diff --git "a/designv10-6.json" "b/designv10-6.json" new file mode 100644--- /dev/null +++ "b/designv10-6.json" @@ -0,0 +1,7935 @@ +[ + { + "image_filename": "designv10_6_0003625_tmech.2008.2010935-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003625_tmech.2008.2010935-Figure1-1.png", + "caption": "Fig. 1. SWM CAD model [1].", + "texts": [ + "ndex Terms\u2014Dipole force model, electromagnet (EM), inverse torque model, spherical actuator. I. INTRODUCTION GROWING demands for miniature devices along with the trend to downscale equipment for automating the manufacture of these products on \u201cdesktops\u201d have motivated the development of mechanically compact actuators for smooth orientation of a workpiece. One such actuator is a ball-jointlike spherical wheel motor (SWM) [1] capable of offering multi-DOF in a single joint. As shown in Fig. 1, the SWM utilizes a distributed set of electromagnets (EMs) to control the rotor consisting of high-coercive permanent magnets (PMs). The spherical motor has more controlling inputs than its mechanical DOF; the overactuating system offers an effective means to minimize energy inputs for a given torque specification. Both forward and inverse torque models are required in the design and control of a spherical motor. The forward model simulates the magnetic torque for a given set of electrical inputs", + " However, unlike the Maxwell stress tensor method or the Lorentz force equation (with the ESL approximation) that require numerical computations of a surface integration, the dipole force equation (replacing integrations with IV. ILLUSTRATIVE 3-DOF ORIENTATION STAGE With EMs and PMs modeled as DMP, the dipole force model is an efficient way to compute the magnetic force in 3-D space for the design of an EM system, especially for wrist-like spherical motors [9] involving a large number of EMs and PMs. As an illustrative example, Fig. 10 shows the computer-aided design (CAD) model of an (ball-joint-like) orientation stage operated on the principle of an SWM [1]. Unlike the SWM (Fig. 1) where the rotor PMs are embedded in the \u201cball,\u201d the PMs of the 3-DOF stage in Fig. 10(a) are housed in the socket-like rotor assembly. In Fig. 10(a), the stator EMs are air-cored and the structure (except PMs) is nonmagnetic. Supported on a bearing, the rotor is concentric with the stator; thus, the system has 3 DOF. The rotor of the 3-DOF orientation stage is subjected to an external torque Text in Fig. 10(b), where the center of gravity coincides with the rotation center Text = r \u00d7 mloadg. (14) Statically, the torque acting on the rotor is equal to the external torque", + " (16) In (15) and (16), the subscripts \u201cr\u201d and \u201cs\u201d denote the rotor and stator, respectively. Unlike the PM, the direction of the EM is defined by the polarity of the current. The orientation stage (Fig. 10) has three layers of eight stator EMs and two layers of 12 rotor PMs; the coordinates are given in Fig. 11. The PMs and EMs are arranged in pairs such that they are electromechanically symmetric. Because of the symmetry, the EMs are grouped into ten electrical inputs (Table IV). Unlike the SWM (Fig. 1), the orientation stage (Fig. 10) has a third layer of EMs (EM17\u2013 EM20) along the equator offering additional torques about the xy-plane. The forward torque model of the PM-based spherical motor with linear magnetic properties has the form [3], [9] T = [TX TY TZ ]T = [ K\u0304 ] I (17) where K\u0304(\u2208 R 3\u00d7ms ) = [ \u21c0 K1 \u00b7 \u00b7 \u00b7 \u21c0 Kp \u00b7 \u00b7 \u00b7 \u21c0 Kms ] (17a) I = [ I1 \u00b7 \u00b7 \u00b7 Ip \u00b7 \u00b7 \u00b7 Ims ]T (17b) where Ip is the current input to the pth EM and ms is the total number of EMs. In (17a), the torque characteristic vector ( \u21c0 Kp \u2208 R 3\u00d71 , contributed by Ip to the whole rotor) at each orientation (\u03c8, \u03b8, \u03c6) can be derived using the dipole force equation \u21c0 Kp = \u00b50 4\u03c0 nr\u2211 i=1 mri np\u2211 j=1 msj [(Rsj + ri + \u2212 Rsj \u2212ri + ) \u00d7Rri + \u2212 (Rsj + ri\u2212 \u2212 Rsj \u2212ri\u2212) \u00d7 Rri\u2212 ] (18) where np (or nr ) is the number of dipoles for each EM (or PM)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure2.40-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure2.40-1.png", + "caption": "Fig. 2.40. Manipulator with cane-form segments", + "texts": [], + "surrounding_texts": [ + "In the previous paragraphs it was shown how driving forces and torques PIt) which produce the prescribed motion of a manipulator are calcula ted. As the output we also obtained the trajectory in the state space i.e. q(t), q(t). This calculation is the basis of the algorithm for dy namic analysis of manipulator motion. But, we are usually also inter ested in some other dynamic characteristics. The calculation of each dynamic characteristic is based on P(t), q(t), q(t), q(t) and represents only an additional block in the algorithm described. We now discuss 79 some interesting dynamic characteristics. 2.5.1. Diagrams of torque vs. r.p.m. One interesting characteristic which can be obtained as the output of the algorithm is the diagram of torque vs. rotation speed of motor. Since the rotation speed of a motor is usually expressed in terms of revolutions per minute (r.p.m.), we talk about torque-r.p.m. diagram. This diagram can be computed for each joint i.e. each motor (actuator) It will be shown that such diagrams are suitable for both manipulators driven by D.C. electromotors and manipulators driven by hydraulic ac tuators. Let.us first consider D.C. actuators. The dynamic analysis algorithm computes the torque Pi and the internal (generalized) velocity q. for .. . 1. 600 each joint Si and each time instant. The r.p.m. for a J01.nt 1.S n i = 21l q i (g. is expressed in rad/s), so each time instant gives one point of the 1. Pi-ni diagram. This diagram is valid for the shaftof the jOint considered. But we are usually interested in the diagram for the motor itself. Then the reducer in the joint must be taken into account. Let us con sider a reducer with the speed reduction ratio equal to N. Then the mo tor r.p.m. is m n. 1. N.n. 1. 1. (2.5.1) If the reducer has the mechanical efficiency n(N, n), then the torque reduction ratio is Non(N, n) and so the motor torque is P. 1. Nion i p~ 1. (2.5.2) Hence the motor diagram p~ - n~ is obtained by calculating (2.5.1) and 1. 1. (2.5.2) in each time instant to' t 1 , t 2 , ... One example of a torque - r.p.m. diagram is shown in Fig. 2.33. Only a qualitative presentation of the diagram is given. Such diagrams are very useful during the synthesis and choice of D.C. servosystems. The producer gives the P:ax - nm motor characteristic in the catalog, where pm is the maximal motor torque at motor r.p.m.=nm. max By comparing the necessary characteristic, obtained by means of the algorithm described, with the one from catalogue, one can decide whether the chosen motor suits its application. The use of these characteristics 80 will be discussed further in 2.6.1. and 4:5. In the case of hydraulic actuator the procedure is similar but usually without reducers. In the case of a rotational hydraulic actuator we ob tain the diagram of torque vs. rotational velocity in the joint i.e. P-q. If a hydraulic actuator with a cylinder (translational motion of the piston) is used then we obtain the characteristic of force vs. lin ear velocity of the piston (there is no r.p.m.). In the case of a hy draulic actuator the maximal characteristic Pmax - q is different from the one holding for D.C. motors. A few things should be pointed out. If a rotational actuator drives a rotational joint then the connection is usually direct (or by means of a reducer). Another simple case appears when hydraulic actuator with cylinder drives a linear joint. But, if an actuator with the hydrau lic cylinder drives a rotational joint then there is usually a non linear dependence between the piston motion and the rotation in joint. This should be kept in mind. 2.5.2. Calculation of the power needed and the energy consumed The next interesting characteristics (e.g. for the choice of actuators) are the power needs in each joint. For a joint Si the power needed in 81 some time instant is obtained as Qi = Pioqi' But the power produced by the motor has to be larger because of the power loss in the reducer. So the necessary motor power in this time instant is Q~ = Pioqi/ni' where ni is the mechanical efficiency of the reducer. Hence, the time history of the power needed is obtained. It should be pointed out that this is the output mechanical power of the motor. The energy consumption may also be easily computed. Let us consider a joint Si and the corresponding actuator. Let E~k) be the energy conk 1. sumed in the first k time steps, and let ~Ei be the energy consumed in the k-th time step (time interval ~tk)' The total energy' consumed by the i-th joint actuator is calculated in such a way that, during the time-iterative procedure of dynamic analysis, summation of the energy at each step ~tk is found: (2.5.3) k To calculate ~Ei' we adopt the medium drive value on the interval where the upper index indicates the k-th time instant. Now k where ~qi (2.5.4) (2.5.5) It should be stressed that this discussion on energy has dealt with the mechanical power and mechanical energy only. If we want to calculate the energy which has to be taken from an energy source (e.g. from an electric battery) then we should take care of the energy lost in actu ators. Thus, the dynamic models of actuators have to be introduced. These models are discussed in 2.9. In this paragraph we give only some ideas of such energy consumption calculation. If a manipulator is driven by D.C. electromotors then the energy loss follows from resistance and friction effects. Let us consider one joint and the corresponding motor. The power required from a source can be computed as Q = u ir where u is control voltage and ir is rotor current. NOw, in a time step ~tk the energy increment is k.k At u.1. Llk 1. r i 82 where the lower index represents the number of joint and the upper in dex indicates the k-th time instant. In the case of a hydraulic actuator one should take care about the loss due to friction and leakage. The energy consumed by the whole manipulator is the sum of energies consumed by actuators. 2.5.3. Calculation of reactions in joints and stresses in segments Reaction forces and moments and, especially, stresses in manipulator segments represent very useful data for manipulator design process. We first derive the procedure for the calculation of reactions in manipu lator joints. At the beginning, it is necessary to discuss in more de tails the case of linear joints. Such a joint was shown in Fig. 2.5. and the vector ~ii was introduced. The vector ~i-1,i was considered constant. Such joint representation was satisfactory for the formation of mathematical model. But, if we wish to calculate reactions and stresses and, leter, elastic deformations, it is necessary to distin guish two different cases of linear joints. These two cases are pre sented in Fig. 2.34. Let us introduce the indicator Pi' which deter mines to which of the two cases linear joint Si belongs: { 1, 0, We now introduce if joint Si is of type (a) (Fig. 2.34) if joint Si is of type (b) (Fig. 2.34) (2.5.6) (2.5.7) Thus, the translation in joint S. is taken into account either through .... , .... l r .. (in case (a)) or through r~ 1 . (case (b)). II l- ,l .... Let us now consider the i-th segment (Fig. 2.35). Let FSi be the total .... force in the joint Si acting on the i-th segment, and let MSi be the total moment in the same joint acting on the i-th segment. Notice that ~ ~ -+ -+ now FSi+1 and MSi+1 act on the (i+1)-th segment, and -FSi+1, -MSi+1 act 83 on the i-th segment. From the theorem of center of gravity motion it follows -+ -+ -+ -+ m.w. FSi FSi+1 + mg l l (2.5.8) i. e. -+ -+ -+ -+ FSi FSi+1 - mig + m.w. l l (2.5.9) 84 + 1. \"'\" I ~- ! \\ + ~ ~ . II g (2\" 5\" i 0) i .. e\" + ( \\ \u2022 i, +1 Si+l - (J i \\ 1 I + -, + .11) where Ai is the transition matrix of the i-th segment~ Since tht: mot. i.on and f thus!t i are known ( equat,ions (2 .. 5 '\" 9) and (2 .. 1 ) offer the possibility of recursive calculation of total forces and moments in manipulator jolnts. The boundary conditions for this backward recursion are -> Fend, (2.5.12a) +1 (2.5.12b) and they are shawIl in Fig~ 1.36. ... F _ and enc:! are the forc(J and the moment the manipulator produces if in contact with some object on the gTound. (:fig. ~36a). If the last segment of the manipulator is free (not in contact with the groundl f niellt if written in b~-f. systems~ + Fend o? = 0 (Fig. 2.36b). Let us now consider a rotat.ional joir!t S1. In that jOint, tilcre is the driving torque 1 (with the directi.on along ), react moment (perpendi.cular ~i)' and the reaction force (Fig. 2.37a \" If the joJnt linear, tllen there is a driving force (along ;. t.he rf..:act ion 51 is force FHi {perpendicular + ~ to. \u20aci) f and the reaction lTlOTllent\" acting on the i-th segment (Fig. 2. 7bi. fI'hu2, tl~e tot.al forCE': in joint Si is: ->- , 1 r F + R:L s p, i. l (2\" 5\" 13) and t.he tot,al moment The reaction force can now be computed as 85 86 -+ s.P. l l and the reaction moment -+ -+ -+ where Pi' FSi ' MSi are already computed. (2.5.15) (2.5.16) When the total joint forces and moments are calculated, it is possible to compute stresses in manipulator segments. We are interested in the maximal bending and maximal torsion stresses. Let us consider a segment on which the forces and moments are acting according to Fig. 2.38. and let us use the notation from that figure. Stresses in a segment depend on its form. They are usually calculated for segments which have some typical form. The algorithm described here contains special subroutines for two standard forms of segments. These are a circular tube (Fig. 2.39 (a)) and a rectangular tube (Fig. 2.39 (b)). For any other form a special subroutine can be programmed and ad ded to the algorithm. For these standard segment forms the algorithm itself adopts body-fixed coordinate system with the z-axis along the segment (Fig. 2.39). Indices i which denote the i-th segments are omit ted for shorter writing. It is suitable to express the forces and moments in the segment b.-f. system. For the segment \"in it is 87 ->-d ->- F = FSi ' FUP ->- -F -Si+1 ->- -Ai ,i+1 FSi+1' (2.5.17) + ~p ->- -M _Si+1 -A. . 1MS' 1 1,1+ 1+ We are interested primarily in maximal bending and torsion stresses. The stresses due to extension, compression, etc. are not taken into account, since these effects can be neglected if compared with bending and torsion. Thus, the moment Md or, the moment MUP is relevant. ->-d ->-up The first components of M and M represent the bending moments around the x-axis of the b.-f. system. Let M1max be the larger of these two values (considered as absolute values). The second components of these vectors are the bending moments around the y-axis. Let M2max be the larger one. Finally, the third components are the torsion moments around the z-axis. Let M3max be the larger one. The maximal stress due to segment bending is now I M~:ax I + I M~:ax I (2.5.18 ) where Wx and Wy are the axial section moduli. The maximal stress due 88 to torsion is where Wo is the polar section modulus. The resulting maximal stress is approximately Thus, the maximal stress is obtained for each segment. For circular-tube segments, section moduli are W Y r R For rectangular-tube segments, they are hx 1jJ =- x H x (2.5.19 ) (2.5.20) (2.5.21 ) (2.5.22) The torsion of rectangular tube cross section requires a longer discus sion for which readers are referred to the literature. 2.5.4. Calculation of elastic deformations One of the most interesting characteristic is the elastic deformation of manipulator segments. Recent efforts toward the optimal deisgn of manipulation robots have resulted in manipulator mechanisms which are not oversized. The segments of such manipulators can no longer be con sidered as rigid bodies. Hence, the calculation of elastic deformations of manipulator segments becomes a very importent problem in optimal de sign. Some efforts have been made in the field of flexible manipulator analysis considering its design and control [22, 24, 32, 33J. Recog nizing the importance of flexible manipulators, the whole volume 7. of this monograph series will be devoted to this problem. Among all the methods proposed for the calculation of elastic deforma- 89 tions we have to choose one and incorporate it into the algorithm for dynamic analysis. The method must solve the deformations in a suffi ciently simple way in order not to be .time consuming. It also has to be suitable for incorporation into the dynamic analysis algorithm. We have used a simplified version of the method explained in [22, 24], but there are no obstacles to using any other more precise method (finite ele ments for instance). Since the method proposed is explained in detail in [22], we give here only a short description. Basic ideas, definitions and assumptions. The method [22] is intended for the solution of flexible manipulator dynamics and for the calcula tion of its oscillations. Here, we are not interested in control, so we do not calculate the oscillations but the quasi static deformations only. These deformations result from static forces and inertial forces of nominal motion. The elastic deformations calculated are used in design methodology so that they are tested against some permitted values. These permitted values are related to positioning accuracy and thus they are given in the form of maximal linear and angular deviation of manipulator tip due to elastic deformation of segments. Hence, we only calculate these tip deviations. Let us also note that the method [22] results in conservative design calculation i.e. the results are always on the safe side. The dynamic analysis algorithm makes possible the calculation of all dynamic characteristics of manipulator nominal motion. Thus, the total ->- ->- joint forces and moments FSi' MSi are considered as known as well as all the velocities and accelerations. The basic idea of this approach to elastic manipulator is to consider it as an open chain of bodies, some of them being rigid and some of them being elastic canes, and to consider weights, inertial forces of nominal motion, and nominal joint forces and moments as known exter nal values calculated by means of dynamic analysis algorithm. Special indicators kei' i=1, \u2022\u2022\u2022 ,n are used to define the segments which are considered as elastic. k . el { 1, 0, for elastic segment \"i\" for rigid segment \"i\" (2.5.23) 90 ->- ->- Let us introduce the values u i ' ~i' i=1, \u2022.\u2022 ,n defining the elastic de->- viations from the nominal motion of rigid structure. u. is the linear ->- l deviation of joint Si+1' and change i.e. rotation vector) corresponding to the point A ~i is the angular deviation (orientation as shown in Fig. 2.41. Let the deviations ->- ->- (Fig. 2.16) be uA and ~A. Let us now make two assumptions. First, we assume that small deforma tions are considered and that these oscillations do not influence the nominal motion. In this way the internal coordinates keep their nominal time histories. Second, we make an approximation assuming that each 91 R, / up segment mass mi is divided into two parts ~i = mi 2 and ~i being concentrated on the lower side of cane (point Si) and R, =umi/2, ~i ~.p on the 1 upper side (point Si+1). The masses of motors and reducers, if they are placed in joints, are added to these joint masses ~i. It is clear that the existence of some masses which are really concentrated in joints reduces the error which appears because of segment mass division. In 2.5.3. we distinguished two sorts of linear joint and introduced the corresponding indicators Pi (relation (2.5.6)). ->- NOw, the length R,i of a segment (between the two joints) is 1. 1 n. 1 1 1+ -+ +-+ -+ r i i + siP i q i e i + r i , i + 1 + s i + 1 (1 -p i + 1 ) q i + 1 e i + 1 (2.5.24) For standard form segments, with the zi-axis of b.-f. system placed along the cane, it holds ->- 'k:. 1 (2.5.25) For the gripper and its point A the length is defined as (2.5.26) ->- Calculation of deformations. Linear deviation u i consists of three or two components (Fig. 2.42) depending on whether the segment \"i\" is elastic or rigid: ->- ->-eR, ->- ->- u i _ 1+ui +~i_1XR,i' ->- ->- -t u. 1 +~. 1 xx,. 1- 1- 1 k . e1 k . e1 (2.5.27) o ->-eR,. h 1 f h 1 u i 1S t e component resu ting rom tee astic deformation of segment \"i\". For the angular deviation one obtains 1 ->- ->-eR, k ->- ~i-1+~i ' ei ~i (2.5.28) ->- ~i-1 k ei 0 h h ->-eR, results f th 1 . d f f t were t e component ~i rom e e ast1c e ormation 0 segmen \"i\". 92 Relations (2.5.27) and (2.5.28) make possible the recursive calculation -+ -+ -+-+ of deviations u i and ~i starting with Uo = 0, ~o = O. But, the deformations ~~1, ~el of the segment \"in still remain to be found. 1 1 The segment \"i\" will be considered as a cantilever beam having the lower end S. fixed and the upper end Si+1 free. The action of the next segment 1 ->-> \"i+1\" is replaced by total joint force -FSi +1 and moment -MSi +1 . The -> -> sign \"-\" follows from the previous assumption that FSi+ 1 ' MSi +1 act on the next segment \"i+1\" (see 2.5.3). Thus, the following forces and mo-> ments (Fig. 2.43) act on the free end of segment \"in: joint force FSi +1 ' moment MS' l' gravity force ~~Pg(g = {O, 0, -9.81}), and nominal iner1+ 1 tial force -~~P~Si+1 (~Si+1 is the nominal acceleration of the point Si+1). 93 Now, the linear deviation ttI~ is: (2.5.29) and the angular deviation (2.5.30) ai' Si' Yi , 0i are matrix influence coefficients. These coefficients will now be discussed but, before that, we conclude that equations (2.5.27) and (2.5.28) combined with (2.5.29) and (2.5.30) allow recur--+ -+ --+--+ sive calculations of ~1'~l, \u2022\u2022\u2022 ,un-1'~n-1 and finally the deviations of gripper point A i.e. uA ' ~A' Influence coefficients. Let us consider a segment \"i\" and its b.-f. system 0ixiYizi (Fig. 2.43). Since the segment is considered as a can tilever beam, in the b.-f. system it holds (2.5.31) and (2.5.32) where a xi 0 0 0 Sxi 0 iii 0 a yi 0 i -Syi 0 0 0 0 a zi 0 0 0 (2.5.33) 0 -Yxi 0 0 xi 0 0 Yi Yyi 0 0 8. 0 0 yi 0 1. 0 0 0 0 0 0 zi a xi is the influence coefficient for the bending deflection (linear deviation) along the axis xi' under the action of the force at the 94 point S. l' Similarly, a . is defined in terms of the Yl\u00b7 axis. l+ yl a zi is the influence coefficient for extension along the zi axis, under the action of the force at Si+1' It can usually be neglected by taking a zi = O. Sxi is the influence coefficient for bending deflection along the xi axis due to the moment acting at Si+1' Likewise for the Yi axis. Yxi is the influence coefficient for the bending angle around x. axis l due to the force acting at Si + 1 . Likewise for Yi axis. 15 xi is the influence coefficient for the bending angle around x. axis l due to the moment acting at Si+1' Likewise for Yi axis. 6 . is the influence coefficient for the torsion around the z. axis due Zl l to the moment acting at Si+1' In order to transform equations (2.5.31), (2.5.32) into external system i.e. to obtain equations (2.5.29), (2.5.30) we transform the influence coefficients by using _ -1 Si - -1 a. AiaiAi ' AiSiAi ' l (2.5.34 ) _ -1 6. - -1 Yi = AiYiAi ' A.6.A. l l l l where Ai is the transition matrix of the segment \"in. For the case of force acting of Si+1 the influence coefficients for de flection and extension are \u00a3~ \u00a3~ \u00a3. a xi l l l 3E.I a yi 3E.I a zi E.l\\:-l yi l xi l l (2.5.35) where E. is Young's modulus for the adopted material, I . and I . are l Xl yl axial moments of inertia of the cross-section and Ai is the cross-section area. If the moment is acting the influence coefficients for segment bending deflection are 2E.I . l yl 2E.I . l Xl 95 (2.5.36) Let us consider angular deviations. If a force is acting at Si+1 the influence coefficients for bending angles are 2E.I . l Xl 2E.I . l yl (2.5.37) and if a moment is acting then the coefficients for bending and torsion angles are <5 . Xl 9.. l ~ l Xl <5 . yl <5 . Zl 9.. l G.I-:l Ol (2.5.38) where Ioi is the polar moment of inertia of the cross-section, and Gi is the torsion modulus. Gi is given by E. l where v. is Poisson's coefficient. l (2.5.39) Let us now discuss the influence coefficients for two standard form cross-sections. We consider a circular tube (Fig. 2.39a) and a rectangular tube (Fig. I. I. Xl yl I . Ol 2.39b). For 4 1TRi 4 -4-( l-1)!i) , and for the rectangular tube I . Xl I . yl the circular tube it holds h . Xl ~, \\)!yi Xl h . -..Y2: H . yl (2.5.40) (2.5.41) The torsion of rectangular cross-section will not be discussed here, so the readers are referred to the literature. 96 There are also some interesting characteristics which are connected with control problems. Some of these characteristics which can be ob tained by means of the dynamic analysis algorithm are explained in 2.9." + ] + }, + { + "image_filename": "designv10_6_0003283_095440705x34757-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003283_095440705x34757-Figure1-1.png", + "caption": "Fig. 1 Gear shift scheme", + "texts": [ + " Keywords: gear rattle, automotive transmission, lubrication 1 INTRODUCTION a series of vibro-impact motions between the teeth of all the unsynchronized gear pairs that are meshing but without loading, in spite of the presence of back-In the automotive industry at present great effort lashes, owing either to design or to manufacturinghas been employed to improve the sound quality of errors and wear. On the other hand, the gear rattlepassengers cars. It is known, in fact, that a low noise itself is a cause of wear.level inside a car gives a perception of good quality of In Fig. 1, as an example, a scheme of a gear withthe product, and this may represent a strategic factor five speeds is reported, in which the first speed isin the highly competitive automotive market. For this shifted to transmit power and the other four meshingreason vehicle manufacturers have developed in gear pairs, which are unladen, represent a possiblerecent years a new research area, known by the gear rattle noise source. In order to set suitableacronym NVH (noise, vibration, and harshness), parameters for the drive line so as to prevent orwith the primary aim of analysing all the sources attenuate this inconvenience, both theoretical [1\u20136]of undesirable vibrations and minimizing acoustic and experimental [7, 8] studies have been conductedeffects transmitted inside the cars" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure13.9-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure13.9-1.png", + "caption": "Fig. 13.9 A magnetostrictive-shape memory piezoelectric actuator composite and experimental setup", + "texts": [ + " The dimensions of the piezoelectric actuator were 3\u00d73\u00d710 mm, and the thickness of each PZT layer was 0.065 mm. To apply the memory effect, an imprint electrical field was applied to the actuator with a 350 V DC potential applied to the driving electrode at 180\u00b0C for 3 h in an electric oven (Yamato Co., Ltd., DKN302). The shape memory piezoelectric actuator and the Terfenol-D magnetostrictive material (Etrema Products Inc., Tb0.3Dy0.7Fe1.92, 1\u00d75\u00d715 mm) were attached using an epoxy-based adhesive to form a composite structure. Figure 13.9 shows the magnetic circuit, which was composed of a permanent magnet (Nd-B-Fe, 0.24 T), silicon steel (Yoke), and the composite device. The magnetic force was measured using a load cell (Kyowa, LTS-1kA). The operating voltage was applied from a function generator (NF Co., Ltd., WF1946) through a voltage amplifier (NF Co., Ltd., 4010). A strain gauge was attached to the shape memory piezoelectric actuator to measure piezoelectric strain in the longitudinal direction. The magnetic force memory was controlled using a pulsed voltage as shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000548_j.isatra.2021.01.062-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000548_j.isatra.2021.01.062-Figure2-1.png", + "caption": "Fig. 2. Working principle of the EOTS.", + "texts": [ + " The \u03b1-th order Caputo fractional-order operator: \u03b1 f (t) = 1 \u0393 (n \u2212 \u03b1) \u222b t t0 f n(\u03c4 ) (t \u2212 \u03c4 )\u03b1+1\u2212n d\u03c4 (4) where n \u2212 1 < \u03b1 < n \u2208 Z+. In the remainder of this paper, the Caputo definition is used for our developed control scheme, which is denoted by D\u03b1 . The differentiation and integration of the function f1(t) = 1 and f2(t) = t2 are illustrated in Fig. 1 as examples of FO calculus. 