dummy weights, and these elements can be easily removed. Removing them and considering the little increase of weight for optional equipment for running, we assume that weight of HRP-ZL will be reduced to 30[kg]. This is about one-fourth of the HRP-l weight:117[kg]"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure2.19-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure2.19-1.png",
+        "caption": "Figure 2.19. A simple spatial mechanism.",
+        "texts": [
+            " The analysis of spatial motions, because of the increased complexity and the difficulty of visualizing the geometrical aspects of a problem, inherently is more difficult; but the use of vector methods in these applications often simplifies their analysis and eliminates our need to perceive all of the geometrical details. The application of vector methods to the solution of spatial problems demonstrates strikingly the power and utility of this invaluable analytical tool. This is illustrated clearly in the following example of a simple spatial mechanism. Numerous additional exam ples will be encountered in Chapter 4. Example 2.9. Two slider blocks A and B are connected by ball joints to a rigid rod, as shown in Fig. 2.19. The motion of A in cP = { F; ik} is controlled so that its translational velocity is constant during an interval of interest. Find 118 Chapter 2 in cP the translational velocity and acceleration of B, and determine the angular velocity and the angular acceleration of the rod in the interval of con cern. Assume for simplicity that the ball joints are centered on the axes of the slider guide shafts, and suppose that the joints are ideally smooth so that the rod suffers no angular velocity about its own longitudinal axis. What will be the effect on the rotation of the rod if the ball joint at B is replaced by a hinge pin and yoke assembly? Solution. The translational velocity of B is given by (2.27). We write v B = ik = v Bk = v A +(I) X I, (2.91) wherein the constant translational velocity of A is VA= yj = VAj (2.92a) and I= -ai - yj + zk, (2.92b) the vector of B from A, is obtained from the geometry shown in Fig. 2.19 for points on the axes of the guide shafts. Of course, (2.93) relates z and y. Differentiation of (2.93) yields 2zi + 2yy = 0, and use in this expression of the component relation from (2.92a) gives the translational velocity of B in cP. I.e., in (2.91 ), we now have (2.94) Kinematics of Rigid Body Motion 119 Moreover, because this equation is valid for all times in the interval of interest, the translational acceleration of B in r:f> may be obtained most easily by differentiation of (2.94 ). With the aid of (2",
+            " The angular velocity and angular acceleration of cp relative to tP at time t0 are given by ffi = 4e 1 + 2e2 - 3e3 rad/sec, Compute the first and second time rates of change of X as seen from cp at the instant of interest. Does v 0 affect the results? .w Problem 4.6. I, 320 Chapter 4 4.7. Consider the hinged joint and slider block shown in Fig. 2.20. Let frame 1 = { B; p, y, k} be fixed in the slider block B, as shown, and introduce another frame 2 = { B; a, p, A} fixed in the hinged yoke of the connecting rod AB so that A is parallel to!. (a) Determine as functions of y the angular velocity of the rod relative to B and the absolute angular velocity of B in the frame t:P = { F; ik} shown in Fig. 2.19. (b) What is the angular speed of the rod relative to the slider block? (c) What is the absolute angular velocity of the rod referred to frame 1? 4.8. Two gears A and B are held in rolling contact by a link of length I between their centers. The gear A rotates with an angular velocity OJ A relative to the fixed frame t:P = { 0; i, j }, while the gear B moves around the periphery of A with an angular velocity OJ B relative to t:P. Find the angular velocity of each gear relative to the link. Problem 4"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002434_0022-4898(91)90017-z-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002434_0022-4898(91)90017-z-Figure5-1.png",
+        "caption": "FIG. 5. At tachment of T-shaped sensors.",
+        "texts": [],
+        "surrounding_texts": [
+            "362 Y. NOHSE et al.\ncalculated f rom the moments of the L-shaped sensors using the equations:\nf = V ' { ( M 2 - M1)/ l l} 2 + {(M3 - M4)//14 + W} 2 (1)\n0 = COS -1 {M2 - M1)/(Fl l )} (2)\nR = {M1 + W ( l + l 3 + 14)}/{F - Lcos (o l - 0)} (3)\nwhere W is the net weight of the wheel system, M1, M2, M3, M4 are the moments measured by the strain gauges 1, 2, 3, and 4, respectively in the L-shaped sensors, I 1, 12, 13, 14, are the distances between the gauges and l is the horizontal distance between the position of gauge 4 and the center of gravity of the net weight of the wheel system. L is the distance f rom gauge 1 to the centre of the wheel, and c~ is the angle between the vertical beam and the straight line connecting these points.\nIn order to check the accuracy of the measurement , the minimum distance R ' f rom the center of the wheel to F was also calculated by\nR ' = T / F (4)\nwhere T is the wheel axle torque.\n(2) Torque. The axle torque of the wheel was measured by a pair of cross strain gauges.\n(3) Rotation angle. The rotation angle of the wheel was measured using a rotational potent iometer attached to the wheel axle.\n(4) Sinkage. The sinkage of the wheel was measured using a linear potent iometer .\n(5) Traveling distance. The traveling distance of the wheel was measured using a linear potent iometer .\n(6) Distribution o f the soil reaction. The normal and tangential stresses of the soil reaction were measured using T-shaped sensors [8, 9] (see Figs 5 and 6). Two groups of three T-shaped sensors (136 m m width each) were used in order to detect the variation of the stresses due to the travelling of the wheel and also the differences between the stresses in the central part and in the two outside parts of the wheel. The first group of three sensors was located where it would face the soil surface in the initial stage of rotation and the second group where it follows 180 \u00b0 later. The",
+            "Strain gauge 50\ncomparisons between the drawbar pull and the contact load measured using L-shaped sensors and those using T-shaped sensors are discussed in the following section.\n(7) Soil deformation. A new method for measuring soil deformation was developed, which uses markers of 25/zm semitransparent polyester film of 5 mm in diameter. One side of each marker had an imprinted black cross, and the reverse side was coated with adhesive. A dab of silicon rubber sealant was applied to the adhesive side, and also sand was sprinkled over it so that the markers would move in accordance with the displacement of soil particles. The markers, a few hundred in number, were wetted in the non-adhesive sides and applied to the inside surface of the acrylic wall at appropriate intervals (Fig. 7), and then the soil bin was filled with",
+            "364 Y. NOHSE et al.\nsand. Photographs of the markers were taken at regular time intervals, and from these the (x, y) coordinates of the centers of the markers were read by a digitizer and transmitted directly to the computer.\nStrain (Cauchy's infinitesimal strain) in the triangular elements formed by the centers of three mutually adjacent markers was calculated in the same manner as in the finite element method. The displacements of the centers of the markers were automatically depicted using computer graphics [10-12].\n(8) Measuring system. Data from all sensors was input to a multi-channel data logger (scanning speed 100 msec/CH) with an analogue-to-digital converter and then transferred to the computer via a GPIB. Mechanical quantities (1)-(7) were analysed and displayed graphically on the on-line computer system. The whole measuring system of the test apparatus is schematically depicted in Fig. 8.\nMeasured curves for each of the basic mechanical quantities of the traveling performance at 16.22% slip are shown in Fig. 9 as an example.\nAt slip within the range from 0 to 15% the drawbar pull increased monotonically to a stable value. With slip higher than 15% the drawbar pull increased to a peak value, decreased to a minimum value, and then recovered to a plateau with some oscillations. This phenomenon became more pronounced as slip increased.\nThe use of the linear bearings, with a frictional resistance between +5% of the contact load in the tests enabled the contact load to be maintained constant.\nThe torque curve showed oscillations synchronous with those in the drawbar pull curve.\nThe sinkage increased with the wheel rotation, gradually approaching a constant value, except when slip approached 100%.\nThe normal and the tangential stresses are the mean values of those detected by the three T-shaped sensors in each group. The peak normal stress measured by the second group was lower than that by the first one due to the increased contact surface area resulting from the increased sinkage as the rotation proceeded.\nThe relation of the maximum and mean drawbar pull to slip are shown in Fig. 10. \"Mean drawbar pull\" is the mean value during the period following the termination of output from the first group of T-shaped sensors and prior to the commencement of output from the second group, i.e. the range of almost 180 \u00b0 in rotation angle in a steady state."
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0003263_004051758805801102-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003263_004051758805801102-Figure3-1.png",
+        "caption": "FIGURE 3. Distribution of fiber cross section into class intervals.",
+        "texts": [
+            " (4) The distance of the center of the chord from the yam axis is x*=rcoscp , ( 5 ) The area is The area s(r) of the darkly outlined portion can be obtained from Equations 6 and 7: ~ ( r ) = ( r cos ~p - rj)V(d/212 - ( r cos ~p - rj)2 + r2 rcoscp- d / 2 t (d/2)* cos-I nd * (8) X (cp - sin cp cos cp) + - 8 where cp is given by Equation 4. Now let the cross section of Yarn be divided into annular rings of equal width h, such that thejth class interva1,j = 1 , 2 , . . . , is defined by the Smaller distance = h ( j - I ) and larger radial distance rj = hj. Consider a fiber, the cross section of which falls into five class intervals, ( j + 1) to ( j + 51, as shown in Figure 3. In the ( j + 1)th class interval, the area of the fiber is .T(Q+~), and in the (i i- 2)th class interval, the arm of the fiber is s(rj+2) - drj+t), etc. Similarly, in the ( j + 5)th class interval, the area of the fiber is S(r, + 4 2 ) - s(r,+,) = *d2/4 - s(r,+d). So by using Equation 8, we a n C ~ I - at Bobst Library, New York University on June 5, 2015trj.sagepub.comDownloaded from NOVEMBER 1988 629 culate the area of the fibers lying in the different class of the cross section. The ratio of the area of fibers in intervals"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002366_fuzzy.1998.687523-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002366_fuzzy.1998.687523-Figure1-1.png",
+        "caption": "Figure 1. Active magnetic bearing setup",
+        "texts": [
+            " Theorem 4 minimize y over Q = QT and Y,, subject to the following LMI constraints (uJi -Q4T+Bg. i .r .r . -71 B2 0 \"') -71 < q20) A,Q+QA~+BI;Y,+Y~BT, , 2 I < qal) -yI 0 CQ 0 -71 Q > q23) Given a solution (Q, Yi) of this minimization problem, the optimal H, state feedback gain is obtained as 4 Application to an Active Magnetic Bearing (AMB) System 4.1 AMB System The experimental setup which will be used is a t w e axis controlled vertical shaft magnetic bearing with 'a symmetric structure. An outline of this system is d e picted in Fig. 1. Due to the small gyroscopic effect of this setup [$I, the system can be divided into two identical subsystems (x-z and y-z planes). Thus, without loss of generality, we will focus our analysis strictly on the x direction motion only. The equations of motion for the AMB including harmonic disturbance can be represented as [8]: where x1 denotes the displacement of the rotor from the center position, x2 is the velocity, and i, is the control input current applied to the electromagnets. The harmonic disturbance w(t) created by the unbalance of the rotor is of the form w(t) = ap2 sin@) (26) where a denotes the unbalance parameter and p is the rotational speed of the rotor"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001397_70.897776-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001397_70.897776-Figure4-1.png",
+        "caption": "Fig. 4. Prototype parallel manipulator.",
+        "texts": [
+            " The noisy input data are obtained either directly from measurements on an experimental prototype or from simulations by adding a Gaussian zero-mean noise to the theoretical joint readouts; the noisy data are then submitted to each of the DPLS and CLS procedures in order to compute their estimates. For simulation, the actual poses of the EE are known from the prescribed trajectory; for experiments, these poses have to be computed from very accurate measurements taken with a coordinate measuring machine (CMM). Shown in Fig. 4 is the experimental prototype, manufactured with rather loose tolerances. Moreover, the joints of the prototype operate under no feedback loop. The EE is held at a specific pose by a stand placed between the two end-plates. A single instrumented leg is used, that is manually placed at each of the six leg locations. Potentiometers are installed on the first three joints. The output voltage of these sensors is sent to a multi-channel 12-bit A/D converter. The resulting digital values are the noisy input data to each of the estimation procedures"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001553_s0045-7825(99)00329-1-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001553_s0045-7825(99)00329-1-Figure4-1.png",
+        "caption": "Fig. 4. Axial pro\u00aeles of hob and worm disks.",
+        "texts": [
+            " The position vector OwN of the worm cross pro\u00aele is determined as qw hP qh hM d hM nh hM ; 13 where d hM MN apr hM \u00ff hP 2: 14 Here, nh hM is the unit normal to the hob cross pro\u00aele at M; apr is the parabola coef\u00aecient of parabolic function d hM . It is easy to be veri\u00aeed that tangency of Rh and Rw (of hob and worm thread surfaces) is identi\u00aeed as internal tangency of two helicoids along a common helix that belongs to the cylinder of radius OhP OwP . Worm pro\u00aele crowned surface Rw: Case 2. The hob thread surface Rh is generated by a shaped disk provided with a surface of revolution Rt. Fig. 4(a) shows that the axial pro\u00aele of Rt is a straight line, if Rt is a cone surface. The axial pro\u00aeles of hob and worm disks are in tangency at a chosen point P and deviate each from other at current point M of hob disk pro\u00aele (Fig. 4(a,b)). The deviation d hM MN is determined similarly to deviation represented in Case 1. Hob and worm thread disks are provided with surfaces Rt and Rc, respectively, that generate the hob and worm thread surfaces Rh and Rw as two helicoids being in tangency along a common helix that passes through point P. Worm double-crowning. The above described methods of worm pro\u00aele crowning of the worm yield that worm thread surface Rw and worm-gear tooth surface R2 are in point contact at every instant and the bearing contact is localized"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002810_iros.2005.1545293-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002810_iros.2005.1545293-Figure4-1.png",
+        "caption": "Fig. 4. Limit Distance Model",
+        "texts": [
+            " Both borders are elliptical shaped and have either the speaker or the speaker and listener at their center. 2) Conversation when two or more objects are close to- gether: When two or more objects in the environment are close together, it is difficult for listener to identify the object to only from pointing gesture and a reference term. We define Limit Distance as the distance in which we cannot distinguish the indicated object from the other objects only using pointing gesture and a reference term. The definition of Limit Distance is shown in Fig. 4. The definition shows that listener cannot distinguish the indicated object, if the edge of the other object intrudes into the scope of \u03b8P from the indicated direction. In other words, Limit Distance dLIM is the distance that includes scope \u03b8P and distance S from the object\u2019s center to its edge. The difficulty to distinguish the indicated object from the other objects is dependent on the distance between one object to another object, the distance from objects to the speaker, and the size of the object",
+            " RTM determines which reference term to use by the following rules: \u2022 If dSO \u2264 dLO \u2013 Use \u201cKORE\u201d when dSO \u2264 fKS(dSL, dSO, \u03b8L) \u2013 Use \u201cSORE\u201d when fKS(dSL, dSO, \u03b8L) \u2264 dSO and dSO \u2264 fSA(dSL, dSO, dLO, \u03b8LO, \u03b8L, \u03b8S) \u2013 Use \u201cARE\u201d when dSO \u2265 fSA(dSL, dSO, dLO, \u03b8LO, \u03b8L, \u03b8S) \u2022 If dSO \u2265 dLO \u2013 Use \u201cSORE\u201d when dLO \u2264 fSA(dSL, dSO, dLO, \u03b8LO, \u03b8L, \u03b8S) \u2013 Use \u201cARE\u201d when dLO \u2265 fSA(dSL, dSO, dLO, \u03b8LO, \u03b8L, \u03b8S) LDM estimates whether or not the listener can identify the indicated object with a pointing gesture and a reference term based on Limit Distance. Limit Distance dLIM is given by dLIM = f(S, L, \u03b8P ) = tan\u03b8P (L + cos\u03b8O1\u2212O2) sin\u03b8O1\u2212O2 where the parameters are described in Fig. 4. LDM decides whether the model uses an object\u2019s property by the following rules: \u2022 Use object\u2019s properties, when dLIM \u2264 f(S, L, \u03b8P ) \u2022 Don\u2019t use, when dLIM \u2265 f(S, L, \u03b8P ) OPM chooses an indicated object\u2019s property different from the other objects, which are all in the Limit Distance. OPM has a list of the object properties of each object, and by comparing each property among objects, the model finds the appropriate property. In this research, OPM, however, has only color as an object property. A system to get object properties and an algorithm to compare them are under consideration"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001423_s1350-4533(99)00095-8-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001423_s1350-4533(99)00095-8-Figure4-1.png",
+        "caption": "Fig. 4. The model assumes the path length of the central slip of the EDL changes primarily where it passes over the joint capsules (bold, black arcs). For a given tendon t at a given joint j, the radius of the joint capsule (rt,j), measured from the axis of joint rotation, is assumed constant. Thus, flexion of joint j from 0 to qj rad increases the path length by rt,jqj.",
+        "texts": [
+            " An\u2019s model, based on three-dimensional coordinates estimated from bi-planar photoradiographs, required six parameters per tendon per joint. The present model, based on one-dimensional measurements of tendon excursion, requires only three. The excursion of the EDL requires terms of two types. The first accounts for the central slip of the EDL; the second accounts for the contribution of the lateral bands. The model assumes that the path length of the central slip of the EDL changes primarily where the tendon passes over the joint capsules surrounding the heads of the metacarpal bone and the proximal phalanx (Fig. 4). Anatomical data [12] suggest that a circular arc is a reasonable approximation for the cross-section of the head of the average metacarpal. Thus, the cross-sections of the relatively thin, flexible joint capsules overlying the MCP and PIP are approximated as circular arcs centered on the axes of flexion. Accordingly, changes in path length are assumed proportional to joint flexion (Eq. (5)). Bt,j5rt,jqj (5) where rt,j is for tendon t, effective radius of joint capsule at joint j, and qj is the flexion angle of joint j in radians",
+            " The insertion of lateral bands is treated similarly. Point p \u2192 lat,union gives coordinates of the union of the lateral bands on the terminal extensor slip with respect to coordinate-system-3. Flexion of the distal joint qDIP is assumed to translate this point along the middle phalanx in the direction of x \u2192 3. coordinates of lumbrical origin (p \u2192 LUMo,straight) may be estimated with respect to the metacarpal bone (coordinate-system-0). Flexion of the finger joints {qMCPf, qPIP, qDIP} allows excursion of the tendon as determined previously (Fig. 4). This excursion is assumed to translate the lumbrical origin proximally by (Dp \u2192 LUMo). the EDL (Fig. 7). For simplicity, the kinematics of the extensor hood are initially calculated with respect to the first phalanx, coordinate-system-2. In this frame of reference, it is reasonable to assume the portion of the EDL central slip in contact with the first phalanx does not translate due to flexion or abduction of the MCP joint. When the finger is straight, a point on the extensor hood is given by ( 2p \u2192 hood,straight)"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002455_j.precisioneng.2004.03.003-Figure7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002455_j.precisioneng.2004.03.003-Figure7-1.png",
+        "caption": "Fig. 7. Location of balls for maximizing and minimizing fc (unit:nm): (a) location of balls for maximizing fc; (b) location of balls for minimizing fc.",
+        "texts": [
+            " The minimum\u2013maximum width, 0.05 m, equals 6\u03c3 (\u03c3, standard deviation) =\u00b1 3\u03c3, in other words \u00b1 0.025 m. The interval of diameter differences is 0.05 m/Z (Z, number of balls). In comparison with Fig. 3, which shows the result in the case that only one ball has a larger diameter by 0.05 m, the expected value decreases. Moreover, the reduction ratio of the fc component also decreases with increasing number of balls. When the fc component is maximized and minimized for Z = 10, the location pattern of balls is shown in Fig. 7. When the fc component is maximized, the larger balls are lined up serially and the smaller balls are lined up at the opposite faces. Furthermore, when the fc component is minimized, a large ball and a small ball are located neighboring each other in order to negate the diameter differences. Balls numbering several hundreds of thousand for rolling bearing are manufactured in a production lot. The required accuracy for each grade and each lot is standardized as in Table 3 [5]. Here, variation of diameter means the maximum (peak) to minimum (valley) value of diameters in one ball",
+            " Tables 4 and 5 show the experimental conditions and the location of balls respectively. The eight balls in type No. 695 bearing are numbered, and the larger diameter ball is symbolized by \u201cL\u201d, and the normal reference diameter ball, \u201cN\u201d in Table 5. The results are shown in Fig. 10. The location of balls has an impact on the fc component although the same number of larger balls are used as shown by the patterns of C and D, E and F and G and H. As a trend, when the larger balls are located serially, the fc component becomes larger similar to that shown in Fig. 7. This experimental result reveals that the location of balls has a significant effect on the fc component value even if the mutual diameter differences of balls are the same in a rolling bearing. This paper focuses on the theoretical analysis for the influence of the mutual diameter differences of balls, which cause the retainer revolution run-out component, fc, as the most important factor in NRRO of rolling bearing. Then, the influence of the location of balls is investigated experimentally. The main conclusions are as follows"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001884_1.1467089-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001884_1.1467089-Figure2-1.png",
+        "caption": "Fig. 2 Analytical model of a tripad slider",
+        "texts": [
+            " In this paper, we investigate the behavior of a tri-pad slider in the near-contact regime using a simple 2-DOF slider model with concentrated air bearing springs and dashpot. In addition, we clarify the effect of the rear to front air bearing stiffness ratio, the friction coefficient and the distance of the head-gap from the rear air bearing center on the spacing variation and the contact or friction force. Figure 1 shows the shape of a typical tri-pad slider with two front air bearing surfaces and one rear air bearing surface. The rear air bearing surface has a contact pad. Figure 1~a! is the bottom view, and Fig. 1~b! is the side view. Figure 2 shows the 2-DOF model of the tri-pad slider and the disk surface waviness which was utilized in this analysis. The tri-pad slider is modeled as a rectangle with length a and height b. The slider suspension system is represented with normal spring stiffness k, angular spring stiffness ku , and damping coefficients c and cu . The air bearing effects are represented by two lumped linear springs ~k f and kr! and dashpot ~c f and cr! which are separated from the center of the mass of the slider by d f and dr , respectively",
+            " Since the disk surface waviness generated by the computer algorithm includes only wavelengths longer than the contact pad length, and wavelengths shorter than the contact pad is regarded as roughness, which is neglected in the calculation, FH and h can be considered to be the height from the averaged envelop line of disk surface roughness. In other words, FH50 in this paper means that FH is equal to the sum of mean value and rms value of the asperity height in actual disks. For example, if the mean value and rms value of asperity height are 2 nm and 1 nm, respectively ~Ra of the disk surface roughness is about 1.4 nm!, FH521.3;2 nm in this paper corresponds to FH51.7;5 nm in actual disks. 3.1 Slider Vibration Modes. Since the slider model shown in Fig. 2 is a 2-DOF system in z-translation and pitch rotation, it has two natural vibration modes which affect dynamic characteristics of the spacing. Furthermore, since the system is changed between non-contact ~flying! and contact states, the lower and higher vibration modes should be considered in each state, in order to understand the following analytical results. Table 2 shows the natural frequency and the node points of the slider vibration modes in each state. f ni and lni are the natural frequencies and the node points, respectively"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002124_3.21202-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002124_3.21202-Figure3-1.png",
+        "caption": "Fig. 3 Phase plane of output q and be.",
+        "texts": [],
+        "surrounding_texts": [
+            "The design procedure can be divided into two steps as follows. A. Sliding Hyperplane Determination While in the sliding mode, i.e., S - 0, a certain linear dependence among the state is as below x2 = ~(GC2r (7a) thus the system in Eq.(4) can be reduced to the following n-m dimensional form (9) there exists a where K = (GC2) 1G. The following lemma is needed. Lemma 712'16: For a matrix C 2 e/? / I x m , matrix G e Rmxp such that K = (GC2)~1G in Eq. (9) can achieve some poles placement if and only if -f]<p- m (10) That is, if Eq. (10) holds, we can select K to stabilize the system in Eq. (9) first, and there exists a suitable G to satisfy G(C2# - /) = 0. Here the solution G may not be unique. Remark 1: It is noted that the exponential term <|) will decay to zero as t \u2014> \u00b0\u00b0 , hence it will not affect the equilibrium point of the system Eq. (7b). That is, the sliding hyperplane in Eq. (6) will converge to the following form: so the preceding determination of the matrix G by neglecting <|) is reasonable. Besides, the response prior to this convergence might be not very good. The decay rate of ty can be speeded up by increasing the value of p, however, the control gain will increase too. B. Existence Condition Satisfaction It is well-known that the output can globally reach the sliding hyperplane if1*2 (lla) Because the system is on the sliding hyperplane initially, we only need to consider the existence condition of the sliding hyperplane, i.e., limS (y)S(y)<0 (lib) (7b) and *(0 = x,(t) -(GC2)\"'GC, 0 -(GC2ylGy(0) exp(-pf) (7c) where / e R m x n m is an identity matrix. For convenience, the following notations are used in the sequel of this paper: <8a) (8b)= A12(GC2)-1Gv(0)exp(-pr) and -(GC2)-1GC1 e Rn x (n-m) (8c) The sliding hyperplane S(y) = 0 is determined by choosing the matrix G to stabilize the reduced-order system in the sliding mode. Neglecting the exponential term $ first, Eq. (7b) can be seen as a usual linear output feedback problem To achieve the existence condition in Eq. (lib), the following approach is helpful. Control Selection: For the given system in Eq. (4) with known bound of initial state jc(0), let the control u(y) be selected as (12) where sgn(S) = [sgn.^), ... , sgn(sm)]r, each sgn(^) is a signum function of s/, i = 1,2,. . . , m, defined as sgn(s;) = 1 for st > 0, 0 for Sj = 0, \u2014 1 for Si < 0. Let the constant control gain k E R satisfy the following inequality k > max [ (||GCA||2 + ||GC||2||AA||2) L + PI|Gv(0)||2] (13) where max(-) represents the maximum value of (\u2022) and L is defined as |(GC2)-!Gy(0)|2 (14) for t > 0, then Eq. (lib) holds, i.e., the existence condition is guaranteed. Reason: Substituting Eq. (12) into Eq. (4a) and differentiating Eq. (5b), it yields S = (15) D ow nl oa de d by U ni ve rs ita et s- u nd L an de sb ib lio th ek D us se ld or f on J an ua ry 1 6, 2 01 4 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .2 12 02 WANG AND FAN: VARIABLE STRUCTURE SYSTEMS 339 It is easy to see, if k > max [ (||GCA||2 + ||GC||2||AA||2) \\\\x(t)\\\\2 + PI|Gy(0)||2] (16) then the existence condition Eq. (lib) can hold. However, x(t) in Eq. (16) is not available, hence Eq. (16) should be modified as follows. Because at the initial instant S[y (0)] = 0, i.e., the initial output is on the sliding hyperplane. From the concept of the equivalent motion, while in the sliding mode, we have the reduced-order system as follows with the aid of Eqs. (8a) and (8b) (17) S(y) = 0 with the initial state *(0). Solving Eq. (17), we get *!\u00ab = exp[A1(r)]jc1(0)+ exp[A1(r-T)]ct)(T)dT (18) For a stable matrix A} and finite vector fy it is clear that both |exp[Ai(f) ]|| 2 and Ij^exptA^-T) ]<|)(T)dT||2 are limited tosome bounded values. The upper bound of the state vector x^t) is I I 2 (19) Further, by Eqs. (7c) and (8c), the upper bound of the state vector x(t) is (GC2) (20) Substituting Eq. (19) into Eq. (20) and according to Eq. (16), Eqs. (13) and (14) are obtained. Remark 2: It is noted that because y (0) lies on the sliding hyperplane 5 = 0 initially, the control u in Eq. (12) with the gain k in Eq. (13) is chosen to force v(r), for t = 0 + Af, 0 < Af <$c 1, remaining on S = 0; moreover, each term of right-hand side of Eq. (13) is taken to be norm value and the maximum value of it is considered. Therefore, we can conclude that Eq. (13) indeed gives a strong enough gain k such that y (f), t > 0, will be kept lying on the sliding hyperplane all the way. Consequently, the control selection is indeed workable. Remark 3: Because the control u in Eq. (12) may give rise to chattering due to the term of signum vector sgn(S), directly applying such a control signal to the plant may be impractical. To obtain a continuous approximation control signal, each element of sgn(S) can be replaced by a smoothing continuous function as17 (21) where each 8,- > 0 is a small positive constant. Because our control design only considers the existence condition of the sliding mode, the output trajectory should be confined to the neighborhood of the sliding hyperplane, so 5, cannot be too large, / = 1, 2 , . . . , m. However, how to choose a set of suitable 8, is still an open problem. IV. Illustrative Example It is difficult to find a practical example with multi-input system. Therefore, for convenience, we adopt the system of aircraft in Ref. 12 to be illustrated. -0.277 1 -0.0002 -17.1 -0.178 -12.2 0 0 -6.67 0 0 6.67 y = 0 1 0 0 0 ij a q A_ (22a) (22b) where a is the attack angle, q is the pitch rate, 8e is the elevator angle, u is the command to the elevator, and y is the measurement D ow nl oa de d by U ni ve rs ita et s- u nd L an de sb ib lio th ek D us se ld or f on J an ua ry 1 6, 2 01 4 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .2 12 02 340 WANG AND FAN: VARIABLE STRUCTURE SYSTEMS 0 .0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 which is not negative semidefinite. Therefore, the S(y) trajectory with initial state Jt(0) = [ 1 0 1 ]T does not decrease, i.e., the reaching condition Eq. (1 la) fails during a certain period of time (see Fig. 4)."
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0001061_s0021-9290(00)00032-4-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001061_s0021-9290(00)00032-4-Figure6-1.png",
+        "caption": "Fig. 6. Rotation from attitude (3) to attitude B was divided into two sections by attitude C. The positive 1803 rotation about the long axis (y-axis) of the limb segment from attitude (3) to attitude B can be obtained by the sum of two positive 903 rotations about the same axis from Attitude (3) to attitude C and from attitude C to attitude B. Therefore the gimbal-lock problem is avoided.",
+        "texts": [
+            " If the full cycle was divided into two sections and the axial rotation angle from the \"rst initial attitude n 1 to the second initial attitude n@ 1 is / 1 , and from the second attitude to any attitude in the second section is /@ 1 , then the axial rotation angle from the \"rst initial attitude to any attitude in the second section can be calculated by the additive law as: / 2 \"/ 1 #/@ 1 . (B.1) In the graphic example (Fig. 2), the axial rotation from attitude (3) to attitude B reaches 1803 that is a gimballock point. If an attitude C between the two attitudes was recorded, the problem can be solved by selecting attitude C as the second initial attitude and dividing the full period of time into two sections, attitude (3) to attitude C and attitude C to attitude B (Fig. 6). In the case there may be more than one gimbal-lock point, the number of sections can be determined depending on how many gimbal-lock points involved in an activity, which can be pre-determined according to the activities to be investigated. In order to avoid errors in computing with small angles (Woltring et al., 1985), it is suggested to keep the number of sections to a minimum in case there is no gimbal-lock point in each section. If the rotation in an activity was less than 1803 it is not necessary to divide the whole period into sections"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001771_elan.1140050107-Figure8-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001771_elan.1140050107-Figure8-1.png",
+        "caption": "FIGURE 8. Dimensionless forward (a) and backward (b) currents of quasi-reversible SW voltammograms; x = 1, y = 0.01 (l), 0.3 (2), and 2 (3). All other parameters are as in Figure 1.",
+        "texts": [
+            " If a SW voltammogram is recorded at a large electrode, when the sphericity is small, inspection of the cathodic and the anodic (i.e., the forward and the back- 36 KomorskyLovriC et al. ward) currents inay offer valuable information on the reversibility of the redox reaction [l]. On very small spherical electrodes, characterized by large sphericity, this information may be lost [5]. The variation of dimensionless foward and backward currents of quasi-reversible SW voltammograms under the influence of dimensionless electrode size ( . y ) are shown in Figure 8. At large values of?), A 4 f loses the maximum, while A+h loses the minimum, and both currents become similar waves separated by 2ESw mV. These principal variations are almost independent of the charge transfer rate. If a redox reaction appears reversible for any y , both currents become waves if y ? 2. The separation between the maximum of A 4 f and minimum of A+b is equal to 20 mV, if y 5 lo-', and increases to 25 mV for y = 0.01, to 35 m V f o r y = O. l , t o6OmVfory=O. j , and to95mVfor y = 1 (all for nAE = -5 mV and nEsw = k 2 5 mV)",
+            " Under these conditions, the SW peak potentials were found to be independent of electrode size if log ( y ) < -2, but depend linearly on log ( y ) , with a slope dEp/d log ( y ) = -2.3 RT/anF, if log ( y ) > 0.5. The simulated SW voltammograms of quasi-reversible reactions were also found to be similar to the corresponding responses found at microhemispherical electrodes. Square-wave voltammograms for oxidation of lo-* M ferrocene in acetonitrile recorded at a 5-pm radius gold inlaid disk microelectrode are shown in Figure 9. Both the forward and the backward components of the SWV response are sigmoidal curves, in agreement with theory (see Figure 8). The SW experiments were performed at four different gold inlaid disk electrodes ( r = 800, 30, 12.5, and 5 pm) and SW frequencies were changed over the range from 10 to 2000 Hz. The heterogeneous charge transfer rate constant for oxidation of ferrocene in acetonitrile has been reported to be equal, or higher than, 6 cm/s [17]. A diffusion coefficient D = 2.3 X cm2 spl was calculated from rotating disk measurements, which is in the range of the literature data [33]. According to the criteria proposed above, a redox reaction appears reversible if x/yo9 > 100"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002091_s0141-6359(99)00027-6-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002091_s0141-6359(99)00027-6-Figure3-1.png",
+        "caption": "Fig. 3. Schematic of the master axis with three capacitance probes.",
+        "texts": [
+            " The experiments are performed on a Bridgeport milling machine equipped with the standard ball-bearing spindle and variable speed drive. As mentioned in the previous section, static or dynamic loads can be applied to the master axis during testing. In the first experiment, a static load is applied in the cross-axis (x)-direction in a rough approximation of an average side milling force. A wire attaches to the master axis stator and carries a static load provided by weights hanging to the side of the machine. The wire cannot carry a moment, resulting in a nearly pure radial load on the master axis. Fig. 3 shows the PMA installed on the vertical milling spindle. In the second experiment, the static load is replaced with a 100 Newton electrodynamic shaker to apply dynamic loads in the x-direction. The PMA shown in Fig. 3 is built from a Professional Instruments BLOCK-HEAD 3R spindle with an integral Data General, 1024 count rotary encoder. The 3R spindle is rated to 15,000 rpm with error motions less than 25 nanometers. The integral rotary encoder provides tachometer and timing pulses used in data collection and spindle error motion calculations. The PMA is held in the milling machine with a collet holding a 2-cm arbor rigidly bolted to the rotor of the master axis. All measurements are made with Lion Precision DMT10 capacitance gauges calibrated to 40 mV/micron"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002386_ip-cta:20030017-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002386_ip-cta:20030017-Figure4-1.png",
+        "caption": "Fig. 4 Regulation based on LFM",
+        "texts": [],
+        "surrounding_texts": [
+            "where and the membership functions RI and R2 are, respectively,\nAssuming that Theorem 3 holds when n = k , then the nonlinear function fx+ I =xIx2...xk+ I can be represented by a weighted linear sum of linear functions of XI in the following form:\n(r:+lnk+l I + 2 rk+lnk+l 2 )),TI\nHence, Theorem 3 holds for all n\nCorollary I [17]: Assume thatx(t) E [Q, Rz]. The nonlinear term\nf ( x ( t ) ) = sin(x(f)) (3 1) can he represented by a linear weighted sum of linear functions of the form\n.fM)) = (i P ; ~ , ( ~ w ) x ( t ) (32)\nwheregl(x(f))= I, g2(x(f))=a and\n11, = rl. r , = , r2=-p2 = r2 sin(.r(f)) - m(f)\n(1 - ' * )X( t )\nx(t) - sinl:~y(t)) (1 - a)z-(t)\nfor x(f) # 0\nr , = I , r2 = 0 for x(t) = 0\na = sin-'(max(R, n,)) Proof It follows directly from Theorem 3. Using Corollary I , an exact T-S fuzzy model of (26) can be represented as follows [17].\nPlant rules:\nRule I : IF xl(f) = RI THEN ~ ( t ) = A,x(t) + B , u ( f )\nand\nRule2: IF x,(t) E THEN ~ ( t ) =A,x(t) + B2a(t) ( 3 3 )\nwhere\n0 1 0 0\n; i :] A z = [ - < - - - I -_ :! B I = ~ = [ ; \\ - 0 -k - 0 - J J aMgl k 0 1 0 0 0 k 0\nJ J J (341\nfor xl(f) # 0 (35)\nr , = I, r2 = 0 for xl(f) = 0\nwhere a = sin-' (max(RI Q,)) and Ti is positive definite for all x l ( f ) E [Q, Q,]. In the simulation, [a, Q2] was chosen as [ -2 .85 2.851.\nAlthough the exact fuzzy model of the flexible joint manipulator does not have any modelling uncertainties since the defizzified output of the T-S fuzzy model is exactly the same as that of the original nonlinear flexible joint manipulator (26), the exact modelling scheme may have some demerit. If the nonlinearities in the system model have very complicated form or the number of them is very large, the methodology presented in Theorem 3 cannot he applied easily.\nAn alternatice T-S fuzzy modelling technique, the linearisation method is often utilised to construct a T-S fuzzy model for a nonlinear system. The linearisation based T-S fuzzy modelling technique is the most popular as it is simple and the consequent rule base becomes intuitive although the modelling error inevitably exists.\nBy applying the Lyapunov linearisation method [17] at operating points xI = - x , 0, x , we obtain the T-S fuzzy model for the robot manipulator as follows:\nR u l e / : I F x l - - x T H E N i = A , x + B I u Rule2: I F r l Z O T H E N i = A 2 x + B Z n Rule 3: IF x, THEN i = A 3 x + B 3 u\nr o 1 0 0 1\nk J\n0 1 0 0\nMgI k 0 - 0 k\n0 0 0 1 k J J\nI\n0 -- k O\nand\n0 Bl = B2 = B, = [ The whole state space formed by the state vector of the original nonlinear equations is partitioned into three different fuzzy subspaces whose centre is located at the centre of the corresponding membership functions shown in Fig. 2.\n4.2 Control results To apply the proposed adaptive fuzzy control scheme, the reference model for the plant state x to follow should be specified. In this simulation, the closed-loop eigenvalues for each subsystem are chosen to he the same, which in\nI\u20ac\u20ac Proc.-Corrml T h m q Appl.. Yol. I50 No. 2. Mcarch 2003",
+            "The PDC controller shares the same fuzzy sets as the fuzzy model to construct its premise part. That is, the PDC controller is of the following form:\n...... reference model 12-\nR': if xi is MF;,\nthen ~ ( t ) = -Ki[.rl xz xi x4]' + L,r(t) (38)\nThe feedback control gains Ki and L; of each fuzzy state feedback controller are updated by adaptive law so that the closed-loop plant follows the reference model (37).\nNow, by using (22), we derive the adaptive law for updating the elements of K j and Lj so that the closedloop plant follows the reference model:\n.\n.'.. ...... LFM based . . .\nwhere B:, = [0 0 0 11\nThe parameters of the nominal plant model used in this simulation are as follows:\nM = 0.2687kg J = 0.03 kgm' L = I m,\nk = 3 1 N / m J = 0 . 0 0 4 k g m 2 and g = 9 . 8 m / s 2\n(40)\nTo test the adaptation abilities of the proposed scheme, the mass oflink is vaned with time as m = 0.2687 + 0.15 sin 3nt and the initial value for state xI is assumed to he xI = n/6.\nThe designed adaptive fuzzy controller was applied to the original nonlinear model of flexible joint maipnlator (26) in the simulation. Figs. 3-5 show the simulation results of regulation of joint angle with exact fuzzy model (EFM) and linearisation based fuzzy model (LFM). From these figures, it is shown that the regulation problem can be solved under parametric uncertainties. Figs. 6-8 show the tracking control results with both EFM and LEM. In both cases, the tracking can be accomplished successfully. The response characteristics of EFM based control such as response time is better than that of LFM based control. This is due to the fuzzy modelling ability of LFM. If more fuzzy rules, that is, linearisation at more operating points can be possible, the difference between the models can be reduced.",
+            "5 Conclusions\nIn this paper, we have developed an altemative T-S fuzzy model based adaptive control scheme via a model reference approach for flexible joint manipulators with parameter uncertainty in their model. We have used an exact fuzzy modelling method and a linearisation based modelling method to represent the flexible joint manipulator. The adaptation law adjusts the contmller parameters on-line so that the plant output tracks the reference model output. The developed adaptive law guarantees the boundedness of all signals in the closed-loop system and ensures that the plant state tracks the state of the reference model asymptotically with time for any bounded reference input signal. The proposed adaptive fuzzy control scheme was ;applied to the tracking control of a single link flexible joint manipulator to verify the validity and effectiveness of the control scheme. From the simulation results, we conclude that the suggested scheme can (effectively\nachieve the trajectory tracking in spite of parameter perturbation.\n6 References\nI KHORASANI, K.: 'Nonlinear fcedback control of flexible joint manipulator: a single link case study', IEEE Truns. Aulom. Conrrol. 1990. 35, ( IO), pp. 1145-1149 2 KHORASANI, K., and SPONG, M.W.: 'lnvafiant manifolds and their application to robot manipulators with flexible joints'. Proc. of IEEE Int. Conf. on Robotics and automation, St. Louis. 1985, pp. 110-1 16 3 KHORASANI, K.. and KOKOTOVIC, P.Y: 'Feedback linearization ofa flexible manipulator near its figid 5 body manifold', Swl. ConIml Lell., 1985,6, pp. 187-192 4 SPONG, M.W.: 'Modeling and control of elastic joint mdnipubdlOrs', ASMEJ Dyn. Swr. Mrur. Cuneoi, 1987, 109, pp. 310-319 5 LOZANO, R., and BROGLIATO, B.: 'Adaptive control of robot manipulators with flexible joints', IEEE Tmns. AuIom. Conool, 1992, 37.\n6 CHEN, K.P., and FU. L.C.: 'Nonlinear adaptive motion control for a manipulator with flexible joints'. Proc. of 1989 IEEE Int. Conf. on Robotics automation, Phoenix. AZ. 1989. pp. 1201-1207 7 TAKAGI, T., and SUGENO, M.: 'Furry identification ofsystcms and its applications to modelling and c u n l ~ d ' , IEEE Tronr. Sy.s~. Mun Cybern.. 1985. IS. (I). pp. l1&132 8 TANAKA, K., and SUGENO. M.: 'Stabiliryanalysis and drsignoffurzy control systems'. Fuzry Seis Sysl.. 1992. 45. (Z), pp. 135-156 9 WANG, H.O., TANAKA, K., and GRIEFIN, M.F.: 'An approach Io fuzzy ccntrol of nonlinear systems: stability and design issues', IEEE Tronr. FtmySy.~f, 1996, 4, ( I ) , pp. 14-23\n10 CHEN, B.S., LEE, C.H., and CHANG, Y.C.: 'H tracking dcsign of uncertain nonlinear SISO systems: adaptive fuzzy approach'. IEEE Tmns. FuzzySy.rt, 1996, 4, ( I ) , pp. 32-43 I 1 SPOONER, J.T., and PASSINO, K.M.: 'Stablc adaptive control u i n g hzy systems and neural networks', IEEE Trans. Fuzzy Svsr., 1996. 4,\n12 WANG, L.X.: 'Stable adaptive furry controllers with application lo invcrted Dendulum trackinr'. IEEE Trans. Fuzzy Swt.. 1996, 26, (5).\npp. 174-181\n(3). pp. 339-359\n- . . pp. 677-691\n13 TSAY, D.L., CHUNG, H.Y., and LEE, C.J.: 'The adaptivc control of nonlinear systems using the Sugeno-type of furry logic', IEEE Foni. Fuzzy $,.TI., 1999, 7, (2). pp. 225-229 14 FISCHLE, K., and SCHRODER, D.: 'An improved stablc adaptive furry control method', IEEE Trans. Furzy Svsr., 1999, 7, ( I ) , pp. 27-40 15 LEU, Y.G., WANG, W.Y., and LEE, T.T.: 'Robust adaptive fuzzy-neural controllers for uncertain nonlinear systems', IEEE TIans. Rohor. Aumm., 1999, IS, (5) . pp. 805-817 16 KAWAMOTO, S.: 'Nonlinear control and \"gorous stabiliry analysis bascd on fuzzy system for inverted pendulum'. Proceedings of IEEE Int. Conf. on F u u y Systcms, New Orleans, Sept. 1996, pp. 1427-1432 17 LEE, H.J., PARK, J.B., and CHEN, G.: 'Robust fuzzy control of nodincar systems with palametric uncertainties', IEEE Tmons. F t r q Svst., 2001, 9, (2), pp. 369-379"
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0003068_3.20450-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003068_3.20450-Figure1-1.png",
+        "caption": "Fig. 1 Problem geometry.",
+        "texts": [
+            " We shall make the following assumptions: 1) The pursuit-evasion conflict is two-dimensional in the horizontal plane. 2) The speeds of the pursuer (P) and the evader (E) are constant. 3) The trajectories of P and E can be linearized around their collision triangle. 4) P applies a fixed-gain proportional navigation. 5) E has complete information on P's system and on the collision course. 6) Each vehicle's acceleration is subject to a first-order lag. 7) E's lateral acceleration is bounded. (P's lateral acceleration may or may not be bounded.) Referring to Fig. 1, by assumptions 1-3 above we get the following equations: (1) (2) and R = Vp cos(7p0) - Vecos(yeQ) \u00ab V'p - V'e = const Joseph Z. Ben-Asher* and Eugene M. Clifft Virginia Polytechnic Institute and State University, Blacksburg, Virginia PURSUIT-EVASION problems traditionally have been classified among the classical examples of differentialgame theory.1 In recent years a different approach2\"5 has been applied to these problems, namely, to fix the pursuer's Received Dec. 21, 1987; revision received April 17, 1988"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001419_robot.1991.131938-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001419_robot.1991.131938-Figure2-1.png",
+        "caption": "Fig. 2: Basic Parameters of Turning Gaits and Coordinate Systems. (a) Clockwise f i r n i n g Gaits. (b) Counterclockwise Turning Gaits.",
+        "texts": [
+            " of nonlinear equations and inequalities and optimized the variables using the nonlinear programming method. In [lo], Zhang and Song also applied the six foot placing sequences to formulate turning gaits of a quadruped. However, they adopted a different approach, which was a combination of analytical and graphical methods, and developed several simple turning gaits. This paper is an extension of the work in [lo]. Assume that, the quadruped used in this study has four parallelpiped leg workspaces which have overlaps in the longitudinal direction (see Fig. 2) . Depending on the location of the turning center, the turning gaits can be categorized into spinning gaits and circling gaits. The for- 2106 CH2969-4/91/0000/2106$01 .OO 0 1991 IEEE mer are applied when the turning center is a t or close to the body center and the la.tter are suitable for a more distant turning cent,er. In the following, we will first discuss some important definitions and determination of gait stabilit,y margin in turning. We will then study the spinning gaits and optimize the gaits for Stability",
+            " We divide the procedure into three st,eps: 2.1. D e t e r m i n a t i o n of S u p p o r t T r a j e c t o r i e s For simplicity sake, we assume that the turning center is at a fixed point and the vehicle is turning about the center with a constant crab angle cy and a constant speed. Thus, the gravity center is tracing a circle. Hence, the supporting feet are also tracing circles with respect t o the body. I t is also assumed that the support trajectory of a leg passes i ts workspace center C;. Referring to Fig. 2, the chain-dashed circular path is the gravity center trajectory with respect t o the ground. The dashed rectangles are the workspaces of the legs. C, denotes the center of the workspace of leg i and S; and T; respectively denote the starting point and terminating point of a largest possible support trajectory. These positions of S; and T; determine the largest @;\u2019S. When the turning center is outside the workspace of leg i, the foot circular path of leg i has only two intersection points with i ts workspace boundaries, and S; and T; can be easily determined",
+            " If the support trajectory has no intersections with the boundaries a t all, i t is assumed that both S, and T, are coincident with the central point C;. If the support trajectory has more than two intersections with the boundaries, the two points, which are adjacent to the central point C;, should be selected to be the-points Si and T,. 2.2. D e t e r m i n a t i o n of G a i t A n g u l a r S t r o k e 9 Once the coordinates of the points S , and T, have been determined, the polar angles cya, and att of points S , and T, with respect t o the f rame X - 0 - Y (see Fig. 2. ) can be calculated. Thus, the largest leg stroke 9, can be computed as: 9, = 7 ( c y t l - c y s l ) , where 7 = $1 for clockwise turning and 7 = -1 for counterclockwise turning. In case that the angle ut? is smaller (or great,er) than cy,, for clockwise (or counterclockwise) turning, the largest angular stroke Q, should be determined by: Q z = 27r + q(atl - c y s l ) . For a regular and periodic gait, all the legs have the same dut,y factor and leg angular strokes. Hence, the maximum gait angular stroke @ is determined by the minimum of the largest +,\u2019S"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002380_ias.2000.882131-Figure8-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002380_ias.2000.882131-Figure8-1.png",
+        "caption": "Fig. 8. Current waveform for hysteresis control",
+        "texts": [
+            " High precision in this technique, however, demands a considerable amount of memory. In order to overcome this shortcoming, integration of the flux measurement with an analytical model of the flux or inductance is recommended. It also must be pointed that this technique cannot be applied at very low speed where integration error is significant. Given the fact that mechanical quantities (speed arid rotor position) change much slower than electrical quantities of the machine, one can use stifiess of the system to solve (8) within one chopping as shown in Fig. 8. Neglecting the effects of mutual inductances and assuming that mechanical quantities don't change within a consecutive rise and fall time, (1 1) can be rewritten as follows: I-' ar, 2vj ton +toff L j + j . - -(- ' c% Ai tonto# Although this method has a limited range of speed, has the advantage of simplicity and does not require any additional hardware [9]. VI. SENSORLESS CONTROL AT HIGH SPEEDS In constant power region, where current pulse is significantly shaped and limited by excessive back emf, absence of idle phases will reduce the options for sensorless operation"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001500_978-1-4899-1465-1-Figure6.13-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001500_978-1-4899-1465-1-Figure6.13-1.png",
+        "caption": "Figure 6.13. Permanent-magnet synchronous motor using surface mounted mag nets.",
+        "texts": [
+            " The figure shows the rotor with the magnet secured in place by slots in the lamination. The slots extending from the mag net cavity toward the periphery of the rotor aid in defining the direct axis magnetic path as a distinctly different magnetic path from the quadrature axis. The torque for the machine is thereby increased be cause of the saliency torque which is proportional to the difference between the reactances in the two axes. In this construction, the mag net is surrounded by die-cast aluminum which fills the rotor slots. A second, commonly used construction is shown in Fig. 6.13. The magnets are secured to the rotor surface and, in this design, there is no no Chapter 6 squirrel cage to provide induction motor-type acceleration. Therefore, the application of this design usually requires an adjustable-frequency power supply. The motor is locked into synchronism at a low frequency and then proceeds to its final operating speed by increasing the fre quency. The absence of the squirrel cage means that the motor must remain operating in synchronism at all times. If the rotor pulls \"out of step\" as a result of an overload or other condition, there is no recovery other than to stop the motor and resynchronize it"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001462_63.712321-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001462_63.712321-Figure6-1.png",
+        "caption": "Fig. 6. Graphical representation of equilibrium points for new DFO scheme at steady state.",
+        "texts": [
+            " Assuming that the system is stable and in steady state, the plant equations (10) and (18) can be replaced by steady-state plant where (29) Combining the plant (29) and the control (16), the necessary condition (30) can be deduced at steady state (30) The above necessary condition at steady state can be rewritten in an angular form (31) using the sum of two complex numbers and (31) with (32) or (33) (34) (35) Confining ourselves now to the case of a machine with positive speed ( ), under positive torque command ( ) and with an observer having a positive resistance error ( ), one can determine the existence of two possible steady-state slip frequencies ( ) which obey (31) through a graphical plot using the loci of and (Fig. 6). These two slip frequencies are given through the vectors and in Fig. 6 after fixing the vector [determined by machine speed and error in resistance and ], the angle (the torque command), and (the angular error in ). The existence of two equilibrium points and confirms the results of the transient analysis with being the stable point because of its lower slip frequency. It corresponds to in the transient analysis. Based on Fig. 6, if the error increases (increase in size of small semicircle) with other parameters ( , , , ) remaining unchanged, the vector increases in magnitude and the two vectors and will approach each other giving the limit condition on the existence of an equilibrium point given in Fig. 7 where . From Fig. 7, we can limit condition (36) The quantity is dependent on and thus also the speed of the machine. The speed that gives the worst situation where is smallest is when . This gives (37) Table I gives the limit condition on the angle for various values of based on (37)"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003316_1.1803609-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003316_1.1803609-Figure2-1.png",
+        "caption": "FIG. 2. Lens directions for the Riemannian cubic.",
+        "texts": [
+            " 11, November 2004 Lyle Noakes 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: 128.143.199.160 On: Sun, 14 Dec 2014 02:19:27 iVs2dstdi2 = c , s9d where b, cPR are constant. Set d=3siCi2+cd and d\u00b1=3siCi\u00b1\u00cecd2. Example 2: Taking v0, vT as 3 0.0000 0.9280 \u2212 0.3725 \u2212 0.6175 \u2212 0.1225 0.2121 0.7866 \u2212 0.2121 \u2212 0.1225 4, 30.0000 \u2212 0.2708 \u2212 0.2380 0.1155 \u2212 0.0224 \u2212 0.0388 0.3415 0.0388 \u2212 0.0224 4 , the curve of lens directions for the Riemannian cubic shown (thick) in Fig. 2 is less wavy in appearance than the curve for the adapted nonrecursive deCastlejau algorithm of Sec. I. These curves were generated in about 7 seconds on a 2 GHz PC running Mathematica. h There is a special class of Lie quadratics for which quite a lot is known: the Lie quadratic V :S\u2192E3 is called null when its constant C is 0. In Ref. 24 null Lie quadratics in E3 are shown to have constant (usually nonzero) curvature, linearly varying torsion, and two axes. The axes are rays through 0, to which V becomes C0 close as t\u2192 \u00b1`"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003153_146441905x63322-Figure14-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003153_146441905x63322-Figure14-1.png",
+        "caption": "Fig. 14 Positioning of visualization equipment",
+        "texts": [
+            " The communication between computers is established using Ethernet. Some examples of different views inside the virtual harbour are presented in Figs 13(c) and (d). The view from the cockpit mounted on the motion platform can be seen in Figs 13(a) and (b). The physical simulator environment is in a ventilated room. The room is painted with non-reflective colours so that the projected view can be seen more clearly and the outside world fades from sight. The view is projected obliquely forward to the motion platform, as shown in Fig. 14. The projection is done using a mirror attached to the floor and the operator sees the view on a transparent screen. This enables the positioning of the projector so that there will be no shadows caused by the structures of the motion platform. Real-time simulators have several advantages comparedwith traditional operator training. Themachine capacity is not tied to training and can be used in productive work. The use of simulators enables training for situations that can cause severe damage to the operator or environment"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002409_j.ecl.2004.01.001-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002409_j.ecl.2004.01.001-Figure4-1.png",
+        "caption": "Fig. 4. Schematics of the Autosensor and Biographer. (From Garg SK, Potts RO, Ackerman NR, et al. Correlation of fingerstick blood glucose measurement with GlucoWatch Biographer glucose results in young patients with type 1 diabetes. Diabetes Care 1999;22:1708; with permission.)",
+        "texts": [
+            " The Biographer is a small, wristwatch-like device that is worn on the forearm and contains sampling and detection means, electronic circuitry, and a digital display (Fig. 3) [15]. Three separate technologies are incorporated into the GlucoWatch Biographer: glucose sample extraction through reverse iontophoresis, glucose sample measurement by amperometric biosensor, and data verification and conversion using an algorithm leading to the display of the glucose reading [15]. The AutoSensor is a single-use, disposable component that snaps into the Biographer (Fig. 4). It has two identical sets of biosensor and iontophoresis electrodes, and two hydrogel disks. Hydrogel discs serve as the biosensor electrolyte as well as the reservoirs into which the glucose is collected. The glucose oxidase enzyme is dissolved into these hydrogel discs at a concentration sufficient to eliminate enzyme kinetics limitations on the biosensor signal. The Biographer provides 12 hours of glucose readings as often as every 10 minutes with up to six readings per hour. The readings are the timeaveraged measurements of the value 10 minutes earlier and the current value"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003897_009-FigureD.1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003897_009-FigureD.1-1.png",
+        "caption": "Figure D.1. Coordinate system for the region near the three-phase contact line.",
+        "texts": [
+            " Inserting that expression demonstrates that hm \u2248 (\u03b4\u03b6 )2 (\u22121)m 2 \u221a \u03c0 (m + 2) [ \u221e\u2211 k=0 2\u2211 i=0 (m + k + 1 2 ) I\u0302 (i) m (\u03b4\u03b6, k + 1) (\u03b4\u03b6/2)k + o(\u03b4\u22123) ] , (C.14) which are the higher-order corrections to hm given in equation (27). All of the ratios go as A2m+ 3 2 ,k+1 (\u03b4\u03b6 ); by substituting that function into equation (C.14), it can be verified that the sums over k are convergent when \u03b4\u03b6 2. D.1. Potential distribution Here we provide the potential distribution in the singular region near the line of three-phase contact and demonstrate that the energetic contribution of this region can be neglected in cases when droplets are large. Figure D.1 shows a coordinate system suitable to treat the contour along which the three phases meet. The region can be approximated as a wedge geometry, amenable to cylindrical coordinates. Let the axis of the cylinder be along the contact line, R denote a radial coordinate extending from the contact line, and give the azimuthal angle of the cylinder, which ranges from 0 at the electrode in region d to \u03c0 at the electrode in region s. With coordinates constructed in this fashion, \u03b1c retains the same definition"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000674_20.497338-Figure10-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000674_20.497338-Figure10-1.png",
+        "caption": "Fig. 10. The rotation angle of the \u2018two magnetization vectors within a pole\u201d tedmique for 2D correclions.",
+        "texts": [
+            " In order to solve this problem, we propose a \u201ctwo magnetization vectors within a pole\u201d technique. We define a variable angle which is determined by the shape of the magnetic field distribution near the surface of a magnet This means that the angle is determined by comparing the difference of the magnetic field distribution between experimental data and the calculated values. We modified the magnetization configuration as shown in Fig. 2 by two magnetization vectors within a pole and the angle between these two vectors is defined as shown in Fig. 10. As an example, Fig. 11 shows the torque at a separation distance of 712 2 mm for a 12-12 poles bonded NdFeB magnet device as a function of the angle defined as shown in Fig. 10. The curve shows an increase with angle from -40\u00b0 (at a) to a maximun near 20\u00b0 (at e). The corresponding calculated magnetic field distributions from (a) to (0 as shown in Fig. 11 are presented in Fig. 12. In general, experimental data are close to either (b) or (d) as shown in Fig. 12. Therefore, we can improve the 2D calculation by properly rotating the angle of the two magnetization vectors within a pole of the magnetic gears. In conclusion, 1.he torque of the radial magnetic coupling between magnetic gears with different magnetic poles and different magnetic materials has been studied as a function of the separation &stance by both 2D and 3D computer aided simulation"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003283_1.1850940-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003283_1.1850940-Figure1-1.png",
+        "caption": "Fig. 1 Actively lubricated tilting-pad bearing and oil injection system",
+        "texts": [
+            " A mathematical model is derived using two different approaches, aiming at including the effect of oil film active forces. Frequency response functions FRFs of the rotating system operating passively under 2005 by ASME Transactions of the ASME 2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded From: http://gasturbine conventional hydrodynamic lubrication and actively under active lubrication are theoretically and experimentally obtained, compared, and discussed. The actively lubricated bearing under investigation is built by four tilting-pads, in a load-on-pad configuration Fig. 1 . The active control forces acting on the rotating shaft are produced by injecting oil into the bearing gap through orifices machined in the pad sliding surfaces Fig. 2 . By coupling two hydraulic servo valves to the pair of pads arranged in the vertical and horizontal directions Fig. 1 , the pressure of the injected oil can be dynamically controlled. Thus, the hydrodynamic pressure, i.e., the main ering for Gas Turbines and Power spower.asmedigitalcollection.asme.org/ on 01/28/2 mechanism of bearing load capacity, can be altered among the different pads, and shaft vibrations can be attenuated aided by properly designing feedback control loops. It is important to emphasize that conventional lubrication is still the main source of load capacity in this hybrid bearing. In addition, the use of active lubrication in tilting-pad journal bearings has the strong advantage of its negligible cross-coupling effects between orthogonal directions"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001842_s0043-1648(01)00542-7-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001842_s0043-1648(01)00542-7-Figure2-1.png",
+        "caption": "Fig. 2. Deformation of a semi-infinite body caused by a line load w.",
+        "texts": [
+            " As it was shown in the above example, this assumption leads to an overestimation of the stiffness of the asperities in the elastoplastic regime. On the other hand, it simplifies the numerical formulation of the problem and minimises the time needed for the solution since it allows for better convergence. This is the reason why, even though the assumption of such a material behaviour is somewhat far from the experimental observations, it is adopted by many researchers [25,28,29,32]. In order to study the deformation of a rough surface, a semi-infinite body subjected to line load w along the line x = \u03be will be considered (Fig. 2). The vertical (i.e. along z-axis) deformation z(x) of a point (x, 0) on the surface is given by the well-known Flamant equation [42] z(x) = 2(1 \u2212 \u03bd2)w \u03c0E ( ln \u2223\u2223\u2223\u2223 d\u221e x \u2212 \u03be \u2223\u2223\u2223\u2223 \u2212 1 2 ) (15) where d\u221e is a distance in the semi-infinite body such as d\u221e x. A reference point (xr, 0) is defined on the surface far from x = \u03be , where the line load is applied. It is arbitrarily chosen since it does not affect the pressure distribution and the shape of the deformed surface. The deformation d(x) measured relative to this point is calculated by Eq"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002799_j.triboint.2005.03.022-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002799_j.triboint.2005.03.022-Figure1-1.png",
+        "caption": "Fig. 1. Hole-entry journa",
+        "texts": [
+            " The effect of surface roughness has been accounted by defining a non-dimensional surface roughness parameter L and a surface pattern parameter g. To account for the flexibility of the bearing, a non-dimensional parameter, called deformation coefficient \u00f0 Dc\u00de has been defined in terms of Young\u2019s modulus of elasticity (E), bearing shell thickness (th), radial clearance (c) and supply pressure (ps). The results presented in this paper are expected to be quite useful to the bearing designers and to the academic community. The geometry of a hole-entry hybrid journal bearing system along with rough surface is shown in Fig. 1. For an elastic bearing, the nominal fluid-film thickness including the bearing shell deformation is expressed as [17,18] h Z 1K XJ cos aK ZJ sin aC w (1) where w is the non-dimensional radial displacement of the fluid-film bearing shell interface. Assuming Gaussian distribution of surface heights, the non-dimensional form of average fluid-film thickness hT is expressed as [23] hT ZEf hC zgZ \u00f0N KN \u00f0 hC z\u00dej\u00f0 z\u00ded z (2) where Ef hC zg is the statistical expectation of local fluidfilm thickness hlZ hC z and j\u00f0 z\u00de is the probability density function of combined roughness z and is expressed as j\u00f0 z\u00deZ 1ffiffiffiffiffiffiffiffiffi 2p s p eK zK2=2 s2 (3) l bearing system",
+            " The bearing shell has been considered to be a threedimensional cylindrical structure of finite length. The deformation field has been discretized using three-dimensional 8-noded hexahedral isoparametric elements. Using three-dimensional linear elasticity equation, virtual work principle and finite element formulation, the system equation governing deformation in an elastic field has been derived [20] as \u00bd K f UgZ Dcf Frg (10) The bearing shell has been assumed to be enclosed in a rigid housing (Fig. 1) and hence, the displacements on the nodes of bush-housing interface is assumed to be zero. f UgZ f0g (11) The solution of the system Eq. (10), after modifications for relevant boundary conditions (Eq. (11)), gives nodal deformations. The bearing static and dynamic performance characteristic parameters are computed using the required expressions presented elsewhere [9,20]. The solution of a compensated hole-entry hybrid journal bearing system considering the combined influence of surface roughness and bearing shell flexibility effects requires an iterative scheme"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002159_6.1993-3761-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002159_6.1993-3761-Figure5-1.png",
+        "caption": "Figure 5, Effect of SCRAMjet Concept on Extemal Forces",
+        "texts": [
+            " So for combustion to occur, the injecton must be accompanied by rapid mixing, the fuel-air ratio must remain in an acceptable range, and the flow conditions in the combustor (e.g., flow ve1ocity)must be maintained. The air flow through the combustor, though su~ersonic. must be held less than the flame v . NC under-~ose NC Ref. Center Under-Afterbody speed, which in turn depends on the mixture ratio. Pressure Olstrlbutlon (e.g. centroid) Pressure Distribution Shown in Fig. 6, from [16,17], is the flame speed and A disadvantage of this concept is that the propulsive system will interact significantly with the aerodynamic control of the vehicle. With reference to Figure 5, from [14], the increased pressure acting on the forebody generates lift and creates a nose-up pitching moment. A counter-acting nose down pitching moment is generated by the external nozzle. Such interactions of the propulsion system with the mixture ratio-relation for hydrogen burning in air. In addition to fuel-flow rate, the engine control effectors may include some form of active inlet device, or some other mechanism for controlling the effective inleddiffuser area ratio AD. In addition, active control of the exit area of the internal nozzle may be required"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002426_s0013-4686(03)00274-3-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002426_s0013-4686(03)00274-3-Figure1-1.png",
+        "caption": "Fig. 1. Schematic view of the optically transparent thin-layer cell. AI, analyte inlet; AO, analyte outlet; CB, printed circuit board; CE, counter electrodes; EF, epoxy resin frame; EH, electrode holder; OS, O-ring sealing; PW, perforation of the working electrode; QW, quartz glass window; RC, reaction chamber; RE, reference electrode; WE, working electrode.",
+        "texts": [
+            " The quartz glass parts are received from Quarzschmelze Ilmenau GmbH, Germany, gold-, platinumand silver-foils from Goodfellow Cambridge Ltd. Furthermore, gold disk electrodes (\u00f8 2 mm, Metrohm) and Ag/AgCl-reference electrodes as well as platinum disk counter electrodes from Kurt-Schwabe-Institut Meinsberg have been used. 4-AP (Fluka, /98%) has been applied as obtained. Tetrabutylammonium hexafluorophosphate (TBAPF6) (Merck, /99.5%) served as supporting electrolyte. All chemicals and solvents were of analytical grade; the solutions were prepared by using double-distilled water. Fig. 1 illustrates schematically the basic design, a characteristic dimension as well as the shape and configuration of the electrode system of a new spectroelectrochemical cell, which has been developed by the Kurt-Schwabe-Institut. The optically transparent working electrode consists of a partially perforated 80 mm thick gold-foil. The lateral length of the square perforations, which were made by laser machining, is 0.4 mm and the strand with 0.1 mm, resulting in an approximate 64% optical transparency of the perforated section of the electrode"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001438_s0094-114x(98)00003-2-Figure7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001438_s0094-114x(98)00003-2-Figure7-1.png",
+        "caption": "Fig. 7. The plane of the object movement.",
+        "texts": [
+            " The minimal value of Finternal is determined by the weight of the object and the coe cient of friction at the contact points between the object and the robot end-e ectors and between the object and the environment. So the value of the internal force is determined by the task to be performed. The desired values of the internal force Fd internal, the maximum internal force Fmax,internal, and the minimum internal force Fmin,internal are given by the task planner. An example: two AdeptOne direct drive robots which have the same con\u00aeguration and physical parameters (Fig. 6), perform cooperative work on a single dynamical object, the motion of which is constrained by a dynamical environment (Fig. 7). The robot parameters are given in Table 1. The manipulated object is a polyhedral with a point contact with the constrained environment, with parameters given in Table 2. The environmental constraint is represented by a set of two mutually independent planes, de\u00aened in the Cartesian reference frame Or, Xr, Yr, Zr (Fig. 7): . horizontal plane zea\u00ff0.4 = 0; . vertical plane 2 3 p xea \u00ff 6yea \u00ff 1 0: 57 According to Eq. (57) and Fig. 7, the angle between the XT r -axes of the Cartesian reference frame OT rX T rY T r translated in the plane of the object movement, and the projection of the XT r - axes onto the plane 2 3 p xea \u00ff 6yea \u00ff 1 0 is a = arctg (yea/xea) = 308. The desired object positions in the XT r -direction and in the YT r -direction are de\u00aened by: xd0a t 0:4\u00ff 0:2 exp \u00fft=0:6 0:5 exp \u00fft=0:8 6 6 m yd0a t Fd ey=ky 1=cos a 3 p =3 xd0a \u00ff 0:2 6 6 m : 58 The desired object orientation is jd 0a 30 59 The coordinated robots have to simultaneously realize the following three tasks: . move the object along the desired object trajectory de\u00aened by Eqs. (58) and (59); . exert a nominal contact force Fd ey=20[N] = const. onto the environment in a direction normal to the environment constraint (Fig. 7); . regulate the internal force in the object in the region 0EFx intE500[N], 0EFy intE500[N]. The time duration of the object movement is t = 5[s]. According to Eqs. (35), (36), (42)\u00b1(44) and (47), with the notation used in the previous paragraphs, the model of cooperative manipulation in the example of cooperative work of two AdeptOne direct drive robots which have the same con\u00aeguration and physical parameters (Fig. 6), has the following form: N q q n q; _q;Y0a; _Y0a t 2 R6 1 60 W0a Y0a Y0a w0a q; _q;Y0a; _Y0a Fe 2 R3 1 61 Wca Yca Yca wca q; _q;Y0a; _Y0a Fc 2 R6 1 62 Yca _J q _q J q q 2 R6 1 63 where q qT1 ; qT2 T 2 R6 1 qi qi1; qi2; qi3 T; i 1; 2 Ya YT 0a ",
+            "06 kg m2 Hi qi I1 m*2l 2 1 m*3l 2 1 m*2l1r2 m*3l1l2 cos qi2 \u00ff qi1 0 m*2l1r2 m*3l1l2 cos qi2 \u00ff qi1 Icol: I2 I3 m*2r 2 2 m*3l 2 2 I3 0 I3 I3 264 375; i 1; 2 C q; _q _q G q C1 q1; _q1 _q1 G1 q1 ; C2 q2; _q2 _q2 G2 q2 2 R6 1 Ci qi; _qi _q1 Gi q1 \u00ff m*2l1r2 m*3l1l2 _q2i2 sin qi2 \u00ff qi1 VV1 _qi1 \u00ff VS1 sgn _qi1 m*2l1r2 m*3l1l2 _q2i1 sin qi2 \u00ff qi1 VV2 _q12 VS2 sgn _qi2 VV3 _qi3 VS3 sgn _qi3 264 375 i 1; 2 J q diag fJ1 q1 ; J2 q2 g 2 R6 6 Ji qi \u00ffl1 sin qi1 \u00ffl2 sin i2 0 l1 cos qi1 l2 cos qi2 0 0 1 1 264 375; _Ji qi \u00ffl1 _qi1 cos qi1 \u00ffl2 _qi2 cos qi2 0 \u00ffl1 _qi1 sin qi1 \u00ffl2 _qi2 sin qi2 0 0 0 0 264 375; i 1; 2: The direct kinematics is given by Yia xia yia jia 24 35 l1 cos qi1 l2 cos qi2 Xi base l1 sin qi1 l2 sin qi2 Yi base qi2 qi3 24 35 2 R3 1; i 1; 2; 65 where (X1(base), Y1)base)) = 0, 0), (X2(base), Y2(base)) = (1, 0) are the coordinates of the ith manipulator fundament (Fig. 7). The inverse kinematics is given by q11 arctg y1a x1a arccos x21a y21a l21 \u00ff l22 2l1 x21a y21a q 0B@ 1CA q12 q11 \u00ff arccos x21a y21a l21 l 2 2 2l1l2 q13 j1a \u00ff q12 q21 p\u00ff arctg y2a X2 base \u00ff x2a \u00ff arccos X2 base \u00ff x2a 2 y22a l21 \u00ff l22 2l1 X2 base \u00ff x2a 2 y22a q 0B@ 1CA q22 q21 \u00ff arccos x2a \u00ff X2 base 2 y22a \u00ff l21 \u00ff l22 2l1l2 ! q23 j2a \u00ff q22: 66 The state vector is z YT 0a 6 6 qT T YT 0a 6 6 qT1 6 6 qT2 T x0a y0a j0a q11 q12 q13 q21 q22 q23 T 2 R9 1 According to Eqs. (45), (35) and (36), matrices Wca and W0a are constant diagonal matrices: Wcadiag m1;m1; lz1;m2;m2lz2 diag m 7 ; m 7 ; lz 150 ; m 7 ; m 7 ; lz 150 2 R6 6 67 W0a diag m0;m0; lz0 5 7 m; 5 7 m; 1 2:61 lz 2 R3 3 68 where m and lz are the mass and the moment of inertia of the manipulated object about its mass center, m0 and lz0 are the mass and the moment of inertia of the manipulated object about its mass center after the contacts between the manipulators and the object are established (see Eq",
+            " (62) gets the form: m1 x1a dx 01 _x1a \u00ff dx 01 _x0a \u00ff kx01x0a \u00ff kx01x1a kx01 x00 \u00ff x10 F1x m1 y1a d y 01 _y1a \u00ff d y 01 _y0a \u00ff k y 01y0a k y 01y1a k y 01 y00 \u00ff y10 F1y Iz1 j1a d j 01 _j1a \u00ff d j 01 _j0a k j 01j1a \u00ff k j 01j0a M1z m2 x2a dx 02 _x2a \u00ff dx 01 _x0a \u00ff kx02x0a kx02x2a kx02 x00 \u00ff x20 F2x m2 y2a dy 02 _y2a \u00ff dy 02 _y0a \u00ff ky02y0a ky02y2a ky02 y00 \u00ff y20 F2y Iz2 j2a dj 02 _j2a \u00ff dj 02 _j0a kj02j2a \u00ff kj02j0a M2z: 72 In the above equations kx0i=ky0i=160,000[N/m], kj0i=30[Nm/rad], i = 1, 2 are adopted values of the sti ness coe cients; dx0i=dy0i=1000[N/m/s], dj0i=15[Nm/rad/s], i = 1, 2 are the adopted values of the damping coe cients of the linear and rotational motion. The generalized force Fe at the contact between the manipulated object and the environment may be decomposed in two contact force components: (i) Fey normal to the environmental constraint, and (ii) Fex_Fey (Fig. 7). The contact force component Fea is a sum of inertia, friction and elastic terms: Fey my y*0a hy _y*0a kyy*0a; 73 while the component Fex of the contact forces along the x* 0a>-axis are the sum of inertial and friction terms Fex mx x*0a hx _x*0a nxFey sgn _x*0a ; 74 where, according to Fig. 7, x* 0aO * 0ay * 0a is a new coordinate system, the x* 0a-axis is placed along the path of the movement of the object mass center when the force component Fey=0; the center O* = XT r +x* 0a; my=m0+me, m0 is the mass of the manipulated object, Eq. (1), me is the equivalent mass representing the inertial contribution of the environment, mx=m0, hy, hx, ky, nx denote viscous friction components, environment sti ness and static friction coe cient, respectively. Note that the x* 0a-axis is parallel to the environmental constraint, and taking into account the distance between the object mass center and the contact point d = 0.03 [m], in the OT r , XT r , YT r coordinate system the x* 0a-axis is represented by y0a 3 p =3 x0a\u00ff0.2. The numerical values are: n 0:14;m0 8 kg ;me 1 kg ; dy 500 N=m=s ; dx 10 N=m=s ; ky 50; 000 N=m : According to Fig. 7, the relation between the coordinates x0a, y0a, and x* 0a, y * 0a is given by: y*0a y0a \u00ff 3 p 3 x0a \u00ff 0:2 cos a 75 x*0a x0a \u00ff p* y*0a sin a 1 cos a ; 76 where p* = 0.346[m] is the solution of Eq. (75) when y* 0=y0=0 (Fig. 7). Having the expression for xd0a, and if F0 ey=20[N] = const. and ky are known, the desired object positions are de\u00aened in both coordinate systems: (i) OT rX T rY T r (Eq. (57)), and (ii) x* 0aO*y* 0a (Eqs. (75) and (76)). If the time duration of the object movement is t = 5 s, the length of the desired object path is L xd0a 5 \u00ff xd0a 0 2 yd0a 5 \u00ff yd0a 0 2 0:5 x d0a 0 \u00ff x d0a 5 0:346 m : The paper presents a mathematical model of multiple non-redundant rigid robot manipulators performing cooperative work on a single dynamical object of motion which is constrained by a dynamical environment"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003664_s0263574704000359-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003664_s0263574704000359-Figure2-1.png",
+        "caption": "Fig. 2. Geometric parameters of the HSM.",
+        "texts": [
+            " This paper is organized as follows: Hexa Slide Manipulator (HSM) and its kinematics are described in Section 2. Section 3 discusses the calibration device along with measurement procedure and formulation. Results of computer simulations are presented in section 4. Section 5 concludes the study. This section introduces the parallel robot, HSM, to which the proposed calibration scheme is applied and presents its kinematics. The schematic of the HSM is shown in figure 1 and the geometric parameters are defined in figure 2. It is a 6 DOF fully parallel manipulator of the PRRS type. In figure 2, Aio and Ail denote the start and the end points of the ith (i = 1,2, . . . ,6) rail axis. Ai denotes the center of ith universal joint and it lies on the line segment AioAil. Rail axes are identical and the nominal link length, , is equal for all kinematic chains. The articular variable, \u03bbi , is the distance between the points Aio and Ai. Bi denotes the center of ith spherical joint at the mobile platform. The posture of the mobile platform is presented by the position of the mobile frame center in the base frame and three Euler angles as X = [x y z \u03c8 \u03b8 \u03c6] (1) The Euler angles are defined as: \u03c8 rotation about the global X-axis, \u03b8 rotation about the global Y-axis and \u03c6 rotation about the rotated local z-axis"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002200_elan.1140060107-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002200_elan.1140060107-Figure2-1.png",
+        "caption": "FIGURE 2. CVs of a CuHCF/Nafion (8 prn)/GCE in 0.1 M phosphate buffer at pH 3.5 without (1) and with the addition of 0.5 mM (2) and 2.0 mM (3) cysteine; scan rate, 100 rnV/s.",
+        "texts": [
+            " Lowering the supporting electrolyte pH, on the other hand, resulted in a decrease of peak currents (by jO%, from pH 5.0 to 1.0) and virtually no variation on peak potentials, indicating that the CuHCF film conductivity is more favored in higher pH solutions. All of these observations are clearly responsible for the negative shift of peak potential and for the decrease of peak current on CVs of the CuHCF/Nafion/GCE on changing the supporting electrolyte from 1.0 M KCl to 0.1 M phosphate buffer at pH 3.0 (not shown). Electroca talysis Figure 2 shows the CVs of the CuHCF/Nafion/GCE in 0.1 M phosphate buffer (pH 3.5) without (curve 1) and with the addition of 0.5 mM (curve 2 ) and 2.0 mM (curve 3) Cys. Upon the addition of the analyte, the anodic peak current increased and the cathodic peak current de- creased, the extent of which was proportional to the Cys concentration added. Such a behavior is exactly what wouId be expected for an electrocatalytic CME oxidation. The electrocatalytic capability of the CuHCF/Nafion/GC toward Acy and GSH was also determined"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000561_a:1009888213333-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000561_a:1009888213333-Figure2-1.png",
+        "caption": "Figure 2. Mass on a plane.",
+        "texts": [
+            " The resulting equations of motion are Differential-Algebraic Equations (DAE) that need to be integrated, verifying that constraints are always maintained to avoid integration drift problems. In the next section, a discussion on the modeling issues is presented and the general numerical algorithm is described. An experimental double pendulum is used to validate the simulation. Before presenting the generalized algorithm applied to robot manipulators, the technique is illustrated through two simple examples. The first is the classical problem of a mass sliding on a horizontal plane as shown in Figure 2a. Using a simple static friction model characterized by the kinetic friction fk, the static friction fs , the relative velocity v, and the acceleration a, a friction model that would include stick-slip is given by the following conditional model: if  |v| > 0 \u21d2 f = sign(v)fk, v = 0 \u21d2 if { |F | \u2265 fs \u21d2 f = sign(F )fs and a 6= 0, |F | < fs \u21d2 f = F and a = 0. (1) This case is trivial since only one force is applied to the system. In Figure 2b, the mass is on an inclined plane, causing a more complex situation due to gravity affecting the motion. Using the same friction model, the conditions become: if  |v| > 0 \u21d2 f = sign(v)fk, (2) v = 0 \u21d2 if { |F \u2212mg sin \u03b8 | \u2265 fs \u21d2 f = sign(F \u2212mg sin \u03b8)fs and a 6= 0, |F \u2212mg sin \u03b8 | < fs \u21d2 f = F \u2212mg sin \u03b8 and a = 0. In both cases, at v 6= 0, friction forces are easily determined from Coulomb\u2019s model and accelerations can be computed. When the mass is at rest, the algorithm checks whether the applied force is high enough to initiate motion or not"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003797_0141-0229(84)90048-6-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003797_0141-0229(84)90048-6-Figure1-1.png",
+        "caption": "Figure 1 Schematic diagram of photomicrobial electrode. A, Polycarbonate membrane; B, immobilized Chlorel la vulgaris; C, Pt cathode; D, Pb anode; E, recorder; F, water bath; G, mirror; H, stirrer; I, reflector lamp",
+        "texts": [
+            " Construct ion o f microbial sensor Immobilization of C vulgaris was performed as follows. Algal suspension ( lml ) containing 1.7x10 s cells was dropped onto a porous polycarbonate membrane (Nucleo- 0141 --0229/84/080355--04 $03.00 \u00a9 1984 Butterworth & Co. (Publishers) Ltd Enzyme Microb. Technol., 1984, vol. 6, August 355 Papers pore filter, Nuclepore Co., Pleasanton, CA, USA, 0.4#m pore size, 2 5 m m diameter, 10/am thickness) with slight suction, and it was fixed on the Teflon membrane of the oxygen electrode. The photomicrobial sensor is shown in Figure 1. The sensor consists of immobilized algae and an oxygen electrode (Ishikawa Seisakujo Co., Model A: diameter 1.7 cm, height 7.2 cm; PVC casing). The sensor was fixed to a 50 ml reaction vessel. Procedure The system for the determination of phosphate was composed of the microbial sensor, a cell, an incubator, a recorder (TOA, Electronics Ltd, Model EPR-200A) and a reflector lamp. The temperature of the cell was maintained at 30 -+ 0.1 \u00b0C, and Tricine buffer (pH 7.6) was employed for the experiments"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003253_j.engfailanal.2004.12.035-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003253_j.engfailanal.2004.12.035-Figure3-1.png",
+        "caption": "Fig. 3. Curing process of the shafts.",
+        "texts": [
+            " Ultimately, this study will become a basis for the enhancement of the capacity of golf shafts and also for the development of their economical manufacturing technologies. Fig. 1 shows the generic patterns of golf shafts which are comprised of a double bias layer followed by the prepreg of a straight layer on the internal mandrel. As shown in Fig. 2, after the completion of laying-up, wrapping is required to maintain the pressure upon the shaft. Polypropylene tape is usually used for wrapping and the line pressure of the shaft is about 30\u201340 kgf/mm. Fig. 3 shows the curing process of the shaft in a hot-air oven. The hardening time in this process depends on the types of resin but the shaft used in this experiment was kept in an oven at 125 C for 90 min. Fig. 4 illustrates the shaft polishing process, which removes its coating and optimizes its delicate surface and size. The characteristics of a golf shaft can be investigated using four different mechanical parameter tests [3]. These four tests are as follows. The frequency of the golf shaft can be defined by its cycles per minute (CPM) when a mass of 205 g iron is hung at its tip, with its butt fixed as shown in Fig"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003358_12.563872-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003358_12.563872-Figure4-1.png",
+        "caption": "Fig. 4. Effective beam width of elliptical beam with triangular dither function",
+        "texts": [],
+        "surrounding_texts": [
+            "An important aspect of the LITI OLED process is the imager, named Alpha. Alpha is a second generation device designed to pattern Gen3 mother glass (550 mm x 650 mm) within an error budget of \u00b12.5 microns over the imaging area. It is based on two 16W Nd:YAG lasers operating in TEM00 mode and focused to a Gaussian spot of 30 microns by 330 microns (at 1/e2 intensity). A block diagram of the optical path is shown in Fig. 2. The system has an optical efficiency of 50% and the power on the film plane can be varied from 0 \u2013 16W. The optical design is based on the premise that transferred line edge quality and precision (e.g. edge roughness variation over the substrate surface) could be improved by increasing the slope of the laser intensity profile in the region of the transfer threshold corresponding to the line edge formation. The method of achieving this goal involves the oscillation of an elliptical beam transverse to the scan direction (figures 3 and 4).22 The oscillation is achieved via acousto-optic beam deflection. Variation of oscillation parameters such as frequency and shape (triangular, sinusoidal, etc.) allow the fluence profile to be tailored to the materials. Figure 5 illustrates the results of a mathematical model of the fluence profile for an undithered beam as well as a beam with three different dither functions. The elliptical beam shape is a factor in achieving the system\u2019s high cross-scan accuracy. However, this comes at the expense of imager in-scan accuracy. The result is that the current imager is configured to write accurate line structures, but not designed to write an arbitrary pattern that requires accuracy in the scan direction (e.g. a delta subpixel configuration). 16 Proc. of SPIE Vol. 5519 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 11/22/2016 Terms of Use: http://spiedigitallibrary.org/ss/termsofuse.aspx The optical design allows for continuous variation of several parameters including laser power, effective beam width, beam oscillation frequency, as well as choices for the dither function (e.g. triangular, truncated triangular, sinusoidal, etc.). Therefore, the Alpha imaging platform can expose donor films using a very large parameter space. In practice, these parameters, in conjunction with those of the donor film, are optimized in order to tailor the imaging process to the materials. -100 -50 0 50 100 0.0 0.2 0.4 0.6 0.8 1.0 N or m al iz ed La se rF lu en ce Distance (microns) -150 -100 -50 0 50 100 150 0.0 0.2 0.4 0.6 0.8 1.0 N or m al iz ed La se rF lu en ce Distance (microns) Fig. 5c truncated triangular dither Fig. 5d sinusoidal dither Figures 5a-5c: Representative Fluence Cross Sections"
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0001393_s0302-4598(98)00186-x-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001393_s0302-4598(98)00186-x-Figure1-1.png",
+        "caption": "Fig. 1. Biosensor assembly.",
+        "texts": [
+            "Sensor U.S. New Orleans USA . The electrode used was \u017dof the gaseous diffusion amperometric type Clark elec.trode . Since the original cap of the commercial electrode used \u017dwas unsuitable for operation in organic solvents which .very quickly corroded it , it was replaced with a similar cap of the same size made of Teflon. Also, the original rubber O-ring used to fix the gas-permeable membrane was replaced with a small Teflon ring. The O determina-2 tion electrode and the modified cap are shown in Fig. 1. The gas-permeable membranes were supplied by Radelkis \u017d .Budapest . The dialysis membrane used was a D-9777 \u017d .type supplied by Sigma St. Louis, MO, USA . The tests were run in a 15 ml thermostatted glass cell provided with \u017da forced circulation water jacket supplied by Marbaglass, .Rome connected to a Julabo model VC 20B thermostat \u017d .Germany . The solvent mixture used in the tests were kept under constant stirring using a magnetic microstirrer from \u017d .Velp Scientifica Italy . The comparative spectrophotometric tests were performed on a Perkin Elmer Lambda 15 \u017d ",
+            "0 ml of the \u017dsolvent to be used respectively, water-saturated chloroform, a 50% by volume mixture of water-saturated chloroform and hexane, water-saturated chloroform containing 1% by volume methanol and a 50% by volume mixture of water-saturated chloroform and hexane containing 1% by volume of methanol, obtaining a solution with a nominal titre of about 3.4 g ly1 in phosphatidylcholine. The titre of phosphatidylcholine standard solutions thus prepared was ( )L. Campanella et al.rBioelectrochemistry and Bioenergetics 47 1998 25\u201338 27 thus monitored spectrophotometrically, using the phospholipid determination kit complete with standard phosphatidylcholine solutions supplied by the manufacturers. \u017d .The proposed biosensor Fig. 1 was obtained by using two enzymes, phospholipase D and choline oxidase, both immobilised in kappa-Carrageenan gel as described in the following section and a gas diffusion amperometric electrode for oxygen as electrochemical transducer. Using this biosensor, on the basis of two enzymatic reactions in series: phospholipaseD lecithin \u2122 cholineqphosphatidic acid choline oxidase cholineq2O qH O \u2122 betaineq2H O2 2 2 2 it is possible to find a correlation between the substrate \u017d .phosphatidylcholine concentration and the oxygen consumed in the enzymatic reaction catalysed by the choline oxidase and, consequently, with the decrease of the current intensity circulating in the measurement apparatus",
+            "0 ml of glycine buffer 0.1 mol ly1, at pH 8.5, and sandwiched between the gas permeable membrane of a gas diffusion amperometric electrode for oxygen and the dialysis membrane. The whole assembly was then fixed to the teflon cap of the electrode with an O-ring, also made of teflon. In the second case, a disk of kappa-Carrageenan gel containing the entrapped enzymes was sandwiched between the gas permeable membrane and the dialysis membrane, and attached to the O electrode as in the preceding2 \u017d .case Fig. 1 . This second procedure, namely immobilisation in kappa-Carrageenan gel, was recently developed by w xour laboratory 17\u201319 . The original procedure involved preparing a 2% prp solution of kappa-Carrageenan obtained by dissolving 0.2 g of the polysaccharide in 10.0 ml of distilled water, and then, after carefully heating, the solution was kept under constant stirring for 15 min. The solution thus obtained was poured on to a Petri dish and allowed to cool, forming a jelly-like disk about 4\u20135 mm thick"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001516_0076-6879(95)46030-6-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001516_0076-6879(95)46030-6-Figure3-1.png",
+        "caption": "FIG. 3. Structure of the long path length OTTLEC thin-layer spectroelectrochemical cell.55",
+        "texts": [
+            " Depending on the length of the hole, the LOPLTTLEC has greater sensitivity than the conventional thin-layer cell. In this cell, the species diffusion is confined within a very thin cylinder. The electrolysis characteristics of the cell are similar to those in other OTTLECs. Zak et al. 54 reported a unique cell containing a glassy carbon or platinum plate with a large area as a WE. The incident light is passed through the solution parallel to the electrode surface. A simpler LOPLTTLEC is shown in Fig. 3. 55 This cell is constructed by inserting the composited one (Fig. 3A) into a colorimetric cell. 55 It can be used in 49 G. Mamantov, V. E. Norvell, and L. N. Klatt, J. Electrochem. Soc. 127, 1768 (1980). 50 S. K. Enger, M. J. Weaver, and R. A. Walton, lnorg. Chim. Acta 129, L1 (1987). 51 j . p. Bullock, D. C. Boyd, and K. R. Mann, Inorg. Chem. 26, 3084 (1987). 52 D. A. Smith, R. C. Elder, and W. R. Heineman, Anal. Chem. 57, 2361 (1985). 53 M. D. Porter and T. Kuwana, Anal. Chem. 56, 529 (1984). 54 j . Zak, M. D. Porter, and T. Kuwana, Anal. Chem. 55, 2219 (1983)"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001265_j.fss.2003.07.001-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001265_j.fss.2003.07.001-Figure2-1.png",
+        "caption": "Fig. 2. A single actuated gyroscopic system.",
+        "texts": [
+            " (a) If the output performance is unsatisfactory, then we can decrease the value in Step 4 to cope with the gains of the disturbances and delayed state uncertainties. In addition, when one decreases the parameter su=ciently, then the upper bound on the steady state errors Ne(t) can be made as small as possible. (b) From the above design procedure, the parameters j; j = 1; 2; : : : ; r, in Step 2 are assigned such that (13) is satis9ed. That is, the system designer can tune the size of the residual set by adjusting properly these parameters which are used in (15) or (29). In this section, we consider a gyroscopic system with single actuating input shown in Fig. 2 which is similar to that of [2] but with some slight di5erence in the assumptions made: the gimbals are rigid but is with a little unbalanced bodies and the conservation of the angular momentum constants are not zero. The gyroscope itself can be mounted on a base (aircraft, missile, etc.) that is moving with respect to the earth. Also, the case of the gyroscope can be mounted on a platform so that it can rotate relative to the base. The inertia of the system is concentrated in the rotor, with J as the radial moment of the inertia and I the axial moment of inertia"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001553_s0045-7825(99)00329-1-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001553_s0045-7825(99)00329-1-Figure3-1.png",
+        "caption": "Fig. 3. Cross-section of hob and pro\u00aele crowned worm.",
+        "texts": [
+            " Such an approach must be avoided because errors of alignment will cause edge contact on worm-gear tooth surface and transmission errors of unfavorable shape and impermissible magnitude [4,6]. The authors propose application of a worm that is double-crowned (in pro\u00aele and longitudinal directions) with respect to the hob to avoid the shortages mentioned above. Worm pro\u00aele crowned surface Rw: Case 1. The worm pro\u00aele crowning is accomplished by deviation of worm thread surface Rw from hob surface Rh. Fig. 3 shows cross-section pro\u00aeles of the hob and the worm that are in tangency at a certain point P, say the point that belongs to the pitch circle. The deviation of current point N of worm pro\u00aele from current point M of hob pro\u00aele is de\u00aened as MN . The position vector OwN of the worm cross pro\u00aele is determined as qw hP qh hM d hM nh hM ; 13 where d hM MN apr hM \u00ff hP 2: 14 Here, nh hM is the unit normal to the hob cross pro\u00aele at M; apr is the parabola coef\u00aecient of parabolic function d hM . It is easy to be veri\u00aeed that tangency of Rh and Rw (of hob and worm thread surfaces) is identi\u00aeed as internal tangency of two helicoids along a common helix that belongs to the cylinder of radius OhP OwP ",
+            " The worm is double-crowned and its surfaces R i w i I; II) and the unit normals to them can be represented as follows: r i w u i c ; h i c ;wc u i c cos a i c cos cc sin h i c sin wc cos h i c cos wc sin cc sin wc u i c sin a i c \u00ff a i \u00ff ci u i c \u00ff u i co \u00ff 2 h i Eo \u00ff apll2 w \u00ff cos wc u i c cos a i c cos cc sin h i c cos w\u00ff cos h i c sin w sin cc cos wc u i c sin a i c \u00ff a i \u00ff ci u i cw \u00ff u i cwo \u00ff 2 h i \u00ff Eo \u00ff apll2 w \u00ff sin wc u i c cos a i c sin cc sin h i c \u00ff pwwc cos cc u i c sin a i c \u00ff a i \u00ff ci u i c \u00ff u i co \u00ff 2 h i 266666666666664 377777777777775 ; 35 n i c v cw c f u i c ; h i c ;wc 0: 36 Here, (35) are the equations of the family of disk surfaces and (36) is the equation of meshing. The pro\u00aele deviation of the worm is determined by parabolic function dP i ci u i c \u00ff \u00ff u i co 2 i I; II ; 37 where u i c and u i co determine the current and initial locations of pro\u00aele point M i (Fig. 3) and ci is the parabola coe cient. The normals to the worm surface are represented by equation of meshing (36) and equation N i w or i w ou i c or i w oh i c ; 38 that yields N i w u i c ; h i c ;wc u i c cos a i c cos wc cos h i c sin a i c \u00ff 2ci u i c \u00ff u i co \u00ff n sin h i c sin wc cos cc sin a i c \u00ff 2ci u i c \u00ff u i co \u00ff sin wc sin cc cos a i c o u i c cos a i c \u00ff sin wc cos h i c sin a i c \u00ff 2ci u i c \u00ff u i co \u00ff n sin h i c cos wc cos cc sin a i c \u00ff 2ci u i c \u00ff u i co \u00ff cos wc sin cc cos a i c o u i c cos a i c sin h i c sin cc sin a i c \u00ff 2ci u i c \u00ff u i co \u00ff n cos cc cos a i c o 266666666664 377777777775 : 39 Simulation of meshing and contact of misaligned gear drive has been performed for a gear drive with design parameters represented in Table 2"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003532_bf00020157-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003532_bf00020157-Figure2-1.png",
+        "caption": "Figure 2. Typical stages of crack growth in compression: (a) unstrained; (b) compressed crack initiation at bound edges; (c) compressed - bulge separates from core; (d) unstrained - showing parabolic crack locus.",
+        "texts": [
+            ") shear modulus (MPa) testpiece thickness (mm) geometrical factor constant displacement subscript loaded area shape fac tor - force free area tearing energy (kJ/m 2) stored strain energy ( J ) strain energy density There is little published reference to the fatigue of rubber in compression. Early investigations by Cadwell, Merrill, Sloman and Yost [1] suggested that failure could occur when rubber blocks were subjected to repeated compression. Hirst [2] has reported that rubber railway buffers, in the form of bonded cylindrical blocks had chunks of rubber removed from the exposed edges similar in form to that depicted in Fig. 2. Lindley and Stevenson [3] have reported a preliminary investigation of fatigue crack growth in non-bonded rubber blocks compressed between rough (high friction) platens. The present paper 47 reports on the extension of this investigation to rubber discs of various sizes and shape factors bonded to metal endpieces. A fracture mechanics analysis is used. determining tearing energy, T (equivalent to strain energy release rate) and crack growth rate. d c / d .~,. The relationship between tearing energy and crack growth rate is compared with that obtained from more conventional fatigue crack growth tests in simple extension",
+            " For conditions of constant deformation, l; where U is the total strain energy stored in the testpiece and A is the area of one surface of the crack. Simple extension. For a uniform rubber strip with a single edge crack of length c, it has been shown [6] that in simple extension (see Fig. 1): r = 2/ wc (31 where W is the strain energy density at strain e, and K is a strain dependent geometrical factor which has been determined experimentally [8] and by finite element analysis [7]. Uniaxial compression. The present analysis refers to solid rubber cylinders bonded to rigid metal discs of the same diameter (see Fig. 2). For such units, the strain energy density W will depend on the shape factor. The shape factor S of a bonded rubber block is defined as the ratio of loaded (i.e. cross sectional) area to the total area of force free surface. For a cylinder of diameter D and thickness h S = D/4h (4) Rubber has a high bulk modulus (2000 MPa) relative to its Young's modulus E ( - 2 MPa) so that most deformations occur with negligible volume change. When a cylinder bonded between rigid end plates is compressed, the rubber bulges to maintain constant volume",
+            " This parabolic shape is consistent with the existence of a parabolic distribution of shear forces in the unit under compression, and has been assumed as a model in the following analysis. Consider a rubber cylinder of radius r, whose centre line is defined by the x-axis in Fig. 3. In this figure, which is a typical cross section, the parabolic crack locus is defined by ABC. The whole testpiece is defined by rotating A C D E about the x-axis. The rubber /meta l bond boundaries lie at x = + d and x = - - d , turned through 90 \u00b0 when compared with Fig. 2. The diameter of the core defined by crack growth is given by 2k. The testpiece thickness is ED, which equals 2d. The equation of the parabolic profile is: y = b x 2 + k , (7) thus r - k d v b = - d 2 and ~ x = 2cx . (8) The length of arc A B C between x = + d and x = - d (twice crack length) is given (b~ integration) as: 2 c = 1 + ( ~ dx d v d 2 2 ( r - / , - ) 2 ( r - k ) / ~ d 'i - 2( r - k ) sinh i d ~- d v d ~ + ~ - r - 7 ~ ~ ( 9 ) Equation (9) indicates that as r - k ~ 0, c -~ d (as expected) and also that as ( r - k ) ~ d, Now for an increase in crack length dc, there will be an increase in crack area dA and a volume of rubber dV from which strain energy is released",
+            " (b) At low compression strains crack initiation will be more likely at the bulge mid-plane and at high strains it will be more likely at the bond edge. (c) As shape factor increases the tendency for radial crack initiation at the bulge will decrease. Crack initiation becomes more likely at the bond at lower applied strains. The predictions (a) (b) and (c) will be compared with actual fatigue test results in Section 6. The compression testpieces consisted of rubber cylinders bonded to metal endpieces of equal diameter (see Fig. 2). The testpiece shape factor S was varied from 0.25 to 5.5 and rubber layer thickness varied from 2 mm to 50 mm. The rubber formulation in parts by weight was natural rubber (SMR CV60) 100 and dicumyl peroxide 1. The compounded rubber was vulcanized in metal moulds for 60 minutes at 160\u00b0C. This formulation gave a translucent rubber which enabled the progress of any cracking into the rubber to be seen with the aid of back illumination. The rubber /metal bonds were formed during vulcanization in the moulds using the bonding system Chemlok 220/205 supplied by Hughson Chemicals, USA",
+            " In one set of experiments with testpieces of shape factor 0,5 compressed to 25% however vertical cracking occurred which grew in a radial direction towards the centre. The inner edge of this type of cracking was observed to be approxi-mately parabolic in shape. These observations concerning the crack Iocii are in agreemeni with the predictions made on the basis of surface strain analysis in Section 4. In each case cracks grew to remove that rubber which at maximum deformation bulged outside the original profile of the cylinder. Thus an inner core was left (see Fig. 2d) beyond which crack growth either did not occur, or at least grew very much more slowly. The shape of the profile of the core was parabolic to a first approximation. It was an interesting feature of crack growth in compression that both the tearing energy, T and the crack growth rate d c / d N were approximately independent of crack length (see Fig. 7 for typical results). This result was the same as that reported previously [3] for fatigue tests with non-bonded rubber cylinders, and is confirmed as a general feature of fatigue crack growth in compression by the present experiments with bonded testpieces"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003550_s0022-460x(86)80032-3-FigureI-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003550_s0022-460x(86)80032-3-FigureI-1.png",
+        "caption": "Figure I. Non-linear frictional systems with (a) one and (b) two degrees o f freedom.",
+        "texts": [],
+        "surrounding_texts": [
+            "Two examples of systems with friction, of one and two degrees of freedom, respectively, which can'be in chaotic motion for some parameter patterns are shown in Figures l(a) and (b). The equation of motion of the system shown in Figure l(a) is ms (1) If I vo-~l ~< ~ (~ being a very small positive number) and Ikox(t)+ k2x3(t)- Po cos ~tJ < mg/.to, then x(t)= rot. Otherwise, more complicated solutions of equation (1) have to be found. In the work reported here, numerical solutions have been obtained by means of digital simulation. In this work the parameters in the equation were systematically varied, to provide a variety of solutions. Among these were a periodic and an almost periodic solution, as shown by their respective Poincar6 maps; i.e., the point sets on the phase plane (x, ~) with co-ordinates x and :~ such that the time interval between two consecutive 178 0022-460x/86/160178+03 $03.00/0 9 1986 Academic Press Inc. (London) Limited ones is T = 2~r/to. The strange attractor shown in Figure 2 was obtained for the following parameters: m = 1 kg; ko=0; k~ = 1 x 104 Nm-3; a =0-05; fl =0.02; #0=0\"6; Vo = 1 ms-~; Po = 10-5 N; to =23 s-L The initial conditions were x ( 0 ) = 0.001 m are ~(0) =0. Figure 3 shows the amplitudes of the Fourier components versus frequency for x(t) (FFT of chaotic motion). The frequency spectrum for the chaotic motion is continuous, whereas for the almost periodic vibrations it is discrete. By means of analysis of Poincar6 maps an assessment of the influences of the amplitude, the excitation frequency, the coefficients of the friction characteristic, and the non-linear rigidity, k~, on the size and position of the strange attractor, has been performed. The strange attractor was found to be most sensitive to the excitation frequency, among these parameters. The equations of motion of the system with two degrees of freedom shown in Figure l (b) are B(6+(k+k2)(l~ -x)l+c(o+koq~-clmlg sin ~ + kltp 3 = Mosin tot mE+ ( k + k2 ) (x - l~) = mg sgn (Vo-:~)[a + b exp (-d(vo-~))]. (2) 180 LETTERS TO THE EDITOR In this case, particular attention has been paid to the influence of the viscous damping coefficient c on the behaviour of the strange attractor. Figure 4 shows an example of a strange attractor for the following data: ko=0; k ~ = 1 0 0 0 0 N m ; c1=0.12m; B = 0.0073 kgm2; l = 0.1 m; m = 10 kg; ml =0 .5 kg; k + k2=3000 Nm-~; Mo=300 Nm; Vo = 0.2 ms-~; to = 10 s-n; d = 10 sm-n; a = 0.36; b = 0.32 and c = 0.001 Nms. For other values as well (c changing from _0.001 to 5.0). The Poincar6 maps on the plane (~p, ~) are sets of points in a particular-two-dimensional region, while on the plane (x, :~) they are sets of points placed on a straight line. The concentration of the points on the Poincar6 maps becomes greater as the damping value c increases."
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0003471_1.96982-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003471_1.96982-Figure3-1.png",
+        "caption": "FIG. 3. Photomicrograph of the 3\u00b7 angle-lapped sample after straining. Up per part shows the original surface, where n-type regions are observed as bright stripes. On the angle lapped region below the stripes, bright 0.4 pm depth n-type regions formed within the dark p-type substrate are observed.",
+        "texts": [
+            " This shows that the donor concentration can be changed by adjusting the pulse energy. Furthermore, it was confirmed that laser annealing of the bare silicon surface without sili con nitride film also resulted in donor formation, although a surface ripple occurred. The formation of a p-n junction between unannealed and annealed regions was confirmed by bevel and stain in the following manner. The sample shown in Fig. I was angle lapped (3\u00b0) and immersed in a solution of 200 cc HF and 0.1 cc HN03 under white light illumination conditions. The stained sample is shown in Fig. 3. Bright 0.4 /-lm depth n type regions formed within the dark p-type substrate are ob served. The diode characteristics of the p-n junction were mea sured by making contacts to a 1000 X 60/-lm n-type region and surrounding p-type substrate. The n-type region was fabricated as follows. After forming I-mm-wide aluminum TABLE l. Laser annealing conditions. Wavelength Pulse repetition Pulse width Pulse energy Beam diameter Scanning speed 0.53 pm 4kHz 50 ns 0-1.75 J/cm2 80llm lOmm/s 1205 Appl Phys Lett 48 (18)"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003364_0020-7403(88)90076-8-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003364_0020-7403(88)90076-8-Figure1-1.png",
+        "caption": "FIG. 1. (a) Contact configuration; (b) model of contact.",
+        "texts": [],
+        "surrounding_texts": [
+            "technique of [5] to analyse the case of steady-state tractive rolling, which often occurs in practical situations."
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure2.17-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure2.17-1.png",
+        "caption": "Figure 2.17. Application to bevel gear design.",
+        "texts": [
+            "82) Notice that the first of (2.81) states that the instantaneous speed s of the points of contact are the same, and the second of (2.81) means that their instantaneous rates of change of speed .~ are the same. Of course, as shown by (2.80), the accelerations of the contact points C and D are not equal. 0 Example 2.7. Bevel gears are used to transmit rotary motion between intersecting axles; and their meshed gear teeth assure that this motion will be transmitted without slip. A typical bevel gear arrangement is shown in Fig. 2.17. The bevel angles (} and 1/J are called pitch angles; their sum is the Kinematics of Rigid Body Motion 115 angle between the gear shafts. If the drive gear with a pitch angle 8 has an angular speed wd, determine the angular speed w1 of the driven, follower gear with a pitch angle \u00a2. Assume that the shafts are fixed in the machine. Solution. Because the gears turn about fixed axles and roll on one another without slipping, each pair of points of contact of the gears along their instantaneous contact line AB must have the same velocity. Let r d and r1 be the radii of the mutual rolling contact point A from points on the fixed axles, as shown in Fig. 2.17. Then, in obvious notation, (2.83) Introducing into (2.83) the pitch angle geometry from Fig. 2.17, we obtain the angular speed of the follower gear: w1= wd sin 8/sin \u00a2. (2.84) We see from this result that the angular speeds are independent of the gear sizes, so the same rule holds for both large gears and small gears. Also, (2.84) shows that WI~ wd fore~\u00a2, with Wt= wd when and only when e =\u00a2.In par ticular, when the shafts intersect in a right angle, 8 + \u00a2 = n/2 and (2.84) becomes 0 < 8<n/2. (2.85) Example 2.8. Helical gears may be used to transmit rotary motion between nonintersecting and nonparallel axles"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003657_j.cma.2005.02.033-Figure8-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003657_j.cma.2005.02.033-Figure8-1.png",
+        "caption": "Fig. 8. Planar slider-crank mechanism.",
+        "texts": [
+            " The formulation is very systematic and has been integrated into the DynaFlex computer software [15,16]. This multibody dynamics program has been written in the Maple programming language, so that the kinematic and dynamic equations are automatically generated in symbolic form. Three examples are given to demonstrate the efficacy of the proposed new formulation and its symbolic computer implementation: a slider-crank mechanism, a 3-DOF parallel robot, and an open-loop spatial manipulator. Shown in Fig. 8 is a planar slider-crank mechanism, moving in a horizontal plane and driven by a piston force F. The linear graph of this mechanism is shown in Fig. 9, where m1 m3 are the three rigid bodies, r4 r7 give the body-fixed locations of revolute joints h8 h10, s11 is the prismatic joint, and F13 is the driving force. To obtain the equations of motion in joint coordinates, qb \u00bc \u00bdb8; b9; s11 T \u00f028\u00de a single tree comprising r4 r7, h8 h9, and s11 is used by DynaFlex to generate both the rotational and translational equations",
+            " To generate the equations in indirect coordinates, the virtual revolute joint vh12 is added to the linear graph in Fig. 9 and selected into the rotational tree in place of h9. At the same time, the revolute joint h10 is selected into the translational tree in place of s11. With this separate tree selection, the number of coordinates is reduced from 3 to 2. The introduction of vh12 into the graph (and rotational tree) results in the set of indirect coordinates, qi \u00bc \u00bdb8; b12 T ; \u00f035\u00de where b12 is the absolute angle shown in Fig. 8. With only two coordinates, there is now only 1 constraint equation generated by DynaFlex, obtained by projecting the translational branch transformation for cotree joint s11 onto its reaction space defined by |\u0302: U\u00f0qi\u00de \u00bc l45 sin b8 l67 sin b12 \u00f036\u00de and the dynamic equations Mi\u20acqi \u00fe JT i ki \u00bc Qi are also reduced in both size and complexity. As an example, the augmented body inertias appearing in Mi are Mi\u00f01; 1\u00de \u00bc I1 \u00fe m1l2 4 \u00fe \u00f0m2 \u00fe m3\u00del2 45; \u00f037\u00de Mi\u00f01; 2\u00de \u00bc \u00f0m2l6 \u00fe m3l67\u00del45 cos\u00f0b12 b8\u00de; \u00f038\u00de Mi\u00f02; 2\u00de \u00bc I2 \u00fe m2l2 6 \u00fe m3l2 67"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003893_0301-679x(83)90004-x-Figure90-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003893_0301-679x(83)90004-x-Figure90-1.png",
+        "caption": "Fig 90ldham-type compensating coupling; {a] exploded view of basic conventional design; (b) stress distribution on contact surfaces in conventional coupling design; (c) Oldham coupling with preloaded rubber-metal laminates",
+        "texts": [
+            " Since the centre of the intermediate member during rotation describes a circle with diameter e and rotates at twice the rotational speed of the connected shafts, then the centrifugal forces within the steel intermediate member can be of very substantial magnitude. \u2022 Continuous sliding (and friction force) reversals in two sliding connections lead to intense noise generation, especially for high-speed applications. \u2022 Two sliding connections with substantial friction lead to noticeable energy losses. For small misalignments, e/D <~ 0.04, efficiency a [ e 7 7 = 1 - 8 - - - (5) rr cD where the factor c, describing the effective diameter of tangential force application (see Fig 90a)), depends on TR I BOLOGY international February 1983 21 the amount of clearance in the coupling (typical value c --- 0.8). For representative values of e(= 0.03 D) and f(= 0.15) the efficiency is only 0.985. \u2022 Angular misalignments of the coupling elements (1,2, 3) lead to a further reduction of effective load-carrying area in the connections and to increased peak pressures. Thus, angular misalignments are allowable only up to 0.5 \u00b0 . It seems natural to use thin-layered rubber-metal laminates to eliminate sliding friction in the Oldham coupling, and this has been proposed 9 "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003502_095440904322804439-Figure8-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003502_095440904322804439-Figure8-1.png",
+        "caption": "Fig. 8 Relative positions of the axle and wheel during the press-\u00aet, simulated by three subsequent passes 1, 2 and 3",
+        "texts": [
+            " The normal load N and tangential load 2F are continuously attained during the test by a PC and elaborated to obtain the mean friction coef\u00aecient: f \u02c6 2F=2 N \u02c6 F N \u20263\u2020 where N is here the average of the two load cells measurements, which are theoretically equal. The complete testing apparatus mounted on the machine is shown in Fig. 7. Some preliminary tests were carried out to investigate the effect of subsequent passes on the same specimen couple. Each pass represents in fact a sliding of 30 mm and subsequent passes can give useful information about the friction characteristic at different relative positions of the axle and wheel, as shown schematically in Fig. 8. The \u00aerst tests were carried out in a dry condition, at a room temperature of about 20 8C and a relative humidity of 40 per cent. A nominal pressure of 80 MPa and a sliding speed of 30 mm/min were applied. The results are reported in Fig. 9 for three subsequent passes, i.e. after a stroke of 90 mm. At a \u00aerst glance, a quite stable friction coef\u00aecient can be noted during each pass, apart from a border effect in the initial zone, which vanishes after about 2 mm. Secondly, the friction tends to slightly reduce its value with increasing passes"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002782_ip-epa:20030192-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002782_ip-epa:20030192-Figure3-1.png",
+        "caption": "Fig. 3 Cross-sectional geometry of the test motor",
+        "texts": [
+            " Then, the amplitude of the pulse should be optimised somehow. Unfortunately, if the displacement pulse is too large, the forces are no longer a linear function of the displacement [8]. The numerical accuracy of the finite element analysis also suffers due to the changes in the airgap mesh. The amplitude of the displacement pulse used in the analysis is 10\u201320% of the airgap. The test motor is a 15kW four-pole cage induction motor. The main parameters of the motor are given in Table 1 and its cross-sectional geometry is shown in Fig. 3. At first, the forces were calculated at no-load condition using rectangular pulse excitation. According to (4), the slips associated with the eccentricity harmonics are simultaneously zero when the whirling frequency is equal to the rotation frequency. The forces are divided into a radial component in the direction of the shortest airgap and a tangential component perpendicular to the radial one. Fig. 4 shows the computed radial and tangential components of the force with respect to the direction of the pulse"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001127_s0022112002002483-Figure11-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001127_s0022112002002483-Figure11-1.png",
+        "caption": "Figure 11. (a\u2013d ) Four possible menisci between two plates S1 and S2 with non-dimensional heights 1 and 2. The interaction force is identical for these four menisci. The plates are curved such that at the triple (solid\u2013liquid\u2013vapour) point the angle of the meniscus with the vertical can take the appropriate values resulting in four different menisci, and yet the meniscus can satisfy the fixed contact angle with the solid. The interaction force between S1 and S2 as a function of x0 is shown in (e) where the points B1\u2013B4 correspond to the menisci B1\u2013B4 of (a)\u2013(d ). The four solutions B1\u2013B4 originate from two bifurcation points P1 and P2. The meniscus, L1L2, between the solids at P1 is also shown. The energy (hydrostatic and surface) as a function of x0 is shown in ( f ). A numerical derivative of the lowest energy with respect to x0 coincides with the corresponding force\u2013distance curve as expected.",
+        "texts": [
+            " The energies corresponding to the four menisci A1\u2013A4 are represented by the filled circles A1\u2013A4 in figure 10( f ). The lowest energy curve is differentiated with respect to x0 numerically and the result is plotted on the force diagram. It matches the corresponding force curve as expected. Figures 11(a)\u201311(d ) show the four possible menisci between two solids S1 and S2 with h1 = 1 and h2 = 2, respectively. Note that h = 2 is the maximum allowable height (see (3.5) and the following paragraph) of the meniscus mR on the right-hand side of S2 with an angle \u03b8R = \u2212 1 2 \u03c0 at the triple point LR . Figure 11(e) shows the interaction force, Fx/\u03b3, which is attractive for all x0. The force corresponding to the four menisci, B1\u2013B4, are shown by filled circles B1\u2013B4 in figure 11(e). The solutions B1 and B3 are two bifurcation branches originating from P1 where the meniscus becomes closed. For x0 < x0P1 , where x0P1 is the distance between L1 and L2 at state P1, the meniscus of type B3 becomes non-physical, since it intersects with itself and continues beyond the point of intersection. Hence, only the meniscus of type B1 is retained. The solutions B2 and B4 originate from P2, and at x0 < x0P2 the meniscus of type B4 becomes non-physical, and the solution of type B2 is retained",
+            " The angle of this meniscus with the vertical when it reaches a height h = 1 must be the same as the initial angle for a single meniscus with h = 1, such as that formed by S1 on its left-hand side with an angle \u03b8L satisfying (3.5) for h = 1. However, \u03c0 \u2212 \u03b8L also satisfies (3.5) which is the value taken by \u03b81 at L1, i.e. \u03b81 = \u03c0\u2212 \u03b8L. At A0, \u03b81 = \u03c0\u2212 \u03b8L and hence the net horizontal force on S1 is \u03b3(sin \u03b8L \u2212 sin(\u03c0 \u2212 \u03b8L)) = 0. No solution for the meniscus exists for x0 < x0A0 . The energy variations for the menisci as a function of x0 are shown in figure 11( f ) where w = 1 is chosen for both the solids. Here, B1\u2013B4 correspond to the menisci B1\u2013B4 in figure 11(a)\u201311(d ). The points P1 and P2 in the force diagram become jumps in the energy diagram owing to the higher energy associated with the loop in the meniscus of types B3 and B4. The lowest energy curve (non-dimensional) is differentiated with respect to x0 numerically using a linear interpolation between adjacent energy values, and the derivative is plotted on the force diagram. As expected, the derivative coincides with the corresponding force\u2013distance curve. The study is motivated by the recent micro fluidic applications where thin plates may form menisci with a liquid and mutually interact with one another"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003292_s0167-8922(08)70696-5-Figure35-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003292_s0167-8922(08)70696-5-Figure35-1.png",
+        "caption": "FIG. 35 FTG. 36",
+        "texts": [
+            " When design ing bear ing arrangements t h e r e a r e c e r t a i n bas ic r u l e s which should be fo l l owed . Wherever p o s s i b l e o n l y one bear ing should be used f o r l o c a t i o n purposes. This means t h a t t he bear ing ou te r r i n g should be he ld a x i a l l y i n i t s housing w i t h t h e inner r i n g l oca ted on t h e s h a f t i n a s i m i l a r manner. All o the r bear ings on t h e same s h a f t should be a x i a l l y f r e e , e i t h e r on the s h a f t o r i n the housing, as shown on Fig.35. I f t h i s bas ic r u l e i s ignored and two a x i a l l y located bear ings a r e used, any s h a f t expansion occu r r - ing due t o generated o r ex te rna l heat could cause severed lock ing (pre loading) across the bear ings, r e s u l t i n g i n premature bear ing f a i l u r e . I n c e r t a i n a p p l i - ca t i ons us ing angular con tac t b a l l o r taper r o l l e r bear ings i t i s n o t p o s s i b l e t o use only one bear ing f o r l o c a t i o n and the bear ings must be adjusted by end covers"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000540_0094-114x(95)00106-9-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000540_0094-114x(95)00106-9-Figure3-1.png",
+        "caption": "Fig. 3. Assembly of third platform point.",
+        "texts": [
+            " the base Z-axis by/$, A A OiP 1 X ( k x OIPt) OtP1] A A A B2Pt x (/~ \u00d7 B2PI) B2PI] (7) the triad is taken parallel to the base-frame, and .~ is The reference position of O1 P2 is taken along the X-axis of this triad, and after a rotation 0, about its Z-axis, the position vector of P2 becomes p ~ = ol +-~[rlcos01 rlsin01 0] T Thus point P2 is fixed and d2x, d2y and d2z are unambiguously determined by , /p y_ / (8) (9) N o w , Pl P2P3 is a rigid triangle rotatable about PI P2, such that P3 moves in a circle [Fig. 3(a)]. But P3 should be at a point of intersection of a circle and a sphere, and at most two such points are possible. For the triangle PI P2P3, we find the foot 02 and length O2P3 = r2 as before. PIP~ + P I P ] - P2P~ COS ~X 2 -- 2Pj P2 x PI P3 sin ~2 = ~/1 - cos 2 ct2 P102 = Pl P3 cos ~X 2 r2 = 02P3 = PIP3 sin ct 2 02 = p ~ + P102 P1 P2 (1 O) A triad .~' similar to .~ is fitted at 02 for the reference of rotation of AP~ P2 P3 (and of point P3)If PI P: is parallel to the base Z-axis, then .~' is the identity matrix, else A A A A "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003734_ip-b:19830027-Figure7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003734_ip-b:19830027-Figure7-1.png",
+        "caption": "Fig. 7",
+        "texts": [
+            " 8 Influence of linear movement on torque and linear force developed by rotary armature a Torque Iz = 1.54 A b Linear force I2 = 1.54 A The rotary and linear speeds were measured by tachometer generators. To measure the torque and linear force, extensometers were used. The measurements and calculations have been made at constant current and a constant-frequency supply equal to 50 Hz. The value of rotor-iron permeability used in calculations was related to the average tangential component of flux density at the rotor-iron surface. The test and theoretical results are shown in Fig. 7. Since the rotor length is 2.0 m only, it was difficult to obtain higher linear speeds than 1 m/s. To illustrate the influence of end effects on RLIM performance, the torque and linear forces have been calculated at different values of linear speed. The results are shown in Fig. 8. It can be seen that the torque decreases at high linear speeds. There is a drag force developed by the rotary armature owing to the end effects. It increases strongly in the high-speed range. Fig. 9 shows the total thrust of the RLIM calculated, as the sum of thrust and drag force of the linear and the rotary armatures, respectively"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002563_robot.1996.506892-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002563_robot.1996.506892-Figure2-1.png",
+        "caption": "Figure 2: Elimination of Gravitational Biasing",
+        "texts": [
+            " Given measurement data and surface geometry of the fingertip one can easily assert the rank condition of DF by computing the above determinant. 3 Elimination of Gravitational Biasing In the previous section, we developed a mathematical model for contact localization without considering the gravitational effect induced by the mass of the finger on the sensor reading. In practice, sensor readings due to gravity force can be significant and subsequently distort the output. The bias reading is a function of the pose of the finger. As shown in Figure 2, in order to eliminate this gravitational biasing, we choose a nominal pose (e.g., when the sensor is vertical) of the sensor where the finger is in no contact with the olbject; record the sensor reading and denote it by fo E R3 and TO E R3. For instance, if the nominal pose is the vertical up pose then fo = (O,O,-mg)T, where m is the mass of the finger and g = 9.8m/s2 is the gravitational constraint. Let the mass center position of the finger be ro = (0, 0, then we have Now, assume that the finger is at a pose E E SO(3) relative to the nominal pose, and in contact with the object at some unknown location r,"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000569_s0045-7949(98)00004-2-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000569_s0045-7949(98)00004-2-Figure5-1.png",
+        "caption": "Fig. 5. The stretching of a rectangle along one of the principal strain directions.",
+        "texts": [
+            " Equation (43a) shows that, after the rigidbody rotation, [U] represents the stretches along the deformed coordinate system and Equation (44b) shows that, after the rigid-body rotation, [V] represents the stretches along the undeformed coordinate system. Hence, [U] represents the transformed tensor of [V], that is, U T V T T 45 which can be proved using Equations (41), (42a) and (44a). Locating the system x1x2x3 Next we use both two- and three-dimensional cases to show that the local coordinate system x1x2x3 is located from the convected system x\u03021x\u03022x\u03023 by using the symmetry of Jaumann strains. Figure 5 shows a rigidly translated and rotated rectangle CDFE and its deformed con\u00aeguration CDF 'E' after stretch along the principal strain axis x1. Because of uniform stretch, it follows from Fig. 5 that AA 0 dx 1 cos y BB 0 dx 2 sin y 46 and hence AA 0 sin y dx 1 BB 0 cos y dx 2 or 1 e1 sin g61 1 e2 sin g62 47 Equation (47) is equal to @u2 @x 1 @u1 @x 2 48 In other words, the system x1x2x3 is located by using the symmetry of Jaumann strains (see Equation (21)). Equation (48) is equivalent to Equation (18) (with m= 2 and n = 1) even if the system x1x2x3 is curvilinear because ui=0. If g61$g62, the rotation of the frame x1x2 is not equal to the average of the rotations of the axes x\u03021 and x\u03022"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003253_j.engfailanal.2004.12.035-Figure12-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003253_j.engfailanal.2004.12.035-Figure12-1.png",
+        "caption": "Fig. 12. Finite element modeling of golf shaft.",
+        "texts": [
+            " The kick point can be described by the percentage of the maximum deflection point from the tip against the entire length of the shaft. All the parameters mentioned above are considerably influenced by the material property of the prepreg, the shape of the mandrels, and their pattern design and all of them become utilized as a standard to evaluate golf shafts. Fig. 11 illustrates the cross-section of a completed golf shaft which has a tube shape. Table 1 shows the compositions of the golf shaft shown in the cross-section of Fig. 11. Fig. 11. Cross-section of golf shaft. As shown in Fig. 12, after a tube-shaped model of the golf shaft is produced for real using of the shape and length, all the boundary conditions relevant to the mechanical parameters are taken into account to analyze the finite elements. Fig. 13 shows the element of structural analysis. The analysis used the composite solid elements of NKTP number 7, which is provided by NISA 8.0 with three dimensions and 20 nodes. For this analysis, it is very important to guarantee the reliability of the final results. Hence, a convergence test was introduced in the employment of both boundary conditions and finite elements in the analysis as a means of ensuring the reliability of the process and results of golf shaft modeling"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001500_978-1-4899-1465-1-Figure7.6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001500_978-1-4899-1465-1-Figure7.6-1.png",
+        "caption": "Figure 7.6. Controlled rectifier and dc motor.",
+        "texts": [
+            " Since most pump and fan appli cations require only a 2: 1 or a 3: 1 speed range, dc drives can readily meet these application requirements. Many dc drives are capable of a considerably wider speed range, 6: 1 is typical, and are also capable of delivering more torque than a fan or pump needs at low speed. For this reason, a high-performance dc drive is not required for a pump or fan application, and the economic payback will be more favorable if the drive is specified to provide only the performance characteristics needed by the fan or pump. Figure 7.6 shows one of the commonly used configurations for a dc motor drive. A controlled rectifier bridge operating directly from a three-phase ac power line provides a dc voltage for the motor arma ture. By controlling the phase angle at which the thyristors in the bridge are placed in conduction, the effective voltage on the motor's armature is controlled and thereby variable speed is achieved. Solid-state inverters are the most common means of achieving variable-speed ac operation. Figure 7.7 displays a family of induction motor speed-torque curves as would be obtained by powering an in- 124 Chapter 7 duction motor from a variable-frequency and variable-voltage source"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003250_aim.2003.1225428-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003250_aim.2003.1225428-Figure3-1.png",
+        "caption": "Figure 3. The Guided Type of Proposed Microrobot",
+        "texts": [
+            "1 Screw Driving Microrobot Figure 2 shows the basic structure of the proposed microrobot driven by screw mechanism. Using the energy of fluid, by screw drive, a micro sphere is made to rotate, and the speed difference with fluid is made. Although the structure of the microrobot is easy, and does not need offer of the energy &om the exterior as a feature of this proposal, it is difficult to obtain big propulsive force. 2.2 The Guided Type of microrobot The structure of a guided type of microrobot is shown in Figure 3. It is made to circle by the magnetic field of external revolution, carrying out surfacing guidance of the main part. By using the wheels, it becomes the structure of washing the inside of a pipe. As the feature of this proposal, the structure is easy and making it move by wireless is mentioned. 2.3 A Fin Type of Microrobot in Pipe Figure 4 shows the structure of a fine type of proposed microrobot. This microrobot consists of the main body made of styrol material shaped as a sphere, a fin made of film sheet (100pm thickness), a permanent magnet and an exchange magnetic field"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000619_1.2832484-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000619_1.2832484-Figure1-1.png",
+        "caption": "Fig. 1 A corrugated foil journal bearing",
+        "texts": [
+            " A finite element implementation of the analytical perturbation method will be used here. The Coulomb damping effect caused by the relative motion in the sub-foil structure will also be included in the calculation. The Reynolds equation for an isothermal perfect gas will be used for the pressure calculation. Although the theoretical model and the finite element formulations are developed for a general structure and fluid, results will be given for an air-lubricated corrugated foil bearing (see Fig. 1). Theoretical predictions of bearing rotor dynamic coefficients will be presented. II Analysis The finite element formulations for both the fluid and struc tural models of the foil bearing will be developed here. An analytical perturbation approach to the prediction of bearing dynamic coefficients was first introduced by Lund and Thomsen (1978) for plain journal bearings, and was successfully applied to the gas foil bearings by Peng and Carpino (1993 and 1994). The basic approach will be extended to foil bearings in this investigation"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003416_s0022-0728(84)80291-0-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003416_s0022-0728(84)80291-0-Figure2-1.png",
+        "caption": "Fig. 2. (A) Cyclic voltammograms for a 0.17 cm 2 graphite electrode coated with 6 X 10 -9 mol cm -2 of co-polymer Fe - I recorded in the absence of dioxygen. Supporting electrolyte: 0.1 M HC104 +0.1 M NaCIO 4. Scan rate: 10 mV s -1. S = 10/xA. (B) Current-potential curve for dioxygen reduction at a 0.17 cm 2 rotating graphite disk electrode coated with 6 x 10 -9 tool cm 2 of co-polymer Fe-I . Supporting electrolyte 0.1 M HC104 +0.1 M NaC104 saturated with 02. Rotation rate: 400 rpm. Scan rate: 10 mV s -1, S = 100/tA. The three points plotted above the current plateau give the steady-state currents that resulted when the potential was stepped instead of scanned.",
+        "texts": [
+            " The reduction of dioxygen at the resulting platinum-plated, Fe-I -coated electrode proceeds at potentials well positive of those required at the Fe-I-coated electrode so that the limiting reduction current could be identified with i s . The quantities of electroactive iron porphyrin groups in coatings of F e - I were measured coulometrically in the absence of dioxygen by stepping the potential of the coated electrodes to values well negative of the formal potential of the FenI /FeU redox couple and integrating the resulting current until it decayed to background levels. Curve A in Fig. 2 is a cyclic voltammogram for an electrode coated with the F e - I copolymer recorded in the absence of dioxygen. The reversible response remains undiminished for long periods (hours) of repetitive cycling. The formal potential obtained from the average of the peak potentials is -0.105 V. The total quantities of electroactive iron-porphyrin centers in such coatings as measured coulometrically (Experimental section) were quite close to the quantities of iron-porphyrin in the Fe - I copolymer used to form the coating for values of the latter as great as I 'Fe = 5 X 10 - 7 mol cm -2 (Table 1). Thus, the high percentage of pyrrolidone groups in the copolymer appears to provide sufficient hydrophilic character to the coatings to yield ready accessibility of the supporting electrolyte throughout essentially all of even rather thick coatings. Curve B in Fig. 2 is a current-potential curve for the reduction of dioxygen at a rotating graphite disk electrode coated with copolymer Fe-I . At bare graphite electrodes or at electrodes coated only with poly(1-vinyl-2-pyrrolidone) the reduction of dioxygen does not begin before -0 .5 V. Thus, the catalytically active iron porphyrin centers in the coating used to record curve B are responsible for the reduction of dioxygen at a potential as positive as 0 V. Comparison of curves A and B in Fig. 2 shows that, as with coatings of monomeric iron porphyrins [15], copolymer Fe- I catalyzes the reduction of dioxygen at potentials more positive than the formal potential of the Fen l /Fe II porphyrin couple ( -0 .105 V). Possible explanations for this behavior have been offered previously [15,16]. At electrodes coated with monomeric iron-tetraphenylporphyrin, dioxygen is reduced first to hydrogen peroxide and then to water in two closely-spaced steps [5,15]. The same is true for coatings of copolymer Fe - I as is demonstrated by the current-potential responses obtained at a rotating platinum ring-graphite disk electrode shown in Fig",
+            " Coating the platinum-plated graphite electrode with poly(1-vinyl-2-pyrrolidone), PVPo, decreased the plateau current for dioxygen reduction to values consistent with hydrogen peroxide as the dominant reduction product (Fig. 6, curve B). Coatings of copolymer Fe-I , which contained over 80% PVPo, yielded a similar response at 0.3 V but a second wave appeared near 0 V where the Fe-porphyr in catalyzed reduction of hydrogen peroxide proceeds at pure graphite electrodes coated with the same copolymer (Fig. 6, curve C). The second wave in curve C is smaller than the corresponding wave obtained with a copolymer coated graphite electrode (Fig. 2) because the Fe-porphyrin in the coating was exposed to hydrogen peroxide for a longer time during the recording of curve C. When the electrode potential was stepped from 0.5 to -0 .1 V, larger and steadier plateau currents resulted. The magnitude of the plateau current for the first wave of curve C in Fig. 6 provides a measure of the rate with which dioxygen permeates through the coatings of the Fe - I copolymer. Figure 7 contains a set of Kouteck2~-Levich plots for platinum-plated graphite electrodes coated with increasing quantities of the F e - I copolymer"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002583_ias.2000.880991-Figure13-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002583_ias.2000.880991-Figure13-1.png",
+        "caption": "Fig. 13. Core back flux in a fully pitched winding SRM.",
+        "texts": [],
+        "surrounding_texts": [
+            "E 6oo (Y 300 00 +a - s o 2 -300 s\n-600 L\n0 90 180 270 360 450 540 630 720\n(a) Phase Voltage\n(b) Phase Flux\n0 90 180 270 360 450 540 630 720\n(c) Tooth Flux\n2000 -\n~ ._ ~\n-500 J ! I ! I ! I 0 90 180 270 360 450 540 630 720\n(d) Tooth MMF\nI8 - 5 12 c e $ 6\n0 0 90 180 270 360 450 540 630 720\n(e) Phase Current\n0 90 I80 270 360 450 540 630 720\nPosition (deg. el.)\n(f) Torque Fig. 9. Operation at 2000 revsimin, under voltage control, with positive\nvoltage applied for one half of a cycle. Mean torque=16.0Nm.\nIV. COMPARISON WITH MEASUREMENT\nComparison between simulated and measured results have been made upon the basis of current waveforms, mean torque produced and torque-speed envelopes. The prototype machine is controlled by a DSP, so that the actual digital controller has many identical algorithms to those contained in the simulator.\nIt is meaningless to compare current waveforms under full current control, since the current is then forced by the controller, so two comparisons are made under other conditions. Fig. I O shows measured and simulated comparison operation under voltage control, with volts applied for 12$ periods, similar to the case of fig. 8. The comparison between measured and simulated currents is within 5% at all positions, with the exception of the current dip at commutation between the other two phases, which shows a slightly larger error.\nFig. 1 1 shows a more unusual case, in which a flux controller has been used to produce waveforms corresponding to operation with a low torque ripple. Considering the highly saturating nature of the machine and the strong mutual coupling, the simulated and measured waveforms agree very well.\nThere has been substantial work concerning the inclusion of mutual coupling in conventionalSRMs. Moreira and Lip0 [ 101 introduced a coupled circuit model to account for mutual coupling between phases. Preston and Lyons [l 11 show that the mutual coupling between phases occurs due to both crossslot leakage and core back saturation, with mutual coupling terms of the order of 10-15% of the self terms. Similar conclusions are also drawn by Pulle and Petersen [ 121, using a model based upon [SI and similar to that presented above.\nThe approach presented so far does not properly model core back saturation effects when a number of sets of stator teeth are simultaneously excited. This effect is not significant in the prototype machine, which has a relatively deep core back, but this may not be the case when the core back depth is reduced towards its magnetic limit. Cross coupling of core back saturation is expected to be most important when the machine is operating under voltage control, with teeth carrying flux for more than one third of a cycle.",
+            "Figs. 13 and 14 indicate how stator core back saturation can be relatively simply incorporated into the model.\nThe flux per phase in a fully pitched winding SRM is effectively the core back flux, so integration of the phase voltage gives the phase flux directly. This may be used in a simple core back reluctance model to determine the core back MMF drop behind each slot. Addition of these MMF drops to the MMF drop in each tooth gives the total MMF drop in the machine. Fig. 14 illustrates in block diagram form how this can be incorporated into the simulation process.\nVI CONCLUSIONS\nA method of modelling switched reluctance motors with strongly coupled windings has been developed. The method takes into account the high nonlinearity of the circuit by decoupling the flux paths into per tooth quantities. The method has been applied to a switched reluctance machine and compared with a range of measurements, which indicate the validity of the approach.\nThe simulated results show the flux and MMF patterns in various parts of the machine, and give an insight into the operation of these machines. It becomes clear that in a fully pitched winding SRM the voltage applied to the windings directly controls the core back flux, whilst in a short pitched winding SRM the tooth flux is directly controlled.\nA method of incorporating core back saturation into the model is introduced. This permits accurate modelling of saturation conditions when a number of sets of stator teeth are simultaneously excited.",
+            "REFERENCES\n1) J.M. Stephenson and J.Corda, \u201cComputation of Torque and Current in Doubly Salient Reluctance Motors from Non-linear Magnetisation Data\u201d, Proc. IEE, 1979, 126,\n2) N.N. Fulton, \u2018The Application of CAD to switched Reluctance Drives\u201d, IEE Conference on Electrical Machines and Drives, London, Dec. 1987, pp275-285.\nT.J.E. Miller and M. McGilp, \u2018Nonlinear Theory of the switched reluctance motor for rapid computer-aided design\u201d, Proceedings IEE, 137, Pt. B, No. 6, pp337-347.\nB.C. Mecrow, \u201cFully-Pitched Winding Switched Reluctance and Stepping Motor Arrangements\u201d, Proc. IEE Part B, Jan 1993. B.C. Mecrow.,\u201dNew winding configurations for doubly salient reluctance machines\u201d, IEEE Industry Applications Society Transactions, November 1996.\n6) B.C. Mecrow, A.C. Clothier, P.G. Barrass and C. Weiner, \u201cDrive Configurations for Fully Pitched Winding Switched Reluctance Machines\u201d, IAS Conference 1998, St. Louis , pp563-570. C.Pollock, M.A. Wallace, J.D.Wale, \u201cThe Flux Switching Motor, a D.C. Motor without Magnets of Brushes\u201d, IAS Conference 1999, Phoenix, pp1980-1987.\n8) F. Liang, T.A. Lipo, \u201cNew Variable Reluctance Motor Utilising An Auxiliary Commutation Winding\u201d, Liang IEEE Transactions o n Industry Applications, Vo1.30,\n9) J.M. Kokemak and D.A. Torrey, \u201cMagnetic\n~~393-396.\n3)\n4)\n5)\n7)\nNo.2, ~423-432, 1994.\nCircuit Model for the Mutually Coupled Switched Reluctance Machine\u201d, IAS 1997, pp302-309.\n10) J.C. Moriera and T.A. Lipo, \u201cSimulationof a Four Phase Switched Reluctance Motor including the Effects of Mutual Coupling\u201d, Electrical Machines and Power Systems,\n11) M.A. Preston and J.P.Lyons, \u201cA Switched Reluctance Motor Model with Mutual Coupling and MultiPhase Excitation\u201d, IEEE Transactions on Magnetics, Vol\nD.W.J. Pulle and I.R. Petersen, \u201cA Generalised Approach to Torque and Current Computation in Switched Reluctance Motors\u201d, EPE97, Trondheim. Pp3.547-3.551.\n1989, Vol. 16, ~~281-299.\n27, NO. 6, NOV. 1991, ~~5423-5425. 12)\nAPPENDIX\nThe prototype machine used for simulation and testing:"
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0001131_etep.4450030405-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001131_etep.4450030405-Figure1-1.png",
+        "caption": "Fig. 1. Dependence of the parameter dE on a,",
+        "texts": [
+            " In the following the system is considered linearized in the magnetic set-point defined by the permanentmagnet excitation. Assume the PSM at standstill. Then, neglecting the armature resistance, the armature voltage equation is obtained (space phasor notation, p. u. time 7): with the complex differential inductance parameter ETEP Vol. 3, No. 4, July/August 1993 277 E TEP It is easy to verify that X\u201d = X , - AXCOS (2Oli) xi, = Axsin(2a,) with Xd.diff Xq.diff , = Xq.diff - Xd,diff 2 x, = t 2 Q j =arg It can be seen that there is a simple coherence between the complex quantity zc and the angle ai (Fig. 1). Similarly, acoherence&;,(2au) (with au =arguSld,,)canbecalculated, which is not shown here. From eqs. ( I ) , (3) and (4) it is evident how to determine the angle 2 q . A test space phasor us is applied to the machine and the reaction AiJAris measured. Using an inverter, this test can be repeated in three different space-phasor directions argys (in the case of a rhreephase machine). Combining two or three measurements, 2a i can be calculated without explicit knowledge of x,,, and Ax. If ai were known, the angle ywould be obvious (Fig. 1). However, since only 2a i can be calculated, the already stated uncertainty of 180\u2019 (electrical) occurs. This problem is solved by using a modified \u201cInform\u201d algorithm. 3 The Modified \u201cInform\u201d Method As pointed out in [2] and [3], the polarity can be detected by shifting the magnetic set point using a considerable flux-parallel (d-axis-) current component. In the following it is shown how to adapt this principle to rotating machines, thus obtaining a full 360\u00b0-information in real-time. line) offset current c) Course of x, due to a negative offset current d) Subtracting the x,-curves in parts b) and c) 3",
+            " Subtracting \u20acoff+ and coff- eliminates disturbing offsets and space harmonics (Fig. 8 to 10). 4 Detecting the Rotor-Angular Position y 4.1 y-Calculation Using the Real Parts ACn Performing three measurements in all three phases according to eq. (7) yields three functions ACz.j ( j = A, B, C) with the following (idealized) mathematical description: ACm,A = AC, cos y, (8) (9) Combining these quantities according to the space phasor definition, yields . 2 R .4x 3 1 . c, := AC,,, + AC,,B e\u2019?; + e J T = - AcmeJr. 2 . (11) Hence, the argument of the complex quantity cm (refer to Fig. 1 la) is the desired rotor angular position. 4.2 YCalculation Using the Imaginary Parts ACi, Similar to AC,?, three functions ACimj (i = A, B, C) and CO~- are de- (12) The expression ACim,j ( j = A, B, C) can be described mathematically in the following way (refer to measurement result Fig. 9): AC,,.A = A&[sin y +const3.sin(3(y +&))I, (13) based on the imaginary parts of fined (refer to Fig. 8): ACim,j (7) = Im{ C ~ + ( Y ) - c o ~ - ( Y ) )j* ACim,B = ACim [sin ( y - - + const3.sin(3(y + $3)) (14) + const3"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002247_robot.2000.844076-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002247_robot.2000.844076-Figure5-1.png",
+        "caption": "Figure 5: Geometric relationships between a door and the camera",
+        "texts": [
+            " Note that the color value H is unstable for monochrome, and that thl is the threshold to determine whether the color value makes sense or not. Although the utilization of both vertical edges and color increases the accuracy of recognition, there can be recognition errors. Other shape features including t,he top and bottom edges, the window, and the knob could help improve the accuracy. Once a door is recognized in the image, the position of the door in the real environment can he estimated using geometric relationships. Fig. 5 shows the geometric relationships between the camera and a door. The parameters are described below, where (xw, y,, z,) denotes a point in the world coordinate system, and (xu, yu, 2,) denotes a point in the camera coordinate system. L : distance in the 5 , direction from the camera to D : distance from the camera to the wall. 8 : angle between the optical axis and the x, &xis. a : angle between the optical axis and the line from D2 : distance between the optical axis and the door\u2019s kD2 : distance between the optical axis and the door\u2019s f : focal length of the camera"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002825_10402008808981820-FigureI-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002825_10402008808981820-FigureI-1.png",
+        "caption": "Fig. I-Typical five shoe tiltlng pad bearing ALL OlMENSlONS I N mm. Flg. 2-RotorlBearing apparatus #1",
+        "texts": [
+            " This spectrum was taken at 10 500 rpm. One can see a large component at the synchronous frequency and a small component at the instability frequency. The phase angle difference between XI and X3 at the synchronous frequency is 1 70\u00b0, very close to the expected 180\". Thus, since the synchronous amplitudes at X1 and X3 are at their maximum and nearly 180\" out of phase at 10 400 rpm, and since the rotor motion is small at X2, a conventional second bending critical mode shape occurs at 10 400 rpm. Also of interest in this figure is the phase relationship between X1 D ow nl oa de d by [ Y or k U ni ve rs ity L ib ra ri es ] at 0 3: 26 2 3 N ov em be r 20 14 Experiments on the Stability of Two Flexible Rotors in Tilting Pad Bearings SINLUUUNUUS PHASE -180.00 I % I I \\ i d 2.50 ' TILTING PAD - SET I 1 XlIX3 CROSS SPECTRUM AT 10,500 RPM SYNCHRONOUS lNSTA8lLlTY 0 o 3000 6000 9000 12boo FREQUENCY, CPM Fig. &Cross spectrum of XI and X3 motlons at 10 500 rpm for rotor 1 TILTING PA0 -SET 2 0.400 LOAD ON PA0 L/D = 0.70 0 .320 Y2 MOTION Cb/R ' 0"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001500_978-1-4899-1465-1-Figure6.12-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001500_978-1-4899-1465-1-Figure6.12-1.png",
+        "caption": "Figure 6.12. Permanent-magnet synchronous motor using buried magnet construc tion (U.S. Patent No. 4,139,790; Charles R. Steen assigned to Reliance Electric Co.).",
+        "texts": [
+            " From an energy conservation standpoint, synchronous motors should be considered in the large horsepower sizes or for slow-speed applications where the combination of high efficiency and high power factor can justify the increased complexity of motor and control. Permanent-magnet (PM) motors have grown in both numbers and importance ever since the introduction of ceramic and high energy-density magnets. For many years PM motors utilized alnico magnets which were vulnerable to demagnetization under overload and fault conditions. The availability of ceramic, samarium cobalt, and, more recently, neodymium iron magnets has improved the per formance of PM motors and they are now being utilized in a much wider range of applications. Figure 6.12 is a schematic view of one type of PM synchronous motor showing the essential construction features. The stator is very similar to a conventional induction motor stator with a polyphase 108 Chapter 6 winding designed to establish a rotating magnetic field when excited with a balanced set of three phase voltages. The rotor, shown in Fig. 6.12, contains four magnetic poles surrounded by a squirrel-cage winding which is short-circuited at both ends, similar to a conven tional induction motor. The motor accelerates from rest as an induc tion machine, which is the reason for including the squirrel cage in the rotor construction. As the rotor rotational speed nears synchronous speed, the rotor pulls into synchronism and operates thereafter as a synchronous motor. During steady-state operation, there is no cur- Single-Phase and Synchronous Motors 109 rent in the rotor, thus no losses, and this contributes to the high effi ciency of the PM synchronous motor"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001404_ectc.2002.1008168-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001404_ectc.2002.1008168-Figure3-1.png",
+        "caption": "Figure 3 - Biaxial orientation is achieved using the counter rotating die",
+        "texts": [
+            " Foster-Miller developed a proprietary processing technology that permits control of the fibrillar LCP orientation to any desired value, including quasi-isotropic, simply by varying the processing parameters (1). By utilizing a novel annular die, sheet and films can be produced with controlled directions of orientation. A combination of rotational shear and elongational flow during the extrusion process orients the LCP molecules. This controlled biaxial orientation, which is compared with uniaxially oriented films in Figure 2, is accomplished with an innovative counter-rotating die that aligns the LCP molecules along two distinct axes within a single ply. LCP film Figure 3 shows how biaxial orientation is achieved with a counter-rotating circular die which takes advantage of the LCPs propensity to self-align in shear flow by using transverse shear to produce transverse orientation. A combination of processing parameters, including rotation rate, blow-up ratio and draw rate, can be used to control the film orientation rate and, subsequently, critical film properties such as CTE, tensile strength and tensile modulus. LCPs have a unique combination of properties, that make them ideally suited for high density electronic substrate applications, including: Excellent electrical properties even up to millimeter wave frequencies (dielectric constant, 2"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003153_146441905x63322-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003153_146441905x63322-Figure5-1.png",
+        "caption": "Fig. 5 Spreader guide arms Fig. 6 Spreader guide arm positioning",
+        "texts": [
+            " The driving torque of the motor, Tm, can be written as Tm \u00bc min (Tm(vm), Trefm) (22) where Tm(vm) is the driving torque of the motor as a function of the motor\u2019s angular velocity and Trefm is the driving torque based on the difference between the required and actual angular velocities _T refm \u00bc Km(vrefm vm) Trefm tm (23) where Km is the amplification coefficient, vrefm the required angular velocity of the motor, vm the existing angular velocity, and tm the time constant. The value for the amplification coefficient Km can be described using the graph of the torque of the motor. The value for the time constant tm is found out by trying different values until the performance of the motor is fast enough. Spreader guide arms, Fig. 5, are used to ease the fastening of the container onto the spreader. Because of the structure of the locking mechanism, the spreader must be positioned within the accuracy of centimetres into the correct position above the container, before the actual locking procedure is enabled. The spreader is a long distance from the operator and attached to ropes, which might cause serious problems and slow down the work. When spreader guide arms are in the reach of the container, they are lowered and used to restrict the movement of the spreader"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000744_s0039-9140(97)00272-5-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000744_s0039-9140(97)00272-5-Figure1-1.png",
+        "caption": "Fig. 1. (a) F.I.A. manifold: (PP) peristaltic pump; (C) optical cell; (P) photomultiplier; (R) recorder; (V) injection valve; (W) waste bottle; (S1, S2) flow streams for the buffered solution of pyrogallol and oxidant, respectively. (b) Details of the cell compartment. (c) Details of the design of the optical cell (dimensions in mm).",
+        "texts": [
+            "1 N standard solution of hypochlorite was prepared by standardising a commercial sodium hypochlorite solution by iodometric titration and then diluting a certain volume of the commercial solution to the appropriate volume with the proper buffer solution. Pyrogallol working solutions were freshly prepared by dissolving the appropriate weight of pyrogallol (Merck) in the desired buffer solution and making up to the proper volume of the volumetric flask with the same buffer solution. Volumes of 100.0 ml were prepared each time and special care was taken to avoid long exposure to light and air. 2.2. Apparatus An F.I.A. manifold equipped with flow-cell CLdetector was used (Fig. 1). The red sensitive photomultiplier (EMI 9865 B) combined with power supply at 1600 V was used for detecting the emission of light. A pH-meter (Crison Micro pH 2000) equipped with pH-electrode (Ingold) and temperature measuring element was used for adjusting the pH of buffer solutions. 2.3. F.I.A. method The method of merging zone was used to mix the stream of oxidant with the stream of pyrogallol (Pg) solution just before entering the flow cell of the detector. 2.4. Mathematical expression of CL-emission under the operating conditions of this apparatus For a CL-reaction (Scheme A) R P1 \u00b7\u00b7\u00b7 P*i Pi \u00b7\u00b7\u00b7 Pn + hn in a batch-type reactor, the general equation for CL-emission is given by Eq"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002746_0278364905060149-Figure28-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002746_0278364905060149-Figure28-1.png",
+        "caption": "Fig. 28. Arrangement of measurement device for frame deformation in another configuration.",
+        "texts": [
+            " If the distances between the surface plate and the joint supports, u1 \u2212 u6, are considerably long, some non-contact displacement sensor systems (e.g., a laser interferometer system) are utilized as shown in Figure 27. The combination of the sensor and the rod also measures the distance changes among the three joint supports, t1 \u2212 t3. In the PKM shown in Figure 2, the mechanism is suspended from the frame. This compensation system can be successfully utilized even if other configurations of the PKM are adopted. For example, a PKM can be held in the inverted position as shown in Figure 28. Figure 29 shows another configuration of a PKM that is manipulating the workpiece. The compensation device for the frame deformation, described in Section 4, was installed in an experimental CMM (Oiwa 1997, 2000) as shown in Figure 8. This CMM uses a parallel manipulator with three degrees of freedom, which is shown in Figure 2(b). A triangular-prism-shaped aluminum truss frame supports the manipulator through three spherical joints. A surface plate made of low-expansion cast iron at UNIVERSITY OF BRIGHTON on July 11, 2014ijr"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure4.29-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure4.29-1.png",
+        "caption": "Figure 4.29. A thin disk rolling on a horizontal surf:1ce.",
+        "texts": [
+            "87d) that the ratio of the output angular speed to the input angular speed decreases with increasing e so that QjwE (4, 2); and according to (4.85e), the ratio of the relative angular speed of the epicyclic gear to the input angular speed grows with e so that w 12/w E (0, oo ). Specifically, for e = tP = 30\u00b0, it may be seen that Qjw = 3 and w 12jw = 2. It is an exercise for the student to plot polar graphs of these speed ratios as functions of the pitch angle e. D Example 4.19. Motion of a Rolling Disk. A thin, circular disk D of radius r, shown in Fig. 4.29, rolls without slipping on a simple, smooth path P in the 294 Chapter 4 horizontal plane H of the ground frame 0 = {F; Ik}. The angle 1/J describes the rotation of the disk about its axle y at 0; the tilt of the plane of the disk from the vertical axis K is denoted by 8; and the rotation of the tangent vector j to the path P is measured by the angle r/J. Of course, the motion of the disk depends upon the forces and torques that act on it; and it will be learned further on that these are related by basic dynamical laws to the acceleration of the center of the disk and to its total angular velocity and angular acceleration",
+            "76d) and append the equation WJ x x = 0. p.282, line below (4.76d); delete the phrase: \"the second equation in (4.67b),\" p.283, last relation in (4.77b); insert R to read: \"-R(1- cosi/J)n\" p.284, equation ( 4. 77f); replace r with R (italics) in the first term; change bold face R to R (italics) in the second p.288, Example 4.17, line 9; read: \"acceleration\" p.290, line 1 of ( 4.83b); in the j' component insert cos\u00a2 to read: \"w2 cos\u00a2 cos pt\" p.293, lines 1 and 2 below (4.87c); replace c with q (2 places) p.293, Figure 4.29; the axis at e from the vertical is k p.297, line 7; replace \"the\" with \"we\" p.298, line 4; replace \"closely approximated\" with \"approximate\" p.298, line 5; insert after the period the following addendum: \"A variety of fac tors that affect this estimate, including the relative motion of the Earth's atmosphere, a dominant influence that causes changes in the Earth's an gular speed, have been ignored. Nevertheless, the approximation suffices to show that time variations in the Earth's rotational rate are extremely small"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000525_1.555410-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000525_1.555410-Figure1-1.png",
+        "caption": "Fig. 1 Geometry and coordinate system of a journal bearing",
+        "texts": [
+            " The thin film lubrication problem with Reynolds boundary conditions, upon neglecting viscosity variation across the film thickness, can be stated as the following free boundary problem @6# 2L~ p\u0304 !5b , p\u0304>0 in V , p\u030450 on ]V (1) where H L~\u2022 !5 ] ]u S h\u03043 ]\u2022 ]u D1 ] ]z S h\u03043 ]\u2022 ]z D b5 x\u0304 sin u2 y\u0304 cos u22~xG cos u1yG sin u! (2) The film thickness is h\u0304511 x\u0304 cos u1 y\u0304 sin u (3) The bar denotes a nondimensional value and the dot denotes differentiation with respect to time. The geometry and coordinate system are shown in Fig. 1. Rohde and Mallister @5# presented a variational formulation for this class of free boundary problems arising from hydrodynamic lubrication. In these cases, the following variational inequality is written: Let H0 1(V) be Sobolev space and let K5$ p\u0304PH0 1(V); p>0 in V% be the subset of the Sobolev space ~see, for example, Milne @7#!. By introducing the symmetric and elliptic bilinear form on H0 1(V)3H0 1(V): a~\u2022,\u2022 !5E E V h\u03043S ]\u2022 ]u ]\u2022 ]u 1 ]\u2022 ]z ]\u2022 ]z D dudz (4) and the linear functional on dual space of H0 1(V): b~\u2022 "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001292_s0014-827x(03)00182-4-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001292_s0014-827x(03)00182-4-Figure2-1.png",
+        "caption": "Fig. 2. Schematic diagram of the flow system used for evaluation of the carbon paste electrode for dipyrone determination. P, peristaltic pump; I, manual injector; S, sample or reference solutions; L, sample volume; C, carrier solution; EFC, electrochemical flow cell; R, amperometer (recorder); W, waste.",
+        "texts": [
+            " This resulting mixture was submitted to magnetic stirring in a beaker (50 ml) containing 20 ml of hexane. The final paste was obtained by the solvent evaporation. The carbon paste was packed into an electrode body (see Fig. 1B), consisting of a polyethylene cylindrical tube (o.d. 7 mm, i.d. 4 mm) equipped with a stainless steel rod serving as an external electric contact. Appropriate packing was achieved by pressing the electrode surface (surface area of 0.126 cm2) against a filter paper. The electrochemical cell was inserted in a one-channel flow injection system schematically represented in Fig. 2. The system was assembled with a peristaltic pump (Ismatec, model 7618-40, Switzerland) and a manual injector made of Perspex\u2020 with two fixed sidebars and a sliding central bar [15]. The manifold connections were made with polyethylene tubing (0.76 mm i.d.). The 0.10 mol l 1 sodium acetate solution was used as the carrier solution (C) at a flow rate of 5.0 ml min 1. The dipyrone reference in 0.10 mol l 1 sodium acetate solution contained in the sample volume loop (l, 408.6 ml) was injected and transported by the carrier stream after the baseline had reached a steady-state value"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002976_0076-6879(86)33084-2-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002976_0076-6879(86)33084-2-Figure3-1.png",
+        "caption": "FIG. 3. Rotating flow mixing device.",
+        "texts": [
+            " 66 However, the mixed solution of TCPO and hydrogen peroxide in ethyl acetate and acetone (1:3, v/v) was found to retain 90% of its original activity after 4 hr storage at room temperature. So, the system shown in Fig. 2 has one pump for the An instantaneous mixing of the two solutions is important for obtaining a stable baseline since the CL reaction occurs instantaneously and the intensity declines very rapidly. For thorough mixing in the flow stream a rotating mixing device has been developed (Fig. 3). The column effluent and the CL reagent solution go into the bottom of the vessel from the opposite sides and are mixed well by rotation. As the mixture rises, it is removed from the top of the vessel. The diameters of the inlets are important to control the flow stream into the vessel of the two solutions to be mixed. A stream flow ratio from 1:4 to 1:10 is preferred for thorough mixing. A delay tube attached to the device is necessary to maintain the appropriate reaction time. Usually 5-40 cm by 0"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001752_jsvi.1997.1511-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001752_jsvi.1997.1511-Figure2-1.png",
+        "caption": "Figure 2. The conical spring.",
+        "texts": [
+            " Then Ca = L(r'2 + cos2 p) GSA(1+ r'2) , Cb = sin2 pL ESA(1+ r'2) , Cd = L(r2 2 + r1 r2 + r2 1) cos2 p 3GSJ(1+ r'2) , Ce = 4r'2L(r2 2 + r1 r2 + r2 1 ) sin2 p 3ESIN (r'2 + cos2 p) , Cc = L(r2 2 + r1 r2 + r2 1 ) sin2 p cos2 p ESIB (1+ r'2)(r'2 + cos2 p) . (24) 4. STATIC EXPERIMENTAL VERIFICATION Since the diameter of each active coil is different in a conical spring, a larger diameter makes the coils more flexible. The phenomenon of coil close must be considered. The most common type of end turns employed in helical compression springs are ends squared and ground or forged, as shown in Figure 2. Since the pitch angles at two ends are smaller in general, the effect of the end turns can be estimated to achieve accurate determination of coil close in the conical springs. By considering the end effect, where the spring coils are not uniformly spaced at the top and bottom coils, let h(s) be the distance from the bottom edge of the first active coil to the upper edge of the fixed coil. Then h(s)=g s 0 sin p(z) dz\u2212 x(s), 0E sELa , (25) where La is the coil length of the first coil, and x(s) denotes the vertical thickness of the fixed coil"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003496_s10008-004-0524-y-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003496_s10008-004-0524-y-Figure2-1.png",
+        "caption": "Fig. 2 Thin layer setup for NIR-spectroelectrochemical experiments, top: vertical cross section of cell setup, bottom: horizontal cross section of glass assembly, for details see text",
+        "texts": [
+            " The lower edge of this sandwich is immersed into the electrolyte solution; a platinum wire acting as counter electrode and a reference electrode are also placed in the lower vessel. The electrolyte solution is sucked into the gap between the glass sheets by capillary action; generally vacuum has now to be applied at the upper edge. The NIR light passes via fiber optics and suitable collimator lenses through the glass plates. Typical results obtained with this setup are shown below. In the case of spectrometers operating with optical choppers, experiments can be conducted without the need of excluding ambient light. In a more sophisticated setup (see Fig. 2) the glass sheets are mounted in PTFE-rods with slits acting as holders which in turn fit into the bottom of a cell body as shown. The gap between the two glass plates (one plate is coated with ITO and serves as a working electrode) is filled with electrolyte solution upon immersion into the solution pool in the bottom part of the cell. The gap between the glass plates is determined by the thickness of the strips of PTFE-tape inserted at the edges of the plates. Electrical contact is made with a brass clamp at the top edge of the ITO-coated glass sheet",
+            " Frequently the assigned absorptions start in the long wavelength UV-Vis range and extend well into the NIR; consequently this phenomenon appearing as a broad absorption or even only an apparently tilted baseline has been called the \u2018\u2018free carrier tail\u2019\u2019. Optical properties (i. e. absorption) in this range are of particularly practical importance when employing NIR illumination for Raman (especially resonance Raman) spectroscopy [97, 98]. A typical example is shown in Fig. 5. NIR-spectra recorded during electropolymerization of polyaniline on an ITO-glass in a setup similar to the one depicted in Fig. 2 show a sloped line indicative of the free charge carriers being present within the freshly formed polymer. This is in its oxi- dized, i. e. conducting state at ERHE=1 V. The bands can be assigned to the first overtone of the N-H-stretch in an aromatic amine (1500 nm) and to the transition from the valence band into the lower polaron band (binding polaron band) of the benzoid polaron type [99]. The rather featureless absorption between 2400 nm and 3000 nm might be related to mobile charge carriers, its correlation with the electrical conductivity measured in situ is currently under investigation"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure2.9-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure2.9-1.png",
+        "caption": "Figure 2.9. Schematic of the vectors associated with the equation v P = v0 + ro x x.",
+        "texts": [
+            " Unless otherwise stated, use of these units is preferred. On the other hand, in engineering practice the common measure of angular motion often is reported in revolutions and time is in minutes, so in this case the units of ro are written as rpm (revolutions per minute). The con version from one set of units to the other is accomplished by recalling that one revolution is equivalent to 2n rad; thus, 1 rpm = 2n/60 rad/sec. 100 Chapter 2 The vectors introduced in (2.27) are shown in the schematic Fig. 2.9. Additional physical relevance may be assigned to the separate terms in (2.27) by examination of the time derivative in l/1 of the position vector X= B + x of the point P. With the aid of (2.25 ), this yields v p = Vo + x; then it follows from (2.27) that X = v p - v 0 = 0) X X. (2.29) Because x describes the velocity of the point P relative to the base point 0, the quantity ro x x is named the relative rigid body velocity; it is the velocity that the point P would have if the base point were fixed in l/J"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002264_j.ijsolstr.2003.09.054-Figure9-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002264_j.ijsolstr.2003.09.054-Figure9-1.png",
+        "caption": "Fig. 9. (a) A fixed-ended helical rod; (b) type of dynamic loads.",
+        "texts": [
+            " In the viscoelastic case, the response of the bar dies out with time. The effect of the damping ratio is obvious; increasing the damping ratio causes the response to reach the static response much faster. The dynamic behaviour of the viscoelastic helical bar will eventually disappear and it will approach the static state. The moment Mz is equal to 0 under static loads. However, in the case of dynamic loads, due to inertia forces it assumes values different from 0 (see Figs. 7d and 8d). Example 2. A fixed-ended helical rod shown in Fig. 9 is now considered. The rod has a circular cross-section with the diameter d \u00bc 12 cm. The pitch angle and radius of the helix circle are chosen as a \u00bc 25:52 and a \u00bc 200 cm, respectively. Material properties are: E \u00bc 2:06 1011 N/m2, q \u00bc 7850 kg/m3 and m \u00bc 0:3. Various dynamic loads with the amplitude P0 \u00bc 5 105 N are applied vertically on the arc-length mid-point of the rod. A time increment Dt of 0.02 s is used in the calculations. Non-dimensional vertical displacement at the arc-length mid-point of the rod and non-dimensional shear force, bending moments at the fixed end are shown in Figs"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003502_095440904322804439-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003502_095440904322804439-Figure2-1.png",
+        "caption": "Fig. 2 Scheme of specimens machining for friction measurements",
+        "texts": [
+            " It can therefore be considered as a valid tool for the press-\u00aet curve prediction and the assessment of the in\u00afuence of process parameters. As mentioned above, the friction measurement procedure requires the specimens to be machined directly from the axle and the wheel, thus reproducing exactly the actual surface conditions during the press-\u00aet, in terms of materials, contact geometry, roughness and anisotropy. In particular, the specimens are taken from the zone near the coupling surfaces, as schematized in Fig. 2: a small specimen (called a punch in the following) and a long specimen (called a body in the following) have to be machined from the two components. In the present experiments the punch was obtained from the axle, the body from the wheel. The geometry of the specimens is reported in Fig. 3. The examined materials are carbon steels for both elements, precisely a normalized steel with 0.3 per cent carbon and HV \u02c6 205 for the axle (A1N-UIC 811\u00b11 O) and a quenched and tempered steel with 0.5 per cent carbon and HV \u02c6 260 for the wheel (R7T-UIC 812\u00b13 O)"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000482_39.666569-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000482_39.666569-Figure1-1.png",
+        "caption": "Figure 1. PF optimization principle illustration",
+        "texts": [
+            " The optimal controller scheme proposed here is implemented on a conventional structure of a Field Oriented Control (FOC) of an induction motor. It leads to setting the Power Factor (PF) to its rated value, according to a simple equation, by adjusting the magnetization current component with respect to the torque current component. The main advantage of the proposed method is its simplicity. In fact, it does not require an apriori knowledge of the induction motor model parameters. Optimization Principle: The optimization principle can be explained by considering Figure 1, describing the induction motor operation by a circle diagram. Here, the optimal PF (approximately rated one) is reached when the stator current vector becomes tangent to the circle. Therefore, several optimal points can be determined. For example, the optimal point P, corresponding to the circle CA and the magnetization current IN; and also the optimal point B, corresponding to the circle CB and the magnetization current Zfl. As illustrated by Fig. 1, the IEEE Power Engineering Review, May 1998 63 point A has a low PF. It is possible to improve this PF, maintaining the same active power, by moving the pointA to B location (optimal PF). In this case, the magnetization current is reduced (I@ < I@). The stator current is then reduced leading to copper losses decrease (i2t). Moreover, magnetization current decrease leads also to iron loss decrease. Finally, loss balance can be obtained approximately leading then to a maximum efficiency. Optimization Algorithm: According to Figure 2, the PF is expressed in the d-q frame by In the da-qa frame, it becomes The following relationship is then deduced"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003008_1.1757488-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003008_1.1757488-Figure3-1.png",
+        "caption": "Fig. 3 Prismatic dislocation loop in a plate. Distributions of virtual loop defects are shown on the plate surfaces.",
+        "texts": [
+            " The energy of the inclusion in a half-space is E5 8pG\u00ab*2~11n!Rsph 3 3~12n! 2 4pG\u00ab*2~11n!2Rsph 3 9~12n! \u2022 1 h\u03033 , Rsph<h . (30) Here the first term is the energy of inclusion in infinite medium and the second term is the interaction energy between inclusion and the free surface. 4.2 Prismatic Dislocation Loop in a Plate and in a HalfSpace. Consider an interstitial prismatic dislocation circular loop with radius a0 that is parallel to the free surfaces of a plate of rom: http://appliedmechanics.asmedigitalcollection.asme.org/ on 01/27/20 thickness t ~Fig. 3!. The center of the loop has coordinates (0,0,h). The plastic distortion of the loop, its total displacements `ui , and elastic stresses `s i j in an infinite medium are given by Eqs. ~5!\u2013~7! by replacing z with z2h . For satisfying the boundary conditions Eqs. ~21! we again represent the resulting elastic field as a sum of the loop field in an infinite medium and an additional field due to the distributions of virtual loops. In this problem we use prismatic dislocation loops and radial disclination loops as virtual defects"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000910_0925-4005(95)01675-9-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000910_0925-4005(95)01675-9-Figure6-1.png",
+        "caption": "Fig. 6. Schematic representation of a planar sensor, with the dye dissolved in a homogeneous membrane.",
+        "texts": [
+            " (b) We find the selectivity for potassium to be highest at a PSD:borate molar ratio of 1:1; cross-sensitivity to anions is no longer found, but the selectivity for potassium is smaller, and the sensitivity is slightly enhanced; similar effects have been reported for the carrier:borate ratio in electrodes [27]. The relative signal change is distinctly higher than in former PSD-based sensors [18-20] but not as big as in the case of sensors based on the ion-exchange mechanism [4 7,11-14,17,28-31], where an acid base equi- A number of observations point to the fact that the sensor 'membranes ' used in this work are not thin films as schematically represented in many illustrations (e.g., Fig. 6). The observations include the following: (a) Before being operative, sensors require preconditioning by storing them for a few hours in an aqueous buffer containing potassium ion. (b) Membranes become turbid when conditioned in buffer. (c) The signal change in PSD sensors is too large. If the sensing layer is planar and the signal change occurs at the water sensor interface only, it ,is difficult to understand how the few fluorophores located near a planar interface would cause the rather large signal change",
+            " In fact, one would assume the fluorophores located in the interior of the membrane, and remaining unaffected by processes occurring at the water interface, to cause a huge background signal. (d) The response time of both the sensors with complete mass transfer (i.e., the ion-exchange or coextraction sensors) and the sensors with partial mass transfer (i.e., the PSD sensors) have response times of the order of minutes, which is clearly too fast for a sensor that is several micrometres thick and completely homogeneous. The above findings can only be explained by assumming the 'membrane ' to have a structure not reflected by the simple model of a planar lipid membrane (Fig. 6). In other words, it is not 'a region of space with uniform properties throughout ' [13]. Rather, the membrane must be considered to be a water-in-polymer micro-emulsion [32,33], schematically represented in Fig. 7. Indeed, it has been shown recently by various authors that plasticized PVC membranes used in electrodes have microdomains of highly varying polarity. Thus, spatial imaging photometry [34] revealed the presence of water droplets in plasticized PVC membranes, the first 40 60 I~m near the surface containing the largest fraction [34,35]"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002463_0954410041322005-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002463_0954410041322005-Figure4-1.png",
+        "caption": "Fig. 4 Angle, position and vector definitions for a flocking boid",
+        "texts": [
+            " \u00f01\u00de and the turn radius, R, by R \u00bc V2 ? g ffiffiffiffiffiffiffiffiffiffiffiffiffi n2 1 p \u00f02\u00de where n is the load factor, defined as n \u00bc L W \u00bc 1 cosf \u00f03\u00de and g is the acceleration due to gravity. The linear velocity of the aircraft is given by _X \u00bc V? cosc \u00f04\u00de _Y \u00bc V? sinc \u00f05\u00de In this section, guidance information in the form of an expression for the demand load factor, n, for a given boid is derived from the flocking rules. This will then be substituted into equation (1) to give a general equation for the flock dynamics. Figure 4 defines the angles, positions and vectors for a boid i within a flock of m similar boids. Boid i is located at Xi and has velocity vector Vi along a heading angle ci. The flock cohesion centroid q is located at Xq with the boid cohesion vector Bi given by Bi \u00bc Xq X i, orientated at an angle bi. The alignment vector, common to all boids, is A and is orientated at an angle a. For the general case of m boids, equation (1) is written as _ci \u00bc g ffiffiffiffiffiffiffiffiffiffiffiffiffi n2i 1 p V? , i \u00bc 1, "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002061_jsvi.2001.4018-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002061_jsvi.2001.4018-Figure2-1.png",
+        "caption": "Figure 2. Simply supported shaft carrying a point force and moment at the location of the rotor.",
+        "texts": [
+            " (16) Similarly, another equation describing the forces transmitted through the bearing at the other end of the machine may be written as F \"[ I] . (17) Combining equations (16) and (17): F F \" I 0 0 I (18) which can be abbreviated as F \"[I] . (19) The magnitude of the reaction forces transmitted by the bearings can also be evaluated in terms of the forces applied to the shaft by the rotor. Considering the shaft to behave as a simply supported beam carrying a point force and moment at the location of the rotor shown in Figure 2, the vertical reaction forces at the shaft ends are f \"(1!a/l)F #(1/l )M , (20a) f \"(a/l)F !(1/l)M (20b) and similarly, the forces in the horizontal direction may be written as f \"(1!a/l)F #(1/l)M , (20c) f \"(a/l )F !(1/l )M . (20d) Recognizing that the forces and moments applied to the shaft by the rotor vary sinusoidally, we arrive at F \" F cos(i t)# F sin(i t), (21a) F \" F sin(i t)# F cos(i t), (21b) M \" M cos(i t)# M sin(i t), (21c) M \" M sin(i t)# M cos(i t). (21d) Substituting these expressions into equation (8), and comparing coe$cients of sin(i t) and cos(i t) leads to the matrix equation F \"[A] F #[A ] F , (22) where [A] and [A ] are determined by the geometrical parameters of the rotor and F \" F , 2 ,F , M , 2 ,M , F , 2 ,F , M , 2 ,M , F , 2 , F , 2 , 2 , M , 2 ,M , [F \" F , 2 , F , F , 2 , F , F , 2 ,F , F , 2 , F , F , 2 , F , 2 , 2 , F , 2 , F "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003054_j.jbiomech.2005.02.011-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003054_j.jbiomech.2005.02.011-Figure1-1.png",
+        "caption": "Fig. 1. The damped hopping surface mounted on a force platform. Surface damping was varied by adjusting the position of the fulcrum on the lever arm connecting the damper to the surface. The damper temperature was maintained by circulating ice water through a copper coil surrounding the damper. The surface was originally described in Moritz and Farley (2003).",
+        "texts": [
+            " We chose to study hopping in place as it is an excellent analog to forward running (Farley et al., 1991), and it is technically more feasible to construct an adjustable damped surface for hopping in place than for running. Eight male subjects (body mass 76:2 1:7 kg; height 176 5 cm; age 28 2; mean7SD) hopped in place on a surface with adjustable stiffness and damping. All subjects gave informed consent, and the University of Colorado and California Human Research Committees approved the protocol. The lightweight hopping surface (effective mass 3.7 kg; Fig. 1) was supported by steel springs (Century Springs, Los Angeles, CA, USA) and a bi-directional hydraulic damper (Taylor Devices, New York, NY, USA). The apparatus was mounted on a force platform (AMTI, Watertown, MA, USA), and we determined surface compression with a linear potentiometer (Omega, Stanford, CT, USA). We collected surface compression and ground reaction force data at 1000Hz using LabView 4.1 software and a computer A/D board (National Instruments, Austin, TX, USA). We fixed surface stiffness at 26"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002767_ma0499021-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002767_ma0499021-Figure5-1.png",
+        "caption": "Figure 5. Side view of a uniformly bent chain portion. The meaning of the symbols is given in the text. The shaded volume slice is obtained by cutting the chain with two coaxial cylinders; their axis goes through the center of curvature C and is orthogonal to the plane defined by the chain axis and the radius of curvature RC.",
+        "texts": [
+            " Considering instead the chain to be either in the molten state or in an athermal dilute solution, we will derive a quantitative estimate of its persistence length, adopting the wormlike chain representation. In both cases we disregard side-group swelling relative to the mesophase, in the assumption that the chain entropy is close to its largest value when its side groups are tightly packed around the main chain. As a result, the overall chain conformation in the liquid state may be described by a distorted cylinder whose axis keeps the same length and whose transverse circular section is the same as in the mesophase (see Figure 5). In the straight-chain portion shown in Figure 2, the average length and radius of the undistorted cylinder are L and D/2, respectively. We confine detailed analysis to class 2 polymers with a number n of bonds in the main chain equal to the number of the side groups, but the results obtained apply with minor changes also to other structures. The main chain has a mean-square length \u2329r2 L\u232a0 ) nC\u221eB l0 2 in the bare unperturbed state, defined as the ideal solution of the bare backbone polymer wherein the side chains are replaced by hydrogen atoms",
+            " Considering a uniaxial deformation that changes L to \u03bbL at constant volume, the diameter D must change in turn to D/x\u03bb. Imposing the stationarity condition for \u03bb ) 1, the free energy is given by Notice that the last equality is roughly verified by class 2 polymers from 8 to 19 (see Table 2) if we take n ) 1, L2 ) \u2329rL 2\u232a0 as the smallest spring element. Let us now see the implications of this result on the random bending of the chain as produced by Brownian forces in a melt or in an athermal solution where its axis may bend freely. We subdivide the chain into chain elements comprising \u03bd skeletal bonds (see Figure 5). The average axial length \u2206L ) \u03bdl of each chain element will be determined by requiring that its average thermal energy of bending is kBT. The physical implication of this requirement is that bending may be regarded as uniform within each chain element, in analogy with the behavior of a single molecular degree of freedom. Defining the bending plane as containing the center of curvature C and the bent axis of the chain element, as shown in Figure 5, the bending planes of contiguous elements along the chain may be regarded as uncorrelated. On these premises, denoting with \u03c4 the root-meansquare angle between the axial chain directions at the two ends of the chain element, the chain persistence length P will be given by according to a recognized mathematical property of the wormlike chain.29 From what precedes we may assume any section orthogonal to the chain axis to remain planar under bending. We also take the chain element radius of curvature Rc . D/2. Let us consider the family of cylinders with a common axis that goes through the center of curvature C and is orthogonal to the bending plane. We consider two points A and B on the upper circular edge of the chain element. From Figure 5 we have AB ) (D/2) d\u03b8, d\u03b8 being a small increment to the angle \u03b8. The thin portion of the chain element (henceforth slice), comprised between the two cylinder surfaces passing through the points A and B, has a uniform strain ratio \u03bb(\u03b8) given by Notice that \u03bb ) 1 is the average value of the strain parameter. The volume fraction of the slice is equated to the surface fraction on the chain section: and from eq 5 the corresponding free energy is G(\u03bb) ) G(\u03bbL,D/x\u03bb) ) 3 2 kBT L2 \u2329rL 2\u232a0 (\u03bb2 + 2 \u03bb); (n (D/2)2 \u2329rD/2 2\u232a0 ) 2 L2 \u2329rL 2\u232a0 ) \u03bb)1 (5) P ) 2\u2206L \u03c42 (6) \u03bb(\u03b8) ) Rc - (D/2) cos \u03b8 Rc (7) dv(\u03b8) ) 2(D/2)2 sin2 \u03b8 d\u03b8 \u03c0D2/4 ) 2 \u03c0 sin2 \u03b8 d\u03b8 (8) dG(\u03b8,Rc) ) 3 2 kBT \u2206L2 \u2329r\u2206L 2\u232a0 (\u03bb(\u03b8) + 2 \u03bb(\u03b8)) dv(\u03b8) G(L,D) ) 3 2 kBT{ L 2 \u2329rL 2\u232a0 + n (D/2)2 \u2329rD/2 2\u232a0 } (4) After subtracting the undeformed free energy contribution, the bending energy of the chain element is Since D/2 , Rc, we may write 1/\u03bb(\u03b8,Rc) = 1 + [(D/2)/ Rc] cos \u03b8 + [(D/2)/Rc)2] cos2 \u03b8, and eq 9 reduces to Putting \u2206G(Rc) ) kBT, we have We may obtain now the persistence length P from eq 6 and eq 11, remembering \u2206L ) nl and \u2329r\u2206L 2\u232a0 ) C\u221eB\u03bd l0 2, l and l0 respectively being the projected and the chemical bond length. The final result is We notice that neither the length \u2206L nor the angle \u03c4 is uniquely determined, unlike the ratio 2\u2206L/\u03c42 that yields a single value for the persistence length P (see Figure 5 and eq 6). Taking indicative values for C\u221eB \u2248 4, for l \u2248 1.2 \u00c5 and for l0 \u2248 1.6 \u00c5, from eq 12 we can estimate \u03b3 ) 0.13 \u00c5-1. A small value of C\u221eB is chosen on account of the large flexibility of the bare backbones of the polymers we are considering. Figure 6 shows the plot of P vs D for the class 2 polymers reported in Table 2. The best-fitting P ) \u03b3D2 curve appears encouraging and yields \u03b3 \u2248 0.16 ( 0.01 \u00c5-1, in semiquantitative agreement with the value estimated from eq 12.30 We notice that the best-fitting value of \u03b3 is influenced by the quality of experimental C\u221e\u2019s for class 2 polymers which, as discussed in ref 18, may present aggregation in solution, poor solubility in noncoordinating solvents, and high polydispersity"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002752_analsci.6.903-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002752_analsci.6.903-Figure1-1.png",
+        "caption": "Fig. 1 Configuration profile of the end of the sensor: (a) sideview, (b) bottom-view; 1, plastic optical fiber; 2, Pt counter",
+        "texts": [
+            " A Nafion-modified electrode was prepared by dropping 3 \u00b5l of 1 wt% Nafion solution (2-propanol/ H2O=9/ 1) on a platinum plate electrode (0.07 cm2) and evaporating to dryness at room temperature. The modified electrode was dipped in 1X103 -M Ru(bpy)32+ aqueous solution for 1 h to incorporate Ru(bpy)32+ into the film and subsequently rinsed in deionized water for 1 h.5 A plastic optical fiber (Mitsubishi Rayon, Esuka SH4001) of 1 mm in diameter mounted in a Teflon rod of 5 mm in diameter was surrounded by three electrodes. The configuration profile of the end of the fiber is represented in Fig. 1. The Ru(bpy)32+/ Nafion-modified working electrode was placed against the end face of the fiber with a 2-mm space. The counter and reference electrodes were a Pt wire (0.8 mm in diameter) and Ag/ AgCI electrode (0.8 mm in diameter). Figure 2 shows a diagram for the ECL sensor system. The potential was controlled with a Nikko Keisoku NPOT-2501 potentiostat. An electrolytic cell was enclosed in a lightproof box. The ECL was detected at room temperature with a Hamamatsu R928 photomultiplier operated at 900 V with a Hamamatsu C665 electrode; 3, Ag/AgCI electrode; 4, working electrode; 5, Teflon rod"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001965_s0167-8922(03)80088-3-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001965_s0167-8922(03)80088-3-Figure2-1.png",
+        "caption": "Figure 2. Photograph of test rig. Left, mechanical system; fight, view of disc specimens in test chamber.",
+        "texts": [],
+        "surrounding_texts": [
+            "A test roller and three counterface rings are employed for each test. The general geometries of both roller and rings are shown in figure 3. Both specimens were manufactured from 16MnCr5 steel to DIN 17210, commonly used in gear industries. Both specimens were gas carburised and heat treated to the specified hardness of 660-700 HV and 730- 770HV for roller and ring respectively with minimum case depth of 0.9 mm for both specimens. The average roughness of each specimen was between Ra = 0.35 ~tm and 0.5 Bm for roller and tings respectively. A poly-alpha-olefin (PAO) base stock was employed in this work. The viscosity of the lubricant was 13.7 cP at 40 ~ and was 2.9 cP at 100 ~ The base stock was tested on its own and also with an anti-wear additive. The additive used in this paper was secondary C6 zinc dialkyl-dithio-phosphate (ZDDP) dissolved in a high-viscosity base. The treat rate for this ZDDP was 1.3% to give 0.1% Phosphorus by mass. For all tests, the roller, the rings, and assembly components including the damper tings were ultrasonically cleaned in solvent before mounted on the shafts. After assembly, the test started by heating up the test oil to the specified temperature. Next, the load was gradually applied at a uniform rate over 5 minutes. When the load reached the required value, the electric motors applied the required rolling and sliding speeds to roller and tings. The rig would then run for a pre-deterrnined period. All the tests in this paper were carried out under the same operating condition, which was at 70 ~ bulk oil temperature, under Hertz pressure of 1.7 GPa, and a slide-roll ratio ( A v / v ) of 5.2 % (roller surface slower) with v = 3.15 m/s. (Here, Av is the difference in speed and v is the mean speed of the surface with respect to the contact). Under these operating conditions, using a simple thermal model proposed by Olver [13], a surface temperature at an inlet of contact was predicted to be 76.2 ~ At this temperature, the corresponding viscosity and pressure viscosity coefficient of the base stock was 4.77 cP and 11.2 GPa -~ respectively. The corresponding smooth-body minimum film thickness was predicted to be 61 nm. The tests were stopped at pre-determined intervals for specimen inspection. The inspection process involved measuring the surface profile across the wear track and taking images of the surface using a Form Talysurf Series 2 stylus profiler with 0.8 mm cut-off length and a digital microscope respectively. For the surface profile measurement, four measurements were made in axial direction of the roller across the wear track. An example of a worn surface profile is shown in figure 4. It can be seen that the wear is greater near the edges of the track. This may be due to the edgepressure from the chamfer comers of the rings. Only the central part of the running track was used for the wear determination. The loss in diameter of the roller against test time was employed as the means to evaluate micropitting wear. From the profile in figure 4, a wear depth was estimated by fitting a reference mean line through the unworn surface profile. The distance between this reference line and the central part of wear track was taken as the wear depth. The loss in diameter was obtained by multiplying the estimated wear depth by two."
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure1.12-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure1.12-1.png",
+        "caption": "Figure 1.12. Geometry in the principal plane of curvature.",
+        "texts": [
+            "64) Hence, C being an arbitrary curve, ( 1.64) shows that the vector dtfds is per pendicular to t. The same result may be seen in more intuitive terms. Because a unit vector has a constant length, the only change it can exhibit is a change in its direction. Since this change can have no component along the invariant unit length of the vector, it must be perpendicular to it, as shown in ( 1.64 ). Hence, the unit vector t(s) must rotate with changes ins, and dtjds must be its rate of rotation. We visualize from Fig. 1.12a that dt/ds = lim,1., ~ 0 Lit/ Lis is perpendicular to t( s) in the direction of the concave side of the path, the direc tion toward which t(s) rotates as s varies. Let n be a unit vector in the direction of dtfds whose magnitude we denote by K. Then, recalling (l.61a), we may write dt d2x -=-=Kn ds d~2 ( l.65a) Kinematics of a Particle 29 with (1.65b) and n\u00b7n=l. ( 1.65c) The unit vector n is called the principal normal vector of C. Since the magnitude K of dt/ds is the rate at which the tangent vector rotates its direc tion with respect to arc length as the particle moves along the curve, K is called the curvature of C. Substitution of ( 1.65a) in ( 1.63) yields the basic equation for the intrinsic acceleration vector: (1.66) This completes our derivation of the equations for the intrinsic velocity and acceleration. However, some additional useful geometrical details remain to be discussed. Our main results will be summarized afterwards. The reciprocal of the curvature, denoted by R = 1/K, has a simple and useful geometrical interpretation that may be readily visualized from Fig. 1.12. Let us consider the plane defined by the tangent vectors t and t + At at two points P and A on C separated by an infinitesimal distance As. This plane, or, more precisely, its limit as As --> 0, is called the plane of principal curvature. 30 Chapter 1 Now let us construct in this plane lines through P and A perpendicular to C. The point B where these lines intersect is named the center of curvature. The circle of radius BP with its center at B is identified as the circle of curvature. This circle assumes the shape of the curve along a small arc that includes the point P. We are going to show that this radius is equal to R; hence, R will be called the radius of curvature. To see this, let L be a line through P fixed in the plane of principal cur vature and making an angle 8 with the tangent at P. We see in Fig. 1.12 that the infinitesimal angle between the tangents at P and A is A8, so As= RA8 and IAtl = ltl L18. These approximations become more precise as Lfs is made smaller. In the limit as As--+ 0, we obtain I d81 =_!_ ds R' l:l=ltl=l. (1.67) We now recall ( 1.65b) and use the chain rule to write K= ldt/dsl = !dtjd8!!d8/ds!. Then substitution of (1.67) yields the important result K= 1:1 = ~~~~ =~. ( 1.68) Thus, as remarked earlier, the curvature K measures the rate of change in the tangent angle 8 with respect to arc length along C; and it is clear that [R] = [K~ 1 ] = [L]",
+            "71) that in every rectilinear motion in the direction t v = St and a = st. ( 1.73) We recall that a uniform motion is a special rectilinear motion with constant speed; thus, v = st = v0 , a constant, and a= 0, as described before. (ii) Circular Motion. It is clear that in a motion on a circle of radius r the tangent vector is tangent to the circle. The principal normal vector at every point around the circle is directed through the center of the circle, so this point is the natural center of curvature of the circle described earlier in Fig. 1.12. Thus, the radius of curvature of a circle is the radius of the circle: R= 1/K=r. Notice that the same result follows from the last of ( 1. 72) and the elemen tary formula s = re for a circle on which e is the angular placement of an arbitrary radial line from a fixed line through the center. Therefore, we have s = rO and s = rli. Substituting these relations into ( 1.70) and ( 1. 71 ), we obtain the special elementary equations for the motion of a particle on a circle of radius r with angular speed w = 0 and angular acceleration dJ = lJ: v= rwt, ( 1"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002670_elan.200403190-Figure7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002670_elan.200403190-Figure7-1.png",
+        "caption": "Fig. 7. SECM characterization of BDD electrodes: SECM image of BDD surface (50 50 mm) reactivity in an aqueous solution containing 10 mM K3Fe(CN)6 and 0.5 M Na2SO4 at constant height (L\u00bc d/a\u00bc 1.3) and at scan speed of 1 mm s 1 (Etip\u00bc 0.1 V vs. Ag/ AgCl, EBDD\u00bc 1.1 V vs. Ag/AgCl), A) prior to 2\u2019-deoxyadenosine oxidation and B) after 2\u2019-deoxyadenosine oxidation (polarization 900 s at 1.55 V (vs. Ag/AgCl) in a 0.5 M Na2SO4 solution containing 2.5 mM of 2\u2019-deoxyadenosine). C) Approach curves in an aqueous solution containing 10 mM K3Fe(CN)6, 0.5 M Na2SO4 and after polarization 900 s in 2\u2019-deoxyadenosine at different concentrations at 1.55 V (vs. Ag/AgCl). Scan rate\u00bc 1 mm s 1, Etip\u00bc 0.4 (vs. Ag/AgCl), EBDD\u00bc 1.05 V (vs. Ag/AgCl).",
+        "texts": [
+            " Three processes, that cannot be fully discriminated by impedance measurements, can be thought of: i) formation of a porous film enabling diffusion of nucleosides within pores or pinholes, ii) formation of a compact film capable of electron transfer and iii) blocking process due to the adsorption of reactant on electroactive sites. To discriminate these three mechanisms, we performed three sets of experiments. Redox mediators were used to probe the BDD modified surface either macroscopically by DPV (Fig. 6C) and CV (results not shown here) or locally by SECM (Fig. 7). DPV experiments were performed using ferrocene methanol as redox indicator to visualize the evolution of the fouling process without possible interactions between 2\u2019-deoxyguanosine and the modified BDD surface and at less anodic potentials to obtain favorable signal to background ratios. Figure 6C shows clearly the decrease of the redox indicator s response with the increasing polarization time. The decrease in the DPV current response of 2\u2019-deoxyguanosine (Fig. 6A, *) and ferocene methanol (Fig. 6A, ~) are thus indication that the same electron transfer is followed by both species. This validates furthermore the use of redox indicators to characterize the adsorption phenomena. We are currently analysing more deeply this adsorption behavior by modelling the voltamperometric responses of these redox indicators. Otherwise, oxidized BDD surface reactivity was probed prior and following polarization in 2\u2019-deoxyadenosine by SECM (Fig. 7). The SECM tip was used in the positive feedback mode using hexacyanoferrate(III) as redox mediator. Figure 7 displays the SECM image of the local BDD electroactivity, scanned over a 50 50 mm2 surface at constant height, before (Fig. 7A) and after polarization (Fig. 7B) in adenosine solution (2.9 mM, 900 s at 1.55 V vs. Ag/AgCl). Prior to oxidation of 2\u2019-deoxyadenosine, the surface 2D-image shows an inhomogeneous surface reactivity, which may be related to BDD surface heterogeneities. After polarization in adenosine, the recorded feedback current was lowered by an average factor of 15% and the resulting SECM image shows \u201chomogenization\u201d of the surface reactivity. Bard and co-workers [44] have already described such a comportment with SAMs modified gold Electroanalysis 2005, 17, No",
+            " In this case, the electroactive surface is partially covered by an alkanethiol layer that could present punctual defects such as pinholes. Individual defects could be detected only if they are well separated and not smaller than 0.1 a, where a is the electrode diameter. If these defects are closely spaced and smaller than the aforementioned critical size, the probed surface will appear partially conductive, thus presenting an average reactivity, which is dependent on the size and the distribution of the defects. The SECM image of our surface appears homogenous as seen in Figure 7B. Moreover, this homogenous decrease in surface reactivity depends clearly on the polarization duration and on the nucleoside concentration. The latter effect as well as the impact of polarization is visibly looking Electroanalysis 2005, 17, No. 5 \u2013 6 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim at the different approach curves to the different surfaces (Fig. 7C). Prior to polarization, the approach curve of the oxidized BDD surface follows the classical shape of the positive feedback mode corresponding to fast mediator regeneration at the BDD interface. Following 900 s polarization of the interface at 1.55 V (vs. SCE) in increasing concentrations of 2\u2019-deoxyadenosine (from 0.2 to 1 mM), the approach curves move away from the pure positive feedback mode and tend to a negative feedback comportment. This behavior is likely to be related to a loss of surface reactivity of the BDD substrate. In the work [44], Bard et al. have developed a model that mimics finite heterogenous kinetic with SAMs modified gold electrodes. This model depends on two parameters: the diffusion coefficient of the redox mediator which is fixed by the choice of the latter and the apparent heterogeneous rate constant keff which represents the sole adjustable parameter. We used this model to fit our approach curves to the BDD modified surface (black lines in Figure 7C correspond to the theoretical positive and negative feedback). In the case of the oxidized BBD surface prior to adsorption, a heterogeneous rate transfer of 0.3 cm s 1 is obtained using Bard s model. However, it is important to note that the estimated heterogeneous transfer rate of ferricyanide is a few orders of magnitude higher than reported using classical electrochemical characterization techniques for oxidized BDD films [1]. The model has thus to be refined for our application. Nevertheless, the modelling of the approach curves following polarization in increasing concentrations of 2\u2019-deoxyadenosine shows a dramatic decrease of this heterogeneous transfer rate with the nucleoside concentration. For example, keff falls to an estimated value of 0.001 cm s 1 for 2\u2019-deoxyadenosine concentration of 1 mM. This variation of keff can be correlated to the surface coverage of the substrate by insulating species. The estimated surface coverage for polarization in the higher 2\u2019-deoxyadenosine concentration (c\u00bc 1 mM) is about 99%. This result is in accordance with quasi-insulating behavior of BDD substrates (Figure 7C) after 900 s polarization in 1 mM adenosine solution. The SECM images and approach curves thus reinforce previous experimental evidences obtained by DPV (Fig. 6C). However, at this stage, SECM does not allow us to discriminate between the three hypothesis proposed to describe adsorption (e.g., blocking electrode, porous film or continuous film). The modelling cyclic voltammetry data are under way to shed more light into this complex process. Boron doped diamond thin films obtained by plasma enhanced CVD were applied to bioanalysis owing to their intrinsic properties: their carbon nature and their enlarged electrochemical window in aqueous media"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002546_jpsj.73.1082-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002546_jpsj.73.1082-Figure5-1.png",
+        "caption": "Fig. 5. Schematic explanation for the investigation of the influence of the consolidation terrace just behind the growth front in migration phase upon the colony expansion.",
+        "texts": [
+            " This means that the cell density has to increase to a certain value for the beginnning of a colony growth and that the threshold density value for the migration phase exists. (iv) From the result (iii), the periodicity in the bacterial motility is considered to reflect physical properties as the group of bacterial cells. Then we can focus our attention on the dependence of the local cell density on their motility. In practice, we sector a part of the outermost ring of a colony together with an agar plate during the migration phase of the colony growth, as shown in Fig. 5. And we investigate the variation of ring formation for removing the influence from the inner concentric rings. As the result of the experiment by P. mirabilis, it has been found that migration phase and consolidation phase of the separated part of the ring are shorter and longer, respectively, than the rest part. It has also been found that the cell density of the separated part in the first migration decreases and that the width of the ring becomes smaller. These results tell us that the end of migration phase depends on the local cell density and suggest the existence of another, lower threshold density for stopping the colony expansion by active bacteria"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001061_s0021-9290(00)00032-4-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001061_s0021-9290(00)00032-4-Figure5-1.png",
+        "caption": "Fig. 5. The rotation of a body-\"xed unit vector about an arbitrary axis (O@OA) in a three-dimensional reference frame (XYZ). n is the unit vector of the rotation axis O@OA, n 1 and n 2 are the body-\"xed vectors before and after the rotation, h is the rotation angle. The body-\"xed unit vector has been transformed onto the rotation axis for the analytical purpose.",
+        "texts": [
+            " Therefore, it is hoped that this method can be easily understood and accepted by clinicians to bridge the communication gap between clinical descriptions and mathematical presentations of limb segment or joint rotations. This method has been successfully used in the kinematic analysis of three upper limb activities; lifting weights, simulated vehicle steering and door opening/closing (Cheng, 1996). It is believed that the method can be used not only in the biomechanics of human movement for describing the 3D rotation of limb segments, but also in other \"elds for describing the 3D rotation of any moving object. Appendix A. Derivation of Eq. (4) In Fig. 5 XYZ is a reference Cartesian coordinate system with base vector e\"[i j k]T. O@OA is the axis of rotation and n is its unit vector. AB and AC represent the positions of a body-\"xed unit vector n 1 and n 2 before and after rotation, respectively. DB is perpendicular to AD, E is the mid-point of BC and DE is perpendicular to BC. A is the starting point of the body-\"xed vector on the axis of rotation. h is the rotation angle. The purpose of the following analysis is to \"nd n 2 from the known n, n 1 and rotation angle h. First some geomet- rical relations in Fig. 5 can be obtained by vector operations as: BC\"n 2 !n 1 , (A.1) AE\"(n 2 #n 1 )/2, (A.2) DBCD\"2D EDtan (h/2). (A.3) Because BC is perpendicular to both n and DE, it can be expressed as: BC\"a 1 n]DE, (A.4) where a 1 is a constant to be determined. The magnitude of vector BC is DBCD\"a 1 DnDD EDsin (p/2)\"a 1 D ED (A.5) because n is a unit vector. From Eqs. (A.3) and (A.5), a 1 can be found as: a 1 \"2 tan (h/2). (A.6) Thus BC\"2 tan (h/2)n]DE \"2 tan (h/2)n](AE!AD) \"2 tan (h/2)n]AE (A.7) because n and AD are parallel"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003758_acc.1986.4789043-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003758_acc.1986.4789043-Figure1-1.png",
+        "caption": "Figure 1: Block Diagram of Computed-Torque Control Scheme",
+        "texts": [
+            " In order to evaluate the effect of approximating the position dependent inertia matrix D(@) by a constant diagonal inertia matrix J we have also implemented the reduced feedforwward compensation scheme. In the sequel, K and K, are the constant and diagonal position and vefocity feedback gain matrices, repectively; 0 and Od are the measured and the reference joint position vectors, repectively; and the symbol denotes the derivative with respect to time. Computed-Torguee Control Scheme (CT) This scheme, depicted in Figure 1, utilizes nonlinear feedback to decouple the manipulator. The control torque T is computed by the inverse dynamics equation in (1), using the commanded acceleration instead of the measured acceleration 0, as: 790 Authorized licensed use limited to: University of Edinburgh. Downloaded on June 14,2020 at 21:17:37 UTC from IEEE Xplore. Restrictions apply. =r fl)(0)1K (O-) + K (%-O) + &,J (2) + ff(oJ,) + j(O) where the \" indicates that the estimated values of the dynamics parameters are used in the computation"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002264_j.ijsolstr.2003.09.054-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002264_j.ijsolstr.2003.09.054-Figure1-1.png",
+        "caption": "Fig. 1. The rod geometry.",
+        "texts": [
+            " Ordinary differential equations with variable coefficients can also be solved exactly in Laplace domain by using the complementary functions method. In the solution of viscoelastic helical rods, the Boltzmann\u2013Volterra theory is considered. Numerical results for elastic\u2013static, quasi-static, elastic\u2013dynamic and viscoelastic dynamic responses of helical rods are presented. Consider a naturally curved and twisted spatial slender rod. The trajectory of geometric center G of the rod is defined as the rod axis and its position vector at t \u00bc 0 is given by r0 \u00bc r0\u00f0s; 0\u00de where s is measured from an arbitrary reference point s \u00bc 0 on the axis (Fig. 1a). Let, at any time t, a moving reference frame be defined by unit vectors t, n, b with the origin of the axis of the rod is chosen such that t \u00bc or0\u00f0s; t\u00de os \u00f01\u00de where t, n and b are unit tangent, normal and binormal vectors respectively. The following differential relations among the unit vectors t, n, b can be obtained with the aid of the Frenet formulas (see Sokolnikoff and Redheffer, 1958) ot=os \u00bc vn; on=os \u00bc sb vt; ob=os \u00bc sn \u00f02\u00de where v and s are the curvature and the natural twist of the axis, respectively",
+            " It is noted that v is always positive and that s is positive for a clockwise rotation about t when advanced in the increasing s-direction. They are expressed in terms of the spatial derivatives of the position vector r0\u00f0s; t\u00de: v \u00bc o2r0 os2 ; s \u00bc or0 os o 2r0 os2 o3r0 os3 v2 \u00f03\u00de For planar rods s \u00bc 0, and for straight rods v \u00bc s \u00bc 0. A second rectangular frame \u00f0x1; x2; x3\u00de is introduced such that the x1-axis is in the direction of t, and x2, x3 axes are the principal axes of the cross-section (Fig. 1b). Let i1, i2 and i3 be the unit vectors along x1, x2, x3. From Fig. 1b Eq. (4) can be written. t \u00bc i1; n \u00bc i2 cos h i3 sin h; b \u00bc i2 sin h\u00fe i3 cos h \u00f04\u00de Let the displacement of a point on the rod axis, and the rotation of the cross-section about an axis passing through G be denoted by U0\u00f0s; t\u00de and X0\u00f0s; t\u00de, respectively. Also, let c0\u00f0s; t\u00de and x0\u00f0s; t\u00de, stand for extension and rotation of the unit length on the rod axis, respectively. On the other hand, let T\u00f0s; t\u00de and M\u00f0s; t\u00de denote, respectively, the resultant of the internal stresses acting on the cross-section, and the resultant moment obtained when T\u00f0s; t\u00de is carried to the geometric center G"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002931_te.2004.825528-Figure7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002931_te.2004.825528-Figure7-1.png",
+        "caption": "Fig. 7. Servomotor shaft position and corresponding required pulsewidths.",
+        "texts": [
+            " The R/C servomotor, equipped with a position feedback control circuit and a decelerating gearbox assembly, provides a simple control mechanism. (The internal construction of the decelerating gearbox assembly and the feedback potentiometer of servomotor are given in [13].) The R/C servomotor is controlled by a PWM signal, which can drive the motor to a desired position according to the width of the pulse. In this design, the Mitsubishi M51660L control chip is adopted as an R/C servomotor controller. (For the details of the driver circuit, refer to [14].) Fig. 7 shows the shaft positions of the servomotor and the corresponding required pulsewidths. Given a 0.5\u20132.5-ms pulsewidth, the R/C servomotor can rotate from 90 to 90 clockwise. The output shaft of the servomotor can drive the linkage so that the movable part of the prosthesis rotates with respect to the swivel and then closes the palm of the prosthesis. The output torque of the servomotor is approximately 3 kg-cm so that the designed prosthesis can easily grasp an object that weighs 1 kg. The students can use a microcontroller to easily generate an appropriate pulsewidth"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001059_12.403696-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001059_12.403696-Figure4-1.png",
+        "caption": "Figure 4. Bending line and deflection curve characterized by (xB, zB, \u03c6B) of a flexure hinge",
+        "texts": [
+            " In figure 3 the displacements of point B of a flexure hinge and of an ideal rotational joint are represented. The resulting deviations are \u2206r = 80 \u00b5m at an angle of \u03c6B = 20\u00b0. To derive a kinematic description of flexure hinges the deflection curve of a point lying on hinge link 2 (l2) has to be determined. The hinge is cantilevered at x = 0 and forces or moments are exerted in point B. The displacement curve of point B is characterized by the coordinates xB, zB and \u03c6B at different loads. Assuming link 2 to be rigid, the angles \u03c6C and \u03c6B are identical and \u03c6B corresponds to the hinge angle (fig. 4). For the determination of the coordinates of point B the deflection curve bending line of the hinge must be calculated. Assuming the geometrical moment of inertia to be a function of the beam length s, the bending line of a cantilever beam can be computed as well.8 Proc. SPIE Vol. 4194160 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/17/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx With the assumption that the material is linear elastic, the undeflected beam axis is straight, the plane of symmetry is identical with the loading plane are, the cross sections remain even and the beam length is large to the cross-sectional dimensions, the following well-known beam moment-curvature differential equation system can be deduced: (s- beam length of curve, x- coordinate along the undeflected beam axis, z- transverse deflection, \u03c6- angular deflection of the beam axis with the x-axis, M- moment, E- Young-Modulus, I- geometrical moment of inertia, d\u03c6/ds=1/R- curvature) )( )( sEI sM ds d M = \u03c6 (2) \u03c6cos= ds dx (3) \u03c6sin= ds dz (4) Loading a flexure hinge it must be assumed that the beam length is not long in comparison to the cross sectional dimensions"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001559_physreve.62.5056-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001559_physreve.62.5056-Figure6-1.png",
+        "caption": "FIG. 6. Schematic representation of molecular configuration. u\u0302 and v\u0302 are unit vectors, L is the distance from the point of intersection to the center of the rod, and g is the bend angle of the V-shaped mesogen. Dotted mesogen illustrates a host mesogen in the mesogen in a position, the interactions of which are overcounted by the independent rod approximation.",
+        "texts": [
+            " Specifically the phenyl-oxygen \u2018\u2018single\u2019\u2019 bond can have highly bent conformers. However a detailed analysis, presented elsewhere @8#, suggests that this is not the case. Thus, given the crudeness of most models for liquid crystalline elastic constants, we feel that it is reasonable to model our dopant as two rigid segments of a molecule attached to each other through a bend of g5120\u00b0. We shall describe the orientation of such a molecule by using the two orthogonal unit vectors u\u0302 and v\u0302 , shown in Fig. 6. The effective interactions of this molecule with the liquid crystal medium will be modeled via an orientation-dependent interaction potential between the rigid segments of the bent molecule and the surrounding liquid crystal. This interaction will be taken to be the sum of the interactions of the two separate segments. We first consider these interactions integrated over all positions and averaged over the orientations of the surrounding liquid crystal. For simplicity, we shall take this to be of the Maier-Saupe form, viz"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002268_tcst.2003.809254-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002268_tcst.2003.809254-Figure2-1.png",
+        "caption": "Fig. 2. XTE-46 engine schematic.",
+        "texts": [
+            " The last derivative, , can be calculated by knowing the functional form of the utility function with respect to control . So the controller NN is updated using the (7) and (8) so that (9) Thus, if (7) or (9) are not satisfied then if correspond to the weights of the NN controller, they are updated in a representative manner as (10) This training process is carried continuously over time so as to approximate the dynamic programming equation. The engine model used for the simulation is a XTE46 turbo-fan engine supplied by General Electric (see Fig. 2). The engine model comprises of a single stage high-pressure ratio fan with variable inlet stator vanes, booster with independent hub and tip stator vanes, high-pressure mixed flow compressor, double annular combustor, high- and low-pressure turbines, afterburner, and nozzle components. The complete engine model is represented as a component level model (CLM), that links the state-space models of the individual components in a way that ensures the proper balance of mass, momentum, and energy. The CLM has three states, namely, fan rotor speed (XNL), core rotor speed (XNH) and the average hot section temperature or the metal temperature (TMPC)"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001941_eurbot.1997.633569-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001941_eurbot.1997.633569-Figure4-1.png",
+        "caption": "Figure 4: SPIKE",
+        "texts": [
+            " However, a combination of both, the differential and the synchro drive is not possible. An interesting fact that has to be taken into account is that this kind of drive causes accelerations in every direction. This means, that the Stewartplatform must dispose of a t least of six degrees of freedom. VIPER has a maximum velocity of U,,,,, = 0,7? and a maximum acceleration of alnaz = 0.4:. Therefore, both vehicles have approximately the same accelation characteristics but in different directions. 3 The Stewart-Platform In figure 4 the Stewart-Platform [SteG5] SPIKE3 is shown. It was built up as a model of a hydraulic 3Stewart Plattform of the IPR KarlsruhE simulation platform in scale 1:4 compared to the origirial[Wil97]. SPIKE is moved by electric motors with spindle drive, instead of hydraulic cylinders like the original. The accuracy of SPIKE is within 10pm. SPIKE has a maximum stroke length of 150 mm and is controlled by a micro processor. [Egn94] developed n riew form of t,hc basic kincniatics for the platform. 111 figurc 5 tlic attac1inic:nts of the servos of the lower (A1 i "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000697_s0003-2670(00)01081-3-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000697_s0003-2670(00)01081-3-Figure1-1.png",
+        "caption": "Fig. 1. Schematic representation (a) of the squeegee action, paste application and of the screens used for the fabrication of SPE; (b) silver layer; (c) overlay pad; (d) working layer ; (e) Ag/AgCl layer.",
+        "texts": [
+            " From the comparison of the experimental and the theoretical data the tetrahydrate form of the product seems to be the most predominant. The molecular weight of the product, [La(C12H6Cl2NO2)3]\u00b74H2O, is 1010.2. It is insoluble in water, almost insoluble in ether and soluble in acetone. The surface modification of spectroscopic graphite rods was made by direct adsorption of DCPI molecules using a solution of DCPI-Na or [DCPI]3-La in acetone. The detailed procedure was reported elsewhere [24]. The screens allow ink to pass through a pre-determined area, which governs the size and the shape of the print, as illustrated in Fig. 1. SPEs were printed in arrays of eight couples consisting of a working and a reference electrode. Firstly, a layer made of silver acts as the conductive track, secondly a carbon layer (overlay pad) ensures isolation between the solution and the silver. Finally, the Ag/AgCl layer (0.3 cm \u00d7 0.8 cm) was printed over the overlay pad (the left one). Each layer was allowed to dry for 20 min at 60\u25e6C. The working layer (0.3 cm \u00d7 0.8 cm) was printed over the overlay pad (the right one) and produced by mixing 5 g of graphite powder containing 0"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003554_13552540510601309-Figure16-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003554_13552540510601309-Figure16-1.png",
+        "caption": "Figure 16 (a) Slice with sharp vertical edge with NVS-based cutter trajectory and (b) resulting cut slice lacking the sharp feature, (c) same slice with cusp volume-based cutter trajectory where sharp edge is captured by one such trajectory (d) resulting cut slice retaining the sharp feature",
+        "texts": [
+            " In case of NVS-based checks at regular intervals around the slice contour, there is considerable chance that the vertical sharp edge (Figure 15) would be missed and thus go undetected. Subsequent slicing, cutter trajectory determination and prototyping would result in loss of that sharp feature altogether. While NVS-based checks at regular intervals will have such problems, there are other checks that crowd points in regions of high curvature and rarify their presence in flatter regions. However, it should be noted that they are all discrete checks and the same limitations apply to them as well. Figure 16(a) shows the cutter trajectory for NVS where the sharp vertical edge is falling in between two NVS sections. As a result of this, the prototype is lacking this feature as shown in Figure 16(b). As a remedial measure, NVS-based checks and other 2D sectional checks generally consider an excess of points around the slice contour to detect surface features. This requires higher computational time. Cusp volume check, on the other hand, would detect a sharp edge by the abnormally high value of a particular cusp volume in comparison to that of its neighbouring cusps. In such a case, an extra cutter trajectory line can be introduced to actually pass through the vertical sharp edge to divide the cusp into two (Figure 16(c) and (d)). The algorithm as explained in Appendix 2 can be carried out so that the cusp volumes associated with the two patches come within user defined limit. Needless to say, the incorporation of an extra cutter trajectory in an intermediate slice would require some follow up action that is not discussed here. As a second example, a horizontal sharp edge \u2013 a thin fin for example (Figure 17) \u2013 can also be missed as the first-order check (de Jager, 1996; Faux and Pratt, 1979) would approximate the surface as part of a sphere and thereby fail to recognize the fin (Figure 18)"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001198_ip-cta:19960058-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001198_ip-cta:19960058-Figure1-1.png",
+        "caption": "Fig. 1 Shifted und clipped sector segion",
+        "texts": [
+            " A similar problem which has attracted many authors\u2019 interests (see [2] and references therein) is the problem of regional pole assignment. That is, the problem of designing a controller which guarantees that the closed loop poles will be located in a specified region of the complex plane. Regions such as strips, disks, sectors and ellipses are of special concern. This problem is of particular interest when the system to be controlled is uncertain. If the closed loop poles of the system are confined to the shifted and clipped sector in Fig. 1, then the system will achieve a specified damping ratio and degree of stability. However, the problem of pole assignment in such a region is quite hard to address. Alternatively, we can consider subregions of the sector region as in [2]. Of particular interest is the circular region D(a, r ) with centre at -a and radius r 5 a (Fig. 2). By placing the closed loop poles in such a region, not only can one guarantee an upper bound on the damping ratio 5, but also a bound on the natural frequency on and damped natural frequency ad"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001841_irds.2002.1044053-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001841_irds.2002.1044053-Figure6-1.png",
+        "caption": "Figure 6: Grasping a Block",
+        "texts": [
+            " When the limb is heated by the heater with 5[V], it takes 3 minutes to change half of it into soft-deformable state, which is enough large part for deformation. On the other hand, it takes 5 minutes for the limbs to be rigid again from 5O[\"C] when they are cooled by heat release in the air at 25[\"C]. Fig.5-left shows the robot walks when the limbs are in the rigid state. They are rigid enough to use as limbs of the robot. Fig.5-right shows the robot deforms the limbs when they are in the soft-deformable state. They are soft enough to change the shape. 3.2 Grasping a Block Fig.6 shows the robot grasping a block with the deformed limbs. In this time the robot hold on to the block with the deformed limbs, while it could only clip it with the straight limbs. In addition the block is set on a small stand of l[cm] height and the robot can insert the deformed limbs under the block. The deformation is done in the following way. First, when the limbs are rigid, robot moves the limbs and puts their tips beneath the body, because the limbs must be bent inside. Then, the robot changes them into the soft-deformable state and puts the body onto the block with the limbs bent inside because they are so soft not to support the body weight"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002362_itsc.2003.1252673-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002362_itsc.2003.1252673-Figure5-1.png",
+        "caption": "Figure 5 Maneuvering parameters",
+        "texts": [
+            " Effectively, according to the vehicle steering scenario described at the former kction two identical circles with tangent point can be formed. For example, a vehicle moves backward from A to B following a path formed by two circular arcs tangentially connected to each other. Supposing B i s parking bay and A is starting position, thereby parallel parking is achieved (see figure 4). The locations of circle center are depending on the detected parking space and the lateral displacement from the aside car. There are several conditions have to fulfill in order to have a collision-free motion (see figure 5) : 1. The length L must be larger than radius of the circle C,. . 2. Thecar mustatacomect position when begin to parking. The right position is determined by AxandAy. 3. The tuning point AT is depending on different value of Ax and hY. In our methodology the vehicle is always track to the tangential circles. Thereby, the location of circles must be determined. When the parking position is decided, which depends on the length of parking space, the center of c, is vertically pe'rpendicularto the final parking position"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002692_0301-679x(88)90113-2-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002692_0301-679x(88)90113-2-Figure2-1.png",
+        "caption": "Fig 2 Distribution o f contact pressure and geometry o f the O-ring mounted in the seal groove and subjected to sealed pressure. From left to right: O-ring; at a sealed pressure p = O; at p = Pl,\" at p = P2",
+        "texts": [
+            " The experimental verification in this paper is limited to the dependence defining the O-ring lubricating film thickness during out-stroke of the sealed element. Blok's s inverse problem of hydrodynamic lubrication gives the following formula for he: hc = 0.94(rlu/p') \u00b0'5 (3) where !/is the dynamic viscosity of the oil, u the velocity and p' the dp/dx value at inflexion of the pressure distribution curve in the lubrication film. To apply Eq (3) practically it is assumed that p ' = max(da/ds) = a' of the contact pressure distribution (Fig 2) The applicability of Eq (3) for the O-ring net leakage, ?/, was first shown by M/iller 6, who found satisfactory agreement between the ~ values calculated using Eq (3) and those measured experimentally. However, ?/ was investigated over a narrow range of r/u. The present author's research a'2 has shown that considerable differences exist between theory and experiment over the whole range of ~/u used in practice. An attempt to explain these discrepancies was given. Nevertheless, Eq (3) is applied today in engineering practice, and it should be considered as an important achievement of the sealing technology of the 1960s which enables many seal operating problems (leakage, friction) to be solved qualitatively",
+            " The film thickness for O-rings may also be determined from the general hydrodynamic lubrication solution for the linear contact zone of low elasticity modulus which defines the minimum lubrication film thickness, hm, ie - c ~ (5) where w is the load contact pressure per unit perimeter of the O-ring. Solutions given by different authors differ in the values of the constant C and the exponents a and b. The film thickness he1 is found from Eq (5) by determining the unit load w and assuming a stable ratio hm/h\u00a2 = 0.78, as defined by Herrebrugh 8 and confirmed in Ref 7 for O-rings. contact width So (Fig 2) of an O-ring with the surface of the sealed element is sold = 2s + 0.13 for 0.07 ~< e ~< 0.25 (6) which gives the unit load of the contact pressure: rcEs~ w - - 1.05ER(2g + 0.13) 2 (7) 6d For e. = 0.1, w = 0.114ER Substitution of w (for e = 0.1) into Eq (5) as determined by Herrebrugh 8 gives hcl/R = 2.74(rIu/ER) \u00b0'6 (8) The experimental Eq (5) of Dowson and Swales 1\u00b0 gives hc I/R = 2.08(qu/ER) \u00b0'57 (9) Fig 3 shows the experimental set-up used for measuring the leakage of the hydraulic seals. Two identical O-rings TRIBOLOGY international 363 are placed inside the pressure chamber (sealed space)"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003477_cnm.913-Figure13-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003477_cnm.913-Figure13-1.png",
+        "caption": "Figure 13. A symmetric dynamic system with four DOFs.",
+        "texts": [
+            " Group-theoretical approach is more systematic and is completely independent of specifications such as the order of the DOFs, but this is one of the most critical requirements in using algebraic method. In this part, three more examples are presented which involve more practical and large-scale problems. In each example, first, by the means of graph model of the system, symmetry operations and symmetry group of the problem are recognized and then, the group-theoretical approach described above is implemented to factorize the system. The resulting factors are then compared with the canonical form factors of the system. Figure 13 shows a vibrating system with four masses and seven translational springs. Having four DOFs, system belongs to vector space R4 and stiffness and mass matrices will be 4\u00d7 4, as follows: K= \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 k1+2k2+k3 \u2212k3 \u2212k2 \u2212k2 \u2212k3 k1+2k2+k3 \u2212k2 \u2212k2 \u2212k2 \u2212k2 2k2 0 \u2212k2 \u2212k2 0 2k2 \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 4\u00d74 and M= \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 m1 m1 m2 m2 \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 4\u00d74 Copyright q 2006 John Wiley & Sons, Ltd. Commun. Numer. Meth. Engng 2007; 23:639\u2013664 DOI: 10.1002/cnm For the graph model of this system, as shown in Figure 15(a), it is possible to identify a C2 principal axis and two vertical planes"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001854_cdc.2001.980101-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001854_cdc.2001.980101-Figure1-1.png",
+        "caption": "Figure 1 4 PMz(t)",
+        "texts": [
+            " This method works for a large coupling, hut it cannot he a p plied to the zero coupling case. ID this paper, we will propose a new design method which makes use of the center of oscillation and the twostep linearization. We will also examine the performance experimentally using a non-minimum phase twin-rotor helicopter model. 2 VTOL aircraft model The model x = -u1sin6'+m2cos0 (1) ji = ulcosB+~u2sinO-1 (2) e = u2 (3) has been employed in [Z] for the motion of a VTOL aircraft in the vertical (z,y)-plane(See Fig. 1). The variables I: and y denote the horizontal position and the altitude of the aircraft center of mass, respectively, and 0 the roll angle. The control inputs U,, up are the thrust and the rolling moment. A non-negative coefficient E represents the coupling between the rolling moment and the lateral acceleration of the aircraft, and the approximate model is given by setting E = 0. 0-7803-7061-9/01/$10.00 8 2001 IEEE 217 Remark 1 The system (1) - (3) has unstable zero dynamics described by 8 = (l/e)sinB for the inputs U I , W and the outputs z, y",
+            "2 Controller design We approximate the term Mgwsy of (40) by Mg and the last term of (41) by zero so that the model has the same dynamics as that of the VTOL aircraft model (1)- (3). Then, the next control law can be derived similarly. (46) (47) (53) ~2 = -k328 - kae(0 - 0.) (54) 4.3 Experiments Case 1) A step reference input with the magnitude 40\" is given to the yar angle a t 5 seconds. Namely, the reference input is z,=o , y v = o ( O < t < 5 ) z, = 40\" , v7 = 0 (5 5 t < 25) Figure 16: PM:O(t) Figure 18: AM:z(t) Figure 1 5 PMy(t) \"I'---? 22 - 25. zr = 0 ,yr=O (0 I t c 5) zr = 18(t-5) z, = 360 ,yp = 15sin(t -5) .gr = 15sin20 (5 I t < 25) (25 I t -< 30) The results of the proposed method and the approximate method are shown in Figs. 14 - 17 and Figs. 18 - 21, respectively, where the dotted line shows the reference inputs. Since our experimental setup has unmodeled dynamics such as the viscous friction at the rotation axis and the control delay and saturation at the trust, the good response of Figs. 14 - 17 implies the robust stability of the proposed method"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002598_s0003-2670(02)00490-7-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002598_s0003-2670(02)00490-7-Figure3-1.png",
+        "caption": "Fig. 3. Linear sweep cathodic stripping voltammograms (LS\u2013CSV) recorded with a mercury microelectrode in a 2 M Na2S + 0.1 M NaClO4 aqueous solution at pH = 12; Ed = \u22120.4 V, td: (a) 0; (b) 10; (c) 30; (d) 60; (e) 300 s. Scan rate 50 mV s\u22121. Inset Ipc vs. td,eff and Qc vs. td,eff plots.",
+        "texts": [
+            " It must be considered, however, that with conventional mercury electrodes, distinguishable anodic processes could be observed only for sulfide concentrations larger than 1 mM [22]. This is probably due to the lower flux of the electroactive species associated to the bigger electrodes with respect to the smaller ones. The influence of deposition time, td, on the cathodic voltammetric responses obtained for sulfide ions solutions, was investigated at two different concentrations. The deposition potential, Ed, was set at \u22120.4 V, td was varied over the range 0\u2013300 s, and the potential was scanned towards more negative values at 50 mV s\u22121. Fig. 3 shows a series of linear sweep cathodic stripping voltammograms (LS\u2013CSV) recorded with the mercury microelectrode in a 2 M Na2S+0.1 M NaClO4 solution at pH = 12. From this figure it is evident that for td \u2264 60 s (Fig. 3, curves a\u2013d), a single or two reduction peaks are obtained. The main peak is characterized by Epc values ranging between \u22120.84 and \u22120.73 V, and w1/2 of 10\u201320 mV. The splitting of the cathodic peak could probably be connected with the phase transition of the HgS formed at the electrode surface [49]. For td > 60 s (Fig. 3, curve e), two overlapped broader peaks, at potential between \u22120.900 and \u22120.960, are instead obtained. The cathodic current and charge values associated to the reduction peaks were analyzed as function of the effective deposition time, td,eff , given by: td,eff = td + (Epc \u2212 Ed) v (2) where Epc and Ed are the peak and deposition potentials, respectively, and v is the scan rate; the additive term represents the scanning period during which HgS accumulation continues [28]. The inset in Fig. 3 shows typical Ipc and Qc versus td,eff plots, for deposition time over the range 0\u2013300 s. The Ipc versus td,eff plot is not linear, as expected, whereas the Qc versus td,eff plot is linear, and its regression analysis yielded a correlation coefficient, R2, higher than 0.999. When relatively more concentrated sulfide solutions were considered, i.e. for Cs \u2265 20 M, a single peak was always observed (not shown). However, it became broader and shifted towards more negative potentials, with increasing the effective deposition time",
+            "1 M NaClO4 over the range of scan rates 20\u2013200 mV/s, using Ed = \u22120.4 V and td = 10 s. The peak current against scan rate yielded a straight line with a correlation coefficient of 0.9993. This is in accordance with the occurrence of an electrode process involving species adsorbed on the electrode surface [51]. The main peak and the width at half height remained almost constant, regardless of scan rate, as expected for a reversible process. It is interesting to note that when the main cathodic peak was accompanied by the small peak (Fig. 3), the latter tended to disappear as the scan rate increased. This result is con- gruent with the occurrence of an HgS phase transition [47]. The reproducibility of the cathodic stripping peak at lower sulfide concentrations was also investigated and, for instance, at 1 M Na2S level, peak current and charge were reproducible within 1.5%. Interesting is to note that LS\u2013CSV, which is not a very sensitive technique, can be employed for the determination of the analytical concentration of sulfide at a concentration level as low as 1 M, by using a deposition time of only a few seconds"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001635_3.20858-Figure7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001635_3.20858-Figure7-1.png",
+        "caption": "Fig. 7 Finite element model of the antenna and location of piezoelectric actuators.",
+        "texts": [
+            " This system is clearly more complex than the preceding one, and since the antenna structural damping is neglected and the overall system is a free body, it is open-loop neutrally stable. Nevertheless, it will be shown that the equivalent PWM control can be successfully applied also to this kind of system. The antenna studied in the present work consists of a large dish connected to the Shuttle by an aluminum L-shaped flexible truss.8 Figures 6-8 depict the topology and dimensions of the antenna, along with its finite element representation consisting of 95 grid points. Three representative points are marked in Fig. 7, and their dynamic behavior will be used to assess the performance of the system, i.e., node 480 at the corner of the flexible truss, node 751 at the center of the dish, and node 920 on the dish boundary. The flexible truss is considered to be clamped to the Shuttle. All of the elements are supposed to be uniform tubular beams with a cross-sectional area of 200 mm2, Young's modulus equal to 72,520 D ow nl oa de d by C O R N E L L U N IV E R SI T Y o n Fe br ua ry 1 , 2 01 5 | h ttp :// ar c. ai aa ",
+            " Six of them exert forces and moments on all six degrees of freedom of the rigid Shuttle; eight thrusters are placed on the flexible truss: four on the truss corner acting in the X and Y directions and four at the end acting in the Y and Z directions. The corresponding sensors are local displacement and velocity sensors. The control of the dish is carried out by using three reaction wheels, acting along the three axes at the connection with the truss, driven by angle and angular rate sensors and by six piezoelectric layers on the dish's outer radial beams, marked in Fig. 7 as Pi-P6- The piezoelectric layers are supposed to work in couples, one acting as an actuator and one as a sensor, measuring local deformations. For the piezoelectric actuators a lead-lag network has also been devised to provide better performance. Let { u s } indicate the forces acting on the Shuttle, { u t } the PWM forces on the truss, \\ u d ] the moments applied at the dish center, and { u p } the forces exerted by the piezoelectric actuators; by partitioning the measurements vector accordingly, the decentralized feedback control law can be expressed as (40a) (40b) (40c) (40d) The most common performance indexes used for antennas are the nominal pointing error and the average shape error, whose definitions and limits for a large reflector are pointing error = V { t f c ) ' \\ & c } / 3 <0"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003502_095440904322804439-Figure14-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003502_095440904322804439-Figure14-1.png",
+        "caption": "Fig. 14 Mesh of the FEM model and radial stress distribution at an intermediate stage of the press-\u00aet",
+        "texts": [
+            " As shown, roughness, materials typologies, lubricant, sliding speed and environmental conditions enter in the experimentally determined friction coef\u00aecient f by means of the constants A, B and C of equation (4), while wheelset geometry, interference and material properties enter directly as input data in the predictive models. The FEM model has been developed by means of the ABAQUS code. It comprehends a part of the axle with the wheel seat and the whole wheel, including the oil injection groove, as shown in Fig. 14. A unilateral contact condition with friction is imposed on the interface surface between the axle and wheel. An elastic\u00b1plastic material behaviour (and therefore the actual stress\u00b1strain diagram) could also be considered with this model, but the corresponding results differ very little from those obtained from the linear elastic hypothesis; the plastic zones are in fact present only for high interference values, but they are always very small and located at the wheel seat chamfer, with a negligible effect on the press-\u00aet curve",
+            " The sum of the reaction loads at the constrained end represents the press-\u00aet load, whose value is expected to increase with the wheel displacement, due to the increasing friction-resistant load. Proc. Instn Mech. Engrs Vol. 218 Part F: J. Rail and Rapid Transit F01203 # IMechE 2004 at HOWARD UNIV UNDERGRAD LIBRARY on February 28, 2015pif.sagepub.comDownlo ded from Several calculations were carried out in order to study the effect of the parameters under investigation. The local effects of the oil injection groove and that of the wheel seat chamfer are visible in Fig. 14, where the radial stresses (i.e. the contact pressures) are plotted for an intermediate stage of the press-\u00aet operation. In particular, the oil injection groove determines, as expected, a local decrease in the contact pressure, while the wheel seat chamfer determines a local increase. This last zone is therefore the most critical for the insurgence of damage mechanisms during the press-\u00aet. The global effects of these two geometrical discontinuities on the press-\u00aet curves are shown in Fig. 17, which refers to the Fiat Ferroviaria wheelset with a sliding speed of 300 mm/min"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003257_tro.2005.844679-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003257_tro.2005.844679-Figure5-1.png",
+        "caption": "Fig. 5. Test for planar cable robot where the outer attachment points of the cables coincide pairwise: Does the line segment from P to Q lie completely within the two reversed triangles? (For this case: No).",
+        "texts": [
+            " Thus, the same geometric criterion applies for force closure in both systems. Example 1: Force closure can easily be checked for the two-pair planar cable robot in Fig. 3(a) as shown in Fig. 4, by extending the lines of the cables and checking whether the line segment from P toQ lies completely within the two reversed open-ended triangles. This geometric criterion may be useful for the synthesis of planar cable robots. More importantly, it is an example of a tool from grasping that carries over to cable robots. Example 2: Shown on the left in Fig. 5 is a cable robot with cable pairs originating from the same point, i.e., the axes of their motors coincide. The corresponding criterion is demonstrated on the right in Fig. 5: Does the line segment from P to Q lie completely in the two reversed open-ended triangles? Note that in this case points P and Q are not located on the mobile platform. This section is based on the spatial antipodal grasp theorem, which can be formulated as follows. Spatial Antipodal Grasp Theorem [11], [12]: A spatial grasp with two soft-finger contacts is force closed if and only if the line connecting the contact points lies inside both friction cones. A grasp satisfying this geometric condition is called antipodal"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002460_63.85913-Figure7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002460_63.85913-Figure7-1.png",
+        "caption": "Fig. 7 . Operation of predictive controller: For r = r, A i Y reaches the tolerance area limit in I . The changing of the converter switching status from k to k, leads AiN back into the hexagon; then A i N does not leave it until Ar = f ( k , ) in 11.",
+        "texts": [
+            " If A i N has to be controlled such that it remains within the i,-tolerance region (hexagon), the reaction of the whole system to a switching decision has to be considered before it is \u201cexecuted\u201d by the converter. Certainly excluded should be that (old) KOLAR er al. : ON-AND-OFF LINE OPTIMIZED PREDICTIVE CURRENT CONTROLLERS 455 switching state k which actually makes necessary a converter switching status change (because the relevant trajectory leaves the hexagon). In general more than one of the remaining seven (only six fork = 0 or k = 7) possible switching states will lead the control error back into the hexagon (Fig. 7). Among these a selection has to be made in an optimal sense. One possible optimization criterion is, e.g., the maximization of the dwell time [ t( k , ) ] of the trajectory within the hexagon, weighted by the number of necessary switchings n ( k , k,) to get from the old converter switching status k to the new one k, (Fig. 8 ) . This acts as a switching frequency minimization. But via n ( k , k , ) / t ( k , ) only the local switching frequency is minimized (as, e.g. , in a steepest descent method) and does not necessarily mean that the global minimum will be found (compare I in Fig"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003206_iros.2004.1389402-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003206_iros.2004.1389402-Figure5-1.png",
+        "caption": "Fig. 5. Accelcrakd Joints in lacd Momcnlum Suppression Slagc",
+        "texts": [],
+        "surrounding_texts": [
+            "The structures on the knees are small and limited because the legs have to be light to give priority to walking. The structure of the hip joint at which three axes cross is very complex, so strong impact should not he applied to the joint. We use the harmonic drive distinguished by its precision and high reduction ratio in joint structures. Though the harmonic drive has a hack drivahility, it might breakdown if large force exerted against driving power of the motor.\nB. Posirion esrirnarion <$the mbot to thefloor The relative positional relationship between the robot and the floor must be found to detect the beginning of the fall and the current state of the motion. We assume that . the floor is a flat horizontal plane, . the falling motion of the robot is on the sagittal plane,\nand the robot is always in contact with the floor. The joint angles of the robot can he sensed by encoders, and the posture of the torso to the floor can be found from the accelerometer and the gyroscope mounted on HRk-2P through Kalman filter. Therefore we can know the relative relationship between the robot and the floor in principle. The remaining mission is how to find the positional relationship between the landing pan of the robot and the touch down point on the floor.\nTo this end, the following conversion is applied to the geometry of the robot.\ns The convex hull of each link is taken. Each convex hull is simplified to make the minimum depth between vertices larger than 2Omm. . The vertices that have no chance to hit the flat floor when the links are connected are removed.\nThe vertices of the simplified model are illustrated in Fig.2, and the number of the vertices for each link is summarized in Table II.\napproximation of the convex hull of the lower link of the legs. Therefore, the control algorithm also must take this into account.\n111. ALGORITHM\nWe propose the following algorithm to soften the landing of the knees while falling forward. The algorithm consists of four stages.\nDetection of falling over: When the projection of the center of the gravity onto the floor is not included in the convex hull of the soles, it is judged that the robot has staned to fall down. Then the mode of the controller is switched into the falling control mode, and the relative relationshin between the robot and the floor is found by the method mentioned above. Knee bending: The goal of this phase is to make the height of the knees as low as possible before its landing, since it is expected that the potential energy of\nWhile we consider the touch down of the knees to the flat floor, the relative relationship between the robot and the floor can be specified by the angle between the line",
+            "the knee can be smaller which will be converted into kinetic energy. To this end, the knee joints are bended at the maximum angular velocity until 8 becomes smaller than a pre-determined threshold (Fig.4).\nFit. 4. Knee bending\nBraking of the landing speed: The hip pitch joint, waist pitch joint and shoulder pitch joint are moved such that 0 should be braked. Landing: The feedback gains of the joints control are made one-tenth to make the joints compliant to the impact of the landing.\nThe details of the braking of the landing speed are as follows. The angular momentum of the robot around the tip of the feet increases while falling forward as\n(1) C = P ( ~ ) x mg: where C is the angular momentum, pft) the position of the center of the gravity, and m the total mass. C can be represented by\nwhere IO is the moment of inertia. When the hip pitch joint, waist pitch joint and shoulder pitch joint are driven actively, the angular momentum of the robot around the tip of the feet should be kept constant since no extemal force is generated. See FigS. Let A0 be the deviation of 8 caused by the motions of the joints, then\n(3)\nc = loa, (2)\n0 = Ioai + I ,& + 1 2 8 2 + I3&,\nwhere 8,,i = 1,. . . , 3 is the joint angle of the hip pitch, waist pitch and shoulder pitch respectively and Ii the moment of the inertia for a,, i = 1 , . . . , 3 respectively. Taking the sum of both sides of Eqs.(Z) and (3), we obtain\n(4)\nwhich means that ),can be braked by controlling ai. From Eq.(3), the desired can be given from a desired ABre\u2019\nc = I0(S +A%) + I101 + 1 2 8 2 + 1383,\nby\nwhere,()? stands for the pseudo inverse of a matrix. Let 8, = 0 + A@, the braked angular velocity, then Eq.(S) can be rewritten by\nwhere\nK1 = y, 1<2 = -70,\nwhere sup() stands for the supremum. Here, the supremum is determined by taking several joint values, because the values do not vary much.\nWe chose y so that S y remains within actual speed limits. Note that K2 depends on 8, but it is,fixed to a constant value, and that the magnitude of (K10o + Kz) is clipped at a specified value.\nIv. EVALUATION OF THE ALGORITHM\nA. Sin~ularions We use the dynamics simulator of OpenHRP [6] to simulate the proposed method. The dynamics parameters and geometry of HRP-ZP are used in the simulations. The integration interval of the dynamics simulation is 1 msec, and the outputs of the controller are updated every 5 msec.\nThe initial posture of the robot is the standing with a slight bending of the knees(Fig.6). Then a forward force with 100[N] is applied to the torso of the robot for 1.0 sec. When the robot s t a s to fall forward, the mode of the controller is switched from balancing mode to falling mode (Fig. 7) and the knees start to bend immediately.",
+            "In the simulation, 0 can be found from the attitude of the body and the vertices of the simplified convex hull. When 0 reaches the first threshold O', the braking of the landing speed stam(Fig. 8). 8' is set to 20 [deg] in the following s@ulations. While the braking is applied, is decreased to 00. When 00 reaches the second threshold 02, the controller goes into landing mode(Fig. 9). O2 is set to 10 [deg] in the simulations.\nThree kinds of the simulations are examined. The first one is the falling without any control, the second one is with the knee bending, and the third one is with the knee\nbending and braking. Fig. 10 shows the trajectories of 0 or Bo when braking is applied. The trajectories are not smooth,\nsince 0 is found by the relative relationship between the vertices on the knee and the floor and the representative vertex may change.\nWhen no control is applied e increases rapidly and the knees hit on the floor with 0 = .5.08[rad/sec]. The trajectory is shown as 'without falling over control' in Fig.10. The landing posture is shown in Fig.] 1 which looks very dangerous to the robot.\nWhen the knee bending is applied without the braking, 6 increases more rapidly in the initial phase than the previous"
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0001177_0954406011524711-Figure8-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001177_0954406011524711-Figure8-1.png",
+        "caption": "Fig. 8 Model of a ball impacting on a freely suspended racket, containing a spring and a damper in parallel (the ball), another spring in series (the stringbed)and a rigid body (the racket)",
+        "texts": [
+            " These parameters are experimentally determined and are dependent on the ball impact velocity. In an actual tennis stroke the racket is supported by the player\u2019s hand. However, it is very di cult to replicate this method of support in a laboratory. As mentioned previously, Brody [8] found that supporting a racket freely was the most valid method of simulating a player\u2019s grip in a laboratory. The ball was modelled as spring and damper in parallel, with the ball properties kb and cb , and the stringbed is modelled as a simple linear spring with stiVness ks , as illustrated in Fig. 8. The racket frame is modelled as a rigid body of mass mr and moment of inertia around the centre of mass (perpendicular axis) Ir . The ball impacts at a distance, d, from the centre of mass and the displacement of this point on the racket is xd . The linear and angular displacement of the centre of mass are de\u00aened as xr and \u00acr respectively. It was assumed that the force acting on the stringbed is applied to the racket frame as a point load, not as a distributed force. Therefore the force balance is F \u02c6 mb xb \u02c6 cb\u2026 _xb \u00a1 _xs\u2020 \u2021 kb\u2026xb \u00a1 xs\u2020 \u02c6 ks\u2026xs \u00a1 kd\u2020 (10) Fig"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001032_1999-01-0974-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001032_1999-01-0974-Figure1-1.png",
+        "caption": "Figure 1. Piston Ring Free Body Diagram",
+        "texts": [
+            " \u2022 Friction effects are from oil shearing only. It is assumed that the following magnitudes are known: \u2022 The instantaneous piston speed (Vp) \u2022 The oil viscosity (\u00b5) \u2022 The pressure behind the ring (P), including pressure due to ring tension and gas pressure \u2022 The basic ring geometry (c, a, and L), shown in Fig(1) The Reynold's equation, considering one-dimensional, incompressible flow will be used to calculate the oil film thickness and oil film pressure. The form of the equation is: (3) Referring the Fig. 1, the ring geometry is considered to be two parabolas, tangent at the point of minimum oil film thickness. The oil film thickness h, when considering this ring profile is: h = hx + ho (4) where: (5) and ho is the minimum oil film thickness. Once the oil film thickness and the oil film pressure are found by solving Eq. (3), the friction force may be obtained. Details are given in [26]. Piston Ring Simplified Model \u2013 The Stribeck curve (Fig. 2) illustrates the dependency of the friction coefficient f on the duty parameter S",
+            " This represent the contribution of the last term (\u2202h/\u2202t) in Eq.(3). This produces a loop in the Stribeck diagram, introducing a small amount of nonlinearity in the curve. A linear regressed relationship of the curve can be expressed as follows: ln(f) = m\u00deln(S) + ln(B) (6) The slope and y-intercept of the appropriate Stribeck curve are m and ln(B) respectively, depending on the ring\u2019s geometry. The curvature of the ring is defined as the ratio of the ring profile recess \u201cc\u201d at the ring edge to the height \u201ca\u201d of the parabolic profile (see Fig. 1). It has been found that varying the height L of the ring while maintaining a constant ring curvature does not influence the dependency of the friction coefficient on the duty parameter significantly [29],[30],[31], but there is a strong relationship between the ring\u2019s curvature and this dependency. Considering this, the model generates unique Stribeck curves for a given ring\u2019s geometry by varying the curvature of the ring. A linear regression has been performed to relate ln(f) to ln(S). When varying c/a from 0"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002931_te.2004.825528-Figure10-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002931_te.2004.825528-Figure10-1.png",
+        "caption": "Fig. 10. (a) Explosion and (b) assembly of the designed prosthesis.",
+        "texts": [
+            " After these two parts are completed, the students can integrate the circuits into a single-board system by soldering. Fig. 9 depicts the resulting circuit board. Making the mechanism of the prosthesis is a rather difficult part of the experiment since most students who major in EE are not competent machinists. To reduce the impact of this weakness, the components of the prosthesis are all made of aluminum or acrylics, since these materials are easy to reprocess and allow components to be made on a simple workbench. Fig. 10 shows the AutoCAD files, named explosion.bmp and assembly.bmp, which are the exploded and assembly drawings, respectively, of the components of this EMG prosthesis. The components of the prosthesis mechanism include a fixed part (A), a movable part (B), a linkage (C), and a main body (D). Using the actual-size data provided by the instructor, students can easily make all the parts of the prosthesis using hand tools. Furthermore, the students can draw the components using AutoCAD and convert the drawing to a DXF file for processing by a computer numerical control (CNC) milling machine"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure4.5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure4.5-1.png",
+        "caption": "Figure 4.5. A constant vector ro 1 in the rotating platform frame cp has a nonzero time derivative in the fixed frame <1> due to the rotation of cp relative to <1>.",
+        "texts": [
+            "17c ), we find the solution dx(A, t) dt (i sin f3 + IP cos /3) i +~sin f3 j + (i cos f3 -IP sin /3) k. (4.17d) This is the velocity of A as seen by an observer situated in the machine foun dation l/J but referred to the moving frame ({J for convenience; it is the (absolute) velocity of A relative to 1/J. The physical ideas illustrated here will be expanded further on. In preparation for our future studies, the student should find it helpful to deter mine the derivative of ( 4.17b) in the frames ({J and 1/J. D Example 4.3. An electric motor M shown in Fig. 4.5 is attached to a platform that rotates with a constant angular speed of 10 rev/sec about aver tical axis. The motor drives a gear G at a constant angular speed w 1 = 300 rev /min relative to the platform. (a) Find the time derivative of the angular velocity vector ro 1 in the fixed spatial frame 1/J. (b) What is & 1 in 1/J? (c) What are these derivatives in the moving frame ({J fixed in the platform? Refer all vectors to the frame ({J shown in Fig. 4.5. Solution. (a) The moving frame ({J = { 0; ik} is fixed in the platform with j directed along the center line of the motor axle. Thus, with modified units and referred to the moving frame ((J, rof = 20n:k rad/sec is the constant angular velocity of the platform frame ({J relative to 1/J, and ro 1 = lOn:j rad/sec is the angular velocity of the gear relative to the platform. It is clear from (4.10) that in the rotating ({J-frame broJ!bt=O; and it follows from the general rule (4.11) or by (4.12) that ( 4",
+            " (c) Because ro 1 is a constant vector in qJ, ali of its derivatives vanish in q>: bnw 1/btn = 0, as we saw above for n = 1, 2. This completes the problem solution. We have determined in ( 4.18a) the angular acceleration ro 1 in frame C/J when the angular velocity vector ro 1 is referred to the reference frame qJ which is turning with angular velocity ro1 in C/J. However, as shown in Example 4.1, we may obtain the same results by referring ro 1 to the preferred frame C/J. First, we must write the moving basis ik in terms of the fixed basis Ik. From the geometry of Fig. 4.5, we have i = cos 8 I + sin 8 J, j = cos 8 J - sin 8 I, k=K. ( 4.18c) Thus, referred to C/J, we have the general formula ro 1 = 10nj =JOn( cos 8 J- sin 8 I) rad/sec; ( 4.18d) and with e = lrotl = 20n radjsec, we obtain ro 1 = -lOnO(sin 8 J +cos 8 I)= -200n2i radjsec2, ( 4.18e) in which the change of basis back to qJ is left for the reader. This is the same as ( 4.18a ). Construction of ro I is left to the student. This method illustrates again that an important advantage of the procedure developed in this chapter of referring a vector to a moving frame is that unnecessarily complicated geometrical considerations may be avoided, particularly in three-dimensional problems, and the calculations are reduced in large measure to easy vector algebraic computations",
+            "25a) ro,o = ro\"\u00b7\" 1 + ro\" 1,o; O)n-1,0 = ron-l,n- 2 + ro,_ 2,0; Upon substituting the second of these into the first, and so on, we reach the important result stated in ( 4.24 ). In particular, for the special case n = 3, we see in the construction above and from ( 4.24) that (4.25b) The composition rule ( 4.22) plainly represents the generalized kinematic chain rule for angular velocity vectors. Some applications of these important results are presented below. Example 4.4. Recall the earlier Example 4.3 of a motor-driven gear mounted on a rotating platform shown in Fig. 4.5. Therein, the constant 244 Chapter 4 angular velocity of the gear relative to the platform is given as ro 1 = 1 Onh rad/sec; and ro1 = 20nk 1 rad/sec is the constant angular velocity of the platform relative to the ground. Determine the total angular velocity of the gear relative to the ground, but referred to a frame fixed in the platform. Label and identify carefully all references frames used. Solution. The problem statement suggests that three imbedded reference frames are relevant. The frames may be labeled in any convenient manner"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003352_j.tecto.2003.11.009-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003352_j.tecto.2003.11.009-Figure3-1.png",
+        "caption": "Fig. 3. Geometrical elements of a curve composed by a quarter of an ellipse and a line segment. This curve is used to fit isoclinal folds.",
+        "texts": [
+            " Since conic sections only range from chevrons to elliptical shapes, some natural folds cannot be fitted by a conic curve with a common middle point. In particular, cuspate folds or isoclinal folds, except those approaching a quarter of an ellipse, cannot be fitted by a conic. Isoclinal folds can be fitted by a function composed by a quarter of an ellipse, as defined by Eq. (1) in the interval [0, x0], and a line segment (x = x0, within bV yV y0) of length c that is a prolongation of the ellipse arc (Fig. 3), as was proposed by Bastida et al. (1999). This function allows us to extend the range of folds with a possible fit as far as the box shape. According to Bastida et al. (1999), the c value to fit an isoclinal fold by the middle point method is given by: c \u00bc y0 yM 1 ffiffiffi 3 p 2 : \u00f09\u00de 4. Graphical classification of folded surface profiles using conic sections The range of fold morphologies that can be represented using these functions can be visualised through the use of an h vs. e diagram (Fig"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003989_cimsa.2004.1397257-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003989_cimsa.2004.1397257-Figure2-1.png",
+        "caption": "Fig. 2. Single Link Flexible Robotic Manipulator",
+        "texts": [
+            " Thus the system will grow eventually. However, at any time instant if the system operating conditions approaches a previously established value, then those corresponding centers are used. Due to the above-mentioned dynamic RBFNN approach the curse of dimensionality issue is addressed. lV. POSITION CONTROL OF SINGLE LINK FLEXIBLE MANIPULATOR The proposed approach is applied to a single link flexible manipulator for tracking the angular position of the desired trajectory for two distinct cases. Figure 2 shows a single link flexible manipulator, which is modeled based on the physical parameters. The model details of the manipulator are presented in Appendix A. A command signal, which is applied for eight seconds, is tracked, and the tip load is varied arbitrarily at different time instant. The variation in the tip load contributes to the mode swings in the model. Different types of such mode swings are applied and the proposed scheme is tested for each case. The focus here is to compare the capability of the proposed intelligent controller with the traditional MRAC with the single reference model and varying reference model(s) to control such changes"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002923_acc.2005.1470620-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002923_acc.2005.1470620-Figure6-1.png",
+        "caption": "Fig. 6. velocity sectors for the ECAV and the phantom point",
+        "texts": [
+            "5 is for such a set of constant bounds which does not result in the phantom being contained within its velocity rectangle. As is clear from Fig.5, for the given set of initial conditions the target waypoint of the phantom is in that region the phantom can never reach. It is clear that the time varying nature of each of the bounds is critical for this particular approach to the problem. Now we consider constraints placed through bounds on the ground speeds of the ECAVs and the phantom point. Such constraints lead to the feasible velocity sectors being annular as illustrated in Fig.6. To allow more flexibility on the initial conditions, the ECAV, the phantom point and the radar (OEP) are constrained to be inline only at the beginning of each time step of the algorithm at which point the direction and speed are set for both the phantom point and ECAV. This collinearity constraint requires ( ) sin sin ( ) r t V R t W (10) A Necessary condition for solutions for (10) to exist is, ( ) sin 1 ( ) r t V R t W (11) where ,V W are the ground speeds of the phantom and ECAV respectively"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003477_cnm.913-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003477_cnm.913-Figure6-1.png",
+        "caption": "Figure 6. Factors of the system with the form II symmetry and its factors: (a) C; and (b) D.",
+        "texts": [
+            " Subspace V (1): 2 = (k1 + 2k2)/m and the subspace V (2): 2 = k1/m It should be noted that by solving characteristic-value problem of the original problem, the same natural frequencies would be attainable. The matrices of the system with canonical form II symmetry in which: AK =[k1 + k2] and BK = [\u2212k2] are decomposed into the submatrices C and D, as follows: CK =AK + BK = [k1] and DK =AK \u2212 BK =[k1 + 2k2] It can be shown that the factors C and D as new subsystems resulted from original system. These factors are depicted in Figure 6. In this figure, the correspondence between decomposition of the system and its graph model can be seen. Copyright q 2006 John Wiley & Sons, Ltd. Commun. Numer. Meth. Engng 2007; 23:639\u2013664 DOI: 10.1002/cnm In symmetry of form III, the axis of symmetry passes through at least one joint of the system. A simple example of such a system is shown in Figure 7. Consider the planar two-storey frame of Figure 7(a). The second storey of this frame consists of two separate rigid diaphragms with the mass of m2 which are connected together with an axial member, modelled as the spring k3"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003686_tmag.2004.824549-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003686_tmag.2004.824549-Figure2-1.png",
+        "caption": "Fig. 2. Radial and tangential components of the force.",
+        "texts": [
+            " The total simulation time was 1 s with a constant time step of 0.05 ms. In the spectral analysis, the number of sample points was 8192 in fast Fourier transform (FFT) and the length of the signal 4 s, by adding the zero level at the end of the sample to increase the frequency resolution of the frequency response of the forces. If the forces are divided into a radial component in the direction of the shortest air gap and a tangential component perpendicular to the radial one, the components are almost independent of time. Fig. 2 illustrates the force components. The advantage of the impulse method is that, from one simulation, the forces and harmonics are reached for a wide whirling frequency range. The use of the impulse method to calculate the electromagnetic forces is verified by conventional calculations for a strongly saturated induction motor in [11] and is validated by measurements in [12]. The results of the verification and validation show very good agreement. III. RESULTS A four-pole 15-kW induction motor was chosen as a test motor"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002883_robot.2004.1302491-Figure13-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002883_robot.2004.1302491-Figure13-1.png",
+        "caption": "Fig. 13 Measurement System of Propulsion",
+        "texts": [
+            " Fig.11 shows the swimming motion in the water surface. Fig.12 shows the swimming motion in the vertical direction reaction in water by changing buoyancy of the microrobot. Actuator ICPF ,4ctuator (0.2*3*15) Electricity (e.g.4V, 0.15A) VI. EXPERIMENTAL RESULTS n 5 3 - 3 2.5 0 c z 1.5 0 1 0.5 .g 0 ' \" ' \" ' . . ' \" \" ' 2 c4 0.10.20.30.40.50.60.70.8 1 2 3 4 5 6 7 8 9 10 frequency of input voltage (Hz) We made the swimming experiments of the prototype microrobot using a measurement system shown in Fig.13. The propulsive forces for various frequencies were measured using a laser displacement sensor, an electric balance and a copper beam. The copper beam is soft enough to be bent by the propulsive force. The electric balance is used for the force evaluation. We also measured the propulsion speed for various frequencies using a high-speed camera. The average value of over 20 data is used as the final test data. By changing the frequency from 0.2Hz to 5Hz at 2.5 voltage input, the experimental results of average propulsive force, and average speed are shown in Fig"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001980_robot.1995.526028-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001980_robot.1995.526028-Figure1-1.png",
+        "caption": "Figure 1 - An Enveloping Grasp",
+        "texts": [
+            " We also allow contact with one or more fixed surfaces (such as a palm or torso), and explicitly take into account the (possibly stabilizing or destabilizing) effect of an external force such as gravity. Note that we use \u201cfingers\u201d as a generic term to represent any finger, fixture, or link in point contact with the grasped object. Our procedure is particularly applicable in the case of enveloping grasps; it is, however, applicable in all grasps, enveloping or not. 2. Modeling and Problem Formulation Consider Figure 1. Let nf be the number of independent fingers in contact with the grasped object, and let \u2018nc be the number of contacts on finger i. The superscript \u201ciJ\u2019 is used to denote the j f h contact on the ith finger. Further, let np be the number of contacts with fixed surfaces, and let the superscript \u201cl\u201d denote the l fh contact with a fixed surface. In Figure 2, we consider a contact between a grasped object and a finger. If the bodies are perfectly rigid we can define the contact point which is the coincidence of two points, iJJoB fixed to the grasped object and i\u2019JoA fixed to the finger"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003057_0141-0229(86)90134-1-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003057_0141-0229(86)90134-1-Figure1-1.png",
+        "caption": "Figure 1 A, d.c. cyclic voltammogram at a 4 mm diameter pyrolyt ic graphite electrode of ferrocene monocarboxylic acid (200 #M) in Tris--HCI (50 mM) buffer pH 7.0 containing MgCl= (20 mM) and glucose (10mM) at ascan rate of 1 mVs -1 a n d 2 0 \u00b0 C . B , A s f o r A but wi th the addit ion of glucose oxidase (11 #M) and subsequently hexokinase 20 U ml -I . Finally, ATP (10 mM) was added and voltammogram B reverted to voltammogram A",
+        "texts": [
+            " cyclic voltammetry to study enzyme catalysed radox reactions which form the basis for the development of biosensors 12 and biofuel cells. 13 Particular attention has been given to the use of ferrocene derivatives as electrochemical mediators. 6'14'1s Here, cyclic voltammetry is used to demonstrate the effect on the electrochemically coupled glucose oxidase catalysed reaction (equations 6 and 7) of hexokinase in the presence of its substrates (equation 2). The cyclic voltammogram of ferrocene monocarboxylic acid in buffer containing glucose (10 mM)is shown in A of Figure 1. This voltammogram is consistent with the electrochemically reversible ferrocene-ferdcinium ion oneelectron redox couple, (E1/2 = 280 mV vs SCE; AEp 60 mV). Addition of glucose oxidase, B of Figure 1, causes a marked increased in the anodic current, consistent with electrochemically coupled oxidation of glucose , 6 as shown in equations (6) and (7). Upon addition of hexokinase (20 U ml -~ ) to the cell no change in the shape of the voltammogram occurred; however, when ATP (10 raM) was also added catalytic behaviour was no longer observed and the voltammogram returns to that of the reversible electrochemistry of the ferrocene, curve A of Figure 1. This observation is consistent with complete phosphorylation of glucose, equation (2), thus removing it as a substrate for the glucose oxidase catalysed reaction. In this experiment only sufficient ATP to phosphorylate all of the glucose initially present was used; consequently, by further addition of glucose the catalytic reaction, curve B of Figure 1, could be restored. Having demonstrated that this coupled reaction sequence for detecting ATP worked in a homogeneous system, it was feasible to study the glucose enzyme electrode, 6 first as an ATP sensor and then for monitoring creatine kinase activity. Glucose enzyme electrode The current-time response of the glucose enzyme electrode in a cell containing 1 ml buffer with glucose (10 #mol) and hexokinase (20 U) was allowed to reach the steady-state ca. 60-90 s. 6 (The initial steady-state current was 10/IA; this corresponds to a rate of glucose consumption by the enzyme electrode of ca"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000980_9.310037-FigureI-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000980_9.310037-FigureI-1.png",
+        "caption": "Fig. I . A model of car.",
+        "texts": [],
+        "surrounding_texts": [
+            ".. System. Moscow-MIR, 1978.\n[IO] V. I. Utkin, \u201cVariable structure systems with sliding modes,\u201d lEEE Trans. Automat. Control, vol. 22, pp. 21 1-222, 1977. [ 1 I ] V. I. Utkin, \u201cVariable structure systems-present and future,\u201d Auto. Remote Contr., pp. 1105-1 120, 1983. [I21 V. I. Utkin and K. D. Yang, \u201cMethods for construction of discontinuity planes in multi-dimensional variable structure systems,\u201d Auto. Remote Contr., pp. 14661470, 1978. [I31 V. 1. Utkin, \u201cEquations of the sliding regime in discontinuous system,\u201d Auto. Remote Contr., pp. 211-218, 1972. [I41 J. J. E. Slotine and S. S. Sastry, \u201cTracking control of nonlinear systems using sliding surface with application to robot manipulators,\u201d Int. J. Control, vol. 38, pp. 465-492, 1983. [ 151 A. F. Filippov, \u201cDifferential equations with discontinuous right hand sides,\u2019\u2019 Am. Math. Soc., vol. 62, pp. 199-231, 1964. [I61 Y. Y. Hsu and W. C. Chan, \u201cOptimal variable structure controller for DC motor speed control,\u201d in Proc. Inst. Elec. Eng., 1984, pp. 233-237. [I71 R. A. DeCarlo, S. H. Zak, and G. P. Matthews, \u201cVariable structure control of nonlinear multivariable systems: A tutorial,\u201d in Proc. IEEE 1988, 1988, pp. 212-232. [ 181 J . J. E. Slotine, \u201cOn modeling and adaptation in robot control,\u201d in Pmc. IEEE Int. Conf: Robotics and Automation, 1986, pp. 1387-1392. [I91 J. S. Reed and P. A. Ioannou, \u201cInstability analysis and robust adaptive control of robotic manipulators,\u201d IEEE Trans. Robotics and Automation, vol. 5, pp. 381-386, 1989. [20] T. C. Hsia, \u201cAdaptive control of robot manipulators-A review,\u201d in Proc. IEEE Int. Conf: Robotics and Automation, pp. 183-189, 1986. [21] S. Dubowsky and D. T. Desforses, \u201cThe application of model referenced adaptive control to robot manipulators,\u201d ASME J. Dynamics Sys., Meas., Contr., vol. 101, pp. 193-200, 1979. [22] J. J. Craig, P. Hsu, and S. S. Sastry, \u201cAdaptive control of mechanical manipulator,\u201d in Proc. IEEE Int. Conf: Robotics and Automation, 1986,\n[23] J. J. E. Slotine, \u201cSliding controller design for nonlinear system,\u201d Int. J. Contr., vol. 40, pp. 421-434, 1984. [24] J. J . E. Slotine and W. Li, \u201cOn the adaptive control of robot manipulators,\u201d presented at the ASME Winter Annual Meeting, Anaheim, CA, pp. 51-56, 1986. [25] -, \u201cAdaptive manipulator control: A case study,\u201d in Proc. IEEE Int. Conf: Robotics and Automation. 1987, pp. 1392-1400. [26] -, Applied Nonlinear Control. Englewood Clifs, NJ: Prentice-Hall, 1991. [27] P. Ioannou and J. Sun, \u201cRobust adaptive control,\u201d class notes of EE685, USC, 1992. [28] L. W. Chen and G. P. Papavassilopoulos, \u201cRobust optimal force variable structure and adaptive control of single-ann and multi-arm dynamics,\u201d Ph.D. dissertation, Department of Electric Engineering-Systems, Univ. Southern Calif., 1991.\npp. 190-195.\nI. INTRODUCTION Let us consider a car moving forward and backward with a lowerbounded turning radius R (without any loss of generality, we assume R = 1) and an upper-bounded velocity. The position and the direction of the car are, respectively, defined by the coordinates ( x . y) of the reference point and the angle 0 between the abscissa axis and the main axis of the car (see Fig. 1). So, the car is completely defined as a point (z, y. 8 ) in the configuration space R2 x SI. If we assume that the linear velocity is constant, the motion is defined by the control system\nwith Iul( t ) l = 1 and I I L Z ( ~ ) ~ 5 1 where u1 and 7 ~ 2 are, respectively, the linear and angular velocity of the car. Such a differential system expresses kinematic constraints which characterize the nonholonomic nature of the car [4]. This is the Reeds and Shepp model.\nInitially this model has been introduced by Dubins [3] for a car that moves only forward (i.e., t i 1 1). He determines a sufficient family of shortest paths.\u2019 Using this result and the result of Melzak [6], Robertson [lo], and Cockayne and Hall [Z] provide the set of accessible positions for the model of Dubins (i.e., ul = 1).\nThe problem of finding a shortest path between two configurations when backward motions are allowed ( 1 1 1 = +l) has been set by Reeds and Shepp in [9]; it has been completely solved after a sequence of different works 111, [9], [ I l l , [12].\nThis paper solves the following problem:\nHow do we compute the set of reachable positions from the origin by path of a given length when the final direction of the car is not specified?\nIt is solved in two steps: among all the paths linking an initial position with fixed direction of the car to a final position with free direction, we point out a shortest one. Then, from the shortest path expression, we obtain the complete analytical description in the plane (0. .T: y ) of the set of positions reachable from the origin by a path of length lesser than some given value. Section I1 presents the state of the art on Reeds and Shepp\u2019s problem. Section I11 shows how to apply the Pontryagin Maximum Principle (PMP) to compute a sufficient family of optimal paths. This family is then reduced by\nManuscript received March 4, 1993; revised August 31, 1993. This work was supported by the ECC Espirit 3 Program within Project 6546 PROMotion.\nThe authors are with LAASCNRS, 7 Avenue du Colonel Roche, 31077 Toulouse, France.\nIEEE Log Number 9401680. \u2019 i.e., a family rich enough to always contain a shortest path to link any two\nconfigurations.\n0018-9286/94$04.00 Q 1994 IEEE",
+            "direct geometric arguments. Section IV presents the synthesis of the optimal paths: i.e., we give the closed-form expression of the optimal control law that steers the system from the origin to any position. Finally, Section IV presents the set of positions reachable from the origin by a path of length lesser than a given value. Our work is based on Optimal Control Theory and uses previous results of Reeds and Shepp [9], Sussmann and Tang [12], and Boissonnat et al. [I]. We complete our proof with geometric arguments.\nRemark 1: For the Reeds and Shepp problem, the synthesis of optimal paths computed in [ 111 provides a partition of the space2 R2 x [-n, n] induced by the shape of the path reaching the origin. In [ 5 ] , Laumond and Soubres have studied the metric induced by the shortest paths for this model of a car. By using the shortest path synthesis, they compute the ball B,I for any value of the radius d. The set of reachable positions by path of length d computed in Section V, is the projection of the ball Bt3d in the horizontal plane (0. .r. y). The method used to compute the partition of the plane (Section IV), and the set of accessibility (Section V) is similar to the methods developed in [ 5 ] , [ 111. Nevertheless, for this two-dimensional problem the transversality conditions given by the PMP (Section 111-B) provide a reduction of the sufficient family. This simplifies the problem.\n11. THE REEDS AND SHEPP\u2019S PROBLEM\nSince 1990, from the pioneering work of Reeds and Shepp [9], several contributors [ 11, [ I I], [ 121 have studied the problem of finding the shortest path between any two configurations.\nNotation: The paths are described using Sussmann\u2019s notations: ( S ) denotes a straight line segment and (C) an arc of a circle with radius 1. The symbol I between two letters indicates the presence of a cusp. The subscripts are positive real numbers referring to the length of the corresponding pieces. We also use 1 for left turn and r for right turn and the superscript + ( - ) denotes forward (backward) motion. When these superscripts are used, the cusp symbol I is redundant and does not appear.\nFirst, using geometric arguments, Reeds and Shepp have proved that the shortest path can always be chosen among 48 simple sequences of at most five pieces, with a piece being a straight\n21n [ I I ] it is shown that it IS equivalent to consider R2 x S\u2019 or R2 x [-T, TI.\nline segment (S) or an arc of a circle (C ) of radius 1. These simple paths contain at most two cusps. Recently, this problem has been studied within the Optimal Control Theory framework by Sussmann and Tang [12] and Boissonnat et al. [l]. They independently give a new proof of Reeds and Shepp\u2019s result by using PMP and also refine it. Particularly, Sussmann and Tang have reduced the number of the sufficient family elements to 46. Finally, Soubres and Laumond [ 111 achieve the synthesis of the shortest path. New limitations appear for the validity of each type. By combining all these conditions, the search for an optimal path can be restricted to the sufficient family as shown in (1) at the bottom of the page. We will call every member of this family a Reeds and Shepp\u2019s path.\n111. THE FREE FINAL DIRECTION PROBLEM\nA. Definition\nLet us denote by A0 the line parallel to the @-axis passing by (2, y, 0) in the configuration space R2 x S1. The final configuration is free on A0 and the final direction 8\u2019 will appear as the result of the shortest path characterization. Thus, our problem can be restated as:\nFind a shortest path between the origin (0, 0, 0) and the line Ao.\nIt is clear that a path reaching (I. y, 8 \u2019 ) optimal for our problem (i.e., optimal among all admissible paths starting from (0, 0, 0) that reach AS) is optimal among all the paths that reach the configuration (s, y. 8 * ) . As there is always a Reeds and Shepp\u2019s path optimal between two entirely specified configurations, there is always a Reeds and Shepp\u2019s path optimal for our problem.\nThis remark allows us to search for an optimal path in the sufficient family ( I ) only.\nB. Maximum Principle and Transversality Condition\nWhen an optimal control problem has some free boundary conditions, the Pontryagin Maximum Principle [8] provides as many additional conditions, called transversality conditions, as free boundary conditions are. Under some regularity assumptions, these conditions mean that if an initial (final) state is free on a given manifold ,U then the adjoint vector 9 at the initial (final) time is orthogonal to the tangent hyperplane of M at the initial (final) state. Since [U 1 I = 1, searching for the shortest paths is equivalent to minimizing the time. Now, let us construct the Hamiltonian function \u2018H\n\u2018H = 90 + 91 cos 8 11 1 + 9 2 sin Ou 1 + 9 3 r r z (2)\nand the differential adjoint system i , = -E = 0 9, = -E = (1\n+ 9 1 is constant =+ 9, isconstant\n9, = -- : - !FL sinoul - !F,cosHrr1 = - 9 2 . i - .",
+            "Here, the third differential equation is integrable and we obtain Pig(t) = @ 1 y ( t ) - ! F z x ( ~ ) +93(0) . Again, the Hamiltonian function Fig' 3' A piece I is Optima' can be written as\nwith\nd1 = !P1 cos19 + Q2 sin8\nand\n4 2 ( t ) = !F3(t) = P l y ( f ) - 9 2 X ( t ) + @3(0).\nFirst, we summarize the results obtained in [I], [12]: The constant QO is never zero on an optimal path, 61 and 4 2 are not simultaneously zero, Then, t f being the final time, we have two kinds of paths: -Paths with u1 singular over [0, t , ] and for which u2 does not\nswitch. These are the paths C I C I C. -Paths with U 1 bang-bang over [0, t r ] . We use the fact that the\nHamiltonian function 1-I is zero along an optimal path. Then, d l = 0 implies that QO + 42u2 = 0. From the expression of d2, this equality defines two parallel lines in the plane (x, y). As in [I] , we call them D+ (respectively, D - ) when u2 = 1 (respectively, u2 = -1). These lines are symmetric with respect to the line Do defined by $2 = 0. DO supports the straight line segments and the points of inflection and the cusps occur perpendicularly on D+ or D-. These paths remain between D+ and D- (see Fig. 2 and [I] for details).\nHere, the initial state is entirely specified, and the final state is free on the line &. Then, the transversality condition expresses that the adjoint vector 9 at the final time t f is orthogonal to that line. In other words\n(4)\nFirst, identifying the transversality condition (4) with the expression of 42, we obtain the following lemma.\n9 3 ( t f ) = * i y ( t f ) - * . L X ( ~ J ) +*3(0) = 0.\nLemma 1: The final point is on the line DO. On the other hand, from the transversality condition, we have the following lemma. Lemma 2: TL cannot be singular on an optimal path. Consequently the Reeds and Shepp's path C I C I C is not optimal here. Proof: From the Maximum Principle [l], the paths C I C I C correspond to the singularity of the control component u 1 . On I L I - singular extremals, the time function d l ( t ) vanishes over the whole interval [0, t f ] . This implies that 31 and PZ are zero over [0, t f ] . As P3( t f ) = 0 by the transversality condition, the adjoint vector P(tf) is the zero vector. By the Maximum Principle, there always exists a\n0 These lemmas provide a first reduction within the sufficient family\n1) First of all, we can draw out the types that never end on the line Do. These types are: CC, I C,C, CSC, C I CC, c 1 CbCG I c, and c I C,j2sC when they are not degenerate (i.e., when the length of each portion does not vanish).\nnonzero adjoint vector Q along an optimal path.\n( I ) as follows:\n2) The type C I C I C does not appear.\n3) Thirdly, concerning the types CC I C, C I Csj2SCa/2 I C, CSC,I~ I C, the last two arcs have necessarily the same length to end on the line DO. Hence we only have to consider the types\nAt this stage, we have shown that an optimal path must belong to one of the following three types: C I C,/2SC,j2 I C,j2, CSC,/2 I Cej2, CC, I C, with a 5 ~ / 3 . Now we use simple geometric arguments to reduce again this family.\nIn these cases we can replace the path by a shorter one by extending the piece of straight line on DO up to the final point. We then construct a path C I C,j2S or CS.\nType CC, 1 C, with a 5 ~ / 3 In this case we have the following lemma.\nLemma 3: A portion C,, I Ca. a 5 ~ / 3 : at the end of a path is not optimal.\nProof: Let CO and C1 denote the two tangent circles with radius 1 which support the curve and I the initial point on CO. F the final point on CI and T the point where the two circles are tangent. Then, for a 5 ~ / 3 , we construct the circle C2 with radius 1, passing through F and tangent to CO at P (see Fig. 3). Let 0, be the center of the circle C, and V the line which passes through 00 and bisects the line segment [OI, 0 2 1 perpendicularly. Let M denote the point of V on the arc&: By symmetry the path ,.IT I &. has the same length as the path M P I P>. The line (I. F) is the line DO: while (00, 01) is the line D+ or D-. Then, :;?. This implies that the path Ip I PF is shorter than the path I T F . Therefore we can conclude that a\nU So the type CC, I C, is not optimal and we have the following theorem. Theorem 1: A sufficient family for the free final direction problem is C, I cT/2sd with a < ir /2 and d 2 0, C, I Cb with a < b < x / 2 , c,sd with U 5 a12 and d 2 0.\nCC, I Ca, csc,/2 I Crj2, c I CS/2SC,/Z I C*j2.\nTypes C I CxpSCaj2 I G j 2 and CSC,/Z I C a p\npath with a final portion C, 1 C, is not optimal.\nIv. OPTIMAL PATH SYNTHESIS\nIn this section, we solve the synthesis problem by simple geometric arguments. We give the closed-form expression of the optimal control law that steers the system from (0, 0, 0) to any given position ( x , y ) .\nIf 7 is a path from (0, 0, 0) to (s. y, 8) then there is a path 7, from (0, 0, 0) to ( x , --y. -8) symmetric to (7) with respect to the abscissa axis. In the same way, there is a path IY from (0, 0, 0) to ( - x , y, -8) symmetric to 7 with respect to the ordinate axis. By combining these two symmetries one can build another path, called -7, symmetric to 7 with respect to the origin, from (0, 0, 0) to\nAccording to this remark, if 7 is optimal for the free final direction problem, then one can build three other optimal paths I,, 'TY, and -7 isometric to 1. So our problem has two perpendicular symmetry axes. Therefore, we shall limit our study to the first quadrant.\n( - X . -y, 8 ) ."