2.2. System kinematic model of EOTS The EOTS is served as the \u2018\u2018eyes\u2019\u2019 for ship, land, and airborne to search, monitor and record targets in real-time. The working principle is shown in Fig. 2. EOTSs are usually operated with computers or other external devices such as remote-controls and synthetic aperture radars. In target searching mode, computers or other external devices that can capture the targets send reference coordinates to EOTSs through serial ports or network interfaces, and then oblige EOTS to point at targets. A kinematic model and a friction model of the EOTS are presented in this section. Note that EOTS consists an inner frame and a outer frame and only the outer frame is studied and experimented" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000562_j.mechmachtheory.2021.104380-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000562_j.mechmachtheory.2021.104380-Figure1-1.png", + "caption": "Fig. 1. A prototype of the studied parallel continuum manipulator.", + "texts": [ + " A discretization-based approach, developed in our prior work [44] , is employed as a framework for the elastostatics modeling of those slender flexible links used in the PCMs. As a result, techniques for robot kinematics and statics can be utilized to establish the kinetostatics models effectively. It is noted that the approach is a general one for the kinetostatics models of spatial parallel continuum manipulators. For ease of discussion, a three-limb parallel continuum manipulator, is taken as an example to illustrate the modeling procedures. As shown in Fig. 1 , The limbs of this manipulator are mounted along the vertical direction and equally distributed on the base frame with a radius. In each limb, the slender flexible limb is actuated by a PR -drives at the proximal end and connected to the moving platform through a passive R joint at the distal end. It is noted that the PR drive generate one linear motion P along the vertical direction and one rotation R along the radial direction. And the direction of passive revolute joint is same as the direction of rotation R " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003055_0094-114x(94)90024-8-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003055_0094-114x(94)90024-8-Figure2-1.png", + "caption": "Fig. 2. The 6 DOF manipulator, general and plan view.", + "texts": [], + "surrounding_texts": [ + "The following system of the equations describes the mathematical model of the manipulator\n/.~ (x3 - x6 ) + M ' ,@3 - Y6) + .,V, (z3 - z6) = i ~ , d L , , ; ( i )\n(X 7 -- X6) 2 4\" 0'7 - -Y6) 2 4\" (:7 -- :6 ) 2 =/62.7, (2)\n/~(x4 - xT) + M,(Y4 - )'7) + N,(:4 - :7) = 14.Td,.u; (3)\n(x, - x,)* + O's -y7)2 + (:s - y 7 )2 = 12,; (4)\nL,o(X5 - xs) + MIo(Y5 - Y s ) 4- N.o(Z5 - Is) : is.sdto.,3; (5)\n(xs - x6) 2 + (Ya - y ~ ) 2 + (*l - *6Y = 1~,; (6)\n('~3 - - X6) 2 \"j\" (Y) - - Y6) 2 4\" (\"3 - - Z6) 2 ---- 1~.6; (7)\n(x4 - XT)= + (y, - y7)2 + (:4 :7)= 2 . - - : 14.';, ( 8 )\n(xs - xs)* + (Ys - Ys) 2 + (*, - zs) 2 : l|.s; (9)\nwhere the coordinates of the joints 6, 7 and 8 are unknown parameters. In order to determine the unknown parameters the decomposition method which is given in detail in [10] is used. Following this method in order to determine the coordinates of joints 6, 7 and 8 we can use modules COR3P and COR3 [10]. However, it is necessary to introduce one additional equation into the system of equations (!)-(9). This equation expresses a variable distance between any of the three sliders and the platform joint, for example, 14.s\n(x, - x~) 2 + (y, - y6) 2 + (z, - *6)' ffi 1~, ffi ~2. (10)\nApplying the decomposition method to the system of equations (I, 7, 10), (3, 8, 2) and (9, 6, 4) using two modules COR3P and one module COR3 step by step determine the coordinates of the", + "joints 6, 7 and 8. After introducing all the unknown parameters into equation (5) we will obtain a non-linear equation,\nF(x, A) = 0, (! l)\nwhere A is the vector of the mechanism constant parameters. Equation (I I) is solved for 0 by using one of the iteration methods. Then by introducing this value of 0 and employing the algorithm mentioned above determine coordinates of the joints 6, 7 and 8. Finally, the direction co~nes of the moving axes and the coordinates of the point O, can be determined.\nIn order to define the inclination angles of the hydraulic cylinders we can use the following expression\n#, .. arccos(LjL, + M/Mk + NjN,),\nwhere i-- 1,2,3;j = II, 12, 13 and k =20,21,22. In addition, there are some limits of the inclination angles for each specific manipulator assembly, which is given by\n#,~,, ~ #, ~< #,~,. (12)\nIt is necessary to check this inequality at each position of the manipulator." + ] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure19.3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure19.3-1.png", + "caption": "Fig. 19.3 Relationship between final concentration of H2O2 and pressure output of the biochemical pump 10 min. after adding H2O2 solution", + "texts": [ + " A water-head change in the glass tubes was monitored as the height differential of buffer solution between enzyme side and non-enzyme side, thus converting the hydraulic pressure value in the biochemical pump. Figure 19.2 shows the typical responses of water-head differential in the tubes of the biochemical pump to varying concentrations of hydrogen peroxide (11.8, 45.7, 83.1, and 123.6 mmol/l). As the figure indicates, the differences of water-head increased gradually following addition of H2O2. The relationship between the final concentration of H2O2 in the funnel area and the output pressure (10 minutes after injection) calculated from water-head differential is illustrated in Figure 19.3. 222 Y. WAKABAYASHI, T. OKAMOTO, H. SAITO, H. KUDO, K. MITSUBAYASHI Biochemical Pump with Enzymatic Reaction 223 As the figure indicates, the output pressure was linearly related to the concentration of hydrogen peroxide over a range of 11.8 to 123.6 mmol/l, with a correlation coefficient of 0.994 deduced by regression analysis as shown by the following equation: Figure 19.4 illustrates the comparison between the pressure changes over time in the enzyme immobilized side and the injection side of the funnel area" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000232_j.ymssp.2021.108403-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000232_j.ymssp.2021.108403-Figure4-1.png", + "caption": "Fig. 4. Cantilever beam model of a single gear tooth. (a) healthy and (b) with surface wear.", + "texts": [ + " The gradual material removal induced by surface wear accumulation will result in deviations from the intended tooth profile, thus altering the backlash of the engaging gear pair. The backlash with surface wear can be expressed as bw = bini + b\u0394 = bini + e(t) (6) where bini denotes the original backlash, b\u0394 indicates the backlash aroused by surface wear. To formulate the mesh stiffness of a gear pair, the potential energy method is utilized in which a single tooth is modeled as a variable cross-section cantilever beam, as shown in Fig. 4. As indicated in Ref. [41], the total potential energies stored in the meshing gear pair contain five components: bending energy Ub, shear energy Us, axial compressive energy Ua, fillet-foundation energy Uf and Hertzian energy Uh, which can be given as Ub = F2 2kb , Us = F2 2ks , Ua = F2 2ka , Uf = F2 2kf , Uh = F2 2kh (7) where F is the action force on the tooth; kb, ks, ka, kf and kh represent bending stiffness, shear stiffness, axial compressive stiffness, filletfoundation stiffness and Hertzian contact stiffness, respectively", + " The effective mesh stiffness of the gear pair can be expressed as [42] k = 1 1 Cs1kf1 + 1 kth + 1 Cs2kf2 (25) kth = \u2211Im i=1 ki th, ki th = 1 1 ki h + 1 ki t1 + 1 ki t2 , kt = 1 1 kb + 1 ks + 1 ka (26) where Cs1 and Cs2 denote the correction coefficient of the fillet-foundation stiffness; i = 1 for the first pair of mesh teeth and i = 2 for the second pair of mesh teeth. When gear damage occurs, the effective area moment of inertia and the area of the cross-section may change accordingly, resulting in the change of mesh stiffness of the engaging gear pairs. As illustrated in Fig. 4(b), the accumulated surface wear will reduce the tooth thickness during the contacting involute profile. As a result, the area moment of inertia and the area of the cross-section with surface wear can be represented as Aw x = ( hx + hw x ) B, Iw x = 1 12 ( hx + hw x )3B, hw x = hx \u2212 hwdcos\u03b2 (27) Replacing the area moment of inertia and the area of the cross-section in Eqs. (8)\u2013(10) by Eq. (27), the bending stiffness, shear stiffness and axial compressive stiffness with surface wear can be determined" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003670_978-3-642-82195-0-Figure5.1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003670_978-3-642-82195-0-Figure5.1-1.png", + "caption": "Fig. 5.1. The three degree-of-freedom manipulator", + "texts": [ + " Therefore it would be very difficult for the optimal solution to satisfy the functionality requirements even if the solution to the canonical system of equation was easily obtainable. For these reasons, the methods for dynamic motion synthesis proposed so far, either make use of some other optimization techniques [62, 64], or simplified dynamic models [60-61]. We will here present a brief review of these methods. The time-op:tUna\u00a3. motioYl .6YYlthe6~ The time-optimal control of open-loop articulated kinematic chains, by solving the canonical system, was analyzed in [59]. The 3 degree-of -freedom manipulator shown in Fig. 5.1 was considered. The system is modelled by the symbolic dynamic model of the mechanism (5.2.23) (with out the actuators), which is the equivalent to . x (5.3.10) \u2022 \u2022 \u2022 T T where x = [ql q2 q3 ql q2 q3] is the state vector, P = [P 1 P 2 P 3 ] - the control vector representing the driving torques, A(X)ER6 , B(x)ER6x3 are the system matrices. The model (5.3.10) represents a set of 6 cou pled, nonlinear, first order differential equations. At the initial time t=to ' the system is assumed to be in the state X(to ) = xo, while at the final time t = tl the state is required to 187 satisfy the terminal constraint x(t1 ) constrained in amplitude x F ", + " Then the minimum principle is stated * * as follows: if P (t) is the optimal control and x (t) the corresponding * optimal trajectory, then there exists an adjoint vector p (t), satisfying (5.3.4), so that, at every time instant t, to < t < t1 * * * * * H (x , p , P ) < H (x , p , P) (5.3.14 ) for all admissible controls P, The optimal control is, therefore, the control which minimizes the Hamiltonian at every instant within the given time interval. By substituting the analytical expressions for the matrices A(X), sIx) for the manipulator shown in Fig. 5.1, into (5.3.13), the Hamiltonian is obtained as an explicit function of the state vector x, costate p and the driving torques P. Using the minimum priniple and by inspection of the Hamiltonian, the optimal control signals are obtained in the form * P. J. i=1,2,3 (5.3.15) 188 where fi(x, p) are nonlinear scalar functions of the state vector x and the costate p. The Equation (5.3.15) shows that the optimal control is bang-bang and the sign reversals depend nonlinearly on both the state and the adjoint variables", + " The control should be determined from the complete model, or the joint coordinates obtained may directly be used as input signals for positional servosysterns. From the standpoint of the complete system the obtained trajectories are suboptimal, since the decentralized, simplified system model was employed. Exampe.e 06 .the qU/L6..top.:tUna.! nom..tna.t :tJu:tj ectoJtIj The above described procedure for quasioptimal trajectory synthesis will be illustrated by an example. The motion of the UMS-1 manipulator will be optimized (Fig. 5.1). The actuator parameters are shown in Ta ble T. 5.1. Motion between the initial point point x F = [0.44 0.47 O.ll T [m] in e x~ = [0.49 0.36 O]T [m] and the final the time T = 0.5 s is considered. The initial and final velocity of the manipulator tip is taken to be zero. The joint coordinates qO=f- 1 (xo ) and qF =f-'1 (xF) are evaluated first. Then, e e the equivalent moments of inertia are estimated H~1 0.66, H~2 = 0.2, H~3 = 0.043 [kgm2]. The moment of inertia H~1 is, for example, evalua ted in the following way" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure7.7-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure7.7-1.png", + "caption": "Fig. 7.7 Developed nozzle flapper type servo valve using slit structure", + "texts": [ + " Measurements are fed to a PC via a 16-bit analog/digital (A/D) converter the control signal are sent from the PC to the servo valves via a digital/analog (D/A) converter. The sampling time of the controller is 0.2 ms. When pressurized air passes through servo valves, noise and pressure fluctuations that adversely affect the precise position control of the system are often experienced at the downstream side. In response to this, we developed a novel nozzle-flapper type servo valve that utilizes a slit structure instead of an orifice [14]. The slit structure shown in 73 Fig.7.7 maintains a laminar flow condition that that minimizes noise and pressure fluctuations. The slit structure is fabricated using etching technology. We investigated the flow characteristics of the slit theoretically and experimentally to evaluate the design specifications and characteristics of the valve. Our experimental results indicated that the noise level decreased by approximately 15 dB and pressure fluctuations could be reduced by 75% in comparison with an ordinal novel nozzle-flapper type servo valve that uses an orifice plate" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002486_978-3-662-03729-4_1-Figure5-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002486_978-3-662-03729-4_1-Figure5-1.png", + "caption": "Fig. 5. Motion of a cube", + "texts": [ + "(5), with the dual angle of rotation J, it is then apparent that the primal part of the latter plays the role of the angle between two lines, while the corresponding dual part plays the role of the distance s between those lines. It is noteworthy that a pure rotation has a dual angle of rotation that is real, while a pure translation has an angle of rotation that is a pure dual number. Example 1: Determination of the screw parameters of a rigid-body motion. We take here an example of (Angeles 1997): The cube of Fig. 5 is displaced from configuration A \u00b0 BO ... HO into configuration AB ... H. Find the Pl\u00fccker coordinates of the Mozzi-Chasles axis of the motion undergone by the cube. Solution: We start by constructing Q: Q == [i* j* k* J, where i*, j*, and k* are the dual unit vectors of lines AB, AD, and AE, respectively. These lines are, in turn, the images of lines AO BO, AO DO, and AO EO under the rigid-body motion at hand. The dual unit vectors of the latter are denoted by iO*, jO*, and kO*, respectively, and are parallel to the X, Y, and Z axes of the figure" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000048_j.measurement.2020.108154-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000048_j.measurement.2020.108154-Figure3-1.png", + "caption": "Fig. 3. Test bearing geometrical specification [16].", + "texts": [ + " The electric motor axis and the rotary shaft axis are aligned in both radial and angular directions using precision alignment equipment with Go-Pro model made by Fixcher Laser [15]. To regulate the electric motor speed by adjusting the frequency of the electric current, a Siemens Micromaster inverter was used. The electric motor and the bearing shaft are connected by a flexible coupling. The whole set is mounted on a steel table supported by four rubber seals. Test ball bearing geometrical specification is shown in Fig. 3. Also, the test rig assembly is shown in Fig. 4. Preloading on the bearing is done by tightening the locking screws on the loading plate and applying the specified torque to the locking screws. Fig. 5 shows the healthy ball bearing without any initial defects. Also, Fig. 6 shows defected bearing after complete failure. The appearance of the defect on the surface of the outer ring of the bearing is visible. In this test, Pico sensor from PAC1 co. was used for acoustic emission data acquisition. The sensor was installed on the pre-prepared area in the test bench" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003009_978-3-642-50995-7_21-Figure7-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003009_978-3-642-50995-7_21-Figure7-1.png", + "caption": "Fig. 7. Automotive Systems Modeled Using ADAMS", + "texts": [ + " By alleviating the need for specialized programming and debugging, quicker turn-around on results can be obtained and overall project schedules can be shortened. The net effect is that better mechanical system designs are produced for less cost with ADAMS. To provide the reader with a clearer picture of the types of mechanical systems that have been modeled and analyzed with ADAMS, the following few paragraphs describe specific ex amples from the general categories of automotive; aeronautics and astronautics; agricul ture, construction, and off-highway equipment; biomechanics; and general machinery and mech anisms. Figure 7 illustrates a small subset of automotive systems modeled with ADAMS. The systems shown include full vehicle\u00b7 models with suspension linkages, torsion bars, stabilizers, struts, steering mechanisms, drivetrains, engines, tires, cam and valve mechanisms, as well as electronic controls for speed, braking, and variable-power steering. These systems are used to predict and evaluate nonlinear, large-displacement, vehicle response to inputs from the following: drivers; wind gusts; aerodynamic lift and drag; road imperfections affecting ride quality, handling, and durability; and obstacles" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000326_j.mechmachtheory.2021.104264-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000326_j.mechmachtheory.2021.104264-Figure4-1.png", + "caption": "Fig. 4. Tangential accelerometers attached (a) to planet gears through (b) rigidly mounted adapter flanges.", + "texts": [ + " Once elastic-body deformation was discovered, additional radial ring gear accelerometers were added to measure all the way around the ring gear and to increase the spatial measurement resolution. Fig. 3 shows the 16 radially-mounted ring gear accelerometers that are suitable for capturing elastic-body vibration. Additional accelerometers for measuring elastic-body deformation could not be easily added to other gear bodies and the existing instrumentation on the carrier, sun gear, and planet gears from prior experiments is not oriented to measure radial elastic-body deformation. For example, Fig. 4 (a) shows that two planet gears have tangentially-mounted accelerometers attached via an accelerometer adapter flange in Fig. 4 (b) bolted rigidly to each planet gear. This sensor orientation is not conducive to studying the motion of interest now, and sensor orientation is not easily changed considering the tight fixture tolerances. Fig. 3 shows that the ring gear accelerometers are mounted to capture only radial elastic-body vibration, not tangential. The literature and our experiments show that this accelerometer configuration is sufficient to capture general motion of the ring gear provided the ring is approximately inextensible [55] ", + " The facewidth of each gear component is thinner than its main body. The FE/CM model uses the facewidth to define the axial thickness of elements, so the additional mass of the thicker gear bodies must be represented separately. Starting from our original work in [53] , we have used the width of the gear teeth in the FE/CM model plus an additional lumped mass/inertia attached to each gear component that accounts for the material in thicker areas of the gear bodies and the added mass/inertia of the planet gear adapter flanges in Fig. 4 b for those components. Dynamic time-based simulation is computationally expensive, so computer simulation mimicking the experiments \u2013 where steady state response is obtained across hundreds of frequency steps \u2013 would be highly time-consuming. Instead, the impulse response from a stimulus at the experimental shaker attachment point is obtained for all degrees of freedom. The impulse simulation consists of four ranges: (1) a single static time step to preload the system, (2) a four time step ramp up with increasing force/torque on the experimentally excited planet gear, (3) a three step ramp back down to the static load, and (4) an 8192 step free vibration response with only the mean load" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure2.26-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure2.26-1.png", + "caption": "Fig. 2.26. Determination of partial orientation", + "texts": [ + " some arbitrary fixed direction on the gripper) has to coincide with the prescribed direction in external space. In order to define a direction on the gripper we use a unit vector fi, where the tilde shows that the vector is expressed via projections onto the axes .... of the corresponding body-fixed system. So, the unit vector fi determines the direction with respect to the gripper b.-f. system. It is constant and represents the input value. The direction in external space will be prescribed by two angles e and ~ (Fig. 2.26). The angles determine the direction with respect to the external system. These two directions have to coincide. Let us point out that the b.-f. system and the external system need not coincide. Fig. 2.26. presents the de termination of a direction with respect to the b.-f. and to the exter nal coordinate system. Hence, the position vector is x g For posi tioning we use (2.4. 13), (2.4. 1 4) i . e \u2022 w n' q + 8' Dimensions of these matrices are: n' (3 x 5), 8' (3xl), q (5Xl). (2.4.33) (2.4.34) In the sequel we shall use transition matrices. Let Ag be the transi tion matrix of the gripper b.-f. system and let A be the transition matrix of the orientation coordinate system. Since the x-axis of the + orientation system coincides with the direction (b) the unit vector h can be expressed in the orientation system via projections [1 0 OlT" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure3.6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure3.6-1.png", + "caption": "Fig. 3.6. Mechanism geometry and driving torques", + "texts": [ + " The upper index \"dO in dicates that the direct branch is consider only. 156 Let us now add the segments 2' and 2\" which close the chain (Figs. 3.5 and 3.6). First, we conclude that the number of d.o.f. does not change. Second, we note that there is no drive in the jOint 53 but there are two independent drives in S2 (in fact S2 represent two independent jOints). One of these drives (P2) acts between the segments 1 and 2 and the other (P 3 ) acts between 1 and 2\". In this way P3 acts between 1 and 3 but via 2\" and 2' (Fig. 3.6). Acceleration energy. Now, let us find the components of acceleration energy corresponding to the segments 2\" and 2', i.e. let us find the way of computing the corresponding matrices W2\", V2 \" and W2 \" V2 ,. We first note that for transition matrices it holds (3.3.1) (3.3.2) It is clear from (3.3.2) that these matrices can be simply computed 157 when the direct chain is solved. For angular velocities and accelerations, the following holds: W2 \" w3 (3.3.3) w2 ' w2 (3.3.4) and hence f 2\" f3 1>3 (3", + "30) If the segments 2\" and 2' are considerably smaller than the segment 2, an approximative model can be formed. We may use the model (3.3.27) with the matrix W calculated for the open chain configuration. This open chain is obtained by taking the direct branch and adding the in ertial effects of segment 2' to the segment 2. In this case the segment 2\" is neglected. Let us discuss one modification of the mechanism considered (Fig. 3.10). It is the mechanism of ASEA robot which contains a kinematic paralelo gram, too. But, instead of driving torques P 2 , P3 (Fig. 3.6), the * * linear drives of mechanism P 2 , P3 are applied (Fig. 3.10). Nonlinear relationships exist between the linear and the rotational drives. 164 This paragraph develops the theory dealing with manipulators having constraints imposed on gripper motion. Each constraint restricts to a certain extent the possibility for gripper motion. In this way the num ber of d.o.f. of the gripper is reduced. In order to avoid a purely theoretical discussion, we consider only these types of constraints which appear in practical problems" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000068_tie.2021.3057002-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000068_tie.2021.3057002-Figure3-1.png", + "caption": "Fig. 3. Three dimensional fluid solid coupling heat transfer calculation model for HVLSSR-PMSM: (a) Computational model of coupled heat transfer between fluid and solid in cooler; (b) Computational model of coupling heat transfer between fluid and solid. 1-Out loop air inlet, 2-Out loop air outlet, 3-Inner loop air inlet of cooler, 4- inlet of internal cooler, 5- inlet of the internal motor, 6- outlet of the motor, a-Aluminum tubes, b-Stator radial duct, c-Shaft, d-Stator core, e-Stator winding, f-Shell.", + "texts": [ + " The following assumptions are proposed based on practical engineering: 1) The effects of the buoyancy and gravity on the fluid flowing are ignored. 