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0002222_1.533555-Figure12-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002222_1.533555-Figure12-1.png",
+        "caption": "Fig. 12 Tooth flank measurement",
+        "texts": [
+            " Once the Path of Contact ~PoC!, e.g., the locus of all contact points on the tooth flank, is obtained, the Bearing Pattern is easily calculated by searching for a given separation between the meshing tooth surfaces along the PoC. A.4 Tooth Surface Measurement and Error Surface. Tooth surface measurement is performed by a Coordinate Measurement Machine, or CMM, using a high precision probing head which, when moved in different directions, detects contact with an obstacle such as a tooth flank ~Fig. 12!. The probe is a small sphere of known radius. The Error Surface is the difference between the theoretical and measured coordinates in the direction of the tooth surface unit normal for each measurement data point. Since measurements correspond to the center of the probe sphere, the measured coordinates are compensated using the following relation: X\u0304comp5X\u0304Meas2R\u2022N\u0304 (A5) where X\u0304comp is the compensated tooth flank coordinate, X\u0304Meas is the measured coordinate, R is the probe sphere radius, and N\u0304 is the tooth flank unit normal vector"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003554_13552540510601309-Figure10-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003554_13552540510601309-Figure10-1.png",
+        "caption": "Figure 10 Equal valued iso-parametric lines of two surface patches on same vertical plane",
+        "texts": [
+            " Further, equal valued isoparametric lines of the two surfaces are contained on the same vertical plane (Figure 9). Last of all, the iso-parametric lines of the ruled patch are all straight lines. A number of such vertical planes separated by small parametric increments are considered across each Bezier surface patch to detect the intersection points. So, the search for intersection between the two surface patches is reduced to a 2D check for intersection between their respective iso-parametric lines in a vertical plane (Figure 10). In order to track down an exact intersection, the horizontal distance between the Bezier iso-parametric and Ruled patch iso-parametric is determined. A flip in the sign of this distance vector indicates the existence of an intersection. The exact Volume deviation in direct slicing Chandan Kumar and A. Roy Choudhury Volume 11 \u00b7 Number 3 \u00b7 2005 \u00b7 174\u2013184 intersection point is located by iterating and reducing the parametric interval within which the intersection is detected. Figure 11(i) shows the CAD model with a locally reconstructed Bezier patch. Few of the intersection points obtained by the above procedure are shown in Figure 11(ii). For calculating the volume deviation (cusp volume), each reconstructed Bezier surface patch is checked for intersection points (Figure 10). If no intersection points are present throughout the Bezier surface patch then cusp volume is given by equation (5). If intersection points were present (as found by the IS algorithm), the Bezier surface has to be apportioned accordingly. First the Bezier surface is separated into strips along one iso-parametric direction. Any one of such strips comprises of two consecutive lines from the set of isoparametric lines used for detecting intersection points in the IS algorithm. Several cases may arise: (1) If the iso-parametric lines constituting the strip do not have any intersection point then the volume deviation (cusp volume) is given by: dv \u00bc jVBP \u00fe VTS \u00fe VRP \u00fe VBSj \u00f06\u00de (2) If the iso-parametric lines constituting the strip have only one intersection point each"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001045_a:1019555013391-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001045_a:1019555013391-Figure2-1.png",
+        "caption": "Figure 2. Body i \u2013 forward kinematics.",
+        "texts": [
+            " In our formalism, the reference point for computing the resultant joint force Fi and pure torque Li (for joint i) being chosen as the point Oi (located on the parent body h), the following augmented parameters are also introduced: bi z = m\u0304izi + bi = \u2211 j :i\u2264j mj dij z ; Ki z = Ii \u2212 \u2211 j :i\u2264j mj d\u0303ij z d\u0303ij z (4) defined with respect to point Oi (Figure 1). The kinematic formulation is of course similar to the one used for the classical recursive Newton\u2013Euler scheme. We shall briefly recall these equations for our case. In Figure 2, the various kinematical elements are represented and in the following equations, \u03d5i and \u03c8 i represent unit vectors aligned with joint i axis, respectively for a revolute and a prismatic joint. For body i, one can write: \u2022 Absolute position vector: pi = ph + dhi z , for the attachment point Oi on body h. (5) \u2022 Absolute velocities: \u2013 angular: \u03c9i = \u03c9h + \u03d5i q\u0307i; (6) \u2013 linear: p\u0307i = p\u0307h + \u03c9\u0303h .dhi z + \u03c8hq\u0307h. (7) \u2022 Absolute accelerations: \u2013 angular: \u03c9\u0307i = \u03c9\u0307h + \u03c9\u0303i .\u03d5i q\u0307i + \u03d5i q\u0308i; (8) \u2013 linear: p\u0308i = p\u0308h + (\u02dc\u0307\u03c9h + \u03c9\u0303h "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003587_1.2125971-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003587_1.2125971-Figure2-1.png",
+        "caption": "Fig. 2 Schematic diagram of the TriVariant",
+        "texts": [
+            " Two are identical UPS limbs and the other is a UP limb whose output link is fixed with the mobile platform. Here, U, P and S represent the universal, prismatic, and spherical joints respectively, and P denotes that the corresponding joint is active. The TriVariant can be considered as a simplified version of the Tricept robot, achieved by integrating one of the three active limbs into the passive one while keeping the required type and degrees of freedom. For simplicity, we use \u201cTricept\u201d and \u201cTriVariant\u201d to refer to the 3-DOF modules in what follows. Figure 2 shows a schematic diagram of the TriVariant, where Bi for i=1, 2, 3 represent the centers of the U joints and Ai for i=1, 2 the centers of the S joints. A3 is the intersection of the axial axis of the UP limb and its normal plane in which Ai i=1, 2 is located. Since limb B3A3 is fixed with the mobile platform, A3 can also be considered as the reference point of the mobile platform. Similar to Tricept 605 9 , it is assumed that the rotation axes of the outer ring of the U-joints of the three limbs are parallel and located in the same plane",
+            " It was reported in 12 that the order of the end polynomial equation of the Tricept is 24, meaning that it may have at most 24 real solutions. Whilst, it is easy to see from Eq. 11 that the order Transactions of the ASME hx?url=/data/journals/jmdedb/27819/ on 03/20/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F of the end polynomial equation of the TriVariant having a general geometry is 8, resulting in at most 8 real solutions though the type and degrees of freedom of two robots are identical. The difference in the number of solutions will be explained in Sec. 5. 3.2 A Special Case. As shown in Fig. 2, if B3\u2212x3y3z3 is placed in such a way that either B3B1 or B3B2 is coincident with the x3 axis, i.e., the rotation axis of the outer ring of the U joint of the UP limb, the position vector of Bi in B3\u2212x3y3z3 becomes bi = bix biy 0 T = bi 0 0 T 13 For simplicity, let i=1, then b1x=b1 and b1y =0, leading to d12 =d13=0. As a result, Eq. 7 for i=1 is simplified as d11 = A1s 3 + B1c 3 + C1 = 0 14 where A1 = 2q3b1, B1 = 2a10xb1, C1 = c1 Thus, 3 can be explicitly obtained by 3 = 2 arctan \u2212 A1 A1 2 + B1 2 \u2212 C1 2 C1 \u2212 B1 15 On this basis, since b2y 0, Eq",
+            " 7 for i=2 becomes A2s 3 + B2c 3 + C2 = 0 16 where A2 = 2b2y a20xs 3 \u2212 q3c 3 , B2 = 2a20yb2y C2 = c2 + 2b2x q3s 3 + a20xc 3 This means that 3 can also be explicitly achieved by 3 = 2 arctan \u2212 A2 A2 2 + B2 2 \u2212 C2 2 C2 \u2212 B2 17 It is easy to see that for this special case the TriVariant may have at most 4 real forward position solutions. Obviously, the same conclusion can be drawn when B3B2 is coincident with the x3 axis. The dimensions of the TriVariant given in 13 is employed for the forward position analysis, with B1B2B3 and A1A2A3 shown in Fig. 2 being equilateral triangles, and the position vectors of Bi in B3\u2212x3y3z3 and Ai in A3\u2212u3v3w3 being given by b1 = 519.62 \u2212 300 0 T b2 = 519.62 300 0 T a10 = 103.92 \u2212 60 0 T a20 = 103.92 60 0 T In order to justify the results of the forward position analysis, the position vector of A3 is arbitrarily chosen within the workspace as follows: r3 = 450 350 850 T 18 This allows a set of limb lengths to be determined by the inverse kinematic analysis as a reference for the forward kinematics. q1 = 1011.69, q2 = 790"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001980_robot.1995.526028-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001980_robot.1995.526028-Figure4-1.png",
+        "caption": "Figure 4 - A Planar Contact",
+        "texts": [
+            " We utilize Equations (17), (24), and ( 5 ) to get: K, = The eigenvalues of KG are strictly greater than zero, and thus the grasp is stable. 4. Planar Grasps A slight change in notation is required. The frame 0 is again the world reference frame, chosen at an arbitrary location, and a frame oc is again defined (fixed in space) at each contact point. However, both are planar x-y frames, and oc is aligned at each contact such that the y-axis is along the inwardly pointing normal of the grasped object, while the xaxis is parallel to the common tangent (see Figure 4). For a gravitational force, the frame ocg coincides with the center of gravity, and is aligned such that y-axis points in the same direction as the gravitational force. The curvature of the grasped object (the signed inverse of the radius of curvature at the point of contact, positive for convex surfaces) is denoted by KB, while the curvature of the fingedfixed surface is given by KA. Finally, the tangential force at equilibrium is denoted as Fto. If we let the force vector F = [F,,, F,, MIT, and let x be the position vector given by x = [x, y , BIT, we get: KG is again given by Equation ( 5 ) where we redefine (.)T as follows: let (dx, dy) be the coordinates of the frame 0 as seen from (.)oc, and let CP be the relative angle of rotation of 0 from the frame (hc (see Figure 4). (.IT is given by: AFIO = KG Axlo (25) cos@ -sin@ = [si;@ co; @ -!x J (26) We define FX and & as: i K ~ is still given by Equation (24), while we can use the spatial results to define Kc as: - 1370 - 1 K, and FX above are written for a frictional contact. If the contact is frictionless, k, and F, should be set equal to zero. 4.1. Example 2 Consider the enveloping grasp of a slippery elliptical object, as shown in Figure 5. Since the coefficient of friction is very low, the contacts are modeled (conservatively) as frictionless"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001930_5326.923273-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001930_5326.923273-Figure2-1.png",
+        "caption": "Fig. 2. Inverted pendulum system.",
+        "texts": [
+            "8) for the region nm 2 0, where Gnm a G nm nm 0 T 0 ; Gnm a Gnm nm 0 T 0 Pa P 0 0 T 0 and Qnm ai = Qnm i Rnm i Rnm T i snmi (i = 1; 2): Proof: By definition, it is clear that the Lyapunov function candidate represented by (27) is continuous, piecewise differentiable, positive definite and descresent so that there exist > 0 and > 0 such that kx(t)k2 V (t) kx(t)k2: (29) The time derivative of V (x) is given as follows: dV dt = _xTa P nm a xa + xTa P nm a _xa + xTa _P nm a xa = Cof(G nm x + nm )TPnmx + xTP nm(Gnm x+ nm ) (Gnm x+ nm )TP nmx + xTP nm(Gnm x+ nm )g: a.e. By following the procedure of Proposition 1 and Corollary 1 with the exception that P is replaced with P nm dV dt < 0 a.e. Then, by the nonautonomous Lyapunov theory [34], the closed-loop fuzzy system is asymptotically stable. IV. EXAMPLE In this section, an illustrative example is provided to demonstrate the validity of the suggested stability analysis method. The plant to be controlled is an inverted pendulum with two states x = (x1 x2) T = ( _ T ) as in Fig. 2. The task here is to design and analyze an FLC that balances the pendulum. Its dynamics are nonlinear and is represented by the Takagi\u2013Sugeno fuzzy model as follows [11]: R1: If x1 is about 0; then _x = A1x+B1u: R2: If x1 is about =4; then _x = A2x+B2u: and other parameters are as follows. The mass of the cart M is 8.0 kg, the mass of the pole m is 2.0 kg, the distance of the center of mass m from the cart is 0.5 m, the gravitational constant g is 9.8 m/s2, and a = 1=(m+M). The FLC fedback by the position ( ) and its derivative is designed by human beings"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003354_1.2101857-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003354_1.2101857-Figure1-1.png",
+        "caption": "Fig. 1 Schematic of brush seal",
+        "texts": [
+            " Findings also indicate that variations in front plate geometry do not directly affect leakage performance. A long front plate or damper shim considerably changes the flow field while at the same time having limited effect on the pressure field. Moreover, a strong suction towards the clearance enhances inward radial flow in clearance operation. DOI: 10.1115/1.2101857 Developments in brush seal design have demonstrated the significance of the flow field dictating seal dynamics and performance. As illustrated in Fig. 1, early designs utilized short front plate configuration. Welded at the outer periphery, front and backing plates clamp the bristle pack. The straight backing plate is extended to provide mechanical support for tiny bristles. This geometry is referred to as the standard or conventional brush seal. The bristle pack is divided radially into two distinct regions, which are labeled the fence height and upper regions Fig. 1 . The fence height is the radial height between bristle tips and backing plate inner diameter. The upper region, on the other hand, is the rest of the bristle height out to the bristle pinch point. The aim of brush seal evolution and continued efforts at development have been to raise brush seal performance, benefits, and usage. A review of the literature reveals that most of the improvements and disclosures to date have focused on the geometry of front and backing plates. The number of issued patents dealing with brush seal geometry is considerably high",
+            " After an extensive effort at calibration, radial pressure on the backing plate, axial pressure on the rotor, and leakage are all compared well with experimental data and other porous medium analyses. Details of the calibration data will be discussed in the results and discussion section. 2.1 Front Plate Configurations. In order to cover common concepts while keeping the number of analyses manageable, five different front plate configurations, as illustrated in Fig. 2, have been selected. The standard seal geometry, which is referred to as case 1, has a short front plate and straight backing plate, as given by Bayley and Long 20 and Turner et al. 21 Fig. 1 . This configuration is set as the baseline. The model uses a bristle pack thickness of 0.75 mm 0.0295 in. . The thickness of the front and backing plates is 1.6 mm 0.0630 in. . The fence height is set at 1.4 mm 0.0551 in. with a free bristle height of 10.68 mm 0.4205 in. . In the second configuration, a long front plate in contact with the bristle pack is employed. In terms of flow formation, this case represents a damper shim application. Case 3 is a typical long front plate configuration with a relief"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002583_ias.2000.880991-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002583_ias.2000.880991-Figure6-1.png",
+        "caption": "Fig. 6. Fully pitched winding SRM",
+        "texts": [
+            " Therefore torque can be derived using: teeth Combining the above equations gives: Therefore, once the tooth flux/MMF/position characteristics are known (whether by FE or measurement) a corresponding torquelcurrentlposition characteristic can be determined. This may then be used to determine the instantaneous running torque. The torque per tooth, derived from the flux1MMF curves of fig. 4 (a), is shown in fig. 5. 111. DETAILED SIMULATION RESULTS The simulation method has been implemented and extensively validated through comparison with measurements, made upon an SRM with three phase fully pitched windings (see fig. 6). Details of this machine are given in the appendix. All results presented here use an asymmetric half bridge converter for each phase supply. The per tooth flux/MMF/position characteristics have been derived by measurement and the results embedded as a lookup table in the simulation software. Comparisons with measurement will be presented in section IV, but it is first worth looking at detailed simulation results, which help explain operation of the machine. The parameters shown in figs. 7 to 9 are in the order that they are calculated in the simulation, as shown in the flow chart of fig"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003764_bf02953383-Figure19-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003764_bf02953383-Figure19-1.png",
+        "caption": "Fig. 19 Negative casting mold for radial bearing pad.",
+        "texts": [
+            " The test showed that there was no instability in the axial direction, since the mass was well below me, but that tilt vibrations would commence as soon as the diametral 88 R. Snoeys and F. AI-Bender 5.2 Non-Deformable Bearing Surfaces Bearing pads with a non-deformable wall may be manufactured with a similar casting technique as indicated in Fig.l8; however, the casting has to be carried out now with respect to an appropriate negative shape. This casting model for a radial bearing pad may by obtained as illus trated in Fig.19. The molding cylinder is provided with a membrane. Cylinder and membrane are accurately machined at the nominal diameter of the bearing pad. The membrane may be deflected radially corresponding to the desired amount of the convergency of the gap. The same technique can be used for axial bearing pads, the bearing pad itself may also be made directly by diamond-tool turning on a precision lathe. 6. CONCLUSIONS (1) A significantly larger carrying capacity may be obtained by using convergent gap shapes"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000403_s0924-0136(98)00412-9-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000403_s0924-0136(98)00412-9-Figure3-1.png",
+        "caption": "Fig. 3. A schematic rendering of three candidate deposition path cross-sections: (a) raster path; (b) profile path; and (c) spiral path.",
+        "texts": [
+            " dimensions of motion (X,Y interpolation and a Z incremental motion) this shape was a good demonstration of the technology because it demonstrated the deposition of a shape that would be difficult or impossible to fabricate using conventional methods. 2.3. Fabrication procedure A substrate plate was fixtured horizontally and the DLF deposition head positioned vertically aligning the focal point of the laser and powder at the surface of the plate. The model allowed a variety of tool paths to be evaluated by simply making changes to the model parameters and regenerating new deposition paths. Geometric renderings of candidate tool paths are shown schematically in Fig. 3. To maintain a consistent build up from one layer to the next, yet achieving full fusion of the deposit from one layer to the next, the system parameters, such as laser power, had to be chosen as a function of the deposition path parameters. The laser head orientation was held constant vertically (normal to the deposited surface). System parameters were automatically sequenced as a function of system commands embedded within the tool path. The numerical control file was loaded into the system controller and run in open loop using the parameter set given in Table 3",
+            " The DLF process is characterized by a much more complicated set of processing conditions that require precise control to achieve an acceptable end product. Presently limited to open loop control, a parameter study is often required when changing materials, or specific geometry. Various candidate deposition path types were evaluated and analyzed. The track width, step-over distance and fill path algorithm were the main parameters considered. The three basic path types first evaluated are shown in Fig. 3. Fig. 3a shows a Type 1 path in which a raster motion is used to traverse the areas to be deposited in a series of connected linear parallel motions. A larger number of short starts and stops are seen along with a number of retractions and traversal movements, shown as dotted lines in Fig. 3a. Associated with the many starts and stops are a number of acceleration/deceleration movements, the cumulative effect of which resulted in an unwanted build-up of fused material, particularly in the narrow wall sections. Retraction and traversal movements connecting the disjointed deposition sections are seen to cross open areas where no deposit was desired, thus requiring a laser shutter closing. The time constants associated with acceleration/deceleration and beam shuttering disturbed the deposition consistency at normal process speeds. Smooth fully fused layers of the deposit were not achievable using the raster deposition path type. Fig. 3 b shows multiple perimeter paths that may be used to ensure a sharp well defined edge along the wall of the deposited part. Fig. 3 c shows a Type Spiral tool path characterized by many fewer starts, stops and traverse motions. More time is spent depositing material and less time spent in traverse moves, acceleration and deceleration. More locations within the area to be spiral deposited suffered from a variation in deposition path spacing as shown in Fig. 3 c than with the Type 1 raster path shown in Fig. 3 a. Faster, smoother deposition was realized with the spiral path, although small unfused regions were observed in the locations corresponding to variations in the step over distance. Table 3 provides the laser parameters used. Fig. 4 a\u2013d show an optimization of the spiral tool path achieved through a selection of a smaller \u2018tool\u2019 size parameter. Fig. 4 a and b show a section of a spiral tool path and the corresponding location in a part cross-section deposited using this path, respectively. A small amount of porosity resulting from insufficient fusing of one trace into the next was seen at the locations of wider deposition path spacing"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001045_a:1019555013391-Figure8-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001045_a:1019555013391-Figure8-1.png",
+        "caption": "Figure 8. Simple two-dimensional human body model.",
+        "texts": [
+            " This problem can be circumvented by moving the reaction forces an torques measurement point. Obviously, the best place would be the trunk since this leads to the minimum length kinematic chain. The idea would be to rigidify the trunk by some lightweight equipment, and to connect this equipment to a force measuring platform. In this case, the maximum number of dof in the kinematic chain reduces to six which is quite better according to Figure 7. In order to compare the results we can expect from both techniques, we have applied them to a rather simple model of the human body (Figure 8), consisting of six bodies interconnected by revolute joints. This model has been used to analyze a recorded movement of block in volleyball. The dynamical parameters will be identified using both techniques and compared to the exact values of the model. Based on the recorded block movement, we will then compare the calculated joint torques based on the two sets of identified parameters to the actual ones. The identification trajectory is composed of six different movements in which each limb is successively moved"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002082_s1350-4533(01)00125-4-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002082_s1350-4533(01)00125-4-Figure1-1.png",
+        "caption": "Fig. 1. Model of the human body, consisting of six segments. All segments were considered to be solid links with constant masses, lengths, and moments of inertia. X1, Y1, Z1 represents the global coordinate system with origin O at ground level. The X-axis is oriented vertically. The Y-axis is in the plane of progression of gait. The Z-axis is orthogonal to the plane of XY. FX and FY represent the tripping forces.",
+        "texts": [
+            " Furthermore, models with one, two, or three links were developed to predict the impact velocity and force of falls to the side from a standing position [30,31]. However, there have been no reports on the application of dynamic simulation during gait to falling. The purpose of this study was to develop an analytical model to simulate and visualize the motion of a body during a muscle relaxed fall after tripping on an obstacle during gait. The human body was modeled as a set of six articulated, rigid segments with revolute joints (Fig. 1). The swing phase of gait was modeled as an open chain linkage with one end of the system (i.e. the stance ankle) fixed to the floor and the other end (i.e. the swing ankle) in space. The segments consisted of the stance foot, shank, and thigh, HAT (head, arms and torso), and the swing thigh and shank. The joints consisted of the stance ankle, knee, and hip joints, and the swing hip and knee joints. The stance ankle was modeled as a three degrees of freedom (dof) joint, the stance and swing knees as single dof joints (flexion\u2013extension) and the stance and swing hips as three dof joints"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000732_s0301-679x(98)00043-7-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000732_s0301-679x(98)00043-7-Figure2-1.png",
+        "caption": "Fig. 2 Detailed drawing of the conical bearing",
+        "texts": [
+            " Therefore, water pressure is increased at the outlet of the feeding holes due to the centrifugal force under rotation and water in the bearing clearance is pumped up by the viscous effect of spiral grooves. This raises water pressure in the bearing clearance and the proposed bearing can have large load capacity and excellent stability at high speeds. Table 1 shows the principal dimensions of the proposed bearing. These values are used in theoretical calculations and the experiment mentioned below. Fig 2 shows the coordinate system of the conical bearing treated in this paper. In numerical calculations, water flow in the bearing clearance is assumed to be laminar, viscous and isothermal. In the calculation of pressure distribution for the groove\u2013ridge region, the narrow groove theory by Vohr6 is adopted. The mass flow rates for unit width in the s and u directions in the bearing clearance, h, are given as follows, considering the centrifugal force qs 5 2 rh3 12m \u2202p \u2202s 1 h3 12m \u00b7 3 10 rs sin2g\u00b7v2 (1) qu 5 2 rh3 12m \u2202p r\u2202u 1 rs sing\u00b7vh 2 The overall pressure derivatives \u2202p\u0304 \u2202s , \u2202p\u0304 r\u2202u are expressed by using the local groove and ridge derivatives \u2202pr \u2202s , \u2202pr r\u2202u , \u2202pg \u2202s and \u2202pg r\u2202u Tribology International Volume 31 Number 6 1998 333 \u2202p\u0304 \u2202s 5 a \u2202pg \u2202s 1 (1 2 a) \u2202pr \u2202s , \u2202p\u0304 r\u2202u 5 a \u2202pg r\u2202u 1 (1 2 a) \u2202pr r\u2202u (2) where a is a fraction of the width of the ridge\u2013groove pair that is occupied by the groove"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000980_9.310037-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000980_9.310037-Figure6-1.png",
+        "caption": "Fig. 6. plane (right). The partition of the first quadrant (left) induces the partition of the",
+        "texts": [
+            " There are four types in the family C,sd. and each of them leads to points lying in a different quadrant. So any additional refinement is unnecessary. D. Partition of the First Quadrant From the sufficient family given in Theorem 1 and the refinement above the partition of the first quadrant is completely built. The three domains of this partition correspond to the paths: l,l:,,s,j with n < ir /2 and d 2 0, 0 l;l$ with a < c < n/2. . l tsf with b 5 i r /2 and d 2 0. The outline of the different domains appears easily (see Fig. 6). The boundary between the domain of points reachable by a path Its+ and the domain of points reachable by a path l ~ Z ~ T l z ) s ~ is obtained when a = 0, b = 7 ~ 1 2 . It is the upper vertical half-line from the point (1, 1). The boundary between the domain of the type l ~ l ~ ~ , s ~ and the domain of the type 1,l: is obtained for n = b , P = 7712. and d = 0. It is an arc of the circle centered at Oo(0. -1) and with radius 6. Between the domain of the type 1;l: and the domain of the type Its:, the boundary is obtained for a = 0"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003382_s11340-006-9257-4-Figure12-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003382_s11340-006-9257-4-Figure12-1.png",
+        "caption": "Fig. 12. Rotation and slide motion of a rigid ball during an oblique impact with a target",
+        "texts": [
+            " The increasing rates of % and q tended to decrease slightly as vi increased. The average tangential velocity vt and angular velocity w were determined by dividing % and q by the contact time tc. The results are plotted in Fig. 11. There was some scattering of the data; however, vt and w increased almost linearly with vi: vt = 3.1, 10.3, and 20.1 m/s while w = 1,297, 3,851, and 9,216 rpm for vi = 10, 29, and 60 m/s, respectively. Note that the values of vt were about 30% of vi. Rigid Body Model The rigid body model illustrated in Fig. 12 was used to study the dynamic contact behavior. Here, the target was stationary and inclined at an angle qi to the vertical, and a ball of mass m and radius r plunged into the target horizontally with an inbound ball velocity vi. The following assumptions were made. First, the ball and target were perfectly rigid. Second, F = 2R, where F is a frictional force between the ball and target, 2 is the coefficient of sliding friction, and R is a reactive force perpendicular to the target surface. Third, the tangential ball velocity vt was gradually reduced due to F, while the angular velocity 5 was gradually increased"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000299_301-Figure8-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000299_301-Figure8-1.png",
+        "caption": "Figure 8 . Figure 9. Figure 10.",
+        "texts": [
+            " EQUIVALENCE O F A C U R R E N T C I R C U I T A N D A M A G N E T I C S H E L L I N ALL M E D I A The confusion mentioned in 5 1 may now be discussed. This arises through forgetting that the forces due to magnets or current circuits immersed in a polarizable medium depend on the shape of the cavity in which they are placed, and further, that a current circuit can be put in two different cavities whereas a magnetic shell cannot. The current circuit can be put in the medium either by removing a cylindrical channel to take just the wire itself (figure 8) or by inserting it as a whole in a disc-shaped cavity (figure 9). The latter cavity is suitable for the equivalent magnetic shell (figure 10) whereas the former is not. I t is easy to see that as long as we treat the circuit T o see this clearly, consider figures 8,9 and 10. 40-2 and magnetic shell in a similar manner they will be equivalent in the medium just as they are in a vacuum. Consider the Internal Magnetic Force at any point P in each case : in figure 8 there is no surface distribution of free pole, so that F , = 0. Hence H = H A and the field is the same as in vacuo. In figures 9 and 10 a surface distribution of 596 pole of amount I appears, equivalent to a row of doublets acting in the opposite direction to the fields of the current and the shell. This produces a force Fl at P, so that we have now H = HA - Fl. We can easily show that this becomes H A / p . Let 4 be the strength of the shell, i.e. the magnetic pole per unit surface, I is the magnetic pole per unit surface of the cavity, so that at P the potential, which is !2 = wC in a vacuum (where w is the solid angle subtended by the shell or circuit at P), becomes i2 = w(+ -I) in the medium = U# (/A - 4myp = ** P Thus the potential, and consequently the force, is reduced in the ratio /A : 1. This clearly applies also to the current circuit in figure 9. The difference between the cases illustrated in figure 8 and figure 10 has led many authors of well-known text-books to be at pains to explain that a current circuit and a magnetic shell which are equivalent in air are no longer so in a medium of permeability p. In fact, it is maintained that the magnetic shell of strength i in air must be of strength pi in the medium. We have seen, however, that a current circuit and a magnetic shell which are equivalent in a vacuum are equivalent in any medium provided that they occupy similar cavities. The force A new treatment of electric and magnetic induction 597 they produce is, in each case, diminished in the'ratio p : 1. A current circuit in which the wire is entirely surrounded by a medium, as is normally the case in gases and liquids, exerts the same magnetic force as in a vacuum. If we consider the force on a current element at P, i.e. the force in a disc-shaped cavity whose axis is parallel to the magnetization, we find : figure 8. B = p H and H = HA4 ; :. B =pH,, or p times as great as in a vacuum. figures 9 and 10. B =pH and H = Ha4/p ; :. B= H,, or the same as in a vacuum. Thus when a current circuit is entirely surrounded by the medium, as in figure 8, the Internal Magnetic Force is unaltered but the Internal Electromagnetic Force or Induction is p times as great. If the circuit is in a cavity as in figure 9, the Internal Electromagnetic Force is unaltered and the Internal Magnetic Force is p times less. No difference arises, however, in the cases illustrated in figures 9 and 10, whether we consider the respective magnetic or the electromagnetic forces. We can conclude therefore that a current circuit and a magnetic shell are wholly equivalent in all media, provided they occupy similar cavities",
+            " In these cases it will be necessary to consider as well the effect of cavities in which the measurements are made, since the assumptions made in choosing our rod-shaped and disc-shaped cavities (suitable only for point-poles) will not in general hold ; the direction and intensity of the magnetization may not, for instance, be constant over the region occupied by the cavity. Such cases will therefore require special treatment. One case of importance can be dealt with : that of the current balance which is used for defining the unit of current. Here the current coils are situated as in figure 8, i.e. surrounded entirely by air or partly by other materials such as marble. The force between the coils is therefore greater than would be the case in a vacuum. The very small value of the permeability of air makes a correction unnecessary. 5 15. T H E FIVE ELECTROMAGNETIC RELATIONS We can now re-state in rather more precise form than usual the five electro- magnetic relations : (1) The magnetic potential at a point produced by a current flowing in a closed linear conductor is equal to the strength of the current i multiplied by the G"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003288_j.conengprac.2004.04.023-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003288_j.conengprac.2004.04.023-Figure2-1.png",
+        "caption": "Fig. 2. Airframe axes.",
+        "texts": [
+            " Typically, if the system is persistently exciting, then all the parameters will converge to their true values. The missile model used in this study derives from a nonlinear model produced by Horton of Matra-British Aerospace (Horton, 1992). This study will look at the reduced problem of a 2 DOF controller for the pitch and yaw planes without roll coupling. The angular and translational equations of motion of the missile airframe are given by \u2019r \u00bc 1 2 I 1yz rV0Sd 1 2 dCnrr \u00fe Cnvv \u00fe V0Cnzz ; \u2019v \u00bc 1 2m rV0S\u00f0Cyvv \u00fe V0Cyzz\u00de Ur; \u00f02\u00de where the variables are defined in Fig. 2 and Tables 1 and 2. Eqs. (2) describe the dynamics of the body rates and velocities under the influence of external forces (e.g. Cyv) and moments (e.g. Cnr), acting on the frame. These forces and moments are derived from wind tunnel measurements and by using polynomial approximation algorithms, Cyv;Cyz;Cnr;Cnv and Cnz (Horton, 1992) can be represented by polynomials which can be fitted to the set of curves taken from look-up tables for different flight conditions. A detailed description of the model can be found in Horton (1992)"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002746_0278364905060149-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002746_0278364905060149-Figure4-1.png",
+        "caption": "Fig. 4. Installation examples of displacement sensors in universal joint and revolute joint.",
+        "texts": [
+            " For the variables gBi and gSi , the direction in which each anvil of the sensor\u2019s head is pushed is decided to be positive. A master ball used in each joint must have proper sphericity to be a reference surface for the runout measurement. In addition, the sensor head\u2019s anvil must preferably be a plane because it is in contact with the spherical surface of the master ball. at UNIVERSITY OF BRIGHTON on July 11, 2014ijr.sagepub.comDownloaded from The master ball can be installed in a universal joint, as shown in Figure 4(a), and in a revolute joint, as shown in Figure 4(b). In any case, the sensor can measure both the elastic deformation and the runout of the spherical joint to compensate for the limb\u2019s length change. In particular, because it is considerably difficult to manufacture joints with both high stiffness and high rotational accuracy, this compensation method is noticeably useful. In an extreme case, the sensor measures any joint play in the limb direction. Generally, some materials with low thermal expansivity, such as Super-Invar (expansivity: 0.3\u20130",
+            "2, respectively, were adopted in an experimental CMM (Oiwa 1997, 2000) shown in Figure 8. This CMM uses the three-degrees-of-freedom parallel manipulator shown in Figure 2(b). The sectional view of an extensible limb is shown in Figure 9 in detail. Using the same method as that shown in Figure 3, an electrical comparator (Mahr 1202IC+1304K) is installed in the spherical joints connecting the limbs with the machine frame. Two electrical comparators are also used to measure the errors of the revolute joint as shown in Figure 4(b). Moreover, Super-Invar rods connect a scale unit (Sony BS75, with measuring length at UNIVERSITY OF BRIGHTON on July 11, 2014ijr.sagepub.comDownloaded from 220 mm and resolution 50 nm) with the spherical joint and the revolute joint, respectively, to eliminate the influence of the limb\u2019s thermal and elastic deformations according to the same method as that shown in Figure 5. The scale unit and the linear scale mounted on Super-Invar plates are guided by using a simple notch type linear spring to allow them to move in the longitudinal direction"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002746_0278364905060149-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002746_0278364905060149-Figure1-1.png",
+        "caption": "Fig. 1. Various causes of relative positioning error between tool and workpiece for conventional machines.",
+        "texts": [
+            "1177/0278364905060149 \u00a92005 Sage Publications KEY WORDS\u2014parallel kinematics machine, error compensation, joint runout, joint deformation, frame deformation, thermal expansion, machine tool, coordinate measuring machine When improvement of machining accuracy and measurement accuracy is required, it is extremely important to accurately obtain the relative position between the tool and the workpiece of the machine tool or the coordinate measuring machine (CMM). In an actual machine, however, internal and external disturbances (shown in Figure 1) noticeably cause positioning errors. Thus, not only moving accuracy but also structural and thermal stability in the whole machine are strongly required for achievement of precision. In general, much improvement in guide element accuracy and structural stiffness has been achieved to decrease the motion error and the elastic deformation caused by external and internal forces (e.g., Ramesh, Mannan, and Poo 2000a; Lee et al. 2004). However, increased mass along with such improvements has caused further motion error and elastic deformation due to increased inertial force and frictional force"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000540_0094-114x(95)00106-9-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000540_0094-114x(95)00106-9-Figure1-1.png",
+        "caption": "Fig. 1. The Stewart platform.",
+        "texts": [
+            " Unlike the convention of developing a set of kinematic equations and then solving them, an alternative approach is proposed which involves just a search and verification purely from geometric considerations. An attempt at conceptual construction of the mechanism under given constraints results in the prediction of tentative solutions, which are subsequently corrected. The algorithm is implemented and two case studies are reported. The proposed algorithm is simple to implement, finds all the real closures and is applicable to the most general case of the Stewart platform. Copyright \u00a9 1996 Elsevier Science Ltd I. I N T R O D U C T I O N The Stewart platform (Fig. 1), a generalization of a mechanism originally proposed by Stewart [l] as a flight simulator, is the most famous parallel manipulator having two bodies connected by six extensible legs with spherical joints at both ends (or spherical joint at one end and universal joint at the other). One of the bodies is fixed to the frame and forms the base, while the other, known as the platform acts as the end-effector. The leg extensions are the six inputs which can provide an arbitrary position and orientation (6-DOF) to the platform within its workspace"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001980_robot.1995.526028-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001980_robot.1995.526028-Figure6-1.png",
+        "caption": "Figure 6 - A Force Closed, Frictionless Grasp",
+        "texts": [
+            " If the intrinsic stiffness matrix is unstable (contains a negative eigenvalue), the grasp stiffness matrix will also be unstable; however, a intrinsic stiffness matrix which is stable (positive definite) does not necessarily imply that the grasp stiffness matrix will also be stable. Nguyen [13] showed that force closed grasp can be made stable essentially by proving that (his version of) the intrinsic stiffness matrix is positive definite. However, the intrinsic stiffness matrix excludes the compliance of the finger joints. Thus, when the entire system is analyzed, it is possible for a force closed grasp to be unstable. idyTi~jKc~~jT + 5 ITT 'K, 'T + cgTT KcgcgT (29) 5.1. Example :3 Consider thle grasp shown in Figure 6, where each of the contacts is frictionless. This is a force closed grasp. We choose the reference frame, 0, coincident with the contact frame ',Ioc. Thus the transformation matrix IsrT is the identity matrix, and the other transformation matrices are given by: The contact stiffness matrix, K,, the Jacobian, Jg, the joint stiffness, K+ and E are the same for all contacts. We have: 0 - 1371 - while k, = 10000 N/cm. In order to insure equilibrium, we have the following two conditions: As written, the grasp stiffness matrix, KG, is a function of both the applied force, \u2019,IF, and the joint stiffness, K,. For relatively stiff joints applying a small force (a low ratio of I\u2019a\u2019FI to K ) this grasp is stable. However as we increase the the grasp becomes progressively less stable. With the values of applied force and joint stiffness given in Figure 6, an easy calculation using the method in this paper shows: 3JF = L J F and 2 4 7 =4,4F = 1,521 ratio of II, ;P FI to K9 (a weaker spring applying a greater force) I 20000 0 95394 0 20000 -15906 842 -368 3787 95394 -15906 485676 -9.9 842 %=[:;.: 198 -3681 The eigenvalues of KO are positive, as expected since the grasp is force closed. But, the eigenvalues of KG are (-16.8, 4009, 190}, and thus the grasp is unstable. 6. Discussion In this paper, we extend the results of Cutkosky and Kao [3] by including curvature in determining the compliance of a grasp"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003257_tro.2005.844679-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003257_tro.2005.844679-Figure4-1.png",
+        "caption": "Fig. 4. Test for full constraint of this planar cable robot: Does the line segment from P to Q lie completely within the two reversed triangles? (For this case: Yes).",
+        "texts": [
+            " Planar Antipodal Cable Theorem: A planar cable robot with two pairs of cableswith coincident attachment pointsP andQ is force closed if, and only if, the line from P to Q lies completely in the two open force triangles defined by the reversed forces of the two cable pairs. Proof: The set of forces the planar cable robot with the above properties can apply to the moving platform is identical to the set of forces that the two-finger planar friction grasp with fingers from the inside in the aboveCorollary can exert on the object to be grasped. Thus, the same geometric criterion applies for force closure in both systems. Example 1: Force closure can easily be checked for the two-pair planar cable robot in Fig. 3(a) as shown in Fig. 4, by extending the lines of the cables and checking whether the line segment from P toQ lies completely within the two reversed open-ended triangles. This geometric criterion may be useful for the synthesis of planar cable robots. More importantly, it is an example of a tool from grasping that carries over to cable robots. Example 2: Shown on the left in Fig. 5 is a cable robot with cable pairs originating from the same point, i.e., the axes of their motors coincide. The corresponding criterion is demonstrated on the right in Fig"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure2.18-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure2.18-1.png",
+        "caption": "Figure 2.18. Crossed helical gears and their velocity components.",
+        "texts": [
+            "In par ticular, when the shafts intersect in a right angle, 8 + \u00a2 = n/2 and (2.84) becomes 0 < 8<n/2. (2.85) Example 2.8. Helical gears may be used to transmit rotary motion between nonintersecting and nonparallel axles. Their helicoidal shaped teeth allow relative sliding of the gear teeth along their common contact line, but the teeth prevent slipping normal to that line. The sliding motion provides a smooth, quiet operation with less shock than is common with other gears having straight teeth. A typical crossed helical gear arrangement is shown in Fig. 2.18. The angles l/1 d and l/1 1 are the constant helix angles of the driver and follower gear teeth, respectively; and their sum is the angle between the gear shafts. Determine the angular speed w1 of the follower gear when the drive gear has an angular speed wd, and the shafts are fixed in the machine. Solution. Let r d and r1 denote the radii of a mutual contact point A from points on the fixed axles, as shown in Fig. 2.18. Then we may write (2.86) 116 Chapter 2 for the respective velocities of the contact point A on the driver and on the follower. The tangent line of the helical teeth at A, denoted by t, forms the helix angles t/1 d and t/11 with the gear axles. Each gear has a sliding component of velocity in the tangential direction t, so the criterion for rolling without slip cannot be applied to the velocities (2.86 ). Rather, only the components of these vectors perpendicular to the teeth are equal: (2.87) wherein n is the normal vector to t as shown in Fig. 2.18. It is seen that the velocity vectors (2.86) make the same angles with n that the shafts make with t; these are the helix angles. Hence, their components in the direction of the normal n satisfy (2.87) when wdr d cos t/1 d = w1 r1 cos t/1 1 . (2.88) Therefore, the angular speed of the follower gear is r d cos t/1 d wf= wd. rrcos t/11 (2.89) Since (2.89) depends on both the helix angles and the gear radii, a variety of angular speed relations is possible. For gears of equal radii, for example, the angular speed of the follower will be greater than that of the driver provided that the helix angle of the follower is the larger",
+            " (2.90) Therefore, the velocities may be equal if and only if 1/J f = -~r d\u00b7 This is possible only when the angle between the shafts is zero, that is, when and only when the shafts are parallel. The negative sign means that the helices of parallel helical gears must have opposite hand so that they slope in opposite direc tions away from the viewer. Crossed helical gears, contrariwise, usually have the same hand so that the helices slope in the same direction away from the viewer, as assumed in Fig. 2.18, which shows right-handed helical gears. The problems studied so far have involved only plane motions for which the angular velocity and the angular acceleration are parallel vectors, and for which use of the geometrical interpretations of the vector products often is especially helpful in their calculation. The analysis of spatial motions, because of the increased complexity and the difficulty of visualizing the geometrical aspects of a problem, inherently is more difficult; but the use of vector methods in these applications often simplifies their analysis and eliminates our need to perceive all of the geometrical details"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure4.13-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure4.13-1.png",
+        "caption": "Figure 4.13. Gyroscopic rotations of a simple machine during a routine aircraft maneuver.",
+        "texts": [
+            " This tendency of the aircraft to pitch forward or backward may be compensated by adjustment of the control flaps, but this causes large stresses to be induced on the structural framework. Analysis of these so-called gyroscopic effects requires under standing of the rotational motion of the spinning device in a rotating reference frame. The following example illustrates the application of the composition rules ( 4.24) and ( 4.35) to the description of a spinning disk supported by a shaft fixed in an aircraft executing simultaneous turn and roll maneuvers. A rotating disk D shown in Fig. 4.13 is driven at a variable angular speed \u00a2 through a shaft BD supported in bearings in an aircraft. Gyroscopic effects arise when the aircraft executes a turn, roll, or dive maneuver. Let us consider the case when the aircraft turns with angular speed ~ about a vertical axis fixed in space and simultaneously rolls with angular speed (} about its central axis BP. We wish to find the angular velocity and angular acceleration of D relative to the ground frame, but not necessarily referred to it. Afterwards, we shall evaluate these quantities at the initial instant when 1/1 = e = 0. We begin as usual by defining some appropriate reference frames. The frame 0 = { G; i, j, k} denotes the ground frame; and frame 1 = { B; a, b, k }, which is fixed to the vertical plane A BD as shown in Fig. 4.13, rotates with angular speed ~ about the vertical axis k of frame 0. Hence, this frame follows the aircraft turn so that the aircraft has only a pure roll relative to it. Frame 2 = { B; b, c, d} is fixed in the aircraft with d directed along the shaft BD and with b in the direction of the aircraft axis normal to the plane ABD; and frame 3 = { D; d, e, f} is fixed in the disk at D. Thus, ro 32 = \u00a2d is the angular velocity of the disk frame 3 relative to the aircraft frame 2. The air- Motion Referred to a Moving Reference Frame and Relative Motion 259 craft frame 2 rolls relative to frame 1; hence, ro 21 = Ob"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003715_acc.2004.1384700-Figure7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003715_acc.2004.1384700-Figure7-1.png",
+        "caption": "Fig. 7. A HoTDeC vehicle, with the vision indicator top",
+        "texts": [],
+        "surrounding_texts": [
+            "To accommodate the SBC and the battery management system the HoTDeC hovercraft vehicle chassis was redesigned using CAD modeling software. The new construction allows for much faster manufacturing and assembly of the hovercraft since little or no hand processing is required to assemble the chassis pieces that are produced using a CNC controlled three axis mill at UIUC. The final piece is a very light aesthetic cover requiring minimal fastening that finishes the craft hiding the electronics and holds the on-board camera or hovercraft-identifying top pattem used in ceiling mounted camera experiments."
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0001510_s0074-7696(08)60767-6-Figure8-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001510_s0074-7696(08)60767-6-Figure8-1.png",
+        "caption": "FIG. 8 The role of independent elastic elements in the Berg and Khan (1983) and Lauger (1988) models. An array of channel complexes attached to elastic elements is shown around a ring originally identified as the M ring. The elastic elements are fixed to the cell wall at their further ends. The channels do not permit free passage of protons between medium and cytoplasm, but rather interact with the periphery of the ring to bring about a \u201cgating\u201d effect. Opening of the gates to proton influx only occurs if the channel complexes step a discrete distance in the CW direction to new binding sites around the ring, thus stretching the elastic elements. The latter consequently generate a torque tending to rotate the ring in the CCW direction as indicated.",
+        "texts": [
+            " This mechanism, which allowed for intrinsic uncoupling, was treated twice, initially using a kinetic analysis in which the elasticity appeared only implicitly (Lauger, 1988, \u201cModel I\u201d ), and later using a stochastic simulation procedure in which the elasticity required direct consideration (Kleutsch and Lauger, 1990). It will be demonstrated that the kinetics of the Berg-Khan and Lauger models are closely related, indeed the former is essentially a limiting case of the latter. Both models may be considered to incorporate the notion of a \u201cgated channel.\u201d As can be seen in Fig. 8, the two models both postulate an array of channel complexes (which might be identified with MotA protein) attached to the cell wall by elastic linkages (which might be identified with MotB protein). The channel complexes are distributed around the periphery of a ring originally identified with the M ring, but which at present might equally well be identified with the switch complex or possibly the newly discovered C ring (see Section 11,D). Torque generation results from the gating mechanism, which requires discrete CW-directed steps (or jumps) of the BACTERIAL FLAGELLAR MOTOR 137 channel complexes to new binding sites around the ring in order to permit proton influx"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001929_952470-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001929_952470-Figure5-1.png",
+        "caption": "Fig. 5 LIF measurement set up.",
+        "texts": [
+            ") The liner segment was supported by a floatin,g holder mounted on a pair of linear bearings. The holder was connected by a load cell to the side plate which was fixed to the block of the Kohler engine. The load ceU wiis set up to measure the force component in the direction of the ring travel. At -mid stroke, two LIF probes were installed. The center of the probe volumes were at 81' crank angle from the TDC position. The fiber optics probes were ~nounted on the side plate and light was focused through the windows on the liner to the lubricating oil film ((Fig. 5). There was no mechanical contact so that no farce was transmitted between the optical fiber and the lither. The quartz windows were custom-made with a radius of curvature at the front surface to match the liner radius. The front surfaces of the windows were lapped after installation. The intent of the two probe locations was to observed whether the film thickness was uniform along the ring. The apparatus was not under temperature colntrol and was ran at the ambient temperature. A thermocouple, however, was mounted between the two window locations to measure the liner temperature during the experiment"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure1.5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure1.5-1.png",
+        "caption": "Figure 1.5. Graph of the dimen sionless cutter velocity as a function of the drive crank angle a:",
+        "texts": [
+            " Thus, in this design C and D are 60\u00b0 from the vertical line AG. This is also evident from the assigned geometry in Fig. 1.4. Since the 1200 arc from C to D through G is one-half as far from D to C through T, and because w is constant, it is easy to see that the time t, required for the return stroke is equal to one-half the time tc expended in the cutting stroke: t, = tc/2. This characterizes the quick return efficiency of this mechanism. A graph of the dimensionless cutter velocity v P ..;- ( 4aw) as a function of the drive crank angle ex is shown in Fig. 1.5. The quick change in the velocity Vp 2cosa-1 4aw = (2 -cos tx) 2 ' Kinematics of a Particle 15 during the return stroke CGD is evident; in fact, the tangent line to the curve at a= n/3 makes an angle of -37.6\u00b0 with the a axis. But this rate decreases rather rapidly during the initial phase of the cutting tool stroke, the tangent line to the curve at 0! = n/2 making an angle of -14\u00b0 with the 0! axis. During the actual tool working interval defined by 0! E [3n/4, 5n/4 ], say, it is seen that the curve is fairly flat so that the actual cutting operation occurs at a nearly constant rate"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001423_s1350-4533(99)00095-8-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001423_s1350-4533(99)00095-8-Figure3-1.png",
+        "caption": "Fig. 3. The model assumes the path length of a flexor tendon changes primarily where it \u201cbowstrings\u201d (bold, black line segments) between the annular/cruciate ligaments fixed to a given bone, and those fixed to an adjacent bone. The distances from the flexion axis in the proximal bone to both of these ligaments (r1), (r2) are assumed constant for a given tendon (t) at a given joint (j), as is the included angle between the ligaments (bt,j) when the finger is straight. Flexion of joint j decreases the included angle between the two ligaments by qj, thereby decreasing the path length of the tendon according to the law of cosines (Eq. (4)).",
+        "texts": [
+            " ,FDS52AFDS,MCP2AFDS,PIP (1) ,FDP52AFDP,MCP2AFDP,PIP2AFDP,DIP (2) ,EDL5BEDL,MCP1BEDL,PIP1CEDL,LAT (3) where ,i is excursion of muscle i (i=FDS, FDP, or EDL), Ai,j is the length of path of tendon of flexor i as it passes joint j (j=MCP or PIP or DIP joint), BEDL,j is the length of path of extensor tendon around joint j (j=MCP or PIP joint), and CEDL,LAT is the additional excursion of extensor caused by taut lateral bands. The model assumes that the path length of the tendons connecting the flexor muscles with the phalanges changes primarily at points where the tendons bowstring (Fig. 3, bold line segments) between annular ligaments fixed to bones on opposite sides of joints. The lengths of the relevant segments of the flexor tendons are calculated by the law of cosines (Eq. (4), first case). If joint flexion becomes large enough to oppose the two annular ligaments, it is assumed that further flexion of the joint does not change the length of the bowstring segment (Eq. (4), second case). Calculating FDS excursion (Eq. (1)) requires two terms of this form, one for qMCPf, and one for qPIP"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002608_physreve.67.011710-Figure9-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002608_physreve.67.011710-Figure9-1.png",
+        "caption": "FIG. 9. ~a! Illustration of the simplified model for a polarization stiffened FLC with pinned surfaces. The director orientation takes on a constant value within the bulk ~thickness tB) and varies linearly in near-surface layers of thickness tS to join with the surfaces. ~b! Comparison of g8(f)5\u00abFg(f)/tSPS and sin f.",
+        "texts": [
+            " We anticipate that there will be FLCs whose PS is large enough for their structure and behavior to approximate that of a 01171 vFLC, yet their PS is not large enough to totally overwhelm surface effects. Here, we consider what the form of FA(f) might be in these intermediate situations. Two cases are considered. In the first case, we assume that surface anchoring is strong and that the director orientations f0 and fL at the surfaces are fixed. In the second case, we assume that the FLC is fully stiffened and that f is everywhere the same. The model here is the same as for the simpler case of Sec. III except that the FLC layer has been divided into three regions as shown in Fig. 9. In the central region of the FLC layer, f is a constant as before. In the two near-surface regions of FLC ~each of thickness tS), we make the approximation that f varies linearly to join the central bulk value ~thickness tB) with the pinned values at the alignment layer surfaces. Charge density within the cell is r~r!5q~r!2\u00b9\u2022P~r!. ~11! We apply Gauss\u2019s law making use of the fact that the electric field outside the cell is zero. The integral is evaluated over a volume confined between two infinite planar surfaces, one lying outside the cell and parallel to the cell faces and a second parallel surface within the cell",
+            "52 V1VSS 11 \u00abA \u00abF tS tA D sin f~y !2g@f~y !# tB12tS1 \u00abF \u00abA 2tA . ~14! As before, the electrostatic torque acting on the FLC dipoles is integrated to determine the corresponding potential energy function @Eq. ~8!#. However, the function g(f) complicates evaluation of the integral. Two simplifications are introduced to help with this. First, we set f052f tF 52p/2, consistent with our assumption of pinned polar anchoring. Second, g(f) is very similar to the sine function on the interval 2p/2<f<p/2 as shown in Fig. 9, so we make the approximation g(f)>tSPSsin f/\u00abF . With this substitution, the integral is readily evaluated and the energy per unit area is found: W~f!5U~f!tB5W08S sin2f1 V VS8 sin f D , ~15! W085W0 S 11 \u00abF \u00abA 2tA tF D S 11 \u00abA \u00abF tS 2tA D S 11 \u00abF \u00abA 2tA tB 1 2tS tB D >W0S 11 \u00abA \u00abF tS 2tA D , VS85VSS 11 \u00abA \u00abF tS 2tA D . The above approximation for W08 applies when 2tS /tB!1, this inequality is satisfied in the stiffened director structure limit studied here. Now consider the twist regions, in which the energy density is the sum of elastic and electrostatic contributions"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003940_1.2338060-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003940_1.2338060-Figure2-1.png",
+        "caption": "Fig. 2 Flexible helicopter",
+        "texts": [],
+        "surrounding_texts": [
+            "om: http://appliedmechanics.asmedigitalcollection.asme.org/ on 01/27/201 this paper, the use of mean axes not only makes matters more complicated but in some cases it can render the formulation at odds with the physical reality. Whatever advantages or disadvantages accrue from the use of mean axes, the procedures used in 4,5 are essentially correct. Unfortunately, the same cannot be said about the subsequent investigations, as at some later time the concept of mean axes was invoked but not really used. Indeed, some later investigators latched onto the notion of mean axes to drop most inertial coupling terms from the equations of motion while failing to enforce the constraints embodied by Eqs. 3 . In fact, some of the investigators did not even give the definition of the mean axes. Typical of investigators regarding the mean axes, Eqs. 3 , as a vehicle to drop the coupling terms with impunity are Nydick and Friedmann 6 and Friedmann, McNamara, Thuruthimattam and Nydick 7 , where the first is a conference presentation and the second is basically a journal version of the first. Indeed, professing to use the mean axes, when in fact they did not, as well as invoking a variety of other assumptions, and confining themselves to the case of steady level cruise, they obtained the greatly simplified equations of motion m V\u03070x + qV0z = X \u2212 mg sin , m V\u03070z \u2212 qV0x = Z + mg cos , jyy 0 q\u0307 = M Mg\u0308 + Cg\u0307 + Kg \u2212 D T\u0303T\u0303 dD = D r\u0303T\u0303T\u0303 dD + Q\u0302 4 in which m is the total aircraft mass, V0x the forward velocity, V0z the plunge velocity, q the pitch velocity, the pitch angle, jyy 0 the mass moment of inertia about the pitch axis y, assumed to be constant, X, Z, and M are associated forces and moment, including those due to aerodynamics, Mg, Cg, and Kg are \u201cgeneralized\u201d mass, damping and stiffness matrices, respectively, is a vector of generalized elastic coordinates, a \u201cmodal\u201d matrix, \u0303 a skew symmetric matrix derived from the angular velocity vector = 0 q 0 T and Q\u0302 a generalized force density vector. Equations 4 are even simpler than they may seem, and we note that the first three are scalar equations and the fourth is a vector equation, as they can be solved independently for the rigid-body translations, rigid-body rotion, and elastic displacements. Indeed, first the third of Eqs. 4 can be solved for the pitch velocity q, and hence for the pitch angle , then the first and second can be solved for V0x and V0z and finally the fourth can be solved for . However, there are several problems with this proposition. In the first place, although the authors do list the definition of the mean axes, Eqs. 3 , they make no attempt to enforce the constraints imposed by them, which can have disturbing implications. Moreover, there is no indication that the aerodynamic forces were ever expressed in terms of mean axes components, nor is there any hint that the aerodynamic forces keep the equations coupled, thus preventing independent solutions of the equations for the rigid body translations, rigid body rotations and elastic deformations. It is clear from 6,7 that the objective is an aeroelasticity analysis, which calls for very simple equations of motion. Yet, the papers begin with a formulation capable of describing the dynamics and control of maneuvering flexible aircraft 8,9 , a very complex problem, and proceed to strip away the elaborate formulation reducing it to Eqs. 4 . In the process of reducing the equations of motion in terms of quasi-coordinates, the authors of 6,7 get tripped by the misuse of mean axes. It appears that the authors of 6,7 would have been better served by beginning directly with aeroelasticity equations rather than with the complex formulation of Ref. 8 . To indicate where 6,7 , went wrong and to highlight some possible negative implication of the use of mean axes, the correct use of the mean axes is discussed later in this paper. Transactions of the ASME 6 Terms of Use: http://www.asme.org/about-asme/terms-of-use n t a a f t h i o t b t r m h u t m b a w v e f r c q e s w t f e t t t a t a d 2 S p s c d t m w a d u t b m b b v s c q J Downloaded Fr The use, and sometimes abuse, of the concept of mean axes is ot confined to missiles, spacecraft, and aircraft. Indeed, abuse of he concept can be found in the case of helicopters as well. From dynamicist\u2019s point of view, helicopters can be regarded broadly s consisting of three parts, the main rotor, the tail rotor and the uselage, all acting together as a single dynamical system. Of hese, the main rotor is by far the most critical part, although a elicopter could not function properly without a tail rotor. Indeed, n the absence of a tail rotor to counteract the angular momentum f the main rotor, the fuselage would spin in a sense opposite to hat of the main rotor. The equations of motion for helicopters can e derived by modifying the approach used for aircraft, modificaions made necessary by the fact that helicopters possess spinning otors. However, this is not the approach used by Cribbs, Friedann and Chiu 10 , who consider the problem of a \u201ccoupled elicopter rotor/flexible fuselage aeroelasticity model\u201d in a very northodox way as far as dynamics is concerned. In particular, hey concentrated on the fuselage alone and invoked the use of ean axes to derive decoupled equations for the fuselage rigidody translations, rigid-body rotations and elastic deformations, s follows: mfx\u0308cm = F, Jf\u0307 + \u0303Jf = Mcm, Mq\u0308e + Kqe = Q 5 here mf is the total mass of the fuselage, xcm the displacement ector of the fuselage mass center, F the resultant vector of all xternal forces acting on the fuselage, Jf the inertia matrix of the uselage, the angular velocity vector of the fuselage, Mcm the esultant vector of all external moments about the fuselage mass enter, M and K are mass and stiffness matrices for the fuselage, e is a vector of generalized coordinates and Q a vector of genralized forces for the fuselage. Equations 5 are very strange in everal respects. In the first place, they are for the fuselage alone, hile insisting that the main rotor was coupled to the fuselage. To his end, they referred to some \u201cequations of equilibrium\u201d derived or the main rotor in a NASA CR dated 22 years earlier, without xplaining how equations of equilibrium derived separately for he main rotor, equations not even given in Ref. 10 , are coupled o equations of motion derived for the fuselage alone. Moreover, he tail rotor is not even mentioned. Finally, it is clear that Eqs. 5 re for a fictitious fuselage at best, as they were derived invoking he use of mean axes, when in fact the mean axes were not used at ll. Later in this paper, it is shown how the problem of helicopter ynamics is to be approached. Proper Formulation for the Dynamics of Aerospace tructures As discussed in the preceding section, the mean axes have been ortrayed as a useful tool in the treatment of such diverse aeropace structures as missiles, spacecraft, aircraft, and helicopters. A loser examination of pertinent investigations, however, paints a ifferent picture. Improper formulations of the equations of moion and/or misuse of the concept of mean axes do not inspire uch confidence in the usefulness of the approach. In this section, e propose to contrast the approach based on misuse of mean xes with a proper formulation of the same problem. From Meirovitch 8 , the motions of a flexible body can be escribed by means of a reference frame xyz Fig. 1 fixed in the ndeformed body and known as body. Then, the rigid-body moions are defined as three translations and three rotations of the ody axes relative to the inertial space XYZ and the elastic deforations as the displacements of points on the body relative to the ody axes. When expressed in terms of components along the ody axes, the rotational velocities are referred to as quasielocities, and the corresponding vector is denoted by . It is hown in Ref. 8 that, when expressed in terms of body-axes omponents, the translational velocities can also be treated as uasi-velocities; they are arranged in the vector V. Note that, un- ournal of Applied Mechanics om: http://appliedmechanics.asmedigitalcollection.asme.org/ on 01/27/201 like ordinary velocities, quasi-velocities cannot be integrated to obtain displacements 2 . Denoting by u and v the three-dimensional elastic displacement and elastic velocity vectors, respectively, where u and v are measured relative to the body axes xyz, it is shown by Meirovitch Ref. 8 that the hybrid dynamical equations of motion in terms of quasi-coordinates can be written in the compact vector-matrix form d dt L V + \u0303 dL V \u2212 C L R = F d dt L + V\u0303 L V + \u0303 L \u2212 ET \u22121 L = M t T\u0302 v \u2212 T\u0302 u + F\u0302 v + Lu = U\u0302 6 where explicit provision was made for damping, in which L is the system Lagrangian, V\u0303 and \u0303 are skew symmetric matrices derived from V and , respectively, C is a matrix of direction cosines between xyz and XYZ, R= RX RY RZ T is the radius vector from the origin OI of XYZ to the origin O of xyz, E is a matrix relating the symbolic angular velocity vector \u0307= \u03071 \u03072 \u03073 T to the angular quasi-velocity vector , T\u0302 is the kinetic energy density of the body, F\u0302 is Rayleigh\u2019s dissipation density function 11 and L is a 3 3 matrix of stiffness differential operators. Moreover, F, M, and U\u0302 are generalized force vectors, which must be expressed in terms of the same body axes components used to express the motion variables. They can be obtained from the actual distributed force vector f r , t and the discrete force vectors Fi t acting at the points r=ri i=1,2 , . . . , p by means of the virtual work expression. Discrete forces can be treated as distributed by writing them in the form Fi t r\u2212ri , where r\u2212ri are spatial Dirac delta functions 11 , so that the virtual work can be written in the form W = D fT r,t + i=1 p Fi T t r \u2212 ri RP * dD 7 where RP * is a virtual displacement vector whose expression can be obtained by considering the velocity vector of a typical point P in the body in terms of components along the body axes as follows: vP = V + r + u + v = V + r\u0303 + u\u0303 T + v 8 where r is the radius vector from O to P and r\u0303+ u\u0303 is the skew symmetric matrix derived from the vector r+u. Using the analogy with Eq. 8 with the term u\u0303T ignored as small compared to r\u0303T , we obtain MAY 2007, Vol. 74 / 499 6 Terms of Use: http://www.asme.org/about-asme/terms-of-use w w v t o w a d o T a a s f a w n g l \u201c o t m n i a e w R t s a r o w 5 Downloaded Fr RP * = R* + r\u0303T + u 9 hich is the virtual displacement vector of point P Fig. 1 , in hich R* is the virtual displacement vector of the origin of xyz, is the virtual angular displacement vector of xyz and u is the irtual elastic displacement vector of point P relative to xyz, all in erms of body-axes components. Inserting Eq. 9 into Eq. 7 , we btain W = D fT r,t + i=1 p Fi T t r \u2212 ri R* + r\u0303T + u dD = FT R* + MT + D U\u0302T udD 10 here F = D fdD + i=1 p Fi, M = D r\u0303fdD + i=1 p r\u0303iFi, U\u0302 = f + i=1 p Fi r \u2212 ri 11 re the desired generalized forces. Closed-form solutions of hybrid sets of differential equations escribing the dynamics of flexible aircraft is not within the state f the art, so that one must be content with approximate solutions. his implies invariably spatial discretization of the elastic varibles 11 . We consider spatial discretization of the system by ssuming that the elastic variables can be approximated to a reaonable degree of accuracy by series of space-dependent shape unctions multiplied by time-dependent generalized coordinates, s follows: u = , v = 12 here = r is a 3 n matrix of shape functions 11 , in which is the number of elastic degrees of freedom, is an n-vector of eneralized coordinates and is an n-vector of generalized veocities. A common misconception is to refer to the entries of as modes\u201d when in fact they are merely shape functions. Of course, ne can always try to choose the shape functions as the eigenfuncions of a somewhat related system, but that does not make them odes. It should be noted that the system described by Eqs. 6 is onlinear and subject to viscous damping. Moreover, in the case n which Eqs. 6 represent the equations of motion for a flexible ircraft, F, M, and U\u0302 include aerodynamic forces. As a result, ven after linearization, any modes are likely to be complex, hereas the entries of are real functions. In the spirit of ayleigh-Ritz, it is shown by Meirovitch 11 that any set of funcions capable of describing any possible elastic deformation of the ystem to a given desired degree of accuracy represents an acceptble set of shape functions. However, the use of shape functions epresents a mere spatial discretization process resulting in a set of rdinary differential equations. Before discretizing Eqs. 6 , we consider Eqs. 8 and 12 and rite the two forms of the kinetic energy T = 1 2 D vP TvPdD = 1 2 mVTV + VTS\u0303T + VT D vdD + T D r\u0303 + u\u0303 vdD + 1 2 TJ + 1 2 vTvdD D 00 / Vol. 74, MAY 2007 om: http://appliedmechanics.asmedigitalcollection.asme.org/ on 01/27/201 1 2 mVTV + VTS\u0303T + VT\u0304 + T D r\u0303 + \u02dc dD + 1 2 TJ + 1 2 T 13 where \u0304 = D dD, S\u0303 = D r\u0303 + \u02dc dD , J = D r\u0303 + \u02dc r\u0303 + \u02dc TdD, = D T dD 14 in which S\u0303 and J are the matrix of first moments of inertia and the inertia matrix, respectively, of Rayleigh\u2019s dissipation function F = D F\u0302dD = 1 2 D cvTvdD 1 2 T D c T dD = 1 2 TC 15 where C = D c T dD 16 is a damping matrix, in which c is a damping density function, and of the strain energy Vstr = 1 2 D uTLudD 1 2 T D TL dD = 1 2 TK 17 where K = D TL dD 18 is a stiffness matrix. Both C and K are symmetric. Then assuming that the Lagrangian does not depend on R and , which is true for flying aircraft, the discrete counterpart of Eqs. 6 are simply d dt L V + \u0303 L V = F, d dt L + V\u0303 L V + \u0303 L = M d dt L \u2212 T + C + K = X 19 in which, from Eq. 13 T = \u2212 \u0304TV\u0303T + D T \u02dcdD \u2212 D T\u03032 r + dD 20 and X = D TU\u0302dD 21 is the discretized generalized elastic force vector. Finally, including some obvious kinematical identities and carrying out the indicated operations, we obtain the discretized set of state equations Transactions of the ASME 6 Terms of Use: http://www.asme.org/about-asme/terms-of-use e F s b F g J Downloaded Fr R\u0307 = CTV, \u0307 = E\u22121 , \u0307 = mV\u0307 + S\u0303T\u0307 + \u0304\u0307 = 2 D \u02dcdD + mV\u0303 + \u0303S\u0303 + F S\u0303V\u0307 + J\u0307 + D r\u0303 + \u02dc dD\u0307 = D \u02dc r\u0303 + \u02dc + r\u0303 + \u02dc \u02dc dD + V\u0303S\u0303 + S\u0303V \u2212 \u0303J + \u0303 D r\u0303 + \u02dc T dD + M \u0304TV\u0307 + D T r\u0303 + \u02dc TdD\u0307 + \u0307 = \u2212 \u0304TV\u0303T \u2212 D T\u03032 r + dD \u2212 2 D T \u02dcTdD \u2212 C \u2212 K + X 22 Next, we address the problem of helicopter dynamics. To this nd, we consider the typical helicopter configuration shown in ig. 2 and assume that the main rotor consists of nm equally paced blades and the tail rotor consists of n equally spaced lades. Then, by analogy with Eqs. 6 and using the notation of ig. 2, the helicopter equations of motion can be expressed in the eneric form d dt L VO + \u0303O L VO \u2212 CO L RO = FO d dt L O + V\u0303O L VO + \u0303O L O \u2212 EO T \u22121 L O = MO t T\u0302f v f \u2212 T\u0302f u f + F\u0302 f v f + L fu f = U\u0302 f ournal of Applied Mechanics om: http://appliedmechanics.asmedigitalcollection.asme.org/ on 01/27/201 t T\u0302mi vmi \u2212 T\u0302mi umi + F\u0302mi vmi + Lmiumi = U\u0302mi, i = 1,2, . . . ,nm t T\u0302 j v j \u2212 T\u0302 j u j + F\u0302 j v j + L ju j = U\u0302 j, j = 1,2, . . . ,n 23 The derivation of explicit equations of motion would require a great deal of perserverance and patience, and is beyond the scope of this paper. To develop an appreciation of the nature of the equations, however, we will outline some of the steps involved in their derivation. The kinetic energy has the general expression T = 1 2 mf V f TV fdmf + 1 2 i=1 nm mi Vmi T Vmidmi + 1 2 j=1 n mj V j T V jdmj 24 where, following an orderly kinematical procedure, the velocity vectors of the individual components are given by V f r f,t = VO t + r\u0303 f + u\u0303f r f,t T O t + v f r j,t Vmi rmi,t = CmiVM + r\u0303mi + u\u0303mi rmi,t T Cmi O + M + vmi rmi,t , i = 1,2, . . . ,nm V j r j,t = C jVT + r\u0303 j + u\u0303 j r j,t T C j O + T + v j r j,t , j = 1,2, . . . ,n 25 in which VM t = V f rOM,t = VO t + r\u0303OM + u\u0303f rOM,t T O t + v f rOM,t VT t = V f rOT,t = VO t + r\u0303OT + u\u0303f rOT,t T O t + v f rOT,t 26 are the velocity vectors of the main rotor hub M and tail rotor hub T, obtained by evaluating V f at M and T, respectively. Moreover, Cmi and C j are matrices of direction cosines between the main rotor blade body axes xmiymizmi and the fuselage body axes xfyfzf and the tail rotor blade body axes x jy jz j and xfyfzf due to the spin of the rotors; both Cmi and C j depend explicitly on time. The kinetic energy is obtained by inserting Eqs. 25 and 26 into Eq. 24 and carrying out the indicated operations. A cursory examination of Eqs. 25 and 26 will reveal that the fuselage, main rotor and tail rotor are all inertially coupled and so are the equations of motion. Furthermore, it is futile to look for mean axes capable of changing this fact. Clearly, the use of mean axes for the fuselage alone, which is the least critical part of a helicopter, cannot be justified. Although we expressed the fuselage stiffness in terms of a stiffness operator matrix L f, this was merely symbolic because it is not feasible to generate a differential operator for such a complex structure as the fuselage. In practice, it is necessary to express the fuselage stiffness, in the context of a spatial discretization process, by means of a stiffness matrix generated by the finite element method. A typical main rotor blade can be modeled as a thin beam undergoing torsion about the longitudinal axis xmi and bending about axes ymi and zmi. Denoting the displacement vector for blade mi by umi= xmi uymi uzmi T, the corresponding stiffness operator matrix can be shown to have the form 11 MAY 2007, Vol. 74 / 501 6 Terms of Use: http://www.asme.org/about-asme/terms-of-use w i b t f f M t w r c w f d p b i o a l t c s t \u201c M a 3 f t c t m c h p t c w o p m 5 Downloaded Fr Lmi = \u2212 xmi GJmi xmi xmi 0 0 0 2 xmi 2 EIzmi xmi 2 xmi 2 0 0 0 2 xmi 2 EIymi xmi 2 xmi 2 \u2212 xmi Pmi xmi xmi 27 here Pmi xmi = xmi Lmi mi Cmi O + M zmi 2 d 28 s the axial force on blade mi due to the centrifugal force caused y the spin of the main rotor hub. The operator matrix L j for the ail rotor can be obtained from Eqs. 27 and 28 in an analogous ashion. Some of the other quantities, such as Rayleigh\u2019s dissipation unction densities F\u0302 f, F\u0302mi, and F\u0302 j and the generalized forces F0, 0, U\u0302 f, U\u0302mi, and U\u0302 j can be obtained by analogy with those for he aircraft, where the forces include the aerodynamic forces, hich are much more complicated than those for aircraft. In this egard, it must be pointed out that the degree of complexity inreases significantly from hover to forward flight. Indeed, in forard flight the blade velocity due to the hub rotation adds to the uselage velocity during half of the rotation and subtracts from it uring the other half. To compensate for this, the blade is made to itch accordingly. Generic equations of motion for whole flexible helicopters can e obtained by inserting Eqs. 24 \u2013 28 into Eqs. 23 and carryng out the indicated operations, which would involve a great deal f symbolic manipulations, well in excess of those for flexible ircraft. It is not difficult to see that the resulting equations are ikely to be extremely complex. Contrasting Eqs. 23 \u2013 28 with he formulation of Ref. 10 , Eqs. 5 of the present paper, one oncludes that the formulation of Ref. 10 is badly flawed, and no ensible simplification of Eqs. 23 \u2013 28 would reduce the equaions of motion to an extent that would make them resemble Eqs. 5 , not even vaguely. Hence, the contention that Eqs. 5 reflect a Coupled Helicopter Rotor/Flexible Fuselage Aeroelastic odel\u2026,\u201d as the title of Ref. 10 implies, is more than questionble. The Use of Mean Axes In deriving Eqs. 22 , a reference frame embedded in the undeormed body was used to define the rigid-body and elastic moions, as well as the forces, moments and distributed forces. This hoice seems only natural. As can be expected, the equations for he rigid-body translations, rigid-body rotations and elastic defor- ations are all coupled. There seems to be a belief that a different hoice of reference frame is able to reduce the coupling, and ence the complexity of the formulation. We wish to examine this roposition. The inertial terms can be simplified to some extent by choosing he body axes as the principal axes with the origin at the mass enter. In this case, we have D rdD = 0, D r\u0303r\u0303TdD = J 0 29 here J 0 represents the diagonal matrix of the principal moments f inertia of the undeformed body. Perhaps more extensive simlifications can be achieved, at least at first sight, by using the ean axes, defined by 02 / Vol. 74, MAY 2007 om: http://appliedmechanics.asmedigitalcollection.asme.org/ on 01/27/201 D udD D dD = \u0304 = 0 , D r udD = D r\u0303udD D r\u0303 dD = * = 0 30 Inserting Eqs. 29 and 30 into the second half of Eqs. 22 , the dynamical part of the state equations reduces to mV\u0307 + \u0304\u0307 = 2 D \u02dcdD + mV\u0303 + F J\u0307 + D \u02dc dD\u0307 = D \u02dc r\u0303 + \u02dc + r\u0303 + \u02dc \u02dc dD \u2212 \u0303J + \u0303 D r\u0303 + \u02dc T dD + M \u0304TV\u0307 + D T \u02dcTdD\u0307 + \u0307 = \u0304TV\u0303T \u2212 D T\u03032 r + dD \u2212 2 D T \u02dcTdD \u2212 C \u2212 K + X 31 Contrasting Eqs. 31 with the simplified equations of Refs. 6,7 , Eqs. 4 of the present paper, we conclude that Eqs. 4 do not describe any real aircraft but some fictitious one that does not exist, so that any analysis based on Eqs. 4 is an exercise in futility."
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0001650_0165-0114(92)90146-u-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001650_0165-0114(92)90146-u-Figure3-1.png",
+        "caption": "Fig. 3. External restrictions.",
+        "texts": [
+            " Palm / Control of a redundant manipulator using fuzz), rules 283 -4 qe~t l qe~ / / ff~4 el q<m X With regard to external restrictions a boundary (wall) as well as an obstacle are considered. Let the wall be a straight line through the points P1 and P2. Then, the shortest distance s between the i-th link and the wall is si = I(Gi - w,) \u00d7 bl (21) 284 R. Palm / Control of a redundant manipulator using fuzzy rules where \u00d7 is the cross product of two vectors. The resulting vector with the absolute value of si stands normal to the x, y-plane. Furthermore let b be a unit vector with b = w 2 - w l I W2 - - Wll ( 2 2 ) (see Figure 3) and W T = (X , , Y l , 0), W T = (x2, Y2, 0) , G T = (Xgi, Ygi, 0), (23) whereas Xg~ and yg~ are computed by (16). Then, for the distance si between the i-th link and the wall one obtains I(Xgi - x , ) . (Y2 - Y , ) - (Ygi - Y , ) \" (x2 - x,)l si -- [(x2 - xl) 2 + (Ye - Yl)Z] 1/2 (24) It can be assumed that each link is able to crash the wall. That means l, > Iw, I, ~ 1, > Iw21. (25) i= l Finally, the distance s~ is standardized according to a maximum distance Smax with s i s = Si/Smax. (26) With the help of such standardization a unique evaluation of internal and external restrictions is possible"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003500_ac061224o-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003500_ac061224o-Figure1-1.png",
+        "caption": "Figure 1. Amperometric ISE body design.",
+        "texts": [
+            " With both, DPV and ADPV, the charge current and the ohmic drop are reduced to a large extent with respect to single pulse techniques and cyclic voltammetry, with this reduction being even more pronounced with ADPV. Although DPV has been applied to some other types of ITIES,17,19-21 the influence of the pulse amplitude has not been studied to our knowledge, and no ADPV study of any ITIES has been reported. We show how the influence of the pulse amplitude on the DPV voltammograms can be exploited in order to obtain peaks centered within the potential window. Apparatus. The design of the sensor is shown in Figure 1. A Pt wire counter electrode was accommodated inside the inner solution compartment of a Fluka ion-selective electrode (ISE) body. The Pt wire electrode was coiled around the Ag/AgCl reference electrode, which had previously been covered by a plastic tube. The electric contact between the inner counter electrode and the external plug was made through a small hole drilled in the glass compartment used to pull an extreme of the Pt wire. This was soldered with conductive cement to a conductive band, which had previously been made all around the glass compartment with conductive cement"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001557_0167-9317(96)00004-4-Figure27-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001557_0167-9317(96)00004-4-Figure27-1.png",
+        "caption": "Fig. 27. Schematic presentation of 'key-lock' interactions between C2Cl4 as a typical organic molecule and cali:g,4)arene with different contributions to the overall interaction energy E,ot as determined from force field calculations: E,o, = s\u00ab:+ LE\",,, +LEo,oc +LEo llP +LEst, +LEbond ' For details, see [30].",
+        "texts": [
+            " Typical molecules to utilize the geometric \" key-lock' I principle are calixarenes which incorporate small organic molecules (see Fig. 7(a)). Signal transduc tion of these sensors is possible by monitoring changes in mass, capacitance , or temperature upon incorporation of organic molecules. The geometry of calixarenes may be modified by substituting atoms in the ring or by using different numbers of repeat units in the ring (Fig. 26). The molecule/ring interaction energies can be calculated with sufficient accuracy by static force field approaches applied to small rings (Fig. 27). Larger rings require the theoretical calculation of dynamically adjusted recognition centres (\" induced fits \") by molecular dynamics concepts (see 98 W. Giipel / Microelectronic Engineering 32 (1996) 75-110 Section 2.7). Such theoretical molecular design concepts become of increasing interest also for developing new pharmaceuticals (\"drug design\"). To achieve a controlled key /lock geometry, the covalent coupling of cage compounds to Au(111) via sulphur bridge bonds may be used to advantage in chemical sensors"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001376_s0967-0661(99)00084-2-Figure8-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001376_s0967-0661(99)00084-2-Figure8-1.png",
+        "caption": "Fig. 8. A specimen of the #ying gyrodine with electromagnetically suspensed rotor (own angular momemtum h g \"2500 N m s) without covers: 1* the rotor of composite materials; 2* the mounting of the precession axis in the gyrocomplex casing; 3 * the gyrodine's frametype casing; 4 * the sensor and axial electromagnet; 5 * sensors and radial electromagnets.",
+        "texts": [
+            " Using numerical methods, the optimization of the stability index was carried out with an assigned oscillability index value and variation of the gyrorotor's proper angular momentum within a wide range of values (Somov, Sorokin & Kondrat'ev, 1997). Then the in#uence of factors such as #exibility, dead band, kinematic defects in the gear, quantization of the control signal, limitation on the gear stepping motor's current, etc., were investigated by both the computer-aided simulation (Somov et al., 1997) and careful experimental tests (Aref'yev et al., 1995), see Fig. 8. As a result, the amplitude of ranges for the gyrodine's precession rate and acceleration were revealed when the command and the true precession rates are shown to be close in spite of the existence of large gyroscopic torques on the gyrodine precession axis by virtue of the spacecraft rapid spatial rotation manoeuver. This means that for selected parameters of the gyrodine control laws, the assumptions of the CMG precession theory are satis\"ed for the indicated ranges of the input command signals, and the vector of the gyrocomplex's output control torque Mg in (Eq"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure1.7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure1.7-1.png",
+        "caption": "Figure 1.7. Torsional vibrations of a disk.",
+        "texts": [
+            " D More applications of the foregoing methods may be found in the problems given at the end of the chapter. It is evident that the foregoing procedures assume that all quantities are expressed as functions of the time. However, this will not always be so. Later on and in some of the problem assignments, we shall have to develop additional methods to handle other situations. An important special procedure is illustrated below. Example 1.8. A circular disk of radius a is suspended by a slender rod attached to its center, as shown in Fig. 1.7. The disk is given an angular twist 00 from its natural state in frame q1 = { 0; ik }, and released to perform tor sional oscillations. The subsequent simple angular acceleration of a particle P on the rim of the disk in its rotation about the vertical axis is determined by the relation lJ = -KO, in which K is a known constant that depends on certain properties of the disk and the rod. (a) Find the velocity and acceleration of P expressed as functions of (] alone. (b) Determine the maximum magnitude of 20 Chapter 1 the angular speed of P"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000570_mssp.1996.0068-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000570_mssp.1996.0068-Figure2-1.png",
+        "caption": "Figure 2. Gearbox.",
+        "texts": [
+            " The car gearbox considered is driven by an asynchronous motor at 75 Hz. A second one brakes the differential output with a momentum of 80 Nm. The vibrations of the whole box are recorded with piezo-electric accelerometers located at 12 selected positions on the casing. Signals are low-pass filtered at 11.2 kHz and sampled with a fixed rate of 22.5 kHz. The angular position of the driving shaft is recorded by means of a pulse generator. The gearbox itself is a complex mechanical device. All five gears are mounted on two shafts (Fig. 2). The five driving wheels are fixed on the driving shaft, while the corresponding driven wheels may be kept fixed or not by using the clutch fork mechanism. The shafts are supported by three ball bearings and one roller bearing. The whole mechanism is assembled in a casing containing the lubricant. The output shaft drives the output gear which transmits motion to the differential. Only helical gears are used. The T 2 Variance of the prediction error Gear 1 0.0471 0.0021 0.0135 0.0143 0.0284 2 0"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002068_bf00052455-Figure8-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002068_bf00052455-Figure8-1.png",
+        "caption": "Fig. 8. Mesh of gears with backlash and relevant force laws.",
+        "texts": [
+            " The equations (19) and (20) describe a multibody system with n bodies and a maximum number of (f = 6n) rigid degrees of freedom and, according to the Ritz-Ansatz (equation (4)) a certain number of elastic degrees of freedom (number of shape functions per body times number of elastic bodies). In practical applications, however, the number of degrees of freedom might be reduced drastically. For example, driveline units with straight-tooth bevels may be sufficiently modeled by rotational degrees of freedom only. To include backlashes we have to implement an algorithm which controls the contact events (Figure 8) by considering contact kinematics and contact forces. A contact at a tooth flank is going to happen if the relative distance in contact k becomes zero (equation (6)) \"Tk(PI, Pj, Ck) = 0. (32) The subsequent deflection of both teeth follow the force laws of the Figures 5 and 6, but the end of the contact is not reached, when we get again \"~k = 0. The correct condition consists in the requirement that the normal force ( ~ k e k i ) (i = 1, 2) (Figure 8) vanishes. As we have a unilateral contact problem a separation takes place when the normal force changes sign, which necessarily is not the case if 7k = 0. Due to the dynamics of the contacting bodies and due to the damping influence of the contact oil model (Figure 6) the normal force changes sign before 7k = 0, that means the tooth separation takes place when the teeth are still deflected. For separation we therefore must interpolate the force condition (Figure 8) ~kn = --eki~k = --eki (ckTk + ~kD(~k , z/k)) = O, for (i = 1,2), (33) where ffkn is the normal force vector and ~kD the damping force law due to oil and structural damping. Things are still more complicated. During free flight motion each gear wheel for example possesses its individual degrees of freedom. During contact the two gear wheels are coupled by a common force law but, additionally, in the point Ci of contact they have common coordinates too, for example Pci = PCj (equation 1) if i and j are the bodies in contact"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001656_1.1330743-Figure9-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001656_1.1330743-Figure9-1.png",
+        "caption": "Fig. 9 The geometry near the trailing edge",
+        "texts": [],
+        "surrounding_texts": [
+            "3.1 Typical Simulated Results of Slider Vibration. We numerically calculated the bouncing vibrations over a random wavy surface for various values of k f , r, zc , m, s, and p. The spacing h (5zp2zd) between the contact pad displacement zp and the original disk surface displacement zd at the same x position in a quasi-steady state from 8.192 ms to 10.24 ms is focused on here. Figure 3 explains typical time histories of slider vibrations and disk surfaces for zc50.2, m51.0, s51.0, nm and p51.5. As seen in Figs. 3~a! and ~c!, the slider is almost perfectly in contact with the disk when r50.01. However, considering r510 as seen in Figs. 3~b! and ~d!, the slider separates from the disk, particularly in the case where k f51.53105 N/m. From Fig. 3~d!, we observe that the spacing becomes large when the slope of the disk surface is positive, i.e., the disk surface displacement under the center of the rear air bearing is larger than that under the contact pad. This means that the slider is following the disk surface not at the contact pad but at the center of the rear air bearing because the rear Transactions of the ASME /data/journals/jotre9/28694/ on 04/18/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F air bearing stiffness is very large. The amount of the spacing caused by the distance between rear air bearing and the trailing edge ~the contact pad! is discussed in Section 3.3. Figures 4~a! to 4~d! show the frequency response functions ~FRFs! of the contact pad displacement to the disk surface waviness, which correspond to Figs. 3~a! to 3~d!. In these figures, the lower and higher natural frequencies on the contact states are indicated by symbols ~,!. The noisy spikes seem to be caused by the bouncing vibrations. In all of the figures, we cannot observe a resonance peak at the lower natural frequency because the node point of the lower vibration mode in a contact state is close to the contact pad. Regarding the higher natural frequency, we can note a broad resonance peak when r50.01. However, when r510 as seen in Figs. 4~b! and ~d!, we note a periodical undulation of FRFs particularly in Fig. 4~d!, where k f51.53105 N/m. The valley frequencies seem to be 120, 360, 600, and 840 kHz. The intervals of those frequencies are 240 kHz which corresponds to the disk waviness whose length equals the distance between the contact pad and the center of the rear air bearing of 62.5 mm when V 515 m/s. At frequencies which are (n21/2) times 240 kHz, the phases of the disk waviness differ by p at the contact pad and the rear air bearing. Therefore, when the rear air bearing stiffness is comparable with the contact stiffness, the exciting forces from disk surface at those particular points cancel each other out at those frequencies. This would be the reason for the valley frequencies. Contrarily, the broad peaks which occur between the valleys are results from the in-phase excitation at these two points. 3.2 Effects of Friction Force on Slider Motion. Figure 5 shows the effects of the coefficient of friction m on the maximum spacing hmax and the maximum contact force Fc max when zc 50.2, s51.0 nm, and p51.5, taking the front air bearing stiffness Journal of Tribology rom: http://tribology.asmedigitalcollection.asme.org/pdfaccess.ashx?url= k f and the rear to front air bearing stiffness ratio r as parameters. The data presented in these figures are the mean values of 8 samples ~the following simulation data are also the mean values of 8 samples!. From Fig. 5, we note that the increase in m increases hmax and decreases Fc max . This is due to the friction force which acts on the contact pad at the trailing edge so that the moment of friction raises the contact pad. In addition, the effects of m on the behavior of the slider is limited. The reason for this is considered to be that the friction force acts only during the contact state. Note that the Fc max shown here includes only a normal contact force. Since the effects of m is limited, we used m51.0 for a smaller friction case and m510 for the larger friction case in the following calculations. 3.3 Effects of Design Parameters on Perfect Contact Sliding Conditions. In order to evaluate the effect of the design parameters on the perfect contact sliding condition, we examined the maximum spacing hmax and the maximum contact force Fc max for various values of k f , r, m, s, and p, taking p as a parameter (p51.0, 1.5, 2.0, and 2.5!, hmax and Fc max are expressed as functions of a standard deviation of the disk surface waviness s in Figs. 6 ~m51.0! and 7 ~m510!. In each figure, ~a! and ~b! are the case of k f55.03104 N/m, ~c! and ~d! are the case of k f51.5 3105 N/m, ~a! and ~c! are the case of r50.01, and ~b! and ~d! are the case of r510. The black lines represent hmax and the broken lines represent Fc max . The dot-dashed lines indicate hmax50 nm. The negative hmax means that the slider is always penetrating into the disk surface and vibrating below the original disk surface, i.e., the slider is sliding perfectly in contact with the disk. Considering r50.01 as seen in Figs. 6~a!, ~c!, and Figs. 7~a!, ~c!, we can get the necessary condition of s for perfect contact sliding. The boundary values of s and the maximum contact force Fc max at the same time are indicated in each figure. When referring to r510 in Figs. 6~b!, 6~d!, 7~b!, and 7~d!, we\u2019re not able to get the meaningful value of s for perfect contact sliding. This is because the rear air bearing stiffness is so large that the slider is following the disk surface not at the contact pad but at the center of rear air bearing. Since the results are different between r50.01 and r510, we will discuss the effects of the design parameters in the case of r 50.01 and r510 separately. When r50.01 ~Figs. 6~a!,~c! and Figs. 7~a!,~c!!, it can be expressed as follows: 1 Since ~a! and ~c! in Figs. 6 and 7 are similar to each other, the front air bearing stiffness doesn\u2019t affect the behavior of the contact pad. In addition, when the rear air bearing stiffness is much smaller than the contact stiffness, the effect of the rear air bearing stiffness on the contact sliding ability can be disregarded. From Figs. 6~a! and 7~a!, the boundary value of the standard deviation of disk surface waviness sb , below which the slider can JANUARY 2001, Vol. 123 \u00d5 163 /data/journals/jotre9/28694/ on 04/18/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F be sliding perfectly in contact with the disk surface, versus p is presented in Fig. 8 for the case where k f55.03104 N/m, r 50.01 and zc50.2. It is apparent that the friction coefficient decreases sb . 2 The maximum contact force Fc max at the boundary of the perfect contact sliding condition are independent from the disk surface waviness parameters ~s and p! and the rear air bearing stiffness; Fc max50.95 mN in Figs. 6~a! and ~c!, and Fc max 50.40 mN in Figs. 7~a! and ~c!. This is because contact force is at its maximum when the contact pad is at the most penetrating position, which does not depend on the disk surface waviness parameters but on the contact stiffness kc , the static contact force Fc0 and the coefficient of friction m. As seen in Figs. 4~a! and ~c!, the FRFs of the contact pad which relate to the disk surface are similar to the single-degree-offreedom ~1-DOF! model of a contact slider. Therefore, we predicted sb of the 2-DOF model with a weak rear air bearing by using the closed form solution of the perfect contact sliding condition of the 1-DOF contact slider on a random disk surface @12#. In this prediction, the higher natural frequency in a contact state is regarded as the contact resonance frequency of the 1-DOF model. The sb value predicted by the 1-DOF model is shown in Fig. 8 for comparison. Taken from Fig. 8, we note that the differences of 1-DOF analysis from the simulated results are less than 10 percent for m51.0 and less than 30 percent for m510. Therefore, it can be said that the perfect contact sliding condition of the 2-DOF model is well predicted by the 1-DOF analysis when the front and rear air bearing stiffnesses are much smaller than the contact stiffness. 164 \u00d5 Vol. 123, JANUARY 2001 rom: http://tribology.asmedigitalcollection.asme.org/pdfaccess.ashx?url= Next, we have discussed the spacing in the case of r510. As seen in Figs. 6~b!, 6~d!, 7~b!, and 7~d!, perfect contact sliding is almost impossible unless s50. This is because the slider is following the disk surface not at the contact pad but at the center of the rear air bearing when the rear air bearing stiffness is comparable with the contact stiffness, as stated in Section 3.3. When the contact damping ratios are as large as 0.2, it is thought that the spacing can be evaluated approximately from only the geometrical Transactions of the ASME /data/journals/jotre9/28694/ on 04/18/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F relation with the assumption that the slider is following perfectly the disk waviness at the rear air bearing center. Figures 9~a! and ~b! show the models of the geometry near the trailing edge of a flat disk and wavy disk, respectively. Since the spacing hr at the rear air bearing is assumed to be constant, the spacing hg at the trailing edge ~contact pad! is given as follows: hg5zd~ t ,xcr!2zd~ t ,0!2dr , (6) where dr is given by Fc0 /kr . If the micro waviness of a disk surface is Gaussian, the standard deviation sg of (zd(t ,xcr) 2zd(t ,0)) can be obtained by its root mean square and is given by sg5A2~s22R~xcr!!, (7) where R(xcr) is a covariant function given as R~xcr!5E 0 ` A~ f d!cosS 2pxcr f d V D d f d , (8) where A( f d) is the frequency component of the disk surface waviness. A( f d) can be calculated from the standard deviation of the disk surface waviness s and the smoothness parameter p. Since the spatial distribution of the disk waviness is Gaussian, the maximum value of (zd(t ,xcr)2zd(t ,0)) can be given by 3sg . Therefore, the maximum spacing hg max is as follows: hg max53sg2dr . (9) Figure 10 shows hg max as a function of xcr when s51.0 nm, dr 50.33 nm and p51.0, 1.5, 2.0, and 2.5. In comparison, the simulated results of hmax for p51.0, 1.5, 2.0, and 2.5, when s51.0 nm, k f51.53105 N/m, dr50.33 nm, r510, m51.0, and xcr 562.5 mm ~from Fig. 6~d!! are shown in Fig. 10 by the symbols ~L!. The symbols ~L! indicate hmax for the cases of p51.0, 1.5, 2.0, and 2.5 from up to down, respectively. Seen in Fig. 10, it can be said that this estimation agrees well with the numerical simulation when p51.5;2.0. The difference between the estimation and the simulation is considered to be caused by the dynamic response of the slider. Taken from Fig. 10, xcr should be less than 8 mm in this particular situation where s51.0 nm and p52.5, in order to achieve perfect contact sliding in this case. However, if the contact pad Journal of Tribology rom: http://tribology.asmedigitalcollection.asme.org/pdfaccess.ashx?url= can be separated from the disk surface by 2 nm, xcr can be designed as 50 mm when s51.0 nm and p51.5. Furthermore, the perfect contact sliding can be obtained if we can increase the static penetration depth dr , contact force Fc0 , or decrease the standard deviation of the disk surface waviness s so that dr .3sg will hold. 3.4 Effects of Static Equilibrium Pitch Angle on Flying Height of Front Air Bearing Surface. In the previous sections, we numerically simulated the behavior of a slider for u0 5300 mrad. However, the tri-pad sliders with a smaller pitch angle are usually used for HDDs. If the pitch angle is small, the front air bearing surfaces of the sliders tend to make contact with the disk surfaces more easily. This may cause a \u2018\u2018head-crash\u2019\u2019 because the area of the front air bearing surface is much larger than that of the contact pad and the large friction force or stiction force is generated at the front part of the slider when the front air bearing surface makes contact with the disk surface. In this section, we examined the relationship between the static equilibrium pitch angle and the flying height of the front air bearing surface and we have discussed the design conditions of the static equilibrium pitch angle. The minimum flying height of the center of the front air bearing surface h f min is shown in Fig. 11 as a function of the static equilibrium pitch angle u0 when k f51.53105 N/m, zc50.2 s51.0, p51.5, r50.01, 10, and m51.0, 10. The relationship between h f min and u0 is almost linear in Fig. 11. One of the reasons for this is the assumption that the air bearings have linear springs. From Fig. 11, it can be stated that the flying height of the front air bearing decreases when r and m are large. This is due to the moment of friction force which has the effect of decreasing the pitch angle and resulting in the decrease in the flying height. In addition, in order to maintain h f min higher than 40 nm and to prevent for the front air bearing surface from contacting with disk surfaces, the static equilibrium pitch angle should be larger than about 70 mrad. 3.5 Design of Tri-Pad Contact Slider. Based on the simulated results, we will discuss the design condition of the tri-pad contact sliders and the disk surfaces in this section. When m is larger than 0.3, yielding occurs at the surface of the weaker body of the two mating bodies by shear stresses @20#. Therefore, we use the maximum friction force mFc max for the criterion of wear durability in this study. At first, we will discuss the design condition pertaining to the case of r50.01. In this case, the slider has a very weak rear air bearing, like the \u2018\u2018T \u2019\u2019 type slider @5#. The conditions of the disk waviness parameters necessary for perfect contact sliding can be obtained from the numerical simulation results as stated in Section 3.3. The boundary values of the standard deviation of the disk waviness sb for perfect contact sliding and the maximum friction force mFc max at the boundary are presented in Fig. 12 as a function of p when k f51.53105 N/m, r50.01, m51.0, 10, and zc JANUARY 2001, Vol. 123 \u00d5 165 /data/journals/jotre9/28694/ on 04/18/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F 50.1, 0.2. The results for the case of k f55.03104 N/m are not shown here because they are not different from the results for the case of k f51.53105 N/m. In Fig. 12, solid lines represent sb for perfect contact sliding, whereas broken lines represent maximum friction force at the boundary conditions. From Fig. 12, we note that the larger zc , the larger p and the smaller m is better for perfect contact sliding. Almost the same values of sb can be obtained in both cases where zc50.1 and m51.0, and zc50.2 and m510. But the maximum friction force mFc max of the latter is about 4 times as large as that of the former. Here, the slider material is assumed to be Al2O3\u2022TiC ~E1 5385 GPa, v150.3! and the disk material is assumed to be glass ~E2571 GPa, v250.21!. Then, the area of the contact pad S becomes 161 mm2 for kc51.53106 N/m by using Eq. ~1!. Taken from Fig. 12, the maximum friction forces mFc max are about 1 mN and 4 mN for m51.0 and m510, respectively. Therefore the maximum shear stress acting on a contact pad area uniformly are 6.1 MPa and 25 MPa for m51.0 and m510, respectively. The surfaces of the contact pad and the disk should be able to withstand these shear stresses. For example, when it is assumed that the friction force of 4 mN acts on the real area of the contact uniformly and that the ratio of the real area of contact to the contact pad area is 0.01, the shear stress on the surface of the real contact area is 2.5 GPa. In general, the yield shear stress is a half of the yield tensile stress. Therefore, the yield tensile stress of the weaker material of the contact pad and the disk should be more than 5 GPa in this specific case. As for the case of r510, i.e., a tri-pad slider which has a strong rear air bearing, it is difficult to achieve perfect contact sliding because of the micro waviness if the rear air bearing center is far from the contact pad. In addition, the maximum contact force will increase with the increase in the distance between the rear air bearing center and the contact pad because of the increase in the penetrating depth due to the micro waviness. Therefore, the reduction of the distance is important in terms of reducing both the spacing and the maximum contact force. From the discussion described above, when designing a tri-pad type contact slider, we should make the distance between the rear air bearing center and the contact pad equal to zero and make the rear air bearing stiffness large. Otherwise, we should make the rear air bearing stiffness much smaller than the contact stiffness."
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0002517_1.1515324-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002517_1.1515324-Figure5-1.png",
+        "caption": "Fig. 5 Analytical model of a link at the instant of collision",
+        "texts": [
+            "4 Angular Velocity Variation Caused by Foot Exchange. In this analysis, it is assumed that the toe collision is plastic and the foot exchange takes place instantly for the sake of analytical simplicity. As shown in Fig. 4, u\u0307 i p4 represents the angular velocity of link i at the moment right before the foot exchange ~posture 4 in Fig. 2!, whereas u\u0307 i p5 stands for the angular velocity of link i at the moment right after the foot exchange ~posture 5 in Fig. 2!. The analytical model of link i at the instant of the foot exchange is shown in Fig. 5. Pi and Pi11 are the impulses caused by the collision at the joints i and i11, respectively. The impulsemomentum equations for link i are written in the forms, mi~v ix p52v ix p4!5Pix2P (i11)x mi~v iy p52v iy p4!5Piy2P (i11)y (4) I i~ u\u0307 i p52 u\u0307 i p4!5ai3Pi1~ li2ai!3Pi11 556 \u00d5 Vol. 124, DECEMBER 2002 rom: http://dynamicsystems.asmedigitalcollection.asme.org/ on 01/28/201 where v i p4 is the mass center velocity of link i at the moment right before foot exchange and vi p5 is the mass center velocity of link i at the moment right after the foot exchange"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000909_027836499901800506-Figure11-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000909_027836499901800506-Figure11-1.png",
+        "caption": "Fig. 11. Grasp on a pyramid with four contact points: the optimal grasp (a); and an unfavorable condition (Td = \u2212j) (b).",
+        "texts": [
+            "5, 0) as the optimal position (Fig. 10a), close to which a minimumfriction coefficient of 0.72 (amax = 5) is required to ensure contact stability. It is interesting to note that the most unfavorable condition is obtained when the torque Td = \u2212i is exerted on the pyramid. Figure 10b reports the values of the normal and tangential forces that are necessary to balance the disturbance torque Td = \u2212i by minimizing the friction coefficient. If the pyramid were to be grasped with four digits, the optimal grasp points (Fig. 11a) would be: P1 (0.5, 0, 0), P2 (0, 0.5, 0), P3 (\u22120.5, 0, 0), and P4 (0, \u22120.5, 0), with fmin = 0.61 (amax = 5). In this case, the most unfavorable condition is obtained when a torque directed along the x- or y-axis is exerted on the object. Figure 11b shows the forces that the fingers would have to exert to balance the torque. The influence the maximum normal force exerted by each digit (amax) has on contact stability may be examined by means of the optimization algorithm. Figure 12 shows the minimum-friction coefficient value required to ensure stability (fmin) as a function of amax for an optimal grasp with three and four contact points. It is interesting to observe that both curves have fmin = 0.5 as an asymptotic value, and therefore a friction coefficient greater than 0"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000704_a:1008228120608-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000704_a:1008228120608-Figure5-1.png",
+        "caption": "Figure 5. Example of a non-periodic motion in the plane X1\u2013X2 (a) and of the corresponding event map (b).",
+        "texts": [],
+        "surrounding_texts": [
+            "If the driving velocity is small the points lying on the line AC into the failure locus represent all the transient motions once the possible global slip phases have ceased [7]. The stretch length d may vary between 0:6764 and 0.6764 which correspond to the points C and A, respectively, of the failure locus of Figure 2. Choosing a grid of initial conditions on this line, it is possible to investigate the global dynamics of the system. Figure 6 is an illustration of the global dynamic behaviour of the system by means of the one-dimensional map. In Figure 6 the thin lines indicate the transient behaviour whereas the thick lines are composed by points belonging to the steady state behaviour of the system. There exist (at least) two attractors, indicated by the numbers \u20181\u2019 and \u20182\u2019, so that the interval CA, where the map is defined, is divided in two basins of attraction; the two sub-intervals B1 and B2 constitute the basin of the attractor \u20182\u2019, the other sub-intervals are the basin of attraction of the attractor \u20181\u2019. The one-dimensional map will be utilised to study the evolution of the attractor \u20182\u2019 as Vdr varies. Figure 7 shows the bifurcation diagram of the attractor \u20182\u2019 in a portion of the range of small driving velocities; starting from Vdr = 0:0846 the attractor undergoes a period-doubling cascade giving birth to an apparently chaotic attractor which suddenly disappears for Vdr 0:08058. A sequence of one-dimensional maps in the non-periodic region can be seen in Figure 8; the shape of those maps constitutes evidence of the chaotic nature of the system. For values of the driving velocity close to Vdr = 0:082377 (see bottom right of Figure 8) and above, the steady state part of the one-dimensional iterated mapping is composed of two (or more) separated branches; see also Figure 9a. This separation into two branches clearly rules out the existence of odd periodic orbits since f(a) :! b, f(b) :! a, and a \\ b = ;, where a and b are the two intervals where the permanent portion of the map is defined. The only exception is a fixed point in between the two branches (not shown). The map is, however, still continuous as the transient part of the map shows (not shown on Figures 8 and 9). Considering Figure 9b and the illustrative trajectories shown, it is evident that the map possesses a so-called snap-back repeller, or in more traditional terms a homoclinic orbit to the unstable fixed point; the fixed point is, of course, a fixed point for the second iterate of f , and in reality is a prime period-2 orbit. The fixed point for the second iterate is located at approximately d = 0:1624. The snap-back repeller is sufficient for the existence of chaos [11, 18]. That is, there exist periodic points of any prime period (for the second iterate), and uncountably many orbits that are not even asymptotically periodic. Finally in some cases it seems possible to detect a partition of intervals a, b, and c on the interval of definition of the \u2018permanent\u2019 map, as suggested by Figures 10a and 10b, corresponding to the values Vdr = 0:0811 and Vdr = 0:0813. It is reasonable to hypothesise the existence of a map with a superstable period-4 orbit which was approximately found for Vdr = 0:0812 (Figure 10c). Such an orbit divides the interval of definition of the \u2018permanent\u2019 map in three sub-intervals a, b, c which are mapped in the following way: f(a) b; f(b) c; f(c) a [ b [ c: (6) The transition matrix A (or Markov graph) is constructed according to the rule: Aij = 1 if f(ai) aj and zero otherwise: A = 0 B@ 0 1 0 0 0 1 1 1 1 1 CA : (7) The construction of the transition matrix enables us to count the number of period-m orbits. If Nm denotes the number of fixed points of fm then: Nm = tr(Am): (8) Part of these Nm orbits are trivial, i.e. they are orbits of periods dividing m. Subtracting the number of trivial points from Nm and then dividing by m makes it possible to obtain the number of the period-m orbits [15]. For example, tr(A2) = 3; there are three fixed points of f2, of those one is a fixed point of f , the trivial period-2 orbit and then there exists a true period-2 orbit; tr(A3) = 7; of those seven fixed points one is trivial and the other six correspond to two period-3 orbits; tr(A6) = 39; f6 has 39 fixed points: one is the fixed point of f , two are the period-2 orbit, six are the two period-3 orbits so that the number of non-trivial fixed points is 30 corresponding to five period-6 orbits. The structure of the Markov graph shows that there are periodic orbits of any period, which are believed to be unstable."
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0003441_978-1-4613-9030-5_27-Figure27.4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003441_978-1-4613-9030-5_27-Figure27.4-1.png",
+        "caption": "Figure 27.4: First fonn of deflection due to instability of the spine (back view): a) the whole spine; b) ver tebrae T8-Ll.",
+        "texts": [
+            "3 presents the spine system displace ments in the state of stability (only vertebrae are shown) deformed by load (in the considered case all muscles work). Because of the symmetry of both the investigated system and the applied load in respect to the sagittal plane, displacements in the frontal plane equal zero. It can be noticed that, in comparison with Figure 27.1a, the load causes an increase of the spine curves (kyphosis and lordosis). When the load is increased by about 20% the spine system loses its stability. A form of spinal deflection is shown in Figure 27.4. Because of linearization of the equations, only the proportions of the displacements and rotation angles of in dividual vertebrae are known, not their absolute values. The form shown in Figure 27.4 is charac- terized by large displacements of vertebrae TlO and T11 and simultaneous rotation of all vertebrae. The rotation angle of vertebrae. beginning at the L5, increases in the lumbar section and attains its maximum value at the Tll. Then it decreases in the thoracic section. The relative rotation axes of the vertebrae are beyond the spinal column. The spine deformation visible from behind is mostly due to the fact that during the rotation the location of the natural spine curves changes (lordosis and kyphosis are now in different planes)"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003613_j.bios.2005.08.010-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003613_j.bios.2005.08.010-Figure5-1.png",
+        "caption": "Fig. 5. Cyclic voltammograms of a FAD/zinc oxide film adhered to a glassy carbon electrode in 10 ml of a deoxygenated phosphate pH 7.0 aqueous solution with: (A) [H2O2] = (a) 0 M; (b) 0.05 M; (c) 0.1 M; (a\u2032) bare glassy carbon electrode and [H2O2] = 0.1 M; (B) a FAD/zinc oxide film in a deoxygenated pH 7.0 aqueous solution with: (a) hemoglobin and H2O2 absence; (b) 4.25 \u00d7 10\u22126 M of hemoglobin; (c) 4.25 \u00d7 10\u22126 M hemoglobin added 0.25 M H2O2; (a\u2032) bare glassy carbon electrode with 4.25 \u00d7 10\u22126 M hemoglobin added 0.25 M H2O2. Scan rate = 0.1 V/s.",
+        "texts": [
+            " The EQCM and cyclic voltammetry were used to study the in situ growth of the FAD/zinc oxide films and the results showed that the hemoglobin did deposit on the FAD/ZnO film and enhanced the electrocatalytic reduction activity of oxygen through the FADH2/FAD redox couple. Fig. 3A explains the consecutive cyclic voltammetry of a FAD/zinc oxide film on the gold electrode in a pH at 7.0 aque- Fig. 3. (A) Repeated cyclic voltammograms of a FAD/zinc oxide film on gold electrode in a solution containing 1 \u00d7 10\u22125 M FAD in an aqueous 0.1 M Zn(NO3)2 pH 7.0. Scan rate = 0.02 V/s. (B) The change in EQCM frequency, recorded concurrent with the consecutive cyclic voltammograms of Fig. 5A. (C) Fig. 5A FAD/zinc oxide film in the (a) absence of oxygen and (b) after adsorbed hemoglobin and presence of oxygen in a pH 7.0 phosphate aqueous solution; (a\u2032 and a\u2032\u2032) bare glassy electrodes in the solutions of absence and presence of oxygen, respectively. Scan rate = 0.1 V/s. 2 edox couple in the absence of hemoglobin (Fig. 2B(b)). The ous solutions. Fig. 3B demonstrates the change in the EQCM frequency recorded during the first 10 cycles of the consecutive cyclic voltammetry. The increase in the voltammetric peak current observed in Fig",
+            " According to the experimental results, the reaction pathways for spectroelectrochemistry of hemoglobin using FAD as a catalyst are as follows: FAD/ZnO/GC electrode + 2H+ + 2e\u2212 \u2192 FADH2/ZnO/GC (6) 2Hemoglobin (FeIII) + FADH2/ZnO/GC \u2192 2Hemoglobin (FeII) + FAD/ZnO/ + 2H+ (7) 3 a a c c I \u2212 i t film. The electrocatalytic reduction of H2O2 by the FAD/ZnO film in presence of hemoglobin in a pH 7.0 buffered solution was studied using cyclic voltammetry with the concentration of 4.25 \u00d7 10\u22126 M hemoglobin added with 0.25 M H2O2. The electrochemical responses are shown in Fig. 5B. The electrocatalytic peak current IPcat (the cathodic peak potential, EPcat, at a potential of about \u22120.47 V) of the FAD/ZnO film of FADH2/FAD redox couple increased noticeably. This arose from the direct electrocatalytic reduction of H2O2 through the FADH2, catalyzed by the FAD/ZnO film and enhanced by the hemoglobin. This behavior obtained from the direct electrocatalytic reduction of H2O2 enhanced by the hemoglobin. Then, the electrocatalytic reduction of O2 was performed by the hemoglobin and FAD/ZnO",
+            " A possible mechanism for the reduction of H2O2 by the heme protein film is that the heme\u2013Fe(III) complex is oxidized to a compound denoted as \u201ccompound I\u201d, i.e., heme\u2013Fe(III) + H2O2 \u2192 compound I + H2O. Then, compound I reacted with H2O2 to form the heme\u2013Fe(III) and O2, i.e., compound I + H2O2 \u2192 heme\u2013Fe(III) + O2 (Taniguchi et al., 1992). .5. Electrocatalytic reduction of H2O2 by FAD/ZnO film nd hemoglobin The electrocatalytic reduction of H2O2 by a FAD/ZnO film nd hemoglobin in pH 7.0 buffered solution was studied by yclic voltammetry between 0 and 0.7 M. The electrochemial responses are shown in Fig. 5A. The catalytic peak current Pcat (the anodic peak potential, EPcat, at a potential of about 0.47 V) of the FAD/ZnO film of FADH2/FAD redox couple ncreased. This arose from the direct electrocatalytic reducion of H2O2 through the FADH2 catalyzed by the FAD/ZnO The electrocatalytic reduction of O2 was, however, performed by the hemoglobin and FAD/ZnO. The electrocatalytic reduction of O2 by FAD/ZnO film using the cyclic voltammetry and rotating ring-disk electrode method in pH 7.0 phosphate aqueous solution in the presence of oxygen (saturated with air) was performed"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003972_robot.2006.1642071-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003972_robot.2006.1642071-Figure5-1.png",
+        "caption": "Fig. 5. Soft-fingered grasping",
+        "texts": [
+            " Let kij and bij be the elastic and viscosity coefficients, respectively, of the soft interface between i-th and j-th masses, and mi represent the mass of Pi. Additionally, let Lij be the natural length of the soft interface between i-th and j-th masses. Physical parameters of the soft interface and mass points are time-invariant and positive. By varying the physical parameters, the model can be used to represent various cases. For example, when we use a high stiffness value as a parameter k13, the model describes the case of a soft-fingered robotic hand grasping a rigid object as shown in Figure 5. C. Formulation of simultaneous control along the x-axis In this section, we formulate the simultaneous positioning of viscoelastic object. As an example, we use PID control for the positioned points nearest to the respective manipulated points as a control law. Also, we use force values as manipulated variables. At time t, the dynamic equation of the masses can be expressed as: \u23a7\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23a9 m0v\u03070 = k01(x1 \u2212 x0 \u2212 L) + b01(v1 \u2212 v0) + fdrive 0 , m1v\u03071 = \u2212k01(x1 \u2212 x0 \u2212 L) \u2212 b01(v1 \u2212 v0) +k13(x3 \u2212 x1 \u2212 L) + b13(v3 \u2212 v1), m3v\u03073 = \u2212k13(x3 \u2212 x1 \u2212 L) \u2212 b13(v3 \u2212 v1) +k32(x2 \u2212 x3 \u2212 L) + b32(v2 \u2212 v3), m2v\u03072 = \u2212k32(x2 \u2212 x3 \u2212 L) \u2212 b32(v2 \u2212 v3) + fdrive 2 , (1) where f drive i is the driving force for the respective manipulated points"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003808_jjap.44.1875-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003808_jjap.44.1875-Figure1-1.png",
+        "caption": "Fig. 1. Structures of a two-domain HAN cell treated by ion beam irradiation.",
+        "texts": [
+            " However, an ionbeam-treated multidomain HAN cell does not suffer from such a problem, because the same kind of organic material is coated on both substrates. A multidomain HAN cell can be fabricated with two different structures using an ion beam. First, the polyimide surface irradiated with using an ion beam with a low energy and a high current density aligns LC vertically. On the other hand, the polyimide surface irradiated with using an ion beam with a high energy and a high current density aligns LC horizontally. Each pixel is divided into two parts and each of the parts is exposed to an ion beam in a reverse direction, as shown in Fig. 1(a). Second, both layers are divided into two parts, one of which is a homeotropically aligned by low-current ion beam irradiation and the other is a homogeneously aligned by high-current ion beam irradiation, as shown in Fig. 1(b). Asymmetry in viewing angle in a conventional HAN LC cell can be compensated by the two-domain structure because a two-domain HAN cell is optically identical to a cell, as shown in Fig. 1. Figure 2 shows a pixel with two domains divided by an ion beam with an experimental setup shown in Fig. 1(b). The domain size is 2000 mm 2000 mm and the ion beam conditions are: For horizontal alignment, the ion beam energy, ion beam exposure time, incident angle and beam current density are 200 eV, 30 s, 30 , and 80 mA/cm2, E-mail address: thyoon@pusan.ac.kr Japanese Journal of Applied Physics Vol. 44, No. 4A, 2005, pp. 1875\u20131878 #2005 The Japan Society of Applied Physics 1875 respectively. For vertical alignment, the ion beam energy, ion beam exposure time, incident angle and beam current density are 80 eV, 10 s, 10 , and 20 mA/cm2, respectively. Figure 2(a) shows the front view of the sample with the structure shown in Fig. 1(b) in the field-off state. Except for a disclination line in the center generated by the mismatch of alignment between the top and the bottom layers, the brightness of the two domains in front of a HAN cell is nearly the same. Figures 2(b) and 2(c) show the right- and the left-hand side views in the field-off state, respectively. These images show obviously that, as depicted in Fig. 1(b), the form of LC directors in the two domains is symmetric to each other. Figure 2(d) shows the front view of the sample in the field-on state (7V). Both domains show an excellent dark state. Figures 2(e) and 2(f) show the right- and the left-hand side views in the field-on state (7V), respectively. They also show obviously that the form of LC directors in the two domains is symmetric to each other. Figures 3(a) and 3(b) show iso-contrast contours of a cell and a two-domain HAN cell calculated without any optical compensation with a pixel size of 200 mm 100 mm"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002546_jpsj.73.1082-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002546_jpsj.73.1082-Figure4-1.png",
+        "caption": "Fig. 4. Schematic representation of experimental procedure to check whether some chemical as an inhibitor and pacemaker cells are necessary for concentric ring pattern formation or not.",
+        "texts": [
+            " If so, the local cell density of bacteria corresponds to an activator. Moreover, it is necessary for the formation of the concentric ring-like pattern that there are pacemaker cells which secrete some chemical periodically at the center of the concentric ring-like colony. Then, the following experiment can be considered in order to check whether any chemical as an inhibitor and pacemaker cells for the appearance of concentric ring exist or not: Cut a colony together with an agar plate as shown in Fig. 4(a) along the dotted lines in Fig. 4(b) during its growth. Then the part of the colony represented by the darker region in Fig. 4(b) is isolated from cells at the center spot which are considered to be a pacemaker for concentric ring pattern formation. If some chemical and pacemaker cells are needed, this isolated part of the colony must grow and produce a colony whose morphology is different from the previous one. In the case of P. mirabilis, it has been confirmed that the colony on the isolated part grows into almost the same concentric ring pattern as the colony on the rest part. Therefore, it is concluded that macroscopically any chemicals and the pacemaker cells are not necessary for the formation of the concentric ring-like colony"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure4.17-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure4.17-1.png",
+        "caption": "Figure 4.17. Cylindrical coordinates and the cylindrical reference frame,",
+        "texts": [
+            " The rectangular coordinate system is a 268 Chapter 4 familiar example of an orthogonal coordinate system in which a point P is located by specification of three directional numbers obtained by measurement of three mutually perpendicular distances along straight coor dinate lines. And this rudimentary coordinate system is used to construct other orthogonal coordinate systems in which some, or possibly all, of the coordinate lines may be curved; and hence these are called curvilinear coor dinate systems. In particular, the cylindrical coordinates (r, \u00a21, z) of a point P in a rec tangular Cartesian frame iP = { F; Id are illustrated in Fig. 4.17. To locate P by its cylindrical coordinates in t'P, measure from Fa radial distance r along the X axis, then trace that end point along a circular arc of radius r through an angle \u00a21 about the Z axis, and, finally, from its place in the XY plane, trans late the point a distance z along a straight line parallel to the Z axis. This program brings us to the unique location of Pin t'P. It is seen in Fig. 4.17 that for a fixed value of r the locus swept out by all such points is a cylindrical sur face of radius r in t'P; therefore, as mentioned above, the three measure num bers r e [0, oo ), \u00a21 e [0, 2n ], and z e (- oo, oo) are named cylindrical coor dinates. Because one of the coordinate lines traversed by the tracing point is a curved line, the cylindrical coordinate is a curvilinear coordinate system. When z = const, the cylindrical coordinates sometimes are called plane polar coordinates. Another reference frame 1/1 = { 0; e\" e9 , ez }, called the cylindrical reference frame, may be introduced to describe this system. The origin for this frame may be chosen anywhere; however, for simplicity, we shall take 0 at F in t'P. The three orthogonal lines labeled r, \u00a21, and z in Fig. 4.17 are parallel to the directions of the orthonormal basis for 1/1, which is shown at P for con venience. The unit vector e, is always in the direction of increasing values of the radius vector r in the XY plane; and ez = K is the usual unit vector parallel to the z axis in the direction of increasing values of z = Z. The unit vector e9 = ez x e, is in the direction of increasing values of the central angle \u00a21, and it Motion Referred to a Moving Reference Frame and Relative Motion 269 is tangent at P to a circle of radius r parallel to the XY plane"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001880_37.664656-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001880_37.664656-Figure5-1.png",
+        "caption": "Fig. 5. Example Case II system.",
+        "texts": [
+            " In the experiments, both the regulation cases were performed for long durations (more than two hours) to check for divergence or instability. It was found that the system consistently exhibited error convergence and stability. The AISE values and eqor bounds for the trackmg case shown in Table l indicate the advantages of the reported adaptive technique over the other two. T O Example Case I1 The Example Case I1 hardware system consists of a nonlinear load driven by a DC'motor. The nonlinear load is a four-bar linkage (Fig. 5a) with\u20ac$ being the input which is controlled by a DC motor, and\u20ac$, 8, arelfunctions of 8,. Since friction in the four-bar linkage load is position- and velocit pressed as Tf = Tf(\u20ac12,62,sgn(6>) Th IEEE Control Systems where Tm is the DC motor control torque, f ( 8 , ,e,) and b( 0,) are known nonlinear functions, and A(@,, 0,) is the unknown non- linear function due to friction and other state dependent uncertainties. Fig. 5b is a representative open-loop dynamics plot showing the large variation in velocity for a constant input torque, as compared to a constant output velocity expected for Example Case I. It shows the nonlinear position dependent nature of the dynamics, details of which are given in Table 2. Based on the scheme shown in Fig. 1, the input for identification is selected as U = U' i- (Jeq - f , (0 , ) ) ( -20, -8) for the actual plant and U = U' + (J., - f,( \u20acI2))[- 26 ' -0 ) forthenominal model, where U' is the training signal, which is a random step excitation input with a maximum magnitude of 0"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000569_s0045-7949(98)00004-2-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000569_s0045-7949(98)00004-2-Figure3-1.png",
+        "caption": "Fig. 3. The undeformed and deformed shapes of a rectangle undergoing a rigid-body rotation: (a) undeformed and (b) deformed.",
+        "texts": [
+            " Using the fact that d(dmn) = 0 and Omn=Onm [2], we obtain \u00ffO12 1 l2 j ~2 jn d 1 l1 j ~1 jn \u00ffO21 1 l1 j ~1 jn d 1 l2 j ~2 jn \u00ffO12d 1 l1 j ~1 jn 1 l2 j ~2 jn \u00ffO12d 1 l1 j ~1 1 l2 j ~2 O12d 2A12 O12dA12 O21dA21 33 Hence, Equation (30) can be rewritten as dP V OijdAij dV 34 which shows that Almansi strains are work-conjugate to Almansi stresses. To show the objectivity of di erent strain measures, we consider an in\u00aenitesimal rectangle undergoing a rigid-body rotation y with respect to the axis x3, as shown in Fig. 3. It follows from Fig. 3 that dy1 dx 1 cos y 35a and the displacement component v1 of the points o, a, and g are vo1 0, va1 dx 1 cos y\u00ff 1 , vg1 \u00ffdx 1 sin 2y 35b Using Equations (35a)\u00b1(b) and the de\u00aenitions of strains shown in Equations (4), (9) and (24), we obtain e\u030211 e11 @v1 @x 1 va1 \u00ff vo1 dx 1 cos y\u00ff 1 6 0 36a l11 @v1 @y1 va1 \u00ff vg1 dy1 1\u00ff cos y 6 0 36b Hence, displacement gradients e\u00c3ij, engineering strains eij and in\u00aenitesimal strains lij are non-objective measures. From Equation (32) one can see that, if there are only rigid-body motions, lk=1, jm\u00c4 jn\u00c4=dmn and Amn=0"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003241_tasc.2004.830317-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003241_tasc.2004.830317-Figure1-1.png",
+        "caption": "Fig. 1. Cross section of the HTS rotor. (a) Straight part (b) end part.",
+        "texts": [
+            " In order to satisfy high efficiency and high starting torque, critical current of the short bars made of HTS tapes, that is, number of HTS tapes which is connected in parallel, must be decided carefully. If the critical current is too large, HTS bars will not quench during the starting. If it is too small, it will not recover from quench after starting. Two HTS tapes which were connected in parallel were used for one bar. Critical current of one HTS tape was 115 A at self field. To accommodate the flat HTS tape, shape of the slot of the HTS rotor should be different from that of the conventional motor. Cross section of the HTS rotor is given in Fig. 1. Figs. 1(a) and (b) show the cross section of straight part and the end part, respectively. Outer diameter and inner diameter of the HTS rotor were 78 mm and 22 mm, respectively. Fig. 2 shows the cage rotor of the conventional and the HTS motor. HTS tapes for the short bars are soldered to the HTS tapes for the short rings. Electrodynamometer was coupled to the motor to apply the load. Fig. 3 shows the test system, where the HTS motor, the electrodynamometer and the cryostat are shown. Electro-dynamometer was placed on the top flange of the cryostat"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001746_0005-1098(92)90062-k-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001746_0005-1098(92)90062-k-Figure1-1.png",
+        "caption": "FIG. 1. The concept of MVSC.",
+        "texts": [
+            " In this paper, we propose a new approach, the modified variable structure controller (MVSC) to eliminate the chattering phenomenon. The concepts of the MVSC will be given in the following section. 2. Some concepts o f the M V S C We are now in a position to propose a modified variable structure controller (MVSC). The central concept of MVSC is based on the utilization of two switching surfaces, S 1 = 0 and S~ = 0, to establish a sliding sector. For ease of statement, in the following we shall give an explanation by using a system with state space as indicated in Fig. 1. The state space is partitioned into three parts by two switching surfaces. In Part tr, the RP lies outside the sliding sector, i.e. in the hitting phase S1S 2 > 0, a feedback control law is adopted to force the state trajectories of the system hitting the sliding sector at some time t > 0 subject to any initial condition. It is important to notice that the structures in Part oc agree with those of the conventional VSC. Our prime concern in this part is the reduction of hitting time; hence high control gain is desired. On the other hand, the design of control law in Part fl and Part ),, i.e. the sliding phase $1S2 < 0 , is to be based on the purpose of eliminating the chattering, whilst retaining good robustness against disturbances and parameter variations. In Part fl and ),, a low-speed-changing structure will be established to reduce switching frequency and the highfrequency unmodelled plant dynamics is thus ignored. As seen from Fig. 1, the low-speed-changing structure is established if the following statements hold: Part fl: If the RP hits S 1 = 0 from S1S2>0 into S1S2<0 , the state trajectory gets near to $2 = 0 and gets far from S~ = 0. AUTO 2B:6-I 1209 Part y: If the RP hits $ 2 = 0 from S~$2>0 into S1S2<0 , the state trajectory gets near to St = 0 and gets far from , ~ = 0 . Combining the above results, it is of interest to observe that due to the addition of another switching surface, MVSC results in a quite small switching frequency"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003839_j.amc.2005.11.048-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003839_j.amc.2005.11.048-Figure1-1.png",
+        "caption": "Fig. 1. Hemispherical bearing model of synovial knee joint.",
+        "texts": [
+            " The introduction of g is due to polar additives in the non-polar lubricant, the ratio g/l has the dimension of length squared and hence characterizes the material length of the fluid. The flow problems discussed by Stokes indicate the significant effects of couple stresses and give hints for measuring various material constants and describe the influence of size effects associated with couple-stress fluid that is not present in non-polar cases. The physical configuration of the problem is shown in Fig. 1. The simulation of the squeeze-film behaviour of a human joint deals with the compression of thin poroelastic surface-a thin layer of fluid over another thin layer of poroelastic material. The articulation of joint is modeled as the case of a upper rough non-spinning spherical rotor (poroelastic cartilage) approaching the lower rough poroelastic hemispherical bearing normally with constant velocity dH/dt. Lubricant in the joint cavity is assumed as Stokes couple-stress fluid. The film thickness is made up of two parts H \u00bc h\u00f0t\u00de \u00fe hs\u00f0x; z; n\u00de; \u00f02:3\u00de where h(t) = Dr(1 + ecosh) represents the nominal smooth part of the film geometry while hs is part due to the surface asperities measured from the nominal level and is a randomly varying quantity of zero mean, n is an index parameter determining a definite roughness structure, e(=e 0 /Dr) is the eccentricity ratio, e 0 is the eccentricity, Dr(=Ro Ri) is radial clearance and h = x/R"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure4.26-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure4.26-1.png",
+        "caption": "Figure 4.26. Motion of a parti~le at the tip of an oscillating fan blade.",
+        "texts": [
+            "80f) The three cases studied here demonstrate that the relations ( 4.46) and ( 4.48) for the velocity and acceleration of a material point referred to a moving frame contain all of the basic equations (1.8), (1.10), (2.27), and (2.30) studied earlier in Chapters 1 and 2. However, in this example, the origin of the moving frame was fixed in the preferred framt:. We turn now to a similar example in which this is not the case. D 288 Chapter 4 Example 4.17. Application to the Motion of an Oscillating Fan Blade. The blade of an oscillating fan shown in Fig. 4.26 spins about a horizontal shaft of length I with a constant, counterclockwise angular speed w 2 \u2022 The fan assembly oscillates about a vertical axis with a variable speed w 1 = w cos pt, where p is the constant frequency of the fan oscillations and w is the maximum angular speed. Find in the ground frame 0 = { F; Ik} the total velocity of a point P at the tip of a blade two ways: (i) referred to the frame 1 = { 0; ik} imbedded in the motor housing, and ( ii) referred to frame 2 = { 0; i/.,} fixed in the blade. What is the total angular acceleraton of the blade for these cases? Solution of (i). In this problem, the particle P is moving relative to the oscillating motor housing frame 1 shown in Fig. 4.26; therefore, we shall employ ( 4.46) to find its absolute velocity. With this objective in mind, we now determine the required terms. The position vector of P in the motor frame 1 is given by x = a( cos 1,6 j + sin 1,6 k ). ( 4.81a) Therefore, the relative velocity of P in frame 1 is (4.81b) in which w 2 = /> is the constant angular speed of the blade in the motor frame. The total angular velocity of the motor frame relative to the ground frame 0 = { F; Ik} is given as Hence, with the aid of (4.81a), we obtain ro1 x x = -aw 1 cos 1,6 i",
+            " Since 0 is a point of a rigid body having the angular velocity ro 1 about a fixed base point at F, its velocity may be found by use of (2.27). Thus, ( 4.81e) Notice that the same result may be gotten by differentiation of B in frame 1; namely, v0 =B=/rofxi=w 1 /j. Substitution of (4.81b), (4.81d), and (4.81e) into (4.46) yields the solution. Thus, the absolute velocity of P referred to the motor frame 1 is v P = -aw 1 cos \u00a2J i + (w 1l- aw 2 sin \u00a2J) j + aw 2 cos \u00a2J k, ( 4.81f) wherein we recall that w1 = w cos pt. Solution of (ii). This problem requires that the motion of P be referred to the blade frame 2 = { 0; i~} shown in Fig. 4.26. Since there is no motion of P relative to the blade frame, (4.46) shows that the velocity is determined by the rigid body formula (2.27): (4.82a) The total angular velocity of the blade is given by = w2 i' + w 1(sin \u00a2J j' +cos \u00a2J k'). (4.82b) Hence, using the position vector x = aj' in frame 2, we get (4.82c) The velocity of the base point 0 is found from tht! first equation in (4.81e) in which B=li'. Thus, referred to the blade frame 2, we have v0 = /ro 1 xi'= lw 1(cos \u00a2J j'- sin \u00a2J k'). (4.82d) Substitution of ( 4",
+            " At the same time, the yoke is rotating about the axis of its supporting rod with a constant angular velocity ro 1 , as 344 Chapter 4 indicated. Find the absolute velocity and acceleration of a point P on the rim of the disk two ways: (i) referred to a frame fixed in the rotating yoke rod, and (ii) referred to a frame fixed in the spinning disk. \\ Problem 4.90. 4.91. The motion of an oscillating fan blade is described in Example 4.17. Use the data assigned in the example, and apply the two methods described there to find in the ground frame 0 = { F; Ik} the total acceleration of the blade point P. See Fig. 4.26. 4.92. A motor-driven gear G of radius a turns, as shown, with a constant angular speed w 1 about a honzontal axle fixea m a table T that concurrently rotates With a constant angular speed w 2 about a vertical axis fixed in the machine structure S. The center of G is at a distance b from the center 0 of the table. Find the total velocity and acceleration of the rim pomt P on G referred to (i) a reference frame fixea in Tat the center of G and (ii) a frame fixed in G. Problem 4.92. 4.93. A gear G of radius a rolls, as shown, on a rack gear R cut in a table T that turns about its normal axis with a constant angular speed w",
+            " Find the absolute acceleration of P referred to 1/J, and thereby derive two equations that may be used to determine x(t) and N(t) as functions oft. The solution of such equations is investigated in Chap ter 6. Problem 4.115. 4.116. (a) Apply the vector component transformation law (3.107) to derive (4.81f) from (4.82e) in Example 4.17. (b) Use the assigned data to derive from (4.81f) the absolute acceleration of the blade point referred to the motor frame 1. Apply the transformation law to determine from this result the absolute acceleration of P referred to the blade frame 2. See Fig. 4.26. 4.117. Begin with the vector equation (4.8) and prove, conversely, that the time rate of change of the Euler rotation tensor is given by (4.106a). Motion Referred to a Moving Reference Frame and Relative Motion 351 4.118. (a) Let T(t) be a tensor in a preferred frame cP but referred to a moving frame <p = { 0; ik} whose angular velocity tensor relative to cP is W 1 . Determine the second total time derivative T(t). (b) Find the formula for \\'\\'1 , and proye that \\'V1 is a skew tensor. (c) Show that the tensor equation for the derivative W1 implies the equivalent vector formula for the angular velocity vector oo1 , which is easily confirmed by ( 4"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002563_robot.1996.506892-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002563_robot.1996.506892-Figure6-1.png",
+        "caption": "Figure 6: Coordinate system of the fingertip surface",
+        "texts": [
+            " Interfacing the custom-made fingertip and the last joint of the robot we have a Lord FT335X force/torque sensor. The control system of the hand consists of a MVME166 6 Conclusions single-board computer, three Delta-Tau PMAC multiaxis motion control boards, a Sun workstation and a VxWork real-time operating system. The experiment we implemented includes calibrating the force/torque sensors with standard weights, programing the sensor to collect raw data of the measured force and moment, and computing the contact locations where the finger touched the object. The experimental results are shown in Figure 6 through Figure 8. Using the coordinate system of the fingertip surface as is shown in Figure 6, we demonstrate the experimental results in Figures 7 and 8. From these figures we see that if we use the maximum absolute value of Arc to express the accuracy of the sensing device, it turns out to be less than 1.80\" when the absolute value of the exerted force is more than five newtons. The experiments also show that within the cylindrical part, the absolute value of Arc seems to be proportional to the distances between the contact points and the working surface of the force/torque sensor along its z-axis"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000496_a:1022548914291-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000496_a:1022548914291-Figure6-1.png",
+        "caption": "Fig. 6. Paths of clocks fixed in k and K.",
+        "texts": [
+            " No tension Non-Time-Orthogonal Reference Frames 419 arises in the disk as it is spun up, and no relativistically induced rupturing occurs. 3.2.3 Time Dilation. Although frames K and k agree on simultaneity, it can be shown that standard clocks in each run at different rates. (Note that two clocks running at different rates can nonetheless both agree on simultaneity, i.e., that no time elapsed off either one between two events.) The time dilation effect can be demonstrated with the aid of the spacetime diagram of Fig. 6, which shows the helical path of a clock fixed on the disk as seen from frame K and that of a clock fixed in K as seen from K. The moving clock travels the path of 3D point p of Fig. 3 extended for one full rotation. The path of that clock is a non-geodesic, while the path of its \"twin\" fixed in K is a geodesic, a straight line. The proper time passed for each clock is simply its path length (divided by ic), and this path length can be measured in any frame we choose since it is frame invariant"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003554_13552540510601309-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003554_13552540510601309-Figure3-1.png",
+        "caption": "Figure 3 Identification of cusp volume",
+        "texts": [
+            " This \u201ccusp volume\u201d can subsequently be used for slice height calculation. It would provide a more accurate and exhaustive estimate of the deviation between CAD model and built-up part than that provided by cusp height error d. A user-defined tolerance can be applied on cusp volume to determine acceptable slice heights. In order to define dv, it will of use to observe the cutter motion in case of LOM. To cut out a layer from sheet material, the cutter linearly interpolates from one position to another along the slice contour (a! b! c; Figure 3(i) and (ii)). By virtue of these paths, the cutter cuts out a series of four-sided ruled patches to form the sidewalls of the layer, shown in bold in Figure 3. Now, dv may be defined as the volume enclosed between Volume deviation in direct slicing Chandan Kumar and A. Roy Choudhury Volume 11 \u00b7 Number 3 \u00b7 2005 \u00b7 174\u2013184 1 the CAD model surface; 2 one such four-sided ruled patch; 3 the two NVSs passing through the lower and upper corner points of the ruled patch; 4 the upper slice associated with the patch; and 5 the lower slice associated with the patch (Figure 3(iii)). Calculation of cusp volume \u2013 theoretical procedure The cusp volume dv, which has been identified, is enclosed by a number of surfaces. If the volumes under those respective surfaces are added together with proper sign convention, the volume dv will result. Therefore, it is required first to determine the volume under a surface. Calculation of volume under surface The volume under a surface R\u00f0u; v\u00de is given by: V \u00bc ZZ z\u00f0u; v\u00dejJjdudv \u00f01\u00de where J \u00bc Jacobian of surface at a point \u00bc \u203ax \u203au \u203ay \u203au \u203ax \u203av \u203ay \u203av \u00f02\u00de x, y, z are the coordinates of point on the surface R\u00f0u; v\u00de: However, the application of this equation has certain restrictions",
+            " Surface re-construction \u2013 Bezier surface fitting to CAD model surface patch The portion of the CAD model surface associated with the cusp volume is not necessarily an iso-parametric patch (i.e. its boundaries are not iso-parametric lines). Hence, straight integration is not possible. Obviously, some forms of re-parameterization or re-defining of the parameters are necessary. In order to do so, it is first necessary to distinctly identify the portion of the CAD model surface involved with dv. In a layer the NVSs and the upper and lower slices compartmentalize the CAD model surface into small \u201csurface patches\u201d (Figure 3(ii)) \u2013 and one such \u201csurface patch\u201d has been shown in Figure 3(iii). It is these CAD model \u201csurface patches\u201d that are re-parameterized into individual Bezier surfaces. Position data of a set of 25 points (5\u00a3 5 grid) on the surface patch are collected and a Bezier surface is passed through them by data fitting or inverse modelling (Figure 5). The deviation of the re-constructed Bezier surfaces from the actual CAD model was determined at a number of points on the CAD model along the respective normals to the CAD model at those points. The deviation was typically of the order of 1025 length units"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001440_s0925-4005(00)00722-x-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001440_s0925-4005(00)00722-x-Figure1-1.png",
+        "caption": "Fig. 1. Schematic diagram of sensor tip consists of reagent solution trapped behind Nafion membrane.",
+        "texts": [
+            " The pool of safranin\u00b1 iodide solution trapped behind an ion-permeable membrane (where Hg(II) can act as a catalyst as well as an analyte that can diffuse through this membrane) has been developed for this type of chemical optode, where the analyte reacts as a catalyst in the sensing mechanism. Thus, the reaction between safranin and iodide can be performed similar to that in the solution phase and the catalytic effect of Hg(II) can also be observed as in the solution phase. A suitable ionpermeable membrane that can be employed in this system is Na\u00aeon supported by nylon mesh for increased strength. Fig. 1 shows a schematic diagram of the design for an optode based on a pool of reagent solution trapped behind an ion-permeable membrane of Na\u00aeon. A solution of safranin\u00b1 iodide, placed behind a plug of Na\u00aeon \u00aelm, cannot pass through the \u00aelm into the sample solution, because the Na\u00aeon contain anionic `\u0300 pores''. In contrast, the Hg(II) ion in the sample solution can diffuse through the membrane into the safranin\u00b1iodide pool where reduction of safranin by iodide can occur. In order to prepare the sensor head, the tip of disposable pipette was cut by scalpel to obtain design as shown in Fig. 1(a) and (b). Several drops of Na\u00aeon solution ( 25 ml) were suspended in the tip of an inverted 150 ml plastic disposable pipette tip, where its end segment was supported with nylon mesh, and the solvent was allowed to evaporate. The Na\u00aeon \u00aelm was dried, leaving the Na\u00aeon \u00aelm intact across the end of the pipette tip segment. The pipette tip was then loaded with reagent solution and \u00aexed onto the end of the bifurcated \u00aebre optic supported in the syringe body. A hole was punched out of the side of the pipette to relieve backpressure and to enable solution of ions to diffuse through the membrane without producing a pressure differential. The pool optodes of the design shown in Fig. 1(a) and (b) are of low cost and relatively easy to prepare. For renewable reagent scheme, the pool optode was also incorporated with pumping system for delivering reagent from a reservoir into the pool via capillary tubing having dimensions similar to the \u00aebre optics (Fig. 2). Reagent pumping was performed by means of syringe pump, which can deliver small volumes in a reproducible manner. Other feature of the pool optode includes its use as a disposable system for single-shot analysis. In order to achieve maximum sensitivity, the pool optode was operated in a batch mode",
+            " 4(a)) is the slow response and slightly lower levels of signal yielded. Furthermore, it also suffers from sensor to sensor irreproducibility and, as a result, the reproducibility of Na\u00aeon \u00aelm thickness could not be guaranteed in such a design due to the \u00aelm being formed at an angle of 458. The probe head of the second pool design has a higher signal intensity with a response time of 2.5 min (Fig. 4(b)), and exhibits moderate \u00aelm thickness reproducibility from probe to probe. Therefore, the probe head of the second pool design (Fig. 1(b)) was selected and use in all further measurements. The mercury-catalysed reduction of safranin by iodide also depends on the concentration of reagent, pH and temperature and catalyst. In this case, room temperature was used due to simplicity of operation. For other parameters, the system was optimised by changing each variable in turn while keeping the others constant. The in\u00afuence of the safranin concentrations was studied in the range 1 10\u00ff6\u00b11 10\u00ff4 M (other conditions, 1 10\u00ff3 M iodide, pH 5, 50 mM Hg(II))"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000732_s0301-679x(98)00043-7-Figure12-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000732_s0301-679x(98)00043-7-Figure12-1.png",
+        "caption": "Fig. 12 Divergent and convergent gaps",
+        "texts": [
+            " At a rotational speed of 120 000 rpm, the measured power loss of the compliant surface bearing is about 20% smaller than that of the rigid surface bearing, but at another rotational speeds only a small difference in the measured power loss between the rigid and compliant surface bearings exists. This is because the magnitude of rubber deformation was not so large in a relatively large bearing clearance. Effect of the error of semicone angle on the load capacity Conical bearings are likely to be manufactured with the convergent or divergent gap for technological reasons as indicated by Kalita et al.7,8. In this paper, we investigate the effect of the divergent or convergent gap shown in Fig 12 in the conical bearing on the load capacity. Fig 13 shows the effect of the error of the semicone angle on load capacity. The divergent gap has a larger effect on the load capacity than the convergent gap and the load capacity is decreased with an increase in the error. It is seen, however, that the compliant surface bearing has less influence of the error on the load capacity than the rigid surface bearing, especially in the divergent gap, because of the elasticity of the rubber film. In this paper, water-lubricated hydrostatic conical bearings with numerous spiral grooves are treated in order to increase the load capacity and reduce the bearing power consumption"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure4.12-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure4.12-1.png",
+        "caption": "Figure 4.12. A planetary bevel gear train.",
+        "texts": [
+            "11 for a quarter revolution of the drive yoke and for various shaft angles. Notice the con siderable variation in the angular speed ratio as the shaft angle ifJ is increased. Usually, however, the universal joint is used in circumstances where the shaft angle is small so that w 2 is very nearly equal to w 1 \u2022 This is evident in Fig. 4.11 for the shaft angle \u00a2J = 10\u00b0, for example. Motion Referred to a Moving Reference Frame and Relative Motion 249 \\81tl ~=----,.-J,-l_,.!.,;..l...;;',,.JU~r-T~i-';;-00 A planetary gear train shown in Fig. 4.12 consists of two bevel gears P 1 and P 2 having perpendicular axles set in bearings connected at A and B to a curved link. The link S is called the sun and P 1 and P 2 , with pitch angles (J 1 and 92 , are named planets. The link turns with angular velocity ro5 relative to a preferred frame cp 0 = { F; I, J, K} fixed in the machine foundation. The planet gear P 1 , whose axis is fixed in <p0 , has angular velocity ro relative to the frame <p 3 = { 0; i, j, k} fixed in S. The rotation of P2 is controlled by the rotations of P 1 and S",
+            "29a) 250 Chapter 4 The planet gears P 1 and P 2 have absolute angular velocities determined by use of the kinematic chain rule ( 4.22 ): (4.29b) respectively, wherein (4.29c) denotes the angular velocity of P 2 relative to S. Use of (4.29a) and (4.29c) in ( 4.29b) yields expressions for the angular velocities of P 1 and P 2 relative to <p 0 , but referred to <p 3 : (4.29d) This completes our immediate use of the chain rules ( 4.29b ). To complete the solution, it remains to find Q. To relate the angular speeds of the gears, we use (2.27) and observe that the velocity in <p 0 of the point of rolling contact at C in Fig. 4.12a must satisfy the equations (4.29e) in which r 1 = r1 a and r 2 = -r2 k. Since the axis OA is fixed in <p 0 , v0 = v A= 0 in <p0 ; and because B belongs also to S, we have v8 =v 0 +ro30 xr 1 in <p0 \u2022 Thus, with the aid of these relations and the first equation in ( 4.29b ), ( 4.29e) may be written as (4.29f) which yields the single component equation (4.29g) speeds of P 2 and P 1 relative to S are related by (4.29h) This result completes the solution. Substitution of ( 4.29h) into ( 4.29d) gives the absolute angular velocities of P 1 , P 2 , and Sin <p 0 , but referred to <p 3: ( 4",
+            "36) delivers the absolute angular acceleration of the claw manipulator as seen by the observer in the machine frame but, for convenience, referred to the yoke frame 1: ro30 = (l]i sin f3 + f].fr cos f3- f]a.) i + <P + a..jJ sin /3) j + (a.+ l]i cos f3- f].fr sin {3) k. (4.40e) It is an exercise for the reader to confirm this result by differentiation of ( 4.40b ). What are the absolute angular velocity and acceleration of the claw referred to the arm frame? Consider what one would do to refer the results to frame 3 in the claw itself. Let us recall the planetary, bevel gear train shown in Fig. 4.12. Consider the case when the link S has a constant angular velocity co30 =cos relative to the machine frame cp0 , and the planet gear P 1 has the constant angular velocity co 13 =co relative to the sun frame cp 3 \u2022 The general composition rules ( 4.22) and ( 4.37) will be applied to determine the angular acceleration of the planet gear P 2 in qJ 0 , but referred to cp 3 . An earlier basic procedure also will be reviewed. With the aid of the composition rules (4.22) and (4.37), we have the following relations for the total angular velocity and angular acceleration of the planet gear P 2 in cp0 : (4",
+            "82b) gives ro 20 already expressed in terms of the basis of the blade frame, the total angular acceleration of the fan blade referred to that frame also may be derived directly from the last equation in (4.82b) by application of (4.14). In either case, we shall find ro20 = w(-p sin pt sin\u00a2+ w2 cos pt) j' - w(p sin pt cos 1/J + w 2 cos pt sin\u00a2) k'. 0 (4.83b) Example 4.18. Application to the Motion of an Epicyclic Gear Train. An epicyclic gear train is a system of gears and shafting in which at least one gear moves around the circumference of other fixed or moving gears. The planet gear P 2 shown in Fig. 4.12 rolls around the circumference of gear P 1 , and so the planetary train studied earlier is an epicyclic gear train. An epicyclic arrangement permits an unusual assembly of gears and shafting and it sometimes provides an uncommon angular velocity ratio while maintaining relative simplicity of the design. The motion of the epicyclic gear train shown in Fig. 4.27 will be studied here. The train consists of three bevel gears A, C, and D and two spur gears B and E arranged so that the shaft of B is concentric with the output shaft of gear D"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001039_960485-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001039_960485-Figure1-1.png",
+        "caption": "Fig. 1 : Vehicle model for computer simulation",
+        "texts": [
+            " ABS improves vehicle stability and steerability around the deceleration limit. Similarly, traction control acts as a limit guard during acceleration to keep a vehicle stable. Also, brake force distribution control, which keeps the vehicle stable while braking during cornering, has been introduced [1] - [2]. Moreover, vehicle control systems using active brake control, so called vehicle stability control, VSC, or vehicle dynamics control, VDC, which improve vehicle directional stability during severe cornering, have been actively developed [3] - [6]. SIMULATION MODEL Fig. 1 shows a vehicle model for computer simulation. The vehicle model is a yaw-plane, fourwheel model with three degrees of freedom: the longitudinal, lateral and yaw directions. Summing the brake and cornering forces in the vehicle body- fixed coordinate system and summing the moments about the center of gravity, e.g., of the vehicle produce the following vehicle model equations: IBF i = M - ( V x - V y v ) SCFi = M \u00ab ( V y - V x - v ) X Meg = Iz * \\\\r (D (2) (3) It is assumed that normal load transfers associated with the vehicle body pitch and roll motions are proportional to longitudinal and lateral accelerations"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002333_a:1025991618087-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002333_a:1025991618087-Figure4-1.png",
+        "caption": "Figure 4. The measuring of trampoline characteristics.",
+        "texts": [
+            " The trampolinist who performed the somersaults was 176 cm tall, and his weight was 68 kg. The measured and estimated characteristics of the student are gathered in Table I, where li , mi and JCi are the lengths, masses and central moments of inertia of the body segments, respectively, and ci are the distances: HC1, HC2, KC3, AC4, SC5, EC6 and WC7. In addition, the distance between the joints H and S is ls = 0.486 m. As said, the trampoline bed was treated as a weightless canvas with some stiffness and damping characteristics. We measured these characteristics in the way shown in Figure 4. The vertical stiffness was estimated by measuring the static response yA to the load G (Figure 4a). Then, for a given vertical deflection yA, the response xA to a horizontal force Px (Figure 4b) and the response \u03b8A to a moment MA = Gd cos \u03b8A (Figure 4c) were measured (see also Figure 2). Some results of the measurements are shown in Figure 5. As it can be seen, in the vertical direction the trampoline behaves as a hardening spring, and the results do not significantly depend on how far from the bed center the load is placed. The horizontal force Px shows linear dependency on xA, while its dependency on yA is negligible. Finally, for a given yA, the dependence of MA on \u03b8A is linear, and the stiffness coefficient k\u03b8 increases (linearly) in function of yA. The damping characteristics of the trampoline were estimated as follows. For a given deflection yA under the corresponding weight G, the vertical, horizontal and rotational free vibrations of the loaded plate (Figure 4) were initiated, and the logarithmic decrements of the vibrations were measured. Then, following the well-known formulae from the linear vibration theory [14], the damping ratios were determined. For the sake of space neither the respective expressions nor the measurement results are reported here. Based on the measurements, the estimated characteristics of the sample trampoline are: Ry = 6230y2 A + 1530yA + (178y2 A + 43.5yA)y\u0307A, Rx = 240xA + 660x\u0307A, M\u03b8 = (22yA \u2212 0.2)\u03b8A + 1.2\u03b8\u0307A, (18) where xA, yA, x\u0307A, y\u0307A, \u03b8A and \u03b8\u0307A should to be substituted respectively in [m], [m/s], [deg], and [1/s] in order to obtain Rx , Ry and M\u03b8 in [N] and [N m]"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003870_1.2401209-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003870_1.2401209-Figure2-1.png",
+        "caption": "Fig. 2 Contact dynamic response wit kb=2\u00c3108 N/m, cb=1\u00c3104 N s/m, =0",
+        "texts": [
+            " For the fixed bushing problem it is evident from Eqs. 32 and 34 that there is a linear dependence of the temperature on the otor speed and friction coefficient. For example, the 3000 rad/s ase of Fig. 4 includes a contact event with a force that just xceeds 35 kN. By interpolating and scaling the predictions of ig. 6, a maximum surface temperature rise of around 1500 K ndicates the scale of problem faced by the auxiliary bearing esigner. 5.2 Moving Inner Race Contact Temperatures. It is noted rom Fig. 2 that the predicted rotor motion eventually settles into forward synchronous rub motion. After a number of rotor ounces of up to 40 kN, the contact force steadies at around 5 kN with residual vibration that may be related to the rotor nbalance. If the auxiliary bearing was of a fixed bushing type, his would result in a continuous heat input that would not be ustainable. However, if the auxiliary bearing is of a rolling eleent type, the spin up of the inner race would greatly reduce the evel of the continuous friction induced heat input"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002102_s1474-6670(17)37076-3-Figure7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002102_s1474-6670(17)37076-3-Figure7-1.png",
+        "caption": "Fig. 7. Planar view of the UVMS. In point A, joint 2 is",
+        "texts": [
+            " It can be recognized that the vehicle is asked to move only when the manipulator itself is in critical situations. In detail, at point A, the vehicle starts moving after the joint 2 approaches the joint limit (120\u00b0). At point B, when the second joint comes back to a safe working configuration, the vehicle is not asked anymore to move. Finally, at point C, the vehicle moves to avoid a singular configuration when the manipulator is outstretched. A planar framed view of the GVMS's movement is reported in Figure 7. Point A is shown where the vehicle has to contribute to the end-effector motion to avoid that the second joint reaches the joint limit. Then, the end-effector trajectory is fulfilled up to limit (q2 ;::; -100\u00b0), Point C is close to a kinematic sin gularity (q2 ;::; _10\u00b0) . The IK algorithm uses redundancy to manage those situations. point B , where the movement of the vehicle keeps the manipulator again in a safe configuration. A similar situation could be drawn for the kinematic singularity case"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001877_robot.2000.846404-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001877_robot.2000.846404-Figure5-1.png",
+        "caption": "Figure 5: An example of overlapping regions. The path shown is extremal, but not optimal.",
+        "texts": [
+            " Now we consider a point in configuration space (z,y,O). If it is in only one region, then the corresponding trajectory type is optimal from that point. 3. When regions overlap, we derive additional necessary conditions for optimality or calculate the actual times for each trajectory type to disambiguate. To illustrate this procedure, we present the following example. The feasible regions for Jjnfio and 4Jnfi overlap. For almost all qs in the overlap, there are two possible extremals but only one true optimal path. Figure 5 illustrates the proof that the AQ line is a decision boundary. First we observe that the alternatives give equal time on the AQ line, because that line is the axis Of reflection for the Ti 0 T2 isometry. SO both paths are optimal on AQ. Now, the argument proceeds by contradiction. Suppose a U n f i o path is optimal from the start pose shown. When the path crosses AQ, the remaining cost is unchanged if it switches to AJnfi. But then the total path would not be a legitimate zigzag. We conclude that for qs to the right of AQ the optimum is ounft"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001177_0954406011524711-Figure9-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001177_0954406011524711-Figure9-1.png",
+        "caption": "Fig. 9 Illustration of freely suspended racket showing pin support method and position trackers",
+        "texts": [
+            " Figures 7a and 7b show that using values of stringbed stiVness, ks , between ks \u02c6 40 and 60 kN/m, gives results for ball rebound velocity in the correct order of magnitude. Therefore these two values of ks will be used for this model. The moment of inertia along the transverse axis of the racket frame was determined using the method described by Brody [19]. The value of Ir was 0.01624 kg m2 , and the mass of the racket, mr , was 0.335 kg. The Spalding Heat 90 racket used previously was supported at the tip on a small pin with its longitudinal axis vertical, as shown in Fig. 9. `Used\u2019 pressurized balls were projected at the longitudinal axis of the racket, perpendicular to the stringbed, at velocities between 14 and 32 m/s (30 and 70 mile/h). Three discrete impact points on the racket were tested as follows: (a) geometric string centre (d \u02c6 0:18 m); (b) 50 mm above geometric string centre (d \u02c6 0:23 m); (c) 50 mm below geometric string centre (d \u02c6 0:13 m). For these impacts, the velocities of the ball before and after impact, de\u00aened as Vb and V 0 b respectively, were determined using light beam speed gates. The velocities of the impact point on the racket and the racket centre of mass (COM) after impact, de\u00aened as V 0 d and V 0 r respectively, were determined using a high-speed video system operating at 400 frames per second. These velocities were determined by sampling the position of two points on the longitudinal axis of the racket, as illustrated in Fig. 9. As before, the model described in this section was compared with experimental data. More speci\u00aecally, the values compared were the ball rebound velocity, V 0 b, and the rebound velocities of the racket centre of mass (COM) and the impact point on the racket, V 0 r and V 0 d respectively. This comparison was made for three diVerent impact points on the racket and two model solutions were obtained using diVerent values of the stringbed stiVness, ks , namely 40 and 60 kN/m. Figures 10a, b and c all show that the model overpredicts the experimental results for the racket COM velocity, V 0 r, and impact point velocity, V 0 d"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003985_tro.2006.878956-Figure8-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003985_tro.2006.878956-Figure8-1.png",
+        "caption": "Fig. 8. Geometric construction for handling Type-A paths.",
+        "texts": [
+            " 7 (right), we show the solution for the line of equation y = 0:1x+2 and the pair (li = 0:3; i = =4); the shortest path is of type l a l + =2s + e r + b , with a = 0:099, b = 0:449, e = 0:268, and total length L = a + b+ e + =2 = 2:386. 2) Handling Type-A Paths: Although the conditions derived in Section IV-A.2 are still valid for this case, they are no longer sufficient, since ijV E (Wp (0; b; e)) = 0 (17) is underspecified (one equation and two parameters). The missing information is recovered with the following geometric reasoning (see Fig. 8): tangency between and Cij V E may occur on points H1, H2 (the intersection of the two circles), or on one of the two arcs bounding ; in Fig. 8, these three tangency conditions are represented by the three generic lines vj , vj , vj . At pointsH1 andH2, the pathCjCjC reduces to a single arcC , thus, the only free parameter can be computed using (17). On the upper (lower) arc of circle, the angular coefficient of vj matches the angle between the vertical radius vector through H1(H2) and the radius vector !r through the tangency point H3. On the other hand, fixes one of the two parameters, i.e., b = on the upper circle and e = on the lower circle [7], then (17) can be used to obtain the second parameter",
+            " Proof: The constraint f 2 Cij EV , expressed as ijEV ( f) = 0, yields the transversality conditions f = MT , where M = @ ijEV ( f) @ f = [sin ( (tf ) + 0 ) cos ( (tf) + 0 ) ( oy + y(tf )) sin ( (tf) + 0 ) + ( ox + x(tf)) cos ( (tf) + 0 )] : Hence, we get 1 = sin ( (tf) + 0 ) 2 = cos ( (tf) + 0 ) 3(tf) = (( oy + y(tf )) sin ( (tf) + 0 ) + ( ox + x(tf)) cos ( (tf) + 0 )) which yields 2 1 = 1 tan ( (tf ) + 0 ) = 1 mi ( (tf)) (19) 3(tf) = 1 (y(tf) oy) 2 (x(tf) ox) : (20) Equation (19) proves point 1 of Lemma 1; from (20), we have 3(t0) = 1oy+ 2ox, which yields 3(t) = 1(y(t) oy) 2(x(t) ox). This relation, together with the contact constraint between oj and the line wi, proves point 2. 2) Handling Type-A Paths: The solution for Type-A paths follows the same approach adopted in the previous section for the LV E case. Referring to Fig. 8, if Cij EV is tangent inH1 orH2, the solution degenerates to a single arc C (lines vj , vj ). If Cij EV is tangent to one of the two arcs of circle (e.g., line vj ), one of the two parameters (e; b) can be computed from the angular coefficient of vj . For instance, if tangency occurs on the upper circle, then e = 0, b = ( + 0), a = 0, tan( + 0) being the angular coefficient of vj . In this section, we will reduce the set of optimal RS paths (5) by showing that four of these families are never optimal, and can be excluded a priori from the computations"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000569_s0045-7949(98)00004-2-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000569_s0045-7949(98)00004-2-Figure6-1.png",
+        "caption": "Fig. 6. The location of the local reference coordinate system x1x2x3 relative to the convected coordinate system x\u03021x\u03022x\u03023.",
+        "texts": [
+            " Equation (48) is equivalent to Equation (18) (with m= 2 and n = 1) even if the system x1x2x3 is curvilinear because ui=0. If g61$g62, the rotation of the frame x1x2 is not equal to the average of the rotations of the axes x\u03021 and x\u03022. This fact may not be important in geometrically nonlinear analysis but it is important in elastoplastic analysis because vg61\u00ffg62v can be large due to e1>>e2 or e1<<e2. To show how to locate the local orthogonal system x1x2x3 from the convected system x\u03021x\u03022x\u03023 in a three-dimensional case, we consider Fig. 6, where OA=dx1, OB=dx2 and OC=dx3 because the system x1x2x3 represents the rigidly translated and rotated con\u00aeguration of the undeformed system x1x2x3 (see Fig. 4). It follows from Fig. 6 that the base vectors along the convected axes x\u03021, x\u03022, and x\u03023 are i1\u0302 cos g1i1 sin g61i2 sin g51i3, i 2\u0302 sin g62i1 cos g2i2 sin g42i3, i3\u0302 sin g53i1 sin g43i2 cos g3i3 49 Moreover, the ij\u00c3 can be represented in terms of the global displacement components vj and their deriva- tives ([F] is assumed to be known from numerical analyses) as i1\u0302 1 1 e1 1 @v1 @x 1 j1 @v2 @x 1 j2 @v3 @x 1 j3 , i 2\u0302 1 1 e2 @v1 @x 2 j1 1 @v2 @x 2 j2 @v3 @x 2 j3 , i3 1 1 e3 @v1 @x 3 j1 @v2 @x 3 j2 1 @v3 @x 3 j3 50 where jk are the base vectors of the undeformed sys- tem x1x2x3 and e1 1 @v1 @x 1 2 @v2 @x 1 2 @v3 @x 1 2 s \u00ff 1, e2 @v1 @x 2 2 1 @v2 @x 2 2 @v3 @x 2 2 s \u00ff 1, e3 @v1 @x 3 2 @v2 @x 3 2 1 @v3 @x 3 2 s \u00ff 1 51 It follows from Equations (40a), (49) and (50) that cos g1 sin g61 sin g51 sin g62 cos g2 sin g42 sin g53 sin g43 cos g3 264 375 1 1 e1 0 0 0 1 1 e2 0 0 0 1 1 e3 266666664 377777775 F T T T 52 To obtain [T], if one knows the geometric meanings of [R] and [T] = [R]T, one can use the following direct method to perform polar decomposition to obtain [T]",
+            " After [C] and [ l]2 are obtained by solving the eigenvectors and eigenvalues of [F]T[F], [T]T can be obtained from Equations (38) and (42b) and [R] = [T]T as T T F U \u00ff1 F C l \u00ff1 C T 54 Substituting Equation (54) (or [F]T[T]T=[U] = [C][ l][C]T) into Equation (52), one can obtain the six unknowns g42, g43, g51, g53, g61 and g62 to locate the system x1x2x3. It follows from Equations (42a) and (52) that U T F cos g1 sin g62 sin g53 sin g61 cos g2 sin g43 sin g51 sin g42 cos g3 264 375 1 e1 0 0 1 e2 0 0 0 1 e3 264 375 55 Moreover, because [U] = [U]T, we have 1 e2 sin g42 1 e3 sin g43, 1 e1 sin g51 1 e3 sin g53, 1 e1 sin g61 1 e2 sin g62 56 One can see from Fig. 6 that Equation (56) is an alternative form of Equation (18). Hence, it is shown again that the local coordinate system x1x2x3 is located by using the symmetry of Jaumann strains. If one does not know that [R] = [T]T in Equation (38), an iteration method can be used to obtain the six unknowns g42, g43, g51, g53, g61 and g62 that locate the system x1x2x3, as shown in Appendix A. This iteration method may not be more e cient than the direct method shown in Equations (52)\u00b1(54), but it reveals the geometric im- plication of polar decomposition and the identity [R] = [T]T",
+            " Cambridge University Press, Cambridge, U.K., 1991. APPENDIX A It follows from Equation (49) that i2\u0302 i3\u0302 sin g62sin g53 cos g2sin g43 cos g3sin g42, i1\u0302 i3\u0302 cos g1sin g53 sin g61sin g43 cos g3sin g51, i1\u0302 i2\u0302 cos g1sin g62 cos g2sin g61 sin g51sin g42 A:1 Moreover, because ij\u00c3 are unitary vectors, cos g1 1\u00ff sin2g51 \u00ff sin2g61 q , cos g2 1\u00ff sin2g42 \u00ff sin2g62 q , cos g3 1\u00ff sin2g43 \u00ff sin2g53 q A:2 where vgivR908 is assumed. Moreover, the components of [U] are obtained from Equations (21) and (39) and Fig. 6 as U11 @u1=@x 1 1 1 e1 cos g1, U22 @u2=@x 2 1 1 e2 cos g2, U33 @u3=@x 3 1 1 e3 cos g3, U12 @u2=@x 1 1 e1 sin g61, U13 @u3=@x 1 1 e1 sin g51, U23 @u3=@x 2 1 e2 sin g42 A:3 An iteration method with the use of a relaxation parameter can be used to solve Equations (56) and (A.1) for gij that locate the system x1x2x3, as shown below. Let sin g42 s1, sin g51 s2, sin g61 s3 A:4 It follows from Equations (50), (56) and (A.2) that sin g43 1 e2 1 e3 s1, sin g53 1 e1 1 e3 s2, sin g62 1 e1 1 e2 s3, cos g1 1\u00ff s22 \u00ff s23 q , cos g2 1\u00ff s21 \u00ff 1 e1 1 e2 2 s23 s , cos g3 1\u00ff 1 e2 1 e3 2 s21 \u00ff 1 e1 1 e3 2 s22 s , im\u0302 in\u0302 dkm @vk=@xm dkn @vk=@xn 1 em 1 en A:5 where ek are given by Equation (51)"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003826_j.ibiod.2006.09.003-Figure12-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003826_j.ibiod.2006.09.003-Figure12-1.png",
+        "caption": "Fig. 12. Reaction device of immobilized HRP.",
+        "texts": [
+            " Control batch experiment was conducted in the same procedure except that there was no HRP enzyme added, and control experiments indicated that there was neglectable PCP removal without the presence of HRP. The preparation of the gel carrier for immobilized enzyme and immobilized enzyme were documented elsewhere (Zhang et al., 2003), and the main reaction step is as follows: ARTICLE IN PRESS J. Zhang et al. / International Biodeterioration & Biodegradation 59 (2007) 307\u2013314 309 Immobilized HRP was packed into a glass condensing tube with a glass filter in one end to support the immobilized HRP gel, as shown in Fig. 12. A typical procedure protocol for using the enzyme column is described as follows: 0.4ml of PCP stock solution was added to 50ml of N2HPO4 citric acid buffer with certain pH; after fully mixing, together with certain amount of immobilized enzyme gel, PCP solution was added into the reactor. Then the system was mixed fully by air mixing, after 30min (through the test of the absorption of immobilized enzyme gel, the adsorption of PCP on the immobilized enzyme can reach the equilibrium state within 30min), 2ml sample was collected to measure PCP concentration"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure1.9-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure1.9-1.png",
+        "caption": "Figure 1.9. Uniform translational motion of a push rod produced by a constant rotary cam motion.",
+        "texts": [
+            " Therefore, after a change of units, I vi= 508 = v = 200 em/sec shows that 8 = 4 rad/sec, which is the constant angular speed of H about point 0 in 1/J. It is now easy to show with (1.9) that a(H, t) = -8(cos 8 i +sin 8 j) m/sec 2, whence follows la(H, t)l = 8 m/sec 2 . The point H has a constant speed; but this result shows that its acceleration is not zero because the velocity vector is changing its direction asH rotates around 0. The motion of His not uniform. D Example 1.10. A cam is a mechanical device used to produce a prescribed motion of another body in contact with it. The cam mechanism illustrated in Fig. 1.9 is to be designed to control the oscillatory motion of a push rod so that both its forward motion on 8 E [0, n] and its return motion Kinematics of a Particle 25 on (} E [ n, 2n] are uniform with the same speed v in each direction over the entire stroke b, called the rise of the cam. The cam is to rotate with a constant clockwise angular speed w = O(t) about an axle at F. Let r(8) denote the variable radial distance from F to the cam surface at the angle (} defined in Fig. 1.9. Find the cam profile r(O) that can produce the desired uniform motion. Solution. We need to relate the shape of the cam defined by r(8) to the prescribed uniform motion condition. Since the motion of the push rod is determined by the shape of the cam as it turns through the variable angle 8(t) about the axle at F, the position vector of the point of contact of the push rod with the cam at P is given by x(P, t) = r(8) i. Thus, with the aid of (1.8) and w = 8, we have (p ) _ dx(P, t) _ dr(8) . V , t - dt - d(} WI for all (} E [0, 2n]",
+            "127) and the derivative rule (1.121) for the unit step function will be applied. The strength of the impulsive acceleration at the end of each stroke will be described and the results exhibited graphically. Example 1.22. Let us reconsider the cam design problem studied in Example 1.10. We recall that two equations (1.58) and (1.59) were needed to describe the entire reciprocating, uniform motion of the push rod as the cam turned with the constant angular speed w through the angle 0, as shown in Fig. 1.9. This occurs because the velocity is discontinuous at the end of each stroke at (J = 0 (or 2n) and (J = n. We wish to show that the entire motion can be easily determined with the aid of singularity functions, and we shall also study the acceleration behavior. Solution. During the forward stroke when (J E [0, n ], the push rod has the uniform forward velocity Vf= vi. This gets turned on at (J = 0 and turned off at (J = n. For the return stroke, defined by (J E [ n, 2n ], the uniform return velocity is v, = -vi",
+            " This gets turned on at (J = n, and it stays on for the rest of the interval. Therefore, recalling ( 1.117 ), we see that the velocity on the entire interval [0, 2n] may be conveniently expressed by ( 1.144) Since v,= -v1 , (1.144) may be rewritten as v(P, t)=v1 [(0-0)0 -2(0-n)0 + (0-2n)0 ] (1.145) Our objective is to derive the cam shape from this expression. The relation ( 1.56 ), in the same way as before, allows us to separate the variables rand 8 in (1.145) to obtain rO) dri=~[f: (8-0) 0 d{J-2 r (8-n) 0 d(J+ I: ({J-2n) 0 d8], wherein r(O) =a, as shown in Fig. 1.9. Application of the integration rule ( 1.132) to the last equation and use of v 1 =vi yields the cam shape function (1.146) for all (J E [0, 2n]. But the rule ( 1.127) shows that the last term vanishes for all 8 ~ 2n, so we may discard it. We recall also that r(n) =a+ b, as shown in Fig. 1.9, whereas ( 1.146) together with (1.127) gives r(n) =a+ (v/w) n; hence, Kinematics of a Particle 59 b = nv/w, as before. Therefore, the cam profile ( 1.146) is determined for all 8 E [0, 2n] by the single equation . h b v Wit -=-. n w ( 1.147) Our earlier equations may now be retrieved by use of (1.127) in (1.147); its expansion yields for 0~ e~n. for 7t ~ e ~ 2n. (1.148) These are the same as ( 1.58) and ( 1.59) given before. The acceleration may be derived from (1.145). With the aid of (1.121), we get (1",
+            " The tip of a cutting tool has a straight line motion in which the cutter starts from rest and increases its speed from 0 to v* with a constant acceleration a*; it retains this constant cutting speed for a time p, as shown in the figure, and ultimately comes to rest at the end of its stroke by a constant deceleration a. The total length of the tool stroke is /. Show that the total time r required for the full machine stroke is given by I v*(a+a*) r= v* + 2aa* \u00b7 76 Chapter 1 viti Problem 1.45. Determine the length A of the cutting stroke and the time p required to execute it. What is the design efficiency relation (see Problem 1.25) for the case when a= a*= 15v*2/l? Assume that the full cycle machine stroke time is 2<. 1.46. A cam mechanism similar to that described in Fig. 1.9 is to be designed to control the motion of the spring-loaded push rod to have a constant acceleration a during its forward motion for 0 E (0, n] and a constant deceleration of the same magnitude during its return motion for 0 E r n, 2n]. Of course, as a consequence, the acceleration will not be well defined at the stroke extremes. The cam must rotate with constant, clockwise angular speed B = w; and the push rod must be at instantaneous rest at 0 = 0, where x(P, 0) = ai, and at 0 = 2n. (a) Determine the cam rise bat 0 = n; and find the required continuous cam profile r( 0) expressed in terms of the geometrical cam design parameters"
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+        "caption": "Figure 3: The Side View and Top View of the Robot",
+        "texts": [],
+        "surrounding_texts": [
+            "four-bar- l inkage, is considered f o r t h e University o f M/nnesota d l rect d n v e r o b o t 181. Thls s t a t i c a l l y - balanced direct d n v e robot has been const ructed f o r s t a b / l i t y a n a l y s l s o f t h e r o b o t In c o n s t r a l n e d manipulat ion (3- 71. As a r e s u l t of t h e e l /minat /on o f t h e QrdVi ty fo rces [w i thout any counter WelQhtSl, smal ler actuators and consequently smal ler ampl / f iers w e r e chosen The motors y ie ld accelerat ion o f 5 9 a t t h e end po /n t w / t h o u t overheat jng. H/Qh torque, l o w speed, brush-less AC synchronous motors a re used t o power t h e robot . Graphlte epoxy compos/te mater ia l Is used f o r t h e const ruct ion o f t h e robot links. A 4-node para l le l processor has been used t o controL the robot . The dynamlc t rack lng accuracy -w i th t h e computed to rque method as a cont ro l law- has been der ived expenmenta l ly .\nArchitecture The a r c h i t e c t u r e o f t h l s arm Is such t h a t t h e g r a v i t y t e r m is comp le te l y e l imlnated f rom t h e dynamic equat ions Thls ba lanced mechanism Is deslgned w i thou t adding a n y e x t r a c o u n t e r b a l a n c e w e l g h t s The new f e a t u r e s o f th ls new design are as fo l l ows . 1. Since t h e m o t o r s a re n e v e r a f f e c t e d b y g rav i t y , t h e s ta t i c l o a d W I L L be ze ro . Hence n o ove rhea t ing r e s u l t s In t h e system In t h e s ta t i c case II. Because o f t h e e l lm lna t l on o f t h e g r a v i t y t e r m s , s m a l l e r m o t o r s w i t h l e s s s t a l l t o r q u e [ a n d\nconsequen t l y s m a l l e r amp l l f l e rs l h a v e been chosen f o r a des i red acce le rs t l on . Ill. Because o f t h e l ack o f g r a v i t y t e r m s , h l g h e r accuracy can b e achleved. Thls is t r u e because t h e l inks h a v e s teady d e f l e c t i o n due t o cons tan t g r a v i t y e f f e c t . Thls w i l l g l v e b e t t e r accu racy and r e p e a t a b i l i t y f o r f lne manlpulat lon tasks. IV. A s d e p l c t e d In F lgure 3, t h e a r c h i t e c t u r e o f t h l s r o b o t a l l o w s f o r a \" l a r g e \" workspace. The h o r l z o n t a l workspace o f t h l s r o b o t Is qu i te a t t r a c t i v e f r o m t h e s t a n d p o l n t o f manu fac tu r lng tasks such a s assembly and debur r l ng .\nFigure 2 shows t h e schernatlc dlagram o f t h e Unlvers l ty o f M i n n e s o t a d i r e c t d r l v e arm. The arm h a s t h r e e degrees o f f reedom, a l l o f whlch a re a r t l c u l a t e d d r l v e Jo lnts . M o t o r 1 p o w e r s t h e sys tem a b o u t a v e r t l c a l E X I S . M o t o r 2 p l tches t h e en t l re four-bar- t lnkage wh i l e m o t o r 3 Is used t o p o w e r t h e four-bar- l lnkage. Llnk 2 Is d i r e c t l y connec ted t o t h e s h a f t o f m o t o r 2. Flgure 3 shows t h e t o p v lew and slde v lew o f t h e r o b o t . The coo rd lna te f rame X,Y,Z,has been asslgned t o l lnk I o f t h e r o b o t f o r I-1,2,..,5. The c e n t e r o f coo rd lna te f rame XIY,Zl co r respond ing t o llnk 1 Is l o c a t e d a t po ln t 0 a s s h o w n In f i gu re 3. The c e n t e r o f t h e l n e r t l a l g l o b a l coo rd ina te f rame XoYoZo Is a l s o Located a t po lnt 0 [The g l o b a l coo rd lna te f r a m e Is n o t shown In t h e f i gu res l . The j o i n t ang les a r e r e p r e s e n t e d b y e , , e 2 , and \u20acI3. e l r e p r e s e n t s t h e r o t a t l o n o f Llnk 1; c o o r d l n a t e f r a m e XIYqZ! co lnc ldes o n g l o b a l coo rd lna te f r a m e X o Y o Z o\nCH2555-1/88/0000/0442$01.00 0 1988 IEEE",
+            "w h e n 8,-0. e2 r e p r e s e n t s t h e p l t c h a n g l e o f t h e four-bar- l inkage as s h o w n in f i gu re 3. e3 r e p r e s e n t s t h e a n g l e b e t w e e n l l nk 2 and l l nk 3. Shown a r e t h e condl t lons u n d e r whlch t h e g r a v i t y t e r m s a r e e l imlnated f r o m t h e dynamlc equations.\nFigure 4 shows t h e four-bar- l lnkage w l t h ass igned coo rd ina te f rames. By lnspect lon t h e condi t ions u n d e r wh ich t h e v e c t o r o f g r a v i t y passes t h r o u g h orlgin, 0. f o r a l l poss ib le v a l u e s o f el and e3 a r e g i v e n b y equat ions 1 and 2. [ m3T3 - t - 1 7 ~ ~ ~ - m5T5 1 sin e3 - o\ng [mt3 + m5] - m2T2 - m 3 [ ~ 2 - g I - m4[T4 - g I\n- [ m3T3 - m , ~ ~ - m5T5 I cose3 - o\n[ll\n[21\nw h e r e : m,,L,- mass and l e n g t h o f each llnk. x i - t h e d is tance o f c e n t e r o f mass f r o m t h e or ig in o f each coo rd lna te f rame, mt3 - mass o f m o t o r 3. Condit lons 1 and 2 r e s u l t in: -\nm3T3 - m 4 ~ 5 - m5T5 - o g[mt3+m51-m2Si2-m3[~2-gl-m4[T4 - g 1 - o\nIf equat lons 3 and 4 e r e satlsf led, t h e n t h e c e n t e r o f g r a v i t y o f t h e fou r -ba r - l i nkage passes t h r o u g h po in t 0 f o r a l l t h e poss ib le conf igurat lons o f t h e arm. No te t h a t t h e g r a v i t y fo rce s t i l l passes t h r o u g h 0 e v e n If t h e p l a n e o f t h e four-bar-Linkage is t l l t e d b y m o t o r 2\n[31\n(41\nf o r e l l v a l u e s of Oz. Since a t l o w speeds, AC t o r q u e mo to rs do n o t t e n d t o cog, l o w speed, h lgh t o r q u e , a n d brush- less A C synch ronous m o t o r s h a v e b e e n chosen t o p o w e r t h e r o b o t . Each m o t o r consis ts o f a r l n g shaped s t a t o r and a r i n g shaped p e r m a n e n t m a g n e t r o t o r w i t h a l a r g e n u m b e r o f p o l e s . T h e r o t o r is made o f r a r e e a r t h magnet ic m a t e r l a l [Neodymium] bonded t o a l o w ca rbon s t e e l yoke w l t h s t r u c t u r a l adhesive. The s t a t o r o f t h e m o t o r [ w i t h w lnd lng l IS f i x e d t o t h e hous lng f o r h e a t dlsslpation. X\nmotor3 m\nFigure 4: Four Bar link Mechanism\nForward K i ne mat i cs The f o r w a r d kinematlc p rob lem Is t o compu te t h e pos l t lon of t h e end po in t In t h e g l o b a l coord inate f rame XoYoZo, g i v e n t h e Joint angles, 81, e2, and 03. The end p o i n t p o s i t i o n o f t h e r o b o t r e l a t i v e t o t h e g l o b a l coo rd ina te f r a m e is c h a r a c t e r i z e d b y P,. P, and P, In t h e g l o b a l coo rd ina te f rame XoYoZo:\nP, - [C,C2C3- S I S 3 l [L3-L51 + C,C2[ L2 - g 1 py - [ S I C ~ C ~ + C I S ~ ~ [ L ~ - L ~ ) ~ SIC, [ L z - Q\n[51\n[61\n[71 P, - 52 [Lz - 1 + S z C 3 [ L3- L5 1 w h e r e S, = Sin (e,], a n d C, - C o s [e,].\nInverse Kinematics The inve rse k inemat ic p rob lem Is t o c a l c u l a t e t h e Jolnt ang les f o r a g i v e n end po in t pos i t l onw l th respec t t o t h e g l o b a l coo rd ina te f rame. The c losed- fo rm o f i n v e r s e k inemat lcs o f t h e p roposed a r m d e r i v e d us ing t h e s t a n d a r d method[2,111. The Jo lnt a n g l e s f o r t h e g l v e n end p o i n t pos i t i on c a n b e de te rm ined us ing t h e f o l l o w l n g equations: el - a tan2 [ P, P, 1 - a tan2 [[L3- L51 sine3,\n+JP,~ + , 2 - [ L ~ - ~ ~ P s i n 2 e 3 I [81\npz e2 - sln-' [ l [91\n[ L ~ - g I + [ L ~ - L~ I c o w 3\nP,2 + P,2 + P,2 -[L2-912 - [L3-L.5) 2 e3 - COS-! [ 1 [I01\n2 [ L2 - g I [L3- L5 I",
+            "The c losed- fo rm dynamlc equa t ions h a v e b e e n d e r l v e d f o r t h e pu rpose o f c o n t r o l l e r des ign. The dynamlc b e h a v i o r o f t h e arm can be p resen ted b y t h e fo t tow lng equa t lon [1,21\nM [ e l e + CE[e1[621 + C O [ e l [ 6 6 1 + G[el - T (111\nWhere: T- [ T ~ T~ T~ IT M [el 3x3 def in i te lner t ls matr lx ,\nC E [ e l 3x3 cen t r i f uga l coef f lc lents rnatr lx,\nco[e i 3x3 Corlol ls coef f lc lents matr lx ,\nG lei\n3x1 v e c t o r o f t h e m o t o r torques,\n3x1 v e c t o r o f g r a v l t y force,\n8\u2019 [ 6 , 6, G3 IT\n[661 [dl82 6 1 6 3 6 ~ 6 3 1 ~\n[ & I [ ~ , 2 a 2 2 d 3 2 IT\nMI\\ M I Z M13 1 , [ 0\nCEIZ C i 1 3 ] M i 2 M22 0 C E [ B l - C E p 0 M13 M33 j CE31 CE32 0\ntoll co12 c013 C O [ @ ) - 0 CO22 CO23 ] , G[el - [\nCO31 0 M 1,- I21 + Cz2[ Ie1 + I e 6 + I e 2 + 2C31e3 + Iy2 + m2T221+ ~ z ~ [ ~ 3 ~ [ I , , + 1 ~ ~ 1 + c~~ + lX2l M i 2 s 2 s 3 [ l e 3 + C 3 [ Ie1 + l e 5 - Ie4 11 M13 c Z [ le1 \u2019 Ie6 + c31e3 1 M~~ - l Z 2 + m2X22 + c~\u2019[I,I + l e 5 ) + s 3 2 ~ e 4 + i e2\n+ 2C31e3\nM33 - ] e l + le6 C E i p - C z s 3 [ Ie3 + C 3 [ lei + le5 - Ie4 I 1 CE13 - - h S 3 1 e 3 - C E Z 1 - S 2 C 2 [ Iy2 - Ix2 + m 2 x Z 2 - S321e5 + C32 [ I e l - I e 4 1\n+ Ie2 + I,, + 2 c 3 1 e 3 1 C E 3 1 - s 3 ( Cz21e3 - s Z 2 c 3 [\nCE32 \u2019 C O I I - - 2 C E 2 1\n\u2019 1,s - Ie4 11 s 3 [ I e 3 + c 3 [ I e l + l e 5 - Ie4 11\nCOl,- - 2 C E 3 1 c o l 3 - - s 2 [ 2 ~ 3 ~ 1 , ~ + l e6 + c o s z e 3 I c o Z 2 - s2[ 2 ~ 3 \u2019 1 ~ 1 + + 2 C 3 i e 3 - c 0 s z e 3 1 i e4 - I ~ ~ I I\nC O 3 1 - - s 2 [\n- i e5 11\nC O 2 3 - - 2 C E 3 2\n+ c o s z e 3 [ i e l + i e5 - 1 ~ ~ 1 +\n+ 2C,Ie31\nm 3 x 3 2 + rn,~,2 + m5X52\nm 3 [L, - Q l2 + m4 [si, - 912 + m,g2\nm 3 T 3 [ ~ 2 - g I - m4 [X4 - ~ I L ~ + m5X5g\n4 3 + 1114 + I y 5\nw h e r e :\nl e l - l e 2 - le3 - l e 4 - 1x3 + 1x4 + 1x5 Ie5 -\n-\nIe6 - I23 + \u2018 2 4 + I z 5 Ix is I y i , and I , , are t h e m a s s moments o f Iner t ia\nr e l a t i v e t o x, y, z axls a t t h e cen te r o f mass o f a llnk I . [ m o t o r 3 Is a p a r t o f l lnk 21. The g r a v i t y t e r m , G[el becomes z e r o when equat ions 3, 4 a re sa t l s f i ed In t h e a r m . T h i s c o n d i t i o n h o l d s f o r a l l p o s s i b l e\nconfigurations.\nHardware An IBM A T m i c r o c o m p u t e r wh ich Is h o s t l n g a 4 -node p a r a l l e l p r o c e s s o r Is Used a s t h e rnaln c o n t r o l l e r o f t h l s r o b o t . The p a r a l l e l p rocesso r has f o u r nodes and a PC/AT bus In te r face . Each node Is a n Independen t 32-blt p rocesso r w l t h l o c a l memory and communlcatlon l inks t o t h e o t h e r nodes In t h e system. A h lgh speed A D / D A c o n v e r t e r has been used f o r read lng t h e v e l o c l t y s l g n s l s a n d send lng a n a l o g command s lgna ls t o t h e s e r v o c o n t r o l l e r un l t . A p a r a l l e l 10 b o a r d [ O / D c o n v e r t e r ] b e t w e e n t h e s e r v o c o n t r o l l e r u n l t a n d t h e c o m p u t e r a l l o w s f o r r e a d l n g t h e R I D [Reso lve r t o Dlg l ta l l c o n v e r t e r . The s e r v o c o n t r o l l e r un i t p roduces t h r e e phase, Pulse Wldth M o d u l a t e d [PUMI, s lnusolda l c u r r e n t s f o r t h e p o w e r a m p l l f l e r . T h e s e r v o c o n t r o l l e r u n l t c o n t a l n s a n I n t e r p o l a t o r , R / D c o n v e r t e r a n d a comrnunlcatlon I n t e r f a c e f o r t h e compu te r . The s e r v o c o n t r o l l e r un l t can b e opera ted In e l t he r a c losed l o o p v e l o c l t y o r c u r r e n t [ t o rque) c o n t r o l mode [ t h e c u r r e n t c o n t r o l Is u s e d ] . A PWM p o w e r a rnp l l f l e r . w h i c h p rov ldes up t o 4 7 Amperes o f d r l v e cu r ren t f rom a 325 v o l t p o w e r supp ly , Is used t o p o w e r t h e mor-tors. The ma ln O C bus p o w e r Is d e r i v e d b y f u l l - w a v e r e c t l f y l n g t h e t h r e e phase 230VAC Incomlng power . Thls y le lds a DC bus v o l t a g e o f 325VDC.\nIBM AT &the NCUBE n parallel processor\nSeNO unit\n(analog)\ninterface 4 mntroller\nFigure 5: The Control Hardware for Minnesota Robot\nThe m o t o r s u s e d in t h l s r o b o t a r e neodymium [NdFeBI magne t A C b rush less synchronous m o t o r Due t o t h e h lgh rnagnetlc f l e l d s t r e n g t h [max imum e n e r g y p r o d u c t s 35 MGOel o f t h e r a r e e a r t h NdFeB magnets, t h e m o t o r s h a v e h igh t o r q u e t o weight r a t i o Pancake t y p e r e s o l v e r s a r e u s e d a s p o s l t l o n a n d v e l o c l t y sensors The peak t o r q u e o f m o t o r 1 Is 118 Nm, w h i l e t h e peak to rques o f m o t o r s 2 and 3 a re 78 and 58 Nm r e p e c t l v e l y\nThe p re l lm lna ry e v a l u a t l o n o f t h e pe r fo rmance o f r o b o t conce rns w l t h t h e dynamlc t r a c k l n g accu racy a l o n g a spec i f i ed t r a j e c t o r y The c o m p u t e d t o r q u e m e t h o d [9,101 Is u s e d t o c o n t r o l t h e r o b o t U h l l e a n o n l l n e a r c o m p e n s a t o r f o r c o m p e n s a t i o n o f t h e f e e d f o r w a r d t e r m s Is cons ldered In t h e f e e d f o r w s r d l oop . e Llnear compensa to r In t h e feedback l o o p has b e e n u s e d t o dec rease t h e e r r o r In each j o l n t The i n e r t l e p a r a m e t e r s u s e d In f e e d f o r w a r d l o o p a r e c o w p u t e d f r o m t h e eng lneer lng d raw lngs The m o t o r dgrlamlcs a n d t h e f r l c t l o n i n t h e dynamlc m o d e l w e r e"
+        ]
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+        "caption": "Fig. 2. Linear Protocols applied in a network of 4 agents",
+        "texts": [
+            " In this sense, one may state that consensus is globally asymptotically reached as proved in [SI. reaching consensus implies that the energy of the graph, and The following example confirms what we say. Example I : : Let us consider a network o f 4 agents depicted hence the ~ ~ ~ l ~ ~ i ~ ~ potential is null. viceversa is me only in Fig. 1. The incidence matrix of the corresponding graph is if certain properties are verified, The system dynamics simulated with initial state 1 0 -1 0 1 0 0 0 1 -1 -1 n is shown in Fig. 2 ( 5 ) B. Constrained Model Unfortunately, a linear protocol cannot be directly applied to our case study. Actually, UAV's rate of climb is limited to 1, without loss of generality, by the capability performance of the vehicles. This necessary implies the introduction of the following input constraints in the network model, (6) Fig. I . The information fbw in a network of 4 agents 0 5 u(t) 5 1. Note that when UAVs implement the linear protocol ( 3 ) and no saturation occurs the sum of all inputs at each time instant is zero"
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+        "caption": "Figure 3. Illustration of the proposed mechanism for the reversible variations in PLGA helix rod orientation upon adsorption and desorption of guest helices and for the electron mediation function of the ferrocenyl moiety on gold substrates: a) pure monolayer II ; b) monolayer II complexed with PLGA-Fc-N; and c) monolayer II complexed with PLGA-Fc-C.",
+        "texts": [
+            " From the value of the ratio D, the tilting angle of the helices is calculated to be 258 (Table 1), which is significantly enhanced in the perpendicular orientation of helical rods, compared with the 518 tilt found before complexation. This result suggests that by complexation of monolayer II with the PLGA-Fc-N helix, a monolayer in a head-to-tail antiparallel orientation, which is energetically more favorable, is spontaneously formed, and consequently achieves a nearly perpendicular helix orientation. This effect is shown schematically in Figure 3 a and 3 b. When this complexed monolayer was treated with water at pH 9.0, the PLGA segments underwent a conformational change from a helix to random coil, then the monolayer released the guest PLGA-Fc-N into the bulk aqueous phase because of the loss of the helix macrodipole. An RA-FTIR spectrum of the monolayer after the pH-induced desorption of PLGA-Fc-N is similar to the original monolayer (Figure 2 d and 2 b), and consequently the tilting angle returns to the original value of monolayer II (Table 1)",
+            " This electrode, when the scan rate was varied at a constant concentration of [Fe(CN)6]4\u00ff (3 mm), yields a linear i versus v1/2 plot, to show the catalyzed reaction is sufficiently fast such that the process is controlled by [Fe(CN)6]4\u00ff diffusion.[28] From these results, it can be assumed that the immobilized ferrocenyl moiety facing the electrode surface behaves successfully as an electrontransfer mediator and the direction of electron transfer must be vectorial as schematically illustrated in Figure 3. To further support this hypothesis, the dependence on the [Fe(CN)6]4\u00ff concentration was examined under conditions similar to those in Figure 4 c (data not shown). The oxidation peak of the ferrocenyl moiety grew upon increasing the concentration of [Fe(CN)6]4\u00ff, as expected for a mediated process.[29] In conclusion, the orientation of helix rods and the precise location of a redox moiety in self-assembled monolayers have been demonstrated to be controlled through the helix \u00b1 helix macrodipole interaction"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001305_0924-0136(94)01333-v-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001305_0924-0136(94)01333-v-Figure3-1.png",
+        "caption": "Fig. 3. Depending on which side of the rectangular doubly-curved panel in Fig. 1 is used in the approximation, different values of 22 are obtained.",
+        "texts": [
+            " Asnafi / Journal of Materials Processing Technology 49 (1995) 13-31 15 and ~2 = [ 1 2 ( 1 - v2)] 1/2 ~2 ( R ) , (5) where R is the radius of the sphere, P is the concentrated load at the apex, E is Young's modulus, t is the shell thickness, v is Poisson's ratio and ~ is the angle between the centre and the edge of the sphere. Furthermore in this figure, ~5 is the deflection at the apex. Note that 22 in Eq. (5) and Fig. 2 is a measure of how large the shell segment is! The greater the value of ~, the larger is the sphere segment. a spherical shell. Depending on which side of the rectangle is used in the approximation, different values of ~2 are obtained: see Fig. 3 and compare it with Fig. 1! Combining Eqs. (2), (3) and (4) p . ~ P - 2 ~ E t a (6) The maximum load that will be used in the stiffness tests is 125 N. Substituting into Eq. (6) this value, the nominal values of R1 and R2 (Fig. 1), E = 20.104 N/mm 2 and t = 0.7 mm, P* = 0.334. which gives the encircled zone in Fig. 2, applicable in the present approximated case. Knowing the different values of 2 2 (Fig. 3), the applicable load~leflect ion zone in the present approximated case, (Fig. 2), and the shape of the load-deflect ion curve in this zone, it is assumed that over this interval and for the present panel p , = C(6/t) m (7) N. Asnafi / Journal of Materials Processing Technology 49 (1995) 13-31 17 in which C and m are different constants. Combining Eqs. (4) and (7), P = C2rtE t3(f/t)m x/~ll R 2 In this study, Eqs. (1) and (8) will be examined. (8) is shown in Fig. 4. T~ arises from the resistance of the outer region to plastic deformation, if the outer region deforms, material being drawn inwards"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002068_bf00052455-FigureI-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002068_bf00052455-FigureI-1.png",
+        "caption": "Fig. I. Typical diesel-engine driveline system and forces in a mesh of gears.",
+        "texts": [],
+        "surrounding_texts": [
+            "Machines and mechanisms are characterized by rigid or elastic bodies interconnected in such a way that certain functions of the machines can be realized. Couplings in machines are never ideal but may have backlashes or some properties which lead to stick-slip phenomena. Under certain circumstances backlashes generate a dynamical load problem if the corresponding couplings are exposed to loads with a time-variant character. A typical example can be found in gear systems of diesel engines, which usually must be designed with large backlashes due to the operating temperature range of such engines, and which are highly loaded with the oscillating torques of the injection pump shafts and of the camshafts. Therefore, the power transmission from the crankshaft to the camshaft and the injection pump shaft takes place discontinuously by an impulsive hammering process in all transmission elements. Figure 1 indicates how the process works. A typical gear unit contains several meshes with backlashes, in the case shown two meshes with backlashes between crankshaft and injection pump shaft and three meshes with backlashes between crankshaft and camshaft. Due to periodical excitations mainly from the injection pumps and subordinately from the crankshaft and the camshaft the tooth flanks separate generating a free flight period within the backlash which is interrupted by impacts with subsequent penetration. The driving flank (working flank) usually receives more impacts than the nonworking flank (Figure 1). Additionally, in all other backlashes of the gear unit similar processes take place, where the state and the impacts in one mesh with backlash influences considerably the state in all other meshes. This behavior must be regarded by the mathematical model. As a definition we use the work \"hammering\" for separation processes within backlashes where high loads cause large impact forces with penetration. Motion within backlashes without loads is called \"rattling\". This represents a noise problem without load problems. It will not be considered here. As a rule, such vibrations may be periodic, quasi-periodic or chaotic with a tendency to chaos for large systems. Considering the driveline-gear-unit as a multibody system with f degrees of freedom and with np backlashes in the gear meshes we model the backlash properties by a nonlinear force characteristic with small forces within the backlash and a linear force law in the case of contact of the flanks. The event of a contact is determined by an evaluation of the relative distance in each backlash, which serves as an indicator function. The indicator function for leaving the contact, i.e. flank separation, is given with the normal force in the point of contact, which changes sign in the case of flank separation. These unsteady points (switching points) must be evaluated very carefully to achieve reproduceable results. The time series of impact forces will be reduced to load distributions in a last step. They might serve as a basis for life time estimates. Dynamical systems with unsteady behavior have been subject to increasing investigations during the last years. With regard to impulsive processes the bouncing ball problem is a very old and famous one [10]. With the progress of nonlinear dynamics in the last two decades a series of publications came out on problems of impact phenomena, in all cases confined to systems with two or three degrees of freedom only [6, 8, 13, 14, 21, 22, 29, 30]. Applications to technical problems were rare and mainly restricted to gear research contributions [23, 24, 26, 27, 28]. The first activities on impulsive processes at the author's institute started in 1982 and lead to a series of contributions on rattling and hammering processes in gear boxes and in drivelines. The fundamental starting point was a general theoretical approach to mechanical systems with unsteady transitions in 1984 [ 15], which was very quickly extended to rattling applications [ 11, 12, 16, 17]. The dissertation [9] deepened the rattling theory and compared one-stage rattling with laboratory tests. From the very beginning all theoretical research focused on general mechanical systems with an arbitrary number of degrees of freedom and with an arbitrary number of backlashes. Application fields are drivelines of large diesel engines, which due to a large temperature operating range usually are designed with large backlashes [1, 20]. The dissertation [20] represents the newest state of research and will be the basis of this paper. The plenary lecture [19] gives a survey on dynamical systems with time-varying or unsteady structures."
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0002572_robot.1996.506595-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002572_robot.1996.506595-Figure5-1.png",
+        "caption": "Fig. 5 Simulation result with y = 0 in eq.(48)",
+        "texts": [
+            " The path for the case when the position and the orientation of the object are fixed has 0.0549 as the value of S. In the case of Fig.3, total value of variations of joint variables becomes smaller by moving the manipulator-A. From this result the meaning of the pseudo inverse is understood. Fig.4 shows the result considering obstacle avoidance. The value of S is 0.0198 for this case. The obstacle is avoided by using the pokential function in eq.(47). Next, 3-dimensional example is considered. Fig.5 shows the simulation result with y = 0 in eq.(48) and Fig.6 shows the result with collision avoidance. 7 Conclusions Our purpose of this paper was to propose an algorithm to plan the cooperative collision free motion for two manipulators system. In general, the two manipulators system has redundancy. By using the redundant degrees of freedom, the desired cooperative motion which executes the specified task can be planned. The potential function method is used for collision avoidance. Numerical examples show the effectiveness of the proposed method"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002263_6.2003-5349-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002263_6.2003-5349-Figure5-1.png",
+        "caption": "Fig. 5 Bell-Hiller system with angular displacements",
+        "texts": [
+            " The flybar and main rotor flapping motions are governed by the same effects, namely the gyroscopic moments due the helicopter roll and pitch rates. But unlike the main rotor, the flybar is not responsible for providing lift or maneuvering ability. Thus, it can be designed to have a slower response and provide the desired stabilization effect. The flybar response can be optimized by varying the ratio of aerodynamic to inertial loads on the paddles. Changing the shape, weight or distance between the paddles are all straightforward ways of tailoring the system. The notation used to describe the Bell-Hiller system is presented in Fig. 5. Due to the Bell-Hiller system, the flybar flapping and blade pitching angles are physically constrained to satisfy [ \u03b80 (\u03c8) \u03b81 (\u03c8) ] = l\u03b4 l\u03b8 l1 l1 + l2\ufe38 \ufe37\ufe37 \ufe38 c1 [ (l4 \u2212 h\u03b4 (\u03c8)) /l\u03b4 \u03b41 (\u03c8) ] + l\u03b2f l\u03b8 l2 l1 + l2\ufe38 \ufe37\ufe37 \ufe38 c2 [ 0 \u03b2f ( \u03c8 + \u03c0 2 ) ] , (13) where \u03b41 is the differential pitch input, given by \u03b41(\u03c8) = \u03b41c cos(\u03c8) + \u03b41s sin(\u03c8). (14) 5 American Institute of Aeronautics and Astronautics Likewise, \u03b2f has no coning mode, since the flybar, as a teetering rotor, can only describe see-saw flapping motions"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002564_robot.1988.12089-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002564_robot.1988.12089-Figure2-1.png",
+        "caption": "Figure 2: Schematic of University of Minnesota Arm",
+        "texts": [
+            " Thls is t r u e because t h e l inks h a v e s teady d e f l e c t i o n due t o cons tan t g r a v i t y e f f e c t . Thls w i l l g l v e b e t t e r accu racy and r e p e a t a b i l i t y f o r f lne manlpulat lon tasks. IV. A s d e p l c t e d In F lgure 3, t h e a r c h i t e c t u r e o f t h l s r o b o t a l l o w s f o r a \" l a r g e \" workspace. The h o r l z o n t a l workspace o f t h l s r o b o t Is qu i te a t t r a c t i v e f r o m t h e s t a n d p o l n t o f manu fac tu r lng tasks such a s assembly and debur r l ng . Figure 2 shows t h e schernatlc dlagram o f t h e Unlvers l ty o f M i n n e s o t a d i r e c t d r l v e arm. The arm h a s t h r e e degrees o f f reedom, a l l o f whlch a re a r t l c u l a t e d d r l v e Jo lnts . M o t o r 1 p o w e r s t h e sys tem a b o u t a v e r t l c a l E X I S . M o t o r 2 p l tches t h e en t l re four-bar- t lnkage wh i l e m o t o r 3 Is used t o p o w e r t h e four-bar- l lnkage. Llnk 2 Is d i r e c t l y connec ted t o t h e s h a f t o f m o t o r 2. Flgure 3 shows t h e t o p v lew and slde v lew o f t h e r o b o t "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000909_027836499901800506-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000909_027836499901800506-Figure3-1.png",
+        "caption": "Fig. 3. The grasp on a circular object with two fingers (left); and the grasp index fmin for different symmetrical grasp configurations (amax = 100 N).",
+        "texts": [
+            " A similar procedure may be followed for the other subdomains of the disturbance actions as present in eq. (5). Also, the friction coefficient of the finger-to-object contact for any external force that has a unit value and is not directed along the axes of the reference system is minimized via the solution to the optimization problem in eq. (4). For a generic external disturbance torque of a unit value (eq. (6)), the friction coefficient at the contact points is directly minimized in the optimization problem (eq. (4)) with h = 5, 6. Figure 3 reports the results obtained for a two-finger grasp of a circular object. In this example, the greatest normal force amax is equal to 100 N, and the optimization problem (eq. (4)) is solved for the different symmetrical grasp configurations detected by the angle \u03b1. The objective function fmin, i.e., the minimum-friction coefficient, is observed to decrease as the angle \u03b1 decreases, until it reaches the lowest value of fmin = 0.005, with \u03b1 = 0. Thus, when the two contact points are diagonally opposite to each other, the lowest friction coefficient is required to balance all the possible disturbance forces and torques",
+            " Once reducing the friction coefficient required to balance the object has been defined as the objective for contact stability, the term fmin may be taken as an index of grasp quality. In particular, when two grasp configurations are compared, the one where the lowest value of fmin is obtained will on at SETON HALL UNIV on April 2, 2015ijr.sagepub.comDownloaded from average require a lower friction coefficient to balance the external forces acting on the object, thus ensuring contact with no slipping. Then, for the example in Figure 3, the optimal grasp configuration is attained when \u03b1 = 0. As in the previous example, Figure 4 reports the results obtained for a three-contact-point grasp of a circular object. Symmetrical grasps are considered for different values of the angle \u03b1, and the objective function fmin reaches its lowest value where \u03b1 = 30\u25e6. This means that the optimal grasp is achieved when the three fingers are placed at the vertices of an equilateral triangle. It then suffices to minimize fmin as the location of the contact points changes, in order to determine the optimal grip points"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002333_a:1025991618087-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002333_a:1025991618087-Figure1-1.png",
+        "caption": "Figure 1. The multibody model of trampolinist.",
+        "texts": [
+            " To meet the requirements of the present study, and intending to build the mathematical model as complex as necessary and as simple as possible, the following limitations have been assumed: \u2022 Planar motion is considered, which limits our analysis to front and back somersaults without twisting. \u2022 The trampolinist is modeled as a multi-rigid-body system with revolute joints, and the effects of muscle forces at the joints are modeled as control torques (many other musculo-skeletal models use similar assumptions, see e.g. [8\u2013 10]). Synchronous motions of two legs and two arms are assumed. \u2022 The trampoline bed is treated as weightless canvas with known stiffness and damping characteristics. The multibody model of trampolinist used for this study is seen in Figure 1. It consists of seven rigid segments, and the number of DOF of the system is nine. The nine generalized coordinates that describe the position of the system with respect to the inertial reference frame xy are q = [xH yH \u03d51 \u03d52 \u03d53 \u03d54 \u03d55 \u03d56 \u03d57]T , where xH and yH are the hip coordinates, and the angular coordinates \u03d5i (i = 1, . . . , 7) are measured from the vertical direction. All the entries of q are thus absolute coordinates. The six control torques that model the moments of muscle forces at the joints are \u03c4 = [\u03c41 \u03c42 \u03c43 \u03c44 \u03c45 \u03c46]T "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001277_s0997-7538(00)00139-x-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001277_s0997-7538(00)00139-x-Figure5-1.png",
+        "caption": "Figure 5. Comparison of journal centre trajectories for unbalanced rigid shaft (\u03b5b = 0.1).",
+        "texts": [],
+        "surrounding_texts": [
+            "The nonlinear dynamic analysis, described in the preceding sections, has been incorporated into MS-Fortran computer programs. In order to validate the results obtained from the optimised short bearing theory, a separate 2-D finite difference program was written to simulate the transient response for three cases of journal bearings operating in laminar and turbulent flow regimes. For 2-D finite difference analysis, which in this paper will be referred to as the exact solution, a grid size of (61\u00d7 21) nodes is used in \u03b8 and z directions, respectively. The number of nodes is chosen in order to ensure accurate results with minimum CPU time. The normalized Reynolds equation (8) is solved by applying the successive over relaxations scheme for each time step, so that a large amount of computation time is required to obtain the journal centre locii. Whereas, in the optimised short bearing analysis, the fluid-film discretization is only carried out in the circumferential direction \u03b8 in order to solve the normalized equation (18), and then the computation time required is considerably less than in the 2-D finite difference analysis. Thus, the optimised short bearing solution has an advantage of reducing a computation time required for the prediction of nonlinear journal centre trajectories. For all the calculations, the following conditions are used: \u2013 the initial position of the journal centre is kept constant for each case and is situated near the geometric centre of bearing (X0 = 0.01, Y0 = 0), \u2013 the initial velocity of the journal centre is assumed to be zero, \u2013 the dimensionless time increment 1\u03c4 used in the calculations was 2\u03c0 200 , \u2013 the effect of the dynamic dissipation, due to the orbital motion of the shaft, on the lubricant viscosity value is not taken into account, \u2013 the convergence criterion for the pressure is kept constant: the relative pressure deviation is 10\u22125, \u2013 for both methods, the over-relaxation coefficient optimum value is equal to 1.80. However, preliminary tests have shown that the change of the initial position of the journal centre and of the time increment do not affect the results. Example 1: To compare the results produced by the developed programs with those obtained experimentally, the test data published by Hashimoto and Wada (1990) were used. The rotating shaft was supported horizontally by two identical bearings with full circumferential grooves at the mid-plane sections as shown in figure 3. Therefore, the rotating shaft was essentially supported on four identical short journal bearings (L/D = 0.5). The weight of the rotating shaft was 108 N. Then, the load applied per bearing was about 27 N. The only applied load, in this case, is the static vertical weight of the rigid rotor. The journal bearing characteristics and the operating conditions are reported in table I. The calculations are made under various rotational shaft speeds and unbalance eccentricities. The nonlinear journal centre trajectories are examined for two values of rotational shaft speed N = 3000 and 6000 rpm. The mean Reynolds numbers for each case are Rm = 2750 and 5500. The unbalance eccentricity ratio \u03b5b varies from 0 to 0.20 which correspond to eb = 0 and eb = 50\u00d7 10\u22126 m, respectively. Figures 4 to 6 show the journal centre trajectories within the rigid bearing taking into account the inertia effects. The solid lines indicate the results by 2D-finite difference method and the dashed lines the results by the optimised short bearing solution for a rigid rotor with and without unbalance forces. To take into account the film rupture, the half-Sommerfeld or Gumbel boundary condition was used in the calculations. It should be noted that only the final form of journal centre orbits are presented in figures 5(a) and 6(a), i.e., the results corresponding to the transient numerical effect due to the initial conditions are omitted. It follows from these figures that: \u2013 the general similarity of the final form of nonlinear journal centre trajectories with those given in the above reference is obvious, \u2013 for both methods, the results obtained agree very well as can be seen by comparing the transient responses of a journal-bearing system. Example 2: To further validate the results obtained from the optimised short bearing theory, an another example from the Abdul-Wahed research work (1982) were simulated. The effect of cavitation in the divergent zone of the film is taken into account using Swift\u2013Stieber or Reynolds boundary conditions. These conditions are satisfied by using the Christopherson algorithm (Christopherson, 1941). The details of bearing geometry and operating conditions are given in table II. As shown in figure 1, the journal bearing system is supplied in lubricant through an axial groove which is located on the static load line. The lubricant viscosity average value is obtained from the application of a simplified approach based on the concept of effective or mean temperature by assuming that all the heat has been evacuated by the lubricant. An iterative procedure is used to seek the average temperature value for static equilibrium conditions. For reasonable unbalance eccentricities (\u03b5b \u227a 0.4), it is generally sufficient to carry out the calculation of the mean temperature for the same static equilibrium conditions since the dissipated energy due to the orbital motion of the journal centre with respect to the whole energy is small. Table III shows that the peak-to-peak displacement amplitudes 1x and 1y, the minimum film thickness hmin and the maximum bearing dynamic transmissibility FDmax calculated by using the optimised short bearing theory compare well with those given by Abdul-Wahed (1982). Figures 7 and 8 illustrate the predicted static pressure profile corresponding to the laminar static equilibrium position defined by the coordinates (x0, y0)= (154.55 \u00b5m, 162.39 \u00b5m). In figure 7, the pressure profile at the mid-plane section of bearing obtained by the suggested approach (solid curve) is compared to that calculated by the classic short bearing theory (dashed curve). It is indicated that the short bearing approximation (Ocvirk solution) predicts a higher value of maximum pressure compared to the optimised short bearing solution, and the difference increases with an increase in the static eccentricity ratio. Figure 8 shows a comparison between the pressure profiles at the central plane of bearing calculated by using the optimised short bearing solution (dashed lines) and 2-D finite difference (solid lines). It is seen that the peak pressure predicted by the proposed approach is over-estimated by about 2% which is acceptable. Example 3: In this case, the bearing characteristics and operating conditions are similar to those given in table II. The principle differences between these operating conditions and the ones used previously are the rotating shaft speed which is equal to 6000 rpm instead of 3000 rpm and the aspect ratio L/D is equal to 1 instead of 0.64. The results of the peak-to-peak displacement amplitudes of the journal centre motion, the minimum film thickness and the maximum bearing dynamic transmissibility obtained by using optimised short bearing solution are compared to the ones by 2-D finite difference technique in table IV. It is seen that the discrepancies are 0.1 percent on the displacement amplitude, 9 percent on the minimum film thickness and 1.8 percent on the dynamic transmissibility coefficient. Although the aspect ratio L/D is equal to 1, the optimised short bearing theory permits to obtain very good results using both the laminar and turbulent flow regimes. As shown in table IV, the optimised short bearing solution requires 20.92 seconds of CPU time on a Personal Computer (Pentium with a 200 Mhz processor) to complete 24 revolutions of the shaft. By comparison, the 2-D finite difference analysis took an estimated 1022 seconds (17 minutes and 2 seconds) of computation time (about 50 times more than the new analysis). Thus, the main objective of optimised short bearing analysis, i.e., to reduce the computing costs to a reasonable level, has certainly been met."
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0003024_1.2103093-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003024_1.2103093-Figure6-1.png",
+        "caption": "Fig. 6 Relative pressure \u201ePa\u2026 contours on the periodic plane in the backing ring corner region",
+        "texts": [
+            "40 mm Bristle diameter D 0.076 mm Young\u2019s modulus E 2.25 1011 N/m2 Minimum initial clearance between bristles 0.0076 mm Number of bristle elements K 20 Initial rotor interference Zrotor 0.00 mm Pressure load P 1.00 bar rapid, and the aerodynamic forces changed by no more than about Transactions of the ASME ?url=/data/journals/jotuei/28726/ on 05/06/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F 10% from the initial undisturbed geometry calculation. As shown by the pressure contours in Fig. 6 and velocity vectors in Fig. 7, the strongest flow occurs near the backing ring edge. In this region, there is a strong flow directed down the backing plate and along the bristles. This is due to the comparatively weak resistance to flow in this direction compared to that normal to the bristles. Not surprisingly, the peak aerodynamic forces occur on the downstream bristle near the backing ring edge. The strong velocities near the backing ring corner in Fig. 7 may explain the negative relative pressures in Fig. 6. Note that assuming a pressure load of 105 Pa distributed evenly over the five bristles in the region overhanging the backing ring would give a uniform aerodynamic force on each bristle of 1.52 N/m. It is interesting to note that values are slightly greater than this in Fig. 5. A thorough investigation of this effect would require study of the influence of outlet boundary conditions including their influ- Journal of Turbomachinery rom: http://turbomachinery.asmedigitalcollection.asme.org/pdfaccess"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002417_0278364903022002001-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002417_0278364903022002001-Figure3-1.png",
+        "caption": "Fig. 3. Car-like steering using linear and circular arcs.",
+        "texts": [
+            " In this paper, we focus on the problem of time optimal paths for point-to-point locomotion for a steered car, but more complex motions, including obstacle avoidance, or task-related motion planning can also be incorporated. First, we recall the results of Dubins (1957) for kinematic mobile robots. It was shown that the time optimal path for a car steering in SE(2) with limits on the turning radius is given by two circular arcs\u2014one arc tangent to each of the initial and final headings\u2014connected by a straight-line segment (see Figure 3). In this section we utilize these paths as the backbone for steering dynamic non-holonomic systems. In order to make the abstraction shown in Figure 1 from the dynamic system to the approximate dynamic system (and hence further to the kinematic, car-like system) work, the approximation must lead to a system that is \u201csteerable\u201d in the sense of a wheeled vehicle. We characterize as steerable any system for which we can use the shape variables to generate body velocities (cf. eq. (1)) of the form \u03be = g\u22121g\u0307 = (v, 0, v/R)T , where v is the forward velocity, and Rmin < R < \u221e is a control variable representing the turning radius (andRmin a turning radius constraint)",
+            " Since we are performing feedback control on a system using periodic gaits, we sample the robot position by averaging the center of mass position and velocity over one gait cycle. This places a theoretical (Nyquist) limit on the controller dynamics of FS/2. In practice, for a 1 Hz drive gait, controller responses of under 5 s are likely not achievable. We use a feedforward law based on the (curvature of the) path generated by the kinematic motion planner. In addition to this, we note that, since the steering is only approximate, the addition of a feedback term is desirable. PROPOSITION 2. A steered cart of the form of Figure 3 can be stabilized by a proportional feedback control law of the form \u03b8\u0307 (t) = k\u03b8(\u03b8d(t) \u2212 \u03b8(t)) \u2212 kd(d) for k\u03b8 > 0 and kd < 0. Proof. If we define d as the signed, perpendicular distance to the desired trajectory (with d negative when the desired trajectory is to the right of the actual trajectory), the motion of a steerable cart (see Figure 3) is described by d\u0307 = v sin(\u03b8d(t) \u2212 \u03b8(t)). Using a proportional feedback control law for the cart of the form \u03b8\u0307 (t) = k\u03b8(\u03b8d(t) \u2212 \u03b8(t)) \u2212 kd(d) it is straightforward to show that the linearized equations of motion can be easily stabilized about a straight path. The characteristic equation for the linearized system is s2 + k\u03b8s \u2212 vkd = 0. The condition for stability of this system therefore is k\u03b8 > 0 and kd < 0 which matches our intuition about steering. Figure 8 shows the path of the eel tracking an oval-shaped path (in simulation) that integrates both circular and straightline segments"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002544_ac00217a013-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002544_ac00217a013-Figure1-1.png",
+        "caption": "Figure 1. Flow cell construction: (1) optical fiber, (2) fiber mounting cylinder, (3) front plate, (4) solution inlet channel, (5) solution outlet channel, (6) front window, (7) slotted gasket, (8) thin film Ca(I1) sensor, (9) diffuse white reflector, (10) back plate.",
+        "texts": [
+            " The films scatter light analogously to the mats commonly employed as references for diffuse reflection spectroscopy. Immobilization was accomplished by immersing a film into an aqueous 0.1 mM calcichrome solution for 24 h at 25 \"C. Under these conditions, the concentration of immobilized calcichrome was -6 mM (1.2 mmol/g of dry film). This value was determined by the optical quantitation of the difference in the amount of colorimetric reagent in solution before and after immobilization. The thickness of an immersed membrane was -800 fim. Flow Cell. The optical sensor and flow cell are shown in Figure 1. The incident light was carried to the cell through 400-fimdiameter optical fibers (Ensign-Bickford Optics Co., Avon, CT). The fiber diameter with cladding is -730 fim. Optical fibers also collected and transmitted the diffusely reflected light to the entrance slit of a monochromator. The optical fiber bundle consisted of 10 fibers, which were arranged in a vertical orientation, with half used to transmit the incident light to the thin film and half used to transmit the diffusely reflected light to the entrance slit of a monochromator"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003241_tasc.2004.830317-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003241_tasc.2004.830317-Figure3-1.png",
+        "caption": "Fig. 3. HTS induction motor coupled with the electrodynamometer.",
+        "texts": [
+            " To accommodate the flat HTS tape, shape of the slot of the HTS rotor should be different from that of the conventional motor. Cross section of the HTS rotor is given in Fig. 1. Figs. 1(a) and (b) show the cross section of straight part and the end part, respectively. Outer diameter and inner diameter of the HTS rotor were 78 mm and 22 mm, respectively. Fig. 2 shows the cage rotor of the conventional and the HTS motor. HTS tapes for the short bars are soldered to the HTS tapes for the short rings. Electrodynamometer was coupled to the motor to apply the load. Fig. 3 shows the test system, where the HTS motor, the electrodynamometer and the cryostat are shown. Electro-dynamometer was placed on the top flange of the cryostat. To simplify the cooling system of the HTS motor, whole motor including stator and rotor was put in the cryostat and immersed in liquid nitrogen. Total height of the test system was 1,321 mm. Speed-torque curve of the HTS motor was obtained by using the equivalent circuit method. To get the parameter of equivalent circuit, no-load test and locked-rotor test have been carried out"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003008_1.1757488-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003008_1.1757488-Figure2-1.png",
+        "caption": "Fig. 2 Spherical inclusion in a plate. Distributions of virtual loop defects are shown on the plate surfaces.",
+        "texts": [
+            " As a result, prismatic dislocation loops, twist disclination loops, and radial disclination ~Somigliana dislocation! loops may be used as virtual defects in polar angle independent elastic problems of cylindrical symmetry. For defects with angle-dependent elastic fields, e.g., edge dislocations, one can utilize another set of virtual loops having the same angle dependence, e.g., glide dislocation loops, @9,11#. 4.1 Spherical Inclusion in a Plate and a Half-Space. Consider a spherical dilatating inclusion located in a plate of thickness t as shown in Fig. 2. The plastic distortion of the inclusion is bxx* 5byy* 5bzz* 5\u00ab*d(Vsph), where d(Vsph)5$0,r\u00b9Vsph 1,rPVsph%, Vsph is the area of the inclusion; and \u00ab*5DR/R characterizes the relative change of the inclusion radius. The latter may also be interpreted as the misfit strain characterizing crystal lattice mismatch between the inclusion and the surrounding matrix. Referring to the geometry and coordinate system shown in Fig. 2 and assuming that the elastic properties of the inclusion and surrounding matrix are the same, the total displacements `u j and elastic stresses `s i j of an inclusion in infinite media are, @21#: 412 \u00d5 Vol. 71, MAY 2004 rom: http://appliedmechanics.asmedigitalcollection.asme.org/ on 01/27/20 `ur ~ in!5 \u00ab*~11n!Rsph 3~12n! \u2022 r\u0303; `uw ~ in!50; `uz ~ in!5 \u00ab*~11n!Rsph 3~12n! \u2022~ z\u03032 h\u0303 !; `ur ~out!5 \u00ab*~11n!Rsph 3~12n! \u2022 r\u0303 ~ r\u030321~ z\u03032 h\u0303 !2!3/2 ; `uw ~out!50; `uz ~out!5 \u00ab*~11n!Rsph 3~12n! \u2022 z\u03032 h\u0303 ~ r\u030321~ z\u03032 h\u0303 ",
+            " On the free surface of the plate the following boundary conditions for the total stress field s i j5 `s i j1 is i j must hold: s jzu$z50 z5t %50, j5r ,w ,z . (21) Transactions of the ASME 16 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F The inclusion stresses `szz and `srz given by Eqs. ~20! contribute to the boundary conditions given in Eqs. ~21!. To satisfy the boundary conditions we assume that an additional field is i j is generated by the distributions of circular prismatic dislocation loops ~ensemble 1! and radial disclination loops ~ensemble 2!, placed on the free surfaces of the plate ~see Fig. 2!. These virtual rom: http://appliedmechanics.asmedigitalcollection.asme.org/ on 01/27/20 defects possess stress components szz and srz and a component swz vanishes. Rewriting Eqs. ~21! with the help of the fields of the virtual loops we obtain the integral equations with respect to unknown functions of loop distributions 12 f (a), 22 f (a) placed on the surface z50 and 11 f (a), 21 f (a) placed on the surface z 5t: `szz ~out!uz501E 0 ` 12 f ~a !\u202212szzuz50da1E 0 ` 11 f ~a !\u202211szzuz50da1E 0 ` 22 f ~a "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001511_978-1-4612-1416-8_9-Figure9.1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001511_978-1-4612-1416-8_9-Figure9.1-1.png",
+        "caption": "FIGURE 9.1. (a) Rotating planar pendulum joint; (b) Rotating universal pendulum joint. We consider a simple rotating pendulum suspended by either type of joint as depicted. The pendulum consists of a link of length e, which we assume to be massless and at the end of which are four equal masses symmetrically distributed as shown so that the moment of inertia of the pendulum is nonsingular.",
+        "texts": [
+            "1 (Rotating heavy chains) The global dynamics ofa heavy (hanging) chain undergoing forced rotation about a vertical axis will be crucially dependent on how the joints between the links of the chain constrain the possible relative motions of the links. This dependence has been explored in Baillieul and Levi [7]. Further insight into the global dynamical effects of relative motion constraints may be developed in terms of the curvatures defined above. Consider the two rotating pendulum systems in Figure 9.1. Both pendula undergo controlled rotations about the vertical axis. In Figure 9.1{a), the joint by which the pendulum is suspended is a single degree~of-freedom revolute joint, while in Figure 9.1{b), the link is sus pended by a (tWQ degree-of-freedom) universal joint. The respective Lagrangians are and L2(\u00a2, l{!, \u00a2, v,; e) = ~ [ (/2 cos2 l{! + a; (1 + sin2 l{!\u00bb) \u00a22 + (a; +12) v,2 + (/2 - a;) cos\u00a2 sin(2l{!) \u00a2e - (a 2 + 2/2) sin\u00a2 V, e + (a 2 cos2 \u00a2 cos2 l{! + (a: + 12) (sin2 \u00a2 + cos2 \u00a2 sin2 l{!) ] e2 + mgl cos \u00a2 cos l{!. 2 (Cf. Baillieul and Levi [7, Section 6], where we identify Ix = Iy = m(l2 + ;-), and I z = ma2.The corresponding controlled dynamics associated with L I and L2 respectively are ~ [m (a2 COS2 \u00a2 + [2 sin2\u00a2)iJ] = u dt 2 (z2 + a 2 2 ) \u00a2 + (a 2 _[2) sin\u00a2 cos\u00a2iJ2 + g[ sin\u00a2 = 0, and (in abbreviated form) d aL2 ---u dt aiJ - , (9"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001869_irds.2002.1043954-Figure7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001869_irds.2002.1043954-Figure7-1.png",
+        "caption": "Figure 7: Evolving tmjectory of a knot",
+        "texts": [],
+        "surrounding_texts": [
+            "the condition for initiating knot motion (relative sliding between the strands) and then the the trajectory of strand end points for the desired knot trajectory. The problems that we are addressing are:\n0 Given the geometry of the knot and f i c t i o n coeficient of the suture, determine the condition under which knot motion will commence.\n0 Given a desired knot placing trajectory, determine the trajectories of suture end points that would achieve this desired knot trajectory.\nAs the starting point of knot placement, we assume a simple knot is already developed by wrapping the loop strand around the post strand and by applying tension forces as shown in Figure 1.\n2.2 Sliding condition Moving the knot requires sliding the two strands relative to each other. To investigate the impending sliding condition, we need to have a static force balance model. The general model of a knotted suture is quite difficult due in part of the flexibility of the suture and complex contact geometry. In this paper, we use a simplified model based on the assumption of a two-point contact between the sutures, as shown in Figure 2. The freebody diagram is shown in Figure\n3. The impending sliding problem can now be stated as:\nGiven &, @2a, A, and A, determine the relationship between the angles 11flb11 ll@\"bII yi's and pi's, i=1,2, when the sliding motion is about to begin.\nDefine Zla = L, &a = L, Z1b = h, and IIFlaII l lFZa11 l l F l b I I\nZ2b = A ll&, and let Zn = e be the unit vec-\ntor along which the normal forces apply and Zt be the unit vector along which the frictiyn forces apply. When the knot is in equilibrium, F = 0, so\nFlaZia + F2aZ2a FlbZIb + F2b&b = 0. (1)\nThis equation has two unknown variables, F1b and F26, which can be uniquely solved in general. The condition of impending motion can be obtained from the free-body diagram of one strand as shown in Figure 4. The impending motion occurs when\n(FIaZla + F&b> . Zt = P(fian -k flbn). (2)\nFrom (2), it is possible to obtain the general sliding condition, but it is quite complicated. Since the desired knot trajectory lies in the normal direction to the tissue, we shall only consider the symmetric\nshown in Figure 5. At the equilibrium, the force and moment equations about p and p' are\nc=e(P = PI = ,927 7 = 71 = 7 2 , F1a = F2a), as\n(4) (5)",
+            "Coulomb\u2019s law states the sliding occurs when\nIt can be further simplified to\n(7) 1 1 tanp tany > 2P, ---\nwhich results in the following sliding condition\n(8) tany\n2p tany + 1 o < p < tan-\u2019( ).\nThis means that the sliding begins when the angle ,8 is sufficiently small to satisfy the inequality condition which depends on the coefficient of friction between the strands and y. Note that when the a p plied force is horizontal, i.e., p = 0, which means that the two leg strands have zero tension. When p is small, for a given tension requirement in the leg strands, the applied force Fla and F2a would be very large. Therefore, when the applied force is constrained (e.g., to avoid breaking the suture), there is a practical lower bound, @min, on p. To summarize, for the knot to move, the applied tension needs to lie in the (Pmin, p,] cone as shown in Figure 6.\n2.3 Trajectory of suture ends for placing a knot\nIf the suture is in tension, the knot motion can be determined from the end motion of the sutures due to the length invariant constraints. Let q be the current knot position and ple and be the current position of each end of strands. During motion, we assume\nthat the length of each strand is constant.\nWhen the suture ends move to new positions, the knot position q\u2019 can be obtained from the following length invariant constraint equations (which is imposed so that the strands remain in tension):\nI I d e - dII + IId -PloII = e1 IIPke - dII + IId - ~ 2 0 1 1 = ~2\n(11) (12)\nBy choosing the suture end position trajectories, we can shape the knot position trajectory. We focus on the case that the desired knot trajectory is a straight line normal to the tissue. This case can be achieved with only symmetric pulling. The problem then becomes finding p l e ( t ) to move the knot along p n ( t ) as shown in Figure 8. Let 6 denote the unit vector along the desired direction of knot motion, and s be the desired sliding rate. The angle y ( t ) and the\ndistance between pb and pn evolve according to",
+            "Due to the sliding condition, (&in 5 p(t) 5 pmU(t) = f(y(t),p)), the trajectory of the suture end to just start knot motion is\nple( t ) = plea + s(t)(cos(P(t))u + sin(p(t))v)* (16)\nExcessive tension at the tissue at pa and pb could damage the tissue. The optimal trajectory in the sense of minimizing the tension force in the leg strand can be obtained by using the minimum p(t) = &in\nple( t ) = plea + b ( t ) ~ + ( s t ) E . (17)\nFigure 9 compares the trajectories with p(t) =\nexerted by environment on the end-effector. In tension control where the motion is relatively slow, Fm can be neglected. The configuration-dependent static wrench due to gravity can be determined in real-time. Therefore, the wrench in the end-effector frame, Fe, can be easily calculated from the measured base wrench:\nPmaz(t) and P(t> = 0.\n3 Tension Regulation 3.1 Tension measurement Measuring tension applied to the suture in minimally invasive surgeries is difficult because of the limited mounting space and sterilization requirement. Strain gauge transducers have been widely used for force measurement, but it is undesirable in the minimally invasive surgical setting. The sensor is sensitive to the temperature variation, contact with tissues during surgeries may cause drift in the sensor output, and it must be sterilized in high temperature after each use. The disposal type of strain gauge sensors addresses sterilization but means high cost and time consuming calibration. In this research, the suture tension is measured through a force/torque sensor in the base of the surgical robot, as shown in Figure 10. This approach has the advantage that the sensor does not need to be sterilized and the force measurement (and hence control) is independent of the tools.\nThe measured wrench at the base sensor can be expressed as sum of the following components:\nFs = Fm + Fg + Fb (18)\nwhere F, is the motion-induced dynamic wrench, Fg is the gravity wrench, and Fb is the base wrench\nwhere Fb x Fs - Fg.\n3.2 Explicit Force Control Scheme To achieve a smooth transition from low tension to required tension, damping is needed. However, direct differentiation of force is not practical due to the noisy measurement and time delay. We therefore add damping to the system through velocity feedback. This approach has been widely used for dealing with impact force regulation in robot force control [9]. We also include the integral force feedback to reduce the steady state error and enhance robustness with respect to the time delay. The overall force control law is of the following form:\nP\n4 Experimental Results A six-axis force/toqrue sensor (AT1 Model 15/50) is mounted between the base plate and the mounting block as shown in Figure 11. The sensor outputs are interfaced to the PC through the serial communication and then, through the Ethernet, to a DSP-based motion controller by ARCS, Inc. The suture that is used in this study is made by USP (the United States Pharmacopeia), model 2-0 suture (coated, braided silk suture). We first experiment with the free tail of the suture k e d on a stand and the needle tail is attached to"
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0003502_095440904322804439-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003502_095440904322804439-Figure3-1.png",
+        "caption": "Fig. 3 Specimens geometry (dimensions in mm)",
+        "texts": [
+            " As mentioned above, the friction measurement procedure requires the specimens to be machined directly from the axle and the wheel, thus reproducing exactly the actual surface conditions during the press-\u00aet, in terms of materials, contact geometry, roughness and anisotropy. In particular, the specimens are taken from the zone near the coupling surfaces, as schematized in Fig. 2: a small specimen (called a punch in the following) and a long specimen (called a body in the following) have to be machined from the two components. In the present experiments the punch was obtained from the axle, the body from the wheel. The geometry of the specimens is reported in Fig. 3. The examined materials are carbon steels for both elements, precisely a normalized steel with 0.3 per cent carbon and HV \u02c6 205 for the axle (A1N-UIC 811\u00b11 O) and a quenched and tempered steel with 0.5 per cent carbon and HV \u02c6 260 for the wheel (R7T-UIC 812\u00b13 O). The initial specimens roughness was Ra \u02c6 0.8 mm for the axle and Ra \u02c6 1.5 mm for the wheel. As stated above, the test apparatus was designed to be mounted on a standard axial testing machine. In particular, in the present experiment a servo-hydraulic INSTRON machine with a maximum load of 100 kN and a maximum grip distance of 300 mm was used"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002044_s0378-4754(02)00027-7-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002044_s0378-4754(02)00027-7-Figure5-1.png",
+        "caption": "Fig. 5. Data capture for door crossing ANN learning.",
+        "texts": [
+            " The first output corresponds to left rotation, the middle output means no rotation and the last one will order the robot to rotate to the right. Thereby, again only the sign of the rotation action is learned, and the magnitude of the rotation is considered fixed. To collect data in order to learn the actions to cross the door, we have used the following methodology: we mark different trajectories on the floor, in which the same actions should be performed and collect sensor data while pushing the robot along that path. Fig. 5 shows the labels assigned to the different viewpoints of the robot with respect to the door. From angle \u03b8 the action to be carried out is \u201cturn right\u201d, from position with angle \u03b1 the robot must not rotate at all, and if the sonar readings indicate that the angle with respect to the door is similar to \u2126 , then the robot will \u201cturn left\u201d. To train the network we have used a set of 22,240 input patterns. Two-thirds of them have been used to train the net and the rest to measure the accuracy, obtaining an efficiency of 97"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003364_0020-7403(88)90076-8-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003364_0020-7403(88)90076-8-Figure6-1.png",
+        "caption": "FIG. 6. Adhesive (free) roll ing, no rma l and shear tract ions. (a) v = 0.3; (b) v = 0.5.",
+        "texts": [
+            " The amount of coupling reduces as the tyre thickness is reduced and consequently the relative magnitude of the shear tractions reduces. For v = 0.5 no coupling is present in the half-plane solution, but it is introduced as the tyre thickness is reduced. The shear tractions induced are of opposite sign to those present for v = 0.3--i.e. the coupling effects due to elastic dissimilarity and finite tyre thickness are opposite in sign. Some sample traction distributions for this configuration are shown here in Fig. 6. Tract ive rolling As mentioned above, it is not possible to obtain a valid solution for the case of tractive rolling unless some slip is permitted. This can be introduced into the formulation as follows. First a guess is made for stick zone boundaries b 1, b 2 together with the direction of slip in each slip zone. The tangential matching equations (17) for those points lying in the slip zones (m/S < b I , m /S > b2) are replaced by #P . + Q. = 0, (18) where the sign is chosen to correspond with the desired direction of slip"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003695_s00604-003-0077-2-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003695_s00604-003-0077-2-Figure1-1.png",
+        "caption": "Fig. 1. Diagram of optical sensing system",
+        "texts": [
+            " A few drops of the resulting solution were immediately transferred and spread over the clear side of a glass cuvette. The sensing membrane was allowed to formulate and stick in position. The resulting sensing membrane was washed with distilled water and stored in either distilled water or basic buffer. Optical Measurements The cuvette with the sensing element stuck on its side wall was secured in the cell holder of a Perkin Elmer conventional spectrophometer such that the sensing element membrane was positioned in the light beam path Fig. 1. The solution in the cuvette was changed by using a disposable pipette. The change in turbidity of the sensing element as a function of analyte concentration was measured as absorbance. The spectrum was obtained at different periods of time until it reached a steady state. Sensing element evaluation was done by measuring the difference in absorbance when the sensing element was cycled between pH 3.0 and pH 9.0 many times and observing the reproducibility of the optical reading (absorption spectrum)"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000572_jsvi.1995.0517-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000572_jsvi.1995.0517-Figure1-1.png",
+        "caption": "Figure 1. A rotor on rolling element bearings.",
+        "texts": [
+            " A curve fitting algorithm is developed to process the response of the Fokker\u2013Planck equation to extract the bearing stiffness parameters. The algorithm is tested by Monte Carlo simulation. 229 0022\u2013460X/95/420229+11 $12.00/0 7 1995 Academic Press Limited .   . . 230 The procedure is illustrated for a laboratory rotor rig and the results are comparedwith those from the analytical formulations of Harris [4] and Ragulskis et al. [9]. The governing equation for a balanced rigid rotor supported at ends in bearings (see Figure 1) with non-linear stiffnesses can be written as x\u0308+2zvnx\u0307+v2 n [x+lG(x)]=f(t), (1) where G can be a polynomial in x and l is the unknown non-linear stiffness contribution parameter. f(t) in equation (1) represents the random excitation to the system (a list of nomenclature is given in the Appendix). The bearing surface imperfections, caused by random deviations from their standard theoretical design and progressive surface and subsurface deterioration, are large enough to cause measurable levels of vibration and can be the primary source of these excitations"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002485_1.1902843-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002485_1.1902843-Figure3-1.png",
+        "caption": "Fig. 3 Flexible-link robot with a new link deflection model",
+        "texts": [
+            " s3d, sx2+w2du\u03072, is the square of the rotational velocity at the end point of the link deflection vector wsx , td, where w2u\u03072 is due to free link elongation. From the math- ematical point of view, w2u\u03072 results in an additional kinetic energy in Eq. s4d, causing the sign problems. In this section, a no-elongation link deflection model is first proposed as a link deflection model, compatible with the bending mechanism of flexible links. Then a new dynamic model is derived based on the new link deflection model. 3.1 A New Link Deflection Model. A new no-elongation link deflection model is shown in Fig. 3. In the figure, x, u, wsx , td, and t are the position along the link of length l, joint angle, link deflection, and joint torque, respectively. X0Y0 and X1Y1 are the Transactions of the ASME Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F inertial and rotating frames, respectively. In addition, g is the deflection angle at position x along the link and is defined with cos g=\u00cex2\u2212w2 /x and sin g=w /x. 3.2 New Dynamic Modeling. As before, the position vector psu ,x ,wd indicating the end point of the deflection vector wsx , td is computed in the inertial coordinates: psu,x,wd = \u00cex2 \u2212 w2fcossu + gdi\u0304 + sinsu + gd j\u0304g = \u00cex2 \u2212 w2S\u00cex2 \u2212 w2 x cos u \u2212 w x sin uD i\u0304 + \u00cex2 \u2212 w2S\u00cex2 \u2212 w2 x sin u + w x cos uD j\u0304 , s16d where i\u0304 and j\u0304 are the base vectors of the inertial coordinates X0 and Y0, respectively"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure4.8-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure4.8-1.png",
+        "caption": "Figure 4.8. A typical universal joint mechanism.",
+        "texts": [
+            "27a) But this is not yet referred to frame 1; it remains to refer y to frame 1. The geometry provides y =sin {J0 i +cos {J0 k with Po= {J(t0 ). (4.27b) 246 Chapter 4 Then use of (4.27b) in (4.27a) delivers ro 30 = 0.1 sin /3 0 i + 0.2j + (0.5 + 0.1 cos /30 ) k radjsec, ( 4.27c) in which /3 0 is the angular placement of the arm at the time t0 shown in Fig. 4. 7. The result ( 4.27c) is the total angular velocity of the claw frame 3 relative to the machine frame 0 and referred to the yoke frame 1, at the instant of interest. The universal joint illustrated in Fig. 4.8 is a mechanism used to connect rotating shafts that intersect in a constant angle ifJ. Each connecting shaft ter minates in a U-shaped yoke. The yokes are connected by a rigid cross link, the ends of which are set in bearings in the yokes at A, B, C, and D. When the drive yoke turns as shown in Fig. 4.8, the cross link must rotate relative to the yoke about its axle AB. The motion of the cross link about the axle CD and relative to the follower yoke is similar. We are going to show by use of the general chain rule ( 4.22) that even if the angular speed w 1 of the drive shaft is constant, the angular speed m2 of the follower shaft will not be uniform. We seek the ratio m2/m 1 of the angular speeds and its maximum and minimum values. The variation in the angular speed ratio with the angle of rotation of the drive yoke for various shaft angles will be described graphically at the end",
+            " Thus, even if the angular speed w1 of the drive shaft is constant, the angular speed w 2 of follower shaft will not be uniform, except for ifJ = 0. The denominator in ( 4.28f) achieves its smallest value cos 2 ifJ at IJ = (0, n) and its greatest value 1 at IJ = (n/2, 3n/2); therefore, the angular velocity ratio has the maximum and minimum values max(w 2/w 1 ) = 1/cos ifJ min(w2/wd =cos ifJ at 0=0, n; at e = n/2, 3n/2. (4.28g) Thus, w 2/w 1 attains its greatest value when the cross link is in the position shown in Fig. 4.8, and its least value occurs after a further 90\u00b0 rotation of the drive shaft. A polar graph of the ratio (4.28f) is shown in Fig. 4.11 for a quarter revolution of the drive yoke and for various shaft angles. Notice the con siderable variation in the angular speed ratio as the shaft angle ifJ is increased. Usually, however, the universal joint is used in circumstances where the shaft angle is small so that w 2 is very nearly equal to w 1 \u2022 This is evident in Fig. 4.11 for the shaft angle \u00a2J = 10\u00b0, for example"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001508_978-1-4615-2135-8_1-Figure1.5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001508_978-1-4615-2135-8_1-Figure1.5-1.png",
+        "caption": "Figure 1.5 Screw geometry affects conveying volume and pressure development.",
+        "texts": [
+            " the match of pumping efficiency with the rheology of the material being extruded 3. strength and wear characteristics 4. surface area for heat transfer and narrow residence time distribution 5. pressure and flow distribution at the entrance to the die 6. the degree of shear or intensive mixing required 7. the degree of barrel fill 8. the motor size. The conveying volume of a screw is a function of the screw speed, dia meter and distance between flights of the screw (referred to as pitch) (see Figure 1.5): or Qv = f [cP (Hp) N] Qv = m NV where Qv = conveying volume, d = diameter of screw, Hp = pitch, N = screw speed and, m = starts on the screw shaft. The pressure (P) which these screws generate over a length (x) can be described as dp _ K [ DNIl ] dx - L2tan9 where K = constant dependent on the degree of screw intermeshing, D = screw diameter, N = screw speed, 11 = material viscosity, L = flight height and 9 = flight helix angle. From this expression it can be seen that the length of the pumping section decreases with increasing screw speed, melt viscosity and decreas ing screw helix angle"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001708_0094-114x(94)90074-4-FigureI-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001708_0094-114x(94)90074-4-FigureI-1.png",
+        "caption": "Fig. I. Three views of feasible solution space,",
+        "texts": [],
+        "surrounding_texts": [
+            "Optimal eagineerin| design of gear ~ 1075\nThe MIWT procedure is briefly illustrated as follows:\n!. Specify the sample size P (according to [17], P should be at least as large as the number of objective functions), number of iterations t (t should be approximately the same as the number of objective functions [17]), and reduction factor r, [(l/P)~'k ~< \u2022 ~< w'- ' ] . 2. Calculate Z* (ideal criterion vector). Z* is calculated by solving the optimization problem k times (k is the number of objective functions). An optimal solution is generated each time as if there was only one objective function. Z* is the combination of the k optimal solutions. In gear design, for example, there are four objective functions. The problem is solved four times; each time dealing with only one objective function, and obtain four optimal solutions. These four solutions form the first Z*. 3. Rescale the objective functions and set the iteration counter c = 0. Let the interval width of weighting factors (::[i) as follows:\n= <0, I>, (18)\nfor i = i , 2 . . . . . k. There are four weighting factors, each associated wi th a design objective. These weighting factors represent the relative importance o f those objectives to the designer. The interval width defines the upper and lower l imits of the weighting factors. In this study, each weighting factor is a number between 0 and I.\n4. Set c = c + I and form a set o f weighting vectors as follows:\nIt can be seen that each vector consists of four weighting factors, and the sum of these factors in each vector is !. In other words, each vector represents a unique set of relative importance of the design objectives to the designer. 5. Randomly generate 50 x P weighting vectors from ~\u00a2cj in Step 4 (suggested in Ref. [ 17]). Note that each vector is tested against all design constraints when it is generated. Those vectors which do not satisfy all constraint functions will not be adopted. Filter those vectors and select the 2 x P most different ones.t Use these 2 x P dominating vectors to solve the 2 x P associated augmented weighted Tchebychcff equation [17]. This will generate 2 x P design solutions (criterion vectors). 6. Filter the criterion vectors from Step 5 and select the P most dominating ones. Present those to the gear designer to select the most preferred one. Let it be Z(\"L If the designer is satisfied with this solution, go to Step ! l. Otherwise, go to Step 7. The designer's involvement in this stage of design is a key. He is given the freedom to explore the impact of different relative \"importance\" of design criteria by selecting different preferred intermediate solutions. By doing so, the designer is able to explore different ideas leading to an optimal solution. 7. This step adjusts the search direction so that it is directed more toward the optimal solution. Let :~('~ be the ~: vector whose components are:\nZ* - ZI'~)-I[Y-, *. i ( Z * - Z~J) - I ] if Z * # Z~ ~ for all i, --,]'t~ -- if Z * = ,:,,\"\u00a2'~ , (20)\nif Z * # 7 (~ but :lj s.t. Z * = 7\"J\n8. This step makes sure that all weighting factors are within bounds (between 0 and I). Use the weighting vector from Step 7 and form:\nwhere\nf<0, \u2022~'J~j - r , I ) [<1~ \"j -- 0.Sr (~', ,;.~' + 0.Sr ('') if i ( { ) - 0.SP '~ ~ 0, if ).c,., + 0.Sr~, ,) >/ I, otherwise.\n(22)\n4\"These 2 x P vectors dominate all others.",
+            "1076 HUNGIaN WANG and H . ~ - I ~ WANG\n9. If e < t, go to Step 4. Otherwise, go to the next step. 10. If the gear designer is not satisfied with the result, go to Step 4. Otherwise, go to Step I 1. I I. Z ~\u00b0 is the overall optimal solution which satisfies all constraints.\nExperience indicates that generating 50 x P sample vectors can be a most critical step in the entire solution procedure. If the samples are not generated appropriately, it may take much longer to obtain the optimal solution. In other words, the efficiency of the solution procedure depends on how well the initial samples are selected.\n2.6. Example The same example used in Refs [I, 2, 5, 8] was tested using the methodology presented in this paper. The results are shown below:",
+            "Optimal enigineerinl desifln o f gear sets 1077\nInput parameters Elastic modulus: 30 x 10 + Poisson's ratio: 0.25 Addendum constant: 1.0 Dedendum constant: 1.25\nDesign remits Center distance: 3.96 (in.) Number of pinion teeth: 16 Diametral pitch: 12.13 (l/in.) Face width: !.25 (in.)\nObjective function values Weight of gear set: 12.59 (lb) Deflection: 7.96 E - 03 (in.) Estimated life: 3.96 E + 06 (rotation)\nA sample session of the optimization program is given on the following pages.\nFigures l(a-c) provide three views of the feasible solution space for the sample problem. Figure 2 is a 3-D view of the same space. Every point in the space is a feasible solution (i.e. it satisfies all constraint requirements).\nReferring to the interactive sample session, in each iteration, the designer is provided with four feasible solutions, among which he selects one. The solutions picked out by the designer from those three iterations are marked in Fig. 2 as points A, B and C. This visual presentation tool was found very helpful in the design process."
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0003355_tmag.1982.1061919-Figure12-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003355_tmag.1982.1061919-Figure12-1.png",
+        "caption": "Fig. 12. Concertina structures at zero external field which satisfy the boundary conditions. (e) One period of the concertina.",
+        "texts": [
+            " The number of periods of the bellows is an VAN DEN BERG AND VATVANI: WALL CLUSTERS 885 N' N N Fig. 11 The linking of the tip domain structures by two triplets having cluster knots at the same edge. Dimensions: 30 X 50 pm. (a), (c), (d) Two triplets with intersecting outermost walls transforming into a triplet. (b), (e) The bifurcation of the quintet into two triplets. integer in case the magnetization in both triangular tip domains are opposite, while one half-period has to be added in case of parallel magnetization (see Fig. 12). The number of periods can be decreased by applying an external field normal to the bar such as previously pointed out by Huyer. D. Conversions of CStructure to LL and D Structures The walls and edges of the rectangle form closed loops in the case of the complete concertina structure, and no wall that fades out in a domain by gradually decreasing its rotation is left. The closed character of the Landau-Lifshitz structure is removed by the separation of the 180' Bloch wall into two parts, as previously discussed"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001042_robot.1994.350911-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001042_robot.1994.350911-Figure1-1.png",
+        "caption": "Figure 1 - Three Identical Grasps of Dissimilar-6Gects",
+        "texts": [
+            " This is because most researchers used rigid body models for analyzing grasps, and the compliance between contacting objects (albeit small, in most cases) was not incorporated. As it turns out, all form closed grasps are stable, but not pll stable grasps need be form closed. It has been shown that all form closed equilibrium grasps are stable [lo]. Stability of non-form closed equilibrium grasps, however, depends not only on the arrangement of contacts, but also on the local curvatures of the grasped body and the fingers, and the magnitude of the contact force. Figure 1 gives an example of three grasps with the same arrangement of (fixed) frictionless fingers exerting identical forces (W and c are identical). Note that we use \u201cfingers\u201d in this paper as a generic term to represent any link, finger, effector, or fixture in point contact with the object being grasped or restrained. In Figure la, it can be seen from inspection that the grasp is stable. In Figure 1 b, however, the grasp is unstable. The stability of the grasp in Figure IC cannot be determined by inspection. Stability of a grasp can also result from external forces. An example of a non-form closed stable grasp is a brick lying on a flat, frictional surface. In this paper we refer to all external forces as \u201cgravity\u201d. Previous work in the area of grasp stability has been done by Hanafusa and Asada [3], who noted the dependence of the stability of certain grasps on local geometry. Cutkosky and Wright [2] studied two finger grasps and noted that the stability depended upon the forces applied and the local curvature"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003477_cnm.913-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003477_cnm.913-Figure1-1.png",
+        "caption": "Figure 1. Symmetric skeletal structures and their symmetry operators: (a) a grid; (b) planar frames; and (c) a 3-D frame.",
+        "texts": [
+            " It is pointed out that this operation is significant when each of the rotation and reflection are not individually among the symmetry operations of the object. (4) Inversion through the centre of symmetry which is a special case of Sn with n = 2, and is denoted by (i). (5) Identical symmetry (e), which maps an arbitrary object into itself, and is one of the symmetry operations of any given object; either symmetric or asymmetric. A number of symmetric skeletal structures and their symmetry operators are depicted in Figure 1. The interpretation of principal axis is simply shown in the grid of Figure 1(a), where there are two Copyright q 2006 John Wiley & Sons, Ltd. Commun. Numer. Meth. Engng 2007; 23:639\u2013664 DOI: 10.1002/cnm C2 axes and one C4 axis. Based on the above definitions, the latter will be the principal axis of the structure. The symmetry centre of this grid is joint \u2018i\u2019. The concept of different kinds of symmetry planes can be recognized from the planar frames of Figure 1(b), and the three-dimensional frame of Figure 1(c). Symmetry operations of an object under the combination of transformation operations comprise a group, which is called a symmetry group. Symmetry groups are classified based on symmetry operations which make a group up. Figure 2 shows some symmetric structures and their symmetry groups. The symmetry group of a finite body is sometimes referred to as the point group. There are several methods for categorizing the point groups. In Figure 2, the point groups are named based on Scheonflies method, which is more conventional than the other approaches"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002414_s0043-1648(03)00173-x-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002414_s0043-1648(03)00173-x-Figure1-1.png",
+        "caption": "Fig. 1. Friction test. (a) Equipment; (b) sphere/plane contact between chert and picrolite or diabase.",
+        "texts": [
+            " The specific abrasion energy (in J/mm3) is defined as the ratio of the energy spent during the scratch process to the wear characterized by the volume of removed material on a settled scratching distance. The simulation of wear by friction is performed to characterize the mechanisms of deformation of materials under specific tribological constraints. The equipment developed is able to apply on the studied surface a normal force of 10 N (constant load) and to measure a maximum tangential force of 5 N, (Fig. 1a). In the case study presented here, a contact sphere/plane was chosen to get read of problems of parallelism that occur while plane/plane contacts. A sphere of picrolite or diabase, showing a radius of curvature of 5 mm (natural convexity of river pebbles, (Fig. 1b), was applied on a knapped surface of Lefkara chert (type B, [3]). The number of cycles were of 256 and a constant normal force of 5 N was applied. Every sequence of friction\u2014 five for the picrolite and five for the diabase\u2014were realized without any additive. The evolution of the surface of the chert is evaluated with the help of two topographic measurements, realized exactly at the same zone, before and after friction. A surface of 2.4 mm \u00d7 1.8 mm was measured with a white light interference microscope, the lateral resolution is 1 m, and the vertical resolution of 2 nm"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure2.15-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure2.15-1.png",
+        "caption": "Figure 2.15. The locus generated by the motion of a point P on the circumference of a circle that rolls without slipping along a straight line is a cycloid.",
+        "texts": [
+            " It should be observed that the acceleration is directed from C toward 0. (e) The equation of the path traced by P in the frame f/J = { G; ik} is determined by integration of (2.27) in which v p = dX(P, t)/dt, v0 =awi, and roxx= -aw(cos.8i+sin8j) are used to express the right-hand side of (2.27) in terms of e and w; namely, dX(P, t)/dt = aw(l- cos O)i- aw sine j. (2.73) Assigning X= 0 at e = 0 and writing w = d8jdt, we determine the motion X(P, t) =Xi- Yj =a(O- sin O)i +a( cos 8-l)j (2.74) whose locus, shown in Fig. 2.15, is a cycloid with parametric equations X= a(O- sin 8), Y=a(l-cos8). (2.75) The reader may find it helpful to demonstrate that the motion (2.74) or (2.75) also may be obtained by geometrical construction based on Fig. 2.15. 0 Two moving rigid bodies that come into contact obviously cannot penetrate one another. In fact, they can maintain their contact with each other only so long as they have the same component of velocity in the direction normal to their surfaces at their instantaneous points of contact; otherwise, the bodies would separate. If their mutual normal velocity component is not 112 Chapter 2 zero, then one body pushes to drive the other in their common normal direc tion. This driving contact, however, may involve slipping in the tangential plane between the two surfaces, so that the tangential velocity components of their instantaneous contact points will not be equal"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001200_jjap.38.5660-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001200_jjap.38.5660-Figure3-1.png",
+        "caption": "Fig. 3. Relationship of unit vectors in the monostable PS-SSFLC, where c and s represent the c-director of the FLC molecules and mesogenic side chains, which is in the direction of \u03c6 = 0, respectively.",
+        "texts": [
+            " We also assume that in Y = 0 to Y = d/2, \u03c6(Y ) =\u03c6s + ( d\u03c6 dY ) Y =\u03c6s + ( \u03c6c \u2212 \u03c6s d/2 ) Y, (6) where \u03c6s and \u03c6c are the azimuthal angle of the c-director of the FLC molecules on the substrate surface and chevron interface, respectively, and are expressed as sin\u03c6s = tan \u03b4 tan \u03b8 + sin \u03b2 sin \u03b8 cos \u03b4, (7) sin\u03c6c = tan \u03b4 tan \u03b8, (8) where \u03b8 is the cone or tilt angle. Then, the in-plane tilt angle of the FLC molecules on the substrate surface (\u03c80 = \u03c8d = \u03c8) is given by tan\u03c8 = sin \u03b8 cos\u03c6s sin \u03b4 sin \u03b8 sin\u03c6s + cos \u03b4 cos \u03b8. (9) In the monostable PS-SSFLC, mesogenic side chains may be directed toward the FLC molecules with \u03c6 = 0 or \u03c0 during the photocure according to the applied voltage. Now if we assume that this direction corresponds to \u03c6 = 0 after the photocure as shown in Fig. 3, then the free energy per unit area in terms of the interaction between the FLC molecules and the side chains at a plane of Y = Y \u2032 ( f Y \u2032 ps ) may be expressed as f Y \u2032 ps =\u2212 \u03b3ps(cY \u2032 \u00b7 s) =\u2212 \u03b3ps cos\u03c6(Y \u2032), (10) where c and s represent the c-director of the FLC molecule and side chain, respectively. If it is defined that f Y \u2032 PS = f Y \u2032 ps 1(Y \u2212 Y \u2032), (11) the free energy in terms of the polymer stabilization FPS is given by FPS = 2 \u222b d/2 0 f Y PSdY, (12) where the effective area A is 1 m2. Thus, the total free energy of the monostable PS-SSFLC (FPS-SS) in the quiesent condition can be expressed as FPS-SS = FSS + FPS"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001353_s0921-8890(96)00041-3-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001353_s0921-8890(96)00041-3-Figure2-1.png",
+        "caption": "Fig. 2. Active suspension system.",
+        "texts": [
+            " Another area of Mechatronics design where major enhancements in performance can be achieved is that of suspension systems for transport vehicles, mobile robots, off-shore boat decks and other applications where it is necessary to \"iron-out\" higher frequency disturbances while sustaining a lower frequency loading. A conventional passive suspension is unable to meet these conflicting demands. However an active, or semi- active system may be designed to do so. If, in addition, consideration is given to the underlying physics of the problem, useful gains in performance can be made [3]. Figure 2 shows a semi-active system that might form the basis of a suspension system for a vehicle in which it is desired that the weight of passengers should not cause net downward deflection of the vehicle body. The air-spring system is the primary low-pass filter for road bumps which would not, in itself, compensate for passenger loading. In parallel is a high-pass active element consisting of a damped spool-valve actuated by the movement of the wheels relative to the body. Fig. 3(a) shows the response of the passive airspring suspension, and Fig"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure1.15-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure1.15-1.png",
+        "caption": "Figure 1.15. Pin motion in a bell crank mechanism.",
+        "texts": [
+            " The result may be established by use of ( 1.82 ). For the case k = 1, we obtain ( 1.85) This formula shows that R is least at x = 0. Hence, Rmin = 1/2 em and Kmax = 2 em -I. The solution, by ( 1.84 ), is a max = SOn = 50i cmjsec2 at the origin (0, 0). The radius of curvature at ( 1, 1) is found from ( 1.85 ); we get R = 5312 ...;-2 em. 0 Example 1.13. A small guide pin Pis attached to a telescopic arm OP of a bell crank mechanism which is hinged at 0. The pin must move in a parabolic track as shown in Fig. 1.15a. At point A it has a speed of 10 ftjsec Kinematics of a Particle 37 and a rate of change of speed of 20 ft/sec 2 along the track. What is the acceleration of the pin at point A in the Cartesian frame t:P = { F; ik} in Fig. 1.15b? Solution. The standard equation of the parabolic track shown in Fig. 1.15 is x = cy2\u2022 Since the curve contains the point ( 4, 4 ), the constant c = 1/4 and the actual path equation is ( 1.86) The problem data being expressed in terms of intrinsic quantities suggest use of the intrinsic representation for the acceleration. With s =10ft/sec and s = 20 ft/sec 2, the acceleration given by ( 1. 71) is a= 20t + 1 00Kn at A. The cur vature of the path (1.86) at A may be determined by (1.81b). Using (1.86), we evaluate dx y dy 2' (1.87) At the point A=(4,4) we have dxjdy=2,d2xjdy2 =1/2; and by (1.81b) we find K = Js/50. Therefore, the acceleration at A is given by a = 20t + 2 Js n ft/sec 2. ( 1.88) But ( 1.88) is referred to the intrinsic basis whereas the solution is required in the Cartesian basis. Therefore, a change of basis from tk into ik is needed. It is clear from the geometry shown in Fig. 1.15b that t = cos a i + sin a j, n = sin ':1. i - cos a j, ( 1.89) wherein a is determined by tan ':1. = dyjdx = 2/y. Evaluating this at A= ( 4, 4 ), we get tan a= 1/2; and from this result we determine sino:= t;Js, coso:= 2/Js. Now (1.89) may be written as t= f (2i +j), D= f (i-2j), Substitution of (1.90) into the acceleration (1.88) yields a=2[1 +4.J5J i+4[.j5-t]jft/sec2 \u2022 ( 1.90) (1.91) This is the acceleration of the guide pin at point A in the Cartesian frame t:P. (See Problem 1.53.) D Example 1",
+            " Find at the instant t0 the intrinsic velocity and acceleration of P in ~. and determine the radius of curvature of the path at the place occupied by P at the instant t0 . 1.56. A P.article P moves with a constant speed of 27m/sec along a parabolic tra jectory y = Js x 2. What is the acceleration of P as it passes the point at x =2m? 1.57. Find the intrinsic velocity and acceleration of the pin P in the device described in Problem 1.16 when the pin is at x = 3 in. What is the curvature at this place? 1.58. The guide pin P of the bell crank device described in Fig. 1.15 has a speed of 10 ftjsec and a rate of change of speed of 20 ft/sec 2 at the point A. What is the angular speed w of the arm OP when Preaches point A? 1.59. The slotted link A of the device in the figure for Problem 1.39 controls the motion of the pin P to move with a constant speed of 25 em/sec in the parabolic groove 3x = y 2 - 9. Find as functions of y the intrinsic velocity and acceleration of P. Determine the velocity and acceleration of the link A in the Cartesian frame rp = { 0; ik} at the instant when y = 2 em"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002923_acc.2005.1470620-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002923_acc.2005.1470620-Figure4-1.png",
+        "caption": "Fig. 4. Feasible velocity sectors for the ECAV and the phantom for bounded rates.",
+        "texts": [
+            " The algorithms are essentially finite dimensional searches which can further be reduced to one dimensional parameter searches. Considered are two cases. For this case we constrain the system dynamics through bounds on the range rate and angular rate of the ECAVs and the Phantom point. We let the phantom state be ),(R , ECAV state be ),(r and the bounds on the rates be such that min max min max min max r r r R R R These constraints lead to feasible velocity sectors being rectangular regions for both the ECAV and the phantom point as shown in Fig.4. The bounds on the rates of the ECAV\u2019s state will be functions of the ECAV\u2019s aerodynamics as well as of its state. The two bounds on the phantom\u2019s range rate will be functions of the ECAV\u2019s aero-dynamics, ECAV\u2019s state and of the dynamics of the range delay. In the absence of adequate knowledge on these bounds, constant bounds are assumed on each of the rates. For the ECAV and the phantom to be contained within their respective velocity rectangles it is clear that each rate has to have bounds of opposite sign"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003244_icsmc.2004.1398398-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003244_icsmc.2004.1398398-Figure3-1.png",
+        "caption": "Figure 3: Schematic representation of the hunk move. The trunk moves horizontally at a constant speed V.",
+        "texts": [
+            " Recorded position of each marker was traced by a motion analysis software (Move-tr/2D, LIBRARY), and the positions, the angles and the angular velocity of each joint were determined. The speed data were smoothed by a six-order low-pass Butterworth Iter with a cutoff frequency of 5 Hz. 2.2 Numerical experiments In this section, the method used in this study to obtain the leg swing trajectory minimizing energy consumption is introduced. 2.2.1 A dynamical model of a leg It was assumed that a leg is a simple two-link system with two joints at a hip and a knee (Fig.2), and the trunk moves horizontally at a constant speed. Vertical movement of the trunk was ignored (Fig.3). The dynamical equation of a leg in swing phase is given as follows TI = (II + I2 + 2A&L1S2 cosSz + Af2L:)& -A4zL1S2(201 + & ) & ~ i n 8 ~ +g(A;r,Sl + A.lr,L,) sin81 +(I2 + A4zLiS2 C O S ~ ' Z ) & +gA42Sz sin(& + 8 2 ) (1) + A ~ ~ L ~ s ~ ~ ~ ~ sin 02 +gAGSz sin(& + 02) (2) T* = ( I 2 +A;12L1S~cosOz)& +12B2 where TI and r2 are a hip and a knee joint torque, respectively, and 81 and B2 are angles of a hip and a knee joint, respectively(Fig.2). I,, Mi, Li and Si represent the inertia moment around center of mass, the mass, the leg length and the center of mass of each link, respectively, and the subscript i=l indicates the thigh and i=2 indicates the leg",
+            " Such a torque pro le results in the almost constant speed of the foot io the rst half duration and the acceleration by a ballistic movement, which brings the peak value of the foot speed in the second half duration (Fig.6(d)). Large positive torque was generated on a knee joint before the end of swing phase regardless of walking speed, which would be reauired to null hack the foot and make the aound (c) I \" \" \" \" ' / 4 \" 20 \" 40 \" 60 \" 80 \" 100 percent swing [%] - contact. These characteristics of torque pro les are coincident with the estimated joint torques in previous studies (see Fig.3 in [27], Fig.5 in [26], Fig.7 in [21]). The above characteristics of leg trajectories and joint torques were also obtained when the constant Y takes Vanous values. Figure Leg trajectories during swing phase by the subject TK relative to the hip position at speeds of 3k\" (solid), 5 k \" (dotted) and 7 k \" (dot-dash). The foot trajectory (a), time Course of the horizontal position (b), vertical position (c), and speed (d) of the foot versus percent of swing. The amount of energy consumption during swing phase is shown in Fig"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002115_s0924-0136(02)00034-1-Figure10-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002115_s0924-0136(02)00034-1-Figure10-1.png",
+        "caption": "Fig. 10. Contours of the temperature field of the roller after quenched in oil for 1 h.",
+        "texts": [],
+        "surrounding_texts": [
+            "The transient temperature field (as shown in Fig. 5) the distribution of the microstructures (as shown in Fig. 6), and the interior stress field (as shown in Fig. 7) when the heating was finished were taken as initial processes of the roller being quenched and then transferred to the tempering furnace. The furnace temperature of 300 8C could be combined to be analyzed because it is in fact a continuous cooling and then isothermal retention process for the center of the bearing roller. Water, oil and UCON were chosen as quenchants. The quenching time was 1 h."