2) The flowing rate of the coolant is much less than that of the sound velocity, so the coolant is treated as an incompressible fluid. To investigate the steady equilibrium state of the fluid and heat transfer in the cooling system, the mathematical model is aimed at the steady flow of the fluid, and the quantity of the equation does not change with time. Due to the complexity of ventilation structure, the motor and the cooler are separated during the analyzing, as shown in Fig. 3. The boundary conditions are given as follows: Authorized licensed use limited to: Shenyang Aerospace University. Downloaded on June 14,2021 at 19:57:11 UTC from IEEE Xplore. Restrictions apply. 0278-0046 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. 1) The inlet of the internal motor (number 5 in Fig 3) adopts the mass flow inlet boundary, which is 0.4 kg/s, and the air temperature of the internal motor inlet is 68 \u2103. 2) The outlet of internal motor (number 6 in Fig 3) adopts the pressure outlet boundary, and the outlet pressure is 1 atm. 3) The inlet of the external cooler (number 1 in Fig. 3) adopts the velocity inlet boundary, that is 8.7m/s, and the air temperature of the inlet of the external cooler is 20.1\u2103. 4) The inlet of internal cooler (number 4 in Fig 3) adopts mass flow inlet boundary, mass flow is 0.4 kg/s, and the air temperature of the inlet of internal cooler is 91.7 \u2103. 5) The outlet of the external cooler (number 2 in Fig. 3) adopts the pressure outlet boundary, and the outlet pressure is 1 atm. 6) Rotating wall boundary conditions are adopted on the surface of the rotor. 7) The multi-reference coordinate system model is used to simulate the fluid in the air gap. In order to determine the losses in motor different components, a two-dimensional transient electromagnetic field model is analyzed by using the time-stepping finite element method (TFEM), as shown in Fig. 4. The assumptions and transient 2-D electromagnetic field calculation equation are proposed in [20]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000161_j.optlastec.2021.107337-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000161_j.optlastec.2021.107337-Figure3-1.png", + "caption": "Fig. 3. Schematic illustrations of the process principle of (a) conventional DED and (b) EHLA and the corresponding sample form and sampling positions.", + "texts": [ + " In EHLA, a dense powder stream focused above the substrate surface and absorbing the primary laser energy intercepts the laser beam so that the laser cannot overheat the substrate but preheat and melt the powder. By this, EHLA is applicable for material deposition with much higher process speeds than those in DED (tens to hundreds of meters per minute in EHLA vs. hundreds of millimeters to several meters per minute in DED). In DED cuboid samples were made through overlapping of straight tracks, as shown in Fig. 3(a) and in EHLA tubular samples were made through overlapping of spiral tracks, as shown in Fig. 3(b). All relevant process parameters are given in Chapter 3. Determination of cross-sectional porosity was used to quantify the relative density between samples in this study. The value is defined as the pore-to-sample cross-section area ratio, as shown in Fig. 4. The sample cross-sections to be measured were successively ground and polished (with 1 \u00b5m diamond grit suspension). The images of the sample cross-sections were acquired using optical microscope and bright field illumination. The cross-section of a pore is contrasted by the surrounding bright viewing polished surface", + " Therefore, a thin film of air may form on the powder particles, thereby increasing the risk of gas entrapment in the melt pool, as shown in Fig. 16 (b). If the entrapped gas can no longer escape from the melt pool, e.g. because of the rapid solidification, then shell-like pores will form. Gas-atomized powders generally have a spherical morphology. T. Zhao et al. Optics and Laser Technology 143 (2021) 107337 However, considering that satellite particles are almost found adhering on the primary powder particles, as shown in Fig. 3, the true sphericity of gas-atomized powder is lower than its appearance. Samples made out of the TiC-modified AlMgScZr-alloy, as shown in Fig. 10 and Fig. 13, were found to have less cross-sectional porosity. Since powder particles will be impacted by the grinding media during ball milling process, it is hard to analyze how the changed powder morphology has a separate influence on the porosity of DED samples. To investigate the influence of the morphology of the particles on the porosity, ground AlMgScZr-1 alloy powders were prepared without the addition of TiC and DED samples were made" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003003_tmag.2004.843349-Figure9-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003003_tmag.2004.843349-Figure9-1.png", + "caption": "Fig. 9. Steady-state temperature distribution.", + "texts": [], + "surrounding_texts": [ + "1) Simulation Procedure and Results: The transient thermal analysis, in which the temperature varies with respect to time, is simulated for different duty cycles. The setting up of boundary conditions has certain steps to be followed using \u201cload step\u201d (LS) files. The value of is set on the meshed model of excited stator poles according to the load pattern. For instance, consider the intermittent load as shown in Fig. 11. The load step (LS) files are sequentially created to take care of the changes in and the respective time period, using solution\u2014time-step\u2014sub-step command. The execution of this command will require the respective values of changing load and time, which has to be systematically input. Finally, write LS command will be used to write the above sequence of LS files as a single file to perform transient thermal analysis. The command outres, all, all must be given before simulation to make the final result of th LS file as the starting values for the th LS file. An example of intermittent load is considered for illustration (Fig. 11). The ON and OFF periods are 900 s each. The heat flux, in W/m , is proportional to 7 A at all the ON periods. It is zero at all the OFF periods. This alternative variation of heat flux and the respective time duration are is sequentially stored in an LS file, and the transient thermal simulation is run. The results of simulation showing temperature rise from 0 to 10 000 s at stator is shown in Fig. 12. 2) Thermal Analysis Considering Eddy-Current Loss: The core loss distribution in SRM is another considerable factor for heat production. Before the boundary conditions are set as detailed in this paper for thermal analysis, an iron loss analysis has to be performed to take into account the core loss distribution. Fig. 13 depicts the results of eddy-current loss distribution as obtained by FEA [15]. The thermal analysis made on this model will be a simulation considering copper loss and eddy-current loss. The results of simulation conducted on this model, showing temperature rise from 0 to 7200 s at stator, for the continuous load of 7 A, is shown in Fig. 14, which indicate that the steady-state temperature is attained at 356 K, whereas without considering the eddy-current loss, it was 350 K. 3) Thermal Analysis Considering Fins: The temperature rise of the electric machines is kept under permissible limits by providing fins. It is possible to increase the heat energy transfer between the outer surface of the machine and the ambient air by increasing the amount of the surface area in contact with the air. Fins are the corrugations provided throughout the outer surface of the frame. When fins are provided on the outer frame of the machine, as shown in Fig. 15, the surface area of heat dissipation gets increased, thus effecting the heat dissipation. It is of the kind called radial fin with rectangular profile. In order to increase the fin effectiveness, various possible combinations of fin dimensions are to be considered. Steadystate thermal analysis has to be carried out for each combination. The fin dimension which produces the least steady-state temperature rise is usually selected for the end product. Table I is the summary of steady-state thermal analysis performed on varying fin dimensions. The fin with a thickness of 2 mm and a length of 3.5 mm is declared for the end product as it produced the least steady-state temperature of 329.893 K. Figs. 16 and 17 respectively represent the results of steady-state and transient thermal analyses on the SRM with radial fins." + ] + }, + { + "image_filename": "designv10_6_0003962_978-3-540-30301-5_3-Figure2.9-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003962_978-3-540-30301-5_3-Figure2.9-1.png", + "caption": "Fig. 2.9 Pathological closed-loop systems", + "texts": [ + " The degree of motion freedom of a kinematic tree is fixed, but that of a closed-loop system can vary. 2. The degree of instantaneous motion freedom is always the same as the degree of finite motion freedom in a kinematic tree, but they can be different in a closed-loop system. 3. Every force in a kinematic tree can be determined, but some forces in a closed-loop system can be indeterminate. This occurs whenever a closed-loop system is overconstrained. Two examples of these phenomena are shown in Fig. 2.9. The mechanism in Fig. 2.9a has no finite motion freedom, but it has two degrees of infinitesimal motion freedom. The mechanism in Fig. 2.9b has one degree of freedom when \u03b8 = 0, but if \u03b8 = 0 then the two arms, A and B, are able to move independently, and the mechanism has two degrees of freedom. Moreover, at the boundary between these two motion regimes, the mechanism has three degrees of infinitesimal motion freedom. Both these mechanisms are planar, and are therefore overconstrained. As a result, the out-of-plane components of the joint constraint forces are indeterminate. This kind of indeterminacy has no effect on the motions of these mechanisms, but it does complicate the calculation of their dynamics" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure8.4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure8.4-1.png", + "caption": "Fig. 8.4 Fabrication process for coil lines by X-ray lithography", + "texts": [ + "3 shows the calculated results of the suction force and permitted currents in coils with different aspect ratios. Here, we used coil parameters as the coil line width of 10 m and the number of coil turns of 675. The gap between the plunger and the fixed core was 1 mm. When the aspect ratio is 5, the suction force may be about 25 times greater than for a coil with an aspect ratio of 1. A spiral microcoil was formed on the surface of the acrylic pipe using X-ray lithography and metallization techniques. Fabrication process for coil lines is shown in Fig.8.4. First, a thread structure was formed on the pipe surface using X-ray lithography. Next, a thin seed layer of copper to be used as an electrode in electroforming was deposited on the pipe by spattering. The pipe was then immersed into a copper plating bath for electroforming and electroforming carried out until the spiral groove was filled with copper film. Finally, the plated copper was chemically etched to remove copper from the surface, but leave copper remaining in the spiral groove thus forming a coil" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002369_s0301-679x(00)00124-9-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002369_s0301-679x(00)00124-9-Figure1-1.png", + "caption": "Fig. 1. The test rig at TUT for grease lubricated rolling bearings used in the present work.", + "texts": [ + " When analysing the influence of solid contaminants in a thin lubricating film on the operation of a grease lubricated bearing, the differences in the rheological properties of lubricating greases and oils, respectively, must be seriously taken into consideration. In the present investigation, the AE measurements employed a bearing test rig in a laboratory environment at Tampere University of Technology (TUT), the Department of Machine Design. The grease mixtures used for the lubrication of the bearings were prepared at VTT Manufacturing Technology. The rolling bearing test rig used in the measurements is shown in Fig. 1. In all measurements the test bearing was a deep groove ball bearing with the size code 6206; the bearing had an inner diameter of 30 mm, an outer diameter of 62 mm and a width of 16 mm, nine balls with a diameter of 9.52 mm and a pressed steel cage. Tolerances and radial internal clearance of the bearings were of the class Normal, according to the bearing manufacturer\u2019s specification. The test bearing housing contained a singular ball bearing. In every measurement the bearing load was static and purely radial", + " The amount of grease that was flushed through the bearing corresponded to about four times the free volume of the bearing housing. The AE signal analysis methods used in the present investigation were the AE pulse count method and the AE time signal method, which are described in more detail in Miettinen and Pataniitty [18] (pp. 289\u2013297). In the pulse count method, pulses of an AE time signal that exceed a defined threshold level are calculated. The pulse count results are presented in the unit of pulses/second. The AE sensor (see Fig. 1) was a resonance type sensor with a resonance frequency of 150 kHz. The signal was filtered with a narrow band-pass filter with centre frequency of 150 kHz. After filtering, the time signal was sampled with a sampling frequency of 1 MHz and converted to digital form with IOtech Wave Book 512 unit. The pulse count analysis was carried out after filtering with an Acutest AETTC pulse count unit. All measurements were stored on CD diskettes for further analysis. For the preparation of the deliberately contaminated grease mixture batches, a mixer built at VTT for this purpose was used" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002548_tsmcb.2003.810443-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002548_tsmcb.2003.810443-Figure3-1.png", + "caption": "Fig. 3. Input and output membership functions.", + "texts": [ + " 2, the fuzzy SMC is designed to have an equivalent controller and two fuzzy switching controllers, . The output of the fuzzy SMC is defined as times the sum of the equivalent control and the outputs of the fuzzy switching controllers , i.e., with 1) Fuzzy Switching Controllers: Let the input and switching output variable of the fuzzy switching controller be simply partitioned into fuzzy sets (negative), (zero), and (positive). The triangular-type input membership functions and the membership functions for output fuzzy singletons are shown in Fig. 3(a) and (b). From (8), it is easy to see that in order to make to guarantee the sliding mode of SCMCS, the fuzzy rules can be derived as the following. 1) If is , then is . 2) If is , then is . 3) If is , then is . With the centroid defuzzification technique, the switching output of the fuzzy SMC is calculated as (12) where are input membership functions, are diagonal matrices with the corresponding values of output fuzzy singletons on the diagonal cells, and is a matrix function to generate a diagonal matrix with the elements of the vector on the corresponding diagonal cells. Note that the denominator of in (12) is equal to an identity matrix, since the triangular membership functions are designed as in Fig. 3(a). Thus, can be simplified as (13) For the switching controller , the input variable is defined as . Similar to the design of the fuzzy switching controller , the fuzzy rules for the switching controller are the following. 1) If is , then is . 2) If is , then is . 3) If is , then is . The input and output membership functions for are shown in Fig. 3(c) and (d). Thus, the output of the switching controller is (14) 2) On-Line Adaptation Mechanism: To simplify the design of the fuzzy switching controllers, in (13) and in (14), are considered to be a scalar (times an identity matrix). As in Fig. 3, the values of the output fuzzy singletons are specified to be symmetrical to zero . Furthermore, it is known that the outputs of the fuzzy switching controllers are zero when the system is in the sliding mode . Thus, the outputs of the fuzzy switching functions and can be simplified as and (15) where are column vectors with the membership values of the corresponding fuzzy sets of the elements in vectors and , respectively. Note that and are negative. The parameter of the fuzzy switching controller is on-line adjusted", + " This adaptation makes the system reach the sliding mode quicker when the sliding function is getting smaller, and the system performance is then improved. Moreover, the chattering can be alleviated with this adaptation mechanism since and are small when the sliding function is large at the beginning of the system operation. With this proposed AFSMC, the sliding mode of the system SCMCS is guaranteed, as described in Theorem 2. Theorem 2: The uncertain system SCMCS with the AFSMC can have its sliding mode guaranteed. Proof: The output of the AFSMC is (17) Then, the reaching rate of the sliding mode is (18) It is known that if then (see Fig. 3). Since Furthermore, because is getting more and more negative with the adaptive law in (16), the term is going to be negative when Likewise, if , the second term in (18) becomes negative when Thus, the reaching rate of the sliding mode is negative in the case of and . If , then . is becoming more negative by following the adaptive law, and finally will be larger than . In this case With the same idea, the second term in (18) can become neagtive when and . Again, and the sliding mode of the uncertain system SCMCS is guaranteed while and ", + " 5 illustrates how the unstable system is stabilized when the sliding mode control is applied. The output of the AFSMC is (23) with the adaptive laws (24) Note that the learning rates are selected with very small values as the initial learning rates. Then, the learning rates are increased to reduce the overshoot and the rising time of the control system. If (the control action is too large and is over the limit) or (the chattering of the control action is large) then the learning rates are decreased. Since the parameters of the input membership functions [see Fig. 3(a)] has the effect of a boundary layer, is assigned to be a small number . Also, is designed because . The performance comparisons for each state of the uncertain system with SMC and AFSMC are provided in Figs. 5\u20137. In Fig. 5, it is shown that the uncertain system with AFSMC has better performance than the uncertain system with the SMC in the sense of smaller undershoot and shorter rising time. The parameters and are indicated in Fig. 8 to empirically conform so that the sliding mode is guaranteed" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003962_978-3-540-30301-5_3-Figure2.5-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003962_978-3-540-30301-5_3-Figure2.5-1.png", + "caption": "Fig. 2.5 Coordinate frames for the first five links and joints of the humanoid robot example", + "texts": [ + " The fictitious 6-DOF joint for a floating base for a mobile robot is also handled relatively easily. For this case, \u03a6i = 1 (6 \u00d7 6 identity matrix) and \u25e6 \u03a6i = 0. Part A 2 .4 The revolute joint and floating-base joint, as well as the universal joint (ni = 2) and spherical joint (ni = 3) are illustrated in the example in the next section. For additional details on joint kinematics, see Sect. 1.3. In order to illustrate the conventions used for the link and joint models, coordinate frames are attached to the first five links (bodies) and fixed base of the humanoid robot as shown in Fig. 2.5. Note that frame Ji is attached to link p(i) = i \u22121 for each of the five joints. For this example, the origin of frame J1 is set coincident with the origin of frame 0, and the origins of frames J2, J3, J4, and J5 are coincident with the origins of frames 2, 3, 4, and 5, respectively. Note that J1 could be set at any position/orientation on the fixed base (B0) to permit the most convenient representation for the motion of the Joint ni JiRp(i) p(i)pJi 1 6 13\u00d73 03\u00d71 2 1 13\u00d73 \u239b \u239c\u239d 0 0 \u2212l1 \u239e \u239f\u23a0 3 3 \u239b \u239c\u239d 1 0 0 0 0 \u22121 0 1 0 \u239e \u239f\u23a0 \u239b \u239c\u239d 0 \u2212l2 0 \u239e \u239f\u23a0 4 1 13\u00d73 \u239b \u239c\u239d 0 2l3 0 \u239e \u239f\u23a0 5 2 \u239b \u239c\u239d 0 \u22121 0 1 0 0 0 0 1 \u239e \u239f\u23a0 \u239b \u239c\u239d 0 2l4 0 \u239e \u239f\u23a0 floating base (B1) relative to the fixed base", + " The rotation JiRp(i) transforms 3-D vectors in p(i) coordinates to Ji coordinates. The position p(i)pJi is the vector giving the position of the origin OJi relative to Op(i), expressed in p(i) coordinates. The spatial transform XL (i) = Ji X p(i) may be composed from these 3-D quantities through the equation for BXA in Table 2.1. The humanoid has a floating base, the torso, a revolute joint between the torso and pelvis (about z\u03022), a spherical joint at the hip, a revolute joint at the knee, and a universal joint at the ankle. As shown in Fig. 2.5, the leg is slightly bent and the foot is turned out to the side (\u2248 90\u25e6 rotation about y\u03023 at the hip). The free modes, velocity variables, and position variables for all of the joint types in the humanoid are given in Tables 1.5 and 1.6. The expressions for j Ri and j pi in these tables give i RT Ji and Ji pi , respectively, through which the joint transform XJ (i) = i XJi may be composed. Revolute joints follow the Denavit\u2013 Hartenberg convention with rotation about the z\u0302i axis. The ankle has a pitch rotation of \u03b15 about the z\u0302 J5 axis followed by a roll rotation of \u03b25 about the y\u03025 axis (see the Z\u2013Y\u2013X Euler angle definitions in Table 1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000327_j.msea.2021.140944-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000327_j.msea.2021.140944-Figure1-1.png", + "caption": "Fig. 1. Scheme of L-PBF building platform and sample orientation.", + "texts": [ + " Three images were taken for each sample and the image magnification was set at 2.5\u00d7. The effect of hatch distance and point distance on the material density was investigated. The combination of parameters that led to the highest density (99,85% \u00b1 0,08%) is shown in Table 3. The optimal combinations of process parameters were used to produce cylindrical samples parallel and orthogonal to the building direction (Z- and XY-samples, respectively) that were machined to produce dogbone specimens for tensile tests. A scheme of the building platform is shown in Fig. 1. The geometry of the specimens (gauge length of 30 mm and cross-section diameter of 6 mm) is in accordance with the ASTM E8 Standard Test Methods for Tension Testing of Metallic Material [11]. F. Belelli et al. Materials Science & Engineering A 808 (2021) 140944 Tensile tests were performed using a Zwick Roell Z100 and a MTS-Alliance RT/100 universal testing machines both equipped with extensometer. The crosshead speed was set at 2 mm/min. Three samples were tested for the 2618Ti/B-L and A20X alloys at room and high temperatures per each condition, respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure3.44-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure3.44-1.png", + "caption": "Fig. 3.44. Arthropoid manipulator in a drawing task", + "texts": [ + "2 can be applied to bilateral manipulation. Case of no relative motion. The connection of the two grippers can be such that no relative motion is permitted. It happens in a task when one \"arm\" hands over the working object to the other. Then, there exists a time interval when both arms are in connection with the object (Fig. 3.43). Something very similar can happen if two manipulators are used together to move a very heavy load. 228 3.7. Examples Example 1 We consider an arthropoid six d.o.f. manipulator shown in Fig. 3.44. Its data are given in the table in Fig. 3.46. The manipulator has to draw a circle on a moving plane (Figs. 3.44, 3.45). Radius of the cir cle is R = 0.4m. At the initial time istant the manipulator is in the resting position and at the same time instant the plane begins to move up with the constant acceleration a = 0.6 m/s2 (Fig. 3.44). During drawing the pencil has to be perpendicular to the plane and produce the force S = 30N upon the plane. The friction coefficient is W=O.3. The drawing task has to be performed in T=2s with the triangular ve locity profile along the circle trajectory. If we follow the theory explained in Para. 3.4.4, the plane constraint is expressed in the form Ao Fig. 3.45. Circle to be drawn x y = f y 1 .2 1 2 z = fz = u 2 + 2 at + 0.4 229 In this example we first illustrate the calculation of\" nominal dynamics" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003628_s11044-008-9121-7-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003628_s11044-008-9121-7-Figure2-1.png", + "caption": "Fig. 2 2(3-RPS) manipulator with a compact topology", + "texts": [ + " Moreover, in order to operate properly a defective parallel manipulator, it is necessary to take into account that when the configuration space is a constraint singularity, distinct modes of operation are expected for the parallel manipulator, Zlatanov et al. [39]. Furthermore, with the purpose to improve the mobility and manipulability of a 3-RPS parallel manipulator, a serial-parallel manipulator or double parallel manipulator can be obtained assembling in series two 3-RPS parallel manipulators; a suitable topology is presented in Fig. 2. The topology proposed in Fig. 2 has the advantage that unlike the method of position analysis introduced in Lu and Leinonen [24], the kinematics of the first parallel manipulator is applicable, without significative changes to the second parallel manipulator, only it is necessary to take into proper account the corresponding reference frames avoiding the inclusion of a large number of parameters. Furthermore, the topology presented in Fig. 2 is compact and can be extended to any number of modules; this is the idea of the present work. In fact, once a module is chosen as the base of the MSHRM, the next module is added in such a way that the axes of its revolute joints are concurrent at the geometric centers of the corre- sponding spherical joints of the previous module. The process is continued until the specific MSHRM has been reached. In particular, the last platform is called the output platform. 