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0002766_j.ijmecsci.2003.09.004-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002766_j.ijmecsci.2003.09.004-Figure4-1.png",
+        "caption": "Fig. 4. System of local coordinate axes.",
+        "texts": [
+            " For the system under consideration, the total kinetic energy is a sum of energies determined for individual masses and it is T (q; q\u0307) = 1 2 5\u2211 i=1 (vT SimivSi + !T i Ji!i): (11) Knowing the values of masses and the moments of inertia with respect to local coordinate axes of all the elements of an excavator, linear velocities of the centres of masses vsi transposed to the constant system and the angular velocities !i determined in local systems of coordinate axes, the total kinetic energy of the system considered was determined. The local systems of coordinate axes taken for calculations are shown in Fig. 4. The kinetic energy of a chassis of a mass m1 is T1 = 1 2 [vT S1 m1vS1 + !T 1J1!1]; (12) where: vS1 = [x\u0307 y\u0307 z\u0307]T; !1 = A[\u2019\u03071 \u2019\u03072 \u2019\u03073]T (13) the transformation matrix has the form A =   cos\u20192 cos\u20193 sin\u20193 0 \u2212cos\u20192 sin\u20193 cos\u20193 0 sin\u20192 0 1   : (14) For small oscillation angles \u20191; \u20192; \u20193, the chassis energy is T1 = 1 2 m1(x\u03072 + y\u0307 2 + z\u03072) + 1 2 Jx1(\u2019\u03071 + \u2019\u03072\u20193)2 + 1 2 Jy1(\u2019\u03072 \u2212 \u2019\u03071\u20193)2 + 1 2 Jz1(\u2019\u03073 + \u2019\u03071\u20192)2: (15) The kinetic energy of a body of a mass m2 is T2 = 1 2 [vT S2 m2vS2 + !T 2J2!2]; (16) where: vS2 = vS1 + A1[",
+            " This energy is Vs(q) = cz \u00b7 a \u00b7 b[z2 + 1 12 \u2019 2 2(3a2 1 + a2) + z \u00b7 \u20191(b02 \u2212 b01) + 1 3 \u2019 2 1(b2 02 \u2212 b01b02 + b2 01)] +1 2 cx[2 \u00b7 x + \u20193(b01 + b02)]2 + 1 2 cy[2 \u00b7 y2 + 1 2 \u2019 2 3(a1 + a)2]: (45) It has been assumed that during the strain a soil foundation is subjected to energy dissipation, which is described by a Rayleigh dissipation function of the form: D(q; q\u0307) = 1 2 k\u2211 i=1 k\u2211 j=1 Rijq\u0307iq\u0307j: (46) Following the determination of rate of strain of the foundation resulting from displacements of the chassis with its caterpillars, the dissipation function of the system of the following form was determined: D(q\u0307) =Rza \u00b7 b[z\u03072 + 1 2 \u2019\u0307 2 2(3 \u00b7 a2 1 + a2) + z\u0307 \u00b7 \u2019\u03071(b02 \u2212 b01) + 1 3 \u2019\u0307 2 1(b2 02 \u2212 b01b02 + b2 01)] + 1 2 Rx[2 \u00b7 x\u0307 + \u2019\u03073(b01 + b02)]2 + 1 2 Ry[2 \u00b7 y\u0307 2 + 1 2 \u2019\u0307 2 3(a1 + a)2]: (47) Non-potential generalized forces result from cutting forces that are formed on the edge of the bucket during operation of an excavator. It has been assumed, in conformance with the literature [6,7], that components of this force, the tangent and the normal, are proportional to corresponding components of the bucket edge velocity during the digging of a soil (point K in Fig. 4) and they are as follows: Pt = P(v) vt(t) vK(t) ; Pn = P(v) vn(t) vK(t) ; (48) where P(v) is the total cutting force applied to the bucket edge, resulting from the values of forces acting in the servo-motors of an excavator gear, while the tangent force Pt and the normal Pn are total forces of cutting of a soil and resistances of friction of the bucket against the soil formed in the tangent and normal direction. Non-potential generalized forces are: Qx = [Pn cos( 2 + 3 \u2212 1) \u2212 Pt sin( 2 + 3 \u2212 1)] sin ; Qy = [Pt sin( 2 + 3 \u2212 1) \u2212 Pn cos( 2 + 3 \u2212 1)] cos ; Qy =Pt cos( 2 + 3 \u2212 1) + Pn sin( 2 + 3 \u2212 1); Q\u20191 =\u2212[Pt sin( 2 + 3 \u2212 1) \u2212 Pn cos( 2 + 3 \u2212 1)] \u00b7[h3 + lw sin 1 \u2212 lr sin( 2 \u2212 1) \u2212 ll sin( 2 + 3 \u2212 1)] cos + [Pt cos( 2 + 3 \u2212 1) + Pn sin( 2 + 3 \u2212 1)] \u00b7{[b3 + lw cos 1 + lr cos( 2 \u2212 1) + ll cos( 2 + 3 \u2212 1)] cos \u2212 b2}; Q\u20192 = [Pn cos( 2 + 3 \u2212 1) \u2212 Pt sin( 2 + 3 \u2212 1)] \u00b7[h3 + lw sin 1 \u2212 lr sin( 2 \u2212 1) \u2212 ll sin( 2 + 3 \u2212 1)] sin + [Pt cos( 2 + 3 \u2212 1) + Pn sin( 2 + 3 \u2212 1)] \u00b7[b3 + lw cos 1 + lr cos( 2 \u2212 1) + ll cos( 2 + 3 \u2212 1)] sin ; Q\u20193 =\u2212[Pt sin( 2 + 3 \u2212 1) \u2212 Pn cos( 2 + 3 \u2212 1)] \u00b7[b3 + lw cos 1 + lr cos( 2 \u2212 1) + ll cos( 2 + 3 \u2212 1)] cos \u00b7 sin \u2212[Pn cos( 2 + 3 \u2212 1) \u2212 Pn sin( 2 + 3 \u2212 1)] \u00b7{[b3 + lw cos 1 + lr cos( 2 \u2212 1) + ll cos( 2 + 3 \u2212 1)] cos \u2212 b2} sin ; (49) where ll is the distance of the cutting edge of the bucket K , from the joint C of the mounting of the bucket and the arm (Fig. 4). After the determination of the kinetic and potential energy, and the dissipation function of the system under consideration, and then performing formal procedures on these expressions with respect to the generalized velocities and time, and with respect to the generalized coordinates on the basis of Eqs. (5), we obtained a coupled system of di8erential, non-linear equations of the second order, describing the dynamics of the excavator analysed during the digging of a soil foundation. In the vector notation, the system of equations obtained has the form: A0 Pq + A1q\u0307 + A2q = f(q\u0307; q; t); (50) where A0, A1, A2 are the matrices of the masses and moments of inertia, respectively, reduced to the system of axes related to the chassis, dumping of the soil foundation and its Dexibility",
+            " Numerical data characterizing a single-bucket excavator on a caterpillar chassis of a bucket capacity of 1:10 m3 and soil foundation of mechanical properties corresponding to =ne-grained cohesive, consolidated soils of modulus of strain E = 10 MPa [4], were applied. \u2022 Basic numerical data are as follows: \u2022 The chassis mass m1 = 11 000 kg. \u2022 The body mass m2 = 6000 kg. \u2022 The jib mass m3 = 3500 kg. \u2022 The arm mass m4 = 1200 kg. \u2022 The bucket mass m5 = 900 kg. \u2022 The length of the jib (the distance AB between the joints mounting the jib with the body and the arm, Fig. 3) lw = 4:4 m. \u2022 The length of the arm (the distance between the joints BC Fig. 3) lr = 2:1 m. \u2022 The distance of the bucket edge K from the mounting joint C (Fig. 4) ll = 1:2 m. \u2022 The width of the caterpillars a = 0:5 m. \u2022 The length of the caterpillars b = 2:8 m. \u2022 The caterpillar track a1 = 2:0 m. \u2022 The equivalent rigidity of a soil foundation in the vertical direction cz = 9; 550; 000 (N=m2)=m. \u2022 The equivalent rigidity of a soil foundation in the horizontal direction cx = cy = 4; 000; 000 N=m. \u2022 The equivalent viscosity of a soil foundation Rx = Ry = Rz = 250 kNs=m. \u2022 The calculations were made for the process of getting a soil with a bucket and with an arm and a bucket"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002746_0278364905060149-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002746_0278364905060149-Figure2-1.png",
+        "caption": "Fig. 2. Two types of PKM using extensible limbs with linear scale units.",
+        "texts": [
+            " After that, we discuss secondly the latter group of factors, the frame deformations. The author\u2019s previous paper (Oiwa 2002) briefly reported fundamentals of two compensation methods for the mechanism error and the frame deformations. In this paper, some experiments demonstrate the effect of the compensation system. The method mentioned in this section can be applied to PKMs employing an actuated prismatic joint that is equipped with a linear scale unit measuring the change in the length of the limb, as shown in Figure 2. Figure 2(a) shows a general hexapod-type six-degrees-of-freedom parallel manipulator consisting of 6-SPU or 6-SPS subchains. Figure 2(b) shows a tripod-type three-degrees-of-freedom parallel manipulator consisting of 3-SPR subchains. Hereafter, S, P, U, and R represent spherical, prismatic, universal, and revolute joints, respectively. Recent studies (Oiwa 2000; Oiwa and Tamaki 2000) have reported that a joint\u2019s translational error in a limb\u2019s direction strongly affects the moving platform\u2019s motion error of PKM. In other words, the distance of the spherical joints located on both ends of the limb (that is, the length of the limb) is very important for positioning the platform accurately",
+            " In addition, because most of the measurement loop is made of a low expansion alloy, the temperature fluctuation has little effect on the length of the measurement loop. Such a structural concept, which separates the measurement system from the machine structure, has been termed a \u201cmetrology frame\u201d (Bryan and Carter 1979). The compensation devices for the joint errors and the link expansion, described in Sections 2.1 and 2.2, respectively, were adopted in an experimental CMM (Oiwa 1997, 2000) shown in Figure 8. This CMM uses the three-degrees-of-freedom parallel manipulator shown in Figure 2(b). The sectional view of an extensible limb is shown in Figure 9 in detail. Using the same method as that shown in Figure 3, an electrical comparator (Mahr 1202IC+1304K) is installed in the spherical joints connecting the limbs with the machine frame. Two electrical comparators are also used to measure the errors of the revolute joint as shown in Figure 4(b). Moreover, Super-Invar rods connect a scale unit (Sony BS75, with measuring length at UNIVERSITY OF BRIGHTON on July 11, 2014ijr.sagepub.comDownloaded from 220 mm and resolution 50 nm) with the spherical joint and the revolute joint, respectively, to eliminate the influence of the limb\u2019s thermal and elastic deformations according to the same method as that shown in Figure 5",
+            " Therefore, in this paper, a surface plate mounting for the workpiece is used as an inert reference surface. If the base platform\u2019s position and orientation, which are represented in a coordinate system located on the surface plate, are measured while the machine is in process, the thermal and elastic deformations of the frame can be compensated independent of the structural and the material configurations of the machine base and the frame. In general, the three joints on the base platform of a tripodtype PKM shown in Figure 2(b) are located at regular intervals of 120 degrees. Moreover, two of the six joints on the base platform of a Hexapod-type PKM, shown in Figure 2(a), are closely located; thus, common PKMs have three joint supports mounting the mechanism. Thus, when three reference points are set on each joint support as shown in Figure 23, the position and orientation of the mechanism\u2019s base platform can be expressed by the coordinates of the reference points. Furthermore, the three distances among them, t1 \u2212 t3, represent the dimensions of the base platform. On the other hand, six reference points placed on the surface plate express its position and orientation",
+            " Then the axis of the rod must pass the reference point or the measurement point to minimize the influence of the joint support\u2019s motion error. The sensor can also be arranged at either end of the rod. If the distances between the surface plate and the joint supports, u1 \u2212 u6, are considerably long, some non-contact displacement sensor systems (e.g., a laser interferometer system) are utilized as shown in Figure 27. The combination of the sensor and the rod also measures the distance changes among the three joint supports, t1 \u2212 t3. In the PKM shown in Figure 2, the mechanism is suspended from the frame. This compensation system can be successfully utilized even if other configurations of the PKM are adopted. For example, a PKM can be held in the inverted position as shown in Figure 28. Figure 29 shows another configuration of a PKM that is manipulating the workpiece. The compensation device for the frame deformation, described in Section 4, was installed in an experimental CMM (Oiwa 1997, 2000) as shown in Figure 8. This CMM uses a parallel manipulator with three degrees of freedom, which is shown in Figure 2(b). A triangular-prism-shaped aluminum truss frame supports the manipulator through three spherical joints. A surface plate made of low-expansion cast iron at UNIVERSITY OF BRIGHTON on July 11, 2014ijr.sagepub.comDownloaded from and the aluminum frame are mounted on a vibration-isolation table made of stainless steel. Each extensible limb of the manipulator is expanded and contracted by an AC servomoter and a ball screw. Three linear scale units (Sony, with measurement length 220 mm and accuracy \u00b10"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000708_s0956-5663(97)00032-8-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000708_s0956-5663(97)00032-8-Figure3-1.png",
+        "caption": "Fig. 3. The configuration of the chemiluminescence flow cells.",
+        "texts": [
+            " The former reagent contained 2\u00b75 units/ml ARP and 12\u00b75 mM luminol in 0\u00b72 M sodium carbonate buffer (pH 10\u00b70), the latter solution contained 12\u00b75 mM luminol and 10 mM 4-iodophenol in 0\u00b72 M sodium carbonate buffer (pH 9\u00b70). These were the optimal conditions reported for each system and the results are shown in Fig. 2. The response of the ARP-luminol system was overwhelmingly higher than that of the HRPluminol-4-iodophenol system, so the ARP-luminol chemiluminescence mixture was used in the subsequent experiments. Next, we investigated the construction of the chemiluminescence flow cell. Four types of flow cells were examined (Fig. 3) and the results (Fig. 4) show that the maximum response was observed with a type IV cell. Therefore, a transparent spiral tube was employed as a chemiluminescence flow cell in this sensor system. We investigated the effects of each reagent, i.e. FAD, TPP, pyruvate and Mg2+, in the PyrOx reaction mixture on the background chemiluminescence. The PyrOx reaction mixture used previously (Ikebukuro et al., 1996b) contained 2 mM pyruvate, 0\u00b76 mM TPP, 0\u00b71 mM FAD and 5 mM MgCl2 in 0\u00b702 M HEPES buffer (pH 7\u00b70)"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003486_j.oceaneng.2004.11.003-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003486_j.oceaneng.2004.11.003-Figure1-1.png",
+        "caption": "Fig. 1. Co-ordinate systems for the description of ship motion.",
+        "texts": [
+            " Between the 18 types of manoeuvering tests only the Turning Test, mainly used to calculate the ship\u2019s steady turning radius and to check how well the steering machine performs under course\u2014changing maneuvers, Z-Manoeuvring Test, used to compare the manoeuvering properties and control characteristic of a ship with those of other ships and the Stopping Test (crash-stop and low-speed) used to determine the ship\u2019s head reach and manoeuverability during emergence situations, are recommended by all Organizations. The remainder of this paper is organised as follows. Section 2 deals with the modelling problem, Section 3 describes the identification procedure and, finally, Section 4 discusses results, highlighting some concluding remarks. In the process of analysing the motion of a ship in 2 degrees of freedom (DOF) it is convenient to define two co-ordinate systems as indicated in Fig. 1. The moving coordinate frame X0 Y0 is conveniently fixed to the ship and is denoted as the body-fixed frame. The origin of this body-fixed frame is usually chosen to coincide with the centre of gravity (CG) when CG is in the principal plane of symmetry. The earth-fixed co-ordinate frame is denoted as X Y. The angle J is the difference between heading and track course, VL is the forward velocity measured by the log, VT is the velocity in starboard direction and d the rudder angle. The co-ordinates (x,y) denotes the ship\u2019s position along the track"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001708_0094-114x(94)90074-4-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001708_0094-114x(94)90074-4-Figure2-1.png",
+        "caption": "Fig. 2. 3-D view of feasible solution space.",
+        "texts": [
+            " The results are shown below: Optimal enigineerinl desifln o f gear sets 1077 Input parameters Elastic modulus: 30 x 10 + Poisson's ratio: 0.25 Addendum constant: 1.0 Dedendum constant: 1.25 Design remits Center distance: 3.96 (in.) Number of pinion teeth: 16 Diametral pitch: 12.13 (l/in.) Face width: !.25 (in.) Objective function values Weight of gear set: 12.59 (lb) Deflection: 7.96 E - 03 (in.) Estimated life: 3.96 E + 06 (rotation) A sample session of the optimization program is given on the following pages. Figures l(a-c) provide three views of the feasible solution space for the sample problem. Figure 2 is a 3-D view of the same space. Every point in the space is a feasible solution (i.e. it satisfies all constraint requirements). Referring to the interactive sample session, in each iteration, the designer is provided with four feasible solutions, among which he selects one. The solutions picked out by the designer from those three iterations are marked in Fig. 2 as points A, B and C. This visual presentation tool was found very helpful in the design process. 1078 HL,~GUN W ~ 3 and Hsu-PtN WANG I 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 17 18 19 2O 21 22 23 24 25 26 27 28 29 3O 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 6] 62 63 64 65 66 67 68 69 70 71 72 73 S A M P L E S E S S I O N INPUT PARAMETER VALUE FOR GEAR DESIGN For FILE INPUT, key in 0 For interactive input, key in 1 0 Please input the data file name '8earl Mat\" * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *** Choose your FAVORITE from the following 4 *** *** alternatives by entering the number"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002731_j.ijmachtools.2004.03.005-Figure9-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002731_j.ijmachtools.2004.03.005-Figure9-1.png",
+        "caption": "Fig. 9. A sample flange ) selected points for both A and B.",
+        "texts": [
+            " 5(b)\u2013(d) occur, a crispy force corresponding to a solid collision is output. This force indicates that the contact is invalid, and the stylus must be repositioned to select a surface point so that only the stylus tip is in contact with an object. The above mechanics model provides a kind of fidelity as if the user is operating on a real CMM. Measuring points are selected according to the tolerance type and its requirement and the shape and size of the part. Taking the measurement of the parallelism between planes A and B of a flange shown in Fig. 9(a) as an example part to demonstrate the measuring point selection process using the haptic device. Planes A and B are selected as reference and actual plane, respectively. Parallelism is a kind of orientation tolerances. Datum plane should be measured first. The haptic point selection procedure of the parallelism measurement of two planes is described as following: 7. Collision in 2D: (a) at time t and (b) at time t\u00fe Fig. 1. Step 1 L oad the CAD model and the tolerance specifications. Step 2 D etermine the sampling strategy according to the tolerance requirement, feature shape and size, and operator\u2019s skill. Fig. 9(b) shows the interface of choosing the number of sampling points. Step 3 R otate, move, or zoom the scene or the part to view the whole shape of a plane, for instance, datum plane A of the flange. Step 4 M ove the stylus of the haptic device to move and control the probe of HVCMM. Step 5 P oint the probe tip at Plane A. If a desired point can be reached, it means this point is accessible. the probe tip and an object: (a) surface normal n in-line with probe; (b) surface normal n at an and its measurement: (a) a flange; (b) choose point number; (c) selected points for A; and (d Step 6 M ark the point and record its coordinates and sequence. Step 7 R epeat Steps 5\u20136 until all desired points on this plane are selected. Fig. 9(c) gives the point selection result of the plane A. Step 8 R epeat Steps 3\u20137 to select points on another plane, for instance, actual plane B of the flange. The point selection results of planes A and B are illustrated in Fig. 9(d). When measuring some features of complex parts, such as holes at different angles, a bent probe is required. Fig. 10 shows the measurement of inclined bores of a simplified V6 engine block with a bent probe. The point selection procedure is the same. The small highlighted points inside bores are selected by moving the stylus. These points are guaranteed to be accessible in real measurement. If a measuring point is not satisfactory, it is free to re-select another point. This paper has presented a novel CMM inspection path planning environment, the HVCMM, which makes use of haptic modeling technique for CMM off-line programming"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000732_s0301-679x(98)00043-7-Figure9-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000732_s0301-679x(98)00043-7-Figure9-1.png",
+        "caption": "Fig. 9 Experimental apparatus",
+        "texts": [
+            " In this case, the pumping effect of the bearing with the compliant surface becomes smaller than that of the rigid surface bearing due to the deformation of the rubber surface shown in Fig 8. At a bearing clearance of 10 or 15 mm, however, higher maximum pressure is obtained in the compliant surface bearing than in the rigid surface bearing. This is because the deformed rubber surface acts as a sort of pocket in a hydrostatic bearing and can keep the water pressure higher. 336 Tribology International Volume 31 Number 6 1998 Comparison with experimental results Fig 9 shows the experimental apparatus. The shaft is set vertically and the load imposed on the shaft is given by the air cylinder located above the shaft. Pressurized water is fed into the rotating shaft through a non-contact seal. In order to measure the bearing torque, the upper conical bearing is supported by an aerostatic journal bearing. The displacement of the shaft is measured by the non-contact displacement probe using the eddy current. The position of the lower conical bearing is also measured to confirm that its position is always constant, even when load is imposed"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000994_91.580792-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000994_91.580792-Figure2-1.png",
+        "caption": "Fig. 2. Membership functions of the input and output linguistic variables (N: negative, ZE: zero, P: positive, B: big, S: small).",
+        "texts": [
+            " The form and the number of the membership functions are defined with the function rulebase( ), which is also used for the creation of the control rules. We have three input linguistic variables: , the reel position on the bar, the speed of the reel, and the angle of the bar, respectively, and one output linguistic variable , the dc voltage of the motor, which is used as the control signal for the system. Their membership functions have the form of a triangle and are placed evenly throughout the whole defined space and , respectively, as shown in Fig. 2. We propose that all input variables have an equal definition space . If we want to fit our variables into a certain definition space, we should multiply each variable with the input gain . The output fuzzy set B in each iteration is calculated with the madmani( ) function mamdani (17) where is the input gain vector determined by a human expert and states and are the estimated states. TABLE I RULES MATRIX FOR THE FUZZY STATE CONTROLLER The control signal is calculated with defzfir( ) function defzfir (18) where equals the output fuzzy set, equals the output definition space, and COG is the defuzzification method"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002333_a:1025991618087-Figure12-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002333_a:1025991618087-Figure12-1.png",
+        "caption": "Figure 12. Graphical illustration of the reactions during the support phase.",
+        "texts": [
+            " During the flying phase (0.4\u00f71.5 sec) the most important for the somersault performance are variations in hip and shoulder control torques. The control torques in elbow and neck play also an essential role. Applying qd(t), q\u0307d(t), q\u0308d(t), Rxd(t) andRyd(t) in the scheme of Equations (17), the joint reactions \u03bbd(t) during the specified motion can be determined as well. The simulation results, limited to the reactions in A, K and H joints, are presented in Figure 11. They are then illustrated graphically in Figure 12 for the support phase. The question of what loads (and in which direction) cross the joints during this and other sport activities may be of considerable interest to the clinicians and trainers. Evidently a more detailed model of muscle forces and joint interactions is needed to make the analysis more valuable. To solve the direct dynamics problem in which the calculated control is used as the input signal, the dynamic equation (15) needs to be rearranged to q\u0308 = M \u22121 (q)(f(q) \u2212 d(q, q\u0307) + r(q) + B T \u03c4 d(t)), (23) where \u03c4 d(t) is a continuous time function fitting the inverse dynamics discrete solution"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure4.9-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure4.9-1.png",
+        "caption": "Figure 4.9. Exploded view of the universal joint showing the three imbedded frames.",
+        "texts": [
+            " We seek the ratio m2/m 1 of the angular speeds and its maximum and minimum values. The variation in the angular speed ratio with the angle of rotation of the drive yoke for various shaft angles will be described graphically at the end. Let ro 10 = ro 1 and ro 20 = ro 2 denote the respective angular velocities of the drive shaft and follower shaft, and write ro 30 for the unknown angular velocity of the cross link, all relative to a preferred frame cp 0 = { F; ik }. These vectors are identified in Fig. 4.9 as the angular velocities in cp 0 of three reference frames: cp 1 ={0;G 1 ,y 1,J1d fixed in the drive yoke; cp 2 ={0;G2 ,\"{ 2 ,J12 } imbedded in the follower yoke; and cp 3 = { 0; y 1 , y 2 , y 3 } attached to the rigid cross link. The kinematic chain rule ( 4.22) thus yields two relations con necting these vectors: (4.28a) wherein ro 31 is the angular velocity of the cross link (frame 3) about the axle Motion Referred to a Moving Reference Frame and Relative Motion 247 We note in Figs. 4.9 and 4",
+            "28c) This completes our application of the kinematic chain rule for angular velocity vectors. The rest of the analysis concerns the interpretation of ( 4.28c) in terms of the shaft angle and the angle of rotation of the drive yoke. Since \"{ 2 is perpendicular to both \"{ 1 and 0' 2 , we may write \"{ 2 =rxa2 X\"{ 1 , where rx is an unknown scalar. Therefore, with 'Y 1 x 'Y 2 = 'Y 1 x ( rxa 2 x 'Y d = rx[a 2 - (\"/ 1 \u2022 a 2 ) \"{ 1], and noting also that \"{ 1 \u00b7 a 1 =0, we obtain from (4.28c) (4.28d) where <P is the shaft angle shown in Fig. 4.9a. Let e denote the angular placement of the director 'Y I of the cross link arm AB, which is just the rotation angle of the drive yoke; and chose <p 0 so that its xy plane contains a 1 and a2 with a 1 =i, as shown in Fig. 4.10. Then the figure geometry gives \"{ 1 = COS {) j + sin {) k, a 2 = cos <P i - sin <P j. (4.28e) Thus, finally, use of ( 4.28e) in the second equality of ( 4.28d) yields the angular speed ratio (4.28f) This formula shows that although both shafts must complete one revolution in the same time, the ratio of their angular speeds varies with the angle of rotation IJ(t) of the driver and is a function also of the shaft angle ifJ",
+            " (b) What is the total angular acceleration of D relative to <Pat the time t0 ? (c) Verify the results for (a) by an alternative method. Problem 4.24. 4.25. (a) Show that the scalar iX and the relative angular speeds in the analysis of the universal joint of Section 4.2.2.1. are given by o.: = ( 1 - sin 2 1> cos 2 1:1) - 1/ 2, w 32 = -w 1 et sin 1> sin l.i. Motion Referred to a Moving Reference Frame and Relative Motion 327 Thus, find the absolute angular velocity ro 30 of the cross link referred to the cross-link frame <p 3 in Fig. 4.9, and expressed in terms of the angular speed w 1 of the drive shaft. (b) Find the form of the result referred to the fixed frame l/>. (c) What are the absolute velocities of the end points A and D on the cross link? (d) Describe an alternative scheme for the determination of the results found here. 4.26. (a) Use the results of the previous problem to determine the absolute angular acceleration of the cross link of the universal joint referred to the cross-link frame <p 3 \u2022 Assume that the angular velocity ro 1 of the drive shaft is constant in l/J"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000500_s0956-5663(98)00119-5-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000500_s0956-5663(98)00119-5-Figure1-1.png",
+        "caption": "Fig. 1. Scheme of the lysine biosensor. 1, PVC electrode body; 2, connector piece; 3, conducting composite (or biocomposite); 4, lysine oxidase membrane; 5, dialysis membrane; 6, circular copper piece; 7, solder; 8, O-ring.",
+        "texts": [
+            " A Selecta Tectron water bath was used to carry out calibrations under thermostatted temperature. pH was measured with a Crison micro-pH 2002 pH-meter using a combined Ingold glass electrode. A Pharmacia LKB autoanalyzer Model Alpha Plus (Series Two) was used for the determination of lysine in the pharmaceutical samples with the standard method. Lysine biosensors were composed of a lysine oxidase membrane assembled on a rigid conducting composite electrode by using a Viton O-ring and a dialysis membrane, as shown in Fig. 1. When not in use, lysine biosensors were stored in a 0.1 M phosphate solution (pH 5 7.5) at 4\u00b0C. For the construction of these biosensors, a circular copper contact was soldered to the connector piece and assembled on the PVC electrode body (18 mm length, 0.6 mm i.d. and 7.2 mm o.d.). This is a standard size in our working group (Santandreu et al., 1998; Santandreu et al., 1997; Morales et al., 1996). Although narrower PVC bodies could be used, this size allows the surface to be highly homogeneous, which is crucial to obtain reproducible results when this surface is renewed by polishing"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001056_s0304-8853(03)00494-3-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001056_s0304-8853(03)00494-3-Figure5-1.png",
+        "caption": "Fig. 5. Schematic description of an axial field generated by a radially magnetized ring. Long arrows indicate the direction of magnetization. Equivalent are, two current disks located at the ends of the permanent ring producing the spatial magnetic field.",
+        "texts": [
+            " In order to get a uniform axial gradient field, several iron rings of length 5mm are attached to the ends of the two rings as indicated in Fig. 3. Fig. 4 shows the axial field distribution along the magnet axis. It indicates that the measured results agree with the PANDIRA [4] calculation very well. The field gradient is 46.4 T/m in the central region, where the axial magnetic field changes from 0.51 to 0.51T in the 711mm space between the rings. The principle for generating an axial field using a radially magnetized ring is shown in Fig. 5. The solid arrows, in the radially outward direction, indicate the easy axis of the ring, and the dashed circular lines indicate the equivalent surface currents. The axial field is effectively generated by the two current disks located at either end of the ring, each having a surface current density Hc: For a radially magnetized ring with length 2l; inner radius R1 and outer radius R2; extending from z \u00bc l to l; the axial field produced at any point z along the axis can be written as Bz\u00f0z\u00de \u00bc Br 2 1 a1 1 a2 1 b1 \u00fe 1 b2 \u00feln \u00f01\u00fe b1\u00de\u00f01\u00fe a2\u00de \u00f01\u00fe b2\u00de\u00f01\u00fe a1\u00de ; \u00f07\u00de where a1 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1\u00fe z \u00fe l R2 2 s ; a2 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1\u00fe z l R2 2 s ; b1 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1\u00fe z \u00fe l R1 2 s ; b2 \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1\u00fe z l R1 2 s : The axial field reaches its maximum at the ends of the ring"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000595_1.2828771-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000595_1.2828771-Figure2-1.png",
+        "caption": "Fig. 2 Kinematic relations and coordinate systems of the hob cutter and CNC hobbing machine",
+        "texts": [
+            " Figure 1 presents a schematic drawing of a 6-axis CNC hobbing machine, where axes X, Y and Z are the radial axis, the tangential axis, and the axial axis, respectively; axes A, B and C are the hob swivel axis, the hob spindle axis and the work table axis, respec tively. However, in today's CNC hobbing machines, axes A and Y are for set-up only and rotational ratio between axes B and C is a constant. Some machines allow an interrelationship between axes X and Z; therefore, today's CNC hobbing machines are 3- axis machines. The proposed 6-axis hobbing machine may be built in the future. Figure 2 illustrates the kinematic relationship among those axes. Coordinate system St,{Xh, K;,, Z/,) is attached to the hob cutter while coordinate system Sp(Xp, Yp, Zp) is attached to the work piece which is cut by the hob cutter. Coordinate system Sf(Xf, Yf, Z/) is the fixed coordinate system attached to the machine housing and coordinate system Sr(Xr, Yr, Zr) is the reference coordinate system, cj),, and 4>p are rotation angles of the hob cutter and gear blank, respectively; and F is the setting angle of hob cutter",
+            " Also, kinematic relation between different coordinate systems can be obtained by applying coor- 108 / Vol. 119, MARCH 1997 Transactions of the ASME Copyright \u00a9 1997 by ASME Downloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/30/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use dinate transformation matrix equations. The transformation ma trix [My] transforms the coordinates from coordinate system Sj(Xj, Yj, Zj) to Si{X,, Fj, Zj). Based on the relationship in Fig. 2, matrices [M,*], [M/-r], and [M,,/] can be represented as follows: [M,\u201e] = [MfA = cos (f),, -s in (ph 0 0 sin 0;, cos <l>h 0 0 0 0 0 0 1 \u20ac,. 0 1 - 1 0 0 0 0 -sin r -cos r 0 0 \u2014cos r sin r \u20ac\u0302 0 1 4 0 (1) (2) and [M\u201ef] = cos cjip \u2014sin (j),, 0 0 sin </\u00bb,, 0 0 cos <l)p 0 0 0 1 0 0 0 1 (3) where 4 = | OfM |, \u20ac, = | MO, |, and (,, = 10,0,, \\. According to the mechanism of a 6-axis CNC hobbing machine, the loci of hob cutter represented in coordinate systems S,, and Sf can be easily obtained by using matrix transformation equations",
+            " In the following section, we apply the proposed gear mathematical model to different types of gear generation by specifying the parameters expressed in the equations of meshing. General Gear Mathematical Model Applicable to Dif ferent Types of Gears Generation A 6-axis CNC hobbing machine can be used to manufacture spur gears, helical gears, worm gears, and noncircular gears. In this section, we discuss different gears manufactured by a 6-axis CNC hobbing machine. Besides, a novel type of gear named \"Helipoid\" is investigated. Examples are chosen to illustrate the gear tooth surfaces obtained by considering multi-equation of meshing. As shown in Fig. 2, axis Z\u0302 is the rotation axis of hob cutter. Point O, is the intersection point of axis Z^ and Xf - Z/plane. (a) Point O,. is fixed As indicated in Figs. 1 and 2, when axes A,X, Y, and Z of a 6-axis CNC hobbing machine are fixed and the reference center point of hob cutter O;, is located at point M, then a worm gear is manufactured. In this case and y^^y^^y^^ 0, 0. (21) By substituting Eq. (21)intoEq. (16), the equation of meshing can be simplified as follows: W/,[(-Z/Cos F - >y sin F + miyf)nxf + (XfSin F \u2014 miXf)nyf + XfCOS Tn^f] = 0, (22) Downloaded From: http://mechanicaldesign",
+            "org/about-asme/terms-of-use where mi = N^INp-, NH is the number of start of the hob cutter and Np is the number of worm gear teeth. The worm gear tooth surface can be obtained by considering the locus of hob cutter represented in coordinate system 5,, and the equation of meshing expressed in Eq. (22), simultaneously. Therefore, Eqs. (6) and (22) represent the worm gear tooth surface. (b) Point Or is moving in Xf - Zf plane In the manufacturing of worm gear, the center of hob cutter can be set at the fixed point M (Fig. 2) . However, when the hobbing machine is used to manufacture spur or helical gears, the motion of hob cutter is in Xf \u2014 Z; plane. Therefore, the motion of point O^ (a point on the hob cutter axis) is a curve and is moving in Xf \u2014 Z/plane. When velocities Vx and Vz have a specific relation in the manufacturing process, the locus of point O, can be expressed as follows: fixfh, Zfh) = 0. Then, the tangent direction can be obtained by tan 7 = dXn (23) (24) where y represents the angle formed by the tangent vector of hob cutter path and Z/-axis",
+            " (28) is simplified as: [-Z/COS r - '\u0302j sin r + i^ cos T + yfNJNp\\n^f -I- \\Xf sin r - 4 sin r - XfNJNp]nyf = 0 (31) The tooth surfaces of a spur gear can be obtained by considering the locus of hob cutter represented in the coordinate system Sp and the equation of meshing shown in Eq. (31), simultaneously. Therefore, Eqs. (6) and (31) represent a spur gear's tooth sur faces. (ii) Noncircular gears manufacturing The generation of noncircular gears can also be considered a two-dimensional problem. However, the distance \u20ac\u0302 shown in Fig. 2 is not a constant in the generation process of noncircular gears. In this case, \u20ac\u0302 is equal to the distance between the center of rotation of noncircular gears Zp and the axis of hob cutters Zi,. A noncircular gear's tooth surface can be obtained by con sidering the locus of hob cutter represented in the coordinate system Sp and the equation of meshing shown in Eq. (31), simultaneously. Therefore, Eqs. (6) and (31) represent the tooth surface of noncircular gears. Because the generation of noncir cular gears can be considered a two-dimensional problem, the rack cutters can be used to develop the mathematical model of noncircular gears"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003926_1.338581-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003926_1.338581-Figure5-1.png",
+        "caption": "FIG. 5. Triangle T(u+,u_) on the (a - /3) plane.",
+        "texts": [
+            " In the case when n is a triangle, the integral (5) can be easily evaluated in terms of F(a,{:J) , which is related to the \"first~order transition curves\" by formula (2). The derivation proceeds as follows: It can be verified that (j2 --[F(a,{:J) (a - {J) ] (ja8p = a 2F(a,p) (a _ (3) + aF(a,{:J) oa a/3 ap _aF~(:.....-a.:!....J3.:.-) . (6) da Using Eqs. (3) and (6), we find 2jt(a,/3) (a _ (3) = 8F(a.{3) _ aF(a,/J) 8P oa (j2 - -- [F(a.{3)(a - {3) ]. (7) aa 8{3 Now, consider a triangle T(u+,u_) swept (see Fig. 5) dur~ ing the input increase from u _ to u +. According to Eq. (5), such input variation is associated with the losses Q(IL,U+) = f f p,(a,/3)(a - (3)da d/3 T(,,+,u ,.) = i~+ ([ jt(a,{J)(a - /3) d/3 )da = iU ,+ (Lu + p(a,/3)(a -fJ)da )d/3. (8) Substituting Eq. (7) into Eq. (8), performing the integra tion and taking into account that F(a,a) = 0, after simple transformations we find 1 rru , lU' Q(u_,u+) = - 2\" Uu_ F(a,u_ )da + \"_ F(u+.{3)d{3 - (u+ - u_ )F(U+,U_\u00bb) . (9) It can be shown that the derived expressions for hysteretic energy losses are consistent with the classical result: the hys teretic energy losses for any cyclic input variation equal the area enclosed by the loop resulting from the cyclic input 3912 J"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003734_ip-b:19830027-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003734_ip-b:19830027-Figure3-1.png",
+        "caption": "Fig. 3 Travelling-rotating wave",
+        "texts": [
+            " I (4) After trigonometric transformation, eqns. 3 and 4 are [5]: Js x(t, z) = X I X \\js xmM exp [j(u>t + (3mz)} (5) i 1 The kl harmonic of function 5 represents two waves travelling in the z-direction with different speeds. The kl harmonic of function 6 consists of two waves travelling with the same speed in the x-direction and with equal but opposite directions along the z-axis. This means that these latter two waves are travelling rotating waves moving helically on the cylindrical surface of the stator (Fig. 3.). If the rotor moves in a helical fashion, then the slip of the rotor related to the kl harmonic of the magnetic field is expressed by the equation ktt \" vxk vzli (7) i l k where vx and vz are rotor speeds in the x-and z-directions and vxk = \u2014 2rxfe/and vzU = \u2014 2Te/,/are speeds of the kl harmonic in the x- and z-directions. Eqn. 7 can be derived in two different ways. One of them, given in Reference 1, is as follows: If the rotor moves with asynchronous speed in relation to the kith field harmonic, it means that the field of kith harmonic varies for each point on the rotor surface",
+            " 12, we obtain vz + vx tan 7 (13) (14) Ski = 1 ~ (15) (16) (17) vzl Since tgy = vzl/vxk, eqn. 17 finally takes the form of eqn. 7. Eqn. 7 can also be obtained by starting with the following definition of the rotary-linear slip: s = 1 (18) where vki is the synchronous speed in the direction of the rotor motion (Fig. 5). Eqn. 7 indicates that the slip depends on two components of the rotor speed. If one of them is zero, then the slip takes the form well known in the theory of conventional motors. Considering the direction of the travelling rotating wave speed (Fig. 3), it is noticed that a change of the TX1 or TZ1 value causes a change of the direction of its movement. If we put Txi ->\u00b0\u00b0 in eqn. 6, we obtain a travelling wave, and if TZI ~*\"\u00b0\u00b0. w e n a v e a rotating wave. That means that the description of a helical movement is more general than that of a travelling or a rotating wave. The remaining analysis will hence be concerned with the helical field. At any time we can consider the travelling field of the linear armature by putting ' xl 2.2 Electromagnetic-field equations To define the electromagnetic field in the RLIM, Maxwell's equations have been used"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002271_robot.1988.12256-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002271_robot.1988.12256-Figure4-1.png",
+        "caption": "Fig. 4",
+        "texts": [
+            " The robot hand has three 3 DOF fingers driven by nine DC servo motors. This hand was developed to research coordinative manipulation by multiple robotic mechanisms [8]. Since precise force control of each finger is required, simple gear reduction and transmission system were adopted. The reduction ratio of each motor is only sixteen. By using the five bar closed link mechanism and a special transmission, the finger structure was simplified as shown in Fig.3, and all the motors were located in the wrist portion. The transmission is shown in Fig.4. The dynamics of the closed link finger mechanism was computed using the computational scheme proposed in section 2. The coordinate frames and the corresponding open link tree structural mechanism are shown in FigS. The coordinate frames were defined according to the Denavit-Hartenberg notation [9]. O i indicates the rotational angle along the z axis of the (i-1)-th coordinate frame. e,, e,, and O3 axes are the actuated joints. Accordingly, 91 = ( e l 82 83)T (27) From the visual inspection, 8, and 8, are represented as the function of e,, \u20acI2, and 8, as follows: e, = 8,- e3 1357 1 0 0 0 1 0 w = 0 0 1 0 1 -1 0 -1 1 "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003974_tia.2005.863911-Figure11-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003974_tia.2005.863911-Figure11-1.png",
+        "caption": "Fig. 11. Shaft radial speed feedback.",
+        "texts": [
+            " 10 shows the experimental results when radial force step disturbance is added as Fext in \u03b2-axis as shown in Fig. 7. The case of H = 0 is a conventional system. For the proposed radial force feedback system, the value of H is set to 10. The gains of PID controller are the same in the both systems. It is seen that the response of the proposed radial force feedback system is 200 \u00b5s faster than the response of the conventional system. It is also found that the proposed radial force feedback has better damping in radial magnetic suspension. Fig. 11 shows the proposed system of radial speed feedback, in addition to radial force feedback. The detected radial force is divided by the shaft weight, and then it is integrated. Thus, the shaft radial speed v\u0302\u03b2 is obtained. The radial speed is added to the output of the derivative controller in a PID controller. The block H2 is added for radial speed feedback loop. It is to be noted that when H2 = 0, then effect of the radial speed feedback is zero. As the H2 is increased, the effects of shaft speed feedback are increased"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000454_s0191-8141(99)00079-6-Figure7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000454_s0191-8141(99)00079-6-Figure7-1.png",
+        "caption": "Fig. 7. Distances used to measure the \u00aet error. (a) Along the y-axis. (b) Along the x-axis.",
+        "texts": [
+            " (4a) and (4b), the \u00aetting function that passes through the point x0=2,yM of the natural fold is de\u00aened by a C value given by: C y0 \u00ff yM 1\u00ff 3 p 2 : 9 The \u00aetting method by coincidence of the functions using their x-middle point is easy to apply and o ers a satisfactory approximation to the natural fold pro\u00aeles. The approximation of natural fold pro\u00aeles to theoretical functions involves a degree of mis\u00aet that must be evaluated in order to know the accuracy of the \u00aetting methods. If yi f xi is the value of the \u00aetting function [Eqs. (1), (3), (4a) and (4b) or Eq. (5)] for xi, and x1,z1 , x2,z2 , . . . , xN,zN are points of the natural fold pro\u00aele (Fig. 7a), the absolute rms error along the y-axis is given by ey 1 N XN i 1 zi \u00ff yi 2 vuut 10 and the relative error expressed as a percentage is ey,r 100 ey y0 : 11 Similarly, if zi g xi f x 0i is the value of the function de\u00aened from the natural fold for xi and of the \u00aetting function for x 0 i (Fig. 7b), the error along the x- axis is given by ex 1 N XN i 1 x 0i \u00ff xi 2 vuut 12 where x 0 i f \u00ff1 zi . The corresponding relative error expressed as a percentage is ex,r 100 ex x0 : 13 From Eqs. (11) and (13), a total relative average error can be de\u00aened as e r ex,r ey,r =2: 14 The \u00aetting error a ects several geometrical parameters of the analysed fold. In the case of alloclinal folds, one of these parameters is the maximum dip (Fig. 1a), which, in general, is di erent in the natural fold pro\u00aele and the \u00aetted curve"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001220_rob.10067-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001220_rob.10067-Figure4-1.png",
+        "caption": "Figure 4. A thirty-link manipulator reaching a point inside a tunnel.",
+        "texts": [
+            " The obstacle is represented by 14 panels (m 14). The manipulator has nine links and each link is 1.0 m long. The start and the goal points are located at (3.0, 0.8, 0.8) and (2.0, 3.0, 1.5), respectively. A value of Vj 8 m/s was determined for all panels. It can be seen that the shape of the obstacles does not stop the manipulator from reaching its goal successfully. Example 3: As the third example, we model a more complicated situation, where a 30-link manipulator (with link lengths of 0.25 m) must reach a goal inside a tunnel (Figure 4). Since the obstacle surfaces are close together in the tunnel example, each tunnel surface was discretized into a number of smaller panels (m 12) in order to have more control on the safe path by changing the value of Vj\u2019s (Vj 14 m/s). For more clarity, the panels\u2019 boundary lines are not shown in the figure. The start and the goal points are located at (0.5, 1.0, 0.0) and (2.0, 2.5, 2.5), respectively. Figure 4 shows the manipulator in four successive configurations while it is reaching the specified goal in the tunnel. The manipulator is able to avoid the tunnel surfaces and reach the goal successfully. Example 4: In our last example, we consider a 3D cluttered environment with several obstacles of different shapes and sizes. The obstacles are represented by 72 panels (m 72). A 22-link manipulator with link lengths of 0.6 m is modeled. The start and the goal points are located at (0.2, 1.0, 1.2) and (2"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002579_robot.1997.606743-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002579_robot.1997.606743-Figure1-1.png",
+        "caption": "Figure 1: 2R free-joint manipulator",
+        "texts": [
+            " The equation represents an autonomous system without E , the amplitude of the perturbation. It implies that the feature of the behavior with a small perturbation is determined by the averaged dynamics independently of E . Since it is necessary to discuss the characteristic of the solution trajectory of the averaged dynamics concretely, we will present control problems of 2R and 3R free-joint manipulators in the following sections. 3 2R free-joint manipulator 3.1 Analysis via the averaging method Figure 1 shows a free-joint manipulator with the first joint actuated and the second joint free, which resides in the horizontal plane. The simplified dynamics is represented by $2 = -(I + ncose2)i1 - nsin02 . (ill2 (7) where Oi denotes a relative angle of the i-th joint and, n = m 2 and I2 denote the mass and inertia of the second link, respectively, and I1 denotes the length of the i-th link and s 2 denotes the length from the i-th joint to the center of mass of the i-th link, as shown in Fig. 1. def m 2 l l s 2 \" 2 + I2 ' With the periodic input and the substitution as in the previous section, the system is represented by the following equation only for the second joint. 2 (8) q = Ep i = -(l+ncosq)f;(t) - ~ n s i n q . ( f & ( t ) ) where p and q denote & / E and 0 2 , respectively. Since its non-perturbed solution is q = qo and p = po - (1 + n cos qo) f&( t ) , the transformation is given by $ = p + ( l + n c o s q ) f & ( t ) (9) The standard form is obtained from Eqs.(8) and (9). q = E(4 - (1 + ncosq)f&(t)) 4 = E +sin q j k ( t> + $ sin 2 q "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002222_1.533555-Figure11-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002222_1.533555-Figure11-1.png",
+        "caption": "Fig. 11 Meshing pinion gear teeth",
+        "texts": [
+            " The surface equation is a function of three variables ac , a3 , and Sr , respectively the cutter angular position, the work roll angle, and the position of a point along the cutter blade edge: S5 f ~ac ,a3! (A2) The position of any point P on the generated tooth surface is therefore defined by a combination (ac ,a3). The solution to Eq. ~A2! is a series of contact points between the cutter blade edge and the work describing a line along the path of the cutter edge defined by angle ac . The bounded envelope, along the work roll angle a3 , of a series of such lines in the work reference frame X, gives the generated pinion tooth shown in Fig. 11. Fig. 11 also shows a nongenerated gear tooth. A Newton\u2013Raphson iterative method is used to numerically solve Eq. ~A2!. rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/27/20 A.3 Tooth Contact Analysis. First pioneered by The Gleason Works in the early sixties, Tooth Contact Analysis is the numerical process by which the kinematic characteristics of a tooth pair, such as Transmission Error and bearing pattern, are obtained. To obtain such characteristics, several contact points must be obtained on the tooth flanks. While several numerical solutions have been proposed in the literature, the basic contact conditions are ~Fig. 11!: Z\u0304P5Z\u0304G (43) N\u0304P5N\u0304G where Z\u0304 are the tooth flank coordinates and N\u0304 are the tooth flank normals, respectively, for the pinion and gear members, expressed in a common reference frame. Equation ~A3! yields five equations, for six unknowns, which may be solved using a Newton\u2013Raphson or similar iterative algorithm. Transmission Error is obtained as the difference in the calculated position of the gear member in reference to its theoretical position: dw35w32Q3mg (A4) where dw3 is the Transmission Error, w3 is the calculated position of the gear member, Q3 is the calculated position of the pinion member, and mg is the speed ratio"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002572_robot.1996.506595-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002572_robot.1996.506595-Figure2-1.png",
+        "caption": "Fig. 2 Three link manipulator system",
+        "texts": [
+            "(21). Where d\"'j&/dt = O b j WT. Using a negative constant kl, y is given by (49) [I] Set i ::= 0. [2] Calculate variations AB, Aq by substituting values of joint variables, B j , qi and variations of task variables, AobjrT, Aobj$T into eq.(48). [3] Set (50) 0i+l = 0, + A0 qi+l = qi + Aq [4) Replace &,q; with B;+l,q;+l. Go back to [2]. 6 Examples First, tlhe proposed algorithm is applied to the cooperative motion planning for two planar manipulators. Each manipulator has three links. As shown in Fig.2, the manipulator-A holds the object rigidly and the manipulator-B executes the task for the object with the tool. The specified task is that the tool moves along the circular arc by 90 degrees as shown in Fig.2. The radius of the obstacle is O.l[m] and in the position (0.8, 1.1). Fig.3 shows the motion path without considering collisions avoidance (y = 0 in eq.(48)). In this case, the sum of squares of variations of joint variables, S, is 0.0025. The path for the case when the position and the orientation of the object are fixed has 0.0549 as the value of S. In the case of Fig.3, total value of variations of joint variables becomes smaller by moving the manipulator-A. From this result the meaning of the pseudo inverse is understood"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002129_09500830210128074-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002129_09500830210128074-Figure4-1.png",
+        "caption": "Figure 4. A possible application is sketched. (a) A bifurcation in the tube where a 2\u00b11\u00b11 structure is propagated (from left to right) leads to two channels of bamboo structure, the bubbles close to the top of the tube going in the upper channel. (b) If a magnet (shown in black) generates a 180\u00b0 twist of the 2\u00b11\u00b11 before the bifurcation, the bubbles will go in the opposite channel compared with (a).",
+        "texts": [],
+        "surrounding_texts": [
+            "Thanks are due to Jean-Claude Bacri and to Nicolas Rivier for stimulating discussions and Valerie Cabuil for providing the ferro\u00afuid."
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0002755_j.triboint.2004.12.003-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002755_j.triboint.2004.12.003-Figure1-1.png",
+        "caption": "Fig. 1. Diagram of lip seal and detail of A.",
+        "texts": [
+            " the global TEHD behaviour of the lip seals using modeling of the structures of the lip very close to reality [19]. Three mathematical models of roughness are considered and the influence on features such as the average and minimal thickness, reverse pumping, power loss and the average temperature reached is analyzed. Taking its geometric shape, lip angle and the spring location into account, the radial flexure of the lip produces an asymmetric distribution of the contact pressure ps leading to a strong rise on the lubricant side and a smooth decrease on the air side (Fig. 1). A new and original approach was presented in a previous paper [19]. The compliant part of the seal is not assumed to have a totally elastic axisymmetric behavior; it is divided into two parts with different mechanical behaviors. We consider the following hypothesis: the lip seal is perfectly elastic, the rotating shaft perfectly smooth and the seal perfectly centered (no whipping). Nomenclature b cell length representing the lip seal (mm) Cij compliance matrix relative to pressure (mm/Pa) Cp specific heat (J/kg K) D universal parameter (pressure in the active zone and replenishment in the inactive zone) Def distortion of the lip due to the pressure (mm) Ej(Ue) functional value at node j of element Ue Eref Young\u2019s modulus at the reference temperature (N/mm2) f(x, y) analytical profile of the lip surface defect (mm) F control function (FZ1 in the active zone; FZ0 in the inactive zone) FL applied load (N) h lubricant film thickness (mm) h0 defect amplitude on the lip surface (mm) hc heat transfer coefficient of oil (W/m2 K) hm elastic contribution to the thickness of the film L shaft longer (mm) nx, ny number of periods of the defect on the lip surface for (x, y) direction P hydrodynamic pressure (Pa) pi nodal pressure (Pa) Q pumping rate (mm3/s) r replenishment (mm) R shaft radius (mm) S cross surface of shaft (mm2) T lip temperature (K) Tref reference temperature (K) Tki compliance matrix relative to the shearing (mm/Pa) DT TKTref (K) U shaft linear speed (mm/s) W, W* weight functions x circumferential coordinate (mm) y axial coordinate (mm) xc, yc location of centre of asperity (mm) a thermoviscosity coefficient (KK1) b thermoelasticity coefficient of Young\u2019s modulus of nitrile rubber (KK1) d circumferential displacement due to shearing (mm) h interference (mm) k heat conductivity (W/m K) l defect wave length on the lip surface (mm) mref lubricant viscosity at the reference temperature (Pa s) r density of lubricant-gas mixture (kg/m3) r0 density of the lubricant (kg/m3) txyi local stress shearing (Pa) The steady state Reynolds equation for an isoviscous case is: v vx rh3 vp vx C v vy rh3 vp vy Z 6mU vrh vx (1) This equation is solved, coupled (through the elasticity matrix) to the elastic behavior of the seal, by controlling the cavitation that must be checked for the active zones (zones under pressure)"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002374_naecon.1994.332886-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002374_naecon.1994.332886-Figure6-1.png",
+        "caption": "Figure 6",
+        "texts": [],
+        "surrounding_texts": [
+            "architecture for each type i s included later in this paper.\nThroughout the development of the several PBW systems described above, the incorporation of Fly-ByWire technology into the servo control scheme has yielded additional advantages in maintainability and control accuracy. In additlon, Fly-By-Light control has been developed, built and tested by Lucas in aircraft flight control systems and has been evaluated for use in future PBW systems.\nDescriptions of previous and ongoing PBW program experience are included in this paper.\nlAPTM\nTECHNICAL DESCRIPTION The lAPTM i s constructed of (4) basic elements: a hydraulic servopump. an electric motor, a hydraulic actuator, and a closed loop control system providing actuator positioning in response to an input command. Several variations of these individual elements can provide wide adaptability of the system and have been used in the design and development of various actuation packages. Figure 2 depicts an lAPTM system schematic incorporating electronic control signalling.\nEach of the major components and their variations i s described below:\nSERVOPUMP - The servopump utilized in the Lucas lAPTM i s an over-center type, variable displacement, variable flow direction, piston pump capable of producing actuator control authority in response to control error signals. The servopump element i s a high efficiency, high reliability, splayed axis type piston pump rotating at a fixed speed. Flow direction and rate is accomplished through the positioning of variable angle swashplate. The positioning of the swashplate i s governed by an internal control loop\nwhich receives the control error input, measures swashplate position and produces control flow to one of two stroke control pistons. An integral fixed displacement boost pump, used to supply control flow and maintain minimum actuator pressure can also be used. Maximum discharge pressure capability of the servopump has been well proven at 5000 psi. A schematic of the servopump is shown in Figure 3.\nELECTRIC MOTOR - Since the servo control of the lAPTM i s performed within the servopump detailed above, the only requirement for the electric motor i s to rotate the servopump at a fixed speed and direction. This requirement can be accomplished with either AC or DC motors. The preferred choice i s AC as this provides a simpler, more readily available design. In addition, AC power minimizes EM1 generation and it's possible degradation of control signalling. In an aircraft system where DC motors are preferred, the lAPTM can be configured with a brushless DC motor and motor controller designed to maintain a relatively fixed speed.\nHYDRAULIC ACTUATOR - The hydraulic actuator incorporated in the lAPTM can be of various configurations. Linear or rotary types can be used as well as dual or tandem configurations. To keep system size and weight to a minimum, equal area actuators are preferred to negate the need for large capacity, fluid storage areas. Position feedback sensors are commonly incorporated into the actuator design during initial fabrication. These sensors can be made with multiple channels as necessary to achieve redundancy goals. The basic actuator design i s very similar to that commonly used in aircraft actuation systems with design improvements added to achieve longer seal l i fe and lower seal leakage. In addition, high pressure technology (up to 5000 psi) can be utilized to reduce system weight and size.\nCONTROL SYSTEM - The basic control function of the lAPTM i s to position an aircraft flight control surface (or utility feature) to a specific location in response to a position command. This positioning must be done accurately, repeatability, efficiently and\n1339",
+            "with maximum stability. The control system of the lAPTM compares the input command to a position feedback of the actuator and produces an error signal to the pump servocontrol system. As the actuator responds and moves toward the commanded position the error signal decreases, providing stable positioning. An internal control function in the pump servo control system acts as a \"loop within a loop\" to provide stable pump response and control. A schematic of a representative control loop i s shown in Figure 4.\nDESIGN EVOLUTION The design evolution of the Lucas lAPTM dates back to the early 1980's and includes design progression in many of the system components. A chronology is listed below:\nMODEL 91E01-1A (1980-1982) This demonstrator system was developed for a nose wheel steering application. To reduce development costs and take advantage of proven, high reliability components, the system was constructed from Lucas's splayed axis piston pump technology previously used for Variable Exhaust Nozzle (VEN) actuation applications on fighter aircraft engines. The unit was a tandem system utilizing two independent channels. The control system was completely mechanical. An input bellcrank was used to command actuator position. This bellcrank acted upon a four bar linkage which received mechanical feedback of actuator position. This mechanism produced movement of a hydraulic shuttle valve, providing servo control. The system was subjected to limited bench testing. A photograph of the package i s shown in Figure 5.\nSYSTEM ADVANCES - Dual channel system provided redundancy. Used 115VAC 400Hz power.\nMODEL 91E03 (1983 - 1988) This demonstrator unit was designed to be used in a nose wheel steering power-by-wire demonstration system. While similar in design to the model 91E01 described above, the control system was modified to incorporate an electrical input and feedback signal. A simple electronic control circuit resolved these signals into a command voltage to a proportional solenoid. The solenoid input the \"error\" signal mechanically into a flow control servovalve. The lAPTM was a single channel design and completed extensive bench testing. A photograph of Model 91E03 system i s shown in Fkure 6.\nSYSTEM ADVANCES - The incorporation of an electric control loop reduces backlash of mechanical input and feedback linkage.\nMODEL 91E05 - (1990 - 1993) This lAPTM was developed specifically for an aircraft rudder application. The system incorporated an external Electronic Control Unit (ECU) to perform the control function. The ECU is a micro-processor driven unit which accepts not only input and feedback signals but Input/Output commands for discrete monitoring and failsafe capability. The control mode i s truly Fly-By-Wire (FBW) The system i s dual channel with independent command, feedback and error circuits for each channel. Signal averaging was incorporated to minimize force fight between channels. This minimum force fight was also accomplished by independent pump control gain setting to match pump performance. The actuation package also incorporated passive/active heat dissipation and overheat protection. The system was extensively bench tested and accomplished limited flight testing. A photograph of the system is shown in Figure 7.\nSYSTEM ADVANCES - The ECU control system allowed for increased performance capability. Dual channel redundancy was attained with minimal force fight. The system thermal performance was acceptable throughout ground and flight testing.\n1340",
+            "SYSTEM ADVANCES - The incorporation of differential pressure as a performance monitor will allow for very accurate system matching of dual channels of a system. Power and heat efficiency are greatly improved over previous packages and allow for incorporation into the aircraft without the addition of power generating capacity. A MIL-STD-1553 communication network allows for remote system data collection, evaluation and fail safe system shutdown.\nFUTURE: DEVELOPMENT Future design advances planned for the lAPTM include:\nMODEL 91E06/9lE07/91E08 (1992 -) These three lAPTM systems are part of an electric spoiler and aileron aircraft demonstration program. The actuation packages are all dual channel systems and are very slmllar In deslgn. As in the Model 91E05 listed above force fight i s minimized through the use of signal averaging, In addition, differential pressure transducers are used to measure actual channel performance against predicted performance and the error signal i s \"trimmed\" to further reduce force fight. The electric drive motors contain a power factor correction feature for optimal motor performance throughout the various operating modes. Active air cooling i s employed to provide maximum heat dissipation for the actuation packages. A Central Interface Unit (CIU) i s included in the aircraft conversion to provide for maintenance data collection from each actuation package individually and provide a single maintenance interface. In addition, the CIU monitors spoiler position to greatly diminish the possibility of aircraft asymmetry. The overall aircraft electric actuation system provides system operational status and i s controlled through the existing aircraft's pilot interface. A photograph of the actuation package is shown in Figure 8. .\nEfficiency upgrade through elimination of hydraulic pump control servo loop and incorporation of electrically driven pump servo control Adaptation to 270 VDC power for use in future aircraft incorporating 270 VDC power generation.\nmicrocircuitry development Incorporation of extensive Fly-By-Light experience into the lAPTM control systems to adapt with future aircraft ARINC 629 or MIL-STD-1773 information networks.\nWeight/Size reduction through ECU\nThese design improvements are part of ongoing and planned development programs at Lucas to improve the IAPTM.\nEMA\nTECHNICAL DESC RI PTlO N The Lucas Electromechanical Actuator is a Power-ByWire device utilizing no hydraulic elements. The control \"loop within a loop\" i s similar to the lAPTM but i s accomplished electronically. A functional diagram of the EMA i s shown in Figure 9.\nThe EMA and i s comprised of two major components:\n1341"
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0001194_analsci.14.203-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001194_analsci.14.203-Figure3-1.png",
+        "caption": "Fig. 3 Variation of the CL intensity with the 8-quinolinol concentration used for the Fe(oxine)3 extraction.",
+        "texts": [
+            " 2, increasing the R value along with a decrease in the CTAC content at a constant amount of water in the reversed micellar solution caused an increase in the CL emission. Further, the intensity reached a maximum at around 0.15 M CTAC and an R of 22.2, which were chosen to be optimal. Beyond the respective optimized levels, the relatively high viscosity of the luminescent reagent solution makes it difficult to obtain sharp and reproducible signals, since rapid mixing with the Fe(oxine)3 solution is hampered in the flow cell. As shown in Fig. 3, the CL intensity increased along with an increase in the concentration of oxine in an aqueous solution which was mixed with the aqueous sample solution of iron(III) for the extraction of the Fe(oxine)3 complex into chloroform. It was observed that a 1.0\u00d710\u20133 M oxine concentration was optimal and a maximum CL intensity was attained at around the concentration. When an aqueous blank solution was used in place of the aqueous sample solution of iron(III), some CL emission resulted, which is presumed to have been caused by the partial extraction of oxine molecules into chloroform"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000909_027836499901800506-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000909_027836499901800506-Figure2-1.png",
+        "caption": "Fig. 2. Unit vectors relating to the contact points.",
+        "texts": [
+            " If a disturbance force (Fh) and a torque (Th) of a unit value directed along the axes of the reference system were to be exerted in turn on the object, the forces at the contact points would have to verify the following relations to ensure equilibrium: Fh + n\u2211 p=1 ( ap,hvN(p) + bp,hvT(p) ) = 0, (3.1) Th + n\u2211 p=1 (P(p) \u2212 C)3 ( ap,hvN(p) + bp,hvT(p) ) = 0, (3.2) |bp,h| \u2264 f ap,h, p = 1, 2, . . . , n, (3.3) ap,h \u2265 0, p = 1, 2, . . . , n, (3.4)   (3) where ap,h and bp,h indicate the normal force (direction vN(p) ) and the tangential force (direction vT(p) ) respectively, at the generic contact point P(P ) (Fig. 2), and f indicates the static friction coefficient. With h = 1, 2, . . . , 6 and the unit vectors F1 = i(N); F2 = j(N); F3 = \u2212i(N); F4 = \u2212j(N); F5 = 0(N); F6 = 0(N); while T5 = k(Nm); T6 = \u2212k(Nm); and Th = 0(Nm) for 1 \u2264 h \u2264 4. Equations (3.1) and (3.2) are the equations for object equilibrium; eq. (3.3) expresses the relations between the normal and tangential components of the contact force (hard finger), and eq. (3.4) defines the presence of unilateral constraints between the fingers and the object"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003364_0020-7403(88)90076-8-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003364_0020-7403(88)90076-8-Figure2-1.png",
+        "caption": "FIG. 2. Discretized model of surface tractions:",
+        "texts": [
+            " In reworking the problem of tractive rolling of homogeneous cylinders [4], we were able to use an accurate integral equation approach. For the tyre problem the complexity of the kernels precludes this and accordingly the method of solution employed here is similar to that of Bentall and Johnson [5] where the surface tractions are modelled by piece-wise linear distributions. Direct and shear tractions in the contact patch are each represented by 2 S - 1 overlapping triangles with equal bases of width 2a/S , as shown in Fig. 2. The heights of the nth triangles are p, and q,, which represent the magnitudes of the direct and shear tractions respectively at x = na/S. We now write down the relative vertical and horizontal surface displacements, v(m) and u(m), at a point x = m a / S (Iml ~< N) due to the total normal and tangential forces exerted [5]: v(m) 4 ( 1 - v 2) 2B s-1 - - - - - ~. [P.IA(n -- m)+ Q.Ia(n-- m)] (3) a xE Z n=-(s- 1) u(m) 4(1-v2)2B s-1 . . . . ~. [ - - P . I B ( n - - m ) -- Q. lc(n - m)], (4) a ~E Z . = - ( s - u where P"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002509_i2002-10164-3-Figure8-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002509_i2002-10164-3-Figure8-1.png",
+        "caption": "Fig. 8. Geometry of the grooved surface. Aw and Pw are, respectively, the amplitude and the period of the grooves.",
+        "texts": [
+            " In the former case of the non-uniform planar anchoring, the directors are assumed to be oriented tangentially to the grooves but without any overall preferred orientation while in the latter uniform case, there is an average preferred molecular direction. The fixed orientation of the nematic director on the grooves is given by n(yw (x) , x) = (cos \u03b8 cos\u03c6, cos \u03b8 sin\u03c6, sin \u03b8) , (15) where the zenithal angle \u03b8 gives the rotation around the z-axis and the azimuthal angle \u03c6 gives the rotation around the y-axis (Fig. 8). In this case, the azimuthal angle \u03c6 takes random values between \u2212\u03c0/2 and \u03c0/2 on the grooved surface, corresponding to surface anchoring case (1). The helix vector at the wall Nw is along k and is hence inhomogeneous: Nw = Nw(x). In addition, \u03c6 is random and the helices are out-of-phase since \u03c6 = \u03c6(x). Figure 9a-c shows a time series visualization of the computed tensor field M(x, y, t) describing the propagation of order in the case where the azimuthal angle \u03c6 takes random values between \u2212\u03c0/2 and \u03c0/2 on the grooved surface"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003465_00423110600871533-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003465_00423110600871533-Figure1-1.png",
+        "caption": "Figure 1. A sketch plan \u2013 dimensions are not realistic \u2013 of a moveable frog (a) and its CAD model (b). Both views are set in a straight direction configuration.",
+        "texts": [
+            " The changing rail profile is taken into account via an interpolation process function of the distance. In practice, the handling of varying rail profiles consists of adding a dimension to contact tables. Guidelines for meshing are given. A case study is conducted. The benefit of the method is demonstrated as soon as it is required to compute stresses accurately. Keywords: Turnouts; Wheel\u2013rail contact forces; Multi-body simulations Moveable frogs are devices that allow vehicles to run on turnouts in high-speed conditions. Such a device is sketched in figure 1(a). Its design enables the wheel to roll on a continuous running surface. As a result, dynamic effects are relatively weak. Figure 1(b) shows a CAD model. The perspective has been cancelled to make it more informative: the longitudinal dimension is about 20 m long though the lateral one is about 0.1 m. The critical zone is the transition between the wing rail and the frog. A turnout\u2019s crossing has already been studied with multi-Hertzian methods [1], and various commercial packages possess functionalities that enable the study of it [2]. However, the results are usually expressed as forces or accelerations. In a rolling-contact fatigue context, it is often required to get more accurate results such as contact stresses",
+            " But, interpolating data tables is not exactly the same as building tables from interpolated profiles. Caution must then be exercised when defining the strip discretization in order to avoid unintended results because of the interpolation process. Furthermore, it is necessary to keep some continuity between strips: from figure 3(b), it is obvious that if strip j is on the tread in cross-section i, and on the flange in cross-section i + 1, the interpolated strip will be twisted leading to uncertain results. Apart from the gap between the wing rail and the frog toe (see figure 1), transitions between strips should be smooth, and the best strategy for avoiding poor results because of meshing consists of having the same strip following the wheel path in a given position, say the centred position. For the other strips, twisted transitions should be prohibited. In other words, strips from one profile to another should have the same angle. Prior to the simulation, several static analyses are made on each profile for a set of relative wheel positions, supplying locations where contact is likely to occur. Strips are concentrated on these locations and follow the centred wheel trajectory. This has the double advantage of minimizing interpolation artefacts and increasing accuracy as only the potential contact areas are finely meshed. 4. Case study 4.1 Model Figure 4(a) shows a mesh of a moveable frog, derived from a CAD model, similar to the one shown in figure 1(b). Strips limits are longitudinal lines, and cross-sections, transversal ones. Perspective effects have been intentionally removed, as the tread is \u223c0.1 m wide and the view spans along 20 m. Strip widths vary between 0.04 and 2 mm. Cross-sections are selected according to two criteria: on one hand, they are associated to varying rail profiles and, on the other hand, to locations where contact will exhibit jumps and transitions. The latter type of cross-section is selected during the quoted static analyses performed prior to the simulation. In the present case, the mesh is concentrated on relatively thin zones, as theoretical profiles are concerned. In worn profiles, contact zones would be more spread over the rail surface. 4.2 Results Figure 4(b) shows a typical result from a dynamic simulation: the black area is the rolling trace of the wheel on the rail when the vehicle runs straightforward (figure 1(a)) on a tangent track without additional irregularities. The model has 250 strips per cross-section and 16 crosssections. The ratio between the computer time and the real time is about 10 on a 2.5 GHz processor PC. Figure 5 shows at the top the Q vertical force (expressed in kN) applied on the rail when the frog is crossed. Figure 5 shows at the bottom, the maximum contact pressure pmax (in MPa). The head of the frog is indicated by a vertical line, and the jump between the wing rail and the frog by a dashed vertical line"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure1.16-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure1.16-1.png",
+        "caption": "Figure 1.16. Pitch triangle for a circular helix.",
+        "texts": [
+            " Hence, the speed also is constant: k \u00b7 t =cosy= A(R2w 2 + A2 ) - 112 , ( 1.92) ( 1.93) ( 1.94) which is a constant. Thus, the tangent at each point on a circular helix makes a constant angle with its axis. This result is more useful than ( 1.94) suggests. More generally, the tangent line property shows that when a helix is rolled on a plane, in one revolution its tangent traces a straight line that forms the hypotenuse of a right triangle of altitude p, the pitch of the helix, and base 2nR as shown in Fig. 1.16. This triangle is called the pitch triangle. When a particle moves on a circular helix, it rotates through an angle wt = O(t) about the helix axis, as described in Fig. 1.2, and it traces in the xy plane a circular arc of length RO(t) as it advances a distance z(t) along that axis. We see from the pitch triangle that tan y = 2nR/p = RO(t)/z(t). Hence, the axial advance along a circular helix is proportional to the angle of rotation about its axis, Kinematics of a Particle 39 and the invariant tangent angle y of a circular helix is determined uniquely by the ratio of the circumference of its base circle to its pitch: tan y = 2nRjp",
+            " The second example will demonstrate three methods that usc cylindrical coordinates to obtain the same problem solution in slightly different ways, one method being the easy direct application of ( 4.59) and ( 4.60 ). Afterwards, two further applications that employ cylindrical coordinates to create meaningful results will be presented. Example 4.10. An electron E moves in a preferred frame cP with a con stant speed v along a cylindrical helix described in cylindrical coordinates by the equations r =a, a constant, and 2nz = pl/J, where p is the constant pitch. [See (1.95) and Fig. 1.16] Find the absolute acceleration of the electron. Solution. To take advantage of the assigned constant speed condition, we first compute the velocity of E. With r =a, f = 0, and i = p~/2n, direct usc of ( 4.59) yields the absolute velocity of E: ( 4.64a) wherein c = 2na. Since the speed I vEl = v is constant, ( 4.64a) shows that the angular speed ~ has the constant value . v [ (p)21-l/2 \u00a2=- 1+- . iJ. c (4.64b) The acceleration may now be obtained easily from (4.60). Because Motion Referred to a Moving Reference Frame and Relative Motion 271 r=fP=z=O, (4"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002381_robot.2001.933052-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002381_robot.2001.933052-Figure5-1.png",
+        "caption": "Figure 5: Fitting into virtual joint model (n=3)",
+        "texts": [
+            " 5 Lumped State Estimation of Virtual Joint Model In this section, we describe a method to transform the distributed state variables of flexible links into lumped state variables of the virtual joint model. When we get the lumped state variables by the proposed method, it is also possible to identify physical parameters of the dynamic model. 5.1 Transformation into Lumped State Variables Here we set the position of virtual passive joints and link tip as the representative points of link i. ( t ) , . . . , zj3n+l(t) denote the position of representative points of link i. As shown in Fig.5, the representative point \u2018 p j ( t ) = [z&.. ,,Z@yj]T (3 = 2 , . . . , n + 1) is determined to locate on the link i shape function yz(z,, t ) . First, \u2018p1( t ) is given by ip,(t) = [ ] (9) then, i@j(t) ( j = 2 , . . . , n + 1) is determined as the point satisfying the following simultaneous equations. From these representative points, the virtual pas- sive joint angles 4,(t) are given by FFT niiulyzcr li=il The virtual passive joint velocity $,(t) = is estimated by numerical differen- The transformation matrix '+lT, from E, to E,+l [&I, &, "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003477_cnm.913-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003477_cnm.913-Figure5-1.png",
+        "caption": "Figure 5. A symmetrical dynamic system with two DOFs and its graph model: (a) planar frame; and (b) the corresponded mass\u2013spring system and its graph model.",
+        "texts": [
+            " Then the efficiency of group-theoretical approach is highlighted though comparison of the results to those of the algebraic methods, for problems with hyper symmetry. The motion associated with a vibrating mechanical system with n degrees of freedom (DOFs) can be expressed in terms of the well-known generalized eigenvalue equation Ku= 2Mu (14) in which M is an n \u00d7 n symmetric, positive semi-definite mass matrix, K is an n \u00d7 n, symmetric stiffness matrix, is a frequency and u is a corresponding mode shape. The mathematical model of a dynamic system consists of masses and springs. A simple symmetric mass\u2013spring system is shown in Figure 5(b), which can be assumed as the mechanical model of the free vibration of planar frame shown in Figure 5(a). The masses and the shear stiffness of each storey are presented in the figure. This is a problem with two DOFs (n = 2). In any mass\u2013spring Copyright q 2006 John Wiley & Sons, Ltd. Commun. Numer. Meth. Engng 2007; 23:639\u2013664 DOI: 10.1002/cnm system, the masses are connected by means of springs. As the mathematical model, a weighted graph can be defined as follows [11]. 1. The supports in the mathematical model are associated with neutral nodes in the graph. 2. For each mass, a node of graph is associated and its weight is taken as the magnitude of the mass",
+            " Comparing the correspondence between the stiffness matrix of the mass\u2013spring system and the Laplacian matrix of its graph model, one can obviously show the similarity of physical properties of the mass\u2013spring system and its graph model. More explanation in this regard can be found in Reference [11]. Forming the graph model for a vibrating system has many advantageous in recognizing the symmetry properties of a symmetrical system, especially in systems consisting of complex symmetries (see Section 5). The graph model of the first example is shown in Figure 5(b). If the mechanical system related to Equation (14) is involved in a symmetry group (say G), then group representation theory can be used to construct an n \u00d7 n orthogonal matrix T such that K\u0303 \u2261 TtKT and M\u0303 \u2261 TtMT (15) in which K\u0303 and M\u0303 have the same block diagonal forms. This reduces Equation (14) to a number of smaller, decoupled eigenvalue problems. It should be pointed out that the mass matrices in the mass\u2013spring problems are always diagonal, so the main focus here will be on the stiffness matrix",
+            " For this purpose, it is necessary to distinguish some of the symmetry operators of the system such as principal axis and reflection planes. The system of our example has only one non-trivial symmetry operation: y , which is a vertical plane. Therefore, the symmetry group of the system will be classified as C1v . Once the point group of system is identified, it is possible to find all of the symmetry operations of the structure; i.e. C1v \u21d2 {e, y} for this case. Let u denote the displacement vector of the system. As shown in Figure 5, the basis for space R2 of the problem will be u= (u1, u2)t. For discrete systems having translational DOFs only, it is possible to construct the i implicitly as follows. If u is an arbitrary displacement field, then each i is defined such that its action on the vector field ( iu) \u2018mimics\u2019 one of the symmetry operations in group G. Thus, iu will be obtained by affecting each symmetry operation of group G on the basis of V (selected before), and ( i ) will show the number of displacement alignments (ui ) that remain unaltered under this transformation"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003985_tro.2006.878956-Figure7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003985_tro.2006.878956-Figure7-1.png",
+        "caption": "Fig. 7. Vertex\u2013Edge case. Projection on the plane (dotted lines) of the contact manifold for two values of (left); an example of shortest path to a line (right).",
+        "texts": [
+            ", the minimization in (14) is performed over the set (which can also be empty) of RS paths landing inside the edge. All the remarks stated for (8) hold also in this case. 1) Handling Type-B Paths: Let y = mjx + nj be the equation of the target edge vj ; by using (9), the contact manifold between qi and vj is defined by Cij V E( ) = f jqi 2 vjg, and is represented as ijV E( ) = y mjx nj limj cos( + i) + li sin( + i) = 0 which represents a 2-D surface whose projection on the plane xy for a given is a line parallel to vj [Fig. 7 (left)]. Lemma 2: If a Type-B path is optimal for problem (ii), then: 1) the line D0 is perpendicular to the line vj ; 2) the contact point lies at the intersection of D0 and vj . Proof: The constraint f 2 Cij V E , expressed as ijV E( f) = 0, yields f = MT , where M = @ ijV E( f)=@ f is given by M = ( mj 1 limj sin( (tf ) + i) + li cos( (tf) + i)): Thus, we get the system 1 = mj 2 = 3(tf) = (limj sin ( (tf) + i) + li cos ( (tf) + i)) from which we get the following relations: 2 1 = 1 mj (15) 3(tf) = 1li sin ( (tf) + i) + 2li cos ( (tf) + i) : (16) Point 1 of Lemma 2 is proved by (15); by using (4), (9), and (16), we can compute the constant 3(t0) = 1qi (tf) + 2qi (tf) that yields 3(t) = 1(y(t) qi (tf))) 2(x(t) qi (tf)), which implies that the point qi at the end of the path must lie on the line D0. Thus, combined with the contact condition between qi(tf) and the target line vj , we prove point 2. Putting together the contact manifold constraint on the final state and the two transversality conditions, we get again a square system of equations for each path pk of Type-B. As an example, in Fig. 7 (right), we show the solution for the line of equation y = 0:1x+2 and the pair (li = 0:3; i = =4); the shortest path is of type l a l + =2s + e r + b , with a = 0:099, b = 0:449, e = 0:268, and total length L = a + b+ e + =2 = 2:386. 2) Handling Type-A Paths: Although the conditions derived in Section IV-A.2 are still valid for this case, they are no longer sufficient, since ijV E (Wp (0; b; e)) = 0 (17) is underspecified (one equation and two parameters). The missing information is recovered with the following geometric reasoning (see Fig"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001586_s0141-0229(99)00192-1-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001586_s0141-0229(99)00192-1-Figure2-1.png",
+        "caption": "Fig. 2. Layout of the screen\u2013printed sensors comprising three electrodes.",
+        "texts": [
+            " Polymer printing inks, also known as polymer thick film inks (Ercon, Wareham MA, USA), were applied onto the polyester support (thickness of 350 mm from Pu\u0308tz\u2013Folien, Taunusstein/Wehen, Germany) through printing screens (Farben\u2013Frikell, Berlin, Germany) by using an ATMA 600 HE screen-printing machine (E.S.C., Bad Salzuflen, Germany). Between the four subsequent printing steps, the struc- tures had to be heated at 80\u00b0C for about 10 min to dry off residual solvents and cure the patterned pastes. The sensor layout is shown in Fig. 2. Each transducer comprised a platinum working electrode with a diameter of 2 mm, a graphite auxiliary electrode sized 4 3 2 mm and an Ag/ AgCl pseudo reference electrode of the same size. The overall dimensions of each transducer was 20 3 52 mm. Sixty sensors were printed on one substrate sheet at the same time and separated afterwards. Before use the transducers were tempered again for 5 h at 130\u00b0C for additional curing. The ink pigment of the pseudo reference electrode is basically silver containing a small amount of silver chloride"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure2.7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure2.7-1.png",
+        "caption": "Figure 2.7. Consecutive finite rotations are not commutative, so they cannot be compounded by vector addition.",
+        "texts": [
+            " This means that the displacement of a rigid body due to successive finite rotations generally will depend upon the order in which the rotations are performed. On the other hand, consecutive infinitesimal rotations obey the commutative law of vector addition; hence, 96 Chapter 2 these are independent of the order of their execution. To visualize this fun damental difference in the properties of finite and infinitesimal rotations, let us begin by considering consecutive finite rotations of a rectangular plate with an edge OP on the x 2 axis and initially oriented in the vertical plane of a spatial frame 1/>, as shown in the diagrams of Fig. 2.7. If the plate shown in Fig. 2.7a is rotated first through a right angle about the x 1 axis and then through a right angle about the x 3 axis, while the same plate shown in Fig. 2.7b suffers the same rotations but in reverse order, we see at once that the final position of 0 P, indeed the orientation of the plate, is not the same. This confirms that the composition of successive finite rotations of a rigid body about concurrent axes is not commutative. The composition of finite rigid body rotations and other related theorems will be studied in the next chapter. Hereafter, we shall focus on the composition of infinitesimal rotations only. In the derivation of (2.19), we have naturally and correctly represented the infinitesimal rotation by a vector symbol L19 =A(} a, without regard for the noncommutative nature of finite rotations",
+            " Therefore, the screw axis passes through the center of rotation 0* whose position vector B* from the origin in ([> is given by We thus find that the given displacement may be reduced to a unique screw displacement consisting of a rotation of 15\u00b0 about an axis a= K through the point at B* together with a pure translation of the body through advance a distance of 2np = 96 em along the axis. (See Problems 3.41 and 3.42.) It was shown in Section 2.7 that successive finite rotations of a rigid body about concurrent axes are neither additive nor commutative. Therefore, as illustrated in Fig. 2.7, the displacement of a rigid body generally will depend upon the order in which the rotations are performed. We saw in a few earlier examples that when the successive rotations are easy to visualize, their com position may be readily written down by use of the direction cosines between the body imbedded axes in their terminal state and those of the spatial set with which they were coincident initially. Needless to say, it is not always easy to perceive the successive and the resultant effects of several complex rotations, so it will be useful to derive the rule for their composition"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002488_s0925-4005(03)00597-5-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002488_s0925-4005(03)00597-5-Figure2-1.png",
+        "caption": "Fig. 2. Schematic diagram of the frame on which the membranes are stretched inside the cuvette.",
+        "texts": [
+            "0159 g of the synthesized reagent in warm distilled water and diluted to 100 ml in a 100 ml standard flask. A Spectronic 20 (Genesys) UV-visible spectrophotometer was used to measure the absorbance of fix wavelength. UV-visible spectra were measured with a Jasco, Model V-570, double beam spectrophotometer. A Perkin-Elmer atomic absorption spectrometer (Model 2380) was used for determination of Ni(II) in hydrogenated vegetable oil. A homemade cell holder [12] was used with a special frame with a size of 8.5 mm \u00d7 35 mm, as shown in Fig. 2. The triacetyl cellulose film was hydrolyzed in order to de-esterify the acetyl groups and to increase the porosity of the membrane by treating the membrane in 0.10 M KOH solution for 24 h and then, the film was washed with distilled water. It was found that further activation processes [13] were not necessary. The cellulose membranes were immediately treated with a 1.0 \u00d7 10\u22123 M ACDA at 30 \u25e6C and in phthalate buffer (pH = 2.2) for 5 h. Then the membranes were washed with distilled water until there was no absorption at the wavelength of the ligand during rising",
+            " Then the sample was heated to 700 \u25e6C for 1.5 h in an electrical furnace. The remained ash was dissolved in 10 ml concentrated HNO3. The solution heated to dryness. Three consecutive additions of 10 ml distilled water were then made and each time the solution evaporated almost to dryness to eliminate excess acid. The residue was dissolved in 50 ml of water and filtered with filter paper (Whatman No. 1). The filtrate solution was used for analysis. The measurements were made on the membrane, which was stretched on a special frame (Fig. 2); with the size of opening of 8.5 mm \u00d7 35 mm. The control sample against which the measurement was performed consisted as cellulose film treated in the same way but without ACDA for study immobilization of ACDA on the film; whereas a cellulose film treated in the same way but without Ni(II) for nickel determination. The control sample was also stretched in the same way inside the cuvettes using a frame of the same size. Kastov and Tzankov [13] showed that only reagent with amino groups could be linked chemically with triacetyl cellulose"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000705_a:1007974811131-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000705_a:1007974811131-Figure1-1.png",
+        "caption": "Figure 1. MANUTEC r3 robot: (a) view; (b) kinematic scheme.",
+        "texts": [
+            " After linearizing Equation (85) in the vicinity of x = 0, it follows [16, 17, 40] that: x\u03072 = A(t)x2 +B(t)x1 + \u03b1(x2, x1, t) + \u03b2(x2, x1, t)\u00b5, (86) where A(t) and B(t) are 2m\u00d7 2m and 2m\u00d7 2(n\u2212m) matrices, respectively and \u03b1(x2, x1, t) = o(\u2016x\u2016) when (x) \u2192 0 and suptA(t) < \u221e since q0(t), q\u03070(t) belong to bounded regions. The sufficient conditions for the asymptotic stability of the system of differential Equations (85) are given by the same theorem [16, 17, 40] mentioned in Section 4. So the control laws (78)\u2013(80) ensure a desired quality of stabilization of the robot interaction force F0(t). At the same time, the stabilization of the robot motion q0(t) can also be achieved. In order to illustrate our new contact control concept, a simulation case study with a MANUTEC r3 [42] industrial robot (see Figure 1) has been performed [43, 44]. The parameter data for the industrial manipulation robot MANUTEC r3 [42] were taken from the catalogue. The parameters of deburring tool and process were used as in the real-system experiment [44] (see Figure 2). The process parameters and the parameters of the tool used in the simulation phase are given in Table I. A general model of impedance was adopted for the environment model, so that the dynamic environment (i.e., the worksurface) resisted the tool motion x(t) in all coordinate directions, including the tool rotation resistances"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000397_s0013-4686(98)00307-7-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000397_s0013-4686(98)00307-7-Figure2-1.png",
+        "caption": "Fig. 2. Cyclic voltammograms of (a) N,N 0-diphenyl-1,4-phenylenediamine and (b) [4-(phenylamino)phenyl]-1,4-phenylenediamine in TBABF4/diphenyl phosphate/acetonitrile solution at a scan rate of 50 mV/s.",
+        "texts": [
+            " Similarly to UV-vis-nir absorption studies, in situ Raman spectroelectrochemical studies were correlated with cyclic voltammetry and performed in the same electrolyte, using the same working, counter and reference electrodes used during the voltammetric measurements. In order to avoid degradation, the laser beam power was limited at 200 mW. By studying the oxidation and reduction of these two phenyl-end-capped oligoanilines in an acidic solution, the range of creation of the radical species can be established. The cyclic voltammograms of phenylend-capped dimer and tetramer in acetonitrile solution at a scan rate of 50 mV/s are shown in Fig. 2. Each voltammetric curve displays two well-de\u00aened reversible waves [8\u00b110]. Scanning in the anodic direction, the dimer shows two one-electron transfers at Epa1=300 mV and Epa2=600 mV vs Ag/Ag+ . The tetramer shows two two-electron transfers at Epa3=250 mV and Epa4=700 mV vs Ag/Ag+ . The model compounds of emeraldine salt, the phenyl-endcapped dimer radical cation and the phenyl-endcapped tetramer radical dication are generated at the potential of the \u00aerst anodic wave. The good reversibility, even after several hundred cycles, conjugated to the invariance of the ratio of the anodic/cathodic peak currents (ipa/ipc=1"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003049_b:tril.0000044509.82345.16-Figure12-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003049_b:tril.0000044509.82345.16-Figure12-1.png",
+        "caption": "Figure 12. Three-dimensional plot of mean shear stress versus pressure and temperature based on computed Hertz pressure and calculated average film temperature at each location (only data at \u2021 1.0 GPa).",
+        "texts": [
+            " Figure 11 shows three computed friction-coefficient maps based in the contact centre being in three different locations, at i \u00bc 10.8, 12.8 and 14.8 grid spacings respectively from the left-hand edge of the region mapped. (The friction coefficient outside of the Hertz contact region has been set to zero). Based on these maps, the contact centre was taken to be at the i \u00bc 12.8, j \u00bc 16.5 grid position in this case. Using this approach, the temperature and pressure at each grid point and each slide-roll ratio studied were determined. Figure 12 shows a 3-D surface plot of calculated shear stress versus film temperature (from equation 8) and computed pressure (from equation 9) obtained by combining results from all of the different slide-roll ratio tests carried out in this study. To obtain this plot, the pressure and film temperature range over which measurements were made was divided into a series of equally sized rectangular domains and all of the measured shear-stress values lying within each of these domains were averaged. This gave a matrix of mean shear-stress values at 0"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003285_0020718508961120-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003285_0020718508961120-Figure2-1.png",
+        "caption": "Figure 2. Example 1.",
+        "texts": [
+            " Ifn=O, thefunctionf(~)ismonotonicfor all t 2 t o ; if n is a finite integer N, I ,= [ th, co) and the function is monotonic for all t 2 t',. For n infinite, Q = l f , I:=(t i , tf) and Figure 1. Properties ofL(t). The difficulties encountered earlier in ordering functions in 9VIo,, , are not entirely avoided by confining our attention to the class A. As shown in the following example, if f , ( . ) , f 2 ( . ) E A, the ratio f,&, while well-defined for all t 2 to, t o E R+, may grow in an unbounded fashion along one sequence, tend to a constant along a second sequence and tend to zero along a third sequence. Example 1. (Fig. 2) Let ( t i ) , { t i ) and ( T ) be three unbounded sequences in R + such that t i c ti < t i + ,, T,=T, =0, T Z i + , =( t j+ , - t i ) + T Z i - , and T , i = ( t i - t j ) + T 2 i - 2 , where i~ { I , 2, ...I. D ow nl oa de d by [ T he U ni ve rs ity o f M an ch es te r L ib ra ry ] at 1 1: 10 1 0 O ct ob er 2 01 4 Stability analysis of adaptive systems Let f , ( . ) and f , ( - ) be two functions defined as Choosing the sequences { t i } and {ti} in such a manner that T + 1 lim -=a i - m we see that ( f l ( t ) / f2 ( t ) l tends to zero on the sequence { t i ) , to infinity on the sequence { t i ) and to unity on a sequence { t i ' ) where ti < t;',- c t i , t i c t';i < t i + t'; = t ; "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003502_095440904322804439-Figure16-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003502_095440904322804439-Figure16-1.png",
+        "caption": "Fig. 16 Boundary and displacement conditions for the press-\u00aet simulation",
+        "texts": [
+            " All the analyses for the press-\u00aet curve determination have therefore been carried out under the linear elastic hypothesis. Three different wheelsets have been examined, named Sao Paolo, United Kingdom and Fiat Ferroviaria, shown in Fig. 15. For each wheelset, a range of possible interferences has been considered, due to the machining tolerance of the axle and wheel. The press-\u00aet operation was simulated constraining one end of the axle in its longitudinal direction and applying a displacement at the wheel, as shown in Fig. 16. The sum of the reaction loads at the constrained end represents the press-\u00aet load, whose value is expected to increase with the wheel displacement, due to the increasing friction-resistant load. Proc. Instn Mech. Engrs Vol. 218 Part F: J. Rail and Rapid Transit F01203 # IMechE 2004 at HOWARD UNIV UNDERGRAD LIBRARY on February 28, 2015pif.sagepub.comDownlo ded from Several calculations were carried out in order to study the effect of the parameters under investigation. The local effects of the oil injection groove and that of the wheel seat chamfer are visible in Fig",
+            " The friction resistant load was then calculated independently from the integral of the friction tangential stresses, which, using Coulomb\u2019s law, was found to be proportional to the local contact pressure. The press load is \u00aenally given by the sum of the friction-resistant loads acting on each of the \u00aeve jth zones: P \u02c6 X j \u2026Lj 0 f \u2026 p\u2026z\u2020\u2020 p\u2026z\u2020 2pR dz \u20267\u2020 where f\u2026 p\u2020 is given by equation (4). To obtain the press-\u00aet curve, equation (7) is calculated for a variable contact length. This is made by considering the contact pressure, given by equation (5), to act only on the wheel length x (see Fig. 16) in contact with the axle. F01203 # IMechE 2004 Proc. Instn Mech. Engrs Vol. 218 Part F: J. Rail and Rapid Transit at HOWARD UNIV UNDERGRAD LIBRARY o February 28, 2015pif.sagepub.comDownloaded from Agreement between the press-\u00aet curves obtained by the FEM and those obtained by the simpli\u00aeed approach were very satisfactory for the wheelsets under investigation, as shown by the example reported in Fig. 22, where a good prediction of the experimental results can also be noted. Obviously, the simpli\u00aeed approach does not take into account the effects of the oil injection groove and that of the wheel seat chamfer, but they have been proved to modify the pressure distribution only locally, without any great in\u00afuence on the press-\u00aet curve and on the maximum press load in particular"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003688_tcst.2004.833622-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003688_tcst.2004.833622-Figure3-1.png",
+        "caption": "Fig. 3. Relative relation diagram in body coordinate.",
+        "texts": [
+            " Finally, to show that Theorem 1 is satisfied, we need to show that before entering ZEM phase, which has been proved in [1]. Therefore, the target-tracking objective during the flight before entering ZEM phase can be completed as derived by the aforementioned proof of theorem 1, but after the ZEM phase, the principal goal of bounded target interception as claimed by the aforementioned theorem can be achieved. Accordingly, the desired overall acceleration perpendicular to the LOS can be derived due to the result in Section III, which together with in the direction leads to the desired acceleration (see Fig. 3) of the missile, namely Hence, the resulting acceleration of the missile due to TVC and DCS together will lie on the plane . We note the following two facts: 1) projection of the desired resulting acceleration onto the axis of is simply and 2) projection of onto the axis perpendicular to the plane will be identically zero. Then, we can derive the following constraint equations of in the body coordinate frame as: By Cramer\u2019s rule, the acceleration [see Fig. 1(b)] generated by the divert control system, denoted as , can be derived as Remark 1: To avoid the singularity for computing the , we propose one possible solution to modify the force from the divert control system when the singularity condition \u201c \u201d occurs as follows: and if and if To validate the proposed sliding-mode guidance and autopilot of the missile system, we provide a realistic computer simulation in this section"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000540_0094-114x(95)00106-9-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000540_0094-114x(95)00106-9-Figure2-1.png",
+        "caption": "Fig. 2. Assembly of second platform point.",
+        "texts": [
+            " T H E O R Y OF T H E P R E D I C T O R A L G O R I T H M The base and the platform reference frames are chosen with their X and Y axes in the corresponding planes, such that b~ = [bix biy 01T (l) p~ =[p~ p~y 0] T (2) p~ = ~ + ~. (3) Selecting the first two direction cosines dlx and dly of the first leg vector (i = 1), we get the third direction cosine as As the solution for the negative value is just the mirror image of the solution with the positive value, we consider only the positive sign for the present. Hence, d,, = x/1 -- dl2x -- d~, (4) The location of the first platform point is then given by ?ix] L., J Now, B2P t =lp~ - b21, B2P2=S2 and PIP2 are all known and they form a rigid triangle [Fig. 2(a)] which ~'an r~tate about the line B2P, constraining the second platform point P2 to move in a circle. In the triangle B2Pj P2, a perpendicular f rom/ '2 on B2PI is drawn [Fig. 2(b)], the foot Ot and the length O1 P2 = r~ is determined from the following relations. B2P~ + B2P~ - P1P~ cos cq = 2B2P1 x B2P 2 sin ~ = 4 1 -- cos 2 cq B20, = B2P2 cos ~1 rl : 01 P2 = B2P2 sin ~1 The position vector of O1 is obtained as follows. A ot = b2 + B20, = ~ + B2OIB:PI (6) Next, we fit a triad .~ at the point O1 to act as a reference for the rotation of AB2PI P2 and hence of the point P2. The Z-axis of .~ is set along O, P~ and the X-axis is taken parallel to the base plane and perpendicular to 01P,, the Y-axis is automatically set by the right hand rule (~ = ~ x ~)"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000517_1616-8984(199607)1:1<1::aid-seup1>3.0.co;2-6-Figure1-9-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000517_1616-8984(199607)1:1<1::aid-seup1>3.0.co;2-6-Figure1-9-1.png",
+        "caption": "Figure 1-9. Surface plasmon resonance (SPR): resonance dependent on (a) angle of incidence and (b) wavelength of incident radiation.",
+        "texts": [
+            " The resonance condition is monitored by use of a position-sensitive linear photodiode array [294]. This principle is commercialized by Pharmacia. At present it is one of the most commonly used bioanalytical systems for examining affinity reactions. (b) Another possibility is to select out of white light the wavelength which fulfils the resonance condition [85]; by use of a diode-array spectrometer, the dip of attenuated reflection is recorded specrroscopically. Both principles are illustrated in Figure 1-9. 1.2 Principles of Optical Transduction 17 As in the case of intrinsic fiber optics, guided radiation can be used to couple via a buffer layer to a metal film and excite surface plasmons at the opposite interface. Suitable refractive indices for buffer layers and the correct wavelength guided in the waveguide are necessary to find a resonance condition. Such devices (slab waveguide-based SPR) can be used as sensing systems [359]. A schematic representation is shown in Figure 1-10. First attempts have been undertaken to achieve a multi-element surface plasmon resonance chip"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002746_0278364905060149-Figure26-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002746_0278364905060149-Figure26-1.png",
+        "caption": "Fig. 26. Measurement device for frame deformation.",
+        "texts": [
+            " In coordinate measuring machines, first a coordinate of the probe tip BPr , which is observed in the moving coordinate system \u2211 B , is calculated by the forward kinematics from the limb\u2019s lengths measured by the linear scale units. Secondly, the measured coordinate BPr is transformed to a coordinate B0Pr represented in the initial coordinate system \u2211 B0 by B0P r = B0P B + B0RB BP r. (7) In brief, all measured coordinates are rewritten in the initial coordinate system. at UNIVERSITY OF BRIGHTON on July 11, 2014ijr.sagepub.comDownloaded from Figure 26 depicts an example of the measurement method for the distance changes, u1 \u2212 u6, shown in Figure 23. The spherical joint is mounted on a joint support made of low thermal expansion cast iron. A Super-Invar rod is used as a spanner between the joint support and the surface plate. One end of the rod is connected to the surface plate by a flexure hinge. The other end is guided via a hole in a holder mounted on the joint support. A displacement sensor installed in the hole measures the displacement change in the rod end\u2019s surface in the longitudinal direction of the rod"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001042_robot.1994.350911-Figure7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001042_robot.1994.350911-Figure7-1.png",
+        "caption": "Figure 7 - A Grasp with Concurrent Forces",
+        "texts": [],
+        "surrounding_texts": [
+            "Figure\nEQUILIBRIUM\n4 - Classification of Planar Equilibrium Grasps\n4.1 Transformation of Stiffness Matrices When modeling multiple contacts, we use a leading subscript to denote the contact. For example, ' K A would be the curvature K A for the finger at the i f h contact and ioc is the fixed frame at the ith contact. Note further that Ax, and Ay, refer to the contact frame, but they can be related to other reference frames through appropriate transformations. We use a fixed frame 0 at an arbitrary point. If we let 'K, be the stiffness matrix from either Equation (1 1) or (17) (whichever is applicable), and (ldB Idy) be the coordinates of 0 as seen from loc, then the change in the wrench referred to the coordinate system at 0 for any infinitesimal rotation or displacement, due to contact i , is given by:\nwhere:\n. .\nAw0= iTT 'K, iT Axo (18)\ncos '@ -sin'@\nand l @ is the angle of rotation of the frame 0 with respect to the contact frame ioc (see Figure 3 for definition of a).\n4.2 Constant External Forces Consider the gravitational force on body B acting through the center of gravity. We define a coordinate system, oCg, fixed in space and coinciding with the center of gravity, where the axes are aligned such that gravity acts in the ycg direction. A rigid body motion of body B will not change the gravitational force, but will result in changes in the moment about the origin of ocg, given by:\n0 0 0 AxXca [ :Ica =[ ;g ; ;Ica[\";,] Or Awcg =% Axcg (19)\nwhere m is the mass of body B and g is the gravitational force. A transformation matrix TCg (analogous to T in (18)) can be employed to express this in the coordinate frame 0.\n4.3 Frictionless Planar Grasps Many of the most common equilibrium grasps are not form closed. To grasp a planar object with form closure\nrequires at least four frictionless point contacts. Whole arm manipulators are capable of establishing only a limited number of contacts with an object. And many, if not most, multifingered hands do not have enough fingers to effect a form closed grip. Here we establish criteria for stability of non-form closed equilibrium grasps (see Figure 4). But first we adopt an equivalent definition of form closure [ 141:\nDefinition: An equilibrium grasp with N unilateral contact wrenches is form closed ifand only $\n1) 3, > 0 such that W ch = 0 (where ch is a\n2) W is full rank vector with elements chi )\n(20)\nNote that condition 1 is a stronger condition than that required for equilibrium since it requires C i > 0 for all i . Non-form closed equilibrium grasps must fail to meet either conditions 1 or 2 above. If an equilibrium grasp is not form closed, we construct a submatrix W* from W as follows. In the case where gexf = 0 in Equation (1), W* consists of the subset of wrenches, wi, of W which satisfy condition 1 in Definition (20). In the case where gext # 0 , W* is formed from the union of the subset of wrenches, wi, which satisfy condition 1 and the subset of wrenches, wi, with a non zero intensity in the equilibrium equation W c = gexf (Eqn 1).\nWe consider two cases. First, let gexf = 0. For non-form closed equilibrium grasps, the wrench submatrix, W*, cannot be full rank. This implies the lines of action of the wrenches in W* either meet at a single point, are parallel to each other, or are collinear. Next, consider the case where gext # 0. In this case, given a non-form closed equilibrium grasps, W* may be full rank. If W* is not full rank, the lines of action of the wrenches in W* either meet at a single point, are parallel to each other, or are collinear. Therefore, all non-form closed equilibrium grasps can be grouped into four categories: 1) Grasps in a external force field (such as gravity) where the Rank(W*) is full.; 2 ) Grasps where all wrenches in W* (including gravity) are concurrent (intersect at a single point), 3) Grasps in which all wrenches in W* (including gravity) are collinear (Rank(W*) = 1); and 4) Grasps in which all wrenches in W* (including gravity) are parallel, but not collinear. The grasp categories can be differentiated by looking at W* (see [5] and Figure 4).\nThe following four theorems establish stability criteria for all of the categories of non-form closed planar grasps, with frictionless point contacts.\nTheorem 1: A planar equilibrium grasp with collinear wrenches (including gravity if non zero) is stable if\n2825\n1-",
+            "Der ~ ' T T i ~ , IT+ T T ~ K ~ ~ T ~ ~ ~ and z-%&iF are both negative, and unstable if either one is positive. I\" i s 1 i=IIKA+'K,\nTheorem 2: A planar equilibrium grasp with N parallel contact wrenches is stable (unstable} if fWi~,, is negative (positive}. i = l KA+'KB\nTheorem 3: Any planar equilibrium grasp, in which all of N contact wrenches (and gravity ifnon zero} are concurrent\nnegative (positive}. Here ir is the signed magnitude of the vector from contact i (the center of gravity of the body, in the case of rcg) to the point where all forces intersect, positive if the vector is in the same direction as the ith normal force, (gravity, in the case of rcg} and negative if it is in the opposite direction.\nTheorem 4 Any planar equilibrium grasp composed of frictionless point contacts in which W* has full rank is stable, except grasps in which one of the contacts in W* is a convex vertex contacting a convex vertex.\nTo prove these theorems, consider the composite stiffness matrix, &,, obtained by summing the contributions\nfrom each 'K, (and IC,-,) after referring it to the coordinate system 0. The system is stable if the eigenvalues of &, are strictly negative and unstable if at least one eigenvalue is positive. Thus stability implies that the determinant of each principle minor of -KO is positive. This leads directly to Theorems 1-4. Details are furnished in [ 5 ] . Theorem 1 can be used to establish a number of special case results:\nLemma 1: A planar equilibrium grasp with two opposed collinear fn'ctionless contacts (in the absence of gravity} is\n2 iKA ' K , ;=I K,+ K R -are both negative, and unstable if either one is\npositive. Here r is the signed magnitude of the vector from contact two to contact one, positive if the vector is in the same direction as the second n o m 1 force, and negative if it is in the opposite direction.\nLemma 2: An equilibrium grasp with a single frictionless contact plus gravity is stable if K A K , and - K A (rKB - 1) are both negative, and unstable if either one is positive. Here r is the signed magnitude of the vector from the center of gravity to the contact, positive if the vector is in the same direction as the gravitational force and negative if it is in the opposite direction.\nLemma 3: Given an equilibrium grasp with two frictionless contacts, all grasps of the form in a} Figure 8a ( ~ K A , lKg, 2 K ~ , 2Kg > 0) are unstable. b} Figure 86 ( I K A , ~ K A >O , KB, 2Kg < 0) are stable. c) Figure 8c ( ~ K A = 2 K ~ = K A < O , ~ K B = 2Kg =Kg>O}\nare stable if r e 2 or r > - 2 , and unstable if K B K.4 - 2 c r < -2 ( r is as dejked in Lemma I} . K B KA\n4.4 Frictionless Grasps of Polygons The above theorems apply to polygons. For contacts on the edges of the grasped polygon, Kg = 0. For contacts on the vertices of the polygon K , -) fm, where K , + +m for a \"convex\" vertex and K, + --oo for a \"concave\" vertex. In these cases each term ( K A , K B , and r) is evaluated as it\napproaches the limiting value (e.g. Lim = K~ 1.\nExample 1: Consider the grasp as shown in Figure 8d. In this case, I K A = 0.5, ' K g = 0, 2 K g = 0, 2 K ~ = 0.5, 3 K ~ = -0.5 cm-', 3Kg = 00, l r = 2r = 5 cm, 3r = -3 cm, and rcg = 4.5 cm. The forces are IF = 10N, 2F = 10N, 3F = 15N, and mg = 4.3N. Applying Theorem 3, we see the grasp is stable\nK , + w K A + K,\nsince 5: ('riKB - l)(iriKA + F, + mgr, = -98.15 < 0. i=l 'K,+'K,",
+            "Lemma 4: A equilibrium grasp with N frictionless point contacts on the edges of a convex polygon (in the absence of gravity) is stable if Rank(F*) = 2, where F* is a 2x.N matrix composed of the force vectors with non zero intensities (the first two rows of W*). See [ 5 ] for aproof.\n4.5 Frictional Grasps If we assume that the frictional forces are bilateral forces and that the frictional constraints are satisfied, all equilibrium grasps are \u201cform closed\u201d and therefore stable. For example, consider a grasp with two frictional contact points (under the assumption that the frictional force is strictly less than the maximum allowable frictional force). When the force displacement relations are added together and the results analyzed, we find that all equilibrium frictional two-contact point grasps are stable. A grasp with only one frictional contact does not have this property, however, and the following lemmas address these cases:\nLemma 5: An equilibrium grasp with one frictional contact opposing a gravitational .force is stable (unstable) if ( K A + K,)r+cos@ is negative (positive). Here r is us defined in Lemma 2, and 0 is the angle of rotation of contact frame 2 with respect to contactframe 1 (see Fig. 3) .\nJ.emma 6; An equilibrium grasp with one frictionless point contact and one .frictional point confucf (without gravity) is\n(positive), where the frictionless contact is contact 2, r is as defined in Lemma 1, and 0 is us defined in Lemma 5.\n5.0 Discussion In this paper, we categorize all planar equilibrium grasps, and establish results which can be used to determine the stability of virtually all planar grasps (including indeterminate grasps) by examining the eigenvalues of the combined stiffness matrix. The exception to this is the case where one of the eigenvalues becomes zero, when Theorems 1, 2, and 3 cannot be used because neither the criteria for stability or instability is satisfied. Note that Trinkle [14] shows a result similar to Theorem 4, but is limited to contact between verticies and suaight edges.\nAlthough most of our results deal with frictionless contacts (which in actuality do not exist), this does not imply our results are meaningless. In fact, the results are extremely useful because they can be used to predict which grasps are stable due to the geometry of the grasp, and thus do not rely on friction for stability. By grasping an object such that the frictionless contact model is stable, underestimating of the coefficient of friction will not potentially result in the object being dropped. Friction can only enhance the stability of the grasp. Also note that the general approach in this paper is easily applied to spatial grasps (see [SI for details).\nIt is interesting to note that the stability of non-form closed grasps with frictionless contacts has much in common with the idea of second order mobility, as proposed by Rimon and Burdick [ l l ] . However, it is incorrect to assume equivalence between second order immobility and stability. In general they are not the same. An exception to this is a two finger grasp without gravity, where the results in [12] are essentially equivalent. It can be speculated that the special case of a second order mobility analysis of a statically determinate frictionless grasps, without gravity, may give the same result as our stability analysis.\nFinally, we close by pointing out that in most grasping situations, stability is a much more important criteria than form closure, even though form closure has received far greater attention. Indeed, often the only reason a researcher tries to obtain a form closed grasp is that it is stable.\nAcknowledgement This work was supported by NSF Grants MSS9157156 and BCS 92-16691. ARPA Grant N0014-88-K-0632 and NATO grant No. 0224/85.\nReferences [ l ] M. Cutkosky and I. Kao, \u201cComputing and Controlling the\nCompliance of a Robotic Hand,\u201d IEEE Trans. on Robotics and Automuion, Vol. 5 , No. 2, pp. 151-165, April 1992. [2] M. Cutkosky and P. Wright, \u201cFriction, Stability and the Design of Robotic Fingers,\u201d Int. J . of Robotics Research, Vol. 5 , No. 4, pp. 20-37. Winter, 1986. [3] H. Hanafusa and H. Asada. \u201dStable Prehension by a Robot Hand with Elastic Fingers.\u201d Robor Morion Planning and Control, ed. M. Brady. Cambridge: MIT Press, 1982. (41 W. Howard and V. Kumar. \u201cA Minimum Principle for the Dynamic Analysis of Systems with Frictional Contacts,\u201d IEEE Cor$ on Robotics and Automuion, pp. 437-442, 1993. [SI W. Howard and V. Kumar, \u201cOn the Stability of Grasped Objects,\u201d Submitted to IEEE Transactions on Robotics and Automarion, Feb. 1994 [6] M. Mason and 1. Salisbury, Robot Hands und the Mechanics of Manipulation Cambridge, MA: MIT Press, 1985. [7] B. Mishra and N . Silver, \u201cSome Discussion of Static Gripping and Its Stability,\u201d IEEE Transacrions on Systems, Man, and Cybernetics, Vol. 19, No. 4, pp. 783-796, July/August 1989 [8] D. Montana, \u201cThe lnematics of Contact and Grasp,\u201d Int. J. of Robotics Research, Vol. 7, No. 3, pp. 17-32, June, 1988. [9] D. Montana, \u201cThe Conditions for Contact Grasp Stability.\u201d IEEE ConJ on Robotics und Automation. pp. 412-417, 1991. [ I O ] V. Nguyen, \u201dConstructing Stable Grasps,\u201d Int. J . of Robofics Research, Vol. 8, No. I , pp. 26-37, February, 1989. [ 111 E. Rimon and J. Burdick, \u201cTowards Planning with Force Constraints: On the Mobility of Bodies in Contact,\u201d IEEE Con5 on Robotics and Automation, pp. 994-1000, 1993. [ 121 E. Rimon and J . Burdick, \u201cA Configuration Space Analysis of Bodies in Contact - Part 2: 2nd Order Analysis,\u201d Submitted to Mechanism and Machine Theory, 1993. [13] N. Sarkar, \u201cControl of Mechanical Systems with Rolling Contacts: Application to Robotics,\u201d Ph.D. Thesis, University of Pennsylvania, 1993. [ 141 1. Trinkle. \u201cOn the Stability and Instantaneous Velocity of Grasped Frictionless Objects.\u201c IEEE Transacfions on Robotics andAutomaiion. Vol. 8. No. 5 , pp. 560-571, October, 1992. [ 151 J . Trinkle, A. Farahat. and P. Stiller. \u201cFirst-Order Stability Cells of Frictionless Rigid Body Systems,\u201d Conditionally accepted by IEEE Trans on Robotics & Automation, Oct. 1993."