3 Kinematic model 3.1 Finite kinematics In this subsection, the forward position analysis (FPA) of the proposed hyper-redundant manipulator is carried out analytically using simple geometric procedures for a detailed explanation of the FPA of a 3-RPS parallel manipulator, which has a direct connection with this subsection; the reader is referred to [36, 40, 41]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002544_robot.1989.100155-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002544_robot.1989.100155-Figure1-1.png", + "caption": "Figure 1. A Mobile Field Robotic Manipulator Concept", + "texts": [ + " Here a planning method is presented which insures that such dynamic disturbances do not exceed the capabilities of a vehicle, and compromise its stability, while permitt ing a mobile manipulator to pcrform its tasks quickly. I. INTRODUCTION Vehicle-mounted mobile manipulators have been proposed for material handling tasks in the construction industry, in areas contaminated by nuclear radiation and in military applications [l]. These systems may be required to manipulate heavy payloads quickly in highly unstructured hostile environments. Such a mobile manipulator, similar to the one shown in Figure 1, is being developed for the US. Army for handling up to 4000 pounds in field environments. But vehicle-mounted mobile manipulators have control and planning problems not found in industrial manipulators securely fastened to factory floors. One problem is to plan the motions of the manipulator so that it can perform its tasks quickly, without generating dynamic forces and moments which are larger than a vehicle can handle and which could cause the system to overturn 12-41. This can be an important problem even when the vehicle is equipped w i t h outriggers such as shown in Figure 1. This paper presents a method for planning the time optimal motions of mobile manipulators. It considers the full nonlinear dynamics of a manipulator and its vehicle. Previous methods developed to plan t h e minimum-time motion of fixed-based manipulators included the constraints imposed by the capabilities of their actuators but not the additional constraints imposed on mobile manipulators by the p h y s i c a l properties of the vehicle [5-11]. The technique proposed here ensures a balance between the forces and moments created by a manipulator's motion, grav i ty , and friction between the ground and the vehicle so that the vehicle maintains contact with the ground at all times, preserving the dynamic stability of the sys tem" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure1.15-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure1.15-1.png", + "caption": "Fig. 1.15. Workspace of RRP - structure", + "texts": [], + "surrounding_texts": [ + "12\n1 ~1 .13. Comparison of the workspaces of\ndifferent minimal configurations\nTo this end we will make the following assumptions:\npermissible rotation of each rotational connection is 3600 ,\n- translation of each prismatic connection equals L,\nthe \"principal\" (greatest) dimension of each segment of the manipu lation robot equals L.\nThe workspaces illustrated suppose some arbitrary wrist, the center of which, 0, is the reference pOint.\n(a) PPP structure\n(b) RPP - structure (or PRP)\nWorkspace is a cube of side L\nv\nWorkspace is a thorus of square cross-section of mean radius Land external radius 2L", + "13\nWorkspace is a hollow sphere of interior radius L and external ra dius 2L\nWorkspace is a cylinder of radius 2L and height L", + "14\nThis comparison demonstrates the evident superiority of the RRP and RRR structures, possessing a workspace approximatelly 30 times greater than the PPP - structure. The RPP and RPR - structures, with workspaces approximatelly 10 times greater, thus offer medium sized workspaces.\n1.2. General Remarks on Up-To-Date Methods for Design of Machines\n1.2.1. Task specification and starting data\nWe witness today a considerable growth of the complexity of problems that should be solved in the process of designing constructions and machines. Realization of machines of a qualitatively new level assumes the use of important achievements of fundamental sciences, design and technology, protection of servicing personnel against vibration, noise and injuries. The task of improving the quality of machines should be solved in the stage of design when it is necessary and possible to thoroughly consider a construction, i.e., take into account a large number of, frequently, contradictory requirements, such as a minimum mass providing a sufficient rigidity and a sufficient reliability, high-speed operation with a lower dynamic load, a low price and a long lifecycle, etc. In the design of machines and mechanisms it is neces sary to achieve an optimal choice of their parameters (structural, kinematic, dynamic, exploitative) which are best suited to the imposed, often numerous, requirements. In the present design practice this task is solved by studying a number of alternative variants and performing appropriate calculations. Elaboration of a large number of alternative variants, based on conventional approaches, connot, in principle, give to a designer the idea about machine capabilities. To illustrate this, let us say that, e.g., if ten different values are assigned to each of ten parameters, it follows that 10 10 variants-tasks should be solved, and this exceeds even the performances of contemporary computers.\nThe costs associated with solving such tasks by classical methods con stantly increase, and the negative effects of accepting nonoptimal so lutions become more and more serious. A further aggravating circum stance is the fact that these are multicriteria tasks with conflicting objective functions. It is therefore difficult for a designer to se lect a compromise solution applying the classical methods for finding the extremum, and most new optimization procedures are predetermined" + ] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure29.10-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure29.10-1.png", + "caption": "Fig. 29.10 schematic illustration of Pd-11at%Ni alloy actuator which exhibits rotational motion", + "texts": [ + " Thus, it is considered that the Pd-11atNi alloy actuator exhibited large displacement increments near the plateau pressure, around 0.8 atm. On the other hand, at pressures over 0.8 atm, the increments in the amount of absorbed hydrogen would decrease, resulting in the decrease in the rate of hydrogen absorption and the displacement increment. From these results, it is suggested that shape change behavior of actuators utilizing HASs can be controlled by controlling hydrogen pressure. 346 Masayuki MIZUMOTO, Takeshi OHGAI and Akio KAGAWA Figure 29.10 shows a schematic illustration of Pd-11at%Ni alloy actuator which exhibits rotational motion. In order to convert the volume expansion of HSA into rotational motion of the actuator, the bimorph structure was flexed to a right angle along the longitudinal direction as shown in the figure. At the flexed corner of the actuator, the bending motion of the wide side is expected to be counterbalanced by the deformation of narrow side, which would suppress the bending motion along the longitudinal direction" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure36.8-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure36.8-1.png", + "caption": "Fig. 36.8 Sketch of piezoelectric ceramic driven the shear mode motor", + "texts": [ + " The rotor contacting with the stator is driven to rotate through a frictional force between the rotor and the stator. The spring gives a pre-pressure between the stator and the rotor. The stator has a mid-cylinder on a metal disc to changes the vertical movement to the horizontal movement. Four pieces of piezoelectric ceramic which is a quarter of a piezoelectric ceramic disc were attached at the bottom of the stator. The ceramic pieces were polarized along the radial direction: two of them are from inner to outer direction and the other two are in the opposite direction as shown in Fig.36.8. To drive the motor, a pair of alternating voltages with a phase shift of 90 degrees, Vosin t and Vocos t, was applied to the bottom electrode segments from a power source. The shear strain can induce a bending mode (shear-shear mode) with a large driving force in a piezoelectric beam under resonance drive with a free-free boundary condition. Since the applied electric field is out of phase, the applied voltages Vosin t and Vocos t will induce the piezoelectric disc to produce two bending modes leading to the rotation" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002878_s0043-1648(97)00076-8-Figure5-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002878_s0043-1648(97)00076-8-Figure5-1.png", + "caption": "Fig. 5. Test grinding machine main spindle.", + "texts": [ + " ) (13) where: \u2022 6r, 6a, q~ are the displacements between bearing rings on radial, axial, and angular directions, respectively; \u2022 Kr, K=, Km are the overall rigidities acting in phase with displacements on radial, axial, and angular directions, respectively, \u2022 Hr, H=, H,~ are the overall hysteretic dampings acting in quadrature. ,-- From these considerations, for a high speed angular contact ball bearing under a complex load, the dynamic model presented i~ Fig. 4 was proposed. 3. Dynamie model validation The validation of the proposed dynamic model was achieved by a theoretical and experimental analysis of the dynamic state of a test grinding machine main spindle ( Fig. 5) in controlled conditions of speed, bearings preload, and load. The level of the transversal vibrations of the main spindle having a major influence on the quality surface in the grinding process was co~sidered in research [ 1,3]. Consequently, were determined both theoretical and experimental amplitudes of the transversal vibrations of the test main spindle offset grinding wheel in controlled conditions of speed for various values of bearings preload Fp, and test force Fs that simulates main grinding force (see Fig. 5). The theoretical amplitudes were determined by the transfer matrix methyl [20]. The experimental validation of the theoretical results obtained was achieved on a test rig schematically presented in Fig. 6. The test main spindle was mounted on a concrete bed insulated from surrounding environment by rubber dampers to remove possible external disturbances and is driven through belt transmissions by an electric motor. The amplitudes of the transversal vibrations of the test main spindle offset grinding wheel were measured by a Bmel & Kjaer measurement chain: accelerometer type 2431, condit':oning amplifier type 2626, frequency analyser type 2113, level recorder type 2305" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure3.43-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure3.43-1.png", + "caption": "Fig. 3.43. Two grippers connected to a working object", + "texts": [ + " Two most interesting tasks with bilateral manipulation are cylindrical and rectangular assembly tasks (Fig. 3.42). The whole discussion on cylindrical assembly task given in Para. 3.6.2 can be applied to bilateral manipulation. Case of no relative motion. The connection of the two grippers can be such that no relative motion is permitted. It happens in a task when one \"arm\" hands over the working object to the other. Then, there exists a time interval when both arms are in connection with the object (Fig. 3.43). Something very similar can happen if two manipulators are used together to move a very heavy load. 228 3.7. Examples Example 1 We consider an arthropoid six d.o.f. manipulator shown in Fig. 3.44. Its data are given in the table in Fig. 3.46. The manipulator has to draw a circle on a moving plane (Figs. 3.44, 3.45). Radius of the cir cle is R = 0.4m. At the initial time istant the manipulator is in the resting position and at the same time instant the plane begins to move up with the constant acceleration a = 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002962_48.544061-Figure14-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002962_48.544061-Figure14-1.png", + "caption": "Fig. 14. Route-planning at the point of intersection.", + "texts": [ + " The obvious advantage of the neural controller lies in its inherent noise-resistant feature. Comparing Fig. 13(b) and (c), it can be seen that the control performance is almost indifferent to the noise, although the input variables to the neural network are not \u201cclean.\u201d B. Track 2: Zigzag Route The second simulation, test compares the performance of the neural and PID controllers for a zigzag route. In this case, there is a distinct change in desired ship headings at the point of intersection (see poinf, T in Fig. 14). To expect the ship to have minimal track error at this turning point, effective \u201ccommunication\u201d between route planning and controller is necessary. One possible approach to such communication is by selection of an allowable error, e, and an anticipation distance, c, together with a circular arc path Pip2 of R, centered on 0 (see Fig. 14). The straight line PIT (TP,) represents a distance, d, between T (the original turning point) and the end of the anticipation distance. Since RZ + d2 = ( R + e)\u2019 and d = R tan p, then solving the resultant quadratic equation in R2, subject to R is real and positive, requires R = A (31) seccp - I \u2019 In Fig. 14, p is specified by Y and X 3 in the defined zigzag maneuver (p = 18.57\u201d), and e and R are specified by the master according to his knowledge about the ship. Hence, a modified route plan with sensible transition from one fixed 520 IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 21, NO. 4, OCTOBER 1996 heading to the next fixed heading is deducible by the controller. In the zigzag simulation where X3 = 2X = 3000 m and Y =500 m, e was chosen to equal 30 m and hence R = 546.2 m. This turning radius is achievable by the MARINER ship model used in this study. Prior to modifying the planned straight line-based zigzag maneuver, $I: 7 r / 2 - p. To allow a smoother transition between the straight line segments for which $12 = $Ifld = 71.43' and $; E $&w = 108.57\", respectively (see Fig. 14), we need to provide values of $e on the arc PI and Pz. The ZHANG er al.: A NEURAL NETWORK APPROACH TO SHIP TRACK-KEEPING CONTROL 521 obvious, but inappropriate, value of $: would be the tangent to the circular transition arc introduced. It is inappropriate because once the ship has taken up the implicit turning circle it is unreasonable to assume that from the point P, onwards the ship can immediately take up and sustain the constant heading I / & ~ . Just as a transition arc was introduced to provide a more sensible route plan, so must 11: on the transition arc be modified so that the ship is capable of sustaining $few after point Pz" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000016_j.mechmachtheory.2020.104097-Figure12-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000016_j.mechmachtheory.2020.104097-Figure12-1.png", + "caption": "Fig. 12. Walking and adjusting modes of the transmission mechanism with the identical parameters.", + "texts": [ + " However, they all have a little smaller \u03b7Fmax , \u03b7Fmin , and a little bigger \u03b7Pmax , \u03b7Pmin ; (2) No. 31 has the biggest \u03b7T in the list, but \u03b7Vmax , \u03b7Vmin are a little small; (3) No. 1 has the biggest \u03b7 , \u03b7 , \u03b7 , \u03b7 in the list, but also has the smallest \u03b7 , \u03b7 ; (4) No. 44 Vmax Vmin Pmax Pmin Fmax Fmin has the biggest \u03b7Fmax , \u03b7Fmin in the list, but also has the smallest \u03b7Vmax , \u03b7Vmin . As a consequence, in order to endow the optimal comprehensive capacities, we identify No. 25 as the optimum non-dimensional parameters, so u 1 = 1 . 5 , u 2 = 1 . 5 , and u 3 = 0 . 5 . As Fig. 12 indicates, the multi-mode transmission mechanism possesses the identical kinematic parameters in both ad- justing mode and walking mode, which are q 1 , q 2 , q 3 , q 4 , q 5 . And there doesn\u2019t exist other new introduced parameters between these two modes. The mode transition between adjusting and walking determines the two modes share the common input and output angles. Hence, a constant equation can be established by substituting the initial conditions of these input and output angles into the position models of both adjusting transmission mechanism and walking transmission mechanism" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002801_20.106510-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002801_20.106510-Figure1-1.png", + "caption": "Fig. 1. (a) Cross section of studied machine; one pole, 658 elements and 348 nodes. (b) Flux distribution at no-load.", + "texts": [], + "surrounding_texts": [ + "where [ 03 and [ F M ] depend, respectively, on the winding and permanent magnets features. On the other hand, in (2), the flux linkage @ can be expressed from the nodal values of the vector potential:\n[ @ I = [GI[AI ( 5 ) where the matrix [ G ] depends as does [ 03 on the winding features. From (2)-(5) we can write the next matrix system:\n( 6 ) In this expression the unknowns are the nodal vector potentials, the currents and their respective derivatives. To solve this time-dependent system, a step-by-step numerical integration as Euler or Cranck-Nicolson algorithm can be used. The Newton-Raphson iterative procedure is used to take into account the nonlinearities of the modeled system [8].\nPROCEDURE TO CONSIDER SKEWING Consider an electric machine where dimensions and structure permit 2-D calculations. If one of the machine parts (rotor and stator) has skewed slots, a 2-D cross section calculation is no longer valid.\nIf the skewed part of axial length 1 is cut into n disks of l / n length, the magnetic circuits of the n machine sections can be modeled by 2-D calculations. Due to this aim, the excitation on the unskewed part must be moved by an angular displacement of a / n for successive sections, where a is the total skew angle.\nIn the case where the magnetic armature reaction is negligible, as mentioned previously, the magnetic and electric circuits can be considered separately. The average flux can then be obtained easily. If armature reaction is strong, the effects of saturation and reluctance in the magnetic circuit imply, as mentioned before, the use of a magnetic-electric coupled model. In such a case, where the unknown current in each slot is the same in the different machine sections (disks), a coupled model implies simultaneous solution of coupled equations in the n disks. The unknowns in this system of equations are the nodal values of vector potential and the slot currents.\nNUMERICAL SIMULATION OF SKEWED SLOTS Considering the foregoing procedure, the finite-element\nequation in section k for an angular displacement (11k is\nLSakl [&kl = ID] [ j ] + [FMakl. (7)\nIf we write (7) for each section, the flux linkage can be expressed from the vector potential by\nn\nFrom (6)-(8), the complete system equation is given by:\n(9)\nThe solution of the nonlinear time-dependent equation (9) is obtained using step-by-step numerical integration and the Newton-Raphson iterative procedure.\nIn the proposed model, the rotation is simulated by an air gap element in which the Laplace equation is solved analytically [4]. Such an element permits armature rotation without changing the nodal coordinates.\nNUMERICAL RESULTS This numerical model has been applied to a six-pole 4.6-N - m 5.9-A, 3200-r/min permanent magnet synchronous machine ( 18 slots skewed of a = 20\"). The cross section (one pole) of this machine and the finite element mesh (658 elements, 348 nodes) are shown in Fig. l(a). The number of machine sections in the axial direction should be enough to consider the skewing effects. This one corresponds to the number of calculated points on the slot harmonic period. On the other hand, the memory storage and computation time depend on the considered number of sections. In the present application, satisfying results have been obtained using nine sections. The flux distribution at no load for a given section is shown in Fig. l(b).\nThe machine electromotive force for a speed of 1000 r/min has been calculated using the proposed model and assuming the machine terminals to be an open circuit. The object of this analysis is only to check the model. The numerical results are shown in Fig. 2(a) and can be compared with experimental results (Fig. 2(b)). To illustrate", + "1098 IEEE TRANSACTIONS ON MAGNETICS. VOL. 26. NO. 2. MARCH 1990\nI I I\nt tms) the effect of slot skewing, the phase EMF in the case of unskewed slots is given in Fig. 2(c). The slot harmonics can be easily observed in this figure.\nA second example has been treated to check the model reliability under transient load conditions. From the noload operation considered in Fig. 2, a three-phase resis-\n(C)\n- 41 Om", + "PIRIOU AND RAZEK: COUPLED MAGNETIC-ELECTRIC CIRCUITS WITH SKEWED SLOTS 1099\n2 A jdir 2 n s l d l r\n3(a)). This figure shows that steady-state voltages are reached almost immediately due to small time constant. The corresponding experimental phase voltages at steady state are shown in Fig. 3(b). Fig. 4 shows the calculated transient phase currents (Fig. 4(a)) and the corresponding experimental phase current at steady state.\nIn a third example, we simulated the operation of the machine connected with a rectifier. Fig. 5 shows the equivalent circuit of such a system. For a speed of 1000 r/min, Fig. 6 shows the calculated and experimental phase current waveforms. For the same operating point, we can see the calculated terminal voltage U , Fig. 7(a), the calculated phase U , Fig. 7(b) (the different voltages are defined on Fig. 5) , and the experimental results Fig. 7(c). From these figures, we can see that the calculated results are in good agreement with experimental results.\n'" + ] + }, + { + "image_filename": "designv10_6_0002576_28.968181-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002576_28.968181-Figure1-1.png", + "caption": "Fig. 1. A-phase winding configuration and principle of radial force production.", + "texts": [ + " The advanced angle is the angle from the middle point of the conduction period of square-wave current to the aligned position of rotor and stator poles. This paper proposes a method of determining the advanced angle of square-wave currents in a bearingless switched reluctance motor. Under any torque condition from no load to full load, a stable operation can be realized by controlling the advanced angle with the proposed method. It is confirmed from experimental results that the proposed method is effective in realizing stable operation. Fig. 1 shows the -phase stator winding configuration and the principle of radial force production. The motor main winding consists of four coils connected in series. On the other 0093\u20139994/01$10.00 \u00a9 2001 IEEE hand, the radial force windings and consist of two coils each. These coils are separately wound around confronting stator teeth. The - and -phase windings are situated on the one-third and two-thirds rotational positions of the -phase, respectively. As the number of stator poles is 12, these three phases are excited for every 15 . The rotor angular position is defined as at the aligned position of the phase. The rotor angular position of Fig. 1 is ( 10 ). The thick solid lines show the symmetrical four-pole fluxes produced by the four-pole motor main winding current . The broken lines show the symmetrical two-pole fluxes produced by the two-pole radial force winding current . It is evident that the flux density in air gap 1 is increased, because the direction of the two-pole fluxes is the same as that of the four-pole fluxes. On the other hand, the flux density in air gap 2 is decreased, as the direction of the two-pole fluxes is opposite to that of the four-pole fluxes" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002903_s0168-874x(01)00100-7-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002903_s0168-874x(01)00100-7-Figure1-1.png", + "caption": "Fig. 1(b) illustrates the relationship between coordinate systems S(P)c and S(P)r , and the formation of the 3-D rack cutter P for the generation of an involute helical pinion. The working surfaces of the pinion are involute screw surfaces generated by straight cutting edges (regions 1 and 3) of rack cutter P. In Fig. 1, symbols \u2018P and uP stand for the parameters of the tool surface. Parameter A represents the pinion\u2019s dedendum, while SP denotes the tooth space. Angles (P)n and P represent the normal pressure angle and the lead angle of the pinion, respectively. The position vector R(i) 1 of the working surfaces of 1 can be represented as follows [1]:", + "texts": [ + " Finally, some numerical examples are presented to demonstrate the FE stress analyses under various design parameters and diIerent contact positions. The proposed helical gear set is composed of an involute pinion and a modi ed helical gear. The modi ed helical gear possesses both pro le crowning and lengthwise crowning. Mathematical models of the pinion and the gear have been developed according to the theory of gearing [16,2] and the proposed generation mechanism [13,1]. For brevity, the equations are not derived in detail here. Gear generation by hob cutters can be simulated using an imaginary rack cutter [16,2]. According to Fig. 1(a), the normal section of the rack cutter surface P used to generate the involute pinion surface, contains four major regions: two straight-edges (regions 1 and 3) and two circular curves (regions 2 and 4). Regions 1 and 3 generate the left-side and right-side involute screw surfaces of the helical pinion, while regions 2 and 4 generate the left-side and right-side llets. Regions 1 and 2 are symmetric with regions 3 and 4, respectively, with respect to the X (P) r -axis. For simplicity, only the parameters of regions 1 and 2 are indicated in Fig. 1(a). The upper and lower signs refer to the left-side and right-side working surfaces, respectively. Parameter r1 denotes the pinion\u2019s pitch radius and 1 is the pinion\u2019s rotational angle during its generation. The llets of the involute helical pinion are generated by regions 2 and 4 (circular curves) of rack cutter P. The equation of the llets of the involute helical pinion are as follows: R(i) 1 = (O(i;P) rx \u2212 r(P)f sin (i;P)f + r1) cos 1 \u00b1 (O(i;P) rx \u2212 r(P)f sin (i;P)f ) cot (i;P)f sin P sin 1 (O(i;P) rx \u2212 r(P)f sin (i;P)f + r1) sin 1 \u2213 (O(i;P) rx \u2212 r(P)f sin (i;P)f ) cot (i;P)f sin P sin 1 \u2212(O(i;P) ry \u00b1 r(P)f cos (i;P)f ) cos P \u2212 ( O(i;P) ry \u00b1 O(i;P) rx cot (i;P)f \u2212 r1 1 sin P ) tan P sin P i = 2 and 4: (2) Similarly, the upper and lower signs refer to the left-side and right-side llets, respectively", + " Therefore, coordinate system S(G)r shifts by a variable amount, EG, with respect to coordinate system S(G)c . Parameter G indicates the position of point O(G) r on the curved-template guide and EG is the corresponding shift of the hob. Parameter (G)max denotes the extreme value of (G) at which the parameter EG reaches its maximum value E(G) 2 . Parameters W and G represent the face width and the helix angle of the gear, respectively. The signi cant diIerences between the normal sections of P (Fig. 1(a)) and G (Fig. 2(a)) are the shapes of regions 1 and 3 which generate the working surfaces of tooth pro les. Regions 1 and 3 of the normal section of rack cutter G are circular arcs rather than straight lines, to produce tooth crowning in the pro le direction of the generated gear. The deviation between the circular-arc and the straight line results in a built-in parabolic TE on the generated tooth