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0000885_s0263-8223(00)00103-3-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000885_s0263-8223(00)00103-3-Figure2-1.png",
+        "caption": "Fig. 2. Production of the composite beam.",
+        "texts": [
+            " Production of the composite beam The composite beam consists of high-density polyethylene as a thermoplastic matrix and steel \u00aebers. Polyethylene is placed into the moulds and they are heated to 190\u00b0C by using electrical heater. Subsequently, the material is held for 5 min under 2,5 MPa at this temperature. The temperature is decreased to 30\u00b0C under 15 MPa pressure in 3 min, and a polyethylene layer is manufactured. The steel \u00aebers are placed between two thermoplastic layers and processed in the same way described above, as shown in Fig. 2. Thus a composite layer is obtained. The thickness of the composite layer is 4 mm. The composite beam is manufactured from two composite layers by using the same way described above. The mechanical properties and the yield strengths of the beam are measured by using strain gages and the Instron tensile machine, as given at Table 1. The yield strengths of the beam in the second and third principal material directions are the same due to the same alignment of the \u00aebers in these directions. As a result, Y Z and p X 2 1 X 2 1 Y 2 \u00ff 1 Z2 \u00ff is equal to 1"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001835_s0301-679x(02)00024-5-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001835_s0301-679x(02)00024-5-Figure2-1.png",
+        "caption": "Fig. 2. Point loading of elastic half-space.",
+        "texts": [
+            " The load-carrying capacity is given by W\u0304 pr\u03042 pp\u0304p 2p 0 1 r\u0304p p\u0304r\u0304dr\u0304dq (5) If an eccentric load acts on the x-axis of the bearing surface only, the moment load-carrying capacity is given by M\u0304 M\u0304y 2p 0 1 r\u0304p p\u0304r\u03042cosqdr\u0304dq (6) The loading point RL is expressed by R\u0304L M\u0304 / F\u0304 (7) where F\u0304 W\u0304 is given for the static characteristics of the bearing. The frictional torque is written as T\u0304 1 2p 2p 0 1 r\u0304p ( w\u0304 3 r\u03043 h\u0304 h\u0304r\u0304 \u2202p\u0304 \u2202q)dr\u0304dq (8) The total power loss \u2014 the sum of leakage and frictional loss \u2014 is given by L\u0304 L\u0304Q L\u0304T p\u0304sQ\u0304out T\u0304w\u0304 (9) . Fig. 2 shows the elastic model for the pad of an elastic half-space. On the x\u2013y plane, the elastic deformation \u03b4e at point B, due to the effect of pressure applied at point A, is written as de (1 n2) pE pr1dr1dq L (10) where L (r2 r2 1 2rr1cosq)1/2 is defined. If the pressure acting on point A is assumed to distribute uniformly around the band-land of the radius r1, the elastic deformation at point B is expressed by [14,15] he (1 n2) pE pr1dr1dq( 1 L1 1 L2 % 1 Ln ) (11) Then, from Eqs. (10) and (11), the elastic deformation \u03b4e at point B, based on the effect of pressure applied at point A, is rewritten as de 1 /L (1 /L1 1 /L2 % 1 /Ln) he (12) where he is given in Eq"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003726_004051758805800306-FigureI-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003726_004051758805800306-FigureI-1.png",
+        "caption": "FIGURE I . Fragment-simulating projectile, 0.22 calibcr. steel.",
+        "texts": [],
+        "surrounding_texts": [
+            "mode of penetration of nylon ballistic panels by fragment-simulating projectiles is a cutting, shearing mechanism: Shear forces required for yarn failure are usually less than tensile forces. Penetration is always at a slight angle, with the 90\" edge of the FSP leading. Many yarn ends terminated in a smooth surface (in a tensile break the filaments break at random places along the yarn). Penetration of the cloth in certain expenmental situations occur in a manner precluding tensile failure. The force required for nylon or Kevlar yam failure is less for a rectangular leading surface than it is for a chisel-shaped leading surface.\nThe tensile work done in breaking nylon filament is known to be velocity dependent [3,4,6]. In Part I of this investigation [ 5 ] , we reported that the work of penetration per interior layer does not vary significantly with the velocity of the fragment-simulating projectile (FSP), provided the mechanism of penetration remains the same. This difference in behavior is the subject of this report. (Part I includes a section on terminology,)\nThe FSP penetrates the nylon ballistic panels by a combination oftensile and shear modes. It may be that the tensile mode is not involved at all. The fact that there is cone formation, the cross patterns at the holes at all layers, and the overlapping of the ends of the (same) yams at the holes refutes this possibility.\nCosgren el al. [ I ] found that the work of tensile failure of nylon 66 filament is velocity dependent from quasi-static conditions UP to about 210 m/s. The ballistic velocities in this study vary from about zero (exiting velocity for VSO determinations) to lo00 m/s. Also we have shown in Part I that penetration proceeds through the intenor layers in two stages, the first of which involves shallow cone formation. Obviously from the trigonometry of the situation, the yams involved in the cone are being extended at a much lower velocity than the speed of the projectile. Thus, there is a definite overlap and no apparent reason why the work of tensile failure should not also be velocity dependent at the higher velocities. If most of the work of yam failure were tensile work, then ballistic penetration\nshould be strongly velocity dependent, and a11 of the plots of Vs? versus layers, as shown in Part I, should be nonlinear. Since this is not the case, we conclude that the work of penetration is weakly (within experimental error) velocity dependent.\nWe have now reconciled one problem but created another. What then is the major mode of penetration? What remains is a cutting, shearing mechanism.\nIs shear failure of the yarns velocity dependent? There is a basic difference between tensile and shear failure. Tensile failure depends on the propaption Of the strain wave to the yam breaking point (a minimum), both of which are velocity dependent. Under shear conditions, the yarn fails at the place where the shear is applied regardless of the velocity of the missile. Consequently, an average value of the shear strength is always involved. We believe that there is a sufficient difference in the manner of failure to accommodate the postulate that shear failure is velocity independent, at least at ballistic velocities.\nEvidence for the Cutting, Shearing Action of FSPs\nThere is considerable evidence to support the hYpothesis that a cutting, shearing action at the 55' and 90' edges, R1 and R2 ofFigure 1, is important in penetration. The missile is certainly going to penetrate the panel in the easiest way possible, that is, the one requiring the lowest force. Table 1 shows some tensile and shear data taken from Finlayson [2].\nAccording to the Dupont handbook On Zflel (nYIon), the tensile strength of nylon is about 12,000 PSI, I This paper reports research sponsored by U.S. Army Natick Research, Development and Engineering Center and h a k n assigned TP-2467b in the series of papen approved for publication.\n0040-5 175/88/58m3-161$2.00 Q Textile Research'Institute\nat Elsevier Scirus on June 5, 2015trj.sagepub.comDownloaded from",
+            "I62 TEXTILE RESEARCH JOURNAL\nTAME 1. Shear and tensile tcnacities for several yams.\nShear tenacity. Tensile tenacity, &denier ddenier\nFortisan ti 1 .17 8.00 Nylon I .27 4.45 Linen 0.92 2.93 Vinyon 1.10 3.08 Viscose 0.12 I .98 Cuprammonium 0.715 2.00 Silk 1.31 3.50 Cotton 0.96 2.63 Celanese 0.65 I .32\nwhereas the shear strength is about 9,600 PSI [7]. Obviously, where both shear (over edge R2) and tensile conditions (over edge R I ) exist and the forces are the same (which appears to be true for this study), the materials in Table I will fail by shear first. FIGURE 3. This second layer shows more clearly that the initial\npenetration is at the 90\" leading edge of the FSP. For isotropic materials in the elastic range,\nI.:=2G(ItNU) ,\nwhere E is the tensile modulus, G is the shear modulus, and NU is Poisson's ratio. Even under theoretical conditions, the tensile modulus is twice the shear modulus. Drawing a polymer yarn generally increases both tensile and shear strength, but increases the former much more (21.\nPhotographs of a 0.22 caliber FSP, which was fired at 0\" obliquity and caught inside a nylon panel, are given in Figures 2, 3, 4, and 5 . All of these figures are from a I2 layer, standard weight, ballistic nylon panel. The photographs show the various stages of penetration of an FSP through a layer of a nylon ballistic panel. These were obtained by removing intact layers of cloth until the leading surface of the missile first appeared, A picture was taken, a layer of cloth was removed, a picture was taken, etc. As Figure 2 shows, the 90\"\nFIGk,RE 4. The { h i d layer again shows that yams crossing the 90\" leading edge of the FSP fail first.\nat Elsevier Scirus on June 5, 2015trj.sagepub.comDownloaded from",
+            "MARCH 1988 I63\n(sharper) edge, R2, appears first, and the projectile a p pears to be at a slight angle (about 15\") to its line of flight. Figure 5 shows that the last yams to yield are those crossing the 55' edges, R 1. These statements have been true for all the arrested FSPs in nylon panels we have examined. In a plot of slope B2 versus obliquity, there is a minimum in the curves for the FSPs at about I5O, which agrees with the observation above.\nFor a projectile with smooth, well-rounded surfaces, there is no doubt that penetration is primarily if not entirely by tensile failure. For FSPs, however, there are several disquieting observations about the ballistic panels, which make penetration solely via tensile strain a rather untenable premise: (a) Figure 6 shows a picture of the cross pattern at a hole in an interior layer of a ballistic panel. Obviously the cross pattern, representing the degree of strain around a hole, is of unequal radius. This indicates that for some inexplicable reason, all the yarns in one direction failed sooner than the cross yarns under the same stress. In some cases there is no strain evidence that the yams that failed were subjected to any tension at all. (b) During a microscopic examination of the holes, we found that many yam ends had smooth surfaces-hardly tensile breaks. (c) For the intenor layers, which are penetrated over a considerable range of velocities, the yarns apparently fail aRer an extension of about 3 mm. Yet many of the yarns that failed in the final layer ( 1) showed much greater extensions. It does not appear reasonable to assign this increase solely to a velocity change in view of the behavior of the interior layers over a range of velocities. Consequently, it appears that the yams that failed in the interior layers were capable of further extension and had not necessarily reached their ultimate strength.\nDuring some preliminary ballistic studies, 1 -inch squares of nylon cloth were interspersed between the layers of cloth of a ballistic panel to see if the squares would act as a drag on the FSPs and, on a weight basis, disproportionately increase the Vs0. Figure 7 shows a picture of a hole in one of these squares aRer firing the 0.22 caliber FSPs at 0\" obliquity. The hole is about 3 mm from the edge of the square. The yarns bordering the hole show no evidence that they have been subjected to tension during penetration. Examination of\nat Elsevier Scirus on June 5, 2015trj.sagepub.comDownloaded from"
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0001078_s0167-6911(02)00185-8-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001078_s0167-6911(02)00185-8-Figure1-1.png",
+        "caption": "Fig. 1. Transversal trajectory of a hybrid system with di;erential inclusions.",
+        "texts": [
+            " Hence, we obtain the estimate \u2016\u2019j(3) \u2212 \u2019(30)\u2016ac6 5(eKT + e2KT + 1)6 35e2KT ; \u2200j\u2208N: (6) Assumption 4. The automaton H satis4es the following: (a) The inclusion x\u0307\u2208Fl(x) at each location l satis4es Assumption 3. (b) For each e\u2208E; ge is either a closed; n-dimensional topological manifold with boundary; or an embedded (n\u2212 1)-dimensional C1 submanifold. (c) re is a lower semicontinuous reset map from Rn to the closed; convex subsets of Rn. Remark 5. Assumption 4(c) makes possible the use of Michael\u2019s selection theorem [1]. The following de4nition is essential for our main result. See Fig. 1. De#nition 6. Let e=(l; ; l\u2032) and x(t); be a solution of x\u0307\u2208Fl(x) de4ned for t \u2208 [t0; t1]; with t0 \u00a1t1 and such that x(t1)\u2208 ge. We say that x(\u00b7) is transversal to ge at x(t1) if it ful4lls the following requirements: (1) If ge is an (n \u2212 1)-dimensional submanifold we require that the solution x(t) of x\u0307\u2208Fl(x) can be suitably extended on some interval (t1; s1]; s1 \u00bft1 in a manner that for some open neighborhood V of x(t1) and local coordinates u=(u1; : : : ; un) centered at x(t1) and mapping V homeomorphicaly onto some open neighborhood of Rn; and satisfying un(V \u2229 ge) = 0; x\u0307(t) \u00b7 \u2207un(v)\u00bf1; \u2200v\u2208V; a:e: on {t: x(t)\u2208V}: (2) If ge is a topological n-manifold with boundary we require that the solution x(t) of x\u0307\u2208Fl(x) can either be continued on some interval (t1; s1]; s1 \u00bft1 in a manner that x(t)\u2208 ge\u25e6; \u2200t \u2208 (t1; s1]; (7a) or there exists s0 \u2208 [t0; t1) such that x(t)\u2208 ge\u25e6; \u2200t \u2208 [s0; t1): (7b) Note that if x(t1) is an interior point of ge then (7b) is trivially satis4ed"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002607_icsmc.1989.71346-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002607_icsmc.1989.71346-Figure1-1.png",
+        "caption": "Figure 1 - Hardware Layout",
+        "texts": [
+            " -A six degree of freedom, force/torque sensing, sensor ball hand controller built by the German Space Agency DFVLR was used as the input device for the tracking experiments. The DFVLR sensor ball can receive three force, or translational, commands and three torque, or rotational, commands and generate corresponding output. Its internal measuring system generates a new set of output data every four milliseconds independent of the rate of requests for data. Each request for data to the ball is acknowledged immediately to keep the response time as low as possible.[4] Figure 1 shows a drawing of the computer hardware and hand controller layout. I 1 EXPERIMENTAL DESIGN The test subjects tracked the dark gray target ball with a white ball that they controlled with the six dof hand controller. The controlled ball was exactly the same shape and dimensions as the target ball. The target ball would move independently and randomly with a cutoff frequency of .025 Hz., providing a relatively slow target movement. Rotational disturbances were limited to a few degrees, preventing the rotation of the cross hairs from going beyond 45 degrees from the center in either direction",
+            " ' Movement could occur in all six degrees of freedom: xtranslation, y-translation, z-translation, x-rotation, y-rotation, and z-rotation. This movement could occur in one dof during a trial or in any combination of the six dof. The coordinate system used in the experiments consisted of translational movement along the horizontal or x-axis, the vertical or y-axis, and the axis coming out of and into the display or the z-axis. These axes are shown in relation to the display and to the hand controller in figure 1. Rotations about each one of the axes was also possible, with x-rotation simulating a pitch movement, y-rotation simulating yaw, and z-rotation simulating roll. The software recalculated the relative positions of the target and controlled ball at a sampling rate, or frame rate, of 10 Hz. At each sampling instance, a root mean square error (rmse) was calculated for each of the degrees of freedom that were operating. This error reflected the deviation in a particular dof between the psitiordonentation of the target ball (desired position) and the position of the controlled ball"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure4.27-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure4.27-1.png",
+        "caption": "Figure 4.27. An epicyclic gear train assembly.",
+        "texts": [
+            " An epicyclic gear train is a system of gears and shafting in which at least one gear moves around the circumference of other fixed or moving gears. The planet gear P 2 shown in Fig. 4.12 rolls around the circumference of gear P 1 , and so the planetary train studied earlier is an epicyclic gear train. An epicyclic arrangement permits an unusual assembly of gears and shafting and it sometimes provides an uncommon angular velocity ratio while maintaining relative simplicity of the design. The motion of the epicyclic gear train shown in Fig. 4.27 will be studied here. The train consists of three bevel gears A, C, and D and two spur gears B and E arranged so that the shaft of B is concentric with the output shaft of gear D. The gear A is fixed in the machine frame 0 = { F; Ik }. The spur gear E is fixed to the input shaft and drives the train through the power gear B which is cut from a special casting that serves as the bearing housing for the epicyclic gear C and as a bearing for the power gear assembly consisting of B and C. The power gear assembly revolves around the concentric supporting output shaft with a specified total angular velocity ro 10 = wi in the machine frame, as indicated in Fig. 4.27. We wish to determine by vector methods (a) the angular velocity of the epicyclic gear C relative to the power gear B, (b) the absolute angular velocity and angular acceleration of C referred to frame I = { B; ik} fixed in B, and (c) the angular speed of the output gear D. The design, as shown in Fig. 4.27, requires that the pitch angles \u00a2 and () satisfy 1/J + 28 = n/2. (4.84) Motion Referred to a Moving Reference Frame and Relative Motion 291 Solution: Part (a). Let frame 3 = { D; nk} be fixed in the output gear D whose absolute angular velocity is denoted by ro30 = .Qn 1 = .QI; and let frame 2 = { C; ek} be fixed in the epicyclic gear C, as shown in Fig. 4.27. Then the angular velocity of the epicyclic frame 2 relative to the power gear frame 1 may be written as ro 21 = w21 e2 = w 21 i2 , and the total angular velocity of C in the machine will be given by (1)20 = 0}21 + (1)10\u00b7 (4.85a) In addition, the three absolute angular speeds of gears B, C, and D are related through the rolling constraint imposed by the gear teeth. Of course, the point Q on gear C is turning relative to the rotating frame 1 in gear B. However, since the reference frames are fixed in the ge:ars, their material points have no motion relative to these frames"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001603_elan.1140071203-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001603_elan.1140071203-Figure1-1.png",
+        "caption": "Fig. 1. Schematic diagram of microdialysis probe: (A) fused silica tube (0.d. 150pm, i.d. 75pm); (B) fused silica tube (0.d. 470pm, i.d. 3 5 0 ~ m ) ; (C) dialysis fiber (0.d. 220pm. i.d. 200pm); (D) stainless steel tube (0.d. 440pm, i.d. 220pm).",
+        "texts": [
+            "0, borate buffer (500 pL) containing acetylcholine esterase (4.6 U) and choline oxidase (0.7U) or choline oxidase (0.7U) and EIe:lectrounaly.~i.s 1995, 7, No. 12 ;i> VtCH Vcrlu~.sgC.FSesC.FSell.sthufi tnhH, 0-69469 Weinlvinz, 1995 1040-0397~YSJI212-I 114 3 5.0Oi.25J0 1115 On-Line Amperometric Assay of Glucose, L-Glutamate and Acetylcholine catalase (3000 U). Each of four enzyme reactors was thoroughly washed with the same buffer used for the immobilization. 2.4. Construction of Microdialysis Probe Microdialysis probes were of a design shown in Figure 1, constructed by inserting a regenerated cellulose dialysis fiber (0.d. 220 pm, i.d. 200 pm; molecular cut-off approximately 50000) into a fused silica tube (0.d. 470 pm, i.d. 350 pm). The fiber was glued in the interior of the fused silica tube, leaving an active length of 3mm, and the fiber tip sealed with epoxy cement. Another two fused silica tubes (0.d. 150 pm, i.d. 75 pm) were also inserted as shown and served as the inlet and outlet. Two fused silica tubes were glued in the interior of the stainless steel tubes (0"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure3.7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure3.7-1.png",
+        "caption": "Figure 3.7. Sketch of the panel orien tation in cp after a 60\u00b0 rotation about a= -i2 \u2022",
+        "texts": [
+            " It must be born in mind, however, that in the design of the mechanism to move the panel to the terminal state found above, the actual rotation may be done in an infinite variety of ways. There are infinitely many combinations of rotations whose resultant leads to the same rotation matrix (3.130); but there is only one Euler rotation to which all are equivalent. The Euler rotation consists of turning the body through 60\u00b0 about the axis o = -i2 in the conventional right-hand sense. Therefore, the antenna panel has the final orientation sketched in Fig. 3.7. Thus, referring to the figure and recalling (3.123b ), we find the transposed basis transformation matrix [ cos 60\u00b0 0 cos 150\u00b0] [ 1/2 AT= 0 1 0 = 0 1 cos 30\u00b0 0 cos 60\u00b0 ./312 0 0 -./3/2] 0 ' 1/2 which is seen to be the same as R in (3.130). D It is important to realize that there are infinitely many lines through the fixed base point 0 about which the body may be turned so as to move any single given particle P from its initial place to its final position that resulted from a previous arbitrary rotation about 0",
+            "178, before the first paragraph starting with: Another interesting ... , insert the subsubheading \"3.6.1.2. The Basis Transformation Tensor\" p.178, last paragraph, first word; read: \"Finally,\" p.179, equation (3.108b); insert prime to read: \"QT'QT\" p.181, change subsubsection \"3. 6.2.1. Invariant ... \" to subsection \"3.6.3. Invariant Properties of Tensors\"; and note the entry in the Table of Contents, p. xvi. 2 p.184, line 5; read: \"we know that\" p.184, last line; read: \"coincide initially\" p.190, The vector \"i~\" nearest the bottom of the page in Figure 3.7 should read \"i1\" p.203, line 4 below (3.147b); revise sentence to read: \"The resultant axis and angle of rotation generally will depend on the order of rotations in (3.147b ). For two rotations, however, it follows ... \" p.203, In the same paragraph below (3.148), add the sentence: \"Note, however, that tr(R3R2Rl) =tr(R1R3R2) yftr(R1R2R3). p.217, Problem 3.18, equation; read numerator: \"2[T[~ 21 + T[~31 + T[~ 11 ] 1 1 2 \" p.218, Problem 3.23; read: \"-J2/10\" (see revised problem solution p.383 below) p"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002334_bcsj.76.1873-Figure8-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002334_bcsj.76.1873-Figure8-1.png",
+        "caption": "Fig. 8. LED-based LCW absorbance flow cell. FO: Optical fibers, 1.3 mm in diameter, are used to connect the LED with the LCW cell, and the transmitted light from the LCW to the detector photodiode (PD). The reference light from the bottom of the LED is similarly connected to the reference photodiode (Ref PD); F: interference filter; AF: Teflon AF-2400 tube; J: Stainless steel tube jacket; R: current limiting resistor.39",
+        "texts": [],
+        "surrounding_texts": [
+            "1. Determination of Hydrogen Peroxide in Water. A procedure for determining hydrogen peroxide in water by a batchwise operation was as follows.29 To a 250 mL water sample, 250 mL of perchloric acid (4.8 M) and 250 mL of the Ti\u2013 TPyP reagent were added, and the mixture was allowed to stand for 5 min at room temperature. The solution was diluted with water to 2.5 mL and this served as a test solution. A blank solution was prepared in a similar manner, using distilled water instead of the sample water. The absorbances of the test and the blank solutions were measured at 432 nm (denoted as AS and AB, respectively). The absorbance decrease ( A432) was obtained by, A432 \u00bc AB AS, from which the hydrogen peroxide content was determined. The A432 value was linear against the hydrogen peroxide concentration with the equation: y \u00bc 1:9 105x\u00fe 0:0097 (y and x being the A432 and the molar concentration of hydrogen peroxide, respectively). The correlation coefficient was 0.999 over the range from 1:0 10 8 to 2:8 10 6 M (from 25 pmol to 7.0 nmol per test). Detection limit was 1:0 10 8 M (25 pmol per test). The relative standard deviation (RSD) was 1.2% at 1:0 10 6 M (2.5 nmol per test). The method was readily applied to determine hydrogen peroxide in well water, tap water, ion-exchanged water and water treated by the NANO pureb system (Barnstead), and the results are shown in Table 5. Hydrogen peroxide in ppb levels was determined for ten samples within 1 h.29 Since hydrogen peroxide in the atmosphere is known as one of the pollutants that cause acid rain, a more sensitive, rapid and simpler analysis method of hydrogen peroxide is highly desirable for checking hydrogen peroxide in rainwater. A FIA method using the Ti\u2013TPyP reagent was thus assessed as an effective means to fill this demand.30 As shown in Fig. 5, a flow injection manifold comprises a two-channel system. CS was distilled water that served as a carrier and RS was the Ti\u2013TPyP reagent (30 mM containing 1.6 M HClO4), and both of them were made to flow at the flow rate of 0.4 mLmin 1. The flow lines were made of polytetrafluoroethylene tubing (0.5 mm i.d.). A 100 mL aliquot of water sample was directly injected into the carrier stream through the sample injector. Hydrogen peroxide contained in the water sample was allowed to merge with the reagent stream to form the peroxo complex in the mixing coil (15 m long, 0.5 mm i.d.). The peroxo complex was monitored at 450 nm by a spectrophotometer and its presence was recorded as the peak height of the flow signal. Typical flow signals obtained with the standard hydrogen peroxide are shown in Fig. 6. The response was linear against the hydrogen peroxide concentration ranging from 1 10 8 to 1 10 5 M (1.0 to 1000 pmol per test, r \u00bc 0:999) and the detection limit was 5 10 9 M (0.5 pmol per test, S/N = 2). The results were accurate with the RSD of 0.97% for the injection of 1 10 6 M of hydrogen peroxide (n \u00bc 10). The FIA operation conditions thus permitted 30 samples per hour to be processed. Because the procedure is simple, without any sample pretreatment prior to the injection into the FIA system, the present method enabled rapid analysis of hydrogen peroxide in water. The detection limit obtained by FIA is considerably lower than that obtained by the batch method. In the batch method, the test solution was made by allowing the reaction of hydrogen peroxide with the Ti\u2013TPyP reagent to proceed under highly acidic condition (1.6 M HClO4), followed by diluting the reaction mixture up to 10-fold with water (cf., Ref. 29). Contrary to this, in the FIA method, hydrogen peroxide in the test solution was detected as the peroxo complex under a less di- luted condition compared to the case of the batch method (cf., Ref. 30). In addition, the FIA technique provides precise data with a good reproducibility under a given set of operating conditions. Contribution of these factors, accordingly, leads to the very low detection limit. The hydrogen peroxide content in rainwater collected in the Tokyo area was determined by this method over the range of 7 10 7\u20134:3 10 5 M (Table 6). The recovery tests were made using 1:00 10 6 M hydrogen peroxide with the satisfactory results of 99\u2013102%, indicating the high reliability of the present method.30 2. Measurement of Gaseous Hydrogen Peroxide. Atmospheric hydrogen peroxide plays a critical role in the conversion of SO2 to H2SO4. 4,5 To determine atmospheric hydrogen peroxide whose concentrations are of the level of about 2 ppbv, a highly sensitive analysis method with high specificity for hydrogen peroxide is required. Dasgupta and his colleagues had attained the requisite sensitivity only by fluoro- metric methods with enzymatically mediated reactions in the measurements of gaseous hydrogen peroxide.38 In these methods, special procedures had still been necessary to prevent interference from concurrently present organic peroxides. Recently, Li and Dasgupta have paid attention to our Ti\u2013 TPyP reagent, and consider it as a promising reagent to advance their studies. They succeeded in showing that the Ti\u2013 TPyP reagent was effective to measure ambient levels of gaseous hydrogen peroxide with a light emitting diode (LED)based liquid-core waveguide (LCW) absorbance detector. Because of the absence of interference from organic peroxides, from SO2 and from O3, the detection limit of tens pptv could successfully be attained.39 The collection/analysis system and the LED-based LCW absorbance flow cell fabricated by them are shown in Figs. 7 and 8. The diffusion scrubber (DS) is used for collecting gaseous hydrogen peroxide into the liquid phase. An air pump (AP) draws sample air and H2O2-free air to the DS. The sampling and H2O2-free modes are alternated by switching a threeway valve (V) automatically at the regulated time intervals, and consequently flow injection type signals are obtained. Water and the reagent solution are aspirated with a peristaltic pump (P) and merged in a tee. The stream flows through a reaction coil and then the LCW absorbance cell. The light (450 nm) transmitted through the cell is coupled to the detector photodiode (PD) by the distal fiber optic. Methyl hydroperoxide (MHP) is the most common atmospheric organic peroxide. The commonly used enzymatically mediated peroxide assays cannot differentiate between hydrogen peroxide and MHP, since both behave as peroxidatic oxidants. Since the Ti\u2013TPyP reagent does not work on a redox principle, it showed very different behavior. An injection of MHP into the analytical system showed no response at all, suggesting that the Ti\u2013TPyP reagent should be essentially specific for H2O2 among peroxides.39 (In the course of our studies, we also found that benzoyl peroxide had no influence on the Ti\u2013 TPyP reagent.) Effects of SO2 and O3 will lead to serious errors in the hydrogen peroxide assay. The former will interfere negatively through its fast redox reaction with hydrogen peroxide. The interference from the latter is more complicated: it reacts with bulk water generating hydrogen peroxide, the reaction being promoted by various surfaces and is also catalyzed by OH .40 However, they found that there was practically no interference from concurrently present gaseous SO2 and O3 using a Nafion membrane collector in the DS.38,39 The observed absorbance at 450 nm was linear with gaseous hydrogen peroxide concentration at least up to 5 ppbv. The typical system output is shown in Fig. 9. The detection limit was 26 pptv at S/N = 3. Owing to the work by Li and Dasgupta, the Ti\u2013TPyP reagent was thus shown to be sufficiently sensitive and selective to measure ambient levels of gaseous hydrogen peroxide, and to be adequate for real atmospheric measurements.39 3. Determination of Components and Additives in Foods. Enzymatic methods using commercial kits have become common for determining several components in foods. However, because of high costs of enzymes and difficulties in the continuous measurements, these methods do not appear to be suitable for routine tests. The present FIA method using the Ti\u2013TPyP reagent incorporating with an immobilized enzyme reactor to yield hydrogen peroxide seems promising for developing a new technique in food analysis. Oxalate:35 Oxalate exerts undesirable effects on foodmanufacturing processes. It adversely affects the food taste, and forms insoluble salts with calcium ions present in water to cause turbidity in beer and fruit juices.41 Sometimes it causes a renal calculus in the human body.42 Common methods for determining oxalate in foods include titration by potassium permanganate,43 ion chromatography,44 gas chromatography45 and enzymatic analysis.46 Among them, enzymatic analysis methods are becoming popular. The methods are based on the detection of hydrogen peroxide or NADH produced through the reaction with the respective enzymes. A kit for oxalate assay by measuring the absorbance of NADH produced with dehydrogenase47 has been marketed. However, the NADH method is liable to be affected by reducible substances in food, and the procedure is somewhat complicated. Since the determination of oxalate is thus important in view of food chemistry, application of the present FIA method in combination with the immobilized oxalate oxidase reactor was examined. A schematic diagram of the FIA system is shown in Fig. 10. The carrier solution (CS) was a 0.05 M succinate buffer (pH 3.0). The test solution was prepared according to the procedure of Hansen et al.,47 and injected using a 20 mL sample loop into the carrier stream. By passing through an immobilized oxalate oxidase column (EC), oxalate in the test solution was converted to hydrogen peroxide through the following enzymatic reaction: Oxalate\u00fe O2 ! oxalate oxidase 2CO2 \u00fe H2O2 \u00f01\u00de The resulting hydrogen peroxide reacted with the Ti\u2013TPyP reagent in the mixing coil to form the peroxo complex, which was detected at 450 nm. To prepare the enzyme column, oxalate oxidase (7U) was immobilized on Sepharose in a usual way, and packed in a Teflon tube (3 cm long, 2 mm i.d.). The column could be used continuously for more than 200 runs over a period of 8 h. When the column was stored in a refrigerator at 4 C, no significant decrease in enzyme activity was observed, even after 6 months. Typical flow signals obtained for the standard oxalate solutions are shown in Fig. 11. Response was linear against the oxalate concentration (r \u00bc 0:999), in the range from 5:0 10 7 to 2:5 10 4 M (10\u20135000 pmol per 20 mL injection). The RSD was 0.48% (2:5 10 5 M, n \u00bc 10). The method was applied to the determination of oxalate in different kinds of foods such as vegetables, fruits and beverages. The results are listed in Tables 7 and 8, together with the results obtained by the conventional method using an F-kit currently available on the market, for comparison. The two data sets were in good agreement with each other. Recovery tests using the standard oxalate spiked in each test solution were made and the results were in the range of 97.7\u2013103.0%, indicating the reliability of the analytical data obtained by the present method. The present method was thus shown to be practical and useful for determining oxalate in foods. Sulfite:32 Sulfite is commonly used as an additive in foodmanufacturing and preserving processes due to its antioxidant, antiseptic and antibacterial abilities. However, it has become apparent that sulfite is liable to cause undesirable effects on the human body as an allergic substance,48 and consequently, the allowable amounts of sulfite added in each food product are officially regulated. Among the methods employed so far for determining sulfite in foods,49\u201351 the Rankin method50 is most commonly used; in this method, sulfuric acid formed through the oxidation of sulfite is determined by alkali titration. Although this method allows the detection of sulfite in ppm levels, the procedure involves the use of a particular piece of distillation equipment and is somewhat too complicated to be suited to practical uses. A simpler, more rapid and sensitive determination of sulfite was realized by the present FIA method in combination with an immobilized sulfite oxidase reactor to yield hydrogen peroxide through the following reaction: SO3 2 \u00fe O2 \u00fe H2O ! sulfite oxidase SO4 2 \u00fe H2O2 \u00f02\u00de The FIA system was essentially the same as that shown in Fig. 10. In this case, a Teflon-tube (6 cm long, 2 mm i.d.) packed with sulfite oxidase-bearing Sepharose was used as an enzyme column. The carrier solution was a Tris\u2013HCl buffer of pH 8.2, and 5 mL of the test solution was injected into the carrier stream. Other FIA operation conditions were the same as those described in the oxalate assay. The peak height of the FIA flow signal showed a good linear relation against the sulfite concentration (r \u00bc 0:999) in the range of 1:0 10 6 to 5:0 10 4 M (5 to 2500 pmol per 5 mL injection), and the RSD value was 0.53% (n \u00bc 10, 1:0 10 4 M). By this method, amounts of sulfite in different kinds of foods, such as wines, fruit juices, and dry and frozen foods, were determined. A part of the results are shown in Table 9 . Because of high sensitivity, very small amounts of naturally occurring sulfite contained in fruit juices could be determined by this method. Sugars:33 Determination of sugars is essential for the quality and process assessment in food manufactures. For determining sugars, chromatographic techniques such as GC52 and HPLC,53 enzymatic method54 and FIA method55\u201357 are commonly employed. Among them, FIA method incorporated with an enzyme reactor seems convenient as a simple and rapid means, however, with this method it is rather difficult to determine each constituent sugar continuously. The present FIA method with several enzyme reactors arranged in parallel, in which each flow line was chosen by a switching valve, permitted the continuous determination of glucose, sucrose, maltose and lactose.33 A flow diagram of the FIA system thus fabricated is shown in Fig. 12. A phosphate buffer (0.05 M, pH 6.6) containing 1 mM MgCl2 was served as a carrier solution. Test solution (20 mL) was injected using a sample loop. b-D-Glucose in the test solution was oxidized to form hydrogen peroxide quantitatively by passing through the glucose reactor (E5) packed with glucose oxidase. Sucrose, maltose and lactose (disaccharides) in the test solution were hydrolyzed to form b-D-glucose through their corresponding hydrolysis reactors (E2, E3 and E4, respectively), and the resulting b-D-glucose was converted continuously to hydrogen peroxide through the glucose reactor (E5). Prior to the determination of sucrose, maltose and lactose, glucose in the test solution was removed by passing through the glucose-eliminating reactor (E1) using a switching valve V1. In the reactor E1, glucose oxidase and catalase were packed. In all cases, the effluent hydrogen peroxide from the glucose reactor (E5) was mixed with the Ti\u2013TPyP reagent in the mixing coil, and detected by the measurement of the absorbance at 450 nm. The enzyme mediated reactions for the four sugars taking place in reactors E2\u2013E5 are as follows:"
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0001349_s0094-114x(00)00051-3-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001349_s0094-114x(00)00051-3-Figure2-1.png",
+        "caption": "Fig. 2. Seven-jointed double-elbow manipulator: (R?R)ptkRkRk(R?R?R)sph.",
+        "texts": [
+            " These degenerate con\u00aegurations and their associated reciprocal screws can be summarized as i S4 0; refWrecip 0; 0; 1; 0; 0; 0f gT; ii S2 C3 0; refWrecip 0; 0; 1; 0; 0; 0f gT ; 21 iii S2 S6 0; refWrecip \u00ffS5; C5; \u00ffC3C4S5\u00ffS3C5 C3S4 ; C5h; S5h; 0 n oT ; iv C5 S6 0; refWrecip \u00ffS5; C5; \u00ffC3C4S5\u00ffS3C5 C3S4 ; C5h; S5h; 0 n oT : Note that the condition sets outlined in (21) are identical to those obtained by Podhorodeski et al. [8] by their decomposition technique. Another seven-jointed manipulator layout is (R?R)ptkRkRk(R?R?R)sph, where pt denotes a pointer joint group and k refers to two successive joints being parallel to one another. This layout is referred to as a double-elbow layout. Denavit and Hartenberg parameters [17] for the manipulator are presented in Table 2. Fig. 2 shows the layout of the manipulator. Choosing a reference frame that is located at the intersection of the wrist spherical group and oriented with xref in the direction of the \u00aenal forearm and yref in the opposite direction of $5 allows the joint screws to be found as ref$1 S234; 0; C234; \u00ffC234f ; C2g C23h C234i; S234ff gT ; ref$2 0; \u00ff1; 0; S34g S4h; 0; C34g C4h if gT; ref$3 0; \u00ff1; 0; S4h; 0; C4h if gT ; ref$4 0; \u00ff1; 0; 0; 0; if gT; 22 ref$5 0; \u00ff1; 0; 0; 0; 0f gT ; ref$6 \u00ffS5; 0; C5; 0; 0; 0f gT; ref$7 C5S6; \u00ffC6; S5S6; 0; 0; 0f gT; where Cij cos hi hj and Sij sin hi hj "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001183_s0020-7683(00)00010-x-Figure12-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001183_s0020-7683(00)00010-x-Figure12-1.png",
+        "caption": "Fig. 12. Test rig for cyclic shear test of isolation bearings.",
+        "texts": [
+            " For multiple-layered rubber bearings, the above sti ness must be modi\u00aeed in the same way as the shear sti ness to account for the presence of the steel shims (Kelly, 1993), EIs EI eff h tr : 67 Assigning the dimensions of the circular bearing and the square bearing into Eqs. (64)\u00b1(67), the ratios of bending sti ness to shear sti ness de\u00aened in Eq. (21) are calculated to be q 7:77 for the circular bearings and q 11:78 for the square bearings, which are independent of the material properties. The testing apparatus for the cyclic shear test of isolation bearings is shown in Fig. 12. As the ends of a bearing specimen have to sustain the vertical compressive force and simultaneously allow the horizontal movement at one end during the test, the test rig requires a pair of identical bearing specimens for each test. The lower end of the lower bearing is \u00aexed to the ground and the upper end of the upper bearing is connected to a vertical hydraulic actuator. During the test, the vertical actuator applies a constant compressive force to the bearings. A horizontal hydraulic actuator is connected with the specimens at the junction of the two bearings"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001933_a:1016348803781-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001933_a:1016348803781-Figure1-1.png",
+        "caption": "Figure 1. Two-roller testing machine and dimensions of test rollers.",
+        "texts": [
+            " In order to evaluate the contribution of such micro-pockets separately, in the present paper, using the roller with a small number of micro-dents marked by a diamond pyramid whose total area was, to minimize the effect of work-hardening, set negligibly small compared to the contact area as the follower in a two-roller testing machine, the pitting durability was tested under poor lubrication conditions and/or several loading levels. The result is discussed comparing with electrolytically polished surfaces [4] and tumbled surfaces [5]. The two-roller testing machine used is shown in Figure 1. Load was applied between the contact surfaces of the rollers by using a link mechanism with dead weight. Slip ratio between the rollers was set at \u22120.25 by a gearing having different tooth numbers. Friction force between the rollers were measured by the strain gage pasted onto the torsion bar connected to the follower spindle. The oil film created between two rollers was measured by the electric circuit shown in Figure 2. The exciting voltage applied, E, was 0.1 V. To evaluate the lubrication condition, \u03b5 defined by the time average value of Vc/E is introduced as an index of oil film creation. If the oil film is not created at all, or breaks down completely, the value of \u03b5 approaches 0. If thick oil films are created and asperities do not interact, the value approaches unity. To evaluate the instantaneous oil film breakdown, real time values of Vc/E are also monitored. If the oil film breaks down to yield local severe contact, the instantaneous value of Vc/E approaches 0 at that moment. The dimensions of each roller are shown in Figure 1. The specification of test rollers are shown in Table 1. The equivalent radius of the two rollers is nearly equal to the equivalent radius of curvature of the mating gear teeth used in Refs. [1] and [3]. The slip ratio of \u22120.25 is also nearly equal to the case of gearing in Ref. [1] and [3]. The materials of driver and follower are shown in Table 2. Details of the rollers machined micro-dents are shown in Figure 3. The 4800 dents were formed on the follower surface by a diamond pyramid of micro-Vickers hardness tester"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002406_318-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002406_318-Figure1-1.png",
+        "caption": "Figure 1. Magnet used for the production of a magnetic cluster.",
+        "texts": [
+            " Thus, we can extract the magnetic clusters from the mixing suspension. The last suspension may also be regarded as the most dilute suspension. Anyway, this method can be used to extract the magnetic clusters from any kind of magnetic fluid containing iron particles of any size. Next, we shake the produced suspension of the magnetic clusters in the absence of a magnetic field, because the magnetic clusters are dispersed uniformly in the suspension. We then apply to the suspension a magnetic field of specific strength. Figure 1 shows the magnetic field distribution used in the present test. The suspension is in a vessel. We touch the permanent magnet having a uniform magnetic field intensity region of Hmax out of the surface of the vessel. We can then obtain magnetic clusters of fixed size according to the magnetic field intensity. Figure 2 shows an example of magnetic clusters produced under Hmax = 4100 G as observed via a microscope. The iron used is carbonyl iron HQ (Yamaishi Metal Company, Japan, 20 g) and the magnetic fluid is water-based W35 (35 wt%, Taiho Industry Company, Japan, 10 cc) mixed with 1 g oleic acid Na and 14"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003711_tmag.2006.875997-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003711_tmag.2006.875997-Figure3-1.png",
+        "caption": "Fig. 3. Flux contours at the rated current: (a) healthy motor and (b) motor with 30% eccentricity.",
+        "texts": [
+            " When the rotor is displaced to the stator poles horizontally, the length of gaps between rotor poles and their corresponding stator poles in one half of the rotor surrounding air are reduced, while rising in the other half. According to Fig. 2(b), this leads to the creation of low magnetic reluctance paths for flux. It is whilst; at high current, iron core saturates and its reluctance increases significantly. Hence, variations in air gap lengths do not have a noticeable effect on the total reluctance of the flux paths. So, as seen in Fig. 3, eccentricity cannot affect motor flux pattern considerably, when operating at the high current. 2) Flux-Linkage Profile: Flux-linkage/rotor angular position characteristic is the most important characteristic of the switched reluctance motors. Fig. 4 compares the flux-linkage/rotor angular position characteristic of phase 1 in the healthy motor and the motor with 30% eccentricity at the current equal to 2 A. At higher currents, where saturation gradually appears, flux-linkage characteristic of the healthy motor and the motor with 30% eccentricity are practically identical and are not shown here"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001757_0022-0728(95)03824-z-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001757_0022-0728(95)03824-z-Figure1-1.png",
+        "caption": "Fig. 1. Principal view of the in situ UV visible spectroelectrochemical cell based on LIGA structures as working electrode in a capillary slit.",
+        "texts": [
+            " The use of a L I G A structure as working electrode opens further possibilities of varying cell parameters. The response behaviour becomes more rapid without decreasing the active optical length and the potential control inside the capillary slit is improved. The shorter response time results from the fact that the active optical length is the sum of both the capillary slits between the L I G A structure and the quartz glass spacers and the length of the microholes inside the structure which is equal to the thickness of the structure (called the structure height; see Fig. 1). The conversion time can be decreased by decreasing the capillary slit and the width of the honeycombed holes inside the electrode material. The sensitivity as well as the response behaviour of the L I G A cell depend on the structure height s h which is one part of the active optical length apart from the slits. The ratio between the spacer width and the hole width influences the loss of light intensity at the structure and therefore the sensitivity. Thus the conversion time and the spectroscopic sensitivity can be optimized by the structure parameters hole width, spacer width and structure height as well as by the width of the capillary slit",
+            " The ideal aspect ratio between the inner diameter and the structure height to have a homogeneous potential distribution at the electrode was found to be 1:5. The experimental cyclic voltammetric curves as well as the experimental dependence of the peak current and the peak potential separation are in good agreement with the calculated cyclic voltammograms, with the theoretical dependences of the peak current and the peak potential separation [17]. 2. Experimental The in situ spectroelectrochemical experiments were carried out with a cell (Fig. 1) based on a screw joint of two Teflon parts to hold the L I G A structure and to isolate the non-structured part at the margin [18]. Quartz rods in the bore of the centre of the Teflon parts conduct the light beam through the cell and limit the diffusion layer at the structured part of the working electrode. A silver wire coated with silver chloride was used as a quasi-reference electrode inside the inlet of the cell and a platinum wire in the outlet as counterelectrode. For the cyclic vol tammograms at a planar electrode the same quasi-reference electrode was used which is connected through a salt bridge with a graphite diaphragm containing the same electrolyte as in the cell",
+            " ' //25/zm LIGA r / (optical length 160/~m i \\ 5; ~o ~ / ,ii\\ o., /'\" 50~tm sl i t cel l ~ ~ . 4 / = 2 5 / z m sl i t cell 5 J \\ '\\ ~ . o . . . . t \\ ? , , o 0 ~ , ~ , ~ ~ ~ + , - - 0.0 0 5. I0 , 15 2 0 2 5 3 0 3 5 4 0 t / s . . . . . . I I 115 ' \" ' \" ' ~ . . . . I ' 0 ' ' 115 ' - ~ 0 5 I0 0 5 2 0 trel/S t 25/~m = 2 . 7 s t 50/~m = I I. 5 S Fi~,. 3. C o m p a r i s o n o f the c a l c u l a t e d f a r a d a i c c h a r g e - t i m e curve for a c o n v e n t i o n a l c a p i l l a ~ slit cell a n d for a L I G A cell (Fig. 1 ) wi th the s ame acl ive op t i ca l c ross sec t ion A~ro~ section ~ 3.14 m m 2 (r~o~ ~ section = 1 mm). Slit w i d t h c o r r e s p o n d i n g to the slit b e t w e e n the q u a r t z g lass rods a n d the s t r uc tu r e : cap i l l a ry slit cell, 1110 /zm (curve 1), 50 /zm (curve 2) a n d 25 /zm (curve 3): L I G A cell, 50 ~ m (curve 4) a n d 25 /~m (curve 5). P a r a m e t e r s of the L I G A s t r u c t u r e u sed for the ca l cu l a t i on : Sw = 15 /zm, , % = 2 5 ~ m , S h = 110 /xm, r~,ctiv ",
+            " The time range of the non-lincarity between the electrochemical converted quantity and the absorbance signal caused by the shape of the concentration gradient at net or gauze as well as at minigrid electrodes decreases from 1-2 s to 150-300 ms at L1GA structures. The calculations as well as the experimental results reveal a fast response behaviour of the LIGA cell. The sensitivity and the response behaviour can be influenced by variation of the aspect ratios between the structure height and the inner diameter as well as the inner diameter of the honeycombs and the spacers between them (Fig. 1). The use of all electrochemical and spectroscopic data permits the analysis of complex electrochemical reaction mechanisms and the study of the kinetics of the chemical reactions before and after the heterogeneous charge transfer at the electrode as is shown for the \"self-protonation\" mechanism of the electrochemical reduction of trithioisatoic anhydride\u2022 Summarising, the advantages of the cell are as follows: - - short response and conversion time (intermediates can be detected if they have lifetimes down to 50-100 ms); - - cyclic voltammetric measurements can be carried 1 \u2022 out up to scan rates of 2-5 V s - - the possibility of a quantitative analysis of the cyclic voltammetric curves (comparison of the measured and the calculated curves) as well as the absorbance-t ime curves; - - in situ spectroscopic measurements in transmission at conventional electrode materials used in electrochemistry"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001877_robot.2000.846404-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001877_robot.2000.846404-Figure1-1.png",
+        "caption": "Figure 1: Notation",
+        "texts": [],
+        "surrounding_texts": [
+            "1 Introduction\nA differential drive robot has two independently driven coaxial wheels. It is the configuration used by most wheelchairs, and due to its simplicity is commonly used by mobile robots. By bounded velocity, we mean that the wheel angular velocities are bounded, but otherwise we allow essentially arbitrary motions of the robot. There are no bounds on wheel angular acceleration. In fact, we do not even require that angular acceleration be defineddiscontinuities in wheel angular velocity are admissible.\nThis paper addresses the question: what are the fastest trajectories for a bounded velocity diff drive robot, in a planar environment free of obstacles? Our companion paper [ I] proves that between given start and goal configurations, the fastest trajectories are composed of at most five segments, where each segment is either a straight line or a rotation about the robot's center. This paper completes the analysis of these trajectories.\nWe present an algorithm for computing all optimal trajectories, and show a few plots illustrating the performance limits of bounded velocity diff drive robots.\n1.1 Previous Work\nMuch of the work reported in this paper is a straightforward application of methods developed in the nonholonomic control and motion planning literature. We have found the surveys by Laumond [ 3 ] and Wen [lo] to be\nvery helpful. Most of the work on time-optimal control with bounded velocity models has focused on steered vehicles rather than diff drives, originating with papers by Dubins [2] and Reeds and Shepp [4]. For diff drives, previous work has assumed bounded acceleration rather than bounded velocity. See, for example, papers by Reister and Pin [5 ] and Renaud and Fourquet [6]. Fortunately, the techniques developed for velocity models of steered cars apply readily differential drives. The present paper follows the techniques developed in the papers by Sussman and Tang [9], by Sou5res and Boissonnat [7] , and by Soukres and Laumond [8].\n2 Assumptions, definitions, notation\nThe state of the robot is q = (x, y l e), where the robot reference point (zl y) is centered between the wheels, and the robot direction 0 is 0 when the robot is facing parallel to the z-axis, and increases in the counterclockwise direction (Figure I). The robot's velocity in the forward direction is v and its angular velocity is w. The robot's width is 2b. The wheel angular velocities are wl and w,.. With suitable choices of units we obtain\n0-7803-5886-4/00/$1 O.OO@ 2000 IEEE 2499",
+            "W\nand\nThe robot is a system with control input w(t) = (w l ( t ) , w7.(t)) and output q( t ) . Admissible controls are bounded Lebesgue measurable functions from time interval [0, T ] to the closed box W = [-1,1] x [-ll 11\nThe admissible control region W provides a convenient comparison with previously studied bounded velocity models. If we plot W in U-w space, we obtain a diamond shape. Steered vehicles are typically modeled as having a bound on the steering ratio w : \u2018U, and on the velocity \u2018U (Figure 2). We also need notation for trajectory types. We will use the symbols fi, 4, .A, and n, to denote forwards, backwards, left tums, and right turns. A trajectory of several segments is indicated by a string. Thus, for example, fin40 means a motion of four segments: forward, right tum, backward, left turn.\n3 Time cost of saturated trajectories\nWe define a saturated trajectory to be one for which the input w(t) is at the boundary of the box W over the entire trajectory. That is, at almost all times either w, or WI is at the limit. We define rectified arc length in the plane of robot positions\n( 5 )\nand in the circle of robot orientations\nFor a saturated trajectory, it is easily shown that\nlvl + blwl = 1 (7)\nalmost everywhere. Integrating this equation yields\ns ( t ) + ba(t) = t (8)\nThus the time for a saturated trajectory is just the sum of the arc length in E2 and the arc length in S\u2019 scaled by the robot radius b. This suggests that to minimize the time we ought to turn in place or make straight lines. Our companion paper [ l ] proves that this is indeed the case using Pontryagin\u2019s maximum principle.\n4 Controllability. Existence of optimal controls. Extremals.\nThis section summarizes the results of our companion paper [l]. The bounded velocity diff drive is globally controllable, and time optimal controls exist. Pontryagin\u2019s Maximum Principle yields necessary conditions for time optimal controls. The trajectories satisfying these conditions are thus a superset of the time optimal trajectories, and are called the extremal trajectories. Using additional necessary conditions an enumeration of extremals is obtained.\nThe extremal trajectories can be expressed as a geometric program, using a construction called the 7-line. It is a directed line in the plane, which divides the plane into a left half plane and a right half plane. Pontryagin\u2019s Maximum Principle implies that for any optimal trajectory there is an 7-line such that the trajectory can be achieved by a control of the form:\nW l { = l E [-1,1] if right wheel is on the line (9)\nW T { = l E [-ll 11 if left wheel is on the line (10)\nif right wheel E right half plane\nif right wheel E left half plane\nif left wheel E left half plane\nif left wheel E right half plane\n= -1\n= -1\nThe behavior of the robot falls into one of the following cases (see Figure 3):\n0 CCW and CW: If the robot is in the left half plane out of reach of the v-line, it turns in the counter-clockwise direction (CCW). CW is similar."
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0002044_s0378-4754(02)00027-7-Figure7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002044_s0378-4754(02)00027-7-Figure7-1.png",
+        "caption": "Fig. 7. Orientations to test the door-confirmation module.",
+        "texts": [
+            " After a lot of experimentation, we conclude that the door-recognition vision module works well under stable light conditions; variations in brightness and reflections alter notably the results of the vision module. In spite of this, when light conditions are adequate the vision module helps gratefully to identify door candidates and to reject false ones. For proving the door-confirmation module, we placed our B21 robot in several positions about 95 cm away from the door. Different headings have also been taken into account from each position as shown in Fig. 7. V1 and V3 correspond to the robot heading towards each edge of the door, and V2 represents that the robot is heading to the center of the door. Table 1 shows the percentages of success obtained from each position. The meaning of each Pi position is represented in Fig. 8. It can be deduced that this module works well between the incidence angles we used for training (less than 30\u25e6 from door center and 1 m far). It also works fine for no-door recognition. Door and no-door cases were clearly differenced"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001909_20.250667-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001909_20.250667-Figure6-1.png",
+        "caption": "Fig 6. The mesh generated",
+        "texts": [
+            " It has 48 slots on the stator and the three phase winding is identical to that of figure 2 except that it contains 4 slots per pole per phase. The representation of the whole stator would be difficult. This is why, we used the results already obtained. The stator has been supplied with a homopolar system of currents so that only one sixth of the machine needs to be represented. Figure 5 shows one portion of the magnetic circuit of the stator. the end windings of the machine and the current density in the end windings. The boundary conditions used to compute the vector potential are Dirichlet on all faces surrounding the machine. Figure 6 shows the mesh generated by FLUX3D. The reactances of the end windings have been compared against analytical formulae used by the manufactuer. Table I shows the results. The error E of 8.2 % is acceptable since we do not know what is the true value. Iv. TWO POLE MACHINE The last machine under investigation was a two pole induction machine stator with 24 slots and a 3 phase winding. This means 4 slots per pole per phase. Figure 7 represents the winding. In this case the simplification of a homopolar supply is no longer valid because the geometry of the winding does not allow such simplification"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001423_s1350-4533(99)00095-8-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001423_s1350-4533(99)00095-8-Figure2-1.png",
+        "caption": "Fig. 2. The kinematic model of the finger segments allows the coordinates of a point on the fingertip (inset, arrow) to be estimated with respect to the metacarpal bone (coordinate-system-0). The axis of MCP abduction/adduction (z0) does not intersect the axis of MCP flexion/extension (z1), because the MCP joint has different radii of curvature for these two movements (left). Each of the x-axes (x1\u2026x3) are chosen to point distally along the long axis of the bone, on a line which intersects the next-most-proximal axis. The axis x0 is chosen to intersect z1 at a right angle when the finger is straight. As shown (right) adjacent coordinate systems are related by rotations (qMCPa\u2026qDIP) and displacements (a1\u2026d4).",
+        "texts": [
+            " The Nomenclature ip \u2192 tip Coordinates of finger tip expressed with respect to coordinate-system-i ip \u2192 LUMo Coordinates of origin of lumbrical muscle ip \u2192 ins Coordinates of insertion of lumbrical and radial interosseous on extensor hood ip \u2192 rIOSSo Coordinates of origin of radial interosseous muscle on metacarpal bone qMCPa MetaCarpoPhalangeal joint abduction (about z0) qMCPf MetaCarpoPhalangeal joint flexion (about z1) qPIP Proximal InterPhalangeal joint flexion (about z2) qDIP Distal InterPhalangeal joint flexion (about z3) ,FDS Length (excursion) of Flexor Digitorum Superficialis muscle ,FDP Length (excursion) of Flexor Digitorum Profundus muscle ,EDL Length (excursion) of Extensor Digitorum Longus muscle ,LUM Length (excursion) of LUMbrical muscle ,rIOSS Length (excursion) of radial InterOSSeous muscle ,uIOSS Length (excursion) of ulnar InterOSSeous muscle i\u22121Ti Homogeneous transform from coordinate-system-i to i21 || ||2 Second (Frobenius) norm of a vector, \u221ax2+y2+z2 for [x y z]T radial and ulnar InterOSSeous (rIOSS, uIOSS) muscles originate on the lateral aspects of the metacarpal, and insert on either side of the extensor hood. These two muscles primarily produce abduction/adduction movements about the MCP joint. However, they also change length with MCP joint flexion. We used a kinematic model of the finger segments [2] to estimate the coordinates of a point on the finger tip (Fig. 2, inset) with respect to the metacarpal bone. The axes (z0\u2026z3) represent the axes of rotation of the finger joints for movements of MCP abduction, MCP flexion, PIP flexion, and DIP flexion (Fig. 2, left). The model describes the finger as a set of pin joints separated by links of fixed length (a1\u2026d4) (Fig. 2, right). Although the model allows for non-parallel flexion axes, our apparatus for estimating finger pose could not measure skew angles. Therefore, the flexion axes of the finger joints are assumed parallel. Anatomical data [11] indicate that this assumption, which has been incorporated into many models of the finger [3,6,9,10], is reasonable. The axis of MCP abduction/adduction is taken to be perpendicular to the axis of MCP flexion. The parameter a1 sets the distance between the axis of MCP joint abduction and the axis of MCP joint flexion. The axes do not intersect, because the metacarpal head has a different radius of curvature for each of these movements. The parameter d2 approximates the distance between the axis of MCP flexion and the axis of PIP flexion. The parameter d3 approximates the distance between the axis of PIP flexion and DIP flexion. The parameter d4 approximates the distance from the axis of DIP flexion to a point on the fingertip (Fig. 2, bold arrows). The axes (z0\u2026z3) and the segments corresponding to the shortest distances between them (a1, d2, d3) suggest coordinate systems (Fig. 2, left). A left superscript indicates the coordinate system in which a point is expressed. For example, 3p \u2192 indicates a point expressed with respect to coordinate-system-3, which is fixed in the head of the middle phalanx (Fig. 2, left). The z-axis of this coordinate system is coincident with the axis of rotation of the DIP-joint. The x-axis points distally along the long axis of the bone, and lies on a line which intersects the next-most-proximal coordinate system. Coordinate system-2 and coordinate-system-1 are defined in the same way. Coordinate-system-0 is fixed with respect to the metacarpal bone. The z-axis of this coordinate system is coincident with the axis of the MCP abduction/adduction. The x-axis is chosen to intersect the z-axis of coordinate-system-1 at a right angle when the finger joints are straight",
+            " Based on manufacturer\u2019s literature, the measurements of IRED coordinates had accuracy of \u00b10.15 mm, and precision of \u00b10.015 mm. Offline, the coordinates of the IREDs were used to estimate the abduction (qMCPa) and flexion (qMCPf) angles of the MetacarpoPhalangeal joint, as well as the flexion angles of the Proximal InterPhalangeal joint (qPIP), and Distal InterPhalangeal Joint (qDIP) (Fig. 8, inset). The offset from the center of the most distal IRED (Fig. 8f) to the point on the finger tip indicated by the arrow (Fig. 2, inset) was measured with approximately \u00b10.5 mm precision with a ruler and protractor prior to data collection. Further references to \u201cthe location of the finger tip\u201d refer to this point, selected to approximate the center of the fingertip contact area during precision pinch, and the most distal portion of the finger pad in contact with an object during power grasp. The following tendons of the finger were attached to thin, woven-wire cables loaded through a system of pulleys and weights with forces (9",
+            " Poses which can only be achieved by imposition of an outside load (qDIP.qPIP) were included in the set. Based on 100 randomly selected pairs of measures taken at identical poses (that is, all joint angle measurements matching within 0.01\u00b0), estimates of marker locations were repeatable with an average precision of \u00b10.23 mm, with no pair of repeated measures disagreeing by more than 1.50 mm. The calibrated kinematic model approximated the x, y, and z-coordinates (Fig. 9, top row) of the finger tip (Fig. 2) with satisfactory precision (RMS error=1.41 mm). The forward kinematic model accounted for nearly all of the variance in finger tip coordinates (VAF%=99.09). The precision of the model was comparable to that achieved for kinematic calibration of the finger of a living subject, using a different apparatus to measure finger pose (RMS error=1.42 mm) [2]. Parameters for estimating kinematics of the finger segments appear in Table 1. Excursions of the three extrinsic muscles (Fig. 9, middle row) were also well approximated"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002294_a:1005694704872-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002294_a:1005694704872-Figure1-1.png",
+        "caption": "Fig. 1. The thick-film electrode consists of 3-electrode system. The enzyme is immobilized on the working electrode in the indicating window.",
+        "texts": [
+            " Measurements were carried out with an electrochemical detector (Biometra EP-30) coupled with a computer. A 25 ml beaker was used as a measuring cell at room temperature (21 \u25e6C), with a magnetic stirrer assuring perfect stirring of the background solution. Disposable thick-film platinum electrodes from SensLab GmbH (Leipzig, Germany) were used, which are composed of a three-electrode arrangement of working and counter electrodes with applied potential at +400 mV against internal Ag/AgCl reference electrode (Figure 1). The prepared sensor was vertically arranged in the measuring cell. Sensor responses were measured by allowing 10 ml phosphate buffer solution to equilibrate with atmospheric oxygen (steady-state current), and then injecting various amounts of sample solution to achieve different analyte concentration in the measuring cell. The sensor response was recorded as the difference in current change (end-point detection). Between measurements the cell was rinsed twice with distilled water. When not specified, the sensor was stored at 4 \u25e6C in moisture condition (tight bottle with wet tissue inside) when not in use"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002068_bf00052455-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002068_bf00052455-Figure2-1.png",
+        "caption": "Fig. 2. Rigid body model [20].",
+        "texts": [
+            " Application fields are drivelines of large diesel engines, which due to a large temperature operating range usually are designed with large backlashes [1, 20]. The dissertation [20] represents the newest state of research and will be the basis of this paper. The plenary lecture [19] gives a survey on dynamical systems with time-varying or unsteady structures. Rigid bodies are characterized by six degrees of freedom, three translational and three rotational ones. We combine these magnitudes in a l~6-vector (Figure 2 and [20]) ( 6~ ) EIl~6 (1) P = rH with (~ -~- ( ~ x , ~ y , ~ z ) T, rH = ( A x H , / k y H , A Z H ) T E R 3. (2) Accordingly, the velocities are v = bH = VH ~ (3) Elastic bodies in gear or driveline units usually are shafts with torsional and/or flexural elasticity. In the following we consider only torsion by applying a Ritz approach [18] to the torsional deflection ~ (Figure 3): ~(z , t ) = W(z)Tqel(t) with w,q~l C ]~7~ (4) where the subscript \"el\" stands for \"elastic\". used in multibody theory [3] the free directions f i of motion of a joint i are given with a matrix ~i C ~6,fi",
+            " It starts with d'Alembert's principle which states that passive forces produce no work or according to Jourdain generate no power [3, 18]. This statement can be used to eliminate the passive forces (constraint forces) and to generate a set of differential equations for the coupled machine system under consideration. We start with the equations of motion for a single rigid body. Combining the momentum and moment of momentum equation and considering the fact that the mass center S has a distance d from the body fixed coordinate frame in H (Figure 2) we come out with where I = d = IH = --fK ~- fs= ( I. ma ) 1 6,6 -racl mE~ E (0, O, d) T E ll~ 3 diag (A, A, C) C I~ 3'3 ~ T T [(~JiH~-~e3) ,0] C ~6 The magnitudes A, C are moments of inertia, ft,\" are gyroscopic, fB acceleration and fE applied forces, f2, (~ are prescribed values of angular velocity and acceleration, respectively. The unit vector e3 is body-fixed in H (Figure 2). By adding components with torsional elasticity we can expect an influence on the rigid body motion only with respect to the third equation of (11). Therefore torsional degrees of freedom can be included in a simple way. The equation of motion for a shaft with torsional flexibility is 0 ~ 0 [ G I p ( Z ) ~ z J - M k ~ ( z - z k ) =0. (13) pip(z) ot 2 Oz (p density, Ip area moment of inertia, G shear modulus, Mk torque at location zk). The total angle ~ has three parts t) = f f~(t) dt + p~(t) + 9~(z, t), (14) ~(z, where ~(t) is the angular velocity program, ~ (t) the z-component of ~I, (equation (2)) and ~(z, t) the torsional deflection (Figure 3)"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000637_ac960779o-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000637_ac960779o-Figure2-1.png",
+        "caption": "Figure 2. Actuated, optical transmittance flow cell. (a) Perfusion and monitoring of an entrapped bead layer. (b) Ejection of spent beads to waste.",
+        "texts": [
+            "; Chowdhury, D. A.; Kamata, S. Anal. Chem. 1994, 66, 1713-7. (6) Riddick, J. A.; Bunger, W. B.; Sakano, T. K. Organic Solvents, 4th ed.; Wiley & Sons: New York, 1986. Anal. Chem. 1997, 69, 1763-1765 S0003-2700(96)00779-2 CCC: $14.00 \u00a9 1997 American Chemical Society Analytical Chemistry, Vol. 69, No. 9, May 1, 1997 1763 An actuated, optical transmittance flow cell was designed for trapping, perfusing, and monitoring beads. Trapped bead layers in the flow cell were perfused while monitoring with fiber optics (Figure 2a) and then ejected to waste (Figure 2b). A difference of one drill size between the rod in Figure 2 and the FEP fluorocarbon block material of the cell was narrow enough to allow solution to flow around the rod while the bead layer was retained. The rod was made of poly(ethyl ether ketone) (PEEK) and was actuated by two solenoids (intermittent-type, 24 V, Guardian Electric, Woodstock, IL) to move 1 mm so that it either blocked or cleared the 0.8 mm diameter flow channel. A PTFE sheet drilled out two drill sizes smaller than the rod served as a gasket. The holes accommodating the fibers were drilled to within 0"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001062_s0167-7799(98)01243-8-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001062_s0167-7799(98)01243-8-Figure2-1.png",
+        "caption": "Figure 2 The structure of an integrated enzymic microbattery. The close-up shows the electrodes with immobilized glucose oxidase (a,b), the ion-exchange membrane (c) and platinum electrodes deposited on the silicon-wafer substrate (d). The cells are all connected in series.",
+        "texts": [
+            " The techniques used to fabricate the microbiosensors could also be applied to the enzyme battery, and an integrated enzyme battery has indeed been fabricated by methods such as anodic bonding and anisotropic etching9\u201311. If an enzyme battery could be fabricated using micromachining techniques, it might be implanted inside the human body and use organic compounds as a fuel. This would be an ideal device for the future microsurgery robot. We have attempted to make an integrated enzyme battery in which between two and six cells were connected in series12. All these individual cells were fabricated on a single silicon wafer and glucose solution was introduced into the cell by the capillary effect (Fig. 2). The electrical-power output of this enzyme battery was found to be several Watts. In addition, by connecting the cells in series, high voltages could be gained (a higher voltage is preferable for an electrostatic micromotor, which must produce a propulsive force for the robot). So far, such a microbattery has problems of lifetime and stability but, by applying the knowledge from the development of biosensors, these should be overcome in the near future. 1 Adlhart, O. J., Rohonyi, P., Modroukas, D"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001615_0263-8223(93)90220-k-Figure8-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001615_0263-8223(93)90220-k-Figure8-1.png",
+        "caption": "Fig. 8. Configuration of the valve spring retainer.",
+        "texts": [
+            " This Change of dynamic modulus and damping at 100 N/mm 2. situation in cross-ply laminates is called the 'characteristic damage state'} The edges of the transverse cracks rub against one another and in doing so raise the energy loss. After a while the crack edges become smooth and the frictional losses decrease. Thus, damping decreases after cracking stops, because no more rubbing surfaces are created and the frictional loss per unit of crack area decreases. A valve spring retainer is a very intense accelerated motor component (Fig. 8). Therefore, it is possible to increase the critical number of revolutions with a mass reduction of this part. The tested part was a 1 : 1 substituent of the retainer made of steel, but its weight was only 3.6 g instead of 17 g? 0.16 - 0.12 0.08 0.04 2 e amox = 40 N / m m 2, emox = 0.4% i mama x 30 N / m m 2, Emax 0.3% ! \u2022 amox 20 N / r a m 2, Emox 0.2% I \u2022 f\\. / ..t \".,,.. /..,, / OCJP m mm ~mmmmm mlmm'm\" mnJm ~ dm \u2022 vvV tvw vvlnV vVv~v I I I I 3 4 5 6 Number of oyeles [log N] Fig. 7. Change of damping at different stress levels"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003897_009-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003897_009-Figure2-1.png",
+        "caption": "Figure 2. Sketch of the experimental geometry.",
+        "texts": [
+            " To elucidate the physical impact of ion-number conservation in the electrowetting of immiscible-electrolytic solutions, we first explore the electrostatics with idealized droplets of fixed shape. The most easily tractable case is a hemispherical droplet, for which exact solutions to the linearized PB equations can be obtained. This section provides the potential and charge distributions for polarized hemispherical droplets in three regimes of size, and determines the ranges of droplet radius over which each asymptotic result is most accurate. A hemispherical droplet is taken to lie between two parallel planar electrodes separated by distance L, as shown in figure 2. The electrode on which the droplet sits is assumed to be an ideal conductor, and thus is an isopotential surface at potential 0. The droplet has a radius of curvature rd. Let z designate the distance perpendicular to the near electrode through the axis of symmetry. We assume the interelectrode distance L rd, making the system semi-infinite with \u2192 0 as z \u2192 \u221e. Designate the phase within the droplet by d and the surrounding phase by s, and the corresponding potentials by d and s. In spherical coordinates, this system is insensitive to the azimuthal angle \u03c8 because it is rotationally symmetric about the z-axis; the potential in phase j , j , depends on the radial coordinate r and polar angle \u03b8 "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003711_tmag.2006.875997-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003711_tmag.2006.875997-Figure2-1.png",
+        "caption": "Fig. 2. Flux contours at 10% of the rated current: (a) healthy motor and (b) motor with 30% eccentricity.",
+        "texts": [
+            " It is observed that at the low current, ec- centricity clearly affects the flux pattern, while this is not the case at the high current. The reason is that there is no iron core saturation at low current and then, flux path reluctance is mainly determined by the length of the air gap. When the rotor is displaced to the stator poles horizontally, the length of gaps between rotor poles and their corresponding stator poles in one half of the rotor surrounding air are reduced, while rising in the other half. According to Fig. 2(b), this leads to the creation of low magnetic reluctance paths for flux. It is whilst; at high current, iron core saturates and its reluctance increases significantly. Hence, variations in air gap lengths do not have a noticeable effect on the total reluctance of the flux paths. So, as seen in Fig. 3, eccentricity cannot affect motor flux pattern considerably, when operating at the high current. 2) Flux-Linkage Profile: Flux-linkage/rotor angular position characteristic is the most important characteristic of the switched reluctance motors"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure3.14-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure3.14-1.png",
+        "caption": "Figure 3.14. Euler angles and rotations.",
+        "texts": [],
+        "surrounding_texts": [
+            "It was shown in Section 2.7 that consecutive infinitesimal rotations are vectors; and their composition, therefore, is both additive and commutative. We are now able to show that the same result may be derived from (3.147b )."
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0001429_robot.1989.100102-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001429_robot.1989.100102-Figure3-1.png",
+        "caption": "Figure 3. Top View and Side View of Two Fingers Grasping a Spherical Object. (I=inertial, O=reference member, B=base, and C=contact coordinate frames.)",
+        "texts": [
+            "9 nt-m 5 5 0.9 nt-m, -1.8 nt-m 5 r2 5 1.8 nt-m, -1.8 nt-m 5 r3 5 1.8 nt-m. For simplicity of presentation only two fingers are first used to manipulate a very dense 2 lb. spherical object which has a radius of 1 inch. Simulation results for the 4-finger case are also obtained and presented later in the paper. Hard point contact with friction is assumed. A circular, simple harmonic motion with respect to the vertical axis is planned. This motion is 30' in magnitude and 2 cycles per second in frequency. Figure 3 shows the top view and side view of the mechanism a t the neutral position of the motion. After briefly presenting the model used to describe the mechanism, the known components (W, F, A, B, and C) in the force distribution problem will be determined next. This will be followed by the approach taken to obtaining the general solution of Eq. (2), for this case. B. Obtaining the Known Components in the Force Distribution Problem In (41, an efficient formulation of the force distribution equations, for simple closed-chain robotic mechanisms, has been developed",
+            " (2), we have 1 0 0 0 1 0 0 0 Oy1 0 0 0 - -0y1 0 0 w = 0 0 1 1 0 0 0 1 0 0 0 1 0 0 oyz 0 0 0 -0y2 0 0 F = (fingers) are in frictional contact with it. The case of 2 fingers is considered ( m = 2), and each finger has 3 degrees of freedom ( N = 3). Also, for hard point contact with friction, 3 degrees of constraint are imposed at the contact points (d = 3). For this example, a reference member coordinate frame (0) is defined with its origin at the geometric center of the object. The unit vector \"y aligns with the line passing through the contact points C1 and Cz, and the unit vector O i points upward. (See Fig. 3.) As was mentioned previously, since point contact is assumed, G has only force components. If G is expressed with respect t o reference member coordinates, then Eq. (2) can be decomposed into two parts (see later discussion). This results in the following -Of' - 0 O f Y 0 . (38) 8.91 nt 0 2 O l f = 0 O n Y 0 O n z ~ 0.0194cos4at nt-m force balance equations: - 1 0 0 0 1 0 0 0 1 0 0 oy1 0 0 0 - O Y 1 0 0 1 0 0 - - o f : - - Of\" - 0 1 0 of: O f Y 0 0 1 \" f i \"= f 0 2 0 0 O Y 2 \"fi\" 0 2 1 0 0 0 of; nu -0yz 0 0 \"fi\" - O n z - where O f 1 = [\"fr Of: contact force vector at C1 onto reference member expressed in reference member coordinate frame, = [\"f; Of; of;]T, contact force vector at C, onto reference member expressed in reference member coordinate frame, oylf'yz) = y component of the position vector to C1 (Cz) expressed with respect to reference member coordinate frame, O f = [\"f\" \"fY 'PIT, resultant force vector onto O f ",
+            " G Irm,,, -JT. G 5 -rmin, where J is the composite matrix, whose dements are the Jacobians for the chains, and which relates the finger contact forces to the joint torques. Also, T~~~ (rmin) is the vector of the maximum (minimum) actuator torques. Combining Eqs. (46), (47), and (48) we have: In fact, Eq. (49) is equivalent to Eq. (3) so that A = [ 9 (49) with rm, = [ 0.9 1.8 1.8 0.9 1.8 1.8 I T nt-m, (52) and rman = -Tmax. (53) To maintain contact, Of: should be positive and Of,\" negative (see Fig. 3). Therefore, in order to prevent crushing of the object, the objective function is specified as: @ = C . G (54) C = [ O -1 0 0 1 0 1 (55) where so that the normal components of the contact forces at the local surface are minimized. 948 and Let W\" = [ \"i, ] and (59) -0y1 0 -\"y2 0 Since 2 distinct contact points are considered, \"y1 # Oyz. Therefore, the rank of W\" is 2 and that of Wxy is 3. Equation (56), then, may be used to solve for the z components of the forces. Equation (57), on the other hand, has 4 variables in 3 equations, therefore multiple solutions exist"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001834_cp:20000267-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001834_cp:20000267-Figure1-1.png",
+        "caption": "Fig. 1 Single-phase brushless dc motor andH-bridge inverter.",
+        "texts": [
+            " In literature [ l - 41, whilst the starting torque of 1-ph BLDC motors was studied extensively, the influence of winding inductances on their torque capability has not been addressed. In order to maximise the motor power density and to minimise the motor peak phase current so as to reduce the power device ratings for high-speed applications, two alternative commutation strategies are studied, one using the phase commutation advancing technique and another using the conducting pulse-width control. The paper describes the techniques and reports the corresponding simulated and measured performance. DESCRIPTION OF MOTOWRIVE SYSTEM Fig. 1 shows the prototype 2-pole, 1-ph BLDC motor, its rotor having isotropic, surface-mounted, bonded NdFeB magnets, having ~ 6 0 % by volume loading of NdFeB powder and an outer carbon fibre wrap of 0.5\" thickness. The magnets have a remanence of 0.5T and a relative recoil permeability of 1.19, and are impulse magnetised. The stator laminations are TRANSIL335, and in order that the motor could be retrofitted to the vacuum cleaner, the axial length and outer diameter of the stator were constrained to be 87.5\" and 76\". respectively, to accommodate the existing impeller and mounting. The open-circuit field distribution is shown in Fig. 1. Single-phase motors can exhibit null-points in their torque waveforms, which can make them difficult to start. To overcome this problem, an asymmetrical graded airgap is employed in the prototype motor to introduce a cogging torque component, which complements the excitation torque and results in a net unidirectional total torque, and to impart a preferred direction of rotation. Fig2 compares the finite element predicted and measured cogging torque waveforms, whilst the measured and finite element predicted backemf waveforms are shown in Fig",
+            "(nd) For very low power applications, in order to reduce the cost of the power devices it is common to use the unipolar inverter [l-31 in which only two power switching devices are required. However, this type of inverter cannot fully utilise the copper and the power density is very low since the phase winding only conducts for half cycle. For relatively high power Power Electronics and Variable Speed Drives, 18-19 September 2000, Conference Publication No. 475 Q IEE 2000 applications a bipolar converter, i.e. H-bridge, as shown in Fig.1, is necessary so that the phase winding will conduct over 180\u2019 for both positive and negative cycles. A Hall sensor can be used for rotor position monitoringkommutation, and the motor was supplied from a MOSFET converter and a simple controller via a rectifier/filter from the single-phase mains power supply. DYNAMIC SIMULATION MODEL The electromagnetic equations for single-phase brushless dc drive are relatively simple, the supplied motor terminal voltage is determined from the commutation strategy and is governed by: di(t) vmOtor ( t ) = e(t) + R ",
+            " As the speed increases, the torque capability is reduced considerably, whilst the proposed two methods show significant improvement and hence they are suitable for high-speed, high power density and low cost applications. 3 2 I I I 1 1 S o c t 5 -1 0 I -2 ! I I I I i -3 4 I 0 0.01 0.02 0.03 0.04 Time (s) (a) conventional commutation, 7 m \" 8 6 4 2 0 -2 -4 4 -8 0 0.01 0.02 0.03 0.04 T i (s) (b) 300 advanced commutation/1800 conduction period, 230m\" 2 1 z g o 6 E 1 I -2 4 4 0 0.01 0.02 0.03 0.04 \" (9 (c) Pulse-width controY12oO conduction period, 14m\" Fig. 1 1 Measured and simulated current waveforms at 5,000rpm and 50V dc link voltage. 0.3 . - E 0.25- z 2 0.2 I- 0.15 - 0.1 0.05 - \\ U 0 A I A 0 0 5ooo loo00 15ooo 20000 speed (W) Fig. 12 Measured and simulated torque-speed characteristics under 120' pulse-width control. 33 1 It has been shown in the previous sections that the optimal advanced commutation angle and the optimal pulse-width depend on the winding inductance and the motor operating speed. It is not difficult to implement the optimal values by using a micro-processor or DSP"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003257_tro.2005.844679-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003257_tro.2005.844679-Figure2-1.png",
+        "caption": "Fig. 2. Convention for direction of friction cones in grasping and force triangles/tetrahedra in cable robots.",
+        "texts": [
+            " Thus, form closure, which is usually more difficult to analyze, deals with kinematic constraints, while force closure deals with force-moment constraints. It is well known, as discussed in detail by Mason [14], that force closure does not entail form closure and neither does form closure entail force closure. In other words, force closure does not guarantee full kinematic constraint or vice versa. This paper deals exclusively with force constraints, thus, force closure. For readers interested in analyzing form closure, we recommend two papers by Rimon and Burdick [16], [17]. shown in Fig. 2(a), where the light triangle (planar cone) points away from the finger. This convention is strictly employed throughout this paper. Equivalently, when examining the set of forces that can be generated by a set of coincident cables in a cable robot, we define the resulting half-open triangle (in two dimensions) or half-open tetrahedron (in three dimensions) to always be drawn such that the forces that the cables can apply point away from the cable intersection point. This convention is illustrated in Fig. 2(b) for two coincident cables. Two different cases are shown in Fig. 2(b): For the case where the cables coincide at the moving platform, the location and direction of the light triangle is obvious, while it is less obvious if the cables coincide at the motor location. A planar cable robot must use at least four cables to achieve force closure. Furthermore for mechanism symmetry, kinematic simplicity, and wire tangling, it is beneficial to use only two attachment points on the moving platform, i.e., two pairs of cables that coincide at the platform. An example is shown in Fig"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000666_bit.260460310-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000666_bit.260460310-Figure2-1.png",
+        "caption": "Figure 2. Effect of PEI addition to the paste on the current response to 5 mM D-lactate and 0.1 mM NADH and the response change during storage. Paste composition per 100 mg graphite powder: 0.87 mg D-LDH, 75 mg N A D + , 3.5 mg redox polymer, and 40 pL paraffin oil; carrier: 0.25 M phosphate buffer, pH 7.0; flow rate: 0.84 mL min- '; injection volume: 50 JLL; applied potential: - 50 mV vs. Ag/AgCl (0.1 M KC1).",
+        "texts": [
+            " However, because of the versatility of possible additives and the lack of fundamental knowledge of how these may affect the system, PEI was chosen as a model additive in this study because of its previously shown general beneficial proper tie^.^\"^ Even though a very dramatic increase in the number of papers describing enzyme, tissue, and whole cell modified carbon paste electrodes is seen during last few years, lo the basic understanding of the electrochemistry as such and how deep substrate and other compounds from the contacting solution may penetrate the paste is virtually unknown today. '' Figure 2 shows the responses of two equally prepared pastes (0.44 mg of LDH, 75 mg of NAD+, and 3.5 mg of redox polymer, per 100 mg of graphite powder with 40 pL of paraffin oil) with the exception that to one paste 100 pL of 0.2% PEI were added per 100 mg of graphite. The responses to 5 mM D-lactate and 0.1 mM NADH, respectively, were 24% and 18% higher registered for the paste electrodes incorporating PEI. This strongly suggested a positive effect of added PEI on the response. Comparing the shape of the flow injection (FI) peaks obtained, one could note a slightly faster response for the PEI-modified paste, revealed by less width at half height and less tailing",
+            "5 mg of redox polymer per 100 mg of graphite powder was chosen. Some sensor characterization can be obtained when replotting calibration data in the form of an electrochemical Eadie-Hofstee plot. l7 The general equation is j = j,,, - KMaPP (i/C) (2) where j is the current density obtained after the addition of substrate and C is the bulk concentration of substrate. Results from an electrode with 50 mg of NAD+ ,0.87 mg (374 U) of D-LDH, 3.5 mg of redox polymer, and 100 pL of 0.2% PEI per 100 mg of graphite powder using the same measuring condition as in Figure 2 are plotted (data not shown), revealing aj,,, of 230 p A cm-* and an apparent Michaelis-Menten constant (KMapp) of 5.6 mM. This indicates that the electrode is suitable for analysis of D-lactate for concentration approximately <0.1 KMaPP for which a straight calibration curve is obtained. The free dissolved form of the enzyme from the same species of bacteria has a K, of 2.2 mM for D-lactate in 0.1 M Tris-HC1 buffer at pH 8.7, 25\u00b0C.6 Possible explanations to the discrepancy between these values may be that there exists an increased diffusional barrier at the electrode-solution interface or that the high content of NAD+ in the paste affects the constant",
+            "\u2019 A positive stabilizing effect of the enzyme in the electrode by addition of PEI is expected. After 4 days storage, a similar response decrease of around 17% was observed in 5 mM D-lactate for all electrodes irrespective of the presence or absence of PEI. However, the response of PEI-containing electrodes decreased 43%, but the electrodes with no PEI only decreased 22% of its initial re- sponse after 1 week storage. A decline of around 50% was seen for both types of electrodes after 29 days of storage (Fig. 2). From the data collected above, it seems that the addition of PEI has no effect on the storage stability of this electrode, although some positive effect has been shown in another study.\u2019 Covering the CP electrode with a membrane would impose a barrier to include the water-soluble components in the paste during measurement. In addition, electrode fouling may be prevented, l 1 interferences e ~ c l u d e d , ~ and the linear response range extended,21 but at the expense of sensitivity. An Eastman AQ cation-exchange membrane was proven beneficial in a previous investigation of a glucose sensor based on glucose dehydr~genase"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001980_robot.1995.526028-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001980_robot.1995.526028-Figure2-1.png",
+        "caption": "Figure 2 - A Spatial Contact",
+        "texts": [
+            " Our procedure is particularly applicable in the case of enveloping grasps; it is, however, applicable in all grasps, enveloping or not. 2. Modeling and Problem Formulation Consider Figure 1. Let nf be the number of independent fingers in contact with the grasped object, and let \u2018nc be the number of contacts on finger i. The superscript \u201ciJ\u2019 is used to denote the j f h contact on the ith finger. Further, let np be the number of contacts with fixed surfaces, and let the superscript \u201cl\u201d denote the l fh contact with a fixed surface. In Figure 2, we consider a contact between a grasped object and a finger. If the bodies are perfectly rigid we can define the contact point which is the coincidence of two points, iJJoB fixed to the grasped object and i\u2019JoA fixed to the finger. Because all real bodies are not perfectly rigid the contact will occur over a small but finite area. However it is still possible to define the points \u2018PJoA and i,JoB as the points at the centroid of the contacting surface [9]. The point i j ~ A is used to define the origin of moving coordinate frame attached to the finger",
+            " Similarly, we can use a linear tangential spring perpendicular to the contact normal and a linear rotational spring about the normal, with spring constants k, and ke, respectively. Consider an individual contact between a finger and the grasped object. A second order model describing the surface of the finger is given by [lo]: where X A and y A are aligned with the principal axes of curvature of the finger, KUA is the curvature along the xA axis, K,,, is the curvature along the Y A axis, and ZA is the outwardly pointing normal (see Figure 2). x A , y A , and zA define an orthogonal coordinate frame, affixed to the finger, which we refer to as oA.The grasped object is likewise modeled, using the subscript \u201cB\u201d (see also [12]) The angle I+Y specifies the orientation about the common normal of one 2Z,4 i- KUA X i f K,,, y ; = 0 (7) 1368 body with respect to the other. In Figure 2b, this angle is defined such that a positive (counterclockwise) rotation of X , about zA through yaligns the axes X A and xB. In general, II# 0 (i.e. the pFinciple axes of curvature are not aligned). In [5,9], we show that following relationship applies: where the contact stiffness matrix, K,, is the 6x6 matrix given by Equation (9) below: F,,L,(L, + c a ) ' t B + k , ~ oZxf -F,,L,(L, + t , ) ' ~ oZxt AF/A = -K, AX^,, (8) Oh* kll orx> 0 (MOL, -F ,d ) (L , + L B ) ' L B AF,\" (F , , ,A-4LA)(LA + c B r ' A I FE A 0 O M ko F,, is the applied normal force, FtXO and Ftyo are the Cartesian components of the applied tangential (frictional) force (in the xA and yA direction, respectively), and M O is the applied torsional moment"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000497_a:1008966218715-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000497_a:1008966218715-Figure1-1.png",
+        "caption": "Figure 1. Scanning range of laser range finder.",
+        "texts": [
+            " The map of the whole environment is essentially a collection of the obstacle regions characterized by their own stochastic parameters. This paper is organized as follows. Section 2 introduces the concept of clustered region and describes the data clustering procedure. Section 3 introduces the concept of obstacle region and presents a map building procedure using the obstacle regions. Experimental results are discussed in Section 4, and conclusions and comments on future research are made in Section 5. Figure 1 shows the scanning range of the laser range finder that covers about 270\u25e6 of the front side. The center position pc of the mobile robot is represented as (xc, yc) in terms of the world coordinate frame. The incoming data are numbered in the counterclockwise direction and l j , j = 0, 1, . . . 270, are the distance values from the center position of the laser range finder to the objects. The object position p j = (x j , y j ) is determined from the measured distance l j as follows: p j = (x j , y j ) = ( xc + l j cos ( ( j \u2212 45)\u03c0 180 + \u03b8c\u2212 \u03c0 2 ) \u2212 ld cos \u03b8c, yc+ l j sin ( ( j \u2212 45)\u03c0 180 + \u03b8c\u2212 \u03c0 2 ) \u2212 ld sin \u03b8c ) = (xc, yc) + ( l j cos ( ( j \u2212 45)\u03c0 180 + \u03b8c \u2212 \u03c0 2 ) \u2212 ld cos \u03b8c, l j sin ( ( j \u2212 45)\u03c0 180 + \u03b8c \u2212 \u03c0 2 )\u2212 ld sin \u03b8c )) = pc + l j where ld is the distance from the center of the laser scanner to that of the mobile robot and \u03b8c is the angle of the mobile robot measured counterclockwise from the positive x-axis"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002923_acc.2005.1470620-Figure8-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002923_acc.2005.1470620-Figure8-1.png",
+        "caption": "Fig. 8. ECAV velocities when the ECAV imposes a restriction on the phantom\u2019s velocity annulus.",
+        "texts": [
+            " For any number of ECAVs, for all realistic initial conditions there will always be a feasible velocity sector for the phantom which would guarantee feasible trajectories for the ECAVs. The algorithm would then pick a velocity for the phantom from its feasible velocity sector which would make it travel towards the final waypoint in minimum time. If any one of the ECAV\u2019s states is such that it imposes a restriction on the phantom\u2019s movement through the sufficient condition, it is interesting to note that no matter what velocity heading is picked for the phantom, the ECAV can travel only in a direction that would relax the restriction placed by it at the phantom. Fig.8 illustrates this point. Here 0 max 0 maxr V R W , this implies for all cr It can be then shown that, Hence in the absence of additional constraints, any restriction placed by ECAVs on the velocity annulus of the phantom only relaxes with travel time and ultimately would cease to apply. It can be shown that the condition for an ECAV to be collinear with the phantom and the radar for all time and not just at the end of time steps of the algorithm is, 0 maxmin max 0 min r WW V R V (13) The initial conditions that all ECAVs should satisfy to guarantee a straight line path for the phantom from its first waypoint to the targeted waypoint is, 0, max 0, min i i r W R V (14) where i indexes the ECAVs. When the ECAVs are free to pick one of two velocity headings as shown in the right hand diagram of Fig.8, the algorithm picks the velocity that would take the ECAV to the range given in (13). The fact that the ECAVs will, for most times, have two velocities to pick from, allows the algorithm to easily implement a lower bound on the range of the ECAVs from their respective radars. The algorithm was coded in MATLAB and Fig. 9 gives the simulation results for the case of four ECAVs when the initial conditions are such that initially restrictions are imposed on the annular velocity sector of the phantom"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000385_s0045-7949(98)00165-5-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000385_s0045-7949(98)00165-5-Figure1-1.png",
+        "caption": "Fig. 1. Triangular plate element with layer-wise approximation.",
+        "texts": [
+            " The element can be considered an extension of the linear/ quadratic Reissner\u00b1Mindlin plate element based in an assumed shear strain approach formulated by Zienkiewicz et al. [4], Taylor and Papadopoulus [5] and On\u00c4 ate et al. [6\u00b18]. The inplane element displacements are interpolated linearly inside every layer and they are eliminated during the global assembly by means of a condensation technique. In the following sections details of the element formulation are presented, together with some examples of applications to static, dynamic and instability analysis of laminated composite plates and shells. Fig. 1 shows the geometry of the element. It is worth noting that the laminate is discretized into n analysis layers and n + 1 interfaces. The analysis layers can or cannot coincide with the real material layers. The horizontal displacements (in plane displacements) for the kth layer are interpolated as 0045-7949/99/$ - see front matter # 1999 Published by Elsevier Science Ltd. All rights reserved. PII: S0045-7949(98 )00165-5 u v n o X3 i 1 Ni x; Z Nk z uki vki Nk 1 z uk 1i vk 1i ( )24 35 X6 i 4 Ni x; Z ei\u00ff3 Nk z Dukti Nk 1 z Duk 1ti h i 2 where Dukti (i = 4, 5, 6) are the nodal displacement increments at the element mid-sides for the kth interface in the direction of the unit vectors ei \u00ff 3 (Fig. 1). The normal displacement is assumed to be constant across the thickness and it is interpolated in terms of the corner values in the standard fashion as w X3 i 1 Ni x; Z wi 3 In Eqs. (2) and (3) Ni x; Z Li i 1; 2; 3 N4 x; Z 4L1L2; N5 x; Z 4L2L3; N6 x; Z 4L1L3 4 where Li are the linear shape functions for the three node triangle [9] and Nk z 1\u00ff z 2 ; Nk 1 z 1 z 2 5 Eqs. (2) and (3) imply a hierarchical quadratic interpolation for the in-plane displacements u and v in the plane of every layer and a linear interpolation for w",
+            " The displacements u 0, v 0 in the element plane corresponding to the kth layer are interpolated by [1\u00b13]: u 0 v 0 X3 i 1 Ni x; Z u 0oi v 0oi Nk z u 0ki v 0ki Nk 1 z u 0k 1i v 0k 1i ( )24 35 X6 i 4 Ni x; Z ei\u00ff3 Nk z Dukti Nk 1 z Duk 1ti h i 16 where u 0oi v 0 oi n o are constant (rigid-body) in-plane displace- ments across the thickness of the laminate, u 0ki v 0k i n o are the in-plane displacements which are variable over the thickness and Dukti are the in-plane displacement increments in the midside nodes of the triangle in the directions de\u00aened by the tangent vectors ei \u00ff 3 (Fig. 1). The normal displacement w 0 is assumed to be constant throughout the thickness. Following this hypothesis it is possible to write w 0 X3 i 1 Ni x; Z w 0i 17 In Eqs. (16) and (17) the shape functions are the same that those given by Eqs. (4) and (5). Eqs. (16) and (17) de\u00aene a quadratic interpolation over every interface for the in-plane displacements u 0 and v 0 and a linear interpolation for the displacement w 0. The local strains for the kth layer are written e 0b @u 0 @x 0 ; @v 0 @y 0 ; @u 0 @y 0 @v 0 @x 0 \" #T Bba 0 18 e 0s @w 0 @x 0 @u 0 @z 0 ; @w 0 @y 0 @v 0 @z 0 \" #T Bsa 0 19 where e 0b are the local strains accounting for membrane and bending e ects and e 0s are the transverse shear strains"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000845_s0967-0661(00)00032-0-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000845_s0967-0661(00)00032-0-Figure2-1.png",
+        "caption": "Fig. 2. Flexible body structure in the pitch plane.",
+        "texts": [
+            "qP 0 , (7) where a, b represent angle of attack and side slip angles, respectively, >b , Za are aerodynamic force coe$cients, M q , Ma , N r , Nb are aerodynamic moment coe$cients, >d , Zd are control force coe$cients, Md , Nd are control moment coe$cients, d y , d z are canard de#ections in the pitch and yaw direction, respectively. If P 0 is equal to zero, the dynamics of the pitch and yaw axis is decoupled completely and the transfer function between the pitch angular velocity and the canard \"n de#ection can be written as q(s) d z (s) \" Mds#(ZdMa!ZaMd ) s2!(Za#M q )s!(Ma!ZaMq ) (8) 2.3.2. Bending vibration dynamics The gyroscope in the rocket attitude control loop measures not only the rigid body motion but also the bending vibration mode due to the #exible body e!ect as in Fig. 2, which can be expressed mathematically as m(l ) L2m(l, t) Lt2 # L2 Ll2 CEI(l ) L2m(l, t) Ll2 D\"Fd(l, t), (9) where m is the mass per rocket unit length, m the rocket de#ection due to bending moment, E the Young's modulus, I the area moment of inertia about neutral axis, Fd the external force of bending vibration. Assume the solution of (9) can be separated in time and space and of the form (Meirovitch, 1967) m(l, t)\" = + i/1 u i (l )g i (t), (10) where u i and g i are the eigenfunction and normal coordinate of ith bending mode"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001799_s0168-874x(02)00056-2-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001799_s0168-874x(02)00056-2-Figure1-1.png",
+        "caption": "Fig. 1. Principle illustration of a rotary forging process: 1\u2014rocker; 2\u2014billet; 3\u2014ram; 4\u2014oil vat.",
+        "texts": [
+            " The pressure distributions of the contact surface along the radial and tangential directions and e9ects of rotary forging parameters on deformation characteristics are given. ? 2002 Elsevier Science B.V. All rights reserved. Keywords: Metal forming; Finite element method; Rotary forging; Ring workpiece A rotary forging process is a kind of metal forming method where a conic upper die, whose axis is deviated an angle from the axis of machine, forges a billet continuously and partially to \"nish the whole deformation, as shown in Fig. 1. To date, much of the research work on rotary forging has been conducted in many countries, such as Britain, Japan, China, Germany, America, Poland and the former Soviet Union. These works concentrated mainly on calculating and verifying the energy parameters and measuring the pressure distributions at the contact area. However, due to the di9erent experimental methods and conditions used by researchers, the results obtained could not show a general agreement. At the same time, because of the complexity of kinematics relationship between \u2217 Corresponding author"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001183_s0020-7683(00)00010-x-Figure10-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001183_s0020-7683(00)00010-x-Figure10-1.png",
+        "caption": "Fig. 10. Dimensions of circular bearings.",
+        "texts": [
+            " (48) is dmax h F0 P 2 jg1j g2 2 g2 3 q : 63 The maximum height reductions calculated from the above equation shows that, subjected to the same compressive force and the same amplitude of horizontal displacement, columns of a smaller rigidity ratio q or a smaller loss factor g have a higher height reduction. Two groups of isolation bearings were used in the cyclic shear tests. One group of bearings were made of high-damping rubber and the other group of bearings were made of normal rubber, which has a lower damping value. The dimensions for the two groups of bearings were identical. Each group had two shapes: circular and square. The circular bearings, whose dimensions are shown in Fig. 10, have 20 thin rubber layers with thickness t 10 mm and 19 steel shims which are 2 mm thick. The total rubber thickness is tr 200 mm and the height of the bearing excluding the end plates is h 238 mm. The shim diameter is d 280 mm and there is 10 mm of cover for a total diameter of 300 mm. The square bearings, whose dimensions are shown in Fig. 11, have the same number of rubber layers and steel shims as do the circular bearings, but the thickness of the rubber layers is t 6 mm. The total rubber thickness is tr 120 mm and the height of the bearing excluding the end plates is h 158 mm"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000423_1.2834110-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000423_1.2834110-Figure1-1.png",
+        "caption": "Fig. 1 Journal bearing cross-section with relevant nomenclature. The journal (inner member) is rotating clockwise and the bearing (outer member) is stationary.",
+        "texts": [
+            " Furthermore, microfabrication concerns impede or exclude ad ditional means of stabilization, such as herringbone grooves (Fleming and Hamrock, 1974), tilting pads (Lund, 1968), and mid-bearing hydrostatic jacking ports (Powell, 1964). This work was undertaken to provide the tools and understand ing necessary to produce stable gas journal bearings for high speed microturbomachines. To do this, a flexible simulation code was written to allow many design options and manufacturing defects, as well as the interplay between them, to be examined. Bearing Nomenclature and Parameterization The geometry and nomenclature used in this work are shown in Fig. 1. In this article, W is the applied load, R is the bearing radius, r is the journal radius, and their difference, the clearance, is denoted by c. The attitude angle, <\u0302 , is the angle between the applied load and a line connecting the journal and bearing cen ters. The excursion of the journal center from the bearing center, denoted by e, is normalized by c and expressed as an \"eccen tricity ratio,\" e, so e = 0 and e = 1 represent fully-centered Contributed by the Tribology Division of THE AMERICAN SOCIETY OF IMECHANICAL ENGINEERS and presented at the Joint ASME/STLE Tribology Conference, Toronto, Canada, October 25-29, 1998",
+            " Toward this end, following Ausman (1961), $ is defined as the pressure, p, times the channel height h. The Reynolds equation for a compressible, isothermal ideal gas in a journal bearing with perfect axial alignment (i.e., discarding terms involving changes of passage height in the axial direction) may then be expressed as: /!* - ^ ' \u2022 d^h ^ dhd^ , - * + h de do de) (6) for a bearing-centered, non-rotating coordinate system. The ^- coordinate refers to the axial direction (perpendicular to the page in Fig. 1) and is normalized by r. Position in the circumfer ential direction is fixed by 0, which is measured counter-clock wise from a vertical line and is zero at the top of the bearing. This equation differs from that employed by Cheng and Pan only in the absence of a grid rotation term. It is very convenient for a spectral method because it is devoid of cross-derivatives and, in total, only four spatial derivatives must be computed. Just two forward transforms and four backward transforms are therefore required per timestep"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001191_0005-1098(93)90125-d-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001191_0005-1098(93)90125-d-Figure2-1.png",
+        "caption": "FIG. 2. Top view and kinematic parameters of a mobile robot.",
+        "texts": [
+            " Its kinematics and dynamics can be modeled based on the necessary assumption that the wheels are ideally rolling. The conditions to achieve rolling without slipping and skidding are presented. 2.1. Kinematic modeling Although the development of Alexander and Maddocks (1989) is based on the assumption of planar motion their analysis holds for the case of general terrains with the additional assumption that the curvature of the floor is such that sufficient contact of the wheels is guaranteed. Consider the top view of a mobile robot (Fig. 2) moving along a trajectory described in a parametric form by r(s) where s is the parametrization variable. The world coordinate frame (Px, Py, Pz) with unit vectors (i, j, k) is fixed at O. The body coordinate frame (pff, p~, p~) is attached to the body at point B and moves along r(s). The motion of the robot is described by r(s) and the orientation angle function O(s), defined as the angle between px and pff. The instant translational velocity of the robot with respect to the world coordinate frame is ~(t) and its rotational velocity is tb ( t )= to(t)/~",
+            " (1986). A strategy for obstacle avoidance and its applications to multi-robot systems. In Proc. of the 1988 IEEE Int. Conf. on Robotics and Automation, pp. 1224-1229. Wu, C. and C. Jou (1988). Design of a controlled spatial curve trajectory for robot manipulators. In Proc. of the 27th Conf. on Decision and Control, pp. 161-166. APPENDIX A: ROBOT INVERSE DYNAMICS If it is known that the object has, at instant t, translational velocity, v(t), orientation angle O and rotational velocity to(t) = O(t) (Fig. 2). Then the instantaneous angular velocity and steering angle of the wheel i, are (Alexander and Maddocks 0989)): b, = 1 r X ~/Iv(t) 2 + Ixffl 2 (to(t)) 2 - 2 \u00d7 Io(t)l txffl to(t) cos (fl - ai - O(s(t))), (A.1) & = t - l / v(t)l sin )6 - Ix~l to(t) sin (o<i + O(s(t))) '~ an ~,lv(t)l cos fl - Ix~l to(t) cos ( ~ + O(s(t)))] - O(s(t)). (A.2) There are the inverse kinematics equations for a general mobile robot, i.e. given v(t), O(t), O(t) equation (A.2) gives the angular velocities Oi(t ) and steering angles ~b~a(t) of every wheel i"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000497_a:1008966218715-Figure11-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000497_a:1008966218715-Figure11-1.png",
+        "caption": "Figure 11. Uncertainties of the robot position.",
+        "texts": [
+            " In order to see how the uncertainty is reflected onto the object position, we write the object position p j introduced in Section 2.1 as p j = pc + l j = p\u2217c +1pc + l\u2217j +1l j = p\u2217j +1pc +1l j , where p\u2217j represents the nominal value of p j , 1pc is the position error of the mobile robot and 1l j is the error of the object position due to the orientation error 1\u03b8 of the mobile robot. 1pc causes a proportional effect on all of the object positions included in Ri and cause Ri to move by 1x and 1y as shown in Fig. 11. Meanwhile, 1l j is determined as 1l j = l j \u2212 l\u2217j = l j [cos(\u03b8 j +1\u03b8c), sin(\u03b8 j +1\u03b8c)] \u2212 l j [cos \u03b8 j , sin \u03b8 j ] = l j [cos(\u03b8 j +1\u03b8c)\u2212 cos \u03b8 j , sin(\u03b8 j +1\u03b8c)\u2212 sin \u03b8 j ] = 2l j sin 1\u03b8c 2 [ sin ( \u03b8 j + 1\u03b8c 2 ) , cos ( \u03b8 j + 1\u03b8c 2 )] . As long as 1\u03b8c is not zero, 1l j depends on l j and \u03b8 j , and cause Ri to rotate as shown in Fig. 11. Consequently, the error in the clustered region Ri due to the error in the robot position can be described as the proportional and rotational errors in the clustered region and they can be reflected on the matching conditions introduced in the previous section. 1l j can be taken into account in matching condition (1) in Section 3.3 by writing it as |\u03b8\u0304k \u2212 \u03b8i | < \u03c3\u03b8 + 1Lmax, where 1Lmax is the threshold constant determined from the maximum bound of 1\u03b8c. 1pc can also be considered in matching condition (2) in Section 3"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000582_1.1316796-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000582_1.1316796-Figure1-1.png",
+        "caption": "Fig. 1 Geometry of interception process",
+        "texts": [
+            " It is followed by the design of continuous-type VSC control laws for the two cases of the longitudinal-axis control being available and unavailable. In Section 4, numerical simulations are presented and compared with those by Realistic True Proportional Navigation design ~Yang and Yang @13#! to illustrate the use of the proposed scheme. Finally, Section 5 summarizes the main results. This paper considers the design of guidance law for homing missile interception. The relative motion between a missile and its target is described by the spherical coordinate system with the origin fixed on the location of the missile as depicted in Fig. 1, where er , eu , and ef denote the three unit coordinate vectors in the spherical coordinate system, respectively. For the design of the guidance law, we assume that both the missile and target are point masses and only system kinematics are considered. The governing equations for the relative motion is given by ~Yang and Yang @13#! r\u03082rf\u030722r u\u03072 cos2 f5aTr2aMr , (1) r u\u0307 cos f12 r\u0307 u\u0307 cos f22rf\u0307u\u0307 sin f5aTu2aMu (2) and rf\u030812 r\u0307f\u03071r u\u03072 cos f sin f5aTf2aMf . (3) Here, r is the relative distance between the missile and target, u and f are the azimuth and pitch angles, respectively, aMr , aMu , and aMf denote the three commanded acceleration components of the missile in the spherical coordinates, which are to be designed to achieve the interception mission"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002038_ls.3010080402-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002038_ls.3010080402-Figure2-1.png",
+        "caption": "Figure 2Definition of distribution parameters of two rough surfaces in contact",
+        "texts": [
+            "23 Modified model The concept of a true area of contact plays a central role in adhesive wear modelling since, without contact between interacting surfaces, there is no wear. Hence the first step, in the approach proposed here, is to examine the probability of contact between the asperities of the interacting surfaces. Williamson24 showed that most machined surfaces have asperity height distributions that are closely Gaussian. Thus, if x is the variable describing the height distribution of the surface contour, as shown in Figure 2, then it may be assumed that a function F(x) for the cumulative probability that the random variable r will not exceed the specific value X exists; this will be called the distribution function. Thus, the probability density function F(x) may be expressed as: Lubrication Science 8-4, July 1996. (8) 320 0954-0075 $1 0.00 + $4.00 32 1 T.A. Stolarski : A System for Wear Prediction in Lubricated Sliding Contacts The probability that the variable x will not exceed a specific value X is given by: X F ( x ) = P(x 5 X) = f(x)dx Referring to Figure 2, we note that the distance between the mean lines of peaks x for a given separation of contacting surfaces h (h can be regarded here as the thickness of a lubricating film for the case of a lubricated contact) is where between surfaces may be defined as: and xp2 are defined in Figure 2. The clearance Ah = i - h l - h 2 where hl and h2 are random variables defined in Figure 2. asperities is then The probability of interference between any two mating where (-Ah) is a random variable that has a Gaussian distribution with probability density function: 1 -(h-Ah) $(-Ah) = - so that is the probability that Ah is negative, i.e., the probability of asperity contact. In the foregoing, is the standard deviation of peaks. 2 1 / 2 = (oil + cp2) Lubrication Science 8-4, July 1996. (8) 321 0954-0075 $10.00 + $4.00 322 T.A. Stolarski : A System for Wear Prediction in Lubricated Sliding Contacts The probability P(Ah I 0) of asperity contact can be found from the normalised contact parameter = Z/o*"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000497_a:1008966218715-Figure10-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000497_a:1008966218715-Figure10-1.png",
+        "caption": "Figure 10. Representation of angle interval of Mk .",
+        "texts": [
+            " In other words, we do not know whether M1 or M2 has been moved or not, because they have not been currently detected. The obstacle region M7 is associated with R4, but it is not updated because part of it is located outside of the field of view. In order to check whether the obstacle region that is not associated with any of Ri \u2019s is located inside of the field of view, we use the angle interval of the obstacle region. The angle interval of Mk is the interval of directions along which the laser range finder detects the obstacles in Mk . As shown in Fig. 10, the angle interval is determined from the major eigenvector of Mk . Its major eigenvector is described as e\u0304k \u2212 s\u0304k , where e\u0304k and s\u0304k represent its start and end positions in the sensor coordinate frame. The angle interval of Mk is then determined as [6 s\u0304k, 6 e\u0304k], where s\u0304k = m\u0304k + \u03bb\u03041k \u03c6\u0304k \u2212 pc, e\u0304k = m\u0304k \u2212 \u03bb\u03041k \u03c6\u0304k \u2212 pc, and pc is the center position of the mobile robot. As shown in Fig. 9, the angle intervals of the obstacle regions such as M1 and M7 range outside of [0, 270] and their parameters remain unchanged"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002052_s0141-6359(02)00227-1-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002052_s0141-6359(02)00227-1-Figure4-1.png",
+        "caption": "Fig. 4. Incline compensation control (method 1).",
+        "texts": [
+            " The disturbance invariably introduces the attitude fluctuation of XY stage. Then, its reformation produces desirable results for higher and precise positioning of XY stage. Concretely, the incline compensation for the main body is realized by generating the driving force in proportional to XY stage position for vertical air-springs. In other words, it is necessary to realize the proportional relationship between XY stage position and the air-spring driving forces. There are two methods concerning the incline compensation. First method is as follows. As shown in Fig. 4, the present XY stage positions are measured by laser interferometers which are used for feedback purpose. Then its signals are fed forward to the vertical air-springs having the pressure feedback. Second method is as follows. As drawn by heavy solid line in Fig. 3, the velocity profile signal of XY stage is fed forward to the vertical air-springs with the pressure feedback through the feed-forward compensator. Concretely, its compensator is PI type and the derived signal through I-element becomes the equivalent position signal, which can mainly correct the incline of the main body"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001599_s0009-2509(96)00506-4-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001599_s0009-2509(96)00506-4-Figure1-1.png",
+        "caption": "Fig. 1. Definition sketch of forward roll coating with deformable rolls.",
+        "texts": [
+            " Usually, controlling the thickness of the coated film is of prime importance. This is done by having the fluid flow between two counterrotating cylinders, the surfaces of which move in the same direction at the nip. Most previous studies of forward roll coating focused on the simple case of two rigid rolls separated by a narrow gap (see e.g. Pitts and Greiller, 1961; Savage, 1982; Coyle, 1984). In many cases, however, one of the rolls is rubber covered, and both rolls are pressed against each other by an external load W (Fig. 1). The coating thickness is thus governed by the operating parameters (speeds and loading), the mechanical properties of the solids, and the mechanical properties of the fluid. The general features of roll coating operations inw)lving a deformable roll have been described by Coyle (1988a). He analysed the flow in the deformable nip by means of two dimensionless numbers, the *Correspondence address: Laboratoire de Rh6ologie, B.P. 53 Domaine Universitaire, 38041 Grenoble Cedex 9, France. elasticity number being the ratio of viscous to elastic forces, q V Es = (1~ ER and the load parameter being the ratio of the external load to the elastic forces, W Fw - "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003985_tro.2006.878956-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003985_tro.2006.878956-Figure3-1.png",
+        "caption": "Fig. 3. Partitioning the distance computation.",
+        "texts": [
+            " As shown by [2], the length of the RS shortest paths induces a metric on the configuration space, and this metric is equivalent to the sub-Riemannian distance [16] associated with the control system representing the RS car model. The length d is, therefore, a distance to the closest obstacle in the configuration space and is a function of the robot\u2019s current state and of the shapes of the robot and the obstacles. In this paper, we will assume, wlog, that the robot starting configuration is the origin (0; 0; 0)T . It is useful to partition the distance computation problem into the three subproblems of bringing into contact (see Fig. 3): (i) one vertex qi of the robot with one vertex oj of the obstacle; (ii) one vertex qi of the robot with the line vj supporting one edge ojoj+1 of the obstacle; (iii) the line wi supporting one edge qiqi+1 of the robot with one vertex of the obstacle oj . If one is able to solve these subtasks, it is possible to find the shortest path to an obstacle by iterating the three steps over all the robot/obstacle vertex/edge combinations, and by choosing the minimum from among the obtained path lengths",
+            ", at least one RS path parameter is outside its range of validity; \u2022 a valid solution exists. In the first two cases, Lp (V Vp (qi; oj)) is discarded by setting it equal to 1. 1) Handling Type-B Paths: Preliminary remark: throughout the following sections, time dependency is omitted when no confusion is possible. In order to find the solution of V Vp (qi; oj) for each path pk of Type-B, we will use a property derived from the transversality conditions on the final state. Let (li; i) be the pair representing the length of the segmentPqi and the angle between the vectors ! Pqi and !v (Fig. 3). The coordinates (qi ; qi ) of the robot vertex are x+ li cos( + i) = qi y + li sin( + i) = qi : (9) Denoted by (oj ; oj ) the Cartesian coordinates of the target vertex oj of the obstacle, we define the 1-D contact manifoldCij V V( )=f jqi=ojg, which can be represented by ijV V ( ) = x oj + li cos( + i) y oj + li sin( + i) = 0 0 : (10) Equation (10) describes a vertical helix centered on oj (Fig. 4) and will be used for finding the solution path, i.e., for determining the three RS path parameters (a; b; e)"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001861_pesw.2000.849993-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001861_pesw.2000.849993-Figure1-1.png",
+        "caption": "Fig. 1 shows only the A-phase stator winding configuration of the experimental motor. The arc angle of the rotor and stator teeth is d 1 2 (15deg). The motor main winding Nmo consists of 4-coils connected in series. On the other hand, the radial force windings NSu, and Nsu2 consist of 2-coils, respectively. These coils are separately wound around confronting stator tooth. The B-phase windings are situated on one third rotational position of the A-phase. The C-phase windings are situated on two thirds rotational position of the A-phase. The radial forces are generated by these three phases for every 15deg. i.e., between the start of overlap and aligned positions.",
+        "texts": [
+            " another control method based on the instantaneous rotational torque and the instantaneous rahal forces for realizing the stable operation under every conhtion from no load to full load was proposed in another paper [ 101. Except a low rotational speed, it is not always necessary to consider the instantaneous rotational torque. Therefore, A new control method is based on the average rotational torque and the instantaneous radial forces for simplifying the drive system and realizing the high speed drive. 0-7803-5935-6/00/$10.00 (c) 2000 IEEE 375 The rotor angular position B is defined as 8 = 0 at tlie abgned position of the A-phase. The rotor angular position B of Fig. 1 is -lOdeg. 111. PRINCIPLE OF RADIAL FORCE PRODUCTION Fig.2 shows the principle of radial force production of the proposed bearingless switched reluctance motor. The thick solid lines show the symmetrical 4-pole fluxes produced from the +pole motor main winding current 1,. The broken lines show the symmetrical 2-pole fluxes produced from the 2-pole radial force winding current isal . It is evident that the flux density in the air-gap 1 is increased. because the direction of the 2-pole fluxes is the same as that of the 4-pole fluxes"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001423_s1350-4533(99)00095-8-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001423_s1350-4533(99)00095-8-Figure6-1.png",
+        "caption": "Fig. 6. The origin of the lumbrical (white ellipse) is assumed fixed on the tendon of the FDP (shown in gray). When the finger is straight, the",
+        "texts": [
+            "0 0 , else J where: 2p \u2192 lat,origin53 xlat,origin+rPIPqPIP \u2212rPIP 0 4 (7) 3p \u2192 lat,union53 xlat,union+rDIPqDIP \u2212rDIP 0 4 (8) F 2p \u2192 lat,union 1 G5 2T3F 3p \u2192 lat,union 1 G (9) where ,band is the effective length of the lateral bands, qPIP is the flexion angle of the PIP joint, qDIP is the flexion angle of the DIP joint, rPIP is the effective radius of the joint capsule surrounding the head of the proximal phalanx, rDIP is the effective radius of the joint capsule surrounding the head of the middle phalanx, xlat,origin is the effective origin of lateral bands when finger joints are straight, x-coordinate with respect to proximal phalanx (coordinate-system-2), xlat,union is the effective union of lateral bands when finger joints are straight, x-coordinate with respect to the middle phalanx (coordinate-system-3), and 2T3 is the homogeneous transform from coordinate-system-3 to 2. The lumbrical muscle originates on the tendon of the FDP, between the wrist and MCP joint. Flexion of the finger joints allows the origin to move toward the wrist, roughly along the long axis of the metacarpal bone (Fig. 6). The instantaneous length of the lumbrical is taken to be the distance between the origin of the muscle, and the insertion of the muscle on the extensor hood. ,LUM5||0p \u2192 ins2 0p \u2192 LUMo||2 (10) where ,LUM is the length of the lumbrical muscle, 0p \u2192 ins are the coordinates of insertion of LUM and rIOSS on the extensor hood, and 0p \u2192 LUMo are the coordinates of origin of the lumbrical on the FDP tendon. The coordinates of the lumbrical origin when the finger is straight ( 0p \u2192 LUMo,straight) are expressed with respect to the metacarpal bone. Excursion of the FDP with finger flexion (Fig. 6) is assumed to translate the lumbrical origin from this location such that: 0p \u2192 LUMo5 0p \u2192 LUMo,straight1 0Dp \u2192 LUMo (11) and: 0Dp \u2192 LUMo5,FDP 0u \u2192 FDP (12) where 0p \u2192 LUMo are the coordinates of lumbrical origin with respect to the metacarpal, 0p \u2192 LUMo,straight are the coordinates of lumbrical origin with respect to the metacarpal when all joints are straight, ,FDP is the excursion of the Flexor Digitorum Profundus from rest (Eq. (2)), 0u \u2192 FDP is the unit vector giving direction in which FDP tendon moves when FDP muscle lengthens, and 0Dp \u2192 LUMo is the displacement of the FDP tendon and lumbrical origin caused by flexion of the finger joints"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003183_3.20488-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003183_3.20488-Figure2-1.png",
+        "caption": "Fig. 2 Labeling position vectors in adjacent bodies.",
+        "texts": [
+            " In the derivation of the equations for the kinematics, we will use the tree array as a basis for our analysis. (Further details on the tree array could be found in Ref. 23.) In the notation, the summation sign is omitted in the equations such that a repeated subscript index in a term implies summation over the range of that index. Superscripts are generally part of the labeling and do not imply summation unless otherwise explicitly stated. III. Kinematics of Flexible Bodies 1. Representation of a Flexible Body In Fig. 2, two typical connecting bodies Bk and Bj where j = T(k) are shown. The connection points assumed to lie on the centroidal line of the respective bodies are denoted by Ok and Of, on Bk and BJ9 respectively. The rigid-body degrees of freedom of Bk are characterized by the relative translation and rotation of the nk axis fixed at Ok with respect to the nk* axis (fixed at Of). Let nk be the body reference axis relative to which the deformation of the body will be defined, Bk will be considered to be composed of Ek number of small elements in the manner shown in Fig. 2, where rki is the undeformed vector from Ok to the mass center of /th element. Let nki represent the axis fixed in this element. Finally, let nk, nk*, and nki be oriented such that \u00bb*, n**, and /if are tangent to the centroidal line and the second and third components form the principal axes of the cross section. The local motion of the element due to deformation with respect to nk can be described by three translation components wf, 1/2', and wf1' and three rotation components 9ki, 0*1', and 9ki representing the rotation of nki with respect to nk",
+            " Angular Accelerations The angular acceleration of the I'th element in Bk is found by differentiating Eq. (20); hence, (25) The vkipm and ^z>w are obtained by replacing the transformation matrices in Eqs. (18) and (19), respectively, by their derivatives utilizing Eq. (12). Note that vk m and \\Jiki m are functions of angular velocity components as well as displacements. 5. Mass Center Velocities and Accelerations The position vector from the fixed reference axis w\u00b0 in R to the mass center of the ith element in Bk is given by (with the notation of Fig. 2) (26) (17) where the summations are carried for the bodies along the path from Bk to R and where dl = 0. D ow nl oa de d by P U R D U E U N IV E R SI T Y o n A pr il 13 , 2 01 5 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /3 .2 04 88 NOV.-DEC. 1989 DYNAMICS OF FLEXIBLE TREELIKE STRUCTURES 833 By differentiation, the mass center velocity of the element is obtained as H(k) H(k) H(k)nP Z where s = Yq(k) and p = T(s). The ds can be written as (27) (28) where qs is the vector in the undeformed state"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002270_robot.2001.933127-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002270_robot.2001.933127-Figure1-1.png",
+        "caption": "Figure 1: Three-link 3R planar robot manipulator. This configuration is known as SCARA. The angles { 0 1 , 0 2 , 0 3 } are measured counterclockwise. {z, y} is the location of the third joint.",
+        "texts": [],
+        "surrounding_texts": [
+            "Lemma 3.2. The vector field V zs decoupling for the mechanical system ( 3 ) zf and only zf\nfol- d l 1 5 b 5 n - rn.\nProof. Consider a curve q ( t ) on Q such that i ( t ) = S( t )V(q ( t ) ) . W e compute the quantityoya using two properties of the covariant derivative; see [14]. Since 0x5' is a. differentiation in the second argument, one call prove that\noyfj = vq ( S V ( q ) ) = SV(q) + so$+$ Furthermore, since VxY is linear in the first argument, oiie can prove that\nNexl,, the mrve q ( t ) is a kinematic motion and I/ is a decoupling vector field if the constraints (8) are satisfied. These can be written as:\nfor all 1 5 b 5 n - 7n. Note that ( ( V , xb)) and ((VI/\\[, Sb)) are equivalent to a(.) and b(s) in equatioii ( t ) , respectively. Since s is an arbitrary time scaling and qo is an arbitrary point, V and V v V niiist separately have a vanishing inner product with -7jb. The sillne argument also shows the other implication U\nR.oughly speaking, equation (11) encodes the requiremeiit tlmt motion along V at constant speed be feasible. Equation (10) requires the system to be able to speed u p and slow down the motion along V .\nNote h a t scalar multiples of decoupling vector fields a.re a.gain decoupling, but linear combinations ma.y not be decoupling. There are mechanical control systems for which no decoupling vector fields can be found. The maximum number of linearly independent decoupling vector fields is m..\nA.s described in the introduction, decoupling vector fields reduce the complexit>y of motion planning problems by turning a dynamic problem in to a driftless kinema.tic one. Accordingly, it is of interest to define the class of systems for which this approach a.mlies.\nDefinition 3.3 (Kinematic con trollability). The m.echanica1 system ( 3 ) is kinematically controllable i f every point in the configuration space Q i s reachable via a sequence of kinematic mmtions. The system ( 3 ) i s locally kinematically controllable i f fo,r any q E Q and any neighborhood U, of q , the set of reachable configurations fr0m.q by kinematic motions remaining in U, contains q in its interior.\nObviously, the main difficulty is that there simply might not be enough decoupling fields for controllability. A sufficient test for local kinematic'controllability is given below. We assume the reader to be familiar with the Lie algebra rank condition for local controllability; see [15]. Lemma 3.4. The system ( 3 ) i s locally kinematicully controllable if there exist p 5 m vector fields {VI , . . . , VP} such that\n(ai) Lie{Vl,. . . , I+} has rank 11 at all q E R\"\nProof, Property ti) ensures that the vector fields V, are decoupling. Property ( i i ) ensures the local con- ~- trollability of the driftless k i k\nP 4 = C K ( ( I ) w c\nC = l\n( W l , . . . ,,uJp) E ((*1,0,. . . (0,. . , o , f\niatic system (2)\nO), (0, *l, 0,. . . , O ) , . . . , )>\nand therefore every point in the configuration space is reachable. In the presence of obstacles, a collisionfree path exists between any two points in an open U connected set of the configuration space.\nFinally, we coinpare our novel characterization of controllability with the notion of small time local configura.tion controllability (STLCC) introduced by Lewis and Murray [lo]. Kinematic controllability implies STLCC, while the opposite is not, true. In other words, kinematic controllability is only one way in which a n1echanica.l system can be STLCC. Kinematic controllability is neither implied by, nor implies, small time local con trollability (STLC).\n3.1 Computing decoupling vector fields\nMotiva.ted by the sufficient, test for local kinematic controllability in Lemma 3.4, we investigate how to look for decounling vector fields V . Intuition about",
+            "the behavior of the system is helpful, but a direct algorithm would simplify the task. According to Lemma 3.2, t WO conditions need to be satisfied. To automatically satisfy the first one while losing no generality, we write\nm\nV(q) = C ha ( q ) Y a ( q ) ,\nwhere h(q) = ( h l ( q ) , . . . , / ~ \u201c ( q ) ) ~ are m arbitrary functions on Q. From [14], we recall the identity V x ( h Y ) = h(VxY) + (.Cxh)Y, where Cxh is the Lie derivative of h along X . We compute\na=l\nm m\nvVv = ( h a h b o y a y b + h a ( ~ , h b ) yb), a=l b=l\nso that the vector field V is decoupling if (iii) Numerous vehicle models including the idealized planar hovercraft (planar body with two forces\n0 = ((xc, Vy,yb))(q) (12) away from center of mass) and a rigid body in SE(3) with three thrusters away from the center of mass. The dynamics of these systems are indefor 5 5 - m. Equation (la) is pendent of the configuration, allowing simplified in the unknown functions i h l , . . . > h m ) uration dependent; no general solution methodology appears to be available. Nonetheless it is possible to 4.1 Three link planar robot manipulator find decoupling vector fields in a number of useful examples by relying on insight into the behavior of the system. we will see in section 4.2, Equation (12)\nm m\na=l b = l\ntests for decoupling vector fields (Section 4.2).\nwith a passive joint\nW e consider a three joint robot manipulator mwing\nordinates will be suited to different tasks: the set {@I, &,e,} consists of the absolute angles (measured 4 Examples and extensions counterclockwise) of the three links with respect to\nNumerous systems fit the requiremen ts of Lemma3.4, the horizontal axis, the set {01, ~ Z I 7 3 ) m ~ ~ ~ e s the allowing the decoupling of trajectory planning, E ; ~ - relative angles a t the second and third joint, and amples include: {z, y, 0 3 ) measures the absolute location of the third\njoint and the absolute angle of the third link.\nActuator configuration (0,1,1;)\nsimplifies considerably for certain vehicle models, in a horizontal Plane (see Fig11re \u20181. Different\n(i) All systems subject to nonholonomic or conservation law constraints for which kinematic equations of motion can be written. These systems W e rely on the coordinate system { Q1, yz, y 3 } , Acare described for example in [161 as cordingly, the input co-vector fields Fl, F2, and the locomotion systems\u201d and in [I13 as \u201ckinematic mechanical systems.\u201d Examples include the upright rolling penny and a 3R planar robot arm\n(0 ,1 ,1) ) .\njoint (actuator configuration (1 ,1 ,0) ) . This was the original motivating example in [7], and it is worked out below in full detail. For the actuator configuration (1 ,0 , l ) , we provide one decoupling vector field, but we do not answer the kinematic In other words, the components of the inertia matrix controllability question. W e present all the 3R are independent of 01 and depend on { Q , r3) in a planar robot configurations in Section 4.1. specific manner.\nannihilator vector field x are\nd F1 = dr2 , F2 = dr3, X = ~\nIt is a straightforward computation to see that the\nwith a passive first joint (actuator configuration 801 \u2018\n(ii) A 3R planar robot arm with a passive third inertia matrix A4 has the following structure:\nMlZ(rZ,r3) M22(r3) M23(r3) . (13) M I I ( ~ z > ~ ~ ) MlZ(rZ,r3) M13(rZ,r3) 1 [ M13 (TZ, r3) M32 (T3) M33",
+            "Leiiiiiia 4.1. Coizszder the maizipulator wtth a passive f irs t joiizt. The system as locally kzizeniatacally coiztrollnble m i d two decouplang vector fields are joint to the center of mass of the third link. kinetic energy of the third link is The\n1 1 2 - ( I 3 + m31:)i ; + p ( i 2 + y2)\nVI = Y1 = AKIF1 = M-ldl.2 + m3/3&(~ cos ~3 - j. sin 03).\nV, = Y i = M-'FZ = M-ldr3 . The input co-vector fields F1, F2, and the annihilator vector field X can be written as Proof. By construction, we have\nd dB3 ' F1 = dx, F2 d y , X = - 0 = ((X > Vl)) = ((X, VZ)),\nancl it is easy to see that\n[Vl, v21 $! span(V1, VZ)\nLemma 4.2. Consider the manipulator with a passive third joint. The system ' i s locally kinenzatically controllable, and two decoupling vector fields are\nd d VI =cos&-- + s i n & _\nV2 = sin&- - cos6'3- + --, Next, we show that 0 = ( ( X , Ov,K)) via Ma.thema.tica.TM. The following code illustrates the d X dY computations required to prove that the conditions in d d l a Lemma. 3.2 are satisfied, so that {VI, V 2 ) are indeed ax a y A d 0 3 decoupling.\n(** Mathematica code f o r SCARA 011.\nNeeds [\"MechSys \"'1 ; q = C t h l , r 2 , r 3 ) ;\nwhere X = ( I 3 + ni,3li)/m313. These motions are translation along the third link and rotation of the third link about its center of pel-cussion, respectively.\nProof. It is easy to compute that\n** ** Configuration, inertia, and connection **)\nM = {{Mll[r2,r3], M12[r2,r31, M13[r2,r3]), (M12 [r2 , r3 ] , M22 [r31 , M23 Cr3l 1 , CM13 [ r2 , r3 ] , M23 [I-31 , M33 11 ; InvM = InverseCMl ; n a b l a = LeviCivitaCM, q l ;\n(** i npu t one-forms and a n n i h i l a t o r **) Fl={O, 1 , O ) ; F2=(O , 0 , 1 ) ; X={l, 0,O);\n(** decoup l ing v e c t o r f i e l d s and ** ** t h e i r c o v a r i a n t d e r i v a t i v e s **) V 1 = InvM . F1; V2 = InvM . F2; V 1 1 = CovariantDerCVl, V1, n a b l a , q l ; V22 = CovariantDerrV2, V2, n a b l a , q l ;\n(** t h e s e q u a n t i t i e s v a n i s h **) Simplify[{Vl.M.X, Vll.M.X, V2.M.X, V22.M.X)I\n0\nNext, we show that 0 = ( ( X , Ov,K)) via MathematicaTM. To streamline the computations, we redefine the terms (M11, M12, M22) to account for the term i m 3 ( k a + y 2 ) , and we scale them by a factor m3l3.\n** (** Mathematica code f o r SCARA 110. ** c o n f i g u r a t i o n , i n e r t i a , and c o n n e c t i o n **) Needs [\"MechSys' \"1 ; q = (x , y , t h 3 3 ; fl = ( (Ml l [x ,y l , M12Cx,yl, -S in[ th31) ,\n{M12[x,yl, M 2 2 h , y l , CosCth31 1, {-Sin[th3] , Cos Cth31, lambda 1) ;\nn a b l a = Simpl i fy [ LeviCivitaCM, 411;\n(** i n p u t one-forms and a n n i h i l a t o r **) F1={1 ,O , O ) ; F2={O, 1 ,Ol; X={O , 0 , 1 ) ;\nActuator configuration ( l , l , O ) (** decoup l ing v e c t o r f i e l d s and **\nv1 = {Cos[th3], Sin[th3], o); W e rely on the coordinate system {x, Y, Q 3 > . The kinetic energy of the first two links can be written as ** t he i r covariant derivatives **)\nV2 = {Sin[ th3] , -Cos[th31, l / l ambda 1; &fll(X, Y) MlZ(X, Y) , V 1 1 = Covar ian tDer[Vl , V1, n a b l a , q l ;\nl % Z ( X , Y ) MZZCX,Y) Y V22 = CovariantDer[V2, V2, n a b l a , q l ; 1 [\"I Let 7 j x 3 , 13 denote the mass and moment of inertia of (** t h e s e q u a n t i t i e s v a n i s h **) the third lillk; let l3 be the distance from the third Simplify[{Vl.M.X, Vll.M.X, V2.M.X, V22.M.XIl"
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0001752_jsvi.1997.1511-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001752_jsvi.1997.1511-Figure1-1.png",
+        "caption": "Figure 1. The intrinsic coordinate system.",
+        "texts": [
+            " Since all energy terms concerned are fully derived, the dynamic equation of a general conical spring turns out to be Gs J(r12y/1s2 + r'1y/1s)= (rIs,m + r3ms )12y/1t2, (5) where r'= 1r/1s. If the radius change r' is zero, i.e., the cylindrical spring, the differential equation can be simplified into the well known undamped wave equation: V2 w 12y/1t2 = 12y/1s2, (6) where V2 w =Gs d2/r(8r2 + d2) and r represent the spring wire density. 3. SPRING RATE FOR A GENERAL HELICAL SPRING In order to derive the spring constant of the general helical spring with variable helix radius and variable pitch angle, a co-ordinate system, as shown in Figure 1, is defined. A general helix parametrized by arc length can be expressed as X (s)= r(s) cos u(s)i + r(s) sin u(s)j + h(s)k , (7) where mean radius r, polar angle u, and local helix height h, are all functions of helical length s. Then the tangent of the parametric curve is expressed as the derivative with respect to the helical length s: T (s)=X '(s)= (r' cos u\u2212 u'r sin u)i +(r' sin u+ u'r cos u)j + h'k . (8) The unit tangent is t =T (s)/=T (s) ==(1/W) [(r' cos u\u2212 u'r sin u)i +(r' sin u+ u'r cos u)j + h'k ], (9) where W=zr'2 + r2u'2 + h'2"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003246_iemdc.2005.195977-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003246_iemdc.2005.195977-Figure4-1.png",
+        "caption": "Fig. 4. Instantaneous frequency of simulated current signal with apparition of load torque oscillation (magnetically coupled electric circuits)",
+        "texts": [
+            " 2 shows the result from the model based on magnetically coupled electric circuits, Fig. 3 from the space phasor simulation. The theoretically calculated interference structure at fs\u00b1fc/2 is clearly visible in both time-frequency distributions. Only slight differences in amplitude exist between the two simulations. Further simulations at higher and lower load levels always show the same effects on the PWD. The calculation of the stator current IF for the previous signal leads to the result displayed in Fig. 4. Small oscillations are already present in the healthy current IF. The load torque oscillation starting at 0.6 s leads to significant IF oscillations. As the simulations agree with the theory and the experimental results, only the last will be commented in details. As a conclusion, it can be stated that the simple machine model is well suited to correctly represent the effect of the load torque oscillation and that there is therefore no need in this case for a time intensive and detailed simulation"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003117_bf00618738-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003117_bf00618738-Figure1-1.png",
+        "caption": "Fig. 1. A schematic diagram of the undivided flow cell A.",
+        "texts": [
+            " The two types of cell (A and B) that were used are shown schematically in Figs. 1 and 2. Cell A was made of four polyethylene blocks machined to have a cylindrical bore (2.5 cm diameter). The dimensions of the cell were 7.6 x 7.6 x 10 cm 3. The electrical connections were a lead rod and a platinum wire for the cathode and anode, respectively; a Luggin capillary, made of a fine vinyl tubing, was connected to the saturated calomel electrode. The cathode had a total surface area of 30 cm 2 and the graphite anode is shown as its actual size in Fig. 1. Cell B was made of a glass tube (5 cm diameter and 10 cm long). Glass beads were placed below the cathode to ensure a uniform current distribution through the packed-bed electrodes. Glass beads were also placed above the anode to decrease the total void space in the cell. Perforated vinyl discs were inserted between the electrodes and glass beads, and a ring-shaped Teflon spacer (1 cm thick) was placed between the anode and cathode. Electrical contacts were made from the top and bottom of the cell (Fig"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001679_(sici)1521-4109(20000301)12:5<343::aid-elan343>3.0.co;2-e-Figure9-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001679_(sici)1521-4109(20000301)12:5<343::aid-elan343>3.0.co;2-e-Figure9-1.png",
+        "caption": "Fig. 9. Glucose calibration plots at 950 mV after subtracting the blank: a) amperometric, b) CV peak heights at 5 mV=s using the Au-RSH-GOxPVP electrode (8 days old).",
+        "texts": [
+            " This is also the reason for the slow scan rates used in the CV scans, as noted previously by Cass et al. [16] for the ferrocene mediator. The calibrations vary in slope and sensitivity according to the sensor membrane composition used. The results of CV scans for increasing glucose concentrations as shown in Figure 3 indicate the increase in the anodic peak together with the disappearance of the cathodic peak as the catalytic anodic current increases with increasing glucose concentration. A plot of peak height against glucose concentration shown in Figure 9 shows linearity up to approximately 15 mM glucose. The calibration from the amperometric mode of operation is also shown for comparison in Figure 9. There is some difference due to the shift in peak voltage as the glucose concentration is increased. The amperometric precision of replicate glucose measurements and rate of response was also measured. Eight replicates of a 5 mM glucose solution gave an RSD of 2.1 % for a mean current value of 1.27 mA. The electrode response reached 95 % of steady state within approximately 50 s and stayed constant for up to 3 min before the electrode was reimmersed in the blank solution. The blank current reading drifted by approximately 0"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003024_1.2103093-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003024_1.2103093-Figure3-1.png",
+        "caption": "Fig. 3 Simple brush seal used in the",
+        "texts": [
+            "url=/data/journals/jotuei/28726/ on 05/06/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use numbers Downloaded From: http://turbomachinery.asmedigitalcollection.asme.org/pdfaccess.ashx generator, it is possible to then obtain a new grid to use in the next CFD simulation. The procedure described above should be continued until convergence in the deformation is found. In order to test the iterative procedure, a simple brush seal configuration, was set up including a row of just five bristles, as shown in Fig. 3. In this test case, both the mechanical and fluid dynamics models assumed periodicity in the circumferential direction. The iterative procedure is described and illustrated below using this simple example. Further results for a simple geometry and a real seal geometry are then given in Sec. 3. 2.2 Mechanical Model. SUBSIS an acronym of Surrey University brush seal iterative simulator was used in this study. This is an iterative code developed to predict the bending behavior of bristles in a brush seal",
+            " Analogous procedures are also possible for other commercial mesh generators. To keep this meshing procedure completely automatic, the following approach was adopted: \u2022 Definition of a volume containing the finer and unstructured part of the mesh, but large enough to contain the deflected bristles. \u2022 Bristles\u2019 radius reduction to avoid bristle intersections as explained in Sec. 2.3. 3.1 Simplified Geometry. The iterative coupling procedure was first used to predict the 3D bending behavior of bristles in the simple brush seal shown in Fig. 3. The parameters employed in this work are as summarized in Table 1 unless otherwise stated. The Young\u2019s modulus used is for a cobalt-based alloy known as Haynes-25 see Ref. 14 . Incompressible flow and an axially directed inflow is assumed in this simplified model. Each iterative calculation in the mechanical model has been continued until the displacement residual was much smaller than the deflection. The axial aerodynamic forces per unit length acting on each of the five bristles and the pressure field on the periodic plane of the incompressible CFD solution are shown in Figs"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000999_978-3-7091-2626-4_4-Figure7.2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000999_978-3-7091-2626-4_4-Figure7.2-1.png",
+        "caption": "Figure 7.2: Square plate with a central circular hole",
+        "texts": [
+            " The value for the load factor (3 obtained by the reduced basis technique was (3 = 18.61. In Fig. 7.1b the iteration history for the classical SQP-algorithm and the special SQP-algorithm is compared. Obviously, the convergence behavior of the latter is superior. Shake-down Analysis 229 7.2 Square plate with a central circular hole A square plate with a central circular hole is considered. The length of the plate is L and the ratio between the diameter of the hole and the length of the plate is 0.2. The system is subjected to the biaxial uniform loads PI and p2 (see Figure 7.2). Both can vary independently of each other between zero and certain maximum magnitudes p1 and p2 \u2022 The load domains are defined by 0 ~\u00b7 PI ~ f3 \"'11 O\"o = PI , 0 ~ P2 ~ /3/2 O\"o = ih , 0 ~ /I < 1 0 ~ /2 < 1' where O\"o is the initial yield stress of the employed material and {3 is the shake-down load factor. Suitable choices of /I and 12 enable us to investigate arbitrary load variation domains with different ratios of the load limit PI to P2\u00b7 The shake-down behavior of this system consisting of elastic, perfectly plastic ma terial firstly was investigated numerically by BELYTSCHKO [3] by use of 26 elements"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003049_b:tril.0000044509.82345.16-Figure11-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003049_b:tril.0000044509.82345.16-Figure11-1.png",
+        "caption": "Figure 11. Maps of calculated friction coefficient calculated assuming a Hertz pressure distribution with centre of pressure at three different grid locations. Test conditions are U \u00bc 1.13 m/s, W \u00bc 50 N, slide roll ratio \u00bc )1.0 (ball faster). Contact inlet on left.",
+        "texts": [
+            " In this work, the contact centre was found iteratively, by guessing its location to lie at various positions within the contact and, based on this, evaluating the pressure map and thus, from the ratio of the shear stress to the pressure at each position, the corresponding friction-coefficient map. It was clear from the shape of this map when the correct contact centre had been located, since only then did the friction map fail to fall sharply to zero at the inlet or exit while being reasonably symmetrical transverse to the sliding direction. Figure 11 shows three computed friction-coefficient maps based in the contact centre being in three different locations, at i \u00bc 10.8, 12.8 and 14.8 grid spacings respectively from the left-hand edge of the region mapped. (The friction coefficient outside of the Hertz contact region has been set to zero). Based on these maps, the contact centre was taken to be at the i \u00bc 12.8, j \u00bc 16.5 grid position in this case. Using this approach, the temperature and pressure at each grid point and each slide-roll ratio studied were determined"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000549_0890-6955(95)00099-2-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000549_0890-6955(95)00099-2-Figure1-1.png",
+        "caption": "Fig. 1. The domain and the finite element mesh.",
+        "texts": [],
+        "surrounding_texts": [
+            "Rolling can be considered as one of the most important processes in industry, and is at the same time one of the oldest metal-working processes. Numerous investigations, both analytical and experimental, have been carried on the rolling process [1-19]. In view of the complexity of the process, these methods make use of several assumptions. A slab method for flat rolling proposed by Orowan [2] assumes that the arcs of contact remain circular while their radii increase according to Hitchcock's formula [20]. He considered the interfacial shear stress t~ to be directly proportional to t,, depending on the friction coefficient IX through the equation t~ = IXt,, subject to the limitation that the maximum value of the interfacial shear stress would be equal to the yield shear stress of the material. He discussed the complicating factor of the inhomogeneity of deformation and introduced an adjusting factor which takes this into account. The method was too complicated to obtain an analytical solution. On account of this, other solutions based on simplifying assumptions were presented [3, 5]. Corrections for the effects of elastic entry and exit are included in the work of Bland and Ford [5]. Alexander [9] computerized Orowan's model and presented adequate predictions of roll force and roll torque. However, he did not include the inhomogeneity factor introduced by Orowan and felt the need of slip-line field solution for the accurate estimation of this factor. An upper bound solution presented by Avitzur [7], which does not rely on the assumption of \"plane sections remain plane\", gave an expression for torque and the position of the neutral point for a nonhardening material, but which does not provide roll force and pressure distribution which are important design parameters. For the cases in which roll flattening is significant and may affect torque, one has to compute roll force by some other method and calculate deformed radius of roll which is then to be substituted in the expression of torque developed by Avitzur. Recently, several attempts have been made to solve the rolling problem by the application of the finite-element technique. The primary concern is to find the roll force, torque and interfacial stresses, and a rigid visco-plastic analysis in the Eulerian reference frame is found to be most suitable. Zienkiewicz et al. [12] considered the rolled material to be rigid-visco-plastic and incompressible. They simulated the friction at the roll-strip interface by introducing a thin Analysis of flat rolling and application of fuzzy set theory 949 layer of elements whose yield strength is assumed to depend on the coefficient of friction and mean stress. The neutral point is not modeled in this method. Mori et al. [13] minimized a functional with respect to the position of neutral point in their formulation, thus making the analysis more realistic. Li and Kobayashi [ 14] developed velocity-dependent friction stress for the treatment of the neutral point problem. Assuming the existence of rigid-plastic material and rigid roll, authors have compared their predictions with the results of AI-Salehi et al. [10] and Shida and Awazuhara [ 11] and observed that there is good agreement. Hwu and Lenard [17] incorporated roll flattening and the variable coefficient of friction in the model of Li and Kobayashi. A comparison of predicted and experimental results indicates better agreement than in the case of Ref. [14]. Prakash et al. [19] presented a FEM formulation in which the neutral point is found iteratively from the condition that the interfacial shear stress changes its sign at the neutral point. In all these FEM analyses, penalty parameter formulation is used--here the selection of the proper value of the penalty parameter is important. Also, since hydrostatic pressure is divergence of the velocity times penalty constant, the accuracy of the former is very sensitive to the accuracy of the velocity field. All the above authors seem to calculate torque by integrating shear stresses along the interface. The accuracy of secondary variables viz. stresses is always lower than that of primary variables viz. velocities throughout the domain. Especially on the interface, secondary derivatives are expected to be more inaccurate, and a slight error in the position of neutral point may cause much inaccuracy in the computation of torque. This necessitates a refined mesh in the plastic zone and a very accurate velocity field. In general a number of iterations are required in these methods, which becomes of concern during mill design or when optimization results are needed for a number of different cases. None of these authors have presented results in the presence of front and back tension. Recently Dixit and Dixit [21] analyzed the wire drawing process by mixed pressure and velocity formulation, in which equations for pressure and velocity system are solved by the Householder method [22]. The drawing force is calculated not by the integration of stresses at the exit of plastic boundary, but by computing the total power of deformation. In the present paper the same methodology is extended to the problem of flat rolling. The method has provision for the presence of front and back tensions. Roll flattening is taken into account by means of Hitchctx:k's formula. Friction at the interface is modeled by the method of Wanheim [23] and Wanheim and Bay [2411 though in cold rolling where coefficient of friction is not high a Coulomb coefficient of friction delivers almost the same results. The model developed here is by no means a perfect one. There are a number of less influencing factors, which have to be considered when a precise analysis is to be made. Consideration of temperature and the strain-rate dependency of flow stress and variation of friction coefficient are a few such factors. Their inclusion in the analysis not only makes analysis complicated, but also poses the difficulty of obtaining experimental data which can model the behavior of various process parameters, thus rendering the analysis to be of academic interest only. It has been observed that in a real material flow stress cannot be reproduced to better than _+_5% accuracy [25]. There is also a limit to the precision of the reported values of other parameters. Apart from this, in metal forming some subjective information does arise when we say a particular grade of material is to be deformed in the presence of a particular lubricant. Naturally the process parameters we have in our mind are not definite numbers, but ranges of numbers in which they can lie. With the element of uncertainty present in process parameters, a designer may be interested in knowing the ranges of design parameters and the uncertainty of information associated with such ranges. Fuzzy set theory [26-29] which has been applied in a number of engineering problems can also be applied to metal forming problems. The model developed in this paper has been studied with fuzzy parameters. The initial value of yield stress, hardening coefficients and friction coefficient are treated as fuzzy numbers. Fuzzy output is presented for representative cases. It is shown that this gives a more realistic simulation of experimental results. Finally, a method to measure the reliability of a design is proposed to help the designer make decisions. Some of the relevant aspects of fuzzy-set theory are presented in appendix B. 950 U.S. Dixit and P. M. Dixit 3. ANALYSIS In the present study, only the steady-state part of the process is considered, and hence an Eulerian formulation is used. A two-dimensional (plane-strain) problem is considered. The elastic effects are neglected as they are significant only at the inlet and the exit. The strainhardening behavior is modeled, but the effects of temperature and strain-rate on the strength of the material are ignored, because the temperature rise and strain rates in a typical cold rolling operation are quite small. Furthermore, they have opposite effects on the flow strength. Roll flattening is taken into account by means of Hitchcock's formula in which the ratio of the radius of the deformed arc of contact to roll radius is given by = 1 + (1) where Fr is the roll force and 8=h~-h2 is the \"draft\" (difference in initial and final thicknesses). The constant C depends on the materials of rolls, its value for steel rolls being 4.62\u00d710'* MN m -2. Hitchcock's formula has been used here in view of its simplicity. Better treatments for roll deformation can be found in other references [16, 17]. 3.1. Material behavior In Eulerian formulation, the strain rate tensor is normally used as a measure of deformation. Here v~ is the component of velocity vector with respect to the Cartesian coordinate x~. For an isotropic rigid-plastic material, the deviatoric part Sij of the stress tensor o 0 is related to eij by the relation [30] S~j = 21~j (3) whilst the hydrostatic part or pressure (p) has to be obtained from the incompressibility constraint. For materials yielding according to the yon Mises criterion, the proportionality factor 11 is given by [30] oy I1 = (3~_) (4) where e = ( 5 ) the second invariant of eij is called the equivalent strain rate and Oy (the flow stress in tension) is assumed to be independent of strain-rate and temperature. When the loading is proportional, the flow stress of an isotropic strain-hardening material can be expressed in terms of the equivalent plastic strain g which can be obtained by integrating i~ along the particle path: g= f'o dt (6) The procedure followed for constructing particle paths and integrating the strain rates is given in [21]. For most metals, the dependence of oy on ~ can be modeled by a power law: Analysis of fiat rolling and application of fuzzy set theory 95 i (~y = ((~y)O(l + ~ ) n (7) Here ((~y)o is the yield stress of the material and b and n are the material dependent coefficients determined from the results of experiments. The mechanical behavior of a material is governed by the continuity and momentum equations. For a steady process, the Eulerian form of these equations is - 0 (8) 8%_ 8p i)S~ /)xj 3x, + ~ = 0 (9) Here in the momentum equation inertia terms have been neglected as they are very small. The domain (or the control volume) along with mesh system is shown in Fig. I. The con- ditions on the boundaries AF and DE are 1)1 = U I , I)2 := 0 on AF; v~ = U2, v2 = 0 on DE where U~ and U2 are respectively the inlet and exit velocities related by (lO) U I = U2(I -- r) (11) and r is the reduction ratio given by h i - h2 r - - - (12) hi In a rolling problem the inlet and exit velocities are not specified, instead the roll velocity is prescribed. In the present formulation the roll velocity corresponding to the specified value of U2 is obtained as the velocity at the neutral point (a point where shear stress changes its sign). The velocity field for the prescribed VR Can then be obtained by multiplying the whole velocity field by an appropriate scaling factor so as to make the velocity of neutral point equal to the roll velocity. 952 U.S. Dixit and P. M. Dixit the x2 direction on the surface except near the entry to the roll gap. Therefore, in the present work, the following boundary conditions are used, tt = 0, v2 = 0 on AB and CD (except the two nodes near entry to roll gap) (13) tt = 0, t2 = 0 on the two nodes near entry to roll gap (14) The boundary FE lies on the plane of symmetry. The symmetry implies the following conditions: tt = 0,vz = 0 on FE (15) On the roll-strip interface (boundary BC), the normal component of velocity must be zero. Thus, vn = 0 on BC (16) The second boundary condition is provided by the friction law It, I = clt.I (17) In the case of Coulomb model c is equal to B, the coefficient of friction. In the case of Wanheim and Bay 's model c is given by B\" [18], where ~la for t, < t , ' B* / Ua*(t.) for t. > t.\" The la'(t,) is given by the expression (18) < r ) . l . * ( / n ) = SS exp - - - t. L o/ '3 - t,,)t.,j (19) where ts\" and t,\" are tangential and normal stresses at the limit of proportionality and f is the friction factor related to the coefficient of friction by the relation [15] f B = (20) 1 + ~ + c o s - I f + ~(1 _ f 2 ) Furthermore, t n ' ?\u00a2 .E2-. 1 + ~+COS-y+ ~t(1 _ f 2 ) ~ ( 1 + ~1 - f ) and (21) Note that so far no boundary condition has been imposed on pressure. In finite element \"-\" = VG-- (22) O r Analysis of flat rolling and application of fuzzy set theory 953 formulation, often a spurious pressure distribution is obtained, giving rise to nonzero average values of pressure at the inlet and/or exit, herein denoted by p,~ and p .... respectively. However, in the case of zero front and back tensions, pressure values at the entry and exit should be zero. Therefore the pressure field is modified by making the average pressures equal to zero at the entry and exit. The method of modifying pressure values in the presence of nonzero front and back tensions is described in Section 3.5\u2022 3.2. Nond im en s io n a l i za t i o n The nondimensionalization of various physical quantities is undertaken using the following relationships: - - X I - - X 2 - - V I - - V 2 x, = h~/2' x2 = h-~2' v, = U22' v2 = U22 (23) - p ~ _ I.t (24) P - ((~y)o/3)' where (Gy)o (25) 11\u00b0 = 3(U21hz) Then the nondimensional versions of continuity and momentum equations are obtained by substituting equations (23)--(25) into equations (8) and (9). 3.3. F in i t e - e l emen t f o r m u l a t i o n Let vz, v2, p be the functions that satisfy all the essential boundary conditions exactly. Then v~, v2, p constitute a weak solution if the following weighted integral of the nondimensionai continuity and momentum equation is satisfied: A [ ( ~ 1 1 \"l\" ~ 2 2 ) W p \"0\" \\ ~XI \"~ ~X 2 ] wxl \"l\" ~ ~X I + ~X 2 ] 14.\"x2 ] d x t d x 2 = 0 (26) where wp, w.; and wx2 are the weight functions that satisfy the homogeneous versions of the boundary conditions and A represents the area of the domain. Integrating the second and third parts of equation (26), we obtain f ,..,..-f -f /4dF~2=O a a G I rx2 (27) where t, = - w , , [ ~ , + ~] \u2022 . .. .. Is = - .~[~,,(w) + ~z2(w)] + 21a[~,,ell(W) + e:zze2z(w) + 2~,z~,2(w)] 13 = tnwx o, I4 = t 2 w x 2 (28) (29) (30) and Fxj and Fx2 are respectively Rose pa~t_, s of the boundary where the traction components Fi and F2 are specified. The terms Etl(w), e22(w), et2(w) are the components of the tensor 1 ~(w) = ~ (Vw + (VwO) (31) 954 u.s . Dixit and P. M. Dixit where w = wx,i~, + wxffx2 (32) The finite-element formulation of the Galerkin integral and the nondimensional version of the boundary conditions are similar to that of a flow problem of a non-Newtonian incompressible fluid, the details of which are described in any standard text, viz. [31]. In the present work, 9-noded rectangular elements are used to discretize the domain (Fig. 2), with biquadratic approximations for the velocity components and bi-linear approximations for the pressure. The assembly of the elemental coefficient matrices and the right-hand side vectors into the global matrix and vector is done by transferring the elements corresponding to a local degree of freedom in each elemental matrix/vector to positions of the corresponding global degrees of freedom in the global matrix/vector. The essential boundary conditions except for those on the roll-strip interface are applied in the usual way. The conditions on the interface are applied by performing certain row operations on the global coefficient matrix and the global righthand side vector, the details of which are given in the thesis of Dixit 132]. In order to apply this boundary condition, it is necessary to know the direction of the interfacial shear stress and thus the location of the neutral point. In this formulation, the neutral point is found by minimizing total power with respect to the position of the neutral point. This is based on the upper bound theorem, the justification for which is given in Appendix A. The initial estimation for the neutral point is found by using the slab method formula [3]. Taking this point in the middle, an interval in which the neutral point may lie is assumed. By the interval reducing method [33], this interval is reduced. After the interval has been sufficiently reduced, the exact position of neutral point is obtained as a quadratic approximation. The global equation after application of all the boundary conditions is [K]IA} = {F} (33) where IK] is the global coefficient matrix, {F} is the global right-hand side vector and {A} is the global vector of primary unknowns (i.e. velocity components and pressure). 3.4. Implementat ion The lengths li and lo of the inlet and exit zones are usually taken as Analysis of flat rolling and application of fuzzy set theory 955 The value of the multiplying factor \"n\" has to be selected such that uniform conditions prevail at the beginning of the inlet zone and the end of the exit zone. After conducting several numerical experiments, a value of three was selected for this analysis. At each assumed position of the neutral point, a number of iterations may be required. According to Ref. [34], a very convenient but powerful method of acceleration has been proposed by Aitken and Steffensen. According to this method, x~, x2 and x3 denote the results of three consecutive iterations. Assuming that they approach their limit x as a geometrical series i.e. X 1 - - X X 2 - - X x 2 - X x 3 - X (35) then the limit can be calculated as x lx 3 - - ~ x - - - (36) x t - - 2 x 2 + x 3 The above procedure was tested and found to be correct to 1% accuracy for torque and force calculations. Thus for each position of neutral point, only four-five iterations are required. A total of 20-25 iterations are sufficient to give the position of the neutral point and values of roll force and torque correctly. 3.5. Modification of pressure field in presence of tensions When the front and back tensions (tf and th) are present, it does not seem possible to incorporate them through the imposition of traction boundary conditions as these boundaries fall in the rigid zone. In the present model, the following approach is proposed. It is assumed that (I) The velocity field and hence the strain rate is not affected significantly in the presence of tensions. The tensions, therefore, only influence the pressure (or hydrostatic stress). (2) The effect of tensions is experienced uniformly across a cross-section of the strip, so that the one-dimensional equations of the slab method become applicable. According to the slab method [6], the roll pressure with tensions (q) is related to the one without tensions (qo) by the relation qo-q = tfe 2~'~ on exit side (37) qo-q = the 2acv\u00b0-v) on entry side (38) Here a = Ix (39) (40) \u00a2 is the angular position of the point (i.e. the angle between the lines joining the center of deformed arc with the exit point and the particular point) and ~o is the value of q/when \u00a2 is equal to the angle of contact (o0. Since the deviatoric part is unaffected by the tensions, q - qo will be equal to p - Po where Po is the pressure (hydrostatic stress) without tensions and p is its value in their presence. Then, using equations (37) and (38), we obtain the following relation between p and Po: 956 U. S. Dixit and P. M. Dixit p = po--(tf + pavo)e ~v on exit side p = po-( tb + pavi)e 2~tvo-~'~ on entry side (41) (42) The additional terms (Pavi and Pavo) in the above equations have been introduced to take care of a spurious pressure distribution which often arises in finite element formulation. Note that in the absence of tensions (tf=tb--O), p should be equal to Po giving rise to Pavi=Pavo=O. This indeed is the condition imposed on pressure in the absence of tensions (see Section 3.1). Furthermore, the spurious pressure distribution may be interpreted as the one arising out of some nonzero value of front and back tensions. 3.6. Calculation o f secondary variables Once the solution of the problem is obtained in the form of nodal velocities and pressures for any assumed position of neutral point, the secondary quantities, viz. the roll torque, the roll pressure and the roll force are calculated as explained below: (i) Roll torque(T)-the roll torque is calculated from the relationship T = PR/VR (43) (a) where the total power P consists of the following three parts: Power required for plastic deformation (Pp). The power dissipated due to plastic deformation is given by PP= fa S~\u00b0dxldX2 (44) (b) Substitution of equations (3)-(5) into this equation leads to Pp = f O ~ dxl dx2 (45) A Power required to overcome friction at the roll-strip interface (Pr). The power dissipated due to friction is given by P,= f[ Itsllv l (46) (c) where vs is the resultant velocity along the interface and l is the arc length. The ts is calculated from equation (17). Power due to tensions (P,). The power required in the presence of front and back tensions is hi Pt = (tb--tf)-~U1 (47) (ii) Roll pressure or interfacial normal stress (t,)-while calculating tn, the stresses a~j are first calculated at 2x2 Gauss points and then they are extrapolated to various points on the roll-strip interface, after which t. is calculated from the expression t. = t.~/ (48) where t, = o ~ (49) Analysis of fiat rolling and application of fuzzy set theory 957 and ti is the unit outward normal to the interface. (iii) Roll force (Fr)-the roll force is given by F~=f'o(t.cos*-t~sinC,)d~ (50) where l is the arc of contact."