surface. A curved-template guide is employed on a conventional hobbing machine to produce a varied plunge of the hob cutter during the gear generation process" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003763_s12239-010-0006-4-Figure5-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003763_s12239-010-0006-4-Figure5-1.png", + "caption": "Figure 5. Boundary conditions applied to the bus structure.", + "texts": [ + " In the attachment of the suspension to the front and rear axle, displacement in the three spatial directions were constrained so that the reaction force in the z direction is the weight. Furthermore, to obtain the torsional stiffness a second load case was run, and therefore, all previous applied loads and constraints were deleted. To apply torsion to the structure in one of the suspension attachments, a vertical displace- ment of 5 mm was applied, and in the three other attachments constraints in the three spatial directions (x, y, z) were imposed, as depicted in Figure 5. Torsional stiffness (KT) of the bus structure is defined as the torsion torque that must be applied for the relative torsion angle between the front and the rear axle to reach one degree. The torsional stiffness is calculated as: [N /deg] (1) where KT is the torsional stiffness, \u2206' is the relative torsion angle between the front and the rear axle, Fz is the reaction force in the z direction, B is the distance between the wheels of the same axle (1.592 m) and \u2206z is the vertical displacement applied so that the bus is subjected to torsion" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003815_j.mechmachtheory.2009.06.001-Figure18-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003815_j.mechmachtheory.2009.06.001-Figure18-1.png", + "caption": "Fig. 18. Defective generators with two identical pitches and two P pairs.", + "texts": [ + " 17, if the four pitches are equal, then \u00bdfH\u00f0A1; u; p\u00degfH\u00f0A2; u; p\u00degfbiH\u00f0A3; u; p\u00deg \u00bc fY\u00f0u; p\u00deg and fH\u00f0A4;u; p\u00deg fY\u00f0u; p\u00deg implies [{H(A1, u, p)}{H(A2, u, p)} {H(A3, u, p)}] {H(A4, u, p)} = {Y(u, p)}{H(A4, u, p)} = {Y(u, p)} \u2013 {X(u)}. Hence, this chain fails in generating Schoenflies motion for any pose and, in other words, it is a defective chain for the generation of X-motion. The four pitches must not be all equal. Pitches may be equal to zero but not all zeros. When four pitches are zeros, the chain generates the planar gliding motion, {Y(u, 0)} = {G(u)}. By the same token, one can demonstrate that if two screw pitches are equal, then two P pairs must not be perpendicular to u. For instance, two chains of Fig. 18 actually generate the 3-dof pseudo-planar motion rather than 4-dof X-motion. Furthermore, if three screw pitches are equal and one P pair is perpendicular to the parallel H axes, as shown in Fig. 19, these chains are trivial chains of a subgroup of pseudo-planar motion and never generate X-motion. One additional defective generator, a series of four prismatic pairs that generates {T} instead of {X(u)}, is displayed in Fig. 20 for completeness. Case B. A product of two factors is a 2D subgroup and one among the other two factors is included into this subgroup" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003670_978-3-642-82195-0-Figure3.3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003670_978-3-642-82195-0-Figure3.3-1.png", + "caption": "Fig. 3.3. An illustration of the modified Newton algorithm", + "texts": [], + "surrounding_texts": [ + "This method has most frequently been used in solving the inverse kine matic problem for non redundant (and redundant) manipulators. We will outline it briefly here. Let us consider the function F(q) = f(q) - xe (3.3.3) where qERn , XeERn and f: Rn+Rn is a continuous, differentiable function which maps joint coordinates into the external coordinates. We should determine the zero of function F which is close to some ap proximate solution qk. By exapanding function F(q) in Taylor's series and keeping the first two terms only, we obtain (3.3.4) where J(qk) = af(qk)/aqERnxn is the Jacobian matrix of partial deriva tives of function f. Equation (3.3.4) is equivalent to -1 k k J (q) (f(q )-xe ) where J- 1 (qk) is inverse Jacobian matrix, ~xk e (3.3.5) 149 ment of external coordinates with respect to the external coordinates which correspond to the approximate solution qk. If q is replaced by qk+1 in (3.3.5) an iterative procedure is obtained. The procedure should be ended when the condition 1 I~xkl 1<\u00a3 is satisfied, where \u00a3 is a small e , positive constant. The Newton method has a quadratic convergency. It is clear that the Newton method yields a single solution for q, the solu tion which is closest to qk However, manipulator motion is frequently set as a continuous trajecto ry in the external coordinates space, or by a set of points xk, k=1, \u2022\u2022\u2022 . k k+1 k e \u2022\u2022\u2022 ,N, so that the 1ncrements ~xe = xe -xe are small. In that case the corresponding trajectory in the space of the joint coordinates is ob tained by a single iteration of the Newton method k+1 q 13.3.6) The solution qk+1 approximately satisfies f(qk+1) ~ x~+1 and it is not necessary to check whether the error is less than \u00a3, since it is assumed that the points xk are sufficiently close to each other. Such a modifi-e cation of the Newton-Raphson algorithm is very common in literature [1,3,7,25]. However, this method of evaluating the trajectory in the space of the joint coordinates, given a trajectory of manipulator hand, inevitably leads to a certain accumulation the linearization error. In order to avoid this accumulation, a compromise between the original Newton -Raphson algorithm and Equation (3.3.6) was proposed in [33]. Namely, the joint coordinates are still evaluated according to (3.3.6) in a . k k k+1 single iteration, but instead of evaluat1ng ~xe from ~xe = xe the increment of external coOrdinates is corrected according to k - x e' (3.3.7) In this case the evaluation of the trajectory in the space of the joint coordinates, given a traj ectory of external coordinates, makes the eval uation of the Jacobian matrix and the real position vector f(qk) neces sary at each sampling interval. The equivalent to this is the relationship between the rates of exter nal and joint coordinates, given a continuous trajectory xe(t) (3.3.8) 150 Given the velocity vector xe(t), one should determine the corresponding joint rates from (3.3.9) This formulation of the inverse kinematic problem is obviously the equivalent of the Newton algorithm (3.3.5) as applied to an infinite simal time interval. A modi6iQ~on 06 N0Wton method In the case when a manipulation task is specified by a set of points in the space of the external coordinates, which cannot be considered as close, the solution of the inverse kinematic problem is obtained by several iterations of the Newton algorithm (if the manipulator is not kinematically simple so that the analytical solution for joint angles is not available). The motion between these points is usually formed as joint-interpolated motion. It is desirable to speed up this process as much as possible. One method of obtaining the inverse problem solution, i.e. finding the zeros of a nonlinear vector function was proposed in [26]. We will here outline the basic idea of this algorithm. We will assume that an initial vector XO and the corresponding vector e qO, which satisfies f(qo) = xO, xOEX ERn, qEQERn are given, together e e e F with the final vector of external coordinates xe. The vector of joint coordinates which satisfies (3.3.10) is to be determined. The modification of the Newton method involves the optimization of a parameter sE(O, 1], defined by * at each iteration k. The optimal value s=s in inertion k is obtained by minimizing the performance index c (3.3.11) The value of the external coordinates vector xe(s) in iteration k is given by 151 (3.3.12) where k k xe = f(q ) (3.3.13) According to the modified Newton-Raphson * and evaluating the optimal value s with algorithm (3.3.12) - (3.3.13) respect to (3.3.11), we obtain k+1 * xe = xe(s ), Fig. (3.3). An approximate evaluation of the minimum of (3.3.11), according to the orthogonality condition, was proposed in [26] * _ xF]T dXe (s)\u00b7 [xe (s ) e ds * o (3.3.14) s= s This equation is a necessary condition for the minimum. According to this procedure s is evaluated iteratively from F T [xe-xe(si)] [xe (si)-xe (si_1)] \\xF-x (s.)l\\x (s,)-x (s, 1)\\ e e ~ e ~ e ~- , i=0,1, .\u2022\u2022 (3.3.15) where So and r have to be chosen. The iterative procedure should be ended when the value of the fraction in (3.3.15) falls under a specified value (e.g. 0.1 or 0.2). However, examples showed that minimiza tion according to (3.3.15) may produce anomalies, when sk+1 yields a value of C greater then the value obtained for sk. This is a consequ ence of the fact that several values of s exist, which satisfy (3.3.14). Practical examples, however indicate that it is sufficient to limit only the maximal number of iterations, without searching for special methods to overcome these problems. 152 The results of experiments [26] showed that the inverse problem solving is significantly accelerated. In a six degree-of-freedom manipulator the average number of iterations was 4-6 (with a maximum 8 for ~q=1200). * Each iteration requires approximately 4 more steps to determine s , but this is less time consuming as it requires only the evaluation of f(q), without J- 1 (q) . The Cheb~hev appnoach method This method was proposed in [27]. The problem is to determine such a * solution q to the system of equations where E = [E 1 maxiE. (~*) I = min maxiE. (q) I . 1. . 1. 1. q 1. * L (3.3.16) (3.3.17) Point q is geometrically closest to the hyperplane (3.3.8), so that in .* .* Chebishev sense vector xe = Jq is closest to the given vector xe. The Chebishev approach to the solution is reduced to the problem of linear programming, so that it is appropriate to take the constraints on joint velocities into account i=1, \u2022.. ,n (3.3.18) together with all other constraints on the mechanism motion. The linear programming technique applied to finding Chebishev approach to the so lution to (3.3.8), with constraints (3.3.18), has the following form: it is necessary to find the negative values of variables x 1 , \u2022\u2022. ,xn +1 which minimize linear function z = x n +1 ' with constraints n L J .. x. - xn+1 <; b1.' j=1 1.J J n L J .. x. + xn+ 1 > b1.' , j=1 1.J J n where b. = L J .. a. + x e ' 1. j=1 1.J J matrix J. This problem is (3.3.19) i=1, .\u2022. ,n x. = q1.' + a., J .. is the i, j element of 1. 1. 1.J efficiently solved by the dual simplex method. 153" + ] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure2.34-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure2.34-1.png", + "caption": "Fig. 2.34. Two types of linear joint", + "texts": [ + " We first derive the procedure for the calculation of reactions in manipu lator joints. At the beginning, it is necessary to discuss in more de tails the case of linear joints. Such a joint was shown in Fig. 2.5. and the vector ~ii was introduced. The vector ~i-1,i was considered constant. Such joint representation was satisfactory for the formation of mathematical model. But, if we wish to calculate reactions and stresses and, leter, elastic deformations, it is necessary to distin guish two different cases of linear joints. These two cases are pre sented in Fig. 2.34. Let us introduce the indicator Pi' which deter mines to which of the two cases linear joint Si belongs: { 1, 0, We now introduce if joint Si is of type (a) (Fig. 2.34) if joint Si is of type (b) (Fig. 2.34) (2.5.6) (2.5.7) Thus, the translation in joint S. is taken into account either through .... , .... l r .. (in case (a)) or through r~ 1 . (case (b)). II l- ,l .... Let us now consider the i-th segment (Fig. 2.35). Let FSi be the total .... force in the joint Si acting on the i-th segment, and let MSi be the total moment in the same joint acting on the i-th segment. Notice that ~ ~ -+ -+ now FSi+1 and MSi+1 act on the (i+1)-th segment, and -FSi+1, -MSi+1 act 83 on the i-th segment. From the theorem of center of gravity motion it follows -+ -+ -+ -+ m" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure11.9-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure11.9-1.png", + "caption": "Fig. 11.9 Schematic drawing of the mirror, which consists of a rigid c-Si drum and the thin film", + "texts": [ + " High-Performance Electrostatic Micromirrors 125 The fast response is necessary especially for the high-resolution laser display. The light-weighted mirror is ideal. There have been efforts realizing the flat mirror with the stretched thin film over the drum frame. Satisfying < /10 is not easy when the thin film is used, because the film bends due to the stress and its distribution inside. The large tension inside the film is considered to flatten the mirror plate. Figure 11.8 shows the illustration. The tensile stress increases the stiffness without increasing the mass. Figure 11.9 shows the calculation of the inertia normalized by the value of the solid disk. The lateral axis is the inner radius of the drum relative to the outer radius. The supposed values are 250 m for outer radius, 50 m for drum thickness, and 0.5 m for the film thickness. When the inner radius increases, the inertia decreases. The mirror based on the same concept 126 Minoru SASAKI has been prepared [12]. Their mirror has 100 nm deflections in peak-to-valley. If the tensile stress can be larger, the larger flattening effect will be obtained" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003742_1.4000277-Figure12-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003742_1.4000277-Figure12-1.png", + "caption": "Fig. 12 Areas under p", + "texts": [ + " 3, a symmetrical FE model is sed, as shown in Figs. 10 and 11. In the FE analysis, if the concentrated forces, which are the eaction forces of the ball load Qij, are applied to the raceway rooves of the carriage and rail, the deformations at the points of he concentrated force applications are overestimated. To prevent hose overestimations, the reaction forces acting on the raceway rooves of the carriage and rail were modeled by the uniform ressures qic and qir, respectively. The areas under the pressures ic and qir are shown in Fig. 12. The uniform pressures qic and qir re given by qic = 1 aicL1 j=1 n Qij, qir = 1 airL1 j=1 n Qij 18 here L1 is the carriage length, ai is the major axis of the contact llipses of the ith ball and raceway grooves, and the suffixes c and refer to the carriage and rail, respectively. If there is no restraint to the carriage in the FE model under the niform pressures qic and qir, the FE analysis shows carriage itching, which occurs due to the inevitable calculation errors. To 11102-6 / Vol. 132, JANUARY 2010 om: http://tribology" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000068_tie.2021.3057002-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000068_tie.2021.3057002-Figure4-1.png", + "caption": "Fig. 4. Two dimensional electromagnetic model of the machine: 1-Stator core; 2-Stator windings; 3-Solid rotor; 4-Solid starting cage bar; 5-Shaft; 6-Stator slot wedge; 7-Rotor slot wedge; 8-Permanent magnet; 9-Magnetism isolating sleeve.", + "texts": [ + " 5) The outlet of the external cooler (number 2 in Fig. 3) adopts the pressure outlet boundary, and the outlet pressure is 1 atm. 6) Rotating wall boundary conditions are adopted on the surface of the rotor. 7) The multi-reference coordinate system model is used to simulate the fluid in the air gap. In order to determine the losses in motor different components, a two-dimensional transient electromagnetic field model is analyzed by using the time-stepping finite element method (TFEM), as shown in Fig. 4. The assumptions and transient 2-D electromagnetic field calculation equation are proposed in [20]. The main electromagnetic losses of HVLSSR-PMSM in normal operation are stator core loss, stator winding copper loss, eddy current loss of solid rotor body, and eddy current losses in starting cage bars, rotor slot wedges, and magnets. The core loss of each element can be calculated by the Steinmetz equation [21], as shown in (3). Considering the low fundamental frequency, 50 Hz, the AC loss in stator wingdings is ignored, and the copper loss could be obtained by (4) [22]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003801_j.camwa.2009.08.011-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003801_j.camwa.2009.08.011-Figure1-1.png", + "caption": "Fig. 1. Diagram of the system under consideration.", + "texts": [ + " The important property of the generalized Zener model is that it is able to predict behavior of the viscoelastic material with significant accuracy, including only four parameters, [6]. We expect that four constants included in the model, determined from the stress relaxation experiment, could give useful information on the state of the muscles. The simplified mechanical model of a hamstring muscle group and human leg is introduced and is similar to the one presented in Tozeren [7]. The hamstring muscle group is modelled by a viscoelastic rod (Fig. 1). Lengths a, b, c and d depend \u2217 Corresponding author. E-mail addresses: ngraho@uns.ns.ac.yu (N.M. Grahovac), mzigic@uns.ns.ac.yu (M.M. \u017digi\u0107). 0898-1221/$ \u2013 see front matter\u00a9 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.camwa.2009.08.011 on an observed sample, so they are considered as known quantities. During the movement of the lower leg OD the length L of the muscle depends only on the angular position of the lower leg. In Fig. 1 a denotes the upper leg length, b stands for the distance between the knee and the position where the hamstring is tied to the lower leg, while c and d describe the connection between the hamstring and the pelvis. The length of the viscoelastic rod representing the muscle can be derived from the following equation L(\u03b3 ) = b+ a cos (5\u03c0/9\u2212 \u03b3 )+ c cos (5\u03c0/9\u2212 \u03b3 \u2212 \u03b2)\u2212 d sin (5\u03c0/9\u2212 \u03b3 \u2212 \u03b2) cos\u03c6 (2.1) where tan\u03c6 = a sin (5\u03c0/9\u2212 \u03b3 )+ c sin (5\u03c0/9\u2212 \u03b3 \u2212 \u03b2)+ d cos (5\u03c0/9\u2212 \u03b3 \u2212 \u03b2) b+ a cos (5\u03c0/9\u2212 \u03b3 )+ c cos (5\u03c0/9\u2212 \u03b3 \u2212 \u03b2)\u2212 d sin (5\u03c0/9\u2212 \u03b3 \u2212 \u03b2) " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003301_physreva.39.5932-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003301_physreva.39.5932-Figure1-1.png", + "caption": "FIG. 1. Solutions to (3.31) are shown in the kI-e plane for fixed values of kL~~, where k& is related to k& and e by (3.29). The numbers attached to the curves represent the value of kL~~. Below the dotted curve, e+k& &0, k2 becomes purely imagi-", + "texts": [ + "32) This condition is also sufficient for the existence of a solution to (3.31). In fact, if (3.32) holds for given positive k, and k'2, (3.31) is always satisfied for some kL~~ because the hyperbolic function on the right-hand side increases more rapidly with increasing kL~~ than that on the left-hand side and the right-hand side vanishes for kL~~ =0. In Appendix C it will be shown that (3.32) is just imposing an upper limit to 8, , (3.33) where 6, is a positive zero point of the following cubic polynomial: 11'\u20145f, (z) =z'+ Sz'+ @+1 z \u20141. (3.34) In Fig. 1 we show curves of k', versus e for kL ~~ =0.6, 1, 2, and ~, the last one representing the marginal curve k;=5, . Here 5,(0)=1 and 5, (ca)=0.296 as a function nary. The value of X, (3.30), can be obtained from k=6 ' \u2014k'I. We have thus arrived at a very simple criterion: there are eigenmodes with negative A, , and the system is unstable if mer size. Thus, if we take into account hF;\u201ez, A, should be modified to 5&5, . (3.36) A. = \u2014(5, \u20145 )k +bk (3.39) (3.37) A, =Rk 2 = \u2014(5, \u20145 ) [ 1 \u2014exp[ \u201425(k \u2014k, )L ~~ ] I k where A, in (3", + "p can be negative with no instability in any materials if deformations are allowed in only one or two directions (see Ref. 33). This is because the vector Bx/BX; is orthogonal to the tangential vector BX;/By. For 0, = 1 each term in (3.31) vanishes and we need to examine this case separately. In Appendix B we see that, if k, =1, there is a class of eigenvectors with A, =6' \u20141 in the region @&0, and that kL~~ is uniquely determined by negative e. These eigenvectors can also be obtained by taking the limit 0'&~1 in (3.26) and (3.27). Note that the curves in Fig. 1 cross the line k, =1 for e &0. Equation (3.31) can be solved explicitly only for a=0 in the form kL1=(2k, ) 'ln[(1+k;)/(I \u2014k)). This shows that kL~~ is real for 0\u00bb 0& & 1 or for 6 ~ A. & 6' \u20141, and that k, is purely imaginary for A, )6'. 2sInterestingly, the equation f, (z)=0 coincides with the equation to determine the propagation velocity c& of the surface (Rayleigh) wave (Ref. 8) in isotropic elastic bodies if z is replaced by 1 \u2014(c& /c, )', c, being the transverse sound velocity. The ratio of the longitudinal sound velocity c& to c, is given by ci/c, =(1+a)' " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure3.26-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure3.26-1.png", + "caption": "Fig. 3.26. Two d.o.f. joint connection", + "texts": [ + " The connection between the two grippers can be of any type considered in Para. 3.4.4- 3.4.10. All the theory from these paragraphs can easily be extended by considering another gripper instead of a moving object. From all different types of connections we choose the three cases which are most interesting for practice. Two d.o.f. joint connection. We consider two manipulators having the grippers connected to each other by means of a joint permitting one ~ relative translation (along the unit vector h) and one relative rotation (around h) (Fig. 3.26) Let the position vectors of the two manipulators (1) and (2) be 201 (3.4.138) If one of the manipulators (or both) has five d.o.f., the corresponding angle ~ does not appear in the position vector. We restrict our con sideration to manipulators having five or six d.o.f. For simplicity we assume n 1 = n 2 = n. Let us apply the theory derived in Para. 3.4.7 but here the gripper of manipulator (2) plays the role of moving object. The motion of this gripper (2) is defined by xA2 (t), YA2 (t) , ZA2 (t) , (3" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003281_027836498600500206-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003281_027836498600500206-Figure2-1.png", + "caption": "Fig. 2. Coordinate systems used for two interconnected links.", + "texts": [ + " 1) and the relative motion between the interconnected links, respectively. We consider that two coordinate systems S~) and S~) are rigidly connected to a link of number k. The coordinate transformation in transition from S~) to S~) is represented by Fig. 1. Here ak and ak are the shortest distance, and the twist angle between the axes of two revolute or cylindrical pairs with which link k is provided. Now consider that two links, k and I, are interconnected by a revolute or a cylindrical pair (see Fig. 2). Fig. 1. Link geometry. Matrix M~g) represents the coordinate transformation in the transition from S~) to S~i) and is represented by Here 1:> /k is the angle of rotation of link 7 with respect to link k (angle 1:>lk is formed between the xl\u2019>- and at UCSF LIBRARY & CKM on December 2, 2014ijr.sagepub.comDownloaded from 54 xk >-axes and is measured counterclockwise from xy> to xJ\u2019~ for an observer located on the positive axis zl\u2019~); Slk is the distance between the origins of coordinate systems SU) and S(i) (OW and 0(i)); and slk is measuredk I k I \u2019 from 0(i) to 0(i) When transforming the projections of a free vector, we will use matrices r~i) and L~g) instead of Gy\u2019> and M(ii), respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002998_j.matdes.2006.04.014-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002998_j.matdes.2006.04.014-Figure3-1.png", + "caption": "Fig. 3. Configuration of the insert (a) and tool holder (b).", + "texts": [ + " Especially, it is preferred for A (mm) Depth of cut 3 (0.25 0.50 and 0.75) B (mm/min) Feed rate 5 (60, 70, 80, 90, and 100) C (m/min) Cutting speed 3 (30, 35 and 40) machining of superalloys. Because it is difficult to machine superalloys, tool holder to which cutting tools are connected (four inserts are connected to the holder) is selected to be suitable to inclined machining. Cutting tools are connected to tool holder in such a way that positive cutting can be done. The geometries of cutting tool and tool holder are shown in Fig. 3 and its values are given in Tables 3. Chamfered cutting tool (0.18 mm) having an angle of 20 is selected in order to prevent breaking of cutting tool on instant cutting process and cutting edge at the top of this tool is selected as knurled in order to distribute stresses formed on cutting process. The cutting tool has an angle of 26 bending backward. Also, cutting tools are designed as having 2 angle with contact length while cutting. The PVD coated tools are the most appropriate for fine medium rough milling" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003570_titb.2008.2008393-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003570_titb.2008.2008393-Figure2-1.png", + "caption": "Fig. 2. (a) During permanent seed prostate brachytherapy, needles carrying radioactive seeds are inserted transperineally into the patient, who is lying on his back [2]. (b) Intraoperative transrectal ultrasound can be used for imaging, but these images do not provide sufficient quality signal to track tissue deformations.", + "texts": [ + " The planner uses optimization to intelligently test different insertion locations and depths to compute the optimal needle offset: a sensorless motion plan, as illustrated in Fig. 1 (right column), greatly reduced placement error in simulation. We apply the planning system to permanent seed prostate brachytherapy, a minimally invasive medical procedure where physicians use needles to permanently implant inside the prostate radioactive seeds that irradiate the surrounding tissue over several months, as shown in Fig. 2. The success of this procedure depends on the accurate placement of radioactive seeds within the prostate gland to ensure that a high dose is delivered to the cancer cells and a low dose is delivered to the surrounding healthy tissues [2], [3]. We define placement error as the Euclidean distance between the desired location for the seed specified by the dosimetric plan (the target) and the actual implanted seed location after needle retraction. Tissue deformations during needle insertion and retraction contribute to seed placement error during brachytherapy [1], [2]", + " During permanent seed prostate brachytherapy, physicians insert into the prostate approximately 20 stiff, hollow needles loaded with radioactive seeds. Physicians use metal guides during insertion to ensure that the needles are all inserted parallel to the z-axis. The needles