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0000858_s0379-6779(98)00128-3-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000858_s0379-6779(98)00128-3-Figure1-1.png",
+        "caption": "Fig. 1. (a) Cyclic voltammogram of a 2.37 \u00d7 10 -3 M solution of I in 0.2 M Bu4NBF4 in CH2C12. Initial potential: 0.0 V, switching potential: 1.7 V, ten recurrent sweeps. (b) Study of the deposit formed in ( a ) in 0.1 M Bu4NBF4 in CH3CN. Initial potential: 0.0 V, switching potential: 1.4 V, five recurrent sweeps. Scan rate: 100 mv s- t. Working electrode: platinum disk of diameter 1 mm.",
+        "texts": [
+            " Cyclic voltammetry analysis I is electrooxidized irreversibly and the oxidation appears as two broad peaks in the potential region at about E J = 1.5 V and E 2 = 1.65 V. These peaks probably correspond to the respective oxidation of the two fluorene units of I. When the oxidation is performed only in the potential range of the first oxidation peak E l, the polymerization occurs slowly and a new redox system is visible between 0.9 and 1.4 V. However, when the oxidation is performed in the potential range including the two oxidation peaks E 1 and E 2 as presented in Fig. 1 (a), an oxidation reduction wave appears also between 0.9 and 1.4 V; but its growth is largely more important, it corresponds to the redox reaction of the polymeric film. The electrode taken out of the solution after the tenth sweep seems unmodified because it is covered by a transparent polymer. However, the modified electrode studied in a CH3CN solution containing 0.1 M Bu4NBF 4 presents a reversible oxidationreduction system shown in Fig. l (b ) . This system is the electrochemical response of the polymer coating the platinum electrode",
+            " The increase of iv at E 1 (i(E1) ) and E 2 (i(E2) ) is linear with the concentration of I. A comparison of fluorene and I oxidations shows that, when the two substrates are in solutions of the same concentration, the oxidation peak of the fluorene (ip(fluorene) measured at 1.5 V) has an intensity lying between i(E 1) and i(E 2) of I. This may be explained by the fact that fluorene diffuses more quickly than I, ip(fluorene) is higher than i(E ~ ) of I but the oxidation of the second fluorene unit of I leads to an i(E 2) higher than ip(fluorene). Fig. 1 shows typical a cyclic voltammogram of I at stationary platinum electrodes in CH2C12 solution containing 0.2 M Bu4NBF4 and 2.37 \u00d7 10 -3 M 9,9'-spirobifluorene for the electrode potential swept continuously between 0.0 and 1.7 V. Polymerization has also been performed by oxidation of I at fixed potential. Fig. 2 presents the redox behaviour of poly(I) deposits obtained by oxidation at 1.6 and 1.9 V in CH2C12 solution containing 0.2 M B u 4 N B F 4 and 4.95 \u00d7 10-3 M 9,9'-spirobifluorene. The electrolytic medium is also CH2C12 solution containing 0"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001325_jsvi.2000.3040-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001325_jsvi.2000.3040-Figure6-1.png",
+        "caption": "Figure 6. Response of the controlled axially moving string with 5% white noise in the amplitude of the sinusoidal excitation. Control force q a1 (x, t)\"0; c\"0)3, d\"0)05, x 3 \"0)25, x 4 \"0)3, a 2 \"0)5.",
+        "texts": [
+            " From equation (29), it is noted that the stability of the uncontrolled string is a!ected by the boundary conditions since u(s)\"h 0 (s)h 1 (s). Consider the \"xed}\"xed boundary, h 0 (s)\"h 1 (s)\"!1. By the theorem, the string is marginally stable because Du (s) D\"1. Thus, the control forces (27) and (28) are also marginally stable. This means that the proposed active vibration control scheme is not robust enough to perform a stable control in real time under a noisy environment of practical test conditions. This is typical of a feedforward control [11]. Figure 6 shows the time response of the controlled axially moving string when there is a 5% white noise in the amplitude of the excitation force applied at x\"0)05. Only one control force q 2 (x, t) is applied at a 2 \"0)5. It is seen that the downstream vibration does not go to zero, but is bounded. However, the control force, shown in Figure 7, appears to increase unboundedly with time. It is thus necessary to resolve the robustness issue of the controllers before they can be applied for real-time control"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001925_84.388115-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001925_84.388115-Figure2-1.png",
+        "caption": "Fig. 2",
+        "texts": [
+            " We have developed a self-driven miniature car to study the locomotive mechanism and moving performance. 11. MOTOR A. Manufacturing Fig. 1 shows the schematic structure and main specifications of the micromotor manufactured for the microcar. The motor is a type of stepmotor that is electromagnetically driven. The rotor is an isotropic barium ferrite magnet. The magnet was machined into a tube shape by a cylindrical grinder. The outer and inner diameter of the tube are 1.0 and 0.25 mm, respectively. The core was then made as a 4-pole magnet by a special apparatus shown in Fig. 2. The apparatus consists of four contact probes having coils that generatea 4-pole magnetic field. The end of the contact probe has a concave shape to fit the rotor. The end firmly contacts the rotor utilizing the Manuscript received March 22, 1994; revised December 29, 1994. Subject The authors are with Research Laboratories, Nippondenso Co., Ltd., Aichi E E E Log Number 941 1737. Editor, R. 0. Warrington. 470-01, Japan. thermal expansion of the probe when the coil is activated. This enables a uniformly magnetized rotor"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001869_irds.2002.1043954-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001869_irds.2002.1043954-Figure2-1.png",
+        "caption": "Figure 2: Two point contact model of knotted suture",
+        "texts": [
+            " As the starting point of knot placement, we assume a simple knot is already developed by wrapping the loop strand around the post strand and by applying tension forces as shown in Figure 1. 2.2 Sliding condition Moving the knot requires sliding the two strands relative to each other. To investigate the impending sliding condition, we need to have a static force balance model. The general model of a knotted suture is quite difficult due in part of the flexibility of the suture and complex contact geometry. In this paper, we use a simplified model based on the assumption of a two-point contact between the sutures, as shown in Figure 2. The freebody diagram is shown in Figure 3. The impending sliding problem can now be stated as: Given &, @2a, A, and A, determine the relationship between the angles 11flb11 ll@\"bII yi's and pi's, i=1,2, when the sliding motion is about to begin. Define Zla = L, &a = L, Z1b = h, and IIFlaII l lFZa11 l l F l b I I Z2b = A ll&, and let Zn = e be the unit vec- tor along which the normal forces apply and Zt be the unit vector along which the frictiyn forces apply. When the knot is in equilibrium, F = 0, so FlaZia + F2aZ2a FlbZIb + F2b&b = 0"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001615_0263-8223(93)90220-k-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001615_0263-8223(93)90220-k-Figure3-1.png",
+        "caption": "Fig. 3. Definitions of stiffnesses on a hysteresis loop.",
+        "texts": [
+            " If a material behaves as a linear-viscoelastic solid, the hysteresis loop takes the form of an ellipse. In this case eqns (3)-(5) can be solved analytically: W 1 = 7tOg Sin 6 (6a) W s = 6~ cos 6 (6b) A = ~t tan 6 (6c) where O and g represent the stress and strain amplitudes, respectively. On the other hand, the definition of the energies according to eqns (3) and (4) has the advantage that it is valid for both linear-visco- elastic materials and non-linear-viscoelastic materials. The mid-curve also enables the definition of various stiffnesses (Fig. 3). The compression stiffness at minimum load, El, emerges at the lower end of the loop and, analogously, the mean stiffness, Em, at mean strain and tensile stiffness, E u, at maximum strain: dOmc E=el =-\u00b0 tan ctl (7a) El = - ~ e e Em d\u00b0mc ~:=em O - = - tan a m (7b) de e E,, dame a = = - tan a~ (7c) The dynamic secant modulus Edy n is obtained from the maximum and minimum stress and strain: E d y n - Ou -- O1 (8) Eu -- El 3 EXPERIMENTAL EQUIPMENT AND PROCEDURE FOR HYSTERESIS MEASUREMENTS The experimental equipment is shown in Fig"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001338_0094-114x(95)00082-a-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001338_0094-114x(95)00082-a-Figure3-1.png",
+        "caption": "Fig, 3. Tip interference during engagement.",
+        "texts": [
+            " 2 (ring gear is the driver in gearing action) the approach contact (CP) ac, recess contact (PB) re and contact ratio Cr are expressed as a\u00a2 = x/~2p - r~,p - rp sin g (3) r~ = r~ s in ~t -- ~ - - r~g (4) C, = (ac + rc)/(zcm cos ~0) (5) Minimum tooth difference 477 where, rp and rg are the working pitch circle radii, rap and rag are the tip radii and rbp and rbg are the base circle radii of the pinion and gear respectively, ~ and ~0 are the working and standard pressure angles respectively, and m is the standard module. 3.1. Tip interference Referring to the two gear epicyclic drive the ring gear is the driver during gearing actions in both type-I and type-II transmissions. Therefore, the flank contact is such that the tip interference does not occur during disengagement if it can be avoided during engagement. Moreover, due to the presence of backlash checking of the interference at one side is sufficient. Figure 3 illustrates the condition when the engagement tip interference just exists in involute internal-external gear pair with internal, i.e. the ring gear as the driver. To avoid the tooth tip interferences the following conditions are to be satisfied [3, 7]: In the case of tip interference during engagement: Angles 0 o and 0g are calculated as follows: cos_,(r~, + A 2 - r~,) _ 0 , = \\ 2At., / ' 00 = cos - ' ( r \u2022 ' - A 2 - r.~p) + ap \\ 2Ar~p ,] (6) (7) (8) where the subscripts g and p refer to the gear and pinion respectively and 'A' is the center distance between gear and pinion"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003804_rnc.1084-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003804_rnc.1084-Figure2-1.png",
+        "caption": "Figure 2. Two inverted pendulums connected by a spring.",
+        "texts": [
+            "1002/rnc Substituting (37) into last equation \u2019Vi \u00bc 1 2 \u00f0eTi L T i Piei \u00fe zT\u00f0Xi\u00deFfiB T i Piei \u00fe zT\u00f0Xi\u00deFgiB T i Pieiui \u00fe wiB T i Piei \u00fe BT i Pieiuia \u00fe aT\u00f0X\u00deFdiB T i Piei \u00fe eTi PiLiei \u00fe eTi PiBiFT fiz\u00f0Xi\u00de \u00fe eTi PiBiwi \u00fe eTi PiBiuia \u00fe eTi PiBiFT giz\u00f0Xi\u00deui \u00fe eTi PiBiFT dia\u00f0X\u00de\u00de \u00fe 1 Z1 FT fi \u2019Ffi \u00fe 1 Z2 FT gi \u2019Fgi \u00fe 1 Z3 FT di \u2019Fdi \u00f045\u00de Substituting (39) into (45) and use \u2019Ffi \u00bc \u2019yfi; \u2019Fgi \u00bc \u2019ygi; \u2019Fdi \u00bc \u2019ydi and fact that eTi PiBi is scalar we get V : i \u00bc 1 2 eTi LT i Pi \u00fe PiLi 2 ri PiBiB T i Pi ei \u00fe 1 2 \u00f0wiB T i Piei \u00fe eTi PiBiwi\u00de \u00fe 1 Z1 FT fi \u00bd\u2019yfi \u00fe Z1e T i PiBiz T\u00f0Xi\u00de \u00fe 1 Z2 FT gi\u00bd\u2019ygi \u00fe Z2e T i PiBiz T\u00f0Xi\u00deui \u00fe 1 Z2 FT di\u00bd\u2019ydi \u00fe Z3e T i PiBia\u00f0X\u00de \u00f046\u00de Using the adaptation laws (40)\u2013(42) along with Riccati-like equation (21), we get \u2019Vi4 1 2 eTi Qiei \u00fe 1 2 r2w2 i \u00f047\u00de The conclusions of Theorem 2 can be obtained by following the same procedure as in the proof of Theorem 1. In this section, we demonstrate the effectiveness of the proposed direct and indirect adaptive fuzzy control algorithms using two illustrative examples. Example 1 A double-inverted pendulum model [19] shown in Figure 2 is considered. Each pendulum may be positioned by a torque input ui applied by a servomotor at its base. It is assumed that both yi and \u2019yi (angular position and velocity) are available to the ith controller for i=1, 2. The equations describing the dynamics of the pendulums are defined by \u2019x11 \u00bc x12 \u00f048\u00de \u2019x12 \u00bc m1gr J1 kr2 4J1 sin\u00f0x11\u00de \u00fe kr 2J1 \u00f0l b\u00de \u00fe u1 J1 \u00fe kr2 4J1 sin\u00f0x21\u00de \u00f049\u00de \u2019x21 \u00bc x22 \u00f050\u00de \u2019x22 \u00bc m2gr J2 kr2 4J2 sin\u00f0x21\u00de kr 2J2 \u00f0l b\u00de \u00fe u2 J2 \u00fe kr2 4J2 sin\u00f0x12\u00de \u00f051\u00de Copyright # 2006 John Wiley & Sons, Ltd"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002121_jp012819k-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002121_jp012819k-Figure4-1.png",
+        "caption": "Figure 4. (a) Illustration of the origin of the attractive component of vertical vortex-vortex interaction (see Text for details). The graph in (b) shows a qualitative profile of the equilibrium separation deq between the centers of two disks as a function of their rotational speed.",
+        "texts": [
+            " The magnitude of the repulsive hydrodynamic force exerted by disk 1 on disk 2 is given by Fh,1(z) \u221d F\u03c92a1 3(z)a2 4(z)/d3, and the total repulsive force FR between the Taylor vortices is obtained by summing repulsive forces between imaginary disks at all elevations within the liquid layer: Integrating and neglecting small exponential terms, FR can be rewritten as The qualitative dependence of this force on the rotational speed is shown in Figure 3d: for small values of \u03c9, the repulsion grows with angular speed until it reaches a maximum, and it decays (approximately exponentially) for high values of rotational speeds. AttractiVe Interaction. As \u03c9 becomes larger, the repulsion described by eq 2 becomes smaller; at the same time, an attraction between disks becomes more important. Consider the flux toward the disk spinning on the lower interface (Figure 4a). The quantity of fluid Q flowing toward this disk depends on the rotational speed \u03c9 and the radius a of the disk:24 Q \u221d a2\u03c91/2. As confirmed by direct observation, the fluid is pumped onto the lower disk from the region near the upper interface. To simplify the argument, we assume that this region is a layer of constant thickness T, and consider the flow within this layer that is directed toward the axis of rotation of the lower disk (the angular component of the flow does not contribute to the transport of liquid onto lower disk)",
+            " This pressure gradient gives rise to a force FA that acts on a neutraly buoyant disk floating on the upper interface and attracts it toward the axis of rotation of the lower disk: FA(d) \u221d (Q/d)2 \u221d \u03c9/d2 (a similar force acts on the lower disks as the result of the liquid transfer from the lower interface toward the upper spinning disk). This attractive force increases monotonically with increasing rotational speed of the disks. Balance of Forces. The equilibrium separation between the axes of rotation of the disks is defined by the balance of the attractive force FA and the repulsive force FR: The qualitative dependence of the equilibrium separation on the rotational speed is illustrated in Figure 4b. At low values of \u03c9, \u03c9/deq 2 ) constant3\u03c9 3/2 exp(-4constant2h\u03c91/2)/deq 3 (3) deq \u221d \u03c91/2 exp(-4constant2h\u03c91/2) (4) FR(d) \u221d \u222bz)0 z)h F\u03c92a1 3(z)a2 4(z)/d3 dz (1) FR(d) \u221d \u03c93/2 exp(-4constant2h\u03c91/2)/d3 (2) the separation between the disks increases with \u03c9 until it reaches a maximum; past this maximum deq decreases approximately exponentially with \u03c9. Also, for a given value of rotational speed, the model predicts an exponential decrease in deq with increasing h. We experimentally observed a stronger-than-linear decrease in the equilibrium separation of disks with both h and \u03c9 (for \u03c9 > \u223c150 rpm)"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003893_0301-679x(83)90004-x-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003893_0301-679x(83)90004-x-Figure2-1.png",
+        "caption": "Fig 2 Displacement transducers: (a) design (b) arrangement",
+        "texts": [
+            " Spherical samples were tested in compression, in shear around the x axis (k= in a-direction, Fig lb), and in torsion around the z-axis (k-/in ~,-direction, Fig lb). Tests were performed on universal precision testing machines - an Instron TT-DM (0.1 MN maximum capacity) and TT-KM (0.25 MN maximum capacity). These machines have very high structural stiffness and sensitive extenso. meters. However, both parameters were found to be inadequate for testing ultrathin-layered laminates in compression. Ultra-sensitive displacement transducers (Fig 2(a)) were used to eliminate the influence of the testing machine structural stiffness on test results. The transducer was machined from a solid block of low-hysteresis (spring) steel, thus eliminating friction in the joints which could affect transducer sensitivity. Four strain gauges provided compensation for machining asymmetry and thermal effects. Using good strain-gauge amplifiers, these transducers can reliably measure displacements as small as 0.05-0.1/am. Standard extensometer amplifiers were used with the testing machines to give resolutions of 0"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000497_a:1008966218715-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000497_a:1008966218715-Figure5-1.png",
+        "caption": "Figure 5. Local map and active circle.",
+        "texts": [
+            " Consequently, it will be time consuming to test all of these obstacle regions to see if they are associated with the clustered regions. In the presented map building method, the obstacle regions located within some distance from the mobile robot are only considered to test its association with the clustered region. We call this set of obstacle regions as local map. To select obstacle regions which included in the local map, we introduce the concept of active circle that represent the region around the mobile robot within the distance dc. Figure 5 shows the example of an active circle. The local map is composed of M1, M2 and M4. The presented world map building method then consists of the following steps. \u2022 Step 1. Determining clustered regions Ri \u2019s at the present sampling time. \u2022 Step 2. Selecting obstacle regions that are located within the local map. \u2022 Step 3. Determining the obstacle region Mk\u2019s that are associated with Ri \u2019s and updating their parameters. \u2022 Step 4. Deleting obstacle regions that are in the field of view but are not associated with any of Ri \u2019s"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure3.13-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure3.13-1.png",
+        "caption": "Figure 3.13. Finite rotations of the solar panel of a spacecraft.",
+        "texts": [
+            "150); and the resultant rotation may be found by the matrix product of the successive rotation matrices in the form provided in (3.147b ). The angle and the axis of the resultant Euler rotation may then be computed in the frame 1/J by aid of (3.89) and (3.90), as usual. It is useful to observe in calculations that the matrix of S is skew and that of a\u00ae a is symmetric. Example 3.14. The solar panel of a spacecraft receives three rotations about axes ak in the spatial frame 1/J = { 0; ek }, as shown in Fig. 3.13. The first rotation is 90\u00b0 about the panel axis a 1 ; the second is 90\u00b0 about the satellite body axis a 2 ; and the last is a 180\u00b0 turn of the satellite about the line a 3 \u2022 Find the angle and axis of the equivalent Euler rotation. What is the final orien tation in 1/J of the satellite body axis? Chapter 3 Solution. The equation for the kth rotation Rk through the angle 8k about the axis ak may be obtained from (3.150): (3.152) without sum on k. Thus, with 81 = n/2, the first rotation is given by R 1 = S 1 + a 1 \u00aea1 , wherein the axis is obtained from the geometry in Fig. 3.13: J3 1 a1=-e2+-e3 2 2 in t/J. Then use of this result in (3.151) yields the matrices -1/2 J312] 0 0 ' 0 0 0 3/4 J314 ;/4]\u00b7 1/4 referred to t/J. It follows from the formula given earlier that the matrix in t/1 of the rotation tensor R 1 = R!qepq is given by [ 0 -1/2 J312] R 1 = 1/2 3/4 j3/4 . - J312 J314 1/4 The second rotation is easily obtained by construction of a basis transfor mation array, as described in Example 3.6, or by use of the same formula given above with 82 = n/2 and a 2 = e3 \u2022 The reader will find the tensor R2 = R~eij whose matrix in t/1 is [0 -1 0] R 2 = 1 0 0 "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001576_042516402776250388-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001576_042516402776250388-Figure1-1.png",
+        "caption": "Fig 1: The completed FE model of one hoof. Solar loading (LC1) is shown and described in the text. Inset shows the location of points on the wall for which principal strains were compared with in vivo data.",
+        "texts": [
+            " (1999) and with the relative strain magnitudes for the 9 gauges. In vivo strain recording Details of the experimental protocol are given by Thomason et al. (2002). Briefly, 5 small rosette gauges (element length, 2 mm) were glued one-third of the way down the right, front hoof wall of 9 Standardbred horses which were unshod but had been trimmed within the previous 3 weeks. Gauges were placed on the medial and lateral quarters and dorsum (toe) and at 2 intermediate positions called medial45 and lateral45 (Fig 1, inset). Each horse was trotted on a treadmill at velocities 3.5\u20137.5 m/s while strains were recorded for between 50 and 110 strides per velocity. Magnitudes of principal compressive strain \u03b52 at midstance were extracted from the complete records. Only values of \u03b52, for a velocity of 5.0 m/s, are used here because this is a medium-paced trot which has significance for the loading of the FE model (see below). For a tenth horse, 9 rosette gauges were attached to the hoof at the medial and lateral quarters and dorsum",
+            " In each of 3 test runs, 5 of the gauges were sampled, with 2 dorsal gauges being common to each run. Twenty or more strides per run were recorded at a trot while the animal was ridden in an indoor arena. Midstance values of \u03b52 were extracted from the records and data were pooled across runs. Rosettes experiencing the highest values were identified. Much of the preparation of the model and the analysis were run using Cosmos/M software1 on a generic Pentium 4 computer (1.3 GHz with 256 Mb RAM). Some calculations of coordinates were done in a spreadsheet2. The completed model is shown in Figure 1 and was constructed as follows on a protocol refined from that in McClinchey (2000): (1) Shape: Scaled, digital photographs were taken of each hoof in dorsal, medial, lateral and solar views. From the solar view, the coordinates of 11 points describing the border of the wall were extracted. From the other views, the following measurements were made: toe (dorsal) angle (TA), toe length (TL), medial and lateral wall angles (MA, LA), medial and lateral wall lengths (ML, LL), heel angle (HA) and medial and lateral heel bulb heights (MH, LH, measured perpendicular to the ground)",
+            " (c) Expansion of shell in B to wall (W) in 2 layers, laminar junction (LJ) and sole (S). (d) Addition of solar dermis (SD) and distal phalanx (PIII). (4) Loading and boundary conditions: The forces and moments acting on PIII during stance are not amenable to direct measurement, but ground reaction forces (GRF) have frequently been recorded (Merkens et al. 1993). For this reason, each model was loaded sequentially in 2 ways. In loading condition one (LC1, solar loading), a uniform pressure was applied to each node on the solar bearing surface of the wall (Fig 1). Magnitude of the pressure was calculated by dividing the area of the bearing surface into a force of 1.15 times the known body mass of each animal. The resultant force on the hoof was equivalent to the peak vertical GRF recorded for horses at a medium-paced trot (Merkens et al. 1993). On the dorsal surface of PIII, 121 nodes were constrained from displacing (Fig 1). The nodes were located near the centre of PIII so stress concentrations around them would be confined within the block and not radiate into surrounding tissue layers. When the analysis was run, reaction forces were calculated at each of these nodes and deriving these forces was the whole purpose of LC1. In loading condition 2 (LC2, skeletal loading), the reaction forces resulting from LC1 were applied to the top of PIII and the distal bearing surface of the wall was partially constrained from moving",
+            " This is equivalent to the hoof being prevented from indenting the substrate but being free to lift from it or slide on it. Two nodes on the bearing surface, at junctions of toe and each quarter, were constrained completely to prevent whole body motion of the model. Only results of LC2 are presented here, because LC1 was just to provide appropriate loads on PIII. (5) Presentation of results: Each model was compared with digital photographs of the real hoof to ascertain which nodes corresponded most closely in position to the location of the 5 rosette gauges (Fig 1, inset). Magnitudes of principal strains \u03b51 and \u03b52 at each node were extracted from the analysis of LC2 and were compared with the corresponding in vivo values. At each site, the predicted value of compressive principal strain \u03b52 were expressed as a percentage of the mean in vivo values, for comparison. Predictions were individually tested for similarity to the mean in vivo values (i.e. lack of statistical difference) using t tests of single values vs. sample means at an alpha level of 0.01. This stringent level broadened the band in which strain values would not be distinguished as different"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001059_12.403696-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001059_12.403696-Figure5-1.png",
+        "caption": "Figure 5. Kinematic model of a flexure hinge with unreeling centroides",
+        "texts": [
+            " If only the deflections are of interest and not the effecting loads and stresses the stress-strain relationship of the material has no influence. Also the factor n, thus a working tensile force or compressive force, and the transverse force Q do not have big influence to the deflection curves of notch flexure hinges from a certain length for l2 up.8,10 Now if the deflection curve of one point of the flexure hinge is well-known during load, the movement of the center of rotation can be calculated. The movement of a body in a plane can always be described by an unreeling movement of a moving centroide on a fixed centroide (fig. 5).11 The curve of the instantaneous centers of rotation can now be determined either graphically or computationally from the coordinates (xB, zB, \u03c6B) of the deflection curve. The coordinates of the instant centers at different joint angles are given by: B B BP d dy xx \u03c6 \u2212= , (11) B B BP d dx yz \u03c6 += . (12) Because the coordinates of point B are determined discretely, xP and zP must be calculated over the difference quotient. A second possibility of calculating xP and zP is to derive functional dependencies yB = f (\u03c6B) and xB = f (\u03c6B) and afterwards form the differential quotient"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003502_095440904322804439-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003502_095440904322804439-Figure4-1.png",
+        "caption": "Fig. 4 Scheme of the friction testing apparatus",
+        "texts": [
+            "3 per cent carbon and HV \u02c6 205 for the axle (A1N-UIC 811\u00b11 O) and a quenched and tempered steel with 0.5 per cent carbon and HV \u02c6 260 for the wheel (R7T-UIC 812\u00b13 O). The initial specimens roughness was Ra \u02c6 0.8 mm for the axle and Ra \u02c6 1.5 mm for the wheel. As stated above, the test apparatus was designed to be mounted on a standard axial testing machine. In particular, in the present experiment a servo-hydraulic INSTRON machine with a maximum load of 100 kN and a maximum grip distance of 300 mm was used. The scheme of the device is shown in Fig. 4. Two couples of the specimens are present in a symmetrical position, in order to avoid bending and torsional effects. The bodies are mounted on a central slide attached to the lower grip of the testing machine, while the punches are mounted on two lateral walls, attached to the higher grip of the machine. Spherical joints are present between the apparatus and the machine grips, in order to avoid any problem of misalignment. A normal load N is applied during the test by means of a bolt, with pivoted axial rolling bearings under the bolt head and under the nut, to avoid the transmission of a torque to the walls during the tightening operation"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002912_6.2004-4911-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002912_6.2004-4911-Figure2-1.png",
+        "caption": "Figure 2: EADS-Quattrocopter MAV",
+        "texts": [
+            " MEMS Components Flight Testing To perform investigations on MEMS-based micro-avionics systems and miniaturised autopilots suited for flight control of MAVs, a rotary wing MAV was designed as a flying testbed. The rotary wing configuration was chosen because it offers the higher challenge for MAV flight control compared to a fixed wing configuration. This MAV serves also as a testbed to investigate the capabilities of small scale hovering surveillance platforms. The so called Quattrocopter (see Fig. 2) is an electrically driven rotary wing platform with four fixed pitch rotors (no swash plates). The flight control is performed through the variation of the motor speed. It has an overall size of 65 cm and a total weight of approximately half a kilogram. The Quattrocopter is designed for a flight duration of about 25min with one charge of the lithium batteries. The micro avionics is comprising a 6DoF MEMS IMU, a pressure sensor, 16bit A/D conversion, a GPS module, a RC-control receiver and power amplifiers for motor control"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000885_s0263-8223(00)00103-3-Figure7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000885_s0263-8223(00)00103-3-Figure7-1.png",
+        "caption": "Fig. 7. The distribution of the residual stress component of rx for the 90\u00b0 orientation angle.",
+        "texts": [],
+        "surrounding_texts": [
+            "5. Results and discussion\nAll the results in this study are found from the analytical solution. When the bending moment values reach the values in Table 2, plastic yielding occurs. As seen from this table, the bending moment which starts the plastic yielding is maximum for the orientations angle of 0\u00b0, as 12629.3 Nmm. It is minimum for the orientation angle of 90\u00b0, as 1706.7 Nmm.\nElastic, elastic\u00b1plastic and residual stress components for 0\u00b0, 30\u00b0, 45\u00b0, 60\u00b0 and 90\u00b0 orientation angles are given in Table 3. As seen from this table, maximum residual stress component is found at upper and lower surfaces. It is the greatest value for the orientation angle of 0\u00b0 as \u00ff17:30 MPa at the lower surface. When the orientation angle is increased, the residual stress component of rx becomes smaller. When h 2 mm, the equivalent plastic strain is maximum for 30\u00b0 orientation angle as 0.9%.",
+            "The displacement components at the mid-point of the free end x 0; y 0 are given in Table 4. As seen from this table, the vertical displacement component v is larger than the horizontal displacement u. The vertical displacement component is maximum for the orientation angle of 30\u00b0 as \u00ff5:98 mm for h 2 mm.\nThe distribution of the residual stress component of rx for the 0\u00b0 orientation angle is shown in Fig. 3. As seen from this \u00aegure, the intensity of the residual stress component is maximum at the upper and lower surfaces for h 4 and 6 mm. But it is maximum at the boundary of the elastic and plastic regions for h 2 mm. The distribution of the residual stress component of rx for 30\u00b0, 45\u00b0, 60\u00b0 and 90\u00b0 orientation angles is shown in Figs. 4\u00b17, respectively. As seen from these \u00aegures, the intensity of the residual stress component rx is maximum at the upper and lower surfaces or at the boundary of the elastic and plastic regions for h 6 and 4 mm. But it is maximum for all the cases at the boundary of the elastic and plastic regions for h 2 mm. It varies nearly linearly in the plastic region for small plastic deformations.\n6. Conclusion\nThe following conclusions are obtained from the analytical solution of the composite cantilever beam: 1. The intensity of the residual stress component of rx is\nmaximum at the upper and lower surfaces or at the boundary of the elastic and plastic regions. 2. If the plastic region is increased further, maximum residual stress is obtained at the boundary of the elastic and the plastic regions. 3. The vertical displacement is larger than the horizontal displacement. 4. The beam gives the greatest vertical displacement at the mid-point of the free end for the orientation angle of 30\u00b0. 5. The residual stress component of rx is the greatest for the orientation angle of 0\u00b0. 6. Maximum equivalent plastic strain is obtained for the orientation angle of 30\u00b0 at h 2 mm.\nReferences\n[1] Jegley D. Impact-damaged graphite-thermoplastic trapezoidal-\ncorrugation sandwich and semi-sandwich panels. J Compos Mater 1993;27(5):526\u00b138. [2] Marissen R, Brouwer R, Linsen J. Notched strength of thermo-\nplastic woven fabric composites. Compos Mater 1995;29:1544\u00b164. [3] Cantwell WJ. The in\u00afuence of stamping temperature on the\nproperties of a glass mat thermoplastic composites. J Compos Mater 1996;30(10):1266\u00b181.",
+            "[4] Shi FF. The mechanical properties and deformation of shear-\ninduced polymer liquid crystalline \u00aebers in an engineering thermoplastic. J Compos Mater 1996;30(14):1613\u00b126. [5] Tavman IH. Thermal and mechanical properties of aluminium\npowder \u00aelled high-density polyethylene composites. J Appl Polym Sci 1996;62:2161\u00b17. [6] Miyazaki M, Hamao T. Solid particle erosion of thermoplastic\nresins reinforced by short \u00aebers. J Compos Mater 1994;28(9): 871\u00b183. [7] Jeronimidis G, Parkyn AT. Residual stress in carbon \u00aebre\u00b1\nthermoplastic matrix laminates. J Compos Mater 1998;22-5:401\u00b1 15. [8] Domb MM, Hansen JS. The e ect of cooling rate on free-edge\nstress development in semi-crystalline thermoplastic laminates. J Compos Mater 1998;32(4):361\u00b185. [9] Akay M, Ozden S. Measurement of residual stresses in injection\nmoulded thermoplastics. Polym Test 1994;13:323\u00b154.\n[10] Akay M, Ozden S. In\u00afuence of residual stresses on mechanical\nand thermal properties of injection moulded polycarbonate. Plastics, Rubber and Compos Processing Appl 1996;25(3): 138\u00b144.\n[11] Karakuzu R, Sayman O. Elasto-plastic \u00aenite element analysis of\northotropic rotating discs with holes. Comput Struct 1994; 51(6):695\u00b1703. [12] Karakuzu R, Ozel A, Sayman O. Elasto-plastic \u00aenite element\nanalysis of metal-matrix plates with edge notches. Comput Struct 1997;63(3):551\u00b18. [13] Sayman O. Elasto-plastic stress analysis in stainless steel \u00aeber\nreinforced aluminum metal laminated plates loaded transversely. Compos Struct 1998;43:147\u00b154. [14] Karakuzu R, Ozcan R. Exact solution of elasto-plastic stresses in\na metal-matrix composite beam of arbitrary orientation subjected to transverse loads. Compos Sci Technol 1996;56:1383\u00b19. [15] Sayman O, Kayrici M. An elastic\u00b1plastic stress analysis in a\nthermoplastic composite cantilever beam. Compos Sci Technol 2000;60:623\u00b131. [16] Lekhniskii SG. Anisotropic plates. London: Gordon and Breach,\n1968.\n[17] Jones RM. Mechanics of composite materials. Tokyo: McGraw-\nHill Kogakusha, 1975.\n[18] Owen DRJ, Hinton E. Finite elements in plasticity. Swansea:\nPineridge, 1980."
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0000517_1616-8984(199607)1:1<1::aid-seup1>3.0.co;2-6-Figure1-8-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000517_1616-8984(199607)1:1<1::aid-seup1>3.0.co;2-6-Figure1-8-1.png",
+        "caption": "Figure 1-8. Interferometric set-up combined with a 3 x 3 coupler arrangement for phase demodulation (according to [429])",
+        "texts": [
+            " Stripe waveguides (diameter approximately 5 urn) at higher refractive index are placed in parallel at a distance such that the evanescent fields can cross-talk from the first waveguide to the second. Such devices are frequently used in telecommunications for phase decoding. For this reason, they are available in various structures [20] and at reasonable prices. A typical form is the socalled 3x3 coupler, shown schematically in Figure 1-7. 14 l Opto-Chemical and Opto-lmmuno Sensors 1.2 Principles of Optical Transduction 15 Combination of such signal processing units with interferometers supply sensitive sensing properties. A complex set-up is shown in Figure 1-8 [429]. Additional literature is cited in Table 1-4. 16 l Opto-Chemical and Opto-Immuno Sensors Surface Plasmon Resonance (SPR) The principle has been explained in Section 1.2.2. Two types of excitation of the surface plasmon resonance [254, 368] are possible: (a) The angle of incidence of monochromatic light is varied. The resonance condition is monitored by use of a position-sensitive linear photodiode array [294]. This principle is commercialized by Pharmacia. At present it is one of the most commonly used bioanalytical systems for examining affinity reactions"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure1.3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure1.3-1.png",
+        "caption": "Figure 1.3. A simple mechanical system in which a small body P is modeled as a particle.",
+        "texts": [
+            " In the preceding example, we started from a given motion relation and derived the velocity and acceleration from it. Most of the time, however, we must obtain the motion relation from other data provided in the problem. Let us look at an illustration of a simple mechanical system in which the motion is obtained by construction of the position vector from geometrical con siderations. Example 1.3. The hinged support H of a thin rod of length L to which a small ball Pis attached moves with constant angular speed d8(t)jdt = w on a vertical circle of radius R as shown in Fig. 1.3. We wish to determine the velocity and acceleration of the ball as it moves in the plane relative to frame t/1 = { 0; i, j} which is fixed in the plane space at 0. Solution. Since the size of P, though unspecified but finite, is apparently very small compared to the lengths L and R, it is reasonable to model P as a particle attached to the end point of the rod. Then, in terms of the angles 8 and ifJ shown in Fig. 1.3, the position vector of P in the fixed Cartesian frame t/1 is given by xi/I(P, t) = x(t) i + y(t) j = [R cos 8(t) + L cos ifJ(t)] i + [R sin 8(t) + L sin f/J(t)] j. * The angular velocity vector ro will be defined carefully in Chapter 2; its magnitude, the angular speed, has the same physical interpretation illustrated in this simpler intuitive setting. 12 Chapter 1 Hence, recalling that 0 = w, we find with ( 1.8) and ( 1.9) that relative to frame 1./J v\"'(P, t) = -(Rw sin 8+ L~ sin ifJ) i + (Rw cos 8+ ~cos ifJ)j, a\"'(P, t) = - (Rw 2 cos 8 + L~2 cos ifJ + L(fi sin ifJ) i ( 1",
+            "* Clearly, its physical dimensions are [T- 2]; and its usual measure units are rad/sec2\u2022 Notice that the same result would be obtained were we to consider, more precisely, that L was the distance from the support H to the center of the ball at P, or to any other point in the ball. In this case it makes no difference what the dimensions of the ball may be. D Example 1.4. Determine the velocity and acceleration of the ball P relative to a moving reference frame J1. = { 0; e 1 , e2 } fixed in the wheel of the device shown in Fig. 1.3. Solution. To find the velocity and acceleration of P relative to a moving frame J1. = { 0; ek} fixed in the wheel at 0, we first write its position vector relative to frame J-L: x1_.(P, t) = R + L[cos ifJ(t) e1 +sin ifJ(t) e2 ] where now R is the constant vector of H from 0. Hence, with (1.8) and (1.9), we find relative to frame J1. v 1-'(P, t) = L~[ -sin ifJ(t) e 1 +cos ifJ(t) e2], a~-'(P, t) = -L[{fi sin ifJ(t) + ~2 cos ifJ{t)] e 1 (1.18) + L[{ficosifJ{t)-~2 sinifJ(t)] e2 \u2022 Notice that in the moving frame J-1",
+            " But a constant speed by itself does not constitute a uniform motion because there are infinitely many paths along which a particle may travel with a con stant speed. A straight line is only one of them. An example of another one studied earlier is the helical path ( 1. 7) for which the constant speed was found to be v = ( w 2 R 2 +A 2 ) 112. For the given initial data x0 and v0 , there is one and only one uniform motion (1.55); but for the same x 0 and v0 there are infinitely many motions of P for which only the speed is uniform. Example 1.9. Suppose that the hinge point H of the system shown in Fig. 1.3 moves with a constant speed v = 2 m/sec on a circle of radius Solution. The position vector of H in 1/1 = { 0; i, j} is given by x(H, t) =50( cos 8 i +sin 8 j) em, where 8(t) denotes the angular placement of H measured from the fixed ver tical line shown in Fig. 1.3. Application of (1.8) to the last equation gives v(H, t) = 508(- sin 8 i +cos 8 j) em/sec. Therefore, after a change of units, I vi= 508 = v = 200 em/sec shows that 8 = 4 rad/sec, which is the constant angular speed of H about point 0 in 1/J. It is now easy to show with (1.9) that a(H, t) = -8(cos 8 i +sin 8 j) m/sec 2, whence follows la(H, t)l = 8 m/sec 2 . The point H has a constant speed; but this result shows that its acceleration is not zero because the velocity vector is changing its direction asH rotates around 0",
+            " At the other extreme, a rigid body is a body with the property that the straight line distance between every pair of its particles is constant in time. This idealization of a body that cannot be deformed, however great may be the forces and torques that act upon it, is so intuitively natural that it is often used without mention. The reader surely will recognize that our basic definition of a reference frame embodied the concept of rigidity. In fact, there were sev,eral occasions in Chapter 1 where the concept was quietly invoked. In particular, it was tacitly supposed for the mechanical device shown in Fig. 1.3 that the radius R of the wheel and the length L of the hinged rod did not vary with time. These are typical examples of rigid bodies whose motions will be investigated in this chapter. The kinematics of a rigid body in general motion in space will be studied. The main objective will be to learn how the velocity and acceleration of the particles of a rigid body are related to the translational and rotational parts of its motion. The theory of the motion of a rigid body rests upo111 a fundamental theorem due to Euler (1775)",
+            "30) for the rigid body velocity and acceleration of a particle P rotating on a circle of radius p with angular speed (J about a fixed axis a= b. 2.14. Use the geometrical interpretations of the terms in (2.27) and (2.30) to determine the velocity and acceleration of the rim particle P in Fig. 1.14. Check your solutions against (1.78). See Example 1.8. 2.15. Apply equations (2.27) and (2.30) to determine for the conditions specified in Problem 1.12 the velocity and acceleration of the mass M. Note the geometrical nature of the terms computed. 2.16. Employ (2.27) and (2.30) to find the velocity and acceleration of the ball P in Fig. 1.3. Use the conditions described in Example 1.3, and compare your results with those in ( 1.17 ). Observe the geometrical character of the terms computed. 2.17. The slider block of a machine oscillates along a straight line; and at the instant illustrated, it has a speed of 30ft/sec and is accelerating at 10 ftjsec 2 toward the right. The connecting rod AB has an angular speed of 4 rad/sec and an angular acceleration of 8 rad/sec2 clockwise about its hinge at A, and the rod is in a vertical position"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001444_48.286641-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001444_48.286641-Figure1-1.png",
+        "caption": "Fig. 1. Mathematical model.",
+        "texts": [
+            " The surface wake of an undersea towed body seems to simulate a similar situation, since the wavelengths involved in its wake can be as long as 60 meters, and produce magnetic fields greater than nT at a 10 km distance along its track. The most sensitive magnetometers or gradiometers available use SQUID technology and have a sensitivity of about II. MATHEMATICAL FORMULATION The mean free surface of the sea is taken to be the plane z = 0 in a rectangular coordinate system, with the z axis directed upward into air, the 2 axis along the direction opposite to that in which the body is traveling, and the y axis chosen to form a right-handed triad. We assume that BE (the geomagnetic induction) is constant everywhere (Fig. 1). Here i , j , k are unit vectors along the three coordinate axes, y is the angle between the 2 axis and magnetic north, and I is the dip angle. We can write: BE = F( icos lcosy + j c o s I s i n y - ks inI ) (1) nT. where F is the magnitude of BE. 0364-9059/94$04.00 0 1994 IEEE 194 Here, we assume the body is located at the point z = -h at time t = 0, and is traveling at a uniform speed U in the \u201c-x\u201d direction. Let q(z , y, z , t) be the velocity of the fluid, which is entirely due to the moving body\u2019s passage, with all other ocean phenomenon such as wind-generated waves and ocean swells being ignored"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002572_robot.1996.506595-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002572_robot.1996.506595-Figure6-1.png",
+        "caption": "Fig. 6 Simulation result with collision avoidance",
+        "texts": [
+            " The path for the case when the position and the orientation of the object are fixed has 0.0549 as the value of S. In the case of Fig.3, total value of variations of joint variables becomes smaller by moving the manipulator-A. From this result the meaning of the pseudo inverse is understood. Fig.4 shows the result considering obstacle avoidance. The value of S is 0.0198 for this case. The obstacle is avoided by using the pokential function in eq.(47). Next, 3-dimensional example is considered. Fig.5 shows the simulation result with y = 0 in eq.(48) and Fig.6 shows the result with collision avoidance. 7 Conclusions Our purpose of this paper was to propose an algorithm to plan the cooperative collision free motion for two manipulators system. In general, the two manipulators system has redundancy. By using the redundant degrees of freedom, the desired cooperative motion which executes the specified task can be planned. The potential function method is used for collision avoidance. Numerical examples show the effectiveness of the proposed method. References [l] C"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002581_robot.1996.503837-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002581_robot.1996.503837-Figure2-1.png",
+        "caption": "Figure 2: The compass gait. During single support, the hip follows the arc of a circle with radius equal to the stance leg length. At exchange of support, there is an instantaneous change in linear velocity of the hip.",
+        "texts": [
+            " In the single support phase, the stance leg is in contact with the ground and carries the weight of the biped, while the swing leg usually moves forward in preparation for the next step. At exchange of support the weight of the robot is transferred from one leg to the other. In this section, we examine exchange of support, discuss why it might not be smooth, and present a set of constraints which ensure smooth exchange of support. Inman et al. [lo] examined bipedal walking in humans and proposed a model of bipedal walking based on the compass gait (Figure 2) . In this gait the leg lengths are fixed, so t,he hip trajectory follows the arc of a circle as the biped pivots about the distal end of the stance leg. At exchange of support, the stance and swing legs trade roles, and the hip begins to follow the arc of a new circle. Because the origins of the two circles are .not coincident, the hip trajectory contains a cusp at exchange of support. Velocity vectors vand v+ attached to the hip trajectory at a cusp indicate translational velocity of the hip just before and just after exchange of support, respectively"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001440_s0925-4005(00)00722-x-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001440_s0925-4005(00)00722-x-Figure2-1.png",
+        "caption": "Fig. 2. Pool optode based on renewable reagent system operated in batch mode.",
+        "texts": [
+            " The pipette tip was then loaded with reagent solution and \u00aexed onto the end of the bifurcated \u00aebre optic supported in the syringe body. A hole was punched out of the side of the pipette to relieve backpressure and to enable solution of ions to diffuse through the membrane without producing a pressure differential. The pool optodes of the design shown in Fig. 1(a) and (b) are of low cost and relatively easy to prepare. For renewable reagent scheme, the pool optode was also incorporated with pumping system for delivering reagent from a reservoir into the pool via capillary tubing having dimensions similar to the \u00aebre optics (Fig. 2). Reagent pumping was performed by means of syringe pump, which can deliver small volumes in a reproducible manner. Other feature of the pool optode includes its use as a disposable system for single-shot analysis. In order to achieve maximum sensitivity, the pool optode was operated in a batch mode. That is, for each measurement the pool of reagent was immersed and stopped for a \u00aexed period of time to preconcentrate analyte until the reaction achieved the steady state. Once measurement has been made, the used reagent was removed from the pool by pumping fresh reagent",
+            " Therefore, it allowed greatly reduced recovery times compared to that obtained with immobilised reagent based sensor. The effects of different parameters on the sensor response were also studied. Initially, the solutions safranin and potassium iodide were added to form a mixture. The solution mixture was kept at room temperature ( 228C), and a small portion of this mixture was added to the probe head, to form the pool optode reagent solution. For operation in this system, the pool optode was immersed in a batch of sample solution (Fig. 2). In order to accelerate the reaction, a magnetic stirrer was also used. The signal response of the mercury sensor was measured at an optimum wavelength of 620 nm (Fig. 3). Each of the pool optode design was tested towards reaction with Hg(II) ion. The responses of the pool optode designs recorded as a function of time are shown in Fig. 4. The principle disadvantage of the probe head of the \u00aerst pool design (Fig. 4(a)) is the slow response and slightly lower levels of signal yielded. Furthermore, it also suffers from sensor to sensor irreproducibility and, as a result, the reproducibility of Na\u00aeon \u00aelm thickness could not be guaranteed in such a design due to the \u00aelm being formed at an angle of 458"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000629_0302-4598(94)01772-s-FigureI-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000629_0302-4598(94)01772-s-FigureI-1.png",
+        "caption": "Fig. I. Typical cyclic voltammograms demonstrating the mediated electron transfer of EEO-SOD(Cu 2+, Zn 2+) by the M V 2 + / M V + couple in DMSO solutions containing 0.I M TEAP and ( . . . . . . ) 2 mM PEO-SOD(Cu 2+, Zn2+), ( . . . . ) 0.2 mM MV 2+ or ( ) 0.2 mM MV2++ 2 mM PEO-SOD(Cu 2+, Zn 2+) under a nitrogen atmosphere. Potential scan rate: (a) 10; (b) 100; (\u00a2) 500 mV s - I .",
+        "texts": [],
+        "surrounding_texts": [
+            "Methyl viologen was found to efficiently mediate the electron transfer between polyethylene oxide-modified superoxide dismutase and the electrode in dimethyl sulphoxide media. Based on the potential-step chronoamperometric experiments, the rate constant for the mediated electron transfer was estimated to be = (1-2) \u00d7 103 M- 1 s- 1.\nKeywords: Mediated electron transfer; polyethylene oxide-modified superoxide dismutase; methyl viologen\n1. Introduction\nSuperoxide dismutases (SODs), which efficiently catalyse the dismutation of superoxide ion to H20 2 and 0 2 via a cyclic oxidation-reduction mechanism, are essential metallo-enzymes and are found in virtually all organisms [1-3]. So far there have been few electrochemical studies on electron transfer of SODs, although it has been well recognized that information on electron transfer is very useful in understanding the intrinsic thermodynamic and kinetic properties and in the practical development of the SOD-based biosensors [1-4]. Recently, Iyer and Schmidt [5] observed the direct, irreversible oxidation of copper-zinc SOD at a bare Au electrode in phosphate buffer solution of pH 4.0, and suggested that a conformational change occurs at the active sites via its adsorption on the electrode surface, thus facilitating direct electron transfer. Borsari and Azab [6] also reported the successful use of some promoters in obtaining the reversible redox response of copper-zinc SOD at an Au electrode in NaC104 aqueous solution (pH 7.2).\nThis type of study concerning the direct electron transfer of SODs seems limited because of their intrinsic electroinactivity, i.e. they lack an external pathway for electron transfer from the protein surface to the active site. On the other hand, the so-called mediated\n* Corresponding author.\n0302-4598/95/$09.50 \u00a9 1995 Elsevier Science S.A. All rights reserved SSDI 0302-4598(94)01772-7\nelectron transfer is possible for such an intrinsic enzyme by using freely mobile, soluble redox species which efficiently mediate electron transfer between the active site of the enzyme and the electrode. In order to clarify the mediated electron-transfer properties of SODs, we have been investigating their electrochemical behaviour. In this paper, we report the preliminary results of the mediated electron transfer of polyethylene oxide (PEO)-modified SOD by methyl viologen (MV 2+) in dimethyl sulphoxide (DMSO) media. The chemical modification of SODs by covalent attachment of PEO to them has recently become of great interest from the viewpoint of increasing in vitro stability, in vivo half-life and protein solubility and decreasing immunogenicity [7,8]. In this study, the main purpose of modifying SOD by PEO with amphiphilic properties is to increase the solubility of SOD in DMSO.\n2. Experimental\nBovine erythrocyte copper-zinc superoxide dismutase (SOD(Cu2+-Zn2+), 3000 units mg -1) was purchased from Wako Pure Chemical Industries (Osaka, Japan). Methyl viologen dichloride (MVCI 2) was obtained from Aldrich. A 0.1 M tetraethylammonium perchlorate (TEAP) solution was used as the supporting electrolyte in dimethyl sulphoxide (DMSO). Polyethylene oxide (PEO)-modified SOD (Cu 2\u00f7, Zn 2\u00f7) (abbreviated as PEO-SOD (Cu 2\u00f7, Zn 2+) henceforth)",
+            "was prepared from PEO monomethoxyl ether (molar mass = 5000) according to the published procedure [9]. The modification percentage was estimated to be about 35% based on the data concerning the percentage of lysines on SOD (Cu 2\u00f7, Zn 2+) (20 per SOD(Cu 2+, Zn z+) dimer) derivatized with PEO [9]. Thus, the molecular weight of the PEO-SOD(Cu 2\u00f7, Zn 2\u00f7) was calculated to be ca. 67 700.\n[CH 30\"(\" CH 2CH 20-~n CCH zCH 2~-- N]m-- ~\n0 u H x (NH2)20.m\nm - 7 , n - l 1 2\nPEO-SOD(Cu 2+, Zn 2+ )\nCyclic voltammetric and potential-step chronoamperometric experiments were carried out using a three-electrode system. A glassy carbon disc (GC-20; Tokai Carbon, diameter 1.0 mm) was used as the working electrode, a platinum wire as the auxiliary electrode and Ag/AgCIO 4 (0.01 M Ag +) as the reference electrode. A cell for a small-volume sample (about 0.2 ml) working under a nitrogen atmosphere at 25 + 2\u00b0C was used. The surface of the glassy carbon electrode was polished before each use with 0.3 /zm alumina powder (Marumoto Kogyo) on a microcloth wetted with deionized water obtained with a Milli-Q water system (Millipore), and was successively carefully sonicated in water and rinsed with water and DMSO.",
+            "diated electron transfer of PEO-SOD(Cu 2+, Zn 2+) by the MV2+/MV + couple:\nM V 2 + + e . ~ M V + 1 (1) kz I\nM V + + P E O - S O D ( C u 2 + ' Z n 2 + ) * M V 2 + + P E O - S O I M C u + , Z n 2 + ) (2)\nThe potential-step chronoamperometric experiments confirmed the above-mentioned cyclic voltammetric results. The typical results for the reduction of MV 2+ to MV + in the absence and presence of PEOSOD(Cu 2+, Zn 2+) are shown as Cottrell plots in Fig. 2. The linear Cottrell plot was, as expected, obtained in the absence of PEO-SOD(Cu 2+, Zn2+), and the slope gave the diffusion coefficient of MV 2+ as 4.8 \u00d7 10 -6 cm 2 s-l. On the other hand, such a linear Cottrell plot was not obtained in the presence of PEO-SOD(Cu 2+, Zn2+). That is, at electrolysis times shorter than ca. 30 ms the current was almost the same as that in the absence of PEO-SOD(Cu 2+, Zn2+), whereas at longer electrolysis times the increment in the current (in comparison with the current obtained when PEOSOD(Cu 2+, Zn 2+) is absent) was observed and it became larger. The increased reduction current is due to the mediated electron-transfer reaction of PEOSOD(Cu 2+, Zn 2+) (Eq. (2)). The data in Fig. 2 were replotted as the current ratio (IMed/I) against t x/2 (Fig. 3), where Iraeu and I represent the reduction current of M V 2+ to M V + in the presence and the absence, respectively, of 2 mM PEO-SOD(Cu 2+, Zn2+). Curves 1-6 are those calculated for typical\nvalues of the rate constant (k 2) for the electron-transfer reaction (Eq. (2)) using the following equation [10]:\nIMeai =/~1/2[ 'WI/2 erf(A1/2)\nwith\nA = ( k 2 C s o D t ) 1/2\nexp(-A) ] + A1/2 (3)\n(4) where Cso D is the concentration of the Cu 2\u00f7 active sites in the PEO-SOD(Cu 2\u00f7, zne+). From Fig. 3, the value of k 2 was estimated to be ca. (1-2) x 103 M-1 S -1 .\nIn conclusion, the mediated electron transfer of PEO-SOD(Cu 2\u00f7, Zn 2+) by the MV2+/MV + couple in DMSO media was observed for the first time by cyclic voltammetry and potential-step chronoamperometry, and the rate constant for the homogeneous electron-transfer reaction between MV \u00f7 and PEOSOD(Cu 2\u00f7, Zn 2\u00f7) was estimated. A related study using other redox mediators is in progress.\nAcknowledgements This work was financially supported by a Grant-inAid for Scientific Research (No. 05453117) and for Priority Area Research on New Development of Organic Electrochemistry (Nos. 05235214 and 06226222) from the Ministry of Education, Science and Culture, Japan, and the Nissan Science Foundation."
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure4.7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure4.7-1.png",
+        "caption": "Figure 4.7. Multiple reference frames applied to the complex rotations of a robot.",
+        "texts": [
+            " However, use of consecutive numerical labels that reflect the chain of angular velocities Motion Referred to a Moving Reference Frame and Relative Motion 245 involved in the problem usually is more convenient, especially for the com putation of the total angular acceleration studied later. In any case, care must be exercised to name and identify the various frames or the bodies in which the frames are imbedded. D Example 4.5. Recall the data for the moment of interest t 0 described in Example 4.1, and suppose further that the claw attached to the telescopic arm of the robot turns about the arm axis with an angular velocity co 3 = 0.1 y rad/sec relative to the arm, as indicated. The data are shown in Fig. 4.7, in which four appropriate reference frames also are defined. Find for the instant t0 the total angular velocity of the claw in the machine frame 0, but referred to frame 1 fixed in the yoke. Solution. Let us write co32 = 0.1 y radjsec for the angular velocity of the claw frame 3 ={A; y, e, f} relative to the arm frame 2 = { 0; y, i', j} whose angular velocity relative to the yoke frame 1 = { 0; i, j, k} is written as co 21 = co2 = 0.2j rad/sec. Let COw= co 1 = 0.5k rad/sec denote the angular velocity of the yoke frame 1 relative to the preferred, machine frame 0 = { 0; I, J, K }",
+            " The frames and angular velocity vectors are shown in Fig. 4. 7, but now we shall ignore the special numerical values assigned before. We want to find the total angular velocity and angular acceleration of the claw in the machine frame, but referred to the yoke frame. Let ~ be the angular speed of the claw relative to the telescopic arm; write iJ for the angular speed of the arm relative to the yoke, and let li denote the angular speed of the yoke relative to the machine frame. Then the corresponding relative angular velocity vectors indicated in Fig. 4.7 are given by (4.40a) Therefore, with the aid of y =sin pi+ cos p k in the first equation in ( 4.40a ), the total angular velocity of the claw in the machine frame and referred to the yoke frame is given by the kinematic chain rule ( 4.25b ). We thereby obtain ro 30 = ~ sin P i + iJj + ( ~ cos p + li) k. (4.40b) The corresponding total angular acceleration may be found from ( 4.36 ). We observe in ( 4.40a) that y is fixed in frame 2; j is in frame 1; and k is in frame 0. Then the relative angular acceleration vectors derive from ( 4",
+            " The second problem concerns a speed control governor and will demonstrate three methods that use spherical coordinates in slightly different ways, one being the direct use of ( 4. 70) and ( 4. 71 ). The final illustration is an application of ( 4.46) and ( 4.48) to the motion of a point on a helicopter blade referred to a spherical reference frame. Motion Referred to a Moving Reference Frame and Relative Motion 279 Example 4.12. The relative angular velocity vectors for the general rotation of the manipulator claw of the robot shown in Fig. 4.7 are given in ( 4.40a ). Recall also that the length /( t) of the telescopic arm, as shown in Fig. 4.4, is a computer-controlled function of time. Find the absolute velocity and acceleration of point A on the claw referred to frame 2 = { 0; y, i', j} shown in Fig. 4.7. Solution. A few moments' reflection will reveal in Fig. 4. 7 that with y = e\" i' = e0 , and j = e.p frame 2 may be identified as the spherical reference frame t/t={O;e\"e0 ,e.p}\u00b7 It is seen that r=l(t),e={J(t), and \u00a2=r~.(t). Therefore, the absolute velocity and acceleration of point A on the manipulator claw may be read directly from (4.70) and (4.71). We find v A= ie, + lri sin {3 e.p + 1Pe8, a A= (i\"-IP2 -lri2 sin2 {J) e, + (2iri sin {J + 2/riP cos {J + Iii sin {3) e.p +UP+ 2iiJ -lri 2 sin {J cos {J) e0 "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002746_0278364905060149-Figure23-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002746_0278364905060149-Figure23-1.png",
+        "caption": "Fig. 23. Reference points on surface plate and base platform.",
+        "texts": [
+            " If the base platform\u2019s position and orientation, which are represented in a coordinate system located on the surface plate, are measured while the machine is in process, the thermal and elastic deformations of the frame can be compensated independent of the structural and the material configurations of the machine base and the frame. In general, the three joints on the base platform of a tripodtype PKM shown in Figure 2(b) are located at regular intervals of 120 degrees. Moreover, two of the six joints on the base platform of a Hexapod-type PKM, shown in Figure 2(a), are closely located; thus, common PKMs have three joint supports mounting the mechanism. Thus, when three reference points are set on each joint support as shown in Figure 23, the position and orientation of the mechanism\u2019s base platform can be expressed by the coordinates of the reference points. Furthermore, the three distances among them, t1 \u2212 t3, represent the dimensions of the base platform. On the other hand, six reference points placed on the surface plate express its position and orientation. Consequently, the base platform\u2019s position and the orientation expressed in the coordinate system located on the surface plate are derived from the six distances among the reference points on both the joint supports and the surface plate, u1 \u2212 u6",
+            " In coordinate measuring machines, first a coordinate of the probe tip BPr , which is observed in the moving coordinate system \u2211 B , is calculated by the forward kinematics from the limb\u2019s lengths measured by the linear scale units. Secondly, the measured coordinate BPr is transformed to a coordinate B0Pr represented in the initial coordinate system \u2211 B0 by B0P r = B0P B + B0RB BP r. (7) In brief, all measured coordinates are rewritten in the initial coordinate system. at UNIVERSITY OF BRIGHTON on July 11, 2014ijr.sagepub.comDownloaded from Figure 26 depicts an example of the measurement method for the distance changes, u1 \u2212 u6, shown in Figure 23. The spherical joint is mounted on a joint support made of low thermal expansion cast iron. A Super-Invar rod is used as a spanner between the joint support and the surface plate. One end of the rod is connected to the surface plate by a flexure hinge. The other end is guided via a hole in a holder mounted on the joint support. A displacement sensor installed in the hole measures the displacement change in the rod end\u2019s surface in the longitudinal direction of the rod. The length of the rod is constant because no external force is applied to the rod"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003319_s0167-8922(08)71045-9-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003319_s0167-8922(08)71045-9-Figure2-1.png",
+        "caption": "Fig. 2 Bearing testing machine.",
+        "texts": [
+            " The inner race had a raceway groove, which the outer race did not have. The pitch circle diameter of the raceway groove of the inner race was 33.5 mm. The retainer was machined, and had a bore diameter of 25.2 mm and an outer diameter of 47 mm. were made of vacuum-degassed ASTM 52100 steel with hardness ranging from 61.4 to 62.4 HRC, while the material of the retainer was ASTM D2. The inner race, the ball and the outer race The bearing testing machine used in the The test bearing was attached to the rolling contact fatigue test is illustrated in Fig.2. bottom end of a spindle. downward axial load was statically applied to the bearing by means of a dead weight lever system. The test bearing was run under an axial load of 3.14 kN at a rotational speed of 660 rev/min in a mineral oil bath. contact pressure induced in the outer race was 5.64 GPa. considering the plastic deformation at the surface of the raceway track. minimum film thickness Ho to the composite surface roughness R was 0.21-0.27. film thickness Ho was calculated according to an The vertical and The maximum This value was obtained by The ratio of the The minimum roughness of the raceway track was measured after the test"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003477_cnm.913-Figure10-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003477_cnm.913-Figure10-1.png",
+        "caption": "Figure 10. Factors of the system with C3v symmetry: (a) in group-theoretical method; and (b) in canonical form III decomposition.",
+        "texts": [
+            " Now the eigenvalues (natural frequencies) of each subspace can be easily calculated. Whereas subspace V (3) is associated with double-repeating roots. The frequency found from subspace V (31) should be identically repeated in the set of answers for the original problem. Subspace V (1): 2 1 = k1/m and subspace V (3): 2 2 = 2 3 = (k1 + 3k2)/m Finally, it is concluded that two problems, each of which is of dimension one, are solved instead of a three-dimensional problem. The decomposed factors of this structure are shown in Figure 10, where the factors obtained above via the group-theoretical approach are shown in Figure 10(a), and the factors which result from the decomposition of canonical form III symmetry are presented in Figure 10(b). By comparing Figures 10(a) and (b) it can be seen that the efficiency of the group-theoretic approach is due to the decomposition of group-invariant subspace V (3) into orthogonal subspaces V (31) and V (32), or in better words, group-theoretical method can recognize the existence of the multi-repeating roots in a problem. Copyright q 2006 John Wiley & Sons, Ltd. Commun. Numer. Meth. Engng 2007; 23:639\u2013664 DOI: 10.1002/cnm As another example, the symmetric dynamic system of Figure 11 is considered"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003075_bf02441586-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003075_bf02441586-Figure5-1.png",
+        "caption": "Fig. 5",
+        "texts": [
+            " (Sampling from a 37~ source for 20 s periods every 120 S at 22~ ambient ensures that the analyte is cooled to less than 27~ at the ChemFET input). The mode of operation of the system is self-explanatory; note that the reference electrode junction is situated immediately downstream of the ChemFET cell to eliminate spurious liquid-junction potentials, and that the inclusion of a three-way input tap is useful for rapidly priming the system during the initial setting-up procedure. The hardware is assembled on a 98 x 4 8 m m printed-circuit board, thus forming a small, robust 'remote sensor unit', shown in Fig. 5, with easy access to all fluid lines and incorporating a LED indicator to show when the valve is being actuated. This unit is mounted on to the end of a spring-cantilevered arm, which is then attached to the instrumentation trolley such that the remote sensor unit can be swivelled and rotated freely, and can be positioned rapidly and easily wherever required by the clinician, thus allowing flexible access for use in a wide variety of applications (e.g. at operating-table height, with cardiopulmonary bypass equipment (where the sampling site is close to the ground), at the bedside)"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001423_s1350-4533(99)00095-8-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001423_s1350-4533(99)00095-8-Figure5-1.png",
+        "caption": "Fig. 5. The model of the lateral bands of the EDL (thickest black line segment) allows for slack in the distal portion of the central slip (serpentine portion of tendon shown in gray), caused by DIP flexion sufficient to tense the lateral bands. The lateral bands are assumed to bowstring from a",
+        "texts": [
+            " Keeping the number of parameters small helps insure that each can be estimated uniquely. The second term contributing to EDL excursion concerns the lateral bands, which divide from the EDL central slip, \u201cbowstring\u201d past the PIP joint without wrapping over the head of the first phalanx, and insert on the distal phalanx. These bands become taut only when the DIP joint is flexed enough to take the slack out of them. Once this point is reached, further flexion of the DIP joint can create slack in the terminus of the central slip, while further stretching the EDL muscle (Fig. 5). The contribution of the lateral bands to changing the length of the EDL depends on tautness (Eq. (6)). The top term reflects poses where the lateral bands are taut; the bottom term reflects poses where the lateral bands are slack. Given the approximate bilateral symmetry of these two tendons [10], one term is used to account for the effects of both the ulnar and radial lateral bands. The model predicts a non-linear relationship between PIP joint angle and EDL length when the lateral bands are taut, as does the model of An [10]"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001061_s0021-9290(00)00032-4-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001061_s0021-9290(00)00032-4-Figure2-1.png",
+        "caption": "Fig. 2. Example of the two-step rotation compared with 3-1-2 sequence Cardan angles. XYZ is a reference Cartesian coordinate system, xyz is a segment \"xed coordinate system, y-axis represents the long axis of the segment.",
+        "texts": [
+            " Attitude AN(1): 903 rotation about z-axis (1)N(2): 903 rotation about x-axis (2)NAttitude B: 903 rotation about y-axis Rotation 2: Attitude AN(3)N Attitude B is long axis rotation#the axial rotation Attitude AN(3): long axis (y-axis) rotate 903 about X-axis of the reference frame (3)NAttitude B: 1803 axial rotation about the long axis Rotation 3: Attitude AN(4)N Attitude B is the axial rotation#the long axis rotation Attitude AN(4): 1803 axial rotation about long axis (4)NAttitude B: long axis (y-axis) rotate 903 about X-axis of the reference frame the long axis of the limb segment about a speci\"c axis passing through the proximal joint and perpendicular to the long axis of the limb segment, and the other is an axial rotation about the long axis (Fig. 1). The two-step rotation is apparently sequence independent. Using the two-step rotation method, the 3D rotation of the limb segment from one attitude to another in the physiological reachable range can be fully determined. To show this, an example is given below and compared with the rotations of Euler/Cardan angles in 3-1-2 sequence. In Fig. 2, XYZ is a reference Cartesian coordinate system, xyz denotes a segment \"xed Cartesian coordinate system and the y-axis represents the long axis of the segment. The segment \"xed frame xyz is assumed to be parallel to the reference coordinate system XYZ before rotation and is denoted as attitude A. In order to create a comparable attitude, \"rst let the segment (xyz frame) rotate from attitude A to attitude B by three ordered rotations, #903 each, following the 3-1-2 sequence used by Tupling and Pierrynowski (1987) as shown in the top of Fig. 2. The two-step rotation from attitude A to attitude B is shown in the middle and bottom of the \"gure. First, in the middle of Fig. 2, the long axis (y-axis) of the segment rotates 903 about the X-axis of the reference frame, then the segment axially rotates 1803 about the long axis (y-axis) of itself. If we change the order of the two rotations as shown in the bottom of Fig. 2, the same result can be obtained. More examples corresponding to other ordered rotations can be carried out by readers. The example shows that the long axis rotation can be uniquely determined by its initial and \"nal positions in the reference frame. Therefore, the segment rotation between any two attitudes can be uniquely described by the two-sequence-independent rotations. Determinations of the two rotations from two known attitudes are given in the following. In Fig. 3, the initial and \"nal positions of the long axis of the limb segment in the reference frame are represented by its unit vectors n 1 and n 2 , respectively",
+            " The gimbal-lock problem occurring in the axial rotation angles can also be resolved by dividing the full cycle of activity into a limited number of sections. If the full cycle was divided into two sections and the axial rotation angle from the \"rst initial attitude n 1 to the second initial attitude n@ 1 is / 1 , and from the second attitude to any attitude in the second section is /@ 1 , then the axial rotation angle from the \"rst initial attitude to any attitude in the second section can be calculated by the additive law as: / 2 \"/ 1 #/@ 1 . (B.1) In the graphic example (Fig. 2), the axial rotation from attitude (3) to attitude B reaches 1803 that is a gimballock point. If an attitude C between the two attitudes was recorded, the problem can be solved by selecting attitude C as the second initial attitude and dividing the full period of time into two sections, attitude (3) to attitude C and attitude C to attitude B (Fig. 6). In the case there may be more than one gimbal-lock point, the number of sections can be determined depending on how many gimbal-lock points involved in an activity, which can be pre-determined according to the activities to be investigated"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003974_tia.2005.863911-Figure8-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003974_tia.2005.863911-Figure8-1.png",
+        "caption": "Fig. 8. Stator windings arrangement.",
+        "texts": [
+            " In the proposed system, the radial force detection block, as shown in Fig. 3, is added in Fig. 7. The radial forces F\u0302\u03b1 and F\u0302\u03b2 are calculated in the radial force detection block. These signals are amplified by a constant H , and subtracted from (1 + H)F \u2217 \u03b1 and (1 + H)F \u2217 \u03b2 . The four-pole windings are used as motor windings. These windings are connected to a motor driver operating indepen- dently from radial positioning. Thus, a motor driver can be commercial power lines, or general-purpose inverters. Fig. 8 shows the arrangement of stator windings in a cross section of a stator core of a three-phase bearingless induction motor. There are 24 slots in the stator core. The Nu4 and Nu2 show the four-pole motor and two-pole radial force winding conductors in the u phase, respectively. The two-pole winding conductor is made of two series and eight parallel 0.55 mm\u03c6 wires. The four-pole winding conductor is made of 5 series and 12 parallel 0.55 mm\u03c6 wires. The v-phase and w-phase windings are arranged symmetrically"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003394_tmag.1985.1064226-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003394_tmag.1985.1064226-Figure4-1.png",
+        "caption": "Fig. 4. Skmded-pole motor",
+        "texts": [],
+        "surrounding_texts": [
+            "respectively. After the discretization by finite elements, if o is assumed as a constant in the conducting regions, the above field equation holds:\n[SllA1+]c,~crfTI[AI= lRl[-agradt~l (3)\nwhere\nsij (NrN) =<L<P grady gradg , dn\nT i l tNxNi = ,//,%i*Xj do (41\nB:,, (N:*NR) = -. / h , 01: - 6 , do\nC r\nP C\nN and NR are respectively the total node number and the t o t a l number of coils ,subregions. [AI is a vector of magnetic vector potential, I-sgrad(g1 is magnetizing currenk INflNI gives the dimension of the matrix. x is approximation polynomial as\nA = 1 K,A. s i\n( S j\nA second equation is provided by Ohms' law\nl D I I I l = iGII-agrad~l-jwnfBITIA1 (6 1\nwhere\n+f- NT, coil 1 through region k\nD,,(NRxNE) = [ 0 others\n(71\nG,,/NR.i;NR) = L,;;di2\nNR is coil number and NT is coil turn. D,, indicates the state of region and the coil turn, positive corresponding coil 1 input region k, negative is output. G,,, is interpreted as the region area.\nIf we eliminate the vector [-a gradyll by combining (3) and {GI, a.n integrodifferential equation can be obtained [GI .\nA circuit equation is presenbd as\njwhlDITIGl-lfBITfAl + IZIIII =[VI (8)\nwhere h is Me axial length of field,, IT/] is a vector of coils voltage, [Zl hresents the external impedance and interior resistance of coils.\nZ,, !NE:<.NEf = 8,, '2, (91\n8, is Kronecker function. Combining (3.), 16) and I81\ndeduces the final equation,\n[ S 1 [ A ] + j ~ a f T I [ A l - j w a l B ~ ~ ~ l ~ ~ ~ B l ~ l A l +jwh[FIIZI-lIFITIAI= IFI[ZI-'IVI\nwhere\nIF1 = IBIIGF'IDI\n2289\n(10)\nI l l )\nAPPLICATION\nApplication to an electromagnetic relax Consider a relay illustrated schematically in Fig. 1. There are two shading rings which support eddy currents and are considered as coils with one turn. The winding has so sufficient turns that the eddy current can be negieted in it, and it is fed by a specified terminal\nOn account of the geometriml symmetry only one half of it is considered. The equipotential lines of magnetic vector potential describe the distribution of flux density as shown in Fig.2. Comparison of the cornputed exciting\nvoltage.",
+            "2290\ncurrent with the measurement versus the air-gap length shows a satisfactory agreement if the air-gap length is SO limited that 2D assumption can be verified I Fig.3 1.\n... , . ,. > .~ .\n- ,. . ,,: ' , - . ,. c ~ ,,\n,,. , .,(, ,..- 1\n.~\n. . . . ,. . . . . . . I\n.. .... .\ni ... .\nFig. 3. {a) Exciting current of the relay (b) Eorces of the relay\nARpiicahon to the shaded-pole motor The method described is also applied to the solution of a four-pole shaded-pole motor. A cross section of the rnotm is shown In Fig.$. The main dimensions of the motor and the action of this type of motor have been described in [?I. All currents are assumed tx be adally direckd and the fielg eylyacjclns reduce to two-dimensional form. All the four pole-pitch of the machirie are analysed becguse of a non integral number o f bars per pole v,lth rotc?r. The Dirichlet boundary condition sahsfied by the finite element formulation is a t the outer surface of the stator. The finite element matrices are computed on the entire cross section of the machine.\nThe final equations must be solved at the rotating reference position of the rotor. The bar number is greater than the pole number for the squirrel cage motor, so the position of the rotor is' not important to the solution and an initial position is taker1 into account.\nThe iron core is laminated, its non saturated\npermeability is pi,=3000, B = p p , H , its conductivity in the axial direction is low and is assumed as zero. In this paper, only linear cas has been taken into account, but tile method described can also be applied to mrl linear cases by means of the multistep method or the equivalent permeability method.\nA finite element mesh of 2906 triangular elements of first order and a t o t a l of 1474 nodes to the entire cross section is shown in Fig.5. The sky-line storied technique is taken. There are 29 average elements per line.\nThe rotor currents for slip s with frequence sf, may be modelled by modification of rotor condu.chvity where f , is the su.pply freqwncy. In the rotor, the equation is\nV V w\nFig. 5 . Einite eiement mesh",
+            "2291\nREFERENCE\nA = A,sinCswt + rp), so\naiiAIht = jwasA = jwcr'A\n6' is equivalent conductivity with 6' = sa. The solution has been performed for slip values from 0 to 1. The equipotential plots are shown in Fig.6 at slip s= 1, and computed exciting currents versus the slip in Fig. 7. '\nCONCLUSION\nThe matrix method which ombines field equations with circuit equations has been, developed for calculating the performances of electromagnetic devices with specified terminal voltages and external impedances of electric circuit. This approach takes into account eddy current effects and creates a symmetric system with respect to the ones mentioned in the literature. I t has been verified using a 4-pOle shaded-pole motor and a electromagnetic relay in which the exciting current is computed. The agreement between computed and experimental results is satisfactory. This method should be useful in calculating electric devices such as relays and induction motors.\n1. M.VX. Chari, \"Finite element solution of the eddy current problem in magnetic structures\", IEEE Trans. Power App. Sys. Vol. PAS-93, 1973. 2. T. Nakata, N. Takahaski, \"Direct finite element analysis of flux and current distributions under specified conditions\", IEEE Trans. Mag., Vol. MAG-18, N02, pp325-330, 1982. 3. S. Williamson, J.W. Ralph, \"Finite element analysis of an induction motor fed from a-constant-voltage source\", Proc. IEE,Vo1.130, Pt.B. N*l,ppt8-24, 1983. 4. P.G. Potter, GX. Cambrell, \"A combined finite element and loop analysis for non-lineary intkracting magnetic fields and circuits\", IEEE Trans. Mag., Vol. MAG- 19, N\"6, ~ ~ 2 3 5 2 - 2 3 5 5 , 1983. 5. M. Ito, N. Fujimoto, H. Okuda, N. Takaski, T. Miyata, \"Analytical model for magnetic field analysis of induction mobr performance\", IEEE Trans. Power App.\n6. A. Konrad, \"The numerical solution of steady-state skin effect problems - an integrodifferential approach\", IEEE Trans. Mag. Vol. MAG- 17, 1981 7. R. Perret, \"Contribution a 1'8tude des moteurs mOnOphaSeS a bobines Ocrans saturk\", These d'Etat, Grenoble, 1974.\nSYS, VOl. PAS-100, N O 1 1, ~~4582-4550 , 1982."
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0002579_robot.1997.606743-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002579_robot.1997.606743-Figure6-1.png",
+        "caption": "Figure 6: 3R free-joint manipulator",
+        "texts": [
+            " We can construct a control of the system such as a free-joint manipulator which has no stable equilibrium points, while Baillieul consider a stabilization to an equilibrium point by energy dissipa- tion. About the subsequent procedure to the convergence to the desired manifold, that is, stopping at the destination, the method was provided in our previous work[l]. In the next section, we show another example for a 3R free-joint manipulator. 4 3R free-joint manipulator 4.1 Averaging the manipulator We consider a 3R free-joint manipulator whose first joint is only actuated and others axe free as shown in Fig. 6. We consider the manipulator resides in the horizontal plane and the mass, the inertia momentum, the length of ith link and the distance from the i th joint to the center of mass of the ith link are denoted by mi, 4, l;, and si , respectively. The dynamics is given by 8) (16) where 2 A1 = 11 4- m1sl2 + mdx2 + m3dl , A2 = I2 + m 2 ~ 2 ~ + m31z2, A3 = 13 + m 3 ~ 3 ~ , B21 = m31112 + m2l1s2, B31 = m311s3, B32 = m31m and cZ1 = cos(& - SI), ~ 3 1 = C O S ( & - el), ~ 3 2 = C O S ( ~ S - & ) , s21 = sin(02-01), a "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001509_978-1-4615-3176-0_10-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001509_978-1-4615-3176-0_10-Figure1-1.png",
+        "caption": "Figure 1: A rigid-body model of a falling cat",
+        "texts": [
+            " Thus, a reasonable model of a falling cat is consisted of the upper body and the lower body, both treated as rigid, coupled to each other by either a ball-in-socket joint or a universal joint. If modeled by a ball-in-socket joint, the upper body would have three degrees of freedom (dof) relative to the lower body, and 2 dof otherwise. In this paper, we will consider both models as a ball-in-socket joint model would give us a system with 6 states and 3 control inputs and universal-joint model a system with 5 states and 2 control inputs. 2.1 A Ball-in-socket Joint Model Consider the system shown in Figure 1. The coordinate frames Co, C1 and C2 are called, respectively, the inertial reference frame, the body fixed frame to body-1 (the upper body) and the body fixed frame to body-2 (the lower body). We assume that the ori gins of the body frames coincide with the mass centers of the respective bodies. For body i = 1,2, we denote by (ri' Ai) E ~ x SO(3) the position and orientation of frame Ci relative to the inertial frame Co, and also by r E ~ the position vector of the mass center of the whole system"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001553_s0045-7825(99)00329-1-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001553_s0045-7825(99)00329-1-Figure6-1.png",
+        "caption": "Fig. 6. Generation of worm by plunging disk.",
+        "texts": [
+            " In case of a misaligned gear drive with imaginary rigid teeth, the contact ratio due to misalignment is one only. The desired parabolic function of transmission errors is obtained by plunging of the disk that generates the pro\u00aele crowned worm surface R 1 w . Thus, the worm thread surface will be crowned in the longitudinal direction also. Henceforth we will use designation R 1 w for the pro\u00aele crowned worm surface and R 2 w for the double-crowned worm surface (crowned in pro\u00aele and longitudinal directions). Drawings of Fig. 6 illustrate how the longitudinal crowning of worm thread surface Rw is accomplished. Fig. 6(b) shows the installment of a disk provided with surface Rc for generation of worm thread surface. The axes of the disk and the worm are crossed and form angle cc kw, where kw is the lead angle of the worm at the surface Rw middle point Ow. The current shortest distance Ec wc (Fig. 6(a)) between the axes of the worm and the disk is varied in the process of worm generation. The disk (with coordinate system Sc) is hold at rest and the worm performs a screw motion about its axis zw. During this motion, the disk is plunged and the current shortest distance Ec wc is executed as Ec wc Eo \u00ff apll2 w: 17 Here, Eo is the initial shortest distance; lw the axial displacement of the worm measured from the middle point Ow; apl the parabola coe cient of the parabolic plunging function Eo \u00ff Ec wc apll2 w: 18 Parameter wc indicates the angle of rotation of the worm in its screw motion (Fig. 6(c)). Disk surface Rc is conjugated to the pro\u00aele crowned worm thread surface R 1 w . This means that Rc will generate R 1 w if only screw motion is provided in the process of worm generation. Double crowned worm surface R 2 w is generated by Rc if plunging of Rc is executed in addition to the screw motion. Surface R 2 w is determined as the envelope to family of surfaces Rc that is generated in coordinate system Sw rigidly connected to the worm. The main goal of simulation of meshing is to determine the shift of the bearing contact and transmission errors caused by gear drive misalignment"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000548_s0584-8547(99)00038-5-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000548_s0584-8547(99)00038-5-Figure2-1.png",
+        "caption": "Fig. 2. Schematic diagram of the incorporation of the graphite \u017d . \u017d . \u017d .tube in the flow system: A sample in; B graphite tube; C \u017d .gaskets; and D sample out.",
+        "texts": [
+            " Schematic diagram of the flow system: A sample; B \u017d . \u017d . \u017d .PTFE tubing; C peristaltic pump; D plexiglass closure; E \u017d . \u017d . \u017d . \u017d .graphite tube; F contact to tube; G cell; H membrane; I \u017d y1 . \u017d . \u017d .counter space 1 mol l HNO ; J counter electrode; K3 \u017d . \u017d .reference electrode; L potentiostat; and M waste. fect flow of the solution along the inner walls of the graphite tube and for the metal deposition only in the central part of the tube. The incorporation of the graphite tube is given in Fig. 2 in detail. The graphite tube is placed on a plexiglass rod, which forms part of the flow-through cell. At the opposite end of the graphite tube a closure from plexiglass with a gasket is inserted. The whole space with the working electrode was washed for 2 min with doubly-distilled water, and then the sample solution was pumped. After deposition the graphite tube was rinsed with doubly-distilled water for 3]5 min, removed from the cell and dried by means of an infra-lamp. Finally it was placed into the graphite furnace for measurement according to the temperature pro\u017d "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000418_s1474-6670(17)40039-5-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000418_s1474-6670(17)40039-5-Figure2-1.png",
+        "caption": "Fig. 2. The free-body diagram of a helicopter in flight",
+        "texts": [
+            " The state is defined as x = [pT VT RT wTV E ~3 X ~3 X 50(3) X ~3 where P and V are the position and velocity vectors of center of mass in spatial coordinates, R is the rotation matrix of the body axes relative to the spatial axes, and the body angular velocity vector is represented by w. The controls are u = [OM OT a bV E ~4 where OM, OT, a and b are the main rotor collective pitch, tail rotor collective pitch , longitudinal cyclic pitch and lateral cyclic pitch , respectively. The state equation consists of the transla tional and rotational kinematic and dynamic equations: where b[ = [0 0 IV and g is the gravitational constant. As shown in Figure 2, J b and T b are the resultant force and torque acting on the body, respectively. Both force and torque are functions of the controls, u. For details, please refer to (Lee et al., August 1993). 3. Hybrid Control Formulation This section describes the hybrid control problem of integrating the continuous con trol laws and system dynamics with the dis crete planning and decision making. In case of the helicopter , the hybrid system design has to consider multiple, sometimes conflict ing objectives such as safety, efficiency, accu racy and reliability of operation"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003219_iros.1992.594551-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003219_iros.1992.594551-Figure4-1.png",
+        "caption": "Fig. 4. Mechanism to be used for excavation. From 1161.",
+        "texts": [
+            " The cost of this simplification is that the selected point in the action space specifies only one dig and at most we can be sure that we have picked the best dig on a per dig basis but not necessarily the one that will provide the most gain over the entire task. Neither can we be certain that the search will escape local extrema. Hence, although we have avoided the issue of a very large search space with complex obstacles to avoid, the second issue of search remains. 111. THE APPROACH In order to provide an intuitive understanding of the proposed approach, let us consider an extended example in a twodimensional world. Fig. 3 Fig. 3 shows a terrain that must be excavated and Fig. 4 shows the conventional version of a mechanism that is to be used. This sort of device is commonly called a \u201cbucket loader\u201d or a \u201cfront-end loader\u201d and can be automated. The loader is M completely excavate the pile, without intruding below the surface of the ground. In this example, we will show how geometrk and force constraints are imposed on the acuon space (a, d , h) from Fig. 2. Force constraints are refined through force feedback data obtained during experimentation. The constrained volume is then searched to select a dig that maximizes the amount of soil obtained",
+            " We will model the excavator as a P-R-R manipulator shown in Fig. 5. Given a candidate dig, that is a trajectory for the bucket tip to follow, a standard inverse kinematics method is used to find the corresponding joint displacements (dl , 02, e3). A candidate dig may fail this constraint if it is required that the excavator reach outside its workspace (exceeds joint limits) or if in the course of the dig, one or more of the links are required to interpenetrate the terrain. The composite constraint surface due to the terrain in Fig. 3 and the excavator in Fig. 4, is shown in Fig. 6. The surface represents the boundary between the reachable and nonreachable digs- all points below the surface represent digs that meet the reachability constraint. Volume Constraint: Since the excavator bucket can only hold a volume Vmax, then an (a, d, h) triplet should not excavate more than this amount of soil. This gives us a further basis on which we can limit the set of feasible digs. This constraint is shown in Fig. 7. Shaping Constraint: This constraint is given by the goal state of the terrain",
+            " $ is also called the angle of internal friction and is directly visible as the angle of repose of a pile of dry, uncompacted granular material like sand and sugar. So far, in this section we have said that if the soil properties (density, angle of internal friction, cohesion) are known, it is possible to get order of magnitude estimates of the resistance force encountered for the type of digging motions that have been proposed. The action space can now be further constrained based on whether or not it is possible for the robot to generate the required forces for perform a candidate dig. Lets say that the excavator in Fig. 4 can develop a maximum of 1000 units of force at the end effector. Also, lets assume that the soil properties are y= 20, @ = 30, c = 5. The constraint surface due to force limitation, given the terrain of Fig. 3, can be seen in Fig. 10. C. Search for an r r O p t i d Dig It remains now to search this space for a point that optimizes a cost function- at least up to an acceptable threshold of the maximum expected. We might note some properties of this optimization problem: the search space is large"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003364_0020-7403(88)90076-8-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003364_0020-7403(88)90076-8-Figure3-1.png",
+        "caption": "FIG. 3. Normal tractions, frictionless contact, v = 0.3.",
+        "texts": [
+            " (14) n= - ( S - 1) This renders the problem determinate, since there are now 2S + 2 equations in as many unknowns--the 2 S - 1 ordinates of pressure P, , D (a measure of the rigid body normal approach), A (a measure of the contact width) and the eccentricity e. It should be noted that from the symmetry of this configuration we expect that e will be zero. The equations are linear and are thus readily solved using a computer library routine. Some sample results obtained with S = I0 and v = 0.3 are shown in Fig. 3. For large tyre thicknesses, the normal pressure distribution approaches that of Hertz [8] for contact between a rigid cylinder and an elastic half-plane. As the tyre thickness is reduced, the contact width decreases and there is a corresponding increase in the peak pressure. The pressure distribution, however, remains approximately parabolic. At very small strip thicknesses the contact patch becomes very small, as the configuration now approximates that of the contact of two rigid cylinders, where point contact applies"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002677_rob.4620070207-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002677_rob.4620070207-Figure2-1.png",
+        "caption": "Figure 2. The PUMA robot.",
+        "texts": [
+            " Then use the relations (11) to detect the existence of possible supplementary eliminations and the relation (27), (29) to detect the particular regrouping of the parameters of link j , for j = 1, . . . , r2. This will concern the translational links between r l and r2, if the axes of the joints between r l and r2 are parallel or perpendicular the relations (34) and (35) can be used. We have developed a program which calculates automatically steps 1 and 2 and Xi and fi needed in step 3.213rr In the following example we get the minimum inertial parameters of the six rotational joint of the 560 PUMA robot. (Fig. 2). The geometric parameters of the robot are given in Table 1. Step (1) the parameters having no effect on the dynamic model are: Step (2) using relation (31) for j = n, . . . , 2 we get: Khalil, Bennis, and Gautier: Minimum Inertial Parameters of Robots 237 j = 6 : The minimum parameters of link 6 are: XXR6, m6, XZ,, Y&, zz6, MX6, M y6. j = 5 : XXRS = XX5 + YY, - YY5 XXR4 = XX4 + Y Y 5 ZZR4 = ZZ4 + YY5 MYR4 = MY, - M Z s 238 Journal of Robotic Systems - 1990 The minimum parameters of link 5 are: XXR5, XY5, X Z 5 , YZ,, ZZR5, MX5, j = 4 : MYR5"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000774_(sici)1097-4628(19961107)62:6<875::aid-app3>3.0.co;2-m-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000774_(sici)1097-4628(19961107)62:6<875::aid-app3>3.0.co;2-m-Figure3-1.png",
+        "caption": "Figure 3 troscopy. Experimental setup used for UV-visible spec-",
+        "texts": [
+            " This solution was used to load the microcapsules with Au-tagged HRP. Gold, being electron dense, can be easily observed within the PPy capsules using the TEM. The microcapsules used for these studies were prepared by the purely chemical method. Monitoring Enzyme Activity We have encapsulated five enzymes and one chemical catalytic system within microcapsules prepared via the electrochemical/chemical method described above. UV-visible spectroscopy was used to assay the activity of the encapsulated enzymes. The experimental setup used is shown in Figure 3. The enzyme-loaded microcapsule array is inserted (using the glass rod) into a cuvette (3 mL) that contains the substrate for the enzyme and the enzyme assay chemistry (see below). The cuvette is present in the sample chamber of a Hitachi U-3501 UV-vis spectrometer. A magnetic stir bar is used to stir the solution in the cuvette. Prior to the monitoring of the enzyme activity, the enzyme-loaded microcapsule array was immersed in the buffer solution a t 4\u00b0C. The solution was stirred for a period of 2 days"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001521_iros.1994.407377-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001521_iros.1994.407377-Figure1-1.png",
+        "caption": "Figure 1: a) Path planned by means of Eq. (1) at k = 60, b) Logarithmic representation of concentration distribution at k = 60",
+        "texts": [
+            " This algorithm updates the distribution function ~ k ; ~ for each time step k by means of simple mathematical operations between M (4 or 8) neighboring cells of T . If k is large enough and R\u2018 and 6R\u2019 are fixed, the function converges to its equilibrium state umir. um;r shows a single peak at TG with a monotonous slope leading to any point T in the workspace (Fig. l(b)). The path from each arbitrary starting point TS to TG is computed by following the gradient of um;r. Interpolation methods have also been utilized to obtain smooth paths (Fig. 1 (a)). As addressed in [7], the diffusion equation algorithm can be directly implemented on a parallel processor system. However, even a sequential implementation meets real time requirements. 2.1 Extended Diffusion Process The diffusion planner in its basic form can be directly applied to path planning for real mobile robots. Robots with circular or quadratic shapes are assumed to be reduced to a point if we apply the principle of obstacle grciwing, i.e. expanding the obstacles by the radius of the robot"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002731_j.ijmachtools.2004.03.005-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002731_j.ijmachtools.2004.03.005-Figure3-1.png",
+        "caption": "Fig. 3. Probes: (a) a straight probe and (b) a bent probe.",
+        "texts": [
+            " The accurate virtual CMM model simulates CMM operation and its measurement process with haptic perception. The CMM off-line programming model does all inspection planning tasks, including all high and low levels inspection planning mentioned above. Fig. 2 shows the HVCMM system working flowchart. The research in this paper focuses on low-level path planning for CMM. We assume that the part is in a given setup and a specific probe has been selected in a specific orientation. A straight probe, shown in Fig. 3(a), is normally attached to the CMM ram, which is much longer than the probe and aligned with its axis. We consider the whole ram/probe assembly as forming the straight probe and make no distinction between the two. For complex parts, a bent probe as shown in Fig. 3(b) is needed to measure some features such as holes at different angles. To position the points to be probed of a part, it is required to view the part\u2019s CAD model or the whole scene, including the part and the HVCMM, from different points of view. In the HVCMM system, the scene can be rotated, translated, and zoomed. There is no coordinate compensation for the rotation and translation of the scene. Fig. 4(a) and (b) show the original and rotated scene, respectively. It is very easy to do it by pressing and holding the button on the stylus of the haptic device",
+            " The following sections describe the proposed methods for collision (or contact) detection and contact force feedback. The collision detection is an important subject for dimensional inspection with CMM. As the HVCMM system is used in this paper for the inspection path planning, the operator is responsible for deciding the zones to be inspected and the positions of points to be probed. Therefore, it is much easier to generate collision-free probe paths. For a contact measurement, the part might collide with the tip, the stylus and the body of a probe [17]. In this paper, a straight probe as shown in Fig. 3 is mainly considered. The diameter of the tip is larger than that of the stylus. Collision with the tip happens when any surface of the part is in the traversing trajectory of the probe, such as the path from A to B shown in Fig. 5(a). Collision with the stylus happens when probing a point near or under a cantilever as shown in Fig. 5(b). Collision with the body of a probe happens when probing points under a cantilever as shown in Fig. 5(c) and the measuring stylus is not long enough when inspecting a narrow slot as shown in Fig"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001656_1.1330743-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001656_1.1330743-Figure2-1.png",
+        "caption": "Fig. 2 Analytical model of a tri-pad contact slider",
+        "texts": [
+            " Furthermore, the design conditions of the contact sliders and the disk surfaces both for perfect contact sliding and wear durability are discussed. Figure 1 shows a typical geometry of a tri-pad slider which has two front air bearing surfaces and one rear air bearing surface with a contact pad. Note that the figure illustrates an example of the tri-pad slider and one can design freely the air bearing surfaces and the contact pad according to the design conditions discussed in this paper. An analytical model of the tri-pad contact slider and the surface of the disk which was utilized in this analysis is shown in Fig. 2 @13#. The tri-pad contact slider is modeled as a rectangle with length a and height b. The slider suspension system is represented as the normal spring stiffness k, the angular spring stiffness ku , and the damping coefficients c and cu . The air bearing effects are represented by two lumped linear springs ~k f and kr! and the dampers ~c f and cr!, which are distant from the center of the mass of the slider by d f and dr , respectively. Although the air bearing has nonlinear stiffness, it was not taken into account for the sake of simplicity"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003210_j.conengprac.2005.06.005-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003210_j.conengprac.2005.06.005-Figure3-1.png",
+        "caption": "Fig. 3. Sketch of a SCARA robot following a contour.",
+        "texts": [
+            " The contact is achieved by means of a proper probe endowed with a ball bearing with an 8mm diameter whose aim is reducing tangential friction forces that may arise from the contact with the piece (see Fig. 2). The PC-based controller is based on a QNX4 real time operating system and the control algorithms were written in C/C++ language. Acquisition and control were performed at a frequency of 1 kHz. The task to be performed by the end-effector of the manipulator is to track the contour of an unknown (planar) object with a given reference tangential velocity and by applying a given force to the object in the normal direction. With reference to Fig. 3, frame (0) refers to the robot base, while the task frame \u00f0T\u00de has its origin on the robot end-effector, its n-axis directed along the normal of the piece contour and its t-axis along its tangent; W is the angle between n-axis and x-axis of frame (0). Let Q \u00bc \u00bdq1; q2 T be the vector of joint positions and _Q; \u20acQ its first and second time derivatives, respectively. Since a suitable belt transmission keeps the end-effector with constant orientation with respect to the absolute frame, the force measurements are directly available in frame (0)",
+            " Note that these testbed workpieces have significant dimensions with respect to the manipulator workspace (see Fig. 5, where the position of the pieces tracked in all the experiments presented in the paper is shown). Both pieces have been tracked counterclockwise with a constant normal reference force of 20N and a tangential velocity of 8mm/s for the disc and 10mm/s for the wooden object. Control law (3) has been used. The robot configuration was such that the joint angle q2 between the second and the first link (see Fig. 3) always maintains a positive value during the contour task. The PID gains have been selected through an extensive trialand-error procedure in order to guarantee that the contact of the probe with the workpiece is not lost because either of the excessive increase of force oscillations or of the excessive normal force error occurring when joint friction torque changes its signs at the motor velocity inversion. As a result of this procedure, the derivative action of the force PID controller was not adopted, actually, as it will be discussed in Section 4"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure3.2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure3.2-1.png",
+        "caption": "Figure 3.2. Direction angles of a unit vector n, and a change of basis.",
+        "texts": [
+            "96) to obtain (3.99) And similarly, reversing the roles of the primed and unprimed sets and using (3.97) while retaining the definition (3.96), we have also (3.100) Either of the transformation rules (3.99) and (3.100) is called a change of basis. The same thing may be seen in more geometrical terms by our recalling that any unit vector n, say, may be expressed in terms of the three cosines of the direction angles 11.1 that it makes with the familiar orthonormal basis direc tions i1 at a point Q, as shown in Fig. 3.2a. Namely, n =cos 11.1 i1 . If we write cos(n, i1 ) for the cosine of the angle 11.1 between n and the i1 direction and agree, as mentioned above, to extend the summation rule to terms in the cuneiform brackets, then n may be written more conveniently as n = Finite Rigid Body Displacements 177 cos<n, i1) i1. Now let {i~} be another orthonormal basis, as shown in Fig.3.2b. Then, for example, with n=i~, we shall have' i;=cos<i;,i1)i1. Similar equations may be written fori; and i;. Thus, in general, we shall have i;=cos<i;, i1) i1 =Ayi1, which, with (3.96), is the same as (3.99) applied to the usual Cartesian bases. Naturally, the change of basis (3.99) induces a chang{: of tensor product basis so that, for example, A similar relation is induced by use of (3.100). We thus obtain for a change of tensor product basis (3.101) The matrix A= [Apq] = [cos<e~, eq)] of direction cosines for the change of basis (3"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001500_978-1-4899-1465-1-Figure5.2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001500_978-1-4899-1465-1-Figure5.2-1.png",
+        "caption": "Figure 5.2. Voltage and current waveforms.",
+        "texts": [
+            "1, the instantaneous power, Pi, is given by (5.1) The average power is obtained by averaging the instantaneous values of the Pi'S over one complete cycle, for example, from 0 to 360\u00b0. Intu- 77 78 '-1-' Z w cr: cr: ::J U ChapterS itively one suspects that this average power will be different depending on the relative phase relationship, the angular shift, between succes sive voltage and current peaks. This angular shift, or phase shift, is shown in Fig. 5.1 as the angle O. The two extreme cases in Fig. 5.2(a) and (b) make this clear. In Fig. 5.2(a) the Vi X ii products will all be positive in the segment between u and wand they will all be negative between wand x. The average power over this half cycle will be zero. Similarly the average power over the second half cycle x, y, and z will also be zero. In Fig. 5.2(b) the Vi X ii products are all positive and the real power is a maximum for this phase relationship between the voltage and current. Tang's7 and many other textbooks on ac circuits derive the relationships between voltage, current, and power so the Power Factor '-1-' Z w a: a: ~ u~ __ ~~~~~~~=-~~ __ ~~~~~ __ ~ __ ~~~ '\" 0 w' (!) \u00ab ~ o > (a) Voltage and current 90\u00b0 out of phase. 79 derivations will be omitted here, but the results are stated in the suc ceeding paragraphs. For constant-frequency cases where the voltage and current waveforms are sinusoidal, phasors can be used as a convenient means to display the phase relationship between voltage and current",
+            " For motoring operation, the values of power factor are between 0 and 1.0. A nega tive value of power factor signifies induction generator operation. Usually, power factor, like efficiency, is expressed as a percentage value, for example, 90%, rather than the per-unit value, 0.9. It is useful to define two additional terms for subsequent discus sions. The apparent power, PA , is (5.3) and the reactive volt-amperes, V AR, are V AR = VI sin() (5.4) For most motor calculations the term KV AR, kilovolt-amperes, is I (c) Voltage and current phasors for Figure 5.2(b). Power Factor 81 more convenient to use. The relationship between the three quantities defined by (5.2), (5.3), and (5.4) can be displayed in a phasor diagram shown in Fig. 5.4. Now, having defined the various components, let us consider their effects on energy consumption. The real power, as previously noted, is delivered to the motor as electrical power and is converted by the motor to mechanical power which is delivered to the load plus losses which escape as heat. This power has to be supplied by the power system and, therefore, some form of fuel-oil, coal, gas, nuclear, etc"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure2.8-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure2.8-1.png",
+        "caption": "Figure 2.8. Composition of successive infinitesimal rotations about concurrent axes.",
+        "texts": [
+            " Therefore, in light of the character of finite rotations, it is of interest to verify that successive infinitesimal rotations of a rigid body about concurrent axes, independently of their order of execution, may be added vectorially to form a single equivalent infinitesimal rotation about another concurrent line. To establish this result, let d 1 and d2 denote two displacements due to consecutive infinitesimal rotations through angles A(} 1 and .182 about the respective concurrent axes a 1 and a2 through a point fixed at 0, as shown in Fig. 2.8a. Then, in view of (2. 18 ), the corresponding infinitesimal dis placements given by (2.13) may be written as d 1 =A9 1 xx, d2 = L19 2 X X1 = .192 X X+ L19 2 X (,19 1 X X), (2.20a) (2.20b) Kinematics of Rigid Body Motion 97 where x 1 = x + d1 is the position vector of a particle P after the first rotation from its initial place at x. The total displacement is d = d1 + d2 \u2022 Now, starting from the same initial position x and using identical rotations but performed with AIJ2 followed by AIJ 1 , as shown in Fig. 2.8b, we see with (2.18) and (2.13) that the corresponding infinitesimal displacement vectors are given by a!= L192 X X, a2 = AOI X XI= AOI X X+ AOI X (L192 X x), (2.21a) (2.21b) wherein X I = X + a I is the position vector of p after the first rotation, and now a= a 1 + a2 defines the total displacement. Upon discarding terms of order larger than the first in AIJ 1 and AIJ2 in (2.20b) and (2.21b), which is consistent with our earlier approximation m (2.18), we find and Therefore, regardless of the order of the rotations, the total displacement, a= a 1 + a2 = d2 + d 1 = d, is the same; and, With the aid Of the foregoing relations, it may be written as Consequently, there exists independently of the order of the rotations an equivalent infinitesimal rotation (2"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001200_jjap.38.5660-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001200_jjap.38.5660-Figure2-1.png",
+        "caption": "Fig. 2. Schematic alignment structure of SSFLC: the molecules on the chevron interface are parallel to each other and to the substrate surface.",
+        "texts": [
+            " (2) represent nonpolar anchoring and symmetric functions of the azimuthal angle of the c-director (\u03c6) about \u00b1\u03c0 /2, and the third term represents polar anchoring and breaks the symmetry mentioned above. If the orientation of the LC molecules is the uniform structure, p0= pd . If it is defined that fS = f 0 s 1(Y )+ f d s 1(Y \u2212 d), (3) the total free energy of a conventional SSFLC cell (FSS), whose effective area is A, at the quiescent condition is given by FSS = \u222b A 0 \u222b d 0 ( felas + fS)dY d A, (4) where we assume that the orientation of the LC directors is homogeneous at the chevron interface as shown in Fig. 2. Furthermore, if we assume that the two substrate surfaces are equally treated, the orientation of the LC molecules is symmetric about the chevron interface and A = 1 m2, eq. (4) can be expressed as FSS = 2 \u222b d/2 0 ( felas + fS)dY, (5) where \u03b4 > 0 in the C2 structure. We also assume that in Y = 0 to Y = d/2, \u03c6(Y ) =\u03c6s + ( d\u03c6 dY ) Y =\u03c6s + ( \u03c6c \u2212 \u03c6s d/2 ) Y, (6) where \u03c6s and \u03c6c are the azimuthal angle of the c-director of the FLC molecules on the substrate surface and chevron interface, respectively, and are expressed as sin\u03c6s = tan \u03b4 tan \u03b8 + sin \u03b2 sin \u03b8 cos \u03b4, (7) sin\u03c6c = tan \u03b4 tan \u03b8, (8) where \u03b8 is the cone or tilt angle"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002362_itsc.2003.1252673-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002362_itsc.2003.1252673-Figure3-1.png",
+        "caption": "Figure 3 Vehicle model",
+        "texts": [],
+        "surrounding_texts": [
+            "1. Introduction An automated parallel parking strategy for a vehicle-like robot is presented. This study i s part ofthc research project in t,hc development of the autonomous vehicle control. I\u2019arallel parking is difficult for human driver especially Ibr beginners. Therefore. this type or problems altracts a great deal of attention from the research community. This research is derived from the study ofmotion-planning ofrobots. There exists many algorithms in robot motion planning and they were difficult to apply those algorithms into fourwheels vehicle parking cases. The research on this topic can be clissifird into two groups: I-stabilization of the vehicle to a point by means o f feedback state; 2 - planning a feasiblc path to reach a point and following the path. I n the lormer category, Yasunobu and Murai [I] have proposcd a controllcr based on human experience to develop a hierarchical fuzzy control and predictive f u v y control for vehicle parking. The vehicle i s controlled moving point by point. That algorithm generates the mancuvering path point by point from the human knowledge base in the predictive fuzzy controller. Researchcn 1101 only concerning the classical four wheels vehicle. trailer vehicle are also considered. Jenkin and Yuhas 121 have reported a simplified neural network controller by decomposition. The neural controller i s decomposed by subtasks. The neural controller is trained based on the kinematics data, however the decomposed neural network require less training time thus i t has simplified the training process. Kin,jo. Wang and Yamamoto [3] have used Genetic Algorithm (GA) to o p l i m k neural Contmller for controlling trailer truck. Initially theneural controller i s produced randomly and GA changes the weighting af the controller to a suitable d u e . The algorithms discussed above are based on the kinematics data to formulate intelligent controllers.\nFor the path planning category. Paromtchik and Laugier 141 presented an approach to parallel parking for a nonholonomic vehicle. In thatapproach. a parking space i s scanned before the vehicle moves backward into i ts parking bay. The vehicle follows a sinusoidal path in backward motion. while the fbrward motion is along a straight line withoot sideways displacement. I n this approach. the possible collision during reverse betwecn thc vehicle and thc longitudinal bnundar) ofthe parking space i s not discussed. Murray and Sastry [ 5 ] worked on steering a nonholonomic system between arbitrary points by means of sinusoids.\nAutomatic parallel parking involves inany problems. such as recognition of driving circumstances. maneuvering path planning. communication and vehicle control. This paper focuses on the maneuvering path planning. \u2018The system works in three phases. I n scanning phases: the parking circumstance, is scanned by infrared srnsors after the parking command is activated. I t then gucs to ncxt phasr. starling phase. after a\nsuitable parking space has been detected. The maneuvering path i s also produced according to the scanned information. The robots movrs backward to the edge ofthr parking position and begins its parking strategy. In order to avoid potential collision. the robot starts at thc suitable position which depends on different dimension of parking space. In the final phase. inaneuvertrackiiig phase. the robot followsthc path 10 a desired parking posi!ion. The parameters ofthe maneuvering path have beenproduced off-line. A database has been built for different ~ i r ~ ~ m s t a n ~ e such as the longitudinal and latrral\ndimension ofparking space, thedimension ofvehicle-like robot. i ts specification ofthe stcrring angle (maximum turning angle) and lateral displacement from the aside car.",
+            "2. Car Modelling A four-wheeled vehicle-like robot is considered. The location of the vehicle reference to the coordinate system is denoted as (x .y ,e ) , where yare the coordinates of the midpoint of the robot's back wheel axisand e is the orientation of vehicle that the angle relative to its parallel position. Therefore, the motion ofvehicle in time-varying can be described as the followings:\ndx -= vcosacose di\n- = Y c o m i n 6 dr dB m i n a dr L where' a i s the steering angle, v is the velocity of the vehicle and L is distance between two wheel axis. Equations ( I ) are valid for the robot moves in flat ground in slow speed and there is no significant slippage. In planar motions, the robot subject to a constraint which is the limits of the steering angle a, -% <a< %. The control parameters in the car model are longitudinal velocity and steering angle ( V , a ) but there are three degree of freedom (x,y,e) 161. When the speed of the robot is constant and its steering angle is fixed, the planar motion is approximately a circle see figure 2. The radius of the locus depends on its steering angle. Thus, the steering angle constraint implies another constraint which is minimum radius of the circular movement. This radius limits longitudinal distnnce of the parking space. Therefore, it specifies the minimum space for parking which is required in the scanning phase. In our maneuvering planning, the vehicle moves in the\n(1)\n_=-\nshortest path and with single iteration move into the parking bay.Thecharacteristicofvehiclekinematics helpsto design the simple parking path.\n3. Maneuvering Planning The parallel parking idea ofthis paper described is coming f\" retrieving a vehicle from parallel parking bay. In real life. . situation, when the parking bay is sufficiently large, human driver normally will steer the front whecl to max angle for retrieving. Whenthe vehicle isretrieved,the drivcrwill steerthe front wheel in reverse direction until the car is parallel to the road. Since this procedure isreversible thus it can be applied in parallel parking problem Furthermore, this procedure is simplified the steering angles to the minimum radius condition. Effectively, according to the vehicle steering scenario described at the former kction two identical circles with tangent point can be formed. For example, a vehicle moves backward from A to B following a path formed by two circular arcs tangentially connected to each other. Supposing B i s parking bay and A is starting position, thereby parallel parking is achieved (see figure 4). The locations of circle center are\ndepending on the detected parking space and the lateral displacement from the aside car. There are several conditions have to fulfill in order to have a collision-free motion (see figure 5) : 1. The length L must be larger than radius of the circle C,. .\n2. Thecar mustatacomect position when begin to parking. The right position is determined by AxandAy. 3. The tuning point AT is depending on different value of Ax and hY.\nIn our methodology the vehicle is always track to the\ntangential circles. Thereby, the location of circles must be determined. When the parking position is decided, which",
+            "depends on the length of parking space, the center of c, is vertically pe'rpendicularto the final parking position. Thus the remaining problem is the location of the centre of c,(cr,c,). However, the center of c, is varied with the lateral distance\nbetween the aside C U ' ( A ~ ) . Figure 6 shows the geometric 'representation of the parameters required for calculation.\ncircular loci are generated. By measuring final positions (in the retrieving process. i.e. the starting position in parking process) on different loci (i.e. different turning point) &and ~j are determined. As a result, a table of relationship between turning point ( x , , y , ) , & a n d ~ ~ o n specific length of parking space are stored. In order to realize the parking algorithm in the robot a series of parking length are emulated and the result are being used in the evaluation of MCU.\n9 I Obstacle I . .\nFigure 7 Retrieving Loci at different tuming point Figure 6 Geometry'representaiionof maneuvering calculation\nCalculating c,(c,,c,) and the turning (x,,y,) the following\nequations are used\n' ' c*:(x-c~)'+~-c,) '=R2 C, :XI + y' = R' dy _ = _ _ dr JR'. at the turning point ( x, , y, ) ,\n(2) x, .........,... A r K For the line equation L: 2 = ' ... ' ... ...... (3)\nSubstitute y=O into (2) to find XI, then y-y ,\nC. = 2Rsin A C, = -2R cosA\nIn order to reduce the load of MCU off-line calculation of parameters are implemented. Since the.parking procedure is a reverse process of retrieving procedure. Therefore the parking parameters can be obtained by simulating the retrieving process. A simulation is wilten to emulate the retrieving process. In the simulation, the length of the parking space can be set. Since the center of the first circle is fixed that is perpendicular to the starting position of the vehicle (in the retrieving process i.e. the final position in parking process), .thus the vehicle follows the path to move. Then different turning points are assigned to the vehicle in the simulation and it is a tangential point between two circles. Therefore, two centers of the circles are then known and different value of Nrning point evaluate' different circle's centre. Several of\nThe system works in three ohases (see fieure 8 )\nAcar-likerobothas beendeveloped with l/lOhscaledmodelcar\n, _ I\nIn scanning phase, the vehicle-like robot scans parking environment by infrared sensor inorderto detect the lateral and longitudinal length of the parking space. Obstacle inside the parking bay can also be detected in this phase. Therefore, potential collision in the parking maneuvering can be avoided from this scanning phase. Those data are used for selection of suitable parking bay (see figure x). Information of bay's dimension and distance between aside car are measured in this phase. In starting phase, the robot moves backward to adjust suitable Ax in order to stm collision-free motion. These parameters are found from look-up table based on parking bay's dimension and which is built by off-line simulation. The detail is described from previous section. In maneuvering phase, the steering angle is turned to maximum right and the robot moves backward with constant speed. It tracks the locus by steps counting in the servo system. It then tumed into maximum left at the predefined turning point. and.eventually stop when ihe robot become parallel to the lane. c\n4. Experimental Studies\nframework is used for OUI experiments. This is a four-wheeled robot with frontdriven and steering wheels. It has the following dimension: 20cm (L) x 48cm 0. It isequipped with low speed DC motor and its steering system is controlled by servo motor for frontdriven. The range measurement system consists of W O Infrared Distance Measure Sensors (GP2D12). The control system is based on micro-controllerAT89cS 1. The objective of experiment is testing the effectiveness of parallel parking algorithm and maneuvering planning strategy."