are inserted, one at a time, to prespecified targets and the seeds are released. In the clinical workflow, the motion planner can be executed after a dosimetric plan is generated and a 2-D image is obtained in the yz plane using standard transrectal ultrasound (as shown in Fig. 2) or by extracting a slice from a 3-D image such as MRI. The planner will provide clinicians with information to estimate the optimal needle insertion coordinate and depth prior to inserting the needle bearing radioactive seeds. We implemented the simulator in C++ using OpenGL for visualization and tested on a 750-MHz Pentium III laptop PC with 256 MB RAM with an Intel 815EM graphics chip with 11 MB video SDRAM. When executed in interactive simulation mode, a physician can guide the needle and implant seeds using a mouse, as shown in Fig", + " When executed in planning mode, we assume the needle is inserted at a constant velocity of 0.5 cm/s and use a fixed simulation time step of h = 1/30 s. The simulation runs on standard PC\u2019s running Windows 2000 or XP. Our anatomy model of the prostate is based on data obtained in the operating room at the University of California, San Francisco (UCSF) Comprehensive Cancer Center from a patient undergoing brachytherapy treatment for prostate cancer. An ultrasound video was recorded using an ultrasound probe in the sagittal plane, as shown in Fig. 2. The first frame of the ultrasound video was manually segmented by a physician from the UCSF Comprehensive Cancer Center. The segmentation was used to manually generate a mesh composed of n = 676 nodes and m = 1250 triangular elements for a 3.5-cm-diameter prostate and surrounding fatty tissue. The ultrasound image also served as the texture map image for the simulator. The boundary of the mesh is defined by a square for which the right face (where the needle is inserted) is free, the bottom face corresponding the transrectal ultrasound probe is rigid, and the other two faces are also marked rigid" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure24.7-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure24.7-1.png", + "caption": "Fig. 24.7 Design of the 6-8 spherical stepping motor", + "texts": [ + " Actuator with Multi Degrees of Freedom 285 Encoder signals are measured and the X-Y positions of the output shaft are plotted on the X-Y plane. Plotted figures are shown in Fig.24.6. According to the plotted figures of the trajectory control, the developed motor moves with a relatively small positioning error. The developed motor showed some good performances, but the output torque is still too small to drive a robot\u2019s joint. I will increase the output torque by using iron cored back yoked armature coils. Figure 24.7 (a) shows a picture of the developed hexahedron-octahedron based spherical stepping motor (6-8 spherical stepping motor) and Fig.24.7 (b) shows the structure of it. Both the rotor and the stator are sphere shaped. The rotor is supported by six spherical bearings. Compressed air is supplied for the three bearings positioned on the bottom to reduce the friction of the balls. Figure 24.8 (a) shows the structure of the rotor and Fig.24.8 (b) shows the structure of the stator. Eight NdFeB permanent magnets are attached on the spherical shell at the vertexes of the virtual hexahedron inscribed in the rotor so that the North and the South poles are located alternately" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000135_j.optlastec.2021.106917-Figure5-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000135_j.optlastec.2021.106917-Figure5-1.png", + "caption": "Fig. 5. Calculated temperature and temperature gradients (arrows marked) distribution under different processing parameters, scanning speed v = 1000 mm/min, powder feeding rate mf = 20 g/min: (a) P = 1000 W, (b) P = 1200 W, (c) P = 1400 W; (d) liquid lifetime (black) and depth to width ratio (blue) under different processing parameters, the dashed line is the results with no fluid calculation, and the solid line is the results of the calculation including the flow field.", + "texts": [ + " For one thing, without the influence factor of Marangoni flow, the heat conduction was stronger in the direction of laser incidence. For another, under the action of buoyancy, the downward movement and heat transfer of the melt were limited in the case considering fluid calculation. Contrarily, the heat transferred from the melt moving zone to both sides promoted the size in the width direction. Consequently, compared with the results ignoring fluid effects, the results considering fluid calculation showed us a more flat and wider molten pool. Fig. 5 presents the transient temperature field at different laser power under the parameter at 0.2 s, when the scanning speed (v = 1000 mm/min) and powder feeding rate (m = 20 g/min) are constant. It is obvious that with the increase of laser intensity, the maximum temperature and the size of the molten pool in all directions also increased. When the laser power was 1000 W, the maximum temperature of the pool surface was 2456.87 K, dimensions of the molten pool were 1.44 mm (width), 0.34 mm (depth). Compared with the former, the width (1", + " During processing, since the matrix at the front of the X. Shi et al. Optics and Laser Technology 138 (2021) 106917 molten pool was still in solid-state and had a lower temperature and a large thermal conductivity, heat diffused faster through the molten matrix. Moreover, heat transferred to the boundary of the molten pool through the movement of the melt, where the convective heat transfer was limited and the accumulated heat diffuses by heat conduction. Thus, a large temperature gradient appeared at the front boundary of the molten pool. Fig. 5(d) shows the liquid lifetime (black) and the depth width ratio (blue) of the molten pool with the increase of laser power. The circle point contains the results of fluid calculation, while the square point represents the results without fluid calculation. With the increase of laser power, the life of the molten pool also increased. In the aspect of depth to width ratio, when considering the melt movement, the depth to width ratio increased with the increase of power. With the increase of laser power, the ratio of depth to width of the molten pool is basically kept at the same level, but slightly decreased before increasing" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000262_j.mechmachtheory.2021.104299-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000262_j.mechmachtheory.2021.104299-Figure3-1.png", + "caption": "Fig. 3. Discrete model of the left side of the wide-faced double-helical gear pair along gear width.", + "texts": [ + " The Timoshenko beam element with 2 nodes and 12 degrees of freedom is employed to establish the model of each shaft element. Both the left and right gear pair are modeled using a series of nonlinear contact elements with different stiffness values and various clearance values. Both the left and right side of the wide-faced double-helical gear pair are discretized into a series of thin slices along gear width, and the engagement process of the left side of the sliced wide-faced gear pair is shown in Fig. 3 , where r p and r g are the radii of base circle of driving and driven gears, \u03c9 p and \u03c9 g are the rotation speeds of driving and driven gears, O p and O g are the rotation centers of driving and driven gears. N 1 N 2 is the theoretical meshing line, B 1 B 2 B 3 B 4 is the plane of action, \u03b2b is the helix angle of the base circle. The model of the i th nonlinear contact element is shown in Fig. 4 , where \u03c8 and \u03b1 are the installation angle and mesh angle, O Li p and O Li g are the rotation centers of the i th nonlinear contact element" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000329_j.mfglet.2021.02.003-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000329_j.mfglet.2021.02.003-Figure1-1.png", + "caption": "Fig. 1. Schematic detailing the two AM techniques used to p", + "texts": [ + " Tensile properties were used as the metric to benchmark the effects of the two processes on the traditionally brittle alloy properties. Thus, tensile specimens were fabricated and tested parallel to the build direction, in the as-built condition, with initial strain rates of 0.004\u20130.013 s 1. Due to the fundamental design constraints for the two AM techniques, different build methodologies were required for constructing tensile specimens. Schematics detailing the two processes used in this study are shown in Fig. 1. For L-PBF (Fig. 1a), the intrinsic design freedom enabled processing of net-shape tensile geometries. Two gage designs were used. One was a square crosssection, referred to as L-PBF Rec, of size 6 mm 3 mm 5 mm. The other, labeled as L-PBF Cir, had a 4 mm cylindrical diameter, 22 mm length, and M12 printed threads on each end of the grips. The cylindrical L-PBF specimens were also fabricated with and without peripheral heat sinks (built concomitantly with the specimen) that terminated near the upper grip (see ref. [39] for more details). Heat sinks were utilized as an additional design feature, uniquely enabled by L-PBF, to limit temperature rise during processing. Conversely, the L-DED process (Fig. 1b) was unable to produce single sets of net-shape tensile specimens due to the processing and design restrictions for overhang features. Thus, to achieve tensile specimens with a vertically oriented build direction along the gage length, bulk blanks approximately 56 mm 12 mm 20 mm (length width height) in size were constructed and tensile specimens were machined out via wire electrodischarge machining (EDM). A similar specimen design was used with a 1 mm square gage cross-section and 4 mm gage length [40,41]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002720_1.1541628-Figure12-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002720_1.1541628-Figure12-1.png", + "caption": "Fig. 12 The three basic types of kinematic pairs", + "texts": [ + "a It is also well known that the relative displacements between a pair of rigid bodies connected by these types of kinematic pairs form subgroups of the Euclidean group. Furthermore, these subgroups are denoted by 1. Revolute joint. R~O , u\u0302 ,u!,E~3 !, uP@0,2p! is the joint variable. (A-4) 2. Screw or Helical joint. S~O , u\u0302 ,u ,p !,E~3 !, uP@0,2p! is the joint variable. (A-5) 3. Prismatic joint. P~ u\u0302 ,s !,E~3 !, uP~2` ,1`! is the joint variable. (A-6) For a graphical explanation of the joint parameters, see Fig. 12. Furthermore, for conciseness sake, any one of these subgroups, of the Euclidean group, will be denoted by H1 . It is possible, now, to advance a formal definition of the mechanical liaison or bond of a pair of bodies in an open kinematic chain, a concept introduced by Herve\u0301 @9#. Definition A-5. Let i and j a pair of links of an open kinematic chain. The Mechanical Liaison or Bond, between i and j, denoted by L(i , j) is the set of all possible Euclidean displacements of j relative to i. As indicated previously, the rigid links will be regarded as different positions of the same rigid body" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure4.5-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure4.5-1.png", + "caption": "Fig. 4.5. Some possible cross-sections of manipulator segments", + "texts": [ + " The forms of segment cross-section (not the cross-section di mensions but only its general form) can be different. Several forms of cross-section can be checked, but in one optimization procedure this is considered to be known. In this way the choice of optimal parameters of manipulator segments reduces to the determination of the optimal di mensions of cross-sections. Usually there are several dimensions which define a cross-section. In the case of a circular cross-section (Fig. 4. Sa) it is enough to prescribe one dimension: the radius. If the cross -section is in the form of a circular tube (Fig. 4.5b) then there are two dimensions: the inside and the outside radius. In the case of a rectangular tube (Fig. 4.5c) there are four dimensions. Let us also point out that there often is more than one segment to be optimized and these segments can have different cross-section forms. Hence, in general, a multiparameter optimization follows. 253 If the energy consumption criterion is considered it is then clear that the masses of segments should be reduced as much as possible. Hence the cross-section dimensions should be reduced too. But an answer as to the dimensions which should be adopted in order to obtain the minimal ener gy consumption along with the satisfaction of the constraints imposed cannot be given before the completion of the optimization procedure", + " The segments 1, 2, 4 and 5 are completely determined by the constructive solutions adopted. The third segment has the form of a cylindrical tube made of steel (p = 7,85.10 3 kg/m3 , E = 2,1.10 11 N/m2, a 5.108 N/m2, safety p coefficient \\! = 3). This tube can be pulled out of the second segment up to 0.8 m. This results in the segment being 1.2 meters long. Thus the cross-section dimensions of this segment remain to be chosen. The cylindrical tube cross-section is defined by the outside radius (R) and the inside radius (r), as shown in Fig. 4.5b. In order to reduce the number of independent parameters we adopt the constant ratio ~ = r/R 0.85. Thus there remains only one parameter to be optimized. It is the outside radius R. Let us define the manipulation task. It is shown in Fig. 4.7. The working object has to be moved along the trajectory AoA1A2 with a triangular velocity profile on each straight-line part. We adopt: T2 = 2T1 where T1 is the execution time T(Ao+A1 ) and T2 = T(A1+A2 ). We perform the optimization with several different values of the total execution time (T = T1 + T2) in order to check whether the results depend on this ex ecution time" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure2.63-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure2.63-1.png", + "caption": "Fig. 2.63. shows the torque-r.p.m. diagrams (pm - nm) for the motor in joint 52 together with the maximal motor characteristic (P~ax - nm). It can be seen that for the execution time T = 3.2s, the diagram is wholly within the permissible domain (defined by maximal torque cha racteristic). For the faster manipulator work, T = 2.8 s, the diagram extends beyond the permissible domain which means that the chosen motor cannot produce this faster work. For T = 2.4 s the constraint is vio lated much earlier.", + "texts": [], + "surrounding_texts": [ + "In this paragraph we discuss briefly the organization of input to the dynamic analysis algorithm from the standpoint of some specific fea tures of the algorithm. Fig. 2.47. presents a block scheme of algorithm input. Let us explain this scheme. The first set of indicators (LB i ) serves to define algorithm printout. There are several dynamic variables and characteristics which can be calculated (Para. 2.5.) and, thus, which can be printed. We use the indicators LBi to define which of these dynamic characteristics will be printed. 105 The indicators LCi define the set of tests. Thus, we choose the tests by using these indicators. On the basis of these two sets of indicators (LB and LC) the algorithm itself decides what should be computed in order to give the required prints and to perform the required tests. The configuration input contains the definition of geometry and iner tial properties. Some other parameters are also defined, for instance the cross section inertial moment if stress or deformation analysis is required. This input block allows the choice of standard-form segments. A set of indicators is used to determine the segment which has a stan dard form and which form it is. For a standard-form segment the algo rithm itself computes the segment mass, inertial tensor, cross section inertial moments etc. on the basis of the input dimensions of standard form and the input data on material. If the actuators tests or torque - r.p.m. prints are required, then the catalog characteristics of actuator and reducers are needed. Spe cial indicators are used to define which actuators have to be tested. If stress or elastic deformation analysis (the corresponding tests or prints) is required, some properties of segments material must be known (e.g. Young's modulus, maximal permitted stress, etc.). A set of indi cators is used to define which segments are considered elastic, and another set to define which segments have to be stress-tested. Manipulation task input has been discussed in 2.4. and the correspon ding input file will be explained through examples in 2.8. 2.S. Examples In this paragraph we present several examples illustrating the opera tion of the algorithm for dynamic analysis. We demonstrate the use of adapting blocks, the calculation of various dynamic characteristics and some testings. The first example (2.8.1) deals with a 4 d.o.f. 106 manipulator. In (2.8.2) and (2.8.3) two 5 d.o.f. manipulators are con sidered. Finally, in (2.8.4) we present an example of a manipulator with 6 d.o.f. 2.8.'. Example' We consider a cylindrical manipulator UMS-2V - variant with 4 d.o.f. The external look and manipulator data are presented in Fig. 2.48a. This figure also shows the choice of generalized coordinates (internal coordinates) q\" q2' q3' q4 and the adopted b.-f. systems. The kinematic scheme of manipulator is shown in Fig. 2.48b. The minimal configuration consists of one rotational (q,) and two linear (q2' q3) degrees of fre ed?m. With this 4 d.o.f. variant, the gripper is connected to the min imal configuration by means of a rotational joint (q4). Manipulation task. The manipulator carries a 3kg mass working object. The moments of inertia of the working object are Ix4 = Iy4 = Iz4 = 0.0' kgm2 (with respect to the corresponding b.-f. system). The object is to be moved along the trajectory Ao A, A2 A3 (Fig. 2.48b). Every part of the trajectory (Ao+A\" A,+A2 , A2+A3 ) is a straight line. Object ro tation for the angle TI/2 has to be performed on the trajectory part Ao+A\" and the backward rotation (- \u00a5) on the part A,+A2 \u2022 The complete scheme of manipulation task is shown in Fig. 2.48b. We have to notice a few things. If a cylindrical manipulator has to reach the points Ao ' A\" A2 , A3 , it usually follows the trajectory rep resented by a dashed line in Fig. 2.49. This is done because of sim plier control synthesis. In this example we have chosen straight line motion betwen two points (full line in Fig. 2.49) in order to demon strate the algorithm possibilities. Triangular velocity profile is adopted. Adapting block 4-2 is suitable for this manipulation task because it T = [x y z q4 l Now, let us discuss the\u00b7 in-uses the position vector X g put values. The manipulator has to move to points Ao ' A\" A2 , A3 one after another, so m = 3. In the starting point Ao we give the initial state q(to ) = [0 -D.' -0.2 OlT, q(to ) = O. In the point A, we give the value of position vector Xg(A,) = Xg , = [0.57 D.' 0.6 TI/2lT and also the time interval in which motion from the previous point is performed T T' = '.5s. Analogous values have to be given for points A2 , (Ao+A,) 107 108 A3 . Thus the input list for the definition of manipulation task is: 110 Results. We now present some results obtained by means of the dynamic analysis algorithm. The trajectory in the state space is shown first. Fig. 2.50. presents the time history of internal coordinates q and Fig. 2.51. presents the same for internal velocities q. The next figure (Fig. 2.52) shows the corresponding time history of the driving forces and torques in manipulator joints. 2.8.2. Example 2 Let us consider the arthropoid manipulator having 5 degrees of freedom. It has been designed for manipulation with heavy loads. The minimal configuration consists of three rotational d.o.f. (q1' q2' q3) and the gripper is connected to the minimal configuration by means of two ro tational joints (q4' q5). The external look, manipulator data, the cho ice of generalized (internal) coordinates, and the adopted b.-f. sys tems are shown in Fig. 2.53. 111 Manipulation task. The manipulator has to move a 250 kg mass object along the trajectory Ao A1 A2 A3 (Fig. 2.54). Every part of the trajec tory (Ao+A\" A1+A2 , A2+A3 ) is a straight line. The velocity profile on each part is triangular. The complete scheme of manipulation task, i.e. the initial position, the trajectory of object motion and the changes in object orientation, is shown in Fig. 2.54. It can be concluded that in this task the partial orientation only is necessary. Thus, this ma nipulation task consists of positioning along with partial orientation, so five d.o.f. are enough. It is evident from the manipulation task scheme (Fig. 2.54) that the direction (b) is the most important. In order to define the direction :1: (b) with respect to the gripper we use the unit vector h = {a, 1, O} (expressed in the gripper b.-f. system 06x6Y6z6). The two angles 8, ~ define the direction (b) with respect to the external system Oxyz. We T use the adapting block 5-2, so the position vector is X =[x y z 8 ~l . g The nubmer of points to be reached is m = 3. The initial position is defined by q(to ) = [0 -n/6 -4n/6 -n/6 OlT. Now, the input list defining the manipulation task is: m 3 Indicator of adapting block 2 Indicators for profiles 222 Initial position q(to ) 0 -n/6 -4n/6 -n/6 0 Xg1 = [x Y z 8 ~]A1 1.5 1.5 0 0 0 T1 = ~Ao+A1) 3. X = g2 [x y z 8 ~]A2 0 2 0.8 n/2 0 T2 = T(A1+A2) 3. X = g3 [x y z 8 ~]A3 1.5 0 0 0 0 T3 = T(A2+A3) 4.5 112 h if(b) Manipulator data Segment-i 1 2 3 4 mi[kg] - 125 98 1 0 2 31 Ixi[kgm ] - 26 0.05 2 I . [kgm ] - 31 26 0.05 yl 2 Izi[kgm ] 15 2.8 2.8 0.05 Length[m] 0.4 1 .5 1.5 0.2 * working object included Fig. 2.53. An arthropoid manipulator * 5 270 38 3 38 0.2 Results. Fig. 2.55. presents time-histories of the internal coordina tes q and Fig. 2.56. presents the corresponding time histories of driving torques in manipulator joints. In performing the task the manipulator consumed 15660 J of energy. From the manipulator configuration and the manipulation task (Figs. 2.53, 2.54) it is clear that the joint S4 does not play an active role. Hence we may consider a manipulator with no drive in that joint (P4=0). In that case the manipulator gripper would behave like some kind of a pendulum. In order to avoid large oscillations we may apply some pas sive amortization. Thus the driving actuator for the joint S4 is not necessary. Let us now discuss the driving torques in the joints S2 and S3' These torques are very large due to large manipulator weight and the heavy payload. In such cases the compensation is usually applied. The hydro or pneumatic compensators may be used or sometimes even active compen sation. 114 2.8.3. Example 3 This example deals with the anthropomorphic manipulator UMS-1V - vari ant with 5 degrees of freedom. The manipulator is shown in Fig. 2.57. The joints S2 and S3 are powered by 23 FRAME MAGNET MOTORS, 2315-P20-0, produced by INDIANA GENERAL. The reduction ratio is N = 100, and the reducer mechanical efficiency n = 0.8. The maximal characteristic (pm _ nm) i.e. the maximal torque depending on motor rotation speed max is obtained by an experiment and it is shown to be almost a straight line (Fig. 2.58). The characteristic differs from a straight line only in the region of slow speeds. If this region is not especially inter esting from the standpoint of constraint violation, we may use a straight line aproximation and in such a way save some computer memory. Here, we work with the original characteristic without approximation. The manipulator has to move a container with liquid along the trajecto- .- N M q L(') o..o..o..c...o.. \\ l. .. _ .. .......... ,.'-1 III lI) <:t' \" (Y') f- N c:( III (Y') \" N f- \\ 1\\ --------~--~~~:~~:~L-\u00b77 ~ o o \"1 o o ,. o o o '\" , o 0 lI) <:r- I I o o rp o (Y') I ,._. : .'. I ,,: o 0 o 0 ~ -. o o o lI) , o 0 N ~ , I .~ 9 o o o <:r-, o , .....\u2022 / .-.~.~. o o \"'1 o \"7 .. o 0 o 0 N (Y') \" I o o o r o 0 N (Y') I' I o o <:r I' o o o 9\" o ., o o lI) I' o lI) I' III (Y') \" f- o 115 . 0. 4 pm M r \\ \u2022 -1 . --- / .... ..r Ao ~ 0. 2 0. 1 \u2022\u2022 .\u2022 \u2022 : ..:- =:: :: I .... .. , ~ 1 0 . ~ ... :; .- -~ .. , . ~ .. , I I 1 . 2. pm m ax \\ m - n ~ (c o n st ra in t) T = 3 .2 5 I 3. F ig . 2 .6 3 . D ia g ra m s pm - nm (t o rq u e . v s . r. p .m .) fo r jo in t 5 2 4 . nm [1 0 3 r .p .m J rv a 121 122 123 profile. The execution time is T Some of the results are shown in Figs. 2.70. and 2.71. Time histories of internal coordinates q and torques P are given in the figures. In performing the task the manipulator consumed 1263 J of energy. No re sistance to the insertion is considered. 124 125" + ] + }, + { + "image_filename": "designv10_6_0003740_j.ab.2007.10.036-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003740_j.ab.2007.10.036-Figure1-1.png", + "caption": "Fig. 1. Schematic diagram of the flow-through biosensor for the determination of glucose: (a) sample; (b) luminol; (c) buffer solution. P, peristaltic pump; V, injection valve; F, flow cell immobilized HRP and GOD; D, detector; PC, personal computer.", + "texts": [ + " GOD (type X-S from Aspergillus niger, 185 U mg 1) and HRP (type VI, 330 U mg 1) were obtained from Sigma (St. Louis, MO, USA). b-D-Glucose was obtained from Xi\u2019an Reagent (Xi\u2019an, China). Glutaraldehyde solution (25%, w/w) in water was purchased from Beijing Chemical Reagents (Beijing, China). The egg was obtained from a local supermarket and stored at 4 C until use. All other chemicals were of analytical reagent grade and used without further purification. The water used was deionized and doubly distilled. The flow system employed in this work is shown in Fig. 1. A peristaltic pump (Zhejiang Xiangshan Shipu Haitian Electronic Instrument, Zhejiang, China) was used to deliver all flow streams at a flow rate of 3.0 ml min 1 (per tube). Polytetrafluoroethene (PTFE) tubing (0.8 mm i.d.) was used as connection material in the flow system. Using a six-way injection valve, 120 ll of mixture solution of sample and luminol was injected into the carrier stream. A colorless glass column (55 mm length, 3 mm i.d.) was used as the CL flow cell. GOD and HRP were coimmobilized with eggshell membrane in the CL flow cell (Fig. 1). The CL flow cell was located directly facing the window of the CR-105 photomultiplier tube (Hamamatsu Photonics, Shizuoka, Japan). The CL signal produced in the flow cell was detected and recorded with a computerized ultraweak luminescence analyzer (type BPCL, manufactured at the Institute of Biophysics, Academia Sinica, Beijing, China). The signal was recorded using an IBM-compatible computer equipped with a data acquisition interface. Data acquisition and treatment were performed with BPCL software running under Windows 95" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002420_robot.1999.770005-Figure5-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002420_robot.1999.770005-Figure5-1.png", + "caption": "Fig. 5 The upper-limb (arm) model of WABIAN", + "texts": [ + " We will adopt a method used by Hirabayashi et a1.