+        ]
+    },
+    {
+        "image_filename": "designv11_6_0001575_1097-4628(20001121)78:8<1566::aid-app140>3.0.co;2-i-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001575_1097-4628(20001121)78:8<1566::aid-app140>3.0.co;2-i-Figure4-1.png",
+        "caption": "Figure 4 Three-dimensional tire model for implicit FEA.",
+        "texts": [
+            " Assuming a deformation during manufacturing process is purely due to pantographic action, the angle and spacing of REBAR in the cured tire can be obtained as follows: a 5 Fr9sin b9 r sin b Ga9, b 5 cos21F r cos b9 r9~1 1 \u00ab!G (1) where a, b, r, and \u00ab are spacing, angle, radius, and elongation factor of fiber reinforcements after lift, respectively. Also, a9, b9, and r9 are spacing, angle, and radius on a tire-building drum. After a tire is mounted on a rim, an inflation pressure of 200 kPa is applied to the axisymmetric tire FE model. Figure 4 shows a three-dimensional FE tire model that can be generated based on the inflated results with the symmetric model generation, and the symmetric results are transferred to a threedimensional format with capability of ABAQUS/ Standard. A pavement is modeled as a rigid element. The steady-state transport analysis capability can be formulated with a moving reference frame technique, so a mesh needs only to be refined in a contact region, as shown in Figure 4. This model has 5976 nodes and 4464 elements. On the other hand, a fine mesh is required in circumferential direction for the explicit finite element technique, as mentioned later.3 Before a cornering simulation of a tire, braking and driving simulations are conducted with slip angle of 0\u00b0 in order to determine a free rolling radius of a tire. In the steady-state rolling simulation based on moving reference frame tech- nique, angular velocity of a tire is required to synchronize with travel velocity"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003002_0021-9797(84)90503-4-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003002_0021-9797(84)90503-4-Figure1-1.png",
+        "caption": "FIG. 1. Schema of the apparatus, m, Stainless steel; [~, Teflon; [], copper; ~, rubber.",
+        "texts": [
+            "4 dyn/cm K at 30\u00b0C below the minimum, to +0.2 dyn/cm K 30\u00b0C above the minimum. The n-hexanol and the n-heptanol (quality puriss) were provided by Fluka. The n-nonanol was purified by distillation under vacuum by Professor R. Vochten. 261 Journal of Colloid and Interface Science, Vol. 98, No. 1, March 1984 The water used is bidistilled (the first distillation being done in presence of KMnO4). In order to create zones at the surface at different temperatures and to observe movements between them, we used the simple setup described in Fig. 1. A Pyrex container Ct (diameter 1 cm, depth 1 cm) contains the solution to be studied. The latter is maintained at the temperature T~ by circulating water in the container C2. A double-wall Pyrex lid filled with water at T3 (/'3 > Tt and T2) prevents air currents from inducing movements at the surface and also prevents condensation of the vapor emitted by the solution. Through the orifice E in the lid, talc powder can be blown on to the liquid surface with an adapted needle. Another circular orifice (diameter 1 cm) allows us to adjust the heating system (or the cooling). It consists of a copper disk (diameter 3 cm, thickness 1 mm) welded to a vertical inox tube (diameter 1 cm) in which water circulates at the temperature T2. The steady temperature is attained in 2 min, this has been checked by using a Pt resistor. A Teflon piece (D) (0.5 mm thick) insulates the bottom and the lateral parts of the copper disk. Small orifices (F) (diameter 1.5 mm) in the copper disk and the Teflon permit the liquid to flow. The whole setup represented in Fig. 1 is placed on the carriage of a profile projector (Nikon Model 6) under a telecentric objective giving a magnification of 10. The device described above can be lit either by the side or from below. 0021-9797/84 $3.00 Copyright \u00a9 1984 by Academic Press, Inc. All rights of reproduction in any form reserved. 262 NOTES NOTES 2 6 3 The movements at the surface are made visible by test bodies. We used either talc powder or glass beads (Type Glaverbel Microcel Type M35, density 0.35, diameter 1/10 mm) the density of which is lower than that of the solution. 3. RESULTS Experiments were carried out with the three prepared solutions by imposing a temperature gradient in the region where the temperature is lower than the one for which the surface tension is minimum; a temperature gradient in the region above this minimum. Each gradient has been applied successively in both senses: for the same difference AT, T2 > TI, then TI > T2. The liquid height in the trough (CI, Fig. 1) was nearly 1 cm. The copper plate was placed at nearly 1 mm (or less) under the free liquid surface. The results concerning the alcohol solutions and pure water are gathered in Table I. An example of surface movement is represented on Fig. 2. In Table I, the two cases marked with stars have led in a reproducible way to the following observations. In the first case (*), the solution of n-nonanol is heated by the copper disk, with the whole solution being below the temperature of the minimum of ~r"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003985_tro.2006.878956-Figure9-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003985_tro.2006.878956-Figure9-1.png",
+        "caption": "Fig. 9. Edge\u2013Vertex case. Angles (left). Projection on the plane (dotted lines) of the contact manifold (right).",
+        "texts": [
+            " (ak; bk; ek) as the map which solves problem (iii) for a specific path pk , theLEV () function is LEV (wi; oj) = min p 2fOPg Lp (EVp (wi; oj)) (18) with Lp(LEV (wi; oj)) = 1 if the contact point lies outside the edge boundaries. 1) Handling Type-B Paths: Let (qi; qi+1) be two adjacent robot vertices. From (9), the linewi can be expressed as y = mi( )x+ni( ), where mi( ) = tan ( + 0 ) ni( ) = qi mi( )qi 0 = arctan l sin( ) l sin( ) l cos( ) l cos( ) and 0 is the angle made by the edge wi and the direction vector !v . Fig. 9 (left) shows, for instance, the angles 0 , 0 relative to two edges w1, w2 for a generic polygonal robot. The coordinates of the target point oj being (ox; oy), the manifold representing oj 2 wi is Cij EV ( ) = f joj 2 wig and is expressed by ijEV ( ) = oy mi( )ox ni( ) = ( ox + x + li cos( + i)) sin ( + 0 ) + (oy y li sin( + i)) cos ( + 0 ) = 0 which describes, as varies, a 2-D surface whose projection on the xy plane is made of straight lines rotating at a fixed distance from oj [Fig. 9 (right)]. Lemma 3: If a Type-B path is optimal for problem (iii), then: 1) line D0 must be perpendicular to the edge wi at the end of the path; 2) the contact point lies at the intersection of D0 and wi. Proof: The constraint f 2 Cij EV , expressed as ijEV ( f) = 0, yields the transversality conditions f = MT , where M = @ ijEV ( f) @ f = [sin ( (tf ) + 0 ) cos ( (tf) + 0 ) ( oy + y(tf )) sin ( (tf) + 0 ) + ( ox + x(tf)) cos ( (tf) + 0 )] : Hence, we get 1 = sin ( (tf) + 0 ) 2 = cos ( (tf) + 0 ) 3(tf) = (( oy + y(tf )) sin ( (tf) + 0 ) + ( ox + x(tf)) cos ( (tf) + 0 )) which yields 2 1 = 1 tan ( (tf ) + 0 ) = 1 mi ( (tf)) (19) 3(tf) = 1 (y(tf) oy) 2 (x(tf) ox) : (20) Equation (19) proves point 1 of Lemma 1; from (20), we have 3(t0) = 1oy+ 2ox, which yields 3(t) = 1(y(t) oy) 2(x(t) ox)"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001325_jsvi.2000.3040-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001325_jsvi.2000.3040-Figure4-1.png",
+        "caption": "Figure 4. Response of the axially moving string under a sinusoidal point load and controlled by the &&real-time'' control forces of Figure 2.",
+        "texts": [
+            " The control force which is applied at t c is de\"ned as &&real time'', i.e., it is computed without any knowledge of the response history during 0)t)t c , and the control force which tracks the response history during 0)t)t c as &&simulation''. The latter is suitably termed &&simulation'' because it can be achieved only in simulations but not in real time control. The &&real time'' and &&simulation'' control forces for this example are plotted in Figures 2 and 3. The corresponding responses of the controlled system are shown in Figures 4 and 5. In Figure 4, it is seen that the controlled vibration does not go to zero as a result of nonzero motions at the boundaries when the control forces are applied at t c . However, the controlled amplitude is much smaller than the uncontrolled one. In Figure 5, as predicted by the control laws, the vibration is suppressed to zero in x)a 1 and x*a 2 . Comparing Figures 4 and 5, it is seen that the control is still e!ective in the presence of non-zero initial conditions at non-\"xed boundaries. For this type of feedforward control, disturbances in the uncontrolled regions and boundary excitations can be attenuated by feedback control [36]"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002756_pcfd.2004.003789-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002756_pcfd.2004.003789-Figure1-1.png",
+        "caption": "Figure 1 Schematic sketch of a stationary GMAW system (not to scale)",
+        "texts": [
+            " NOMENCLATURE Av constant in equation (20) B\u03b8 self-induced azimuthal magnetic field c specific heat C inertial coefficient e electronic charge f mass fraction F volume of fluid function Fsa surface tension force per unit interfacial area Fsv surface tension force per unit volume g gravitational acceleration h enthalpy hl defined in equation (12) hc effective heat-transfer coefficient \u2206H latent heat of fusion I welding current je electron current density ji iron current density jr radial current density jz axial current density k thermal conductivity keff effective conductivity at the anode-plasma interface K permeability Kb Boltzmann\u2019s constant L latent heat of vaporization n normal direction n\u0302 unit normal vector to the local free surface p pressure Q inflow rate of shielding gas qev heat loss by evaporation r \u2013 z cylindrical coordinate system Rl radius of the electrode 2 R internal radius of shielding gas Re Reynolds number SR radiation heat loss t time T temperature T0 reference temperature for natural convection Tanode anode temperature Tarc arc temperature Te electron temperature Tl liquidus temperature Ts solidus temperature T\u221e ambient temperature u velocity in r-direction v velocity in z-direction V velocity vector Vi ionization potential of the gas Vls relative velocity between liquid phase and solid phase Vr relative velocity between plasma and liquid metal Vw wire feed speed Greek symbols \u03b2T thermal expansion coefficient \u03b4 thickness of anode sheath \u03b3 surface tension \u03b5 emissivity of surface \u03ba free surface curvature \u00b5 viscosity of arc plasma \u00b5l dynamic viscosity of molten metal \u00b50 magnetic permeability of free space \u03c6 electrical potential \u03c6W work function of the anode material \u03c3 electrical conductivity \u03c1 density Subscripts 0 initial condition l liquid phase r relative to solid velocity s solid phase Gas metal arc welding (GMAW) is an arc welding process that uses plasma arc between a continuous, consumable filler-metal electrode and the weld pool, Figure 1. Due to its high productivity, the GMAW process has been the predominant welding method. The welding quality depends on various parameters, such as welding current, electrode, wire feed rate, travel speed, and shielding gas. A comprehensive dynamic model of the GMAW process would provide many helpful insights on key process parameters leading to the improvement of weld quality. In such a model, there are three major coupling events to be considered: 1 the generation and changing process of arc plasma 2 the dynamic process of electrode melting, droplet formation, detachment, and impingement onto the weld pool 3 the dynamics of welding pool under the influences of arc plasma and the periodical impingement of droplets",
+            " In this paper, a two-dimensional mathematical model employing the volume of fluid (VOF) technique and the continuum formulation [19] is developed to simulate the coupled transport phenomena including the arc plasma, electrode melting, droplet formation, detachment, and impingement onto the base metal, and the dynamics of the weld pool. The VOF technique can handle transient deformed weld pool free surface and droplet surface, while the continuum formulation can handle fusion and solidification for the entire metal domain, including the liquid region, the mush zone, and the solid region. Figure 1 shows a schematic sketch of a stationary axisymmetric GMAW process. The electrode is fed downward at a constant speed. A constant current is applied to the electrode, providing heat to melt the electrode and to generate droplets. The inert gas (argon) with fully developed initial velocity profile is also assumed, providing shielding effect to prevent the molten metal from oxidation. Very high temperature arc plasma exists between the electrode and the weld pool, providing additional heat to melt the electrode and the weld pool",
+            " Conservation of current 1 0r r zr r z \u03c6 \u03c6 \u03c3 \u03c3    \u2202 \u2202       \u2202 \u2202 \u2202 \u2202 + = \u2202 \u2202 (8) where \u03c6 is the electrical potential. According to Ohm\u2019s law, the current densities are given by ,rj r \u03c6 \u03c3 \u2202 = \u2212 \u2202 zj z \u03c6 \u03c3 \u2202 = \u2212 \u2202 (9) The self-induced magnetic field B\u03b8 is calculated by the following Ampere\u2019s law: 0 0 d r zB j r r r\u03b8 \u00b5 = \u222b (10) where \u00b50 = 4\u03c0 \u00d7 10\u20137 Hm\u20131 is the magnetic permeability of free space. In order to solve equation (8) to obtain current density, the required boundary conditions for the domain and boundary surfaces as shown in Figure 1 are summarized in the following table: Boundaries AB BD DF FG GA B.C.s 2 1 \u03c6\u03c3 \u03c0 \u2202\u2212 = \u2202 I z R 0\u03c6\u2202 = \u2202z 0\u03c6\u2202 = \u2202r \u03c6 = 0 0\u03c6\u2202 = \u2202r where R1 is the radius of the electrode. Equations (1)\u2013(10) define the basic governing equations and variables describing the physical conditions of the arc, the electrode, and the weld pool. The variables involved are: pressure (p), temperature (T), radial velocity (u), axial velocity (v), electrical potential (\u03c6), radial and axial current densities (jr and jz), and azimuthal magnetic field (B\u03b8)",
+            " In our model, the VOF function of F is chosen to be the characteristic function, and the final expression for Fsv(x) is given by ( ) 2 ( ) ( ) ( )svF x x F x F x\u03b3 \u03ba= \u2207 (14) where the curvature \u03ba(x) is calculated from ( )\u02c6( )x n\u03ba = \u2212 \u2207\u22c5 (15) where n\u0302 is the unit vector normal to the surface, and it is ( ) ( ) ( ) \u02c6 F x n x F x \u2207 = \u2207 (16) Hence, with the volume force Fsv, the surface tension effect at the free surface is modelled as a body force in the momentum transport equation. The boundary conditions for metal domain are summarized into several boundary surfaces as shown in Figure 1. To the surface cells of molten electrode, the surface is a free surface. The arc plasma will not have effects on the velocity of liquid metal. The pressure of the surface cells is equal to the pressure of adjacent arc plasma cells since the surface tension has been converted to a body force. liquid metal arc=p p (17) The friction drag on the surface is [25]: 0 r s V n \u03c4 \u00b5 \u2202 =   \u2202 (18) where \u00b5 is the viscosity of arc plasma, Vr is the relative velocity between plasma and liquid metal, n is the normal direction, and the subscript s means at the surface",
+            " / 0v r\u2202 \u2202 = (26) 0u = (27) / 0p r\u2202 \u2202 = (28) / 0T r\u2202 \u2202 = (29) / 0u r\u2202 \u2202 = (30) 0v = (31) / 0v z\u2202 \u2202 = (33) u = 0 (34) For the inflow gas from the nozzle, the radial velocity component is neglected and the axial velocity component is determined as follows [31]: ( ) ( ) ( ) ( ) ( ) 22 2 2 2 22 2 1 2 1 22 2 2 2 14 4 2 1 1 2 1 ln lnln2 \u03c0 ln ln r R RR r R R R RQ rv Vw RR R R R R R R   \u2212 + \u2212    = +  \u2212 \u2212 +     (36) where Q is the inflow rate of shielding gas, R1 is the radius of electrode, R2 is the internal radius of shielding nozzle, and Vw is the wire feed speed. The temperature boundary is T = 300 K. (37) surface (BNM, KJ in Figure 1) Since an interface has a vanishing mass, it cannot store momentum, therefore the velocity must be continuous across the interface: gas liquid metalu u=v v (38) For the temperature boundary condition, the energy equation is modified to include an additional source term _a apS expressing the corresponding cooling effects due to the sheath ( )eff arc anode _ 5 2 b e a ap a R k T T K T S j F e\u03b4 \u2212 = \u2212 \u2212 \u2212 (39) The velocity boundary condition follows equation (38). For the temperature boundary condition, the energy equation is modified to include an additional source term _c apS expressing the corresponding cooling effects due to the sheath ( )_ 5 2 b c ap i i e c R k T S j V j h T T F e \u221e= \u2212 + + \u2212 \u2212 (40) The boundary conditions are the same equations as given in Section 2",
+            " As the droplet contains superheated thermal energy and the base metal is simultaneously heated by the arc heat flux, the droplet does not solidify immediately. In fact, some base metal begins to melt and mix with the droplet. Since the first droplet is not fully solidified before the second one reaches the base metal, a liquid weld pool starts to form immediately after the first droplet. The LHS of Figure 6 shows the velocity profiles for arc plasma corresponding to Figure 5 at 50 L/min of inert gas flow rate; while the RHS figures are for gas flow rate at 10 L/min. The inner diameter of the nozzle is 9.4 mm, as shown in Figure 1. Two streamlines starting from r = 2 mm and r = 4 mm are drawn to show how the gas flow rate influences the shielding effect. At the high gas flow rate (10 L/min), it is seen that the electrode, droplet and weld pool surface all are \u2018protected\u2019 by the inert gas. On the other hand, at the lower gas flow rate (10 L/min), the shielding gas cannot prevent the weld pool from exposure to the ambient air, leading to a possibility of oxidation. While the shielding effects are very different, the gas flow rate does not significantly influence the generation and detachment of droplets and the weld pool shape, as shown in Figure 6"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002201_ac025918i-Figure10-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002201_ac025918i-Figure10-1.png",
+        "caption": "Figure 10. Effect of the interaction parameter r on the peak broadening. 1 is a CV diagram calculated by taking into account different ionic concentrations inside the film: reduction 5 M, oxidation 0.001 M (eq 9); 2 is a CV diagram calculated by taking into account both different ionic concentrations and interaction parameter: r ) -1.0 (eq 11). Parameters used in the calculations are the same as in Figure 9.",
+        "texts": [
+            " Figure 9 illustrates the effect of the difference of ionic concentrations during oxidation and reduction processes on the peak separation. In the present work, the experimental peak broadening has been described by taking into account the concentration depend- ence of the surface activity coefficients of the redox centers in the framework of the lattice theory (eq 1). The applicability of the lattice theory to our films has been discussed in the previous subsection. Substitution of eq 1 into eq 5 leads to the following expressions: and Figure 10 illustrates the peak broadening when r in eq 11 is negative in accordance with the literature data.31,33,34 As mentioned in the introduction, the negative value of the interaction parameter corresponds to a situation when a mixture of oxidized and reduced molecules is the energetically preferable state, leading to the peak broadening. Thus, eq 11 expresses the reversible voltammetric response of a multilayer film when the interfacial potential distribution and concentration dependence of surface activity coefficients of the oxidized and reduced molecules are taken into account"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001338_0094-114x(95)00082-a-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001338_0094-114x(95)00082-a-Figure5-1.png",
+        "caption": "Fig. 5. Harmonic drive.",
+        "texts": [
+            " On the other hand, very high reduction in single stage gives rise to other design and kinematic problems. In harmonic drives the tooth difference is usually kept to two, which is essential for the kinematic requirement. The possibility of tip interference reduces in harmonic drive as the pinion acts as a flex-spline of elliptical shape. In fact much before the tip interference the rim of the flex-spline deflected inwardly along with the teeth and after the tip interference zone the teeth are again engaged (see Fig. 5). Although there are few reports on the modified tooth geometry for harmonic drives [4, 5] the open literature is lacking in reporting how the tip interference is avoided in such units with involute gearing. The involute profiles are easily cut at lower costs and have some definite advantages over the other conjugate profiles used for gear teeth. The present work, therefore, also aims at crystallizing the theoretical relations on the avoidance of tip interference phenomenon in harmonic drives with involute gear pair",
+            " Also for 22.5 \u00b0 involute gears the difference cannot be lower than 5 even after corrections. On the other hand for 30 \u00b0 involute gears the difference can not be lower than 4 which is achieved without any corrections (see Table 5). Preceding analyses will be useful for circular pinion, i.e. pinion with undeflected rim. The primary concern is to verify the tip interference, after modifying the tooth and keeping the contact ratio within satisfactory limits. In the cases of common type harmonic drives (see Fig. 5) double contacts of the pinion with the internal gear at 180 \u00b0 phase are achieved by allowing the pinion rim to deflect. An elliptical cam is used for this purpose. With such an arrangement dynamic imbalance, as in the case of multiple planet other two gear epicyclic drives, is eliminated. The geometric and kinematic relations of the gears and cam of such a unit are established [4, 5]. However, the conditions of tip interference and its avoidance with reference to the deformed elliptical shape of the pinion are not discussed"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002672_j.sysconle.2004.11.014-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002672_j.sysconle.2004.11.014-Figure4-1.png",
+        "caption": "Fig. 4. Non-zero measure invariant sets.",
+        "texts": [
+            " Now consider a transversal section L to the trajectory through z, that is, a closed line segment containing no equilibrium points and such that at every point the field f is not parallel to the direction of L. On this section L, we can find a point y0, arbitrarily close to z, whose -limit is the origin, since this kind of trajectories are dense in the plane. Then, as in the Poincar\u00e9\u2013Bendixson theorem, we can construct a closed path with the negative trajectory through z, a piece of the transversal section L and the positive trajectory through y0.2 This path limits a closed region of the plane, with a finite number of equilibrium points inside it. The first situation we can have is the one shown in Fig. 4(a). On the transversal section, we can find two points whose -limit sets are the origin and their -limit sets are some singular point (could be other than the origin). The trajectories through these points are like the bold ones in Fig. 4(a). The other case is shown in 4(b) and the result is the same as case (a). In both situations, the sets limited by the bold trajectories are invariant and have non-zero Lebesgue measure. This is absurd and then the origin is locally stable equilibrium point. 2 For details of this construction, see [3, Chapter 7]. Remarks. \u2022 If the measure is monotone, then condition (2) is fulfilled for every set with finite -measure. \u2022 If the origin is almost global stable, then the density of the attracted trajectories is fulfilled",
+            " We know that N attracts a dense set of initial conditions to the past and that we can define a Borel measure on the sphere in a way that given any non-zero Lebesgue measure neighborhood Y of N with S /\u2208 Y\u0304 , it verifies 0< (Y ) < \u221e and for every t > 0, [f t (Y )] > (Y ). Then we consider the reversed system x\u0307 = \u2212f (x) on the sphere and we obtain that N attracts a dense set of initial conditions. We can reconstruct the proof of Theorem 3.2, denying the thesis and getting the existence of the bold trajectories of Fig. 4. If the set A enclosed by this curve has finite measure , it is absurd, just as in the previous proof. So, the question we must answer is if S \u2208 A\u0304. But if it was the case, S would be the -limit of the bold trajectories and then S could not attract almost all the initial conditions of the original system. In order to see this, consider again the closed path constructed with the negative trajectory of z, the positive trajectory of y0 and a piece of the transversal section through z. We draw again the picture in Fig"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000673_b006664h-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000673_b006664h-Figure1-1.png",
+        "caption": "Fig. 1 Schematic view of the disposable enzyme sensor based on H+sensitive electrode with integrated Ag/AgCl reference electrode. A, Crosssectional view. B, Front and rear view.",
+        "texts": [
+            " The concentrated enzyme solution was stored at 220 \u00b0C until use. Progress of the purification process was monitored by determining specific activity and by analysis with sodium dodecyl sulfate\u2013polyacrylamide gel electrophoresis (SDS-PAGE). Enzymatic activity was measured by monitoring the change in absorbance at 400 nm, when paraoxon was hydrolyzed to diethyl phosphate and p-nitrophenol (e400 = 17 mM21 cm21) in 20 mM glycine buffer (pH 9.0), 100 mM sodium chloride. One unit (U) of activity is defined as 1 mmol paraoxon hydrolyzed per minute. Fig. 1 shows a schematic view of the screen-printed H+sensitive electrode with integrated Ag/AgCl reference electrode which was used as transducer for the disposable enzyme sensor. The working electrodes were produced in a batch process similar to that described previously.20,24 Conducting lines of the electrodes were screen-printed with silver carbon ink (Auromal L 180, Doduco, Pforzheim, Germany) on a sheet of a 150 mm thick polyester\u2013polyethylene heat sealing film (Team Codor, DUBO-Schweitzer GmbH, Haltern, Germany)",
+            " D ow nl oa de d by U ni ve rs ity o f Il lin oi s at C hi ca go o n 13 /0 8/ 20 13 1 2: 49 :3 6. sensitive membrane and a contact pad of 5 mm length at the electrode\u2019s upper part. The reference electrode was screen-printed on the back side of the heat sealing film of the working electrode using screenprinting ink (Elektrodag 6037 SS, Acheson, Scheemda, Netherlands) with Ag and AgCl in a ratio of 3+2.25 After curing for 1 h at 80 \u00b0C filter paper strips (4 3 20 mm, Schleicher & Schuell, Dassel, Germany) were positioned on the conducting lines (Fig. 1). Encapsulation of the reference electrode was carried out by lamination with a further heat sealing film at 125 \u00b0C leaving a contact pad of 5 mm uncovered at the upper part of the electrode. Upon immersion of the completed electrode in measuring buffer, which contained 100 mM sodium chloride as electrolyte, an opening at the lower part of the reference electrode allowed the spontaneous filling of the filter paper by capillary forces. Preparation of H+-sensitive double matrix membranes (DMM) The working electrodes received the H+-sensitive character by positioning a defined membrane mixture on to the filter paper",
+            "17,26,27 In brief, 300 mg of PCS prepolymer (33.4%) were mixed with 300 ml of 10.0 mM glycine buffer (pH 9.0), 100 mM sodium chloride. Poly(ethyleneimine) (2.5% m/v in water) was added under constant mixing to adjust the pH to 6.4\u20136.5. After centrifugation to remove polymerized particles, PCS and OPH solution (10 000\u2013270 000 U ml21) were mixed at a ratio of 1+1. A total volume of 3.0 ml of the mixture was deposited on the heat sealing film in a spot directly adjacent to the H+-sensitive membrane (Fig. 1) and allowed to polymerize for 30 min at 30 \u00b0C. Subsequently, the sensors were ready for use or stored under dry conditions at 4 \u00b0C. Experimental set-up for sensor measurements All measurements were carried out in a stirred measuring cell containing 2 ml of 1.0 mM HEPES buffer (pH 9.3) and 100 mM sodium chloride at 37 \u00b0C. Stock solutions of OP compounds and Soxhlet extraction of soil samples were prepared with methanol. When adding OP insecticides the change in potential due to the release of protons after hydrolysis was recorded with a microprocessor pH analyser (microprocessor pH meter 3000 with multiplex 3000, WTW, Weilheim, Germany) connected to a computer"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003378_0734-743x(86)90024-2-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003378_0734-743x(86)90024-2-Figure1-1.png",
+        "caption": "FIG. 1. Relative approach: s=z-w.",
+        "texts": [
+            " A physical explanation of this is given in the final discussion of this paper. T H E O R Y A sphere which strikes an infinite, thin shallow spherical shell at normal incidence will be considered. Both the sphere and the shell are assumed to be linear elastic. Elastic impact of spheres 13 An equation of the impact process can be obtained by simultaneously solving the equations of motion for the sphere and for the shell. Taking z as the displacement of the centre of the sphere from its position at initial contact (see Fig. 1), we can write 2=-F/m (l) Here, m is the mass of the sphere, and F is the reaction of the shell to the sphere. Henceforth, F will be referred to as the contact force. Since the shell response is expected to be primarily transverse in nature during the time of contact, longitudinal inertia will be neglected in the description of the shell. First, a concentrated normal impulse load Fog(t), applied at the shell pole, is considered, where Fo is a constant with force dimensions and 8(0 is the Dirac delta function",
+            " As r~ becomes smaller, the 'period', 2~r'rr~, becomes shorter. The shell response to a point load, F(t), of arbitrary time dependence, can thus be expressed as In order to eliminate the unknown impact force F, the Hertzian assumption [11] can be used which states that the stresses and deformations close to the contact area can be 14 M. (;. KoI I,KR and M. 13USl;N.,XRt calculated at any instant as if the contact were static. Consequently, k is essentially a function of the relative displacement s between the sphere and the sheli (see Fig. 1 ). F is explicitly given by F=ks ~:, (5} where s=z-w. 16) The Hertzian constant k is an abbreviation of k 4 E'bE's [ r b ' r ~ 1/2 ( 7 ) where Ks E'b= l _ E - - ~ v b b a n d E ' ~ = ~ . Eb and Vb denote the Young's modulus and the Poisson's ratio, respectively, of the impinging sphere, and rb is the radius of the sphere. A single integro-differential equation may now be obtained in only one dependent variable, s, by differentiating equation (4) twice with respect to time, and then subtracting this equation from equation (1)"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003124_0891-5849(88)90101-3-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003124_0891-5849(88)90101-3-Figure4-1.png",
+        "caption": "Fig. 4. Effect of exposure milieu on the inactivation of catalase by ozone. Catalas\u00a2 was diluted to a final concentration of 0.2 mg/ml in the following solvents: chelexed phosphate buffer (50 mM), pH 7.0; unchelexed phosphate buffer pH 7.0; and double distilled water. Solutions were then exposed to ozone and assayed for catalase activity as described in Figure 1. Data from the exposures was exp~ssed as percent activity remaining as function of exposure time. Line A, unchelexed buffer; line B, distilled water; line C, chelexed buffer.",
+        "texts": [
+            "2 mg/ml) was exposed to ozone in double-distilled water, chelexed potassium phosphate buffer (50 mM, pH 7.0), or in unchelexed phosphate buffer, pH 7.0, in order to determine their effect on the rate of inactivation. Chelexed phosphate buffer was prepared according to the method of Buettner 2s by adding chelex 100 resin (100-200 mesh, sodium form) to the buffer (10 g/liter of buffer). The chelex resinbuffer mixture was stirred overnight and subsequently filtered before use. Similar rates of inactivation were observed for catalase solutions exposed in unchelexed buffer or distilled water (Fig. 4). Catalase exposed in chelexed buffer showed an enhanced rate of inactivation in response to ozone (Fig. 4). gers against catalase inactivation by ozone. Bar graph # 1 represents the average percent catalase activity remaining in all the control catalase solutions exposed without antioxidant compounds. Alcohols, scavengers of hydroxyl radicals, were not generally good protectors against catalase inactivation by ozone. Only ethanol exhibited a partial protective effect. Butyl alcohol was not only ineffective as a protectant but had an attributory effect. No significant reduction of the catalase inactivation was observed when catalase solutions were exposed in the presence of superoxide dismutase, a specific scavenger of superoxide radicals"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003628_13.57074-Figure8-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003628_13.57074-Figure8-1.png",
+        "caption": "Fig. 8. Coupled drive system.",
+        "texts": [
+            "1 and natural frequency 10 rad/s. The transfer function also incorporates two zeros whose locations can be manipulated to illustrate nonminimum phase behavior and transmission zeros on thejw axis in the complex plane. A Material Transport System-ne Coupled-Drives System The aim of this system is to illustrate the type of problems encountered in the production and transport of con- tinuous webs of material such as textile yam, paper, magnetic tape, strip metal, and plastics. The equipment consists (Fig. 8) of two identical dc motors which are coupled by a continuous flexible belt. The belt passes over pulleys mounted directly on the motor shafts and over a jockey pulley. The control objective is to regulate the belt speed and tension at the jockey pulley. The control inputs are the drive voltages to the dc servomotor amplifiers. The servomotors are equipped with tachogenerators; however, the primary output variables are the belt tension and speed as measured at the jockey pulley. Accordingly, the jockey pulley is equipped with a tachogenerator for speed measurement"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001077_1.1533072-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001077_1.1533072-Figure1-1.png",
+        "caption": "FIGURE 1. Schematic of NO delivery system: \u201ea\u2026 stirred chamber of 120 mL; \u201eb\u2026 partial cross section of Silastic tubing and surrounding liquid film.",
+        "texts": [
+            " was prepared by dissolving appropriate amounts of dibasic and monobasic potassium phosphate salts in deionized water, supplemented with 0.1 mM diethylene-triamine-pentaacetic acid ~DTPA!. Phosphate salts, DTPA, potassium iodide, and sulfuric acid were obtained from Sigma ~St. Louis, MO!. A nitrite standard solution was purchased from World Precision Instruments ~Sarasota, FL! and a nitrate/nitrite assay kit was obtained from Kamiya Biomedical Co. ~Seattle, WA!. Delivery Apparatus. As shown in Fig. 1~a!, the delivery device consisted of a closed, liquid-filled container, in which NO and O2 were supplied via separate loops of gas-permeable tubing. The Teflon container of 120 mL ~Cole-Parmer, Vernon Hills, IL, model E-06103-30! had a magnetic stirrer bar ~3.8 cm length, 0.8 cm diameter! placed at the bottom. The container cap was modified to include stainless steel compression fittings for insertion of a Clark-type O2 electrode ~Orion, Beverly, MA, model 810A plus! and a 2 mm diameter NO sensor ~World Precision Instruments, ISO\u2013NO Mark II system",
+            " To investigate the factors that underly the composition dependence of the parameters in the macroscopic model, microscopic diffusion-reaction models were developed for the aqueous boundary layer and membrane. Three such models were examined, differing only in their chemical complexity. The features common to all are described first, and then the special aspects of each model are discussed. The microscopic models were based on a stagnantfilm approximation for the liquid boundary layer. Because each mass transfer coefficient was measured using single-gas delivery experiments, the following models describe mass transfer and/or reactions at the one \u2018\u2018active\u2019\u2019 tubing loop. As shown in Fig. 1~b!, an aqueous film of thickness d was assumed to reside next to a Silastic tube of inner radius ri and outer radius ro . The concentrations in the film and membrane are denoted as C\u0302 j(r ,t) and C\u0304 j(r ,t), respectively, where r is the radial coordinate. ~The relatively thick tubing wall, with ri /ro 50.75, makes curvature important and requires the use of cylindrical coordinates.! Although the concentrations are time dependent, the film and membrane problems are both pseudosteady. That is, the characteristic times for diffusion were all much shorter than the experimental time scale of about 20\u201330 min"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure1.14-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure1.14-1.png",
+        "caption": "Figure 1.14. Torsional oscillations around a circle referred to the intrinsic frame.",
+        "texts": [
+            " As a consequence, he always finds ( 1.70) and ( 1.71 ). The relation between motion referred to an arbitrary moving reference frame and motion relative to it will be discussed in greater detail in Chapter 4. To see this more graphically, let us return to our earlier example of the torsional oscillations of a circular disk. The motion, velocity, and acceleration of a particle P on the rim of the disk are given by ( 1.38 ), ( 1.39 ), and ( 1.40) relative to the fixed Cartesian frame cp = { 0; ik} shown in Fig. 1.14a. Guided by our previous discussion of motion on a circle, we know that the intrinsic frame 1/J = { P; tk} has the instantaneous orientation shown in Fig. 1.14a. We want to show that the intrinsic velocity and acceleration components are the 34 Chapter 1 instantaneous projections upon the moving, intrinsic frame 1/J of the velocity and acceleration relative to frame r.p. The relevant problem geometry is illustrated in Fig. 1.14b. It is seen that the instantaneous projections of the unit vectors i and j upon the intrinsic directions t and n are given by i = sin et - cos e n, j = -cos e t - sin e n. (1.77) Substitution of ( 1. 77) into ( 1.38 ), ( 1.39 ), and ( 1.40 ), and use of a familiar trigonometric identity yields the results desired: x(P, t) = -an, v(P, t)= -aflt, a(P, t) = -aD't + afl 2n. ( 1.78a) (1.78b) ( 1.78c) These equations still describe the motion, velocity, and acceleration of P relative to the fixed Cartesian frame r.p = { 0; ik }, but the vectors are now referred to the moving, intrinsic frame 1/1 = { P; tk}. Their new simplicity is evident. Of course, the equations (1.78b) and (1.78c) may be derived directly from (1.74) for the circular motion of a particle. We must remember, however, that e in Fig. 1.14a initially is decreasing in time. Therefore, with w = -8, w = -{J, and r =a, it is seen that ( 1.78b) and ( 1.78c) follow easily from ( 1.74 ). 1.7.4. Some Applications of the Intrinsic Velocity and Acceleration Some examples that illustrate various methods used in the analysis of problems involving intrinsic quantities will be studied next. The formula for the curvature of a plane curve will be reviewed in the solution of the first example, and the formula will be used in two others that follow",
+            " Conversely, suppose that a body moves so that in every motion the velocity of each of its particles is given by (2.27). Prove that the body is rigid. 2.13. Use (1.70), (1.71), and the relation s=pO to derive the equations (2.27) and (2.30) for the rigid body velocity and acceleration of a particle P rotating on a circle of radius p with angular speed (J about a fixed axis a= b. 2.14. Use the geometrical interpretations of the terms in (2.27) and (2.30) to determine the velocity and acceleration of the rim particle P in Fig. 1.14. Check your solutions against (1.78). See Example 1.8. 2.15. Apply equations (2.27) and (2.30) to determine for the conditions specified in Problem 1.12 the velocity and acceleration of the mass M. Note the geometrical nature of the terms computed. 2.16. Employ (2.27) and (2.30) to find the velocity and acceleration of the ball P in Fig. 1.3. Use the conditions described in Example 1.3, and compare your results with those in ( 1.17 ). Observe the geometrical character of the terms computed. 2.17"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure3.17-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure3.17-1.png",
+        "caption": "Figure 3.17. Schematic of consecutive rotational displacements about nonintersecting axes.",
+        "texts": [
+            " Since the second axis is through the displaced point denoted as B', the reversed rotation produces no motion of B'; and the resultant dis placement is a pure translation in which all points of the body experience the same translational displacement d(P) = b0 = b in accordance with (3.160). Thus, reversed rotations about distinct parallel lines will produce a dis placement that is similar to a common walking motion. Although the composition of rotations is not additive, under appropriate conditions, any given displacement may be decomposed into a sum of rotational displacements about certain lines which generally do not intersect. To see this, let us suppose in Fig. 3.17a that for a given displacement (3.161) the resultant rotation about the base point 0 is decomposed into two con secutive rotations R 1 and R 2 about concurrent axes a 1 and a2 , such that a 1 is any given direction and a 2 is perpendicular to the translation vector b*. Since T*=T 1 +T2 R1, (3.161) may be written as d*=T 1x+b*+T 2 x, where X= R I X is the position vector from 0 to the final position r of the particle p Finite Rigid Body Displacements 213 after the first rotation alone. Since a 2 \u00b7 b* = 0, we may apply the parallel axis theorem in Fig. 3.17b to find a parallel line through another base point 0' such that d = b* + T 2 x = T 2 x' is a pure rotation about 0', where x' is the location of P' from 0'. Thus, as shown in Fig. 3.18, the given displacement d*(P) is the sum of two pure rotational displacements d 1 = T 1 x and d2 = T 2 x' about 0 and 0', so that (3.162) Hence, any given rigid body displacement (3.161) may be represented by the sum of two consecutive pure rotational displacements about, in general, non intersecting axes a 1 and a 2 , where a 1 is any assigned direction and a 2 is perpen dicular to the parallel translation vector of the assigned displacement"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002061_jsvi.2001.4018-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002061_jsvi.2001.4018-Figure1-1.png",
+        "caption": "Figure 1. Single mass rotor on a light shaft, running in #uid lubricated bearing.",
+        "texts": [
+            " 1 5 sin 7 t2 , (11a) m \"1/2 I 1 2 # 7 6 cos t# 1 2 cos 2 t# 1 30 cos 3 t! 6 105 cos 5 t! 12 35 cos 7 t2 . (11b) Considering equation (9), the additional forces can be written as f \" Q sin i t, f \" P cos i t. (12a,b) Similarly, according to equation (11), the additional moments may be written as: m \" = sin i t, m \" O cos i t. (13a,b) 3. ROTOR AND BEARING SYSTEM The total de#ection of the rotor is the vector sum of the de#ection of the rotor relative to the shaft ends plus that of the shaft ends in the bearings (Figure 1). The de#ection of the shaft ends in the bearing is related to the force transmitted through the bearings by the bearing sti!ness and damping coe$cients as follows: f \"k m#k n#c mR #c nR , (14a) f \"k m#k n#c m#c n, (14b) where m and n are the instantaneous displacements of the shaft ends relative to the bearings in the horizontal and vertical directions, respectively, and take the form m\" M sin(i t)# M cos(i t), (15a) n\" N cos(i t)# N sin(i t), (15b) f \" F sin(i t)# F cos(i t), (15c) f \" F cos(i t)# F sin(i t)"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003629_ramech.2006.252627-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003629_ramech.2006.252627-Figure1-1.png",
+        "caption": "Fig. 1. Autonomous mini-robot Tinyphoon, http://www.tinyphoon.com",
+        "texts": [
+            " In the presented approach both gyro and acceleration sensors are transiently substituted for wheel encoder data when necessary, thus enabling reliable side-slip angle estimation and tangential slip detection and ultimately allowing for slip control. The proposed navigation system is used in conjunction with the predictive trajectory tracking algorithm from [9]. Experimental results show that the combined navigation and control system enables appropriate tracking of highly dynamic trajectories. The autonomous robot Tinyphoon (www.tinyphoon.com), [10], Fig. 1, has two wheels with rubber tires and two felt shoes, one at the front and one at the rear to stabilise it around the pitch axis. It fits into a cuboid with a 75mm square footprint. The two wheels are supported by ball bearings and powered by two individual DC-motors. Exhibiting a power-mass-ratio of 22.5W/kg, the robot is capable of accelerating far beyond the slip boundary. Its maximum velocity is approximately 4m/s. The robot is equipped with two single-chip two-axis acceleration sensors measuring tangential and lateral acceleration, 1\u20134244\u20130025\u20132/06/$20"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001191_0005-1098(93)90125-d-Figure7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001191_0005-1098(93)90125-d-Figure7-1.png",
+        "caption": "FIG, 7. Environment with a mobile robot and a moving obstacle.",
+        "texts": [
+            "t equation (11)-(15) (81) n w ui sin (~\u00b0(s(t))) = u (given), i = l that can be reformulated as max w X w -< r/EF 2 - 2 2 ( f ix+f/y) , i = 1 . . . . . nw, w_>0 equation (11)-(15) n w ui \u00d7 sin (tp\u00b0(s(t))) i = 1 -- u (given in equation (80)), (82) where X = [f ixf ly\" ' fn,xf~,y F l ' ' ' F~w~2wl . The idea behind this optimization is to try to allocate the forces ui in a such a way so that saturation of the available friction at each wheel is avoided. 4. SIMULATION RESULTS In this section a case study is presented. A mobile robot and a moving obstacle with geometric shapes, moving in the same environment (Fig. 7). The shape of both the mobile robot and the moving obstacle is rectangle with dimensions 0.3 m x 0.52 m and 0.28 m x 0.28 m, respectively. The scenario is that when the mobile robot is about to start moving, an obstacle with kinematic parameters x0 = 4.0 m, Y0 = 7.0 m, Vx = 0.04 m sec -1, vy = -0 .075 m sec -1, ax = 0.094 m sec -2, Or = -0.041 m sec -2, is going to collide with it under the current plan. The mobile robot has parameters: Mass (M) : 60 kg. Inertia (Izz) : 32 kg m 2. Maximum accelerating force (U1): 140 N. Minimum decelerating force (U2) : -60 N. Maximum velocity (Vmax) : 8 m sec -2. Wheel-f loor friction coefficient (r/) : -0 .12 . It has the task of going from configuration A to configuration B within T = 12.1753 sec. An offline path planning stage is done and a path r(s) O<-s<-s I with total length s 1 ~ 1 4 . 6 0 m is computed. The parameters of r(s) are indicated on Fig. 7. Initial and final velocities are zero (VA = VB = 0). The resulting velocity profile from the Potential Fields Strategy (PFS) is plotted with solid line on Fig. 8. The dotted ( . . . ) line is the velocity vn(s) of the nominal plan. Line ( - - - ) is the maximum velocity Vmax(S) along r(s). The noisy components of the velocity profile results from the fact that numerical differentiation was actually done to calculate the distance derivatives. The time functions for PFS (tpfs(s)) and the nominal plant (thorn(S)) are plotted on Fig"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002455_j.precisioneng.2004.03.003-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002455_j.precisioneng.2004.03.003-Figure1-1.png",
+        "caption": "Fig. 1. Ball bearing model for calculating NRRO.",
+        "texts": [
+            " 0141-6359/$ \u2013 see front matter \u00a9 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.precisioneng.2004.03.003 The radial NRRO is a problem to be investigated from the viewpoint of ball bearings used in magnetic disc devices. In this research, on the assumption that the ball bearing can be treated as a two-dimensional model, the radial behavior of the center position is analyzed considering the dynamical balance of the Herzian contacting stress between the inner and outer raceways and balls. Fig. 1 shows a NRRO analytical model of the ball bearing. The X- and Y-axes run across the center, O, of the surface of the outer raceway, and x and y represent the coordinates from O\u2032, which is the center of the surface of the inner raceway surface. Since the geometrical errors of the surfaces of the raceways and the balls are small, it is assumed that the balls never slide, but roll perfectly, and have elastic contact with the surfaces of the inner and outer raceways. When the angle of the running inner raceway is \u03c9t , the angles of balls\u2019 positions and the angle of balls\u2019 rotation are given by the following equations"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001968_3-540-45118-8_19-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001968_3-540-45118-8_19-Figure1-1.png",
+        "caption": "Figure 1. Schematic view of the steering device",
+        "texts": [
+            " given sti ness of the inner components increases when reducing the endoscope diameter. Moreover, the technology selection must withstand the sterilization process (140oC during 20 minutes). It has to make the system as simple as possible and to facilitate its manufacturing at small scale. The controllably bendable portion of the instrument must be able to adapt Segments its local curvature to the interior geometry by a spontaneous reaction to the interactions with the environment while the viewing tip follows a track in a vessel or in a cavity. Figure 1 schematically illustrated the endoscopic system we designed. The mechanical structure of the device can be viewed as an hyper-redundant manipulator which embrace the endoscope components (optic bundle, light guides, tool chanels). It is a serial arrangement of tubular segments articulated to each other by pin joints. This design is modular, the number of segments can be adjusted to the application and is in theory in nite. On the actual design, the segment length is 4 mm, the inner diameter 5.4 mm and the outer diameter (including the outer elastomer cover) is 8 mm"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure4.15-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure4.15-1.png",
+        "caption": "Figure 4.15. Simple relative motion of a ball apparent to a ferris wheel rider.",
+        "texts": [
+            "51 ), we have vJ/=0 and a11 =0; that is, no particle may have a nontrivial velocity or acceleration relative to itself Thus, by (4.51), the mutual velocity and acceleration vectors for each pair of origin points are equal and oppositely direc ted: (4.52) Finally, with the aid of (4.51), we derive the following kinematic chain rules for simple relative motion: ( 4.53) a,o= an,n- l +an-l,n-2 + ''. + a2l + alO\u00b7 The easy application of the foregoing chain rules will be demonstrated next. Motion Referred to a Moving Reference Frame and Relative Motion 265 Examples 4.8. The ferris wheel shown in Fig. 4.15 is turning with a con stant, counterclockwise angular speed w = (1/2) radjsec (about 5 rpm). A ball v BG = ~ 15i ~ 4j ft/sec, aBG = ~32j ftjsec 2\u2022 (4.54a) What are the velocity and the acceleration of the ball apparent to the rider at the position shown? Assume that the seat does not swing to and fro about its axle. Solution. Since the seat does not swing about its axle, as the wheel turns, the moving frame rp at A always remains parallel to the ground frame r[J at G. Therefore, bearing in mind the assigned data in ( 4",
+            "54a ), the velocity and the acceleration of the ball B relative to the rider A are given by the chain rules (4.51): (4.54b) It remains to determine the velocity and the acceleration of G relative to A. Since point 0 is fixed in rfJ, the absolute velocity and acceleration of A in r[J are given by (2.27) and (2.30). Taking into account the rule (4.52), we find VAG= ~vGA = V AO = 0) X X= 10j ft/sec, aAG= ~aGA=aA0 =rox(roxx)= ~5ift/sec2, (4.54c) wherein x = 20i ft and ro = ( 1/2) k rad/sec in accordance with Fig. 4.15. Of course, m=O in (2.30). Thus, substitution of (4.54a) and (4.54c) into (4.54b) determines the velocity and acceleration of the ball apparent to the rider: v BA = ~ 15i ~ 14j ft/sec. anA= ~32j + 5i ft/sec 2. (4.54d) 266 Chapter 4 Since the frames are parallel, the results may be referred to either basis set with ik = Ik. 0 Example 4.9. A pin P shown in Fig. 4.16 is constrained to move in a cir cular groove milled to a radius of 3ft in a large rectangular plate. The pin also slides in the straight slot of a slanted link mechanism which is moving toward the right with a constant speed of 5 ftjsec"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003688_tcst.2004.833622-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003688_tcst.2004.833622-Figure1-1.png",
+        "caption": "Fig. 1. (a) TVC actuator with single nozzle and rolling torque scheme. (b) Missile\u2019s divert control system (bottom view). (c) Two angles of TVC in body coordinate frame.",
+        "texts": [
+            " A missile equipped with thrust vector control (TVC) can effectively control its acceleration direction [1] when the missile\u2019s fin fails, which in turn implies that the maneuverability/controllability of the missile can be greatly enhanced during the stage when the speed of the missile is slow and/or the air density surrounding the missile is low. In this brief, we investigate the variable structure (VS)-based missile guidance/autopilot problem for a missile equipped with TVC and divert control system (DCS) so that the intercepting missile is able to fulfill the purpose of successful interception of an inbound target missile in a single intercepting phase. The motion of a missile can be described in two parts as follows: Translation: (1) Rotation: (2) where , and all the variables are defined in the nomenclature. After referring to Fig. 1(a)\u2013(c), the force and torque exerted on the missile can be, respectively, expressed in the body coordinate frame as (3) (4) where is the aforementioned variable moment in the axial direction of the missile. Let the rotation matrix denote the transformation from the body coordinate frame to the inertial coordinate frame. From (1) to (4), the motion model of the missile can then be written as (5) (6) where and . B. Zero-Effort-Miss Phase Assume that both the missile and the target are moving only with constant gravitational acceleration, i",
+            " Accordingly, the desired overall acceleration perpendicular to the LOS can be derived due to the result in Section III, which together with in the direction leads to the desired acceleration (see Fig. 3) of the missile, namely Hence, the resulting acceleration of the missile due to TVC and DCS together will lie on the plane . We note the following two facts: 1) projection of the desired resulting acceleration onto the axis of is simply and 2) projection of onto the axis perpendicular to the plane will be identically zero. Then, we can derive the following constraint equations of in the body coordinate frame as: By Cramer\u2019s rule, the acceleration [see Fig. 1(b)] generated by the divert control system, denoted as , can be derived as Remark 1: To avoid the singularity for computing the , we propose one possible solution to modify the force from the divert control system when the singularity condition \u201c \u201d occurs as follows: and if and if To validate the proposed sliding-mode guidance and autopilot of the missile system, we provide a realistic computer simulation in this section. We assume the target is launched from somewhere 600 km far away. The missile has a sampling period of 10 ms"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003477_cnm.913-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003477_cnm.913-Figure3-1.png",
+        "caption": "Figure 3. Symmetric graph with the canonical form II symmetry and its factors: (a) D; and (b) C.",
+        "texts": [
+            " Canonical form II: For this case, matrix [M] can be decomposed into the following form: [M] = [[A]n\u00d7n [B]n\u00d7n [B]n\u00d7n [A]n\u00d7n ] N\u00d7N (8) The eigenvalues of [M] can be calculated as { (M)} = { (C)}\u222a{ (D)} (9) Copyright q 2006 John Wiley & Sons, Ltd. Commun. Numer. Meth. Engng 2007; 23:639\u2013664 DOI: 10.1002/cnm where: [C] = [A] + [B] and [D] = [A] \u2212 [B] (10) [C] and [D] are called condensed submatrices of [M]. The axis of symmetry in a graph of the form II symmetry passes through the members but not the nodes. The members cut by the axis of symmetry are called link members. Link members connect two isomorphic subgraphs S1 and S2 to each other. Figure 3 shows a symmetric graph with the canonical form II and its decomposed factors. Canonical form III: This form has a form II submatrix augmented by some rows and columns as shown in the following: [M] = \u23a1 \u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a2\u23a3 L11 . . . L1k [A] [B] L21 . . . L2k Ln1 . . . Lnk L11 . . . L1k [B] [A] L21 L2k Ln1 . . . Lnk C(2n+1, 1) . C(2n+1, 2n) C(2n+1, 2n+1) . . . C(2n+1, 2n+k) . . . . . . . . Z(2n+k, 1) . Z(2n+k, 2n) Z(2n+k, 2n+1) . . . Z(2n+k, 2n+k) \u23a4 \u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a5\u23a6 (11) where [M] is a (2n + k) \u00d7 (2n + k) matrix, with a 2n \u00d7 2n submatrix with the pattern of form II, and k augmented columns and rows"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000577_(sici)1521-4109(199911)11:17<1259::aid-elan1259>3.0.co;2-b-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000577_(sici)1521-4109(199911)11:17<1259::aid-elan1259>3.0.co;2-b-Figure5-1.png",
+        "caption": "Fig. 5. Schematic diagram of the \u00aerst electrode design.",
+        "texts": [
+            " It should be noted that methylene blue binds to the surface of Zr(HPO4)2 whether crystalline or amorphous, but it was found that photocurrents obtained with a mixture of methylene blue and amorphous Zr(HPO4)2 were signi\u00aecantly smaller than those obtained after methylene blue had been intercalated into the lattice. In initial photochemical experiments the working electrode and light pen were aligned manually and were separate, the working electrode consisting of a Te\u00afon rod with a copper rod along its central axis. The end of the Te\u00afon contained a hole of diameter 5 mm and depth 0.5 mm which was \u00aelled with the graphite=mineral oil=a-Zr(HPO4)2 H2O mixture. This experimental set-up is shown in Figure 5. However, the initial success of this electrode in exhibiting signi\u00aecant photocurrents with ascorbic acid led to the development of an all-in-one light source and working electrode. Analytical measurements were made using this novel design of the electrode, which is shown in Figure 6. Graphite (99.9 %, Aldrich) was crushed using a pestle and mortar before mixing with the dye=phosphate compound, this was also mixed with mineral oil. ESR experiments were performed using a Bruker ER 200D \u00b1 SRC spectrometer, at a centre \u00aeeld value of 3500 G, with a sweep width of 150 G, in accordance with procedures outlined previously [12]"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000385_s0045-7949(98)00165-5-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000385_s0045-7949(98)00165-5-Figure5-1.png",
+        "caption": "Fig. 5. Simply supported laminated shell (three graphite-epoxy layers with orientations 908/08/908 referred to the global y-axis). Geometry and material properties (y= 308).",
+        "texts": [
+            " Again one-quarter of the plate was analyzed due to symmetry. Results are shown for two di erent meshes (m = 2 and m = 4) giving practically the same period and small changes in the amplitudes. The same results are practically obtained when the number of analysis layers increases. This example corresponds to a simply supported laminated cylindrical shell. The shell is composed by three graphite-epoxy layers of high elastic modulus. The orientations are 908/08/908 referred to the global y-axis (Fig. 5). Fig. 5 also shows the geometry and material properties. The analysis is made by considering three di erent meshes: 4 4, 6 6 and 8 8 elements. For computational purposes the thickness is divided into 3, 6 and 24 analysis layers for the 4 4 mesh and in 24 layers for the other meshes. Table 4 shows some numerical results for the displacement and stresses at di erent points. The variation of the displacements across the thickness is shown in Fig. 6. Fig. 7 displays the distribution of syz and sxz across the thickness"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003443_bf00934465-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003443_bf00934465-Figure3-1.png",
+        "caption": "Fig. 3. Optimal accelerations for a given \u00a2*.",
+        "texts": [
+            " (26) and (27) yield A (0) = A (0) = y(O)/II y(0)tl ~- -\u00a2*, (28) (* being a constant unit vector on each optimal trajectory. (26) (27) JOTA: VOL, 43, NO. 3, JULY 1984 437 The candidate optimal strategy pair can now be determined by u*, v* = arg rain max H = arg max min H, (29) u~U v c V v~V u~U yielding U* = -- a e M T M p ~ * / II MeG* li, (30) v* = -aeMT Mz~*/I1ME~:* II, with P L 0 ME=[C\u00b0oXE ~]. (31) The optimization results by maximizing the projection of the admissible accelerator vector on the direction opposite to the unit vector ~*, as depicted in Fig. 3. From this figure, it is easy to see that the respective acceleration components in the Y and Z directions are u* = ae sin \u2022*, and (32) and Op(~) a= HMe(II = (~:~ cos z Xe + ~2)1/2 OE (~) A lfM~sCl[ = (sc~ cos 2 Xz + ~:~)1/2. (38) This candidate solution is indeed optimal if the sufficiency condition, requiring smooth isocost surfaces (Ref. 8), is satisfied. The construction of the isocost surfaces has to be carried out in two consecutive steps, using Eq. (36) for both. First, the direction of ~* maximizing the bracket in Eq",
+            " (35) The optimal cost j* = I[Y*(0)l I can be obtained by multiplying the vector y*(0) by a unit vector in its own direction. Such vector is -~* [see Eq. (28)]. The search for this, a priori unknown, direction is the major part of the optimal game solution. Since any point in the game space (y, 0) can be considered as an initial condition, J*(y, O)= sup { -~Ty -p (O)Qe( ( )+e (O)O~( ( ) } , (36) tJ~tl = a with p(O) ~= ap@[02/2 - ~0(0)], e(O) A= a .r2(02/2), (37) JOTA: VOL. 43, NO. 3, JULY 1984 439 can be characterized by the angle/3\" (see Fig. 3), ~:* = -cos fl*, ~* = -sin/3\", (39) and the solution can be expressed as /3* =/3*(y, 0). (40) The next step is to substitute Eq. (40) into Eq. (36) and to set a constant value C for J*, J*[y, o,/3*(y, 0)] = C. (41) This last expression is the equation of the isocost surface J* = C to be tested for smoothness. is the existence of a unique solution/3* of Eq. (36) for any given (y, 0). The maximization process (using/3 as the variable) leads to the following equation: Yl sin/3 - Y2 cos fl + sin/3 cos/3 [ p ( 0 ) / Op (/3) ] sin 2 Xe - [e(0)/Q~ (/3)] sin 2 XE = 0, (42) where Qp(/3) and QE (/3) are obtained by substituting Eq",
+            " Singularity is detected when, in a part of the state space, the gradient of the optimal cost cannot be uniquely defined. The origin of this singular behaviour is the difference in the minor to major axis ratios of the respective ellipses (cos Xv > cos X~, as shown in Fig. 2). This property is an inherent feature of the missile/aircraft collision course trajectory for Ve > VE and sin XE ~ 0 (see Fig. 1). As a consequence of this difference, the effective missile/aircraft maneuver ratio ~er, defined in Eq. (48), depends on the gradient direction (see Fig. 3), indicating the preference of the evader to orient its acceleration in the direction of the major axis ([3* -- ~r/2). The singular region of the state space is small. It is confined to a part of the plane of symmetry Y2 = 0 inside the isocost tube J * = Cx [see Eq. (55)] for 0 < 0x [Eq. (53)] only. This region is divided into two different JOTA: VOL. 43, NO. 3, JULY 1984 455 types of singular surfaces (see Fig. 11): a dispersal zone of the evader D1XOs and a focal surface FIXOs. The dispersal zone is a set of initial conditions (Yl, 0) for a pair of symmetrical trajectories departing toward opposite y2-directions"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002529_s0379-6779(02)00099-1-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002529_s0379-6779(02)00099-1-Figure2-1.png",
+        "caption": "Fig. 2. Cyclic voltammograms of Ni electrode between 0.2 and 0.6 V at different scan rates subsequent to an initial cycle in the potential range between 0.2 and 1.2 V in 0.5 M H2SO4 consisting of 0.1 M aniline and 50 mM Fe2\u00fe/Fe3\u00fe.",
+        "texts": [
+            " However, there is a simultaneous increase in DEp. After about four cycles, there is a rapid increase in DEp (Fig. 1 inset). Thus, this experiment facilitates monitoring of the redox process simultaneously with the growth of PANI layer on Ni. In another type of experiment, a thin layer PANI was deposited on the Ni in 0.5 M H2SO4 \u00fe 0:5 M aniline\u00fe 50 mM Fe2\u00fe=Fe3\u00fe during the initial potentiodynamic cycle between \u20130.2 and 1.2 V, and subsequently cycled in the same electrolyte only between 0.2 and 0.6 V (Fig. 2). The redox peaks of Fe2\u00fe=Fe3\u00fe reaction alone appear in the potential range between 0.2 and 0.6 V and the values of ip and DEp remain unaltered for repeated potential sweeps (not shown) at a given scan rate. Since the potential sweep is reversed at 0.6 V, further growth of the PANI (which occur at a potential of >0.6 V) does not take place and therefore thickness of the PANI remains unaltered. As a result, the voltammograms corresponding to Fe2\u00fe=Fe3\u00fe are reproducible during repeated cycling at a given scan rate, and the magnitude ip increases with an increase in sweep rate (Fig. 2). Furthermore, the electrode was removed from the electrolyte, washed repeatedly in 0.5 M H2SO4 and cyclic voltammograms were recorded in 0.5 M H2SO4 containing 50 mM of Fe2\u00fe=Fe3\u00fe electrolyte. The voltammograms recorded at several sweep rates were identical to those shown in Fig. 2. In the experiments described above, the electrolyte contained Fe2\u00fe=Fe3\u00fe redox species during the deposition of PANI. It may be anticipated that Fe2\u00fe and/or Fe3\u00fe ions are included within the PANI layer. The catalytic behaviour of the PANI on Ni may thus be attributed to the included ions. In order to examine this aspect, PANI was deposited on Ni during the initial potential cycle in 0.5 M H2SO4 \u00fe 0:1 M aniline (hereafter referred to as PANI modified Ni electrode), the electrode was copiously washed in 0.5 M H2SO4, and then cycled between 0.2 and 0.6 V in an electrolyte of 0.5 M H2SO4 containing 50 mM of Fe2\u00fe=Fe3\u00fe. The voltammograms of the redox reaction (Fig. 3) resemble to those shown in Fig. 2 in shape as well as in magnitude of the peak currents and the peak potential values. These results suggest that the catalytic behavior of PANI deposited in presence and absence of redox ions is alike towards reaction (1). For the purpose of comparison, cyclic voltammograms of both Pt and PANI modified Ni electrodes were recorded in 0.5 M H2SO4 supporting electrolyte consisting of Fe2\u00fe=Fe3\u00fe (Fig. 4). Peak current of the PANI modified Ni electrode is higher than that of the Pt electrode. Similar observation is made at several concentrations of the redox couple and several sweep rates"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002606_iros.1997.655141-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002606_iros.1997.655141-Figure2-1.png",
+        "caption": "Figure 2: Classical approach",
+        "texts": [
+            " H will be written as follows : Note that H components for each position and orientation of the gripper are directly supplied by the outputs of the robot encoders. 0 L : homogeneous transformation matrix from F,, to Fe. L must be computed by performing extrinsic calibration. However, it should be stressed that the extrinsic calibration is in most cases greatly dependent on intrinsic parameters calibration and 1059 image detections. sometimes quite inaccurate. So, L estimation might be (7) R1 3 L = ( o 1 ) According to the figure 2, it is obvious that AX = X 3 (8) (3) 0 T : homogeneous transformation matrix from Fm where A and B are known and X represents the handeye calibration transformation that is to be estimated. t.o Fm - I ' _ _ At least three different robot motions are necessary to solve the system [3]. In practice, a set of n positions ( n 2 3) is selected and the system is overdetermined. T represents the location of the calibration object in the robot world coordinate sytem. There is a lot of possibilities to solve for (AiX = X B i ) i E [l..n] (9) (4) Rt Tt T = ( 0 1 ) 0 X : homogeneous transformation matrix from Fe to Fh is the unknown hand-eye transformation. (5) Figure 1 explains the relationships between the different frames and the various homogeneous matrices. 2.2 Classical Approach Let's consider two different positions i and j of the gripper inside the robot workspace (see fig.2). Then, matrices H and L have to be indexed by i and j corresponding to these two different stations of the gripper. Matrix X doesn't have any index since the camera is rigidly mounted on one of the robot links. As H, and H j are known, it is possible to estimate the transformation A that gives the location of the second gripper position relative to the first position. A = (Ha)-'(Hj) (6) Similarly, Li and Lj can be computed and it is also possible to determine B : [a] and [3] propose closed-form solutions"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001338_0094-114x(95)00082-a-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001338_0094-114x(95)00082-a-Figure2-1.png",
+        "caption": "Fig. 2. Gear geometry for contact ratio.",
+        "texts": [
+            " However, minimum value of (Z s - Zp) after avoiding tip interference will be further limited by the accepted value of contact ratio. 2.2. Contact ratio Both the approach contact and recess contact vary with the addendum truncation as well as center distance modification. With a greater number of corrections sometimes one of them becomes negative although their sum remains positive and gives a satisfactory contact ratio. But it is undesirable for gearing action. Therefore, in the present work these two contacts are verified separately in computation. Referring to Fig. 2 (ring gear is the driver in gearing action) the approach contact (CP) ac, recess contact (PB) re and contact ratio Cr are expressed as a\u00a2 = x/~2p - r~,p - rp sin g (3) r~ = r~ s in ~t -- ~ - - r~g (4) C, = (ac + rc)/(zcm cos ~0) (5) Minimum tooth difference 477 where, rp and rg are the working pitch circle radii, rap and rag are the tip radii and rbp and rbg are the base circle radii of the pinion and gear respectively, ~ and ~0 are the working and standard pressure angles respectively, and m is the standard module"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003657_j.cma.2005.02.033-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003657_j.cma.2005.02.033-Figure3-1.png",
+        "caption": "Fig. 3. Open-loop multibody system [4].",
+        "texts": [
+            " (2) Spherical joint\u2014in this case, the orientation of the body on the distal side of the spherical joint is measured relative to the ground body. Once again, the indirect coordinates correspond to the absolute angular coordinates for the distal body. (3) Two prismatic joints with parallel axes\u2014the translation of the body on the distal side of the distal prismatic joint is measured relative to the body on the proximal side of the proximal joint. This rule is very similar to rule 1 for revolute joints. To demonstrate, consider the example from Fayet and Pfister shown in Fig. 3. Four bodies (m1, m2, m3, m4) are connected in series to the ground by a revolute joint (h12), two revolute joints (h13 and h14) with parallel axes, and a spherical joint (b15). The indirect coordinates for this system consist of the first and second revolute joint coordinates, which locate m1 and m2. The orientation of the third body m3 is measured relative to m1 using rule 1 above. Finally, the orientation of the distal body m4 is measured relative to the ground, in accordance with rule 2. Fayet and Pfister present a systematic formulation of the kinematic and dynamic equations for open-loop systems in terms of indirect coordinates, and give some examples of the resulting simplifications in the dynamic equations",
+            " To extend this graph-theoretic approach to indirect coordinates, the concept of \u2018\u2018virtual joints\u2019\u2019 must be introduced. Essentially, a virtual joint, sometimes called a \u2018\u2018free\u2019\u2019 joint or sensor element, is used to measure the relative motion of any two bodies in a system. The joint is \u2018\u2018virtual\u2019\u2019 since it does not necessarily correspond to a physical joint in the multibody system. To demonstrate, consider the linear graph shown in Fig. 7. This graph represents Fayet and Pfister s multibody system from Fig. 3, which is superimposed on the graph in dotted lines. The graph consists of four rigid body elements m1 m4, seven arm elements r5 r11, three revolute joints h12 h14, and one spherical joint b15. In addition, two virtual joints are added to the graph: a virtual revolute joint vh16 between bodies m1 and m3, and a virtual spherical joint vb17 between the ground and body m4. These virtual joints correspond to Fayet and Pfister s guidelines for defining indirect coordinates, described previously in Section 2"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003610_j.aca.2005.08.037-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003610_j.aca.2005.08.037-Figure2-1.png",
+        "caption": "Fig. 2. Schematic representation of the design used for the optical flow-cell: (1) quartz slide with two holes, (2) clamp for fixation, (3) Teflon tubing for sample flow, (4) glass tube glued to the quartz slide used for housing the Teflon tubing, (5) quartz slide as substrate for the optical film, (6) sensing film, and (7) Teflon gasket to control the cell volume.",
+        "texts": [
+            " 1A for chemical structure), sodium perchlorate, sodium odide, 2-morpholinoethanesulfonic acid (MES), sodium saliylate, and sodium nitrate were purchased from Sigma\u2013Aldrich ntific; Pittsburgh, PA) was positioned by applying vacuum in spin-coating device (model SCS-G3-8 obtained from Cookon Electronics; Providence, RI). The quartz plate was rotated t 600 rpm, and 100 L of the membrane cocktail was injected nto the rotating glass plate. After spinning for \u223c5 s, the quartz late coated with the thin polymeric film was removed from the pin coater and dried in air for \u223c10 min. When not in use, the lm was stored in the dark. The thickness of the sensing film was estimated to be in the range of 2\u20133 m [23] (see Fig. 2 in Ref. [23]). A quartz plate coated with the fluoride sensitive film was mounted in a custom-built spectrophotometer flow-cell (see Fig. 2 for schematic representation of this cell). The sample volume of the cell was estimated to be about 25 L when using a Teflon gasket with a thickness of 0.14 mm. The flow-cell was then mounted into a Perkin-Elmer double-beam UV\u2013vis spectrophotometer (model Lambda 35; Boston, MA). Using a Gilson Minipuls-3 peristaltic pump (Middleton, WI), a buffer was allowed to flow over the surface of the film for 20 min with a flow rate of 1.4 mL/min to pre-condition the sensing film. The response of the optical sensing film toward different anions was evaluated by adding known aliquots of the test solution to a stirred reservoir containing 50 mL of buffer",
+            " L+ + Ind\u2212 + H+ (a) + F\u2212 (a) IndH + LF (1) The co-extraction constant (K) corresponding to this equilibrium is expressed as: K = [IndH][LF] [Ind\u2212][L+] 1 aH+ \u00b7 aF\u2212 (2) To describe the response characteristics of this sensor system, it is quite useful to use the relative absorbance, \u03b1 [28], which is the fraction of the total indicator (IndT) that is present in the d \u2212 i \u03b1 w a u p s a a K m r K a i a acid dye (Ind\u2212) to ensure electroneutrality in the bulk of the thin polymeric film (see sensing scheme in Fig. 3). This protonation of the chromoionophore leads to a large change in the absorbance of the optical film. Indeed, as shown in Fig. 4, the absorbance spectrum of a polymeric film formulated with 2 DOS:1 PVC and impregnated with Al-Sal/ETH-7075, measured in 50 mM glycine-phosphate buffer, pH 3.00, is highly dependent on the fluoride ion concentration in the bathing sample phase (using flow-through configuration shown in Fig. 2). With increasing fluoride concentrations, the extent of protonation of the acid dye in the film by proton co-extraction becomes greater, yielding a lower absorbance for the deprotonated form of the indicator (\u03bbmax = 529 nm) and higher absorbance of the protonated form (\u03bbmax = 441 nm) with an isobestic point at 474 nm. Plotting the background corrected absorbance values at 529 nm versus the total fluoride concentration (Fig. 5) demonstrates that the Al-Sal based optical film responds with high sensitivity to fluoride with a sub-micromolar detection limit and a dynamic measurement range from 0"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003635_rob.4620060406-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003635_rob.4620060406-Figure1-1.png",
+        "caption": "Figure 1. Elastic links.",
+        "texts": [
+            " In cases of flexible arms, the transformation Low: Solution Schemes for the System Equations of Flexible Robots 385 matrices are, in general, functions of the corresponding joint displacements and the elastic slopes. In the following, a derivation for the kinematic equations of flexible robots is first presented. The author then introduces a general transformation matrix associated with the elastic deformation. Consequently, the possibilities of simplifying the expression of the matrix from the assumption that the strain components and elastic slopes are small compared to unity are investigated. As shown in Figure 1, the position vector for the tip-point of a flexible robot (point 2\u201d\u2019) relative to the origin of the inertial frame is expressed as PI = Pi + D1+ (P2 + C2) + D2 PI = Roipi + Roidi + RoiR11, R 1 2 ~ 2 +RoiRi I* R142 (1 ) (2) in which Ro, and RIP2 are the transformation matrices associated with the rigid-body motion, whereas R l l , is due to the elastic slopes of the end of the previous link. The vectors pi and dj ( j = 1.2) denote the vectors relative to local coordinate systems. Note that system 0 is the inertial frame"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002517_1.1515324-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002517_1.1515324-Figure4-1.png",
+        "caption": "Fig. 4 Change of constraints by foot change",
+        "texts": [
+            ", we can derive the equation of motion in the second phase as follows: F M 11 M 121M 13 M 121M 13 M 2212M 231M 33 G H u\u03081 u\u03082 J 1F 0 c121c13 2c122c13 2c23 G 3H u\u03071 2 u\u03072 2J 1 H K1 K21K3 J 5 H 0 0J . (2) Equation ~2! is rewritten in the form, u\u03085 f ~u , u\u0307 ! (3) where u5$u1 ,u2% T. 2.4 Angular Velocity Variation Caused by Foot Exchange. In this analysis, it is assumed that the toe collision is plastic and the foot exchange takes place instantly for the sake of analytical simplicity. As shown in Fig. 4, u\u0307 i p4 represents the angular velocity of link i at the moment right before the foot exchange ~posture 4 in Fig. 2!, whereas u\u0307 i p5 stands for the angular velocity of link i at the moment right after the foot exchange ~posture 5 in Fig. 2!. The analytical model of link i at the instant of the foot exchange is shown in Fig. 5. Pi and Pi11 are the impulses caused by the collision at the joints i and i11, respectively. The impulsemomentum equations for link i are written in the forms, mi~v ix p52v ix p4",
+            "5Pix2P (i11)x mi~v iy p52v iy p4!5Piy2P (i11)y (4) I i~ u\u0307 i p52 u\u0307 i p4!5ai3Pi1~ li2ai!3Pi11 556 \u00d5 Vol. 124, DECEMBER 2002 rom: http://dynamicsystems.asmedigitalcollection.asme.org/ on 01/28/201 where v i p4 is the mass center velocity of link i at the moment right before foot exchange and vi p5 is the mass center velocity of link i at the moment right after the foot exchange. Before the foot exchange, the swing leg is in a straight line and the analytical model is a 2-dof link system as shown in the left side of Fig. 4. After the foot exchange, however, the model turns into a 3-dof system. The relationship of the link angular velocities during the foot exchange is derived from ~4! as follows: F H11 H12 H21 0 H31 0 G H u\u03071 p4 u\u03072 p4J 5F M 11 M 12 M 13 M 22 M 23 Sym M 33 G H u\u03071 p5 u\u03072 p5 u\u03073 p5 J , (5) where M i j is the same as Eq. ~1!, and Hi j is as follows: H1152@m1a11m2~ l21l32a2!1m3~ l32a3!#l1 cos~u12u2! H125I12m1a1~ l12a1! H215I22m2a2~ l21l32a2!2m3l2~ l32a3! H315I32m3a3~ l32a3!. 2.5 Cyclic Walking Locomotion Condition",
+            " In order to realize the cyclic walking locomotion, the motion state at posture 5 must be the same as that at posture 1. Therefore, we get up55up1 (6) u\u0307p55u\u0307p1 We note that there are two zero elements in @H# as shown in Eq. ~5!. By substituting the formula ~6! into Eq. ~5!, we have the relationship between u\u03071 p1, u\u03072 p1 and u\u03073 p1 of the form, Transactions of the ASME 6 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F S M 212 H21 H31 M 31D u\u03071 p11S M 222 H21 H31 M 32D u\u03072 p11S M 23 2 H21 H31 M 33D u\u03073 p150 (7) The angular position at posture 4 is calculated as follows from Fig. 4 and Eq. ~6!: u1 p45u2 p11p (8) u2 p45u1 p12p . From Eqs. ~5! and ~6!, the angular velocities u\u03071 p4 and u\u03072 p4 are solved as functions of u\u0307p1 as follows: u\u03071 p45 1 H21 ~M 21u\u03071 p11M 22u\u03072 p11M 23u\u03073 p1! (9) u\u03072 p45 u\u03073 p45 1 H12H21 ~a u\u03071 p11b u\u03072 p11c u\u03073 p1!. where a5H21M 112H11M 21 , b5H21M 122H11M 22 , c5H21M 13 2H11M 23 . By setting c15u and c25 u\u03075c\u03071 , Eq. ~3! is rewritten in the following form of one order differential equation c\u03075H c\u03071 c\u03072 J 5 H c2 f ~c1 ,c2!J 5L~c!. (10) We apply the backward time Runge-Kutta integration method and integrate Eq"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000517_1616-8984(199607)1:1<1::aid-seup1>3.0.co;2-6-Figure1-10-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000517_1616-8984(199607)1:1<1::aid-seup1>3.0.co;2-6-Figure1-10-1.png",
+        "caption": "Figure 1-10. Slab waveguide-based SPR [359].",
+        "texts": [
+            " Both principles are illustrated in Figure 1-9. 1.2 Principles of Optical Transduction 17 As in the case of intrinsic fiber optics, guided radiation can be used to couple via a buffer layer to a metal film and excite surface plasmons at the opposite interface. Suitable refractive indices for buffer layers and the correct wavelength guided in the waveguide are necessary to find a resonance condition. Such devices (slab waveguide-based SPR) can be used as sensing systems [359]. A schematic representation is shown in Figure 1-10. First attempts have been undertaken to achieve a multi-element surface plasmon resonance chip. Using the set-up with a variation of the angle of incidence, four sensor elements have been published [299]. In contrast, the slab waveguide-based SPR chips are expected to allow even more elements to be interrogated, since optical micro-structuring becomes a common process. Recently, fiber optical-supported surface plasmon resonance spectroscopy [235] has been developed using coated multimode fibers excited by polychromatic light"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002517_1.1515324-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002517_1.1515324-Figure3-1.png",
+        "caption": "Fig. 3 3-dof analytical model of a biped walking mechanism",
+        "texts": [
+            " Here, the toe collision is also assumed to be inelastic, so that the toe does not bounce from the ground. From posture 5, the next step starts. Because both the knee collision and foot exchange take place instantly, the one step period is t11t2 . An efficient and natural walking locomotion of a 3-dof walking mechanism in the first phase is solved by the optimal trajectory planning method. 2.2 3-dof Analytical Model and Equation of Motion in the First Section. The analytical model of the 3-dof biped walking mechanism used for the optimal trajectory planning in the first section is shown in Fig. 3. Notation ui is the input torque at joint i , l i is the i-th link length, mi is the i-th link mass, ai is the distance of the mass center of the i-th link from the joint i , and I i is the inertia moment of the i-th link about the mass center. Using Lagrange\u2019s equation, the equation of motion with respect to u1 , u2 , and u3 is derived as follows: F M 11 M 12 M 13 M 22 M 23 Sym M 33 G H u\u03081 u\u03082 u\u03083 J 1F 0 c12 c13 0 c23 AntiSym 0 G \u2022H u\u03071 2 u\u03072 2 u\u03073 2 J 1H K1 K2 K3 J 5H u12u2 u22u3 u3 J (1) where M 115I11m1a1 21~m21m3"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure4.16-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure4.16-1.png",
+        "caption": "Figure 4.16. Simple relative motion of a sliding pin of a mechanism.",
+        "texts": [
+            "52), we find VAG= ~vGA = V AO = 0) X X= 10j ft/sec, aAG= ~aGA=aA0 =rox(roxx)= ~5ift/sec2, (4.54c) wherein x = 20i ft and ro = ( 1/2) k rad/sec in accordance with Fig. 4.15. Of course, m=O in (2.30). Thus, substitution of (4.54a) and (4.54c) into (4.54b) determines the velocity and acceleration of the ball apparent to the rider: v BA = ~ 15i ~ 14j ft/sec. anA= ~32j + 5i ft/sec 2. (4.54d) 266 Chapter 4 Since the frames are parallel, the results may be referred to either basis set with ik = Ik. 0 Example 4.9. A pin P shown in Fig. 4.16 is constrained to move in a cir cular groove milled to a radius of 3ft in a large rectangular plate. The pin also slides in the straight slot of a slanted link mechanism which is moving toward the right with a constant speed of 5 ftjsec. The slot makes an angle of 30\u00b0 with the horizontal drive shaft, as illustrated. Find for the instant shown the velocity and the acceleration of P relative to the plate and to the link. Solution. Let the frame f/J = { F; I, J, K} be fixed in the plate, and let <p = { 0; i, j, k} = { 0; I, J, K} be a parallel frame fixed in the slotted link",
+            " With the present labels, we have V PF= V PO+ VoF> aPF= apo\u00b7 (4.55b) Each of these vector equations involves two unknown vector quantities; hence, additional information about their components must be furnished in order to solve ( 4.55b) for the unknown vectors. This is done by considering the nature of the motion of the pin in the separate frames. The observer in f/J sees P move on a circle of radius R = 3 ft whereas the observer in <p sees P move along the straight slot; hence, at the moment of interest shown in Fig. 4.16, the unknown velocity and acceleration vectors may be written as VpF= -VpFj, Vpo= -Vp0 i, apF= -.i'j-Ks2i, ap0 ='= -ap0 i (4.55c) ( 4.55d) Motion Referred to a Moving Reference Frame and Relative Motion 267 in terms of the unknown intrinsic variables at the position shown, and wherein s = lv PFI and K = 1/R = (1/3) n-'. [See (1.70) and (1.71).] Thus, after collecting ( 4.55a ), ( 4.55c ), and ( 4.55d) into ( 4.55b) and equating the corresponding scalar components, we obtain the values s = v PF = 5/2, s= 0, Vpo = 5 j3;2, and ap0 = 25/12",
+            " The motion of the pins A and B of a Scotch mechanism shown in the figure are controlled by the link C which moves to the right with a constant speed of 6 ftjsec during a period of its motion. The pins are constrained to move in a parabolic track y Problem 4.33. Motion Referred to a Moring Reference Frame and Relative Motion 329 described by y 2 = 3(3- x) in the frame r/> = { F; ik}. Find the velocity and acceleration of pin A in frame r/> when the link is in the configuration shown. What are the velocity and acceleration of A relative to B at this instant? 4.34. Suppose that the mechanism described in Example 4.9 has the initial position shown in Fig. 4.16. Find the velocity and acceleration of the pin P relative to the frames r/> and qJ at the instant t = 0.4 sec. 4.35. A pin P controls the motion of two slotted links so that they move on guide rods at right angles to one another. At the instant illustrated, link A has a speed to the right of 15 cm(sec and is decelerating at the rate of 50 cmfsec2. Concurrently, the link B is moving upward with a speed of 20 em/sec and is slowing down at the rate of 75 cmfsec each second. What is the radius of curvature of the trajectory of P at this instant"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003972_robot.2006.1642071-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003972_robot.2006.1642071-Figure2-1.png",
+        "caption": "Fig. 2. Simultaneous control of motion and deformation in 1D",
+        "texts": [
+            " In this section, we formulate the simultaneous control of motion and deformation of the soft material. First, we model the soft object using particle based model [9]. We use linear mass-damper-spring components. Next, we formulate the system including the control laws. Finally, we analyze the stability of the system by the Rauth-Hurwitz Criterion. A. Description of motion and deformation of soft material along the x-axis In this paper, we consider a simultaneous control of a soft object as shown in Figure 2. The soft object moves along the x-axis, and includes two positioned points and two manipulated points. The positioned and the manipulated points are mass points. We can control the motion and the deformation of the soft object by regulating all the positioned points to respective desired points. In general, physical parameters of a soft object, especially viscosity, is unknown. Hence, it is difficult to use a feedforward control as a control law. We use a feedback control as a control law. Concretely, we use PID control for the positioned points",
+            " In this model, we use linear mass-damper-spring components and consider the motion and deformation of the soft object along the x-axis. Let Pi represent the i-th mass point. Let xi and vi represent the position and velocity of Pi at time t, respectively. Note that the number of masses is not serialized along the x-axis to utilize the symmetry of the model in analysis. In Figure 4, P0 and P2 are manipulated points, while P1 and P3 are positioned points. We regulate the positioned points to the respective desired points by controlling the manipulated points to control the motion and the deformation simultaneously, as shown in Figure 2. Let kij and bij be the elastic and viscosity coefficients, respectively, of the soft interface between i-th and j-th masses, and mi represent the mass of Pi. Additionally, let Lij be the natural length of the soft interface between i-th and j-th masses. Physical parameters of the soft interface and mass points are time-invariant and positive. By varying the physical parameters, the model can be used to represent various cases. For example, when we use a high stiffness value as a parameter k13, the model describes the case of a soft-fingered robotic hand grasping a rigid object as shown in Figure 5"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002283_20.917638-Figure6-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002283_20.917638-Figure6-1.png",
+        "caption": "Fig. 6. Power spectra of velocity measurement between disk B and the slider (SD).",
+        "texts": [
+            " The FH was numerically calculated by the Computer Mechanics Laboratory (CML) Air Bearing Design Code and plotted as a function of disk RPM as shown in Fig. 5(b). Before measuring the repeatable FHM of the slider, we evaluated the flyability of the slider by the \u201cspin-down\u201d test measuring friction and AE and also measuring the velocity response between the slider and disk (SD). From the velocity response with disk B for different RPM, we saw that the slider strongly oscillates if the disk velocity is less than 20.6 m/s. Fig. 6 shows the frequency domain data of single SD velocity time captures from 12 to 22.3 m/s (increasing air-bearing resonant amplitudes as RPM decreases). Even at 20.6 m/s, the bursts in the velocity history indicate that the slider did not steadily fly over disk B. In fact, the velocity output of the LDV is much better than the displacement output in detecting this kind of small bursts. Similarly, below 20.6 m/s there were very strong AE signals, which saturated our data acquisition system even with a very low amplifier gain, and high friction values were also recorded. From both the \u201cspin-down\u201d flyability test and the measurement of the time histories of the velocity of the slider flying with disk A (SD) for disk RPM ranging from 10.3 to 17.2 m/s, it was observed that the slider could steadily fly with disk A at and above 12 m/s. Fig. 7 shows the frequency domain of SD of a single time capture with the same scaling as in Fig. 6. The air-bearing resonance at 12 m/s, which results in a large FH variation, can be seen. We measured the responses of all three sliders mentioned previously, and they all showed very similar phenomena. During the experiment, we found the strong oscillations of the slider are not very repeatable, therefore they cannot be easily observed in the time domain with the trigger. If the air-bearing resonance is not clear in the time averaged frequency domain but appears strongly in the frequency averaged data, then the excitation of the air-bearing is nonrepeatable"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003502_095440904322804439-Figure15-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003502_095440904322804439-Figure15-1.png",
+        "caption": "Fig. 15 The three different wheelsets analysed with the FEM model",
+        "texts": [
+            " An elastic\u00b1plastic material behaviour (and therefore the actual stress\u00b1strain diagram) could also be considered with this model, but the corresponding results differ very little from those obtained from the linear elastic hypothesis; the plastic zones are in fact present only for high interference values, but they are always very small and located at the wheel seat chamfer, with a negligible effect on the press-\u00aet curve. All the analyses for the press-\u00aet curve determination have therefore been carried out under the linear elastic hypothesis. Three different wheelsets have been examined, named Sao Paolo, United Kingdom and Fiat Ferroviaria, shown in Fig. 15. For each wheelset, a range of possible interferences has been considered, due to the machining tolerance of the axle and wheel. The press-\u00aet operation was simulated constraining one end of the axle in its longitudinal direction and applying a displacement at the wheel, as shown in Fig. 16. The sum of the reaction loads at the constrained end represents the press-\u00aet load, whose value is expected to increase with the wheel displacement, due to the increasing friction-resistant load. Proc. Instn Mech"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003657_j.cma.2005.02.033-Figure10-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003657_j.cma.2005.02.033-Figure10-1.png",
+        "caption": "Fig. 10. 3-DOF RPR planar parallel robot.",
+        "texts": [
+            " For 12 s of simulated mechanism motion, the solution time for the indirect coordinate equations is reduced to less than half the time required to solve the equivalent joint coordinate equations. The time required to formulate the motion equations is also reduced when indirect coordinates are used. Note that the formulation time is less important than the solution time since, in a symbolic approach such as this, the equations are only formulated once prior to subsequent simulations\u2014 unlike in a numerical approach where the equations are re-assembled at each time step of a forward dynamic simulation. The two-dimensional, 3-DOF parallel robot shown in Fig. 10 has three revolute-prismatic-revolute chains acting in parallel on the end effector, body 7. The three chains are driven by rotational motors at joints A, B, and C. This configuration is known [17] as the 3-RPR planar parallel mechanism (PPM), where the underlined letter indicates which joint is driven in each kinematic chain. The linear graph of the 3-DOF parallel robot is shown in Fig. 11. A planar joint pl28, which allows 2 translational and 1 rotational DOF, has been added so that the end-effector variables can be included directly in the dynamic equations"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000482_39.666569-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000482_39.666569-Figure2-1.png",
+        "caption": "Figure 2. The da-qa frame",
+        "texts": [
+            " 1, the IEEE Power Engineering Review, May 1998 63 point A has a low PF. It is possible to improve this PF, maintaining the same active power, by moving the pointA to B location (optimal PF). In this case, the magnetization current is reduced (I@ < I@). The stator current is then reduced leading to copper losses decrease (i2t). Moreover, magnetization current decrease leads also to iron loss decrease. Finally, loss balance can be obtained approximately leading then to a maximum efficiency. Optimization Algorithm: According to Figure 2, the PF is expressed in the d-q frame by In the da-qa frame, it becomes The following relationship is then deduced. Isdc = \u2018qa \u2018g9-I (3) Therefore, the PF optimal value is reached when equation cp = \u2018pa is (4) Going back to the d-q frame leads to the basic equation of the opti- insured. In this case, (3) could be replaced by I,, = K,Isq,; KO = tgcp-\u2019 mization algorithm (\u2019control variable). where is called the e~ciency-optimizationfactor (EOF). As it is shown by (6), one main advantage of the proposed method is that it is insensitive to parameter variations contrary to the loss-minimization factor (LMF) presented in [3]"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001280_0022-0728(94)03651-i-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001280_0022-0728(94)03651-i-Figure4-1.png",
+        "caption": "Fig. 4. Cyclic voltammograms obtained with a Pf-CP(BQ)E in (A) the base solution of pH 7.0 and (B) a solution containing 10 mM nicotinic acid. Scan rate, 2 mV s 1.",
+        "texts": [
+            " The effectiveness of the compounds as mediators may depend on such factors as their reactivity with the enzyme in the bacterial membranes and the permeability of the membranes to the compounds. Since BQ is as effective as PMS as the mediator and is more stable than PMS, we used BQ as the mediator in the following experiments. Dialysis-membrane-covered Pf-modified CPEs containing BQ (Pf-CP(BQ)Es) were prepared in a similar manner to that reported [18] for the preparat ion of enzyme-modified CPEs containing BQ. Pf-CP(BQ)Es containing 3% w / w BQ were used unless stated otherwise. Fig. 4 shows cyclic vol tammograms recorded with a Pf-CP(BQ)E in (A) the base solution and (B) the base solution containing 10 mM nicotinic acid. The Pf-CP(BQ)E produced cathodic and anodic waves starting from +0.04 V and +0.15 V respectively in the base solution, which are attributable to the redox reaction of BQ entrapped in the immobilized Pf layer between the electrode and the dialysis membrane as was confirmed previously in the case of a CPE containing BQ with immobilized oxidoreductase behind a dialysis membrane [19]"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003534_j.talanta.2006.08.037-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003534_j.talanta.2006.08.037-Figure4-1.png",
+        "caption": "Fig. 4. Chemiluminescence response from the reaction of manganese(IV) ( ( o",
+        "texts": [
+            " The se of 3 mol L\u22121 formaldehyde produced the greatest chemiluinescence response above the background: a 500-fold increase n signal intensity (Fig. 3) compared to responses obtained when nalyte and carrier solutions contained no formaldehyde. Yet, espite this notable enhancement in manganese(IV) chemiluinescence intensity, the reactions were still not visible to the aked eye in a darkened room. An increase in both signal and background intensity was also bserved using higher orthophosphoric acid concentrations to ilute the stock manganese(IV) solution (Fig. 4). For example, he use of 6 mol L\u22121 orthophosphoric acid gave approximately 12-fold increase in signal (compared to the 3 mol L\u22121 diluion used in previous chemiluminescence studies [1\u201311]), and he reagent remained stable for over 4 months without preciptating. These improvements in chemiluminescence response nd reagent stability are possibly due to the stabilising effect f orthophosphoric acid on the manganese dioxide particles in olution via adsorption to the particle\u2019s surface [15,19]. Howver, concentrations above 3 mol L\u22121 orthophosphoric acid were enerally avoided due to the viscosity of the solutions and the arge increases in background signal, which compromised low evel detection"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002168_s0039-9140(03)00075-4-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002168_s0039-9140(03)00075-4-Figure1-1.png",
+        "caption": "Fig. 1. (A) Scheme of the flow cell used in the measurements (see test for description); (B) Picture of the flow cell placed into the sample compartment of the luminometer. (a) Stainless steel piece; (b) y; (c) inlet and outlet; (d) methacrylate piece; (e) optical fiber.",
+        "texts": [
+            "1 ml of a phosphate buffer solution contain- ing 20 mg of acrylamide, 4 mg of bis-acrylamide and 8 mg of ammonium persulphate (as a reaction precursor) were mixed with 0.1 ml of the GOx-FS solution. Dissolved oxygen was eliminated by bubbling nitrogen through the solution. The cocktail was spread on a 0.5 mm hollow made in a glass film (20 /9 /0.1 mm), covered with a Mylar film and a glass film, and irradiated with the UV-lamp (254 nm) for 50 min. The film was then stored in the phosphate buffer solution at 4 8C. The flow cell was designed in our laboratory (Fig. 1A). The main part of the cell (a) was a stainless steel piece (2 /2.5 /2 cm) with a hollow (0.5 /1.5 /0.3 cm) in which the sensor film (b) is fixed with a holed Mylar film (c). The flow cell was covered with a methacrylate piece (d) containing two stainless steel tubes (2 mm, outer diameter) for circulation of the fluid in the cell; the space between tubes was just wide enough for the optical fiber termination (Fig. 1B). Pieces (a) and (d) were joined by means of four screws and a silicon washer (e) to avoid fluid loss. The sensor had a 225 ml capacity. The phosphate buffer solution flowed across the flow cell at 0.7 ml min 1 and the fluorescence intensity began to be monitored at lexc /490 and lem /520 nm (I0 being the initial fluorescence intensity of the film). Three hundred microlitres of the sample (or glucose standard solution) were injected and a transient signal obtained, Imax being the fluorescence intensity at the maximum",
+            " 2A shows how the fluorescence intensity of the sensor changes when the flow-cell is fed in a continuous mode with solutions of different glucose concen- tration; as the glucose concentration increases the rate of the intensity variation with time increases but the maximum intensity changes very slightly; if a random time t is considered after the beginning of the glucose feed and before the maximum is reached, the intensity at this time (It) changes with the glucose concentration. When glucose solutions are injected in FIA mode (discrete sample volume) two opposite effects take place: (1) the increase in fluorescence intensity due to the enzymatic reaction; and (2) the decrease in intensity due to dilution of glucose and regeneration of the enzyme. These opposite effects give a FIA-like peak in which the analytical parameters described in Section 2.6, change with glucose concentration (Fig. 2B). Prior to the system shown in Fig. 1, two other flow cell systems were designed. Firstly, a system (Fig. 3A) consisting of a methacrylate piece (a; 7.7 /5 /0.4 cm) with a central hollow (b; 1.1 / 0.5 /0.5 cm; 275 ml volume) and two lateral orifices (c and d; 0.5 mm diameter) for sample inlet and outlet. Two Mylar films (e, f) fixed with silicone closed the central hollow; the rear film (e) contained the polyacrylamide-GOx-FS sensor film (g). Finally, a reflecting mirror (h) was fixed to the back part of the system to increase the optical path-length"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001511_978-1-4612-1416-8_9-Figure9.2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001511_978-1-4612-1416-8_9-Figure9.2-1.png",
+        "caption": "FIGURE 9.2. (a) Controlled planar body with a pendulum attachment; (b) Controlled pla nar body with an extending pendulum attachment. The length of the extensible pendulum is ax, where x is the x-coordinate of the hinge point connecting the two bodies.",
+        "texts": [
+            " The nonvanishing of the curvatures associated with both the 3 x 3 inertia tensor of the unreduced system and the 2 x 2 inertia tensor of the reduced system imply that there is no change of coordinates such that the dynamical dependence on input accelerations is eliminated and the dynamics of the configuration variables \u00a2 and 1/1 are also decoupled. Whether one can simply eliminate the input accelerations by a choice of coordinates in which there is inertial coupling of the \u00a2 and 1/1 dynamics remains for the moment an open question. Example 9.3.2 (Controlled planar body with pendulum attachment) Here we consider a pair of rigid bodies which are connected by a simple frictionless single degree-of-freedom hinge as illustrated in Figure 9.2(a). One of the bodies (the larger one depicted in the figure) is assumed to have actuators allowing its motion in the plane to be controlled to follow any prescribed smooth path. No actuation is applied directly to the pendulum, and hence it moves entirely under the influence of gravity and motion of the controlled body. Take as generalized coordinates for the system x (the horizontal displacement of the large body), y (the vertical displacement of the large body), and e (the angular displacement ofthe pendulum from the vertical, downward pointing configuration)",
+            " It is also easy to verify that the vanishing conditions of Theorem 9.3.1 are satisfied. Indeed, the reduced inertia tensor, M = h, is a scalar, and hence the Riemannian curvature is trivially zero. The input connection f li}, i, j = 1,2 is zero, and hence the input curvature is also zero. Example 9.3.3 (Controlled planar body coupled with extending pendulum at tachment) The concluding example treats another system for which the curvature vanishing conditions of Theorem 9.3.1 are not satisfied. The mechanism depicted in Figure 9.2(b) is similar to the previous example, with the significant difference being that we assume there is an internal mechanism which causes the length of the pendulum attachment to depend on the x-coordinate of the body. Specifically, we assume the length of the pendulum is ax, where a > 0 is some fixed constant. We assume again that the pendulum is attached by a frictionless hinge. To simplify the discussion (and with no loss of generality) we idealize the model so that the pendulum is comprised of a point mass mb and a massless linkage between the point mass and hinge"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003893_0301-679x(83)90004-x-Figure10-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003893_0301-679x(83)90004-x-Figure10-1.png",
+        "caption": "Fig 10 Universal joint with rubber-metal laminated bushings",
+        "texts": [
+            " A typical joint has two yokes attached to the shafts to be connected and a spider with four trunnions, each pair of the trunnions rotationally engaged with its respective yoke and the axes of two pairs in one plane and orthogonal. Both sliding and rolling friction bearings are used in universal joints, and for both types their use in these joints is one of the most trying possible applications because of the oscillatory character of the motion. Again, the application of thin-layered rubber-metal laminates for U-joint yoke bearings (Fig 10) ~l seems to be a logical solution of the problem. Detailed calculations have shown that using the types of laminates discussed in the first part of this paper, with one-layer thickness of 0.01-0.1 mm, only a small fraction of the load-supporting area of the trunnion is needed for transmission of the rated load for a given size of the joint. Reduction of this area greatly reduces the shear stiffness of the laminated bearings. The greatest advantages of universal joints with rubber laminated bearings are: elimination of lubrication and sealing devices; elimination of wear and backlash in the connection; very substantial attenuation of radial forces and/or vibrational excitations transmitted through the connection"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002374_naecon.1994.332886-Figure12-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002374_naecon.1994.332886-Figure12-1.png",
+        "caption": "Figure 12",
+        "texts": [
+            " AIRCRAFT SPOILER (1988 - ) This prototype subsystem was built specifically for use in a commuter aircraft spoiler actuation application. It was designed with assistance from the aircraft manufacturer to fit the aircraft envelope. Extensive bench testing was performed on the EMA in a simulated aircraft installation with al l performance criteria successfully verified. The use of 270 VDC allowed lower current levels and higher reliability switching devices. A photograph of this EMA i s shown in Figure 12. 1343 SYSTEM ADVANCES - Brushless DC motor, 270 VDC power supply DIGITAL MISSLE CONTROL (1990-) This prototype subsystem was designed to accomplish steering of a missile system. This EMA incorporated a microprocessor driven control system which allowed fault management. The overall subsystem predicted reliability was increased along with heat management. SYSTEM ADVANCES - Digital control, MIL-STD1553 data bus interface, digital slaving. LARGE AIRCRAFT AILERON (1990-) This long term development program includes several phases of development ranging from feasibility studies to fabrication of flight quality demonstrators"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003704_robot.2003.1241965-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003704_robot.2003.1241965-Figure1-1.png",
+        "caption": "Figure 1: Model of compass-like biped robot",
+        "texts": [
+            " The potential energy in walking down the slope changes the robot\u2019s kinetic energy. The robot loses energy when the swing leg contacts the ground. In the c a e of stable gait, it keeps a balance between the energy lost at the ground impact and the energy s u p plied by potential energy. In this study, the stability and dynamics around the fixed point before and af - ter period-doubling bifurcation are investigated. Especially, we focus on the stored energy of the robot and the rate of change of this energy 2 Compass-like Biped Model Figure 1 shows the model of compass-like biped robot. In this figure, m is the mass of each leg. 1 is the leg length, and a is the distance from the tip 0-7803-7736-2/03/$17.00 02003 IEEE 2478 of leg to the center of mass of it. I is the moment of inertia about its center of mass. 8,, and Os, are the angles of stance leg and swing leg with respect to the horizon respectively. a is the inter-leg angle. y is the angle of slope. The gait consists of the swing phase and the transition phase. During the swing phase, the contact point +of stance leg is not off at any time"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001419_robot.1991.131938-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001419_robot.1991.131938-Figure5-1.png",
+        "caption": "Fig. 5 : First Method to Select a Support Trajectory of Circling Gaits.",
+        "texts": [
+            " Since the crab walking gait is a special case of circling gaits, the four wave-circling gaits should possess a similar feature. In other words, for a given turning center, if the stabilit,y margin at, ,B = 3/4 is zero, it should be more stable when /3 > 3/4. Based on this inference, two st,rat,egies for the selection of support trajectories are developed. The distinguishing feature of the first, strategy is that the support trajectories of the four legs pa.ss through their workspace centers. Referring to Fig. 5 . since the largest leg angular stroke 91 is less than the largest leg stroke + 4 , leg 1 has less adjusta.bility and the support trajectory of leg 1 is selected first. As shown in Fig. 5 , the middle portion of 91, the solid arc Tis;, is chosen to be the support trajectory of leg 1. At the moment right before leg 2 is placed, leg 1 is a t the position of Ml. In order t o have a zero stability margin a t this moment, leg 4 should be a t the position of M4, which is the intersection of the straight line passing through M1 and the gravity center with the circular path of leg 4. By using M4 as a reference point, the support trajectory of leg 4 can be selected, as shown in Fig. 5 . I t is possible that the selected support trajectory of leg 4 is outside the workspace of leg 4 or that the straight line M ~ M I and the circular path of leg 4 do not intersect. Under these circumstances, the turning gait is considered to be unstable. Similarly, we can select the support trajectories of leg 2 and leg 3. This strategy can be also applied to +y type, - z type and --y type wave-circling gaits. In the second strategy, the two support trajectories with larger available leg angular strokes do not necessarily pass through their workspace centers"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002374_naecon.1994.332886-Figure3-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002374_naecon.1994.332886-Figure3-1.png",
+        "caption": "Figure 3",
+        "texts": [
+            " Flow direction and rate is accomplished through the positioning of variable angle swashplate. The positioning of the swashplate i s governed by an internal control loop which receives the control error input, measures swashplate position and produces control flow to one of two stroke control pistons. An integral fixed displacement boost pump, used to supply control flow and maintain minimum actuator pressure can also be used. Maximum discharge pressure capability of the servopump has been well proven at 5000 psi. A schematic of the servopump is shown in Figure 3. ELECTRIC MOTOR - Since the servo control of the lAPTM i s performed within the servopump detailed above, the only requirement for the electric motor i s to rotate the servopump at a fixed speed and direction. This requirement can be accomplished with either AC or DC motors. The preferred choice i s AC as this provides a simpler, more readily available design. In addition, AC power minimizes EM1 generation and it's possible degradation of control signalling. In an aircraft system where DC motors are preferred, the lAPTM can be configured with a brushless DC motor and motor controller designed to maintain a relatively fixed speed"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000497_a:1008966218715-Figure9-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000497_a:1008966218715-Figure9-1.png",
+        "caption": "Figure 9. The field of view, the clustered regions and the obstacle regions.",
+        "texts": [
+            " After updating the parameters of the associated obstacle regions by using the corresponding clustered regions, we now move on to delete the obstacle regions that are in the field of view and not associated with any of the clustered regions. The field of view is the scanning range of the laser scanner where the distance of view depends on whether a clustered region Ri exists in the direction of view. If Ri exists in the direction of view, then the distance of view is the distance up to Ri . Otherwise, it stretches up to the detection limit of the active circle dc. An example of the field of view is shown in Fig. 9. As shown in Fig. 9, the obstacle regions M3 and M4 are located in the field of view and they are not associated with any of Ri \u2019s. Consequently, they must have been moved to another location and must be deleted from the map. The obstacle regions M1 and M2 are not associated with any of Ri \u2019s either, but they are not deleted from the map because they are outside of the field of view. In other words, we do not know whether M1 or M2 has been moved or not, because they have not been currently detected. The obstacle region M7 is associated with R4, but it is not updated because part of it is located outside of the field of view",
+            " The angle interval of Mk is the interval of directions along which the laser range finder detects the obstacles in Mk . As shown in Fig. 10, the angle interval is determined from the major eigenvector of Mk . Its major eigenvector is described as e\u0304k \u2212 s\u0304k , where e\u0304k and s\u0304k represent its start and end positions in the sensor coordinate frame. The angle interval of Mk is then determined as [6 s\u0304k, 6 e\u0304k], where s\u0304k = m\u0304k + \u03bb\u03041k \u03c6\u0304k \u2212 pc, e\u0304k = m\u0304k \u2212 \u03bb\u03041k \u03c6\u0304k \u2212 pc, and pc is the center position of the mobile robot. As shown in Fig. 9, the angle intervals of the obstacle regions such as M1 and M7 range outside of [0, 270] and their parameters remain unchanged. On the other hand, the angle interval of R1 fully covers that of M2 and the distance of M2 is longer than the that of R1. Consequently, M2 is located behind R1 and its parameters remain unchanged. Finally, if Ri is not associated with any of the existing Mk\u2019s, then a new obstacle region is created with Ri and is included in the map. For example, R2 in Fig. 9 is not associated with any of Mk\u2019s, and a new obstacle region is created with R2. The object position p j determined from dead reckoning and measured distance value l j is bound to have uncertainty, which may cause mismatch between the map and the real environment. In general, there are two types of uncertainty sources: one is the noise inherent in the measured data, and the other is the mechanical aspects of the mobile robot such as slippage and upsetting events. The gaussian random noise inherent in the object position p j is essentially cancelled out in the presented algorithm because all of the object positions included in the same clustered region Ri are averaged to determine the stochastic parameters of Ri "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001850_jsen.2003.814649-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001850_jsen.2003.814649-Figure2-1.png",
+        "caption": "Fig. 2. Photo image of fabricated three electrode cell for glucose and its cross section view. (a) Photo image. (b) Cross section view.",
+        "texts": [
+            " A Conventional Ag/AgCl (3 M KCl) electrode was used as a reference electrode during the potential measurements and the electro-deposition of platinum and enzyme layers. Electrochemical measurements were carried out in PBS (phosphate buffered saline) solution containing 0.1 M Na HPO , 0.15 M NaCl, and 0.1 g/l NaN (pH 7.4). Potentials were measured under open-circuit condition. Performance evaluation of the glucose sensors was carried out with the on-chip plasma-treated Ag/AgCl reference electrode without any additional electrode. Fig. 2 shows the photo image and its cross section diagram of fabricated sensor array. The order of the electrode placement was, from the center, working, counter, and reference electrodes. Uncompensated solution resistance can be minimized if the reference electrode is positioned to the nearest of working electrode. However, in this paper, it was placed at the outside of the counter electrode to avoid the electrical short to the working electrode due to the dissolved silver ions. The area of working, counter, and reference electrode was 0"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003734_ip-b:19830027-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003734_ip-b:19830027-Figure4-1.png",
+        "caption": "Fig. 4 Explanation of slip derivation (eqn. 7)",
+        "texts": [
+            " If the rotor moves in a helical fashion, then the slip of the rotor related to the kl harmonic of the magnetic field is expressed by the equation ktt \" vxk vzli (7) i l k where vx and vz are rotor speeds in the x-and z-directions and vxk = \u2014 2rxfe/and vzU = \u2014 2Te/,/are speeds of the kl harmonic in the x- and z-directions. Eqn. 7 can be derived in two different ways. One of them, given in Reference 1, is as follows: If the rotor moves with asynchronous speed in relation to the kith field harmonic, it means that the field of kith harmonic varies for each point on the rotor surface. Thus, for the moving point P[Xi(t), zt(t)] on the rotor surface (Fig. 4), we have: JSz(t,X,z) = (6) ^ i , z i ) = 5mWexp / \\tot+ \u2014 xt +\u2014 zx [ \\ Txk Tzl = variable (8) IEEPROC, Vol. 130, Pt. B, No. 3, MA Y1983 187 Hence u>t n H (9) where a(t) is the angle between point P and the wavefront of the kith harmonic. Differentiating each side of eqn. 9, we obtain: CO + Vx+ Vz = Txk Tzl (10) where vx, vz are the rotary and linear rotor speeds, respectively, and dt is the angular speed of point P in relation to the kith field harmonic. Similarly, as in the theory of conventional induction motors, we can write Thus, from eqns"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002362_itsc.2003.1252673-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002362_itsc.2003.1252673-Figure4-1.png",
+        "caption": "Figure 4 Reference point of vehicle",
+        "texts": [
+            " Since this procedure isreversible thus it can be applied in parallel parking problem Furthermore, this procedure is simplified the steering angles to the minimum radius condition. Effectively, according to the vehicle steering scenario described at the former kction two identical circles with tangent point can be formed. For example, a vehicle moves backward from A to B following a path formed by two circular arcs tangentially connected to each other. Supposing B i s parking bay and A is starting position, thereby parallel parking is achieved (see figure 4). The locations of circle center are depending on the detected parking space and the lateral displacement from the aside car. There are several conditions have to fulfill in order to have a collision-free motion (see figure 5) : 1. The length L must be larger than radius of the circle C,. . 2. Thecar mustatacomect position when begin to parking. The right position is determined by AxandAy. 3. The tuning point AT is depending on different value of Ax and hY. In our methodology the vehicle is always track to the tangential circles"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003008_1.1757488-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003008_1.1757488-Figure4-1.png",
+        "caption": "Fig. 4 Twist disclination loop of radius a0 coaxial to a cylinder. Distribution of virtual twist disclination loops is shown on cylinder surface.",
+        "texts": [
+            "u z5h r5a0 1 2h a0 J**~1,1;1 !u z5h r5a0 1 2h2 a0 2 J**~1,1;2 !u z5h r5a0D G , (34) where rcore is the core cutoff radius of the loop. The first term in Eq. ~34! is the energy of the prismatic dislocation loop in an infinite medium and the second term is the interaction energy between the prismatic loop and the free surface. 4.3 Twist Disclination Loop Coaxial to a Circular Cylinder. Consider a twist disclination loop of radius a0 placed coaxially in an infinitely long elastic circular cylinder of radius r0 as shown in Fig. 4; the coordinates of the loop center are ~0,0,0!. On the free surface of the cylinder, the following boundary conditions for the stress field must be fulfilled: sr jur5r0 50, j5r ,w ,z . (35) The twist disclination loop has the stress component srw ~see Eqs. ~10!! contributing to the conditions Eqs. ~35!. We present the resulting field of the twist disclination loop in the cylinder in the form of Eqs. ~15!. The additional field ipi j is produced by the virtual twist loops distributed in the manner shown in Fig. 4. All virtual loops have the same radius r0 . Then the boundary conditions Eqs. ~35! can be rewritten in terms of the distribution function f (z0) of the virtual twist disclination loops: Transactions of the ASME 16 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F 2 Gv 2 sgn~z !J~2,2;1 !ur5r0 1E 2` ` f ~z0!F2 Gv 2 sgn~z 2z0!E 0 ` J2~k!J2~k!expF2 uz2z0u r0 kGkdkGdz050. (36) Applying the Fourier transformation to Eq. ~36!, one can find the Fourier transform of the distribution function f\u0302 "
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002455_j.precisioneng.2004.03.003-Figure9-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002455_j.precisioneng.2004.03.003-Figure9-1.png",
+        "caption": "Fig. 9. Structure of experimental apparatus for measuring NRRO.",
+        "texts": [
+            " Additionally, in the case of the same value of mutual diameter differences of balls, a larger number of balls makes the fc component smaller. However, if the mutual diameter differences of balls are minified by 0.01 m, the contributing ratio to reduce the expected value of the fc component is 20% for Z = 8 and 17\u201318% for Z = 10. Here, the contributing ratio is defined as the diminution of the expected value of fc component divided by the diminution of the mutual diameter differences of balls in a production lot. Fig. 9 shows an experimental apparatus for investigating the influence of location of balls on the fc component [2]. As the NRRO measuring device methods for single ball bearing, the following techniques are reported. The first is a measurement technique of radial runout of the spindle axis which is constructed by the rolling bearing to be measured and another rolling bearing [9,10]. The second is an imitative technique of the revolution error measurement method for rolling bearings described in JIS B 1515, using aerostatic Oldham coupling [11]"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000481_j.1470-8744.1999.tb01149.x-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000481_j.1470-8744.1999.tb01149.x-Figure1-1.png",
+        "caption": "Figure 1 Schematic design of the BChE\u2013ChO sensor",
+        "texts": [
+            " After removal of the membrane, the solution was added to a mixture consisting of a 4-aminoantipyrine} Labels : a, platinum wire ; b, glass ; c, Teflon cap ; d, HEMA\u2013VCA membrane. phenol}peroxidase mixture ; the activity was calculated from the A500 value. Free BChE activity was determined spectrophotometrically by using a kinetic method that followed the increase in A405 due to 5-thio-2-nitrobenzoate produced by the reaction between 0.4 mM 5,5\u00ab-dithiobis-(2-nitrobenzoic acid) and thiocholine formed in the enzymic hydrolysis of butyrylthiocholine iodide [0.335 mM in phosphate buffer (pH 7.0)]. As shown in Figure 1, the amperometric transducer consisted of a platinum wire (0.5 mm diameter) sealed in a glass tube (5 mm diameter) and polished with alumina powder to ensure a flat surface. The HEMA\u2013VCA membrane containing the two immobilized enzymes was placed on the flat electrode surface and fixed with a Teflon cap having a 3 mm hole. The good mechanical properties of the wet membranes and the fixing system used allowed their easy replacement and also the possibility of using them again. When not in use the membranes were stored at 4 \u00b0C in a suitable buffer or in the dry state"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001305_0924-0136(94)01333-v-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001305_0924-0136(94)01333-v-Figure1-1.png",
+        "caption": "Fig. 1. The shape of the panels in the present study (dimensions: mm).",
+        "texts": [
+            " (i) Can the tensile behaviour of the virgin material be used for prediction of the yield strength of a panel pressed in the same material? (ii) What does replacement of a mild steel sheet by a high strength steel sheet mean in terms of strain level in the panel? (iii) How can the stiffness of the panel be characterized? (iv) On what does the dent resistance of the panel depend? The present investigation has been carried out in order to answer the above questions. The panels pressed in this study are a small-size version of the roof panel of an existing car body and are double-curved, Fig. 1. The yield strength of the panel is to be determined at its centre by the drawing of tensile specimen cut at 0 \u00b0, 45 \u00b0 and 90 \u00b0 to the original rolling direction, whilst the 0924-0136/95/$09.50 \u00a9 1995 Elsevier Science S.A. All rights reserved. SSDI 0 9 2 4 - 0 1 3 6 ( 9 4 ) 0 1 3 3 3 - V stiftness of the panel at its centre is to be measured using a flat-headed punch with a diameter 100 mm. The dent depth is to be measured at the centre of the panel also, in this test a hemispherical punch with a diameter of 100 mm being used",
+            " Asnafi / Journal of Materials Processing Technology 49 (1995) 13-31 15 and ~2 = [ 1 2 ( 1 - v2)] 1/2 ~2 ( R ) , (5) where R is the radius of the sphere, P is the concentrated load at the apex, E is Young's modulus, t is the shell thickness, v is Poisson's ratio and ~ is the angle between the centre and the edge of the sphere. Furthermore in this figure, ~5 is the deflection at the apex. Note that 22 in Eq. (5) and Fig. 2 is a measure of how large the shell segment is! The greater the value of ~, the larger is the sphere segment. a spherical shell. Depending on which side of the rectangle is used in the approximation, different values of ~2 are obtained: see Fig. 3 and compare it with Fig. 1! Combining Eqs. (2), (3) and (4) p . ~ P - 2 ~ E t a (6) The maximum load that will be used in the stiffness tests is 125 N. Substituting into Eq. (6) this value, the nominal values of R1 and R2 (Fig. 1), E = 20.104 N/mm 2 and t = 0.7 mm, P* = 0.334. which gives the encircled zone in Fig. 2, applicable in the present approximated case. Knowing the different values of 2 2 (Fig. 3), the applicable load~leflect ion zone in the present approximated case, (Fig. 2), and the shape of the load-deflect ion curve in this zone, it is assumed that over this interval and for the present panel p , = C(6/t) m (7) N. Asnafi / Journal of Materials Processing Technology 49 (1995) 13-31 17 in which C and m are different constants"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001553_s0045-7825(99)00329-1-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001553_s0045-7825(99)00329-1-Figure2-1.png",
+        "caption": "Fig. 2. Illustration of line of singularities and two branches of generated surface.",
+        "texts": [
+            " ; 3) are formed by respective elements of matrix A. The simultaneous equality to zero of the three determinants represented above means D2 1 D2 2 D2 3 0; 10 that yields the following equation F2h ut;wt;wh 0: 11 Step 3: The sought for limiting line Lh on surface Rh is determined as follows: rh rh ut;wt ; f2h ut;wt;wh 0; F2h ut;wt;wh 0: 12 Step 4: Using the coordinate transformation from Sh to S2, we may determine E2, the line of singularities on worm-gear tooth surface R2. Singularities of R2 can be avoided by limitation of dimensions of R2. Fig. 2 shows line E2 of singularities on surface R2 that is simultaneously the envelope to contact lines on R2 and the edge of regression; E2 is the common line of two branches of R2 as well. Note: It was mentioned above that for determination of F2h 0 (see Eq. (11)) it is necessary to use Eq. (10) as the requirement of equality to zero of three determinants: D1, D2, and D3. In most cases, it is suf\u00aecient to require equality to zero only of one of the three determinants (to derive F2h 0). The equality to zero of two remaining determinants will be in agreement with F2h 0 as well"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000619_1.2832484-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000619_1.2832484-Figure2-1.png",
+        "caption": "Fig. 2 The coordinate system and the sign convention of the journal forces",
+        "texts": [
+            " For a given journal speed, the pressure p and the bearing lubricant film thickness h are functions of the journal position and the rate of change of position. The pressure and the film thickness can be expanded in Taylor's series to the first order as follows: P = Po + Px^x + pAx + PyAy -t- p^y ( l a ) h ~ ho + h^x + hAx + hyAy + h^y ( lb) where the subscript \" 0 \" denotes the equilibrium position, ( );i represents a partial derivative with respect to the x perturbation, ( )i is a partial derivative with respect to the x perturbation, and similarly for y and y. With the coordinate system shown in Fig. 2, the bearing stiffness and damping coefficients are obtained in terms of the pressure perturbations as (Peng and Carpino, 1993): Contributed by the Tribology Division for publication in the JOURNAL OF TRIBOUOGY. Manuscript received by the Tribology Division February 29, 1996; revised manuscript received May 17, 1996, Associate Technical Editor: D. E. Brewe. Kyx ^j'j'J J-LnJoi \\_Px cos 9 Py cos 9 sin 6 Py sin 6 Rd9dz (2a) Journal of Tribology JANUARY 1997, Vol. 1 1 9 / 8 5 Copyright \u00a9 1997 by ASME Downloaded From: http://tribology"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003341_bf01213545-Figure8-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003341_bf01213545-Figure8-1.png",
+        "caption": "Fig. 8. Variation of T with 7~3 for different values of",
+        "texts": [
+            " C is found to be quite high for viscous fluid compared with couple stress fluid of the same viscosity for a given value of ~1. C decreases for increasing values of B. Figure 7, contains the graphs showing the variation of C with A for fixed value of #1 --~ 7.65 \u2022 10 _5 and B = 0.5 for different values of u C decreases for increase in Y values, which indicates the suitability of couple stress fluid as efficient lubricant. Porous slider bearing with couple stress fluid 109 110 N. M. Bujurke, H. P. Patil, and S. G. Bh~vi Porous slider bearing with couple stress fluid 111 In Fig. 8, the variation of squeeze film time is shown for different values of couple stress fluid parameters. The squeezing t ime of the step bearing with couple stress fluid is longer t han tha t with a Newtonian fluid. This is a very desirable finding since longer squeeze film t ime results in a smaller co-efficient of friction and almost negligible rate of wear of the bearing. From Fig. 9, it is observed that approaching t ime increases when the porosity of the 112 N.M. Bujurke, H. P. Patti, and S. G"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001929_952470-Figure4-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001929_952470-Figure4-1.png",
+        "caption": "Fig. 4 (a) Rin holder; (b) ring guide; (c) load cell 9 normal oad measurement.",
+        "texts": [
+            " The speed range for this configuration was from 100 to 600 rpm. The pulley system could be reconfigurated in future experiments to a 1: 1 speed ratio for a range of 900 to 3600 rpm. The head of the engine was removed so that a reciprocating fixture could be mounted on the top of the piston. This fixture is guided by two linear bearings to minimize any lateral motion. The assembled recip~ocating fixture and ring holder fixture are shown in Fig. 2. The pieces of the ring holder fixture are shown in Fig. 3. The ring was mounted on a ring holder (Fig. 4a) which was allowed to slide in a ring guide (Fig. 4b) so that the ring was constrained laterally by the liner segment in front and the front surface of the ring guide at the back. A load cell was mounted at the interface between the ring holder and the ring guide (Fig. 4c) so that the normal force on the ring could be measured. The ring guide was connected to the reciprocating fixture by a pneumatically driven air cylinder so that the normal force exerted on the ring could be varied by varying the driving pressure. The rin,g radius could be adjusted to conform to the liner radius of Fig. Redprocator with dng (Only one of ll curvature by two set screws each of which was located at the side of the ring holder (Fig. 4a). two linear bearings is shown.) The liner segment was supported by a floatin,g holder mounted on a pair of linear bearings. The holder was connected by a load cell to the side plate which was fixed to the block of the Kohler engine. The load ceU wiis set up to measure the force component in the direction of the ring travel. At -mid stroke, two LIF probes were installed. The center of the probe volumes were at 81' crank angle from the TDC position. The fiber optics probes were ~nounted on the side plate and light was focused through the windows on the liner to the lubricating oil film ((Fig",
+            "12, in which the LIF signal (uncalibrated) and the normal and frictional forces are shown over 10 cycles. The cycle-to-cycle repeatability is better than 10%. The run-torun repeatability is of the same order. Normal Force Measurements An example of the normal force exerted by the air cylinder on the ring as measured by the load cell is shown in Fig.13a. The force was very repeatable from cycle to cycle but it was not uniform over a cycle. There was a consistent difference between the upstroke and the downstroke value. This non-uniform reading was traced back to the load cell arrangement (Fig. 4c): the load was only measured at the load cell \"button\" which was about 9 mm2 in area. There could be secondary contact points between the ring holder guide, which was driven by the air cylinder, and the ring holder. The variation in force reading could be due to the redistribution of forces at the contact points. The variation was especially pronounce at light loading and high rpm. Frictional Force Measurements A typical friction force measurement is shown in Fig. 13b. The signal was noisy and had been averaged over 10 cycles of data"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003845_3.9671-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003845_3.9671-Figure1-1.png",
+        "caption": "Fig. 1 Rod and tip weight before deformation.",
+        "texts": [
+            " 2) The matrices [M2]0, [ K 2 ] 0 , [ JT4]0, [K5]0, and [M2]0 are assembled as described in the text between Eqs. (20) and (24). 3) The matrices [KQ] and [M0] are assembled according to Eqs. (27). 4) The eigenvalue problem [Eq. (26)] is solved and the frequencies and mode shapes are obtained. Results and Discussion To check the accuracy of the model derived above, the theoretical results are compared in this section with existing experimental and other theoretical results.4'5 The case under consideration is shown in Fig. 1. A cantilevered rod is loaded transversely by a tip weight that causes a substantial deformation. Then, the deformed rod is excited in both the flatwise and edgewise directions (z and y, respectively) and the frequencies of the first natural mode in each direction is found. The experiments included changes in the tip weight magnitude and the load angle y (see Fig. 1). Two aluminum rods with identical rectangular cross sections but different lengths have been used. The rod properties are outlined in Table 1. In Ref. 2, the value for El was taken as that which made the theoretically predicted deflection match experiment for one specific load angle. This provided a structural base from which nonlinear effects as influenced by load angle changes could be assessed. It was not possible to determine EI^ directly from the static experiments, so its value was obtained by dividing EI^ by 16, based on a cross-sectional width-tothickness ratio of 4"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000726_s0043-1648(96)07463-7-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000726_s0043-1648(96)07463-7-Figure1-1.png",
+        "caption": "Fig. 1. Schematic diagram of rotary lip seal.",
+        "texts": [
+            " Furthermore, if a successful seal is reverse mounted (inverting the air and liquid sides), then the seal will leak excessively [6]. 7. A relatively new seal is bidirectional. However, if a seal has been run with the shaft rotation in one direction for a long period of time, then the seal will leak when the rotation is reversed. The above observations provide a basis on which a lip seal model can be constructed. Any prospective model should be capable of explaining all these observations. 2. Model Fig. 1 shows a schematic diagram of a typical lip seal, while Fig. 2 shows the region near the sealing zone, assuming Journal: WEA (Wear) Article: 7463 that the meniscus that separates the sealed liquid from the atmosphere is on the air side of the seal. The pressure P l on the liquid side of themeniscus is below atmospheric pressure, as a result of the action of surface tension forces, while the sealed pressure P s is assumed to be above atmospheric pressure. The flow field within the sealing zone can be thought of as the superposition of two flows",
+            " b axial width of seal E Young\u2019s modulus F cavitation index h film thickness h 0 average film thickness h 1 half-height of asperities h m film thickness at meniscus location hU dimensionless film thickness, h/h 1 hU 0 dimensionless average film thickness, h 0 /h 1 hU 1 dimensionless half-height of asperities, h 1 /b hU m dimensionless film thickness at meniscus location, h m /h 1 I 1 influence coefficient for normal (radial) deformation I 2 influence coefficient for shear (circumferential) deformation I m distance from air-side edge of sealing zone to meniscus, averaged over one wavelength in x direction, when meniscus is on air side of seal l U m dimensionless distance from air-side edge of sealing zone to meniscus, l m /h 1 N number of asperities across axial width of sealing zone P pressure P a ambient pressure P avg pressure averaged over one wavelength in x direction Journal: WEA (Wear) Article: 7463 P c cavitation pressure P contact contact pressure P s sealed pressure P l pressure on liquid side of meniscus PU dimensionless pressure for fluid mechanics analysis, (PyP c )/(mV/h 1 ) PUU dimensionless pressure for deformation analysis, P/E Q leakage rate per wavelength QU dimensionless leakage rate, Q/(lh E/m)2 1 R lip radius R m radius of curvature of meniscus RU dimensionless lip radius, R/b V surface speed of shaft V U dimensionless surface speed of shaft, mV/bE x circumferential coordinate xU dimensionless circumferential coordinate, x/l y axial coordinate y m axial location of meniscus, within sealing zone yU dimensionless axial coordinate, y/b Greek letters g U 6l/h 1 DyU distance between nodes in yU direction d circumferential displacement of lip surface dU dimensionless circumferential displacement of lip surface, d/l u lip angle (see Fig. 1) l wavelength of micro-geometry in x direction lU dimensionless wavelength, l/b m viscosity r density r liq density of the sealed liquid rU dimensionless density, r/r liq s surface tension sU dimensionless surface tension, s/h 1 E t shear stress tU dimensionless shear stress, t/E f dimensionless pressure in the liquid region, related to the dimensionless density in the cavitation region ( ) avg averaged over one wavelength in xU direction ( )i evaluated at ith node [1] R.F. Salant, Elastohydrodynamic model of the rotary lip seal, ASME J"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0002263_6.2003-5349-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0002263_6.2003-5349-Figure1-1.png",
+        "caption": "Fig. 1 Vario X-Treme helicopter",
+        "texts": [
+            " The second section presents the trimming results obtained for the Vario X-Treme model-scale helicopter followed by a stability analysis of the stabilizing bar impact on the helicopter dynamics. The third section focuses on the design and implementation of a forward flight control system for the Vario X-Treme helicopter, and presents the simulation results obtained with the full nonlinear dynamic model. The last section summarizes the contents of the paper and points out directions for future work. This section presents the dynamic model of a single main rotor and tail rotor helicopter equipped with a Bell-Hiller stabilizing bar, as the one depicted in Fig. 1. A comprehensive study of the helicopter dynamic model can be found in 3. For in depth coverage of helicopter flight dynamics, the reader is referred to Johnson7 and Padfield11. The dynamics of the helicopter can be described using a 6 DoF rigid body model driven by forces and moments that explicitly include the effects of the main rotor, Bell-Hiller stabilizing bar, tail rotor, fuselage, horizontal tailplane, and vertical fin. To derive the equations of motion, the following notation is required: {U} - universal coordinate frame; {CM} - body-fixed coordinate frame, with origin at the vehicle\u2019s centre of mass; p = [ x y z ]T - position of the vehicle\u2019s center of mass, expressed in {U}; \u03bb = [ \u03c6 \u03b8 \u03c8 ]T - Z-Y-X Euler angles that parametrize locally the orientation of the vehicle relative to {U}; v = [ u v w ]T - body-fixed linear velocity vector; \u03c9 = [ p q r ]T - body-fixed angular velocity vector"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003284_978-1-4899-7285-9-Figure1.18-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003284_978-1-4899-7285-9-Figure1.18-1.png",
+        "caption": "Figure 1.18. Comparison of the hodograph motion and the particle motion.",
+        "texts": [
+            " The velocity vector is tangent to the path traced by the position vector, and the acceleration is directed in the osculating plane toward the concave side of the path. In this section, we introduce a simpler kind of geometrical description for the velocity and acceleration that uses the velocity vector as the path writer. Imagine a fictitious particle PH whose \"position vector\" xH relative to an origin 0' is equal to the velocity vector of the particle P in the actual motion; and let us write v H = xH for the \"velocity\" of PH\u00b7 Then VH=a. (1.116a) (1.116b) The \"motion\" xH is called the hodograph motion; and the path !l'H traced by xH=v, as shown in Fig. 1.18b, is called the hodograph. In these terms, (1.116) Kinematics of a Particle 47 shows that the \"velocity\" v H in the hodograph motion, called the hodograph velocity, is equal to the acceleration in the actual motion. Hence, the acceleration in the particle motion always is tangent to the hodograph. This is to be compared with the intrinsic description of the actual motion in Fig. 1.18a. Some examples follow. Example 1.17. The velocity vector in a uniform motion of a particle is a constant vector v = v0 \u2022 Therefore, the hodograph is a point xH = v0 , constant. Notice from ( 1.116b) that the hodograph velocity is zero: v H =a = 0. D Example 1.18. If a particle has constant acceleration a # 0, the hodograph is a path described with constant velocity v H =a. The equation of the hodograph is obtained by integrating a= XH; We get XH = V =at+ C, where c is a constant vector. Hence, the hodograph is a straight line"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003241_tasc.2004.830317-Figure2-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003241_tasc.2004.830317-Figure2-1.png",
+        "caption": "Fig. 2. Squirrel cage rotor of the induction motor. (a) Conventional motor (b) HTS motor 1, 5: rotor core 2,6: short ring 3, 7: bar 4, 8: assembled rotor.",
+        "texts": [
+            " If it is too small, it will not recover from quench after starting. Two HTS tapes which were connected in parallel were used for one bar. Critical current of one HTS tape was 115 A at self field. To accommodate the flat HTS tape, shape of the slot of the HTS rotor should be different from that of the conventional motor. Cross section of the HTS rotor is given in Fig. 1. Figs. 1(a) and (b) show the cross section of straight part and the end part, respectively. Outer diameter and inner diameter of the HTS rotor were 78 mm and 22 mm, respectively. Fig. 2 shows the cage rotor of the conventional and the HTS motor. HTS tapes for the short bars are soldered to the HTS tapes for the short rings. Electrodynamometer was coupled to the motor to apply the load. Fig. 3 shows the test system, where the HTS motor, the electrodynamometer and the cryostat are shown. Electro-dynamometer was placed on the top flange of the cryostat. To simplify the cooling system of the HTS motor, whole motor including stator and rotor was put in the cryostat and immersed in liquid nitrogen"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003646_robot.2006.1642337-Figure5-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003646_robot.2006.1642337-Figure5-1.png",
+        "caption": "Fig. 5. Pan tilt unit has 2 D.O.F. and the depth as a virtual D.O.F.",
+        "texts": [
+            " \u00b7 \u201e j\u22121Q i=1 MiLj j\u22121Q i=1 fMj\u2212i \u00ab\u2013 dqj (39) Since j\u22121\u220f i=1 Mi n\u220f i=j Mi = n\u220f i=1 Mi we have dx\u2032 p = n\u2211 j=1 [( n\u220f i=1 Mixp n\u220f i=1 M\u0303n\u2212i+1 ) \u00b7 ( j\u22121\u220f i=1 MiLj j\u22121\u220f i=1 M\u0303j\u2212i )] dqj (40) Recall the equation (30) of the direct kinematics, since in (40) appears again x\u2032 p, we can replace (30) in (40) to get dx\u2032 p = n\u2211 j=1 [ x\u2032 p \u00b7 ( j\u22121\u220f i=1 MiLj j\u22121\u220f i=1 M\u0303j\u2212i )] dqj (41) If we define L\u2032 as function of L as follows L\u2032 j = j\u22121\u220f i=1 MiLj j\u22121\u220f i=1 M\u0303j\u2212i, (42) we get a very compact expression of differential kinematics. dx\u2032 p = n\u2211 j=1 [ x\u2032 p \u00b7 L\u2032 j ] dqj , (43) in this way we can finally write: x\u0307\u2032 p = ( x\u2032 p \u00b7 L\u2032 1 \u00b7 \u00b7 \u00b7 x\u2032 p \u00b7 L \u2032 n )\u239b\u239c\u239d q\u03071 ... q\u0307n \u239e \u239f\u23a0 (44) VI. KINEMATIC CONTROL FOR A PAN-TILT UNIT. We will show an example using our new formulation of the Jacobian. This is the control of a pan-tilt unit. A. The Pan-Tilt unit We implement algorithm for the velocity control of a pantilt unit (PTU Fig. 5) assuming three degree of freedom. We consider the stereo depth as one virtual D.O.F. thus the PTU has a similar kinematic behavior as a robot with three D.O.F. In order to carry out a velocity control, we need first to compute the direct kinematics, this is very easy to do, as we know the axis lines: L1 = \u2212e31 (45) L2 = e12 + d1e1e\u221e (46) L3 = e1e\u221e (47) Since Mi = e\u2212 1 2 qiLi and M\u0303i = e 1 2 qiLi , we can compute the position of end effector using (30) as: xp(q) = x\u2032 p = M1M2M3xpM\u03033M\u03032M\u03031, (48) The estate variable representation of the system is as follows\u23a7\u23aa\u23aa\u23a8 \u23aa\u23aa\u23a9 x\u0307\u2032 p = x\u2032 \u00b7 ( L\u2032 1 L\u2032 2 L\u2032 3 )\u239b\u239du1 u2 u3 \u239e \u23a0 y = x\u2032 p (49) where the position of end effector at home position xp is the conformal mapping of xpe = d3e1 + (d1 + d2)e2 (see eq"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0003271_eurcon.2005.1629898-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0003271_eurcon.2005.1629898-Figure1-1.png",
+        "caption": "Fig. 1. a: A PUMA 560 on a mobile platform. b: Two PUMA 560s on the ground.",
+        "texts": [
+            " These cases were tested on the Itree and the original SBL-PRM algorithms for comparison. The manipulator model used was the PUMA 560 with six degrees of freedom. Figures la and lb are referring to case 1 (ci) and case 4 (c4) respectively. Case 2 (c2) is a PUMA 560 on the ground and case 3 (c3) is two PUMA 560 each of of them mounted on a mobile platform. The object model in the simulation is a car and the task is to move the manipulator(s) from a start configuration to the goal position (at the other end of the line path) as shown in Figure 1. the s-ants but the paths connected from the food, g, to any of s-ants trail will definitely give the path to the food, s. However, the g-ants will get the shortest path by choosing the appropriate trails with the heuristic provided in the global table. Finally when all g-ants have made the In each of the experiments, the number of configurations was calculated and the running time was recorded. The results in Figure 1 and Figure 2 shown below were obtained on 2.60 GHz Pentium4 processor with 512 MB of main memory running Microsoft Visual C++ 6.0. The parameter p was set to 0.15 and the resolution E to 0.012. A path in configuration space between two configurations is considered collision free if a series of points on the path in every successive point are closer apart than some e. As can be seen in Figure 2, Itree-ACO has shown a smaller number of configurations generated on the robot(s) path than the configurations generated by SBLPRM"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0000606_(sici)1096-9845(199610)25:10<1139::aid-eqe606>3.0.co;2-s-Figure1-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0000606_(sici)1096-9845(199610)25:10<1139::aid-eqe606>3.0.co;2-s-Figure1-1.png",
+        "caption": "Figure 1. Slide rotation of the body with a fixed direction of the friction force",
+        "texts": [
+            " For example, if the ground motion is harmonic with respect to time, ig = uo cos ot (1) then sliding certainly occurs if p < 0.537ag/g (2) where ag = u o o . Thus, we accept the third assumption to be realized: (3) the friction coefficient p is small enough to provide sliding. If the body starts to slide the direction of relative sliding between the body and the ground is fixed for a period of time, when we call 'the first phase' of the motion. For this phase the friction force Ff does not change its direction, and we have (see Figure 1) Fc = ~ L N (3) where N is a normal reaction of the ground. The plane motion of the block is described by the following equations: mx, = Ff my, = N - mg I $ = Fryc - N ( a cos cp - h sin cp) where y , = asin cp + hcos cp. SLIDE ROTATION O F RIGID BODIES 1141 Here (x,y) is the fixed Cartesian co-ordinate system, 2a the width of the block, 2h its height. The point above any variable denotes its derivative with respect to the time t. The moment of inertia m 3 I , = - (a2 + h 2 ) It follows from equations (3)-(5) that N = m ( j c + g) yc = (acoscp - hsincp)$ - (asin cp + hcoscp)qj2 I,$ = m ( j c + 9) [ p ( a sin cp + h cos cp) - (a cos cp - h sin cp)] Taking into account equalities (6) and (7b) the last equation can be rewritten as follows: al(cp)$ + bl((P)q2 = C l ( c p ) where al(cp)= 1 +a2-3(coscp-asincp)[(p+u)sincp+(pa-1)coscp] bl (cp) = 3(sin cp + u cos cp) [( p + u) sin cp + ( p a - 1) cos cp] 9 cl(cp) = 3 - [(p + u) sin cp + ( p a - 1) cos cp] U The main geometric parameter h a = - U is a relative height of the construction"
+        ],
+        "surrounding_texts": []
+    },
+    {
+        "image_filename": "designv11_6_0001419_robot.1991.131938-Figure7-1.png",
+        "original_path": "designv11-6/openalex_figure/designv11_6_0001419_robot.1991.131938-Figure7-1.png",
+        "caption": "Fig. 7: Unstable Area of Circling Gaits Based on the First Method with p = 314.",
+        "texts": [
+            " Since At2 is greater than x , the gait stability margin of the +a: type wave-circling gait is less than zero. Similarly, we can prove that +y type, -y type and -y type wave-circling gaits have a negative stability margin when the turning center is coincident with the gravity center. Therefore, for a given angle T, there should exist a critical turning radius R, so that the gait is st.able when R 2 R,. By calculat,ing the R, for many y, we can construct an unstable area of turning center for the wave-circling gaits. The unstable area of the wave-circling gait of t h e walk- ing chair is shown in Fig. 7 by using the first strategy. The unstable area is symmetrical about the body longitudinal and lateral axes due to the symmetrical leg workspaces. Fig. 8 shows the unstable area of the wave-circling gaits with the second strategy. Compared to first strategy, the unstable area is greatly reduced. Thus, the second strategy is more effective and we will apply the second strategy in the following examples. Fig. 9.a shows the relationship between S,,, and a in the following range 0\u2019 5 cy 5 360\u2019. The duty factor /3 is equal to 5/6 and turning radius R is a constant"
+        ],
+        "surrounding_texts": []
+    }
+]
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