[6]. By this method, the compliance motion equation of the robot hand is expressed by: where M (6x6 diagonal matrix) is the virtual mass matrix, K (6x6 diagonal matrix) is the stiffness coefficient matrix, C (6x6 diagonal matrix) is the viscosity coefficient matrix, f (6x1 matrix) is the vector of external force act on the robot hand, v (6x1 matrix) is the velocity vector, and x (6x1 matrix) is the hand deviation vector. We set the robot arm coordinate system as shown in Fig.5. In the case where our target is the full tracking ability of the hand, -just like method generally used in the direct teaching of a manipulator-we may disregard the stiffhess component. Also, when the control loop time we apply is very short (5[msec]), we may think of the virtual mass as equal to zero. Thus, we can rewrite Eq. (10) in a simply way, i.e.: 7 = e-\u2019? (1 1) According to the redundancy of WABIAN\u2019s arm, we used the pseudo-inverse matrix method to calculate the joint angle velocity fiom the hand velocity" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003620_tcst.2009.2028877-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003620_tcst.2009.2028877-Figure1-1.png", + "caption": "Fig. 1. Schematics of the laboratory experiment 3DOF helicopter.", + "texts": [ + "ndex Terms\u2014Boundary value problem, feedforward control, input constraints, laboratory helicopter, nonlinear control, state constraints. I. INTRODUCTION T HE 3DOF helicopter under consideration is a laboratory experiment that is often used in control research and education for the design and implementation of (non)linear control concepts (see also [1] and [2]). As depicted in Fig. 1, the helicopter basically consists of three hinge-mounted rigid body systems. The helicopter base, which can turn about the travel angle , carries the arm that can rotate about the elevation angle . One end of the arm is attached to a counterweight that tares the weight of the third mechanical subsystem, i.e., the helicopter body. The rotation of this body is described by the pitch angle . Two propellers driven by dc motors are attached to each end of the body. The voltages and supplied to the dc motors serve as control inputs to the system", + " Finally, the brief closes with a short conclusion in Section V. The mathematical model of the helicopter laboratory experimental setup can be derived by means of Lagrange\u2019s formalism. The equations of motion can be written in matrix notation in the well-known form (1) with the generalized inertia matrix , the Coriolis matrix , the gravity vector , and the generalized forces (see, e.g., [14] and [15]). A detailed derivation of the helicopter model can be found in [7]. Therein, the rotation of the propellers, described by the angles and according to Fig. 1, and the dynamics of the dc motors are taken into account in addition to the three degrees of freedom given by the travel, elevation, and pitch angle , , and . For the controller design, the model has to be simplified such that it can be handled within the framework of nonlinear control theory. However, this simplified model should still capture the essential nonlinearities of the system. In this context, the fast dynamics of the electrical subsystems given by the dc motors and the dynamics of the propellers, described by the angles and , can be approximated in a quasi-static way utilizing the singular perturbation theory (see, e", + " Obviously, the BVP (14a) is overdetermined since four BCs (14b) have to be satisfied for one second-order ODE (14a). Following the basic idea of the approach presented in [11], the solvability of the BVP requires two free parameters in the desired output trajectories and . Thereby, some freedom exists concerning how the free parameters are distributed to the two output functions. From a physical point of view, the acceleration of the travel axis is directly related to the pitch angle of the helicopter body (see Fig. 1). Thus, it is reasonable to provide both parameters in the second output , whereas the first output is determined as a predefined setup function . The setup functions and are constructed as polynomials (see, e.g., [19]) and have to satisfy the BCs (12b) and (12c). The solution of the resulting BVP with free parameters comprises the parameter set as well as the trajectory of the travel axis of the helicopter. Thereby, the parameter set determines the shape of the output trajectory . The solution of this type of BVP with free parameters is a standard task in numerics" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure33.6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure33.6-1.png", + "caption": "Fig. 33.6 Photograph of prototype (b) Prototype of motor", + "texts": [ + " NAKAJIMA Development of Ultrasonic Micro Motor with a Coil Type Stator 391 torque, namely N-T curve, can be calculated taking an approximated curve of N-t and inertia of motor, and the dashed line is almost inverse proportional. The deviation may be caused by an uncertainty of the frictional behavior between rotor and stator. The starting torque was so small as 0.2 Nm and seems not enough for a practical use and some better method to give optimum preload has to be developed. The rotor must be covered with outer case when practical use is considered. Fig.33.6 and Table 33.2 show the photograph of prototype and its specification. Stainless steel was used for rotor and stator and polyimid resin (Ti polymer) was adopted for the case taking smoother rotation and smaller wear at the same time. By this design, the rotor is supported both radically and axially. 392 In spite of these design, the prototype rotates rather in-stably as shown in Fig.33.7 that may be cased from an unsteady contact between rotor and stator as in the case of 1st prototype. This second prototype was miniaturized by the help of wrist watch production of Seiko Instruments Inc" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002565_s0043-1648(03)00338-7-Figure5-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002565_s0043-1648(03)00338-7-Figure5-1.png", + "caption": "Fig. 5. FE model of gear pair.", + "texts": [ + " We use eight-noded isoparametric quadrilateral elements to represent the complicated geometry of the gear teeth in a proper way. In order to capture the local contact deformations, we use such a dense FE mesh in the contact regions so that at least two elements on every contacting gear flank will be in full contact with the mating flank elements after the gears have deformed due to the loading. FE contact simulations are non-linear and can be very time-consuming. Therefore, we use coarse mesh in the rest of the gears (see Fig. 5). Then these FE meshes are tied together with a Lagrange multiplier method [14]. The resulting deformations of the gear will be very good, but the stress fields at the FE mesh interfaces will be discontinuous. Cavaciuti et al. used a similar approach when they investigated the contact of spiral bevel gears [15]. To speed up the FE contact simulation, the degrees of freedom of the FE meshes are reduced by static condensation (or substructure generation) [14]. If the two gear bodies are disconnected at any point during the FE contact simulation, the stiffness matrix will be singular" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000133_j.wear.2021.203616-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000133_j.wear.2021.203616-Figure1-1.png", + "caption": "Fig. 1. Schematic representation of the gearbox test rig: (a) Method of abstraction, (b) oblique view of the test rig without top housing, (c) mid-plane cross section of the test rig.", + "texts": [ + " For the purpose of comparability, the material-lubricant combination was chosen similar to previous studies on sliding bearing behavior [24\u201326]. The lubricant in the system test rig was the commercial gear oil Mobilgear SHC XMP 320. The measured kinematic viscosity were at 40 \u25e6C is 275.3 mm2 s\u2212 1 and 31.6 mm2 s\u2212 1 at 100 \u25e6C. Notably, this oil is widely used in gearboxes for wind turbines [27,28]. The wear behavior of sliding bearings under steady operating conditions was investigated using a special test rig for sliding bearings in planetary gearbox application shown in Fig. 1. The test rig reproduces the loads, which are acting on a planetary sliding bearing (\u201ctest bearing\u201d). The method of abstraction is illustrated in Fig. 1a. For this reason, the test rig in Fig. 1b consists of three helical gears, which represent the sun gear, planet gear and ring gear. Similar to the real application, the sliding bearing was subjected to the gear loads from both gear contacts. As shown in Fig. 1c, the advantage of the test concept is that the shaft, which supports the planet wheel, is not moving, so sensors can be applied easily. In contrast to conventional sliding bearing systems, the bearing material is on the outer surface of the shaft and the oil is supplied to the bearing by a bore in the shaft. To avoid wear by three-body abrasion, the oil is filtered by a 10 \u03bcm return line filter. At the beginning of the test, the bearing was operated in a hydrodynamic reference point with a load of 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003670_978-3-642-82195-0-Figure6.13-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003670_978-3-642-82195-0-Figure6.13-1.png", + "caption": "Fig. 6.13. Redundant manipulator motion -configuration space performance index", + "texts": [], + "surrounding_texts": [ + "Presence of Obstacles 249 In this section we will present a real-time implementable algorithm for redundant manipulator motion synthesis in an obstacle-cluttered envi ronment [105-106]. This procedure is based on the application of the performance indices which take the presence of the obstacles into ac count and thus prevent the arm from drawing too close to the obstacle. This problem considered is the same as in the previous section. Nemely, the initial manipulator configuration qOEQCRn is given, as well as the manipulator end-effector trajectory in the external coordinates space x (t)ERm, tE[O, T] between the initial point x (0) = XO = f(qo) and the e e e final point x!. The disposition of obstacles is also given. The problem is to find the appropriate joint motion for the avoidance of obstacles. As before, we will assume that the information on the distance between the critical point on the arm and the obstacle, and the location of the critical point Xc is available from a higher control level. The defi nition of the distance is introduced by Equations (6.4.1)-(6.4.3) in Section 6.4 (see Fig. 6.8). In the case when the manipulator is far from the obstacle, i.e. dIS, C\u00bb > dmax ' the solution for the joint rates may be obtained in the usual manner, most frequently as the minimum norm solution, or by applying any of the procedures presented in Sections 6.2 and 6.3. However, when the distance between the critical point Xc on the arm and the obstacle lies between two given values (6.5.1) the presence of the obstacle should be taken into account, possibly by modifying the performance criteria so that motion is collission-free. We will here discuss the usefulness of several of the optimality cri teria which may be applied. The solution to the underdetermined linear system of equations J(q)q, m \u00b1 y) + r2 cos 4>2 + r^ sin y, y '\u0302* = /-fc cos (^ - 1// \u00b1 yf = n cos {\u20ac,,\u201e- iji \u00b1 4> + rhim sin (C,\u201e - ijj \u00b1^\u00b1y) ~ r/sin(^,\u201e - ip \u00b1(^\u00b1y) + rf sin ($,\u201e -ip\u00b1(i>\u00b1y + 9) + 2\u0302 sin ()>2 ~ r^ cos y, and t y) 2 + '\"c sin y, y) (21) In Eqs. (18) and (19), superscript i indicates regions 1 through re cos (\u0302 ,\u201e - 41 \u00b1 4> + d) = ri, cos 6 - ri,^\u201e, sin 6 + rf sin 6, where 0 s ^ s (7r/2) - tan\"' (^\u201e, - (rj/ri,)), and ; = 2 and 5. The upper sign indicates that the fillet surface of the noncircu lar gear is generated by region 2 of the shaper cutter, while the lower sign by region 5. (3) Bottom Lands of the Noncircular Gear Tooth Surfaces. Bottom lands of the noncircular gear tooth surfaces are gener ated by the top lands (regions 3 and 4) of the shaper cutter surfaces, as shown in Fig. 1. Substituting Eqs. (16) and (17) Downloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/29/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use into Eqs. (18) and (19) we obtain the bottom lands of the /g.\\ noncircular gear by X2' = +r\u201e sin (rj \u2014 if/ \u00b1 (j} \u2014 y) + ^2 cos 4>2 + re sin 7, y2^ = ra cos (?7 - i/f \u00b1 (/) \u00b1 7) + 2\u0302 sin ) = 0, where ;' = 3 and 4, and p = L + P -Jrl + (ri,C,\u201e - rf)^ + Vf, tan V C. n tan a \u2014 a + 2N, The upper sign indicates that the bottom land of the noncircular gear tooth surface is generated by region 3 of the shaper cutter, and the lower sign by region 4", + " Substituting Eqs. (39) and (42) into Eq. (44) and (45), we obtain the conditions for tooth undercutting of noncircular gears as follows: e rcixi2 + pu} r,uj2 tan a. (46) This is the general undercutting condition for noncircular gears manufactured using shaper cutter. When the normal of pitch curve passes through O2, then u)2 = uj, and Eq. (46) can be simplified to c r, + p tan a. (47) Assume that the distance measured from the pitch circle to the end point of the involute curve is h = fm, as shown in Fig. 1, where m is the shaper cutter module. According to the property of an involute curve and the basic geometry of the shaper cutter, we found that (FC + fniy = (TC cos a)^ + (r^S, cos a)^ e = rl sin^ a -F Ircfm + / W r\\ cos^ a (48) (49) When Yc = {mNsl2), where m is the module and Ns is the number of shaper cutter teeth, Eqs. (47) and (49) yield that rn^ifNs + f^) - mNsp sin\" a - p^ sin' a = 0. (50) The maximum allowable shaper-cutter module can be obtained by solving Eq. (50). If a rack cutter is used to manufacture noncircular gears, i" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000562_j.mechmachtheory.2021.104380-Figure12-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000562_j.mechmachtheory.2021.104380-Figure12-1.png", + "caption": "Fig. 12. The measured trajectories with different radii and different heights.", + "texts": [ + " Further, in order to demonstrate the motion capability of the developed PCM prototype, three circular trajectories with different radii ( r = 15 mm,25 mm,35 mm)on the different height planes( h = 0 ,30 mm,60 mm) are prescribed for the moving platform with its orientation fixed. In this experiment, each circular trajectory is equally discretized into 180 separated positions. According to the proposed kinetostatics analysis, the corresponding inputs of the three active PR joints can be derived readily, and then implemented directly in the control module of DC motors via the developed communication SoftBUS. As well, the OptiTrack system is used to capture the actual poses of the moving platform in the discretized configurations. As the Fig. 12 shows, it is known that, using the proposed kinetostatics modeling and analysis method, the moving platform of the studied parallel manipulator can basically follow the prescribed circular trajectory. The mean and maximal position errors of the nine trajectories are 1.04 mm and 2.52 mm, respectively, while the corresponding orientation errors are 2 . 17 \u25e6 and 5 . 06 \u25e6. Obviously, they are close to those within the square workspace assessed in the above section. As mentioned in the above, although the positioning accuracy of the developed PCM prototype is not as high as its rigid counterparts in the current stage, there are many unconsidered aspects can be taken into account to minish the influence" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure3.10-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure3.10-1.png", + "caption": "Fig. 3.10. Modified mechanism with a parallelogram", + "texts": [ + "27) we can sub tract the third equation of this system from the second one, thus ob taining where * .. W q * W .. lJ * P + U (3.3.29 ) * U. l (3.3.30) If the segments 2\" and 2' are considerably smaller than the segment 2, an approximative model can be formed. We may use the model (3.3.27) with the matrix W calculated for the open chain configuration. This open chain is obtained by taking the direct branch and adding the in ertial effects of segment 2' to the segment 2. In this case the segment 2\" is neglected. Let us discuss one modification of the mechanism considered (Fig. 3.10). It is the mechanism of ASEA robot which contains a kinematic paralelo gram, too. But, instead of driving torques P 2 , P3 (Fig. 3.6), the * * linear drives of mechanism P 2 , P3 are applied (Fig. 3.10). Nonlinear relationships exist between the linear and the rotational drives. 164 This paragraph develops the theory dealing with manipulators having constraints imposed on gripper motion. Each constraint restricts to a certain extent the possibility for gripper motion. In this way the num ber of d.o.f. of the gripper is reduced. In order to avoid a purely theoretical discussion, we consider only these types of constraints which appear in practical problems. But, there are no obstacles to ex panding the theory to cover any type of constraints" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000211_j.matchar.2021.111158-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000211_j.matchar.2021.111158-Figure1-1.png", + "caption": "Fig. 1. Schematic illustration of sampling location and geometry of each sample.", + "texts": [ + " One of the applied two PHTs was performed at 871 \u25e6C for 6 h in the air, followed by water quenching based on Ref. [23]. Note that this PHT at 871 \u25e6C for 6 h has been confirmed to be an effective process for the stress relief treatment of nickel-base alloy weldment components produced by LB welding [23] and GTAW [24]. The other PHT was carried out for the solution annealing at 1177 \u25e6C for 30 min in the air, then water quenched following Ref. [25]. The sampling locations and dimensions of the mechanical testing and metallographic analyses are shown in Fig. 1. To avoid element dilution from the substrate and a stable microstructure, the test samples were extracted at least four layers away from the substrate and 10 mm away from the side regions in the as-deposited materials. Metallographic samples were observed on the deposition crosssection (y-z plane). Samples were prepared by mounting, grinding, and polishing followed by etching using standard metallographic procedures for nickel-base alloys. The electro-etching was performed in a solution containing 5 mL oxalic acid and 15 mL hydrochloric acid for 2 s at 6 V direct current at room temperature", + " ImageJ software was applied to calculate the size of the dendrites [26]. Transmission electron microscope (TEM) analyses were carried out on the JEOL JEM-ARM 200F instrument operating at 200 kV. Thin lamellae for TEM examination were machined using a focused ion beam (FIB) by FEI Helios Nanolab G3 CX. The precipitates were identified by selected area electron diffraction (SAD). Twenty tensile test samples in traveling direction (x-y plane) and five in deposition direction (y-z plane) were extracted for testing (Fig. 1). Tensile tests were performed at room temperature using an Instron\u00ae universal tensile testing machine at a constant crosshead displacement rate of 1 mm/min. Vickers microhardness was measured using a Matsuzawa Via-F automatic Vickers tester, using an indentation load of 500 N, a step size of 0.5 mm and a dwelling time of 15 s. X-ray diffraction (XRD) was performed for phase identification of the samples taken from the longitudinal region (y-z plane) (Fig. 1). A GBC diffractometer equipped with the Cu K\u03b1 radiation (\u03bb = 1.5418 \u00c5) and a graphite monochromator was used for the data collection over a 2\u03b8 range from Z. Qiu et al. Materials Characterization 177 (2021) 111158 30\u25e6 to 100\u25e6. Fig. 2 shows the microstructures of the as-built and heat-treated (871 \u25e6C and 1177 \u25e6C) samples. For all the three conditions investigated, a columnar dendrite microstructure was observed. As shown in Fig. 2a, the as-built sample was dominated by large columnar grains in the microstructure which was composed of aligned dendrites oriented closely along the deposition direction" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002964_tsmca.2005.855777-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002964_tsmca.2005.855777-Figure4-1.png", + "caption": "Fig. 4. Approximate link model M52).", + "texts": [ + " Therefore, to estimate motion or form in 3-D space, the best model for the purpose is selected from Table I, the gyro sensors are placed on the corresponding rod or body part, the angular velocity of each part is measured, and the Euler transformation is applied using (6). The position of the part of interest in the 3-D absolute coordinate system can be obtained by the summation of the coordinate of each position towards the interested part. This formulation of measurement is the forward procedure. An example of a measurement of head position using model M52) follows. Fig. 4 shows model M52), in which parts of the right and left leg, right and left thigh, and hip are represented by one rod of length l0, the section from hip F to waist W is given by rod FW of length l1, the section from waist W to shoulder S is given by rod WS of length l2, and the section from shoulder S to head H is given by rod SH of length l3. This model is a fourlink model. Angles formed by FW, WS, and SH from the Y -axis are designated \u03b81, \u03b82, and \u03b83, respectively. The initial positions of the top of the rods pOF(0), pFW(0), pWS(0), and pSH(0) are given by (5) as pOF(0) = 0 l0 0 , pFW(0) = 0 l1 cos \u03b81 l1 sin \u03b81 , pWS(0) = 0 l2 cos \u03b82 l2 sin \u03b82 , pSH(0) = 0 l3 cos \u03b83 l3 sin \u03b83 ", + " The criteria of golf form were derived from the driver-swing form outlined in golf training textbooks by accomplished world-class golfers Hogan [18] and Nicklaus [19]. Although these criteria were not scientifically established, this measurement system was able to verify the criteria scientifically by quantification of data collected during the golf swing. An For the quantitative evaluation of criterion R1), motion elements measured must include the angles of the waist and the shoulder. For criterion R2), the 3-D translations of the waist, shoulder, and head must be measured. To obtain these measurements, link model M52), as shown in Fig. 4, was employed. Model M52) includes aspects of models M33) and M42), therefore, the translations of waist, shoulder, and head are measurable. Fig. 11(a) shows the angles of the waist, shoulder, and head in the local coordinate system. Fig. 11(b) shows the displacements of the waist, shoulder, and head in the global coordinate system. Fig. 11(c) shows the loci of the waist, shoulder, and head movement during the swing from address to finish. In Fig. 11(c), the circular mark shows the address, the star mark shows the impact, and the square mark shows the finish" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000339_j.jmatprotec.2021.117179-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000339_j.jmatprotec.2021.117179-Figure1-1.png", + "caption": "Fig. 1. Definitions of coupon specimens all dimensions in mm. Samples derived from a 25 \u00d7 20 flat plate at 45\u030a inclination angle. Experiment variables: R1 is the radius curvature along the inclined slope, R2 is the perpendicular radius of curvature across the slope T: normal thickness of the surface. The build platen is shown as datum A.", + "texts": [ + " The approach is demonstrated using a case study into a commonly manufactured cellular structure based on a triply periodic minimal surface (TPMS) - the double gyroid. This approach has wider potential applications in design for AM, but is particularly relevant for designs with intricate curved geometry, where post processing is not feasible. To understand the impact of surface geometry on manufacturability, coupon-style samples were designed to investigate the impact of adding curvature to a flat plate at 45\u25e6 inclination as shown in Fig. 1. The geometry was generated by adding two perpendicular components of curvature to a flat surface with thickness \u2018t\u2019 at 45\u25e6 inclination. Curvature was added in two perpendicular principal directions. R1 represents the radius of curvature along the inclined slope, and R2 represents the perpendicular radius of curvature across the slope. Each sample (Fig. 1) includes datum plate \u2018A\u2019, which is coplanar with the build platen, which is used to ensure similar connection to the build plate across all samples. The datum plate also acts as a locating feature for comparison between the as-designed surface and as-manufactured surface. Magnitude of curvature in any direction, \u03ba, is inversely proportional to the radius of curvature at any given point (Eq. 1), where a positive curvature is a convex surface, and negative curvature represents a concave surface. The principal curvatures, \u03ba1 and \u03ba2 are the maximum and minimum curvatures, together they provide a description of the local shape of a surface" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure27.2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure27.2-1.png", + "caption": "Fig. 27.2 Schematic structure of polymer-ion-gel actuator in this study. Actually, two glasses to support at fixed part are sandwiched on the cupper electrodes (not shown)", + "texts": [ + " We developed polymer ion-gel actuator using a mixture of activated carbon (AC) and acetylene black (AB) as electrodes, poly(methyl methacrylate) (PMMA) as the network polymer, and 1-ethyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide ([C2mim][NTf2]) as the ionic liquid. The structural formulae of these materials are depicted in Fig.27.1. The polymer ion-gel actuators used in this study, as well as those used in previous ones, comprised electrode layers and an electrolyte layer, as depicted in Fig.27.2. A strip of the ion gelcarbon electrode composite immediately changes its shape when the polarity of the applied voltage is changed. We observed the tip of a 4 mm-long strip underwent a displacement of ca. 100 m toward the anodic side when the other side was clamped and a voltage of \u00b11.5 V was applied. Thus, we successfully fabricated EAP actuators that can be driven at low voltages under atmospheric conditions and that overcome drawbacks of conventional EAP actuators [8]. In addition, Development of a Polymer Actuator Utilizing Ion-Gel as Electrolyte 317 since we utilize of commercially available carbon materials such as AC, we can fabricated this type of actuator at low cost", + " An ion gel consisting of [C2mim][NTf2] and P(VDF/HFP) (17 wt%) was prepared using the following procedure: P(VDF/HFP) was dissolved in [C2mim][NTf2] at 120\u00b0C for 3 h. The heated soluti polymer, was prepared using the following procedure. The mixtures were c pletely mixe and 4 MPa to reduce the contact resistance at the electrolyte-electrode interface, an electrolyte sheet was sandwiched between two electrode sheets under a pressure in a thermoregulated oven at 130\u00b0C for 3 h. The polymer ion-gel actuators were made by cutting the electrolyte-electrode composite into a 2 \u00d7 7 mm strip and sandwiching it between two cupper electrodes to fix one end (Fig.27.2). 320 Hisashi KOKUBO and Masayoshi WATANABE SMSs were dissolved in tetrahydrofuran (THF) as cosolvent, and the solutions n was cast on a Petri dish at cosolvent, and then dried under vacuum at 100 \u00b0C for 12 h. The obtained films were sandwiched between glass slides the thickness of the Teflon spacer used being 0.1 \u2013 0.5 mm, and pressed at 130 \u00b0C. main material of the electrode; rather, it is an auxiliary conductive material. This is because of the lower electric conductivity of AC and OC. Figure 27" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002661_robot.1999.774054-Figure5-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002661_robot.1999.774054-Figure5-1.png", + "caption": "Figure 5 : Musculo-skeletal structure of the snake and its schematic model; wherein, (a) is the Musculoskeletal st*ructure, and (b) is the Schematic model of musculo-skeletal structure", + "texts": [ + " That is, This relation among the muscle contractive force, the muscle contractive velocity, and the muscle contractive length is the curved line L shown in figure 4. 2.2 Musculo-skeletal structure of Snake Snakes have at least 130 vertebrae between head and cloaca, a.nd thus number can exceed 300 [6]. For the snakes that are lack of limps, the long body is necessary for them to perform possible locomotion. Moreover, only a few movements are possible between the two vertebtaes, and these have limited amplitude. The long body is thus only one function for snakes to execute possible locomotion. Figure 5 (a) shows Musculo-skeletal structure of the snake. The lateral muscles of a snake lie on eit,her side of a frame formed by t.he vertebrae and costae, and stretch from one rib to the next, or from robs to vertebrae. The musculoskeletal mechanism by which bending movements are produced is by no means a simple one. However, to permit the kinemat.ic arid static analysis, we consider a schematic model shown in figurr 5 (b). If the range of movement, of the sirigle-joint, 68 is small (actually 3008 about f 4 \u2019 at most) , the displacement between two rib (or costa) can be given by he,, = a68", + " In addition, if we compare two distribution of muscular force, one obtained by quantitative analysis shown in figure 9 (b) and another obtained by qualitative analysis shown in figure 9 (a), both satisfied the condition 1) and 2), but the one by quantitative analysis shown in figure 9 (b) is more fitting to the condition 3). As a result, the distribution of muscular force obtained by quantitative analysis of muscle characteristics, makes the snake\u2019s muscle to have more natural expansion and contraction, and more fitting to the one of real snakes. 5 Comparison of Locomotive Efficiencies As shown in figure 5, a schematic model is used to kinematic and static analysis, where Ss is the length of one vertebra and a is the distance from joint t o muscle. In case of static analysis, a moment of rotation T ( s ) = (ufm(s)) is generated by the force of contraction fm(s), when one side of the muscles contract. From distribution of the moment T ( s ) in the segment OP, the tangential force along the body ( o r propulsive force), F F p , the normal force perpendicular to the body, F:p, and the power density function while the snake is moving at a fixed speed v along the body axis s were derived and given by [12] 301 1 P o w e r dens i t y : P ( s ) = v T ( s ) - d 4 S ) d s ' The kinematic conditions required to produce creeping locomotion are: first, that friction with the gliding surface be overcome and that sufficient propulsive force be generated in the direction tangential to the body; and second, in order that the pattern of motion peculiar to creeping, in which the whole trunk follows the same path, can be adopted, slippage in the normal direction must be prevented" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003384_20.278859-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003384_20.278859-Figure1-1.png", + "caption": "Fig. 1 - SRM Equivalent circuit Model", + "texts": [ + " This paper describes an equivalent circuit model for SRMs which includes multi-phase excitation with distributed saturable elements. It describes: methods for calculating or functionally representing values for the circuit elements given the machine geometry and a minimum number of finiteelement models, a method for modeling saturable materials and a method for solving the resulting mesh for flux values given excitation levels. Finally, the model results are compared with intermediate (i.e. other than those used to calculate circuit element values) finite-element results . II. MODEL DESCRIPTION Fig. 1 shows the new SRh4 model for a 614 3-phase motor. The reluctances Rrc, Rrp, Rrt, Rst, Rsp and Rsc are saturable while Rg, Rpp and Rpc are not. The phase excitation is 2Ni ampere-turns. The phase airgap reluctance is a periodic function of the electrical rotor angle relative to pole alignment, 8, and is modeled as (1) where the constants ai, a2 and p are determined from three finite-element models 8 = 0.90 and 1800 (aligned. unaligned and half way between) with the iron permeability set to a very large value to eliminate saturation effects. Leakage and mutualcoupling effects are removed by considering only flux crossing from the rotor to the stator when calculating gap 1 Rg = 011 + 012 I C O S ( ~ / ~ ) I P * The pole-to-pole reluctance Rpp is determined using one of the above unsaturated finite-element models. The pole-tocore reluctance Rpc is determined in a similar manner. The model of Fig. 1 assumes that pole-to-pole and pole-to-core fluxes fully link the phase winding. In relating flux to flux linkage this assumption should be modified by some constant factor obtainable from the finite-element models. If higher accuracy is required, then more model elements should be added in this area[l]. The rotor and stator pole tip reluctances Rrt and Rst are given by (2) lrt M$rtlArt(W Art(@ \u2019 Rfl= and (3) where l a and 1st are the pole tip depths and are taken as half the pole widths and Art and Ast are defined by (4) A(8) = &(a3 + a k0~(8/2)1q) , Manuscript received July 12, 1991", + " Note that although the rotor core reluctance length between adjacent poles is 1/6 rather than 1/4, tooth base flux spreading (Fig. 6) makes this effectively correct . III. SATURABLE MATERIAL MODEL There are several ways to model saturable materials[3]. The most straight-forward method which still gives fairly accurate results and stable circuit mesh solutions is where p i , P2and r are constants. This can be extended with more power terms as required. Using Eqn. 11, Eqn. (6) becomes (12) 1 Pi + P2 ICp/Al(r-l) p(Cp/N = IV. CIRCUIT MESH SOLUTION The circuit mesh for fig. 1 results, making use of two pole symmetry, in a matrix equation of the form R(O,Cp/A) 'P - M = 0 (13) where R is reluctance - 9x9, CP is flux - 9x1, M is excitation - 9x1 and 0 is zero - 9x1. To solve this system of nonlinear equations a Newton-Raphson method can be applied[4]. This consists of evaluating R for CP=O, solving Eqn. 13, for a new CP calculating a new R using that 'P, solving Eqn. 13 and so on until the difference between 0 solutions reaches some specified small value. It should be noted that the R matrix used in Eqn" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002797_elan.200403010-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002797_elan.200403010-Figure1-1.png", + "caption": "Fig. 1. Chemical modification of carbohydrate moieties in laccase and immobilization on amine terminated thiol monolayers on gold.", + "texts": [ + "6 Vwith scan rate of 20 mV/sec from anodic to the cathodic side. The onset potential corresponding to the oxygen reduction reaction is determined by the potential at which the reduction current starts rising above the x-axis. The shift in the onset potential towards the positive side is described as the anodic shift. Three different thiol monolayers were formed on the gold surface using l-cysteine, cystamine and 4-aminothiophenol. The schematic representation of the covalent coupling chemistry is as shown in Figure 1. Physical adsorption of neither the fungal nor the tree laccase on the monolayermodified gold did not show any significant catalytic activity in any of the three different monolayers. The absence of the electrocatalysis at the electrodes after physical adsorption of laccases might be due to the quick desorption of the laccases from the electrode surface or non-productive electronic contact between the laccase molecules and the surface of the electrode. On the other hand, covalent coupling of laccase on the electrode showed significant catalytic activity, as seen from the voltammograms in Figures 2 and 3" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002803_ja055815s-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002803_ja055815s-Figure1-1.png", + "caption": "Figure 1. (A) Schematic of the microtubules functionalized with the cobalt ferrite particles on a kinesin surface. (B) Schematic of the magnet, flow cell, and objective configuration.", + "texts": [ + " A flow cell was constructed by affixing a glass slide to a cover slip with double-sided tape (volume \u223c 20 \u00b5L); the internal surfaces of the cell were sequentially exposed to buffer solutions containing 5 mg/mL of casein (5 min) and, in some cases, 6.6 \u00b5g/mL of hexaHis-tagged Drosophila melanogaster kinesin9 (5 min). The solution containing the magnetic particle functionalized microtubules was then injected into the flow cell. A schematic of the resulting microtubule assembly, magnetic particle-conjugated microtubules bound to kinesin motors on the glass surface, is shown in Figure 1A. To test the effectiveness of controlling and aligning the magnetic particle-modified microtubules, this cell was placed on top of a NdFeB permanent magnet for 3-10 min and visualized using fluorescence microscopy (Figure 1B). When a casein-passivated surface (in the absence of kinesin motors) was used, we observed that, upon introduction of the magnetically functionalized microtubules into the flow cell, their orientation and transport in solution could be manipulated with a small permanent magnet. The fluorescence microscopy images in Figure 2 were obtained while the magnetic field orientation was \u2020 Department of Chemistry. \u2021 Department of Bioengineering. Published on Web 10/19/2005 15686 9 J. AM. CHEM. SOC. 2005, 127, 15686-15687 10" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure4.9-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure4.9-1.png", + "caption": "Fig. 4.9. Method of feasible directions for two-parameter optimization", + "texts": [ + " This problem is very complicated because there is no explicit function of the criterion and no explicit expressions for the constraints. Both the value of the criterion and the answer as to whether a point in parameter space is feasible or not follow from the dynamic analysis algorithm. This fact restricts to a great extent the possibility of selecting the optimization method among those given in literature. Here we use one variant of the feasible di rections method [10]. This method is almost the only one that suits the problem considered. Let us describe the optimization procedure. It is illustrated in Fig. 4.9. The procedure starts at a feasible point A. Four probes are made around the point A. We locate the improved feasible point B and accept it. We proceed in the same manner until we reach point D. At D, no probe produces an improved feasible point. We then choose a new point E by interpolating between the best feasible point H and the best non feasible point G. Such a procedure leads us towards the optimum (qua dratic point in Fig. 4.9). 259 This procedure can also be used for optimization when there are more than two independent parameters. One should take care of the fact that if the number of parameters increases the procedure may become very time-consuming. Hence, we suggest two or three independent parameters. We think that in almost all problems we are interested in, the number of independent parameters can be reduced to two or three. Let us see an example. Example. We consider again the arthropoid manipulator VE-2 (Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000474_s00170-020-06432-1-Figure12-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000474_s00170-020-06432-1-Figure12-1.png", + "caption": "Fig. 12 Thermal camera setup. a Side view of the laser powder bed fusion (L-PBF) machine, custom door, andthermal camera. b CAD solid model of L-PBF machine build chamber and custom viewport. c Optical axis, plane of focus, and vertical iFoV projected on the build plane (reproduced from [14], copyright (2017), with permission from Elsevier)", + "texts": [ + " [47] found that the combination of high laser power and high scanning speed can reduce the occurrence of spheroidization. Criales et al. [14] used real-time thermal imaging device to collect themelt and surrounding temperature. It is possible to infer changes in the sizes of melt pools from the thermal camera recording by observing the size of the measurable isotherms surrounding the actual liquidmelt pool. The result of image segmentation using liqui dus temperature as threshold on single frame is shown in Fig. 12, where the molten region is marked red and the cooler region is marked blue. Krauss et al. [35] established a low-cost radiometer camera for process monitoring and studied its sensitivity to process deviation detection. The camera has a long-wave infrared range (LWIR) and a sampling rate of 50 Hz. The device can identify the deviation caused by process parameter drift or random process error during the molding process and detect the inner cavity and defect at the same time. However, the monitoring range of the equipment is 160\u2013120 mm, which accounts for about 30% of the total forming area" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003626_s0076-6879(80)69040-5-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003626_s0076-6879(80)69040-5-Figure1-1.png", + "caption": "FIG. 1. The cuvette assembly. Two ports of the water-jacketed cuvette received the electrode, E, and the stopper, S. Liquid level in the cuvette was maintained slightly above the point of seal between glass bali and bottom of the ground glass taper.", + "texts": [ + " With currently available operational amplifiers employing field effect transistors (FET), current to output transfer ratio as small as one nA/V can easily be achieved. The advantage of electrochemical detection of hydrogen is obvious. Wang, Healey, and Myers ~ introduced the use of the amperometric hydrogen electrode, which is sensitive, fast and specific for hydrogen measurement. In order to achieve satisfactory performance, certain precautions, given herein, must be taken. An apparatus, such as the one shown in Fig. 1, consisting of a OX 700 Clark-type electrode (equivalent to YSI 5331, platinum electrode about 0.5 mm) and OX 705 water-jacketed cuvette from Gilson Medical Electronics (Middleton, Wisconsin, 53562) may be used. This apparatus was intended for use as an oxygen electrode. The electrode (E) contains a small platinum wire at the center surrounded by a much larger reference silver electrode. For hydrogen measurement, the following reaction occurs at the silver electrode. AgCI + e - ~ A g + CI- This reaction complements the oxidation of hydrogen at the platinum electrode" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002703_ip-cta:19971032-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002703_ip-cta:19971032-Figure1-1.png", + "caption": "Fig. 1 Coordinate system for the description of ship motion The angle 7p is the difference between actual heading and track course, U is the forward velocity measured by the log, v is the cross velocity to starboard, x is the position along the track, y is the cross-track-error", + "texts": [ + " Simple low pass filtering of the individual position components is disastrous. For a commercial track controller the amount of installation work has to be quite low, so the model must have a small number of parameters, identifiable from on-board measurements. The linearisation of the 0 IEE, 1997 hydrodynamic equations of motion of a ship leads to a IEE Proceedings online no. 19971032 second-order model in the state variables: rate of turn r Paper first received 3rd April and in revised form 3rd October 1996 and sway velocity v. See Fig. 1 and [5 ] . This model is The author is with Hamburg Polytechnic, Sandkamp 13a, D-24259 often ill-conditioned with respect to identification when Westensee, Germany using on-board measurements [6]. The well-known IEE Proc-Control Theory Appl., Vol. 144, No. 2, March 1997 121 simplified model after Nomoto [7] seems preferable. 1 1 For the sway velocity, v = ar is assumed. The parameters K, T of the simple linear model in eqn. 1 can be roughly derived from general ship data. (2) L U T=To- K = K o - U L The remaining states can be deduced from kinematic relations according to Fig. 1. 2 =ucos$++sin$+d, (3) jl = usin$ + v cos$ + d, (4) The forward velocity U of the ship is measured by the speed log, and can thus be viewed as a known parameter. The linearisation of this model is straightforward and the fully linearised model is given in eqn. 5. f +\\ 0 1 0 0 0 0 0 0 0 + T 0 -1 - $ 0 0 0 0 0 0 r c 0 0 0 0 -U? 0 0 0 0 5 - E = 0 0 0 1 -2Dh-wh 0 0 0 0 f Y U a 0 0 0 0 1 0 0 y b 0 0 0 0 0 0 0 0 0 b d?J 0 0 0 0 0 0 0 0 0 d , X 0 0 0 0 0 0 0 0 1 X dz 0 0 0 0 0 0 0 0 0 d , 0 0 0 0 0 0 0 0 0 0 0 0 0 0 o u 0 0 0 0 0 0 1 (5) The model includes a coloured noise to model periodic disturbances of the heading signal, due to coupled roll and pitch motion in rough sea" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000543_j.jallcom.2020.158377-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000543_j.jallcom.2020.158377-Figure2-1.png", + "caption": "Fig. 2. Schematic of (a) laser scanning strategy and (b) tensile specimen.", + "texts": [ + " The chemical composition of the as-atomized Ren\u00e9 104 powder employed in this study is listed in Table 1. The nearly spherical powders with the particle size distribution of Dv (10) = 21.8 \u00b5m, Dv (50) = 38.3 \u00b5m, and Dv (90) = 59.8 \u00b5m are exhibited in Fig. 1a and b. In this work, all SLM fabricated cubic parts (10 \u00d7 10 \u00d7 10 mm) and tensile specimens were manufactured using Renishaw AM400 equipped with a 400 W IPG fiber laser. The experiments were carried out under the protection of argon atmosphere, and the substrate was pre-heated to 170 \u2103. As depicted in Fig. 2a, the scanning direction was rotated by 67\u00b0 between the n st layer and n + 1st layer during SLM. The optimum processing parameters were explored by altering the laser power (P = 150~300 W) and exposure time (t = 60~100 \u03bcs), other parameters remained unchanged, layer thickness (d = 40 \u00b5m) and hatch distance (h = 90 \u00b5m). Volume energy density \u03b7 is a function of laser power, exposure time, hatch spacing and layer thickness, which was computed by the following formula: = P t d h1.5 2 (1) where P, t, h and d are laser power (W), exposure time (\u03bcs), hatch spacing (\u03bcm) and layer thickness (\u03bcm), respectively", + " Transmission electron microscopy (TEM, FEI, Titan G2 60\u2013300, USA) and related selected area electron diffraction (SAED) analyses were performed to identify the microstructure and crystalline structures of the phases with an accelerating voltage of 300 kV. Samples for the TEM characterization were prepared by sample cutting, polishing, pre-thinning to 50~60 \u00b5m, and then electropolishing in 10% perchloric acid methanol at a voltage of 25 V and - 30 \u2103 using an electrolytic double spray thinning instrument (STRURES, Tenupol-5, Denmark). Tensile test was carried out with an Instron 3369 machine at a constant strain rate of 1.0 \u00d7 10\u22123 s\u22121. The specimens used for tensile testing were processed in accordance with ASTM E8M standard (Fig. 2b). Each experiment results are obtained from average value of five tensile specimens. The fracture surfaces were characterized by SEM. The relationship between the relative densities of all SLMed Ren\u00e9 104 samples and energy densities are presented in Fig. 3a. It can be observed that the relative densities of the SLMed Ren\u00e9 104 samples first increase and then decrease as the energy density \u03b7 rise. Fig. 3b-d describe the OM microstructure of the samples prepared with three different energy densities" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure2.24-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure2.24-1.png", + "caption": "Fig. 2.24. Manipulator with four d.o.f.", + "texts": [ + " Manipulator with four degrees of freedom The first block (block 4-1). For a manipulator it is possible to cho ose a position vector to be equal to the internal coordinates vector. For a 4 d.o.f. manipulator it is 57 x g q (2.4.23) Thus if X is given it means that q is given and no calculation is ne-g eded. Such an approach understands that the motion is prescribed directly in terms of internal coordinates. This approach may simply be used for some configurations such as the cylindrical manipulator (Fig. 2.24) . The second block (4-2). A manipulator with 4 d.o.f. solves the posi tioning task by using three d.o.f., while the remaining one performs operations frequently sufficient for many practical manipulation tasks (Fig. 2.24). Hence we choose a generalized position vector X g (2.4.24) where (x, y, z) represent the Cartesian coordinates of some point of the gripper. Thus the manipulation task is defined via positioning plus one internal coordinate which is given directly. From (2.4.13) and (2.4.14), it follows that: 58 w rl' + 8' (2.4.25 ) For prescribed Xg [x y z q4 l , (2.4.25) represents a system of 3 equa tions with 3 unknowns Q1' Q2' Q3. After solving these equations the whole vector q = [q1 q2 q3 q4lT becomes known" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002444_3477.891149-Figure6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002444_3477.891149-Figure6-1.png", + "caption": "Fig. 6. Outputs of the system tracking the reference signal illustrated in Example 2 [with disturbance 0.01 sin(20t)].", + "texts": [ + " We choose the following membership functions: F (x1) = exp[ (x1 + 1)2] F (x1) = exp[ (x1 + 0:5)2] F (x1) = exp( x21) F (x1) = exp[ (x1 0:5)2] F (x1) = exp[ (x1 1)2]: (4.12) The results are written down directly as follows: The control law is u = ( 2 + yr) (4.13) where 2 = z1 + c2 1 2 2 z2 + @ 1 @x1 x2 + \u0302 T 1 '1 + @ 1 @\u03021 12 + @ 1 @yr _yr; and 1 = c1 1 2 1 z1 \u0302 T 1 '1: The update laws are _\u0302 1 = 12 (4.14) 12 = z1 z2 @ 1 @x1 '1 (4.15) where = 0.1 I . We choose c = c1 = c2 = 10 and = 1 = 2 = 0.2, 0.1, and 0.05. The initial value of \u03021(0) is set to be zero. Fig. 6 shows the trajectories of the output of the system as well as the reference signal. Fig. 7 shows the tracking errors of the output of the system. Since c is fixed as 10, the attenuation level is only dependent on the stabilizing factor . Figs. 6 and 7 indicate the smaller the value of (or the attenuation level ), the better tracking performance. Fig. 8 shows the tracking error by using the proposed method with x (0) = [1, 0]. However, in [12], it has been shown that this situation may lead to the larger control input u and it is a tradeoff between the amplitude of control input and the tracking performance" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003255_09544070d21604-Figure11-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003255_09544070d21604-Figure11-1.png", + "caption": "Fig. 11 Spline chamfer contact geometry", + "texts": [ + " 9 Displacement of the synchro ring issued from thermal dilatationsand higher on the gear cone. Clearly, heat production D21604 \u00a9 IMechE 2006 Proc. IMechE Vol. 220 Part D: J. Automobile Engineering at SUNY MAIN LIBRARY on March 12, 2015pid.sagepub.comDownloaded from can also be introduced (106\u20135\u00d7107 N/m for a surface separation less than 10\u22125 mm). Contact damping c c can also be introduced (5\u00d7105 N s m [23] for a surface separation less than 10\u22125 mm) coming from the oil film. A geometrical model describing the approach of the sleeve chamfer and the gear chamfer surface is given in Fig. 11 [23]. Equations describing the process are given in Appendix 2, section 2.5. 3.2.5 A gear-turning model After separation of the synchro ring from the gear cone, the sleeve has to turn the gear. The equationFig. 10 Model of deformation for the synchro ring proposed to describe the turning force can be found in Appendix 2, section 2.6. During turning, the axialangles [27, 28]. Note that these values change owing velocity of the sleeve increases from the value result-to continuous wear of the conical surfaces", + " The equations of the deformation model [15, 22] the gear splines at the end of the synchronization. During turning, the sleeve is assumed to move(Fig. 9) and the thermal expansion model [15, 22] (Fig. 10) give these pressure values. The second part forward first with constant axial acceleration, starting from the axial velocity inherited from the previousof the tangential force comes from contact force existing between the sleeve and gear spline chamfers phase. At the same time, it is assumed that the turning force accelerates the gear with a constant angular(Fig. 11). Equations of the geometry and the contact model (Appendix 2, section 2.5), [22, 23] give this acceleration. After the sleeve has reached the maximum axial velocity, the axial acceleration stops.force value. There is a second chamfer of angle xmanufactured As the angular acceleration is linked to the axial acceleration, it stops at the same time. Gear splineon the spline sides of the sleeve (Fig. 21). When the sleeve is meshed with the gear splines, this chamfer tangential velocity will have exactly the value needed to leave space for the approaching sleeve", + " 220 Part D: J. Automobile Engineering at SUNY MAIN LIBRARY on March 12, 2015pid.sagepub.comDownloaded from 2.5 Equations describing the start of the second Here, a negative sign means that the sleeve is slowed down by the chamfer contact force. A positivebump sign means that a supplementary axial force isThis phase is described by solid mechanics laws. The applied in order to maintain the original axialnormal distance between the spline chamfer surfaces velocity of the sleeve. This supplementary force(Fig. 11) is given by the following equations [22, 23]: increases the second bump peak. The original axialfor the rear side of the gear chamfer velocity increases the axial force needed in the h1= \u221a[(1\u2212j)p\u2212Ld+dPF ]2+(hd\u2212dB)2 following phase. For more information, see refer- ence [22]. \u00d7cosCb\u2212arctanA hd\u2212dB (1\u2212j)p\u2212Ld+dPFBD (23) 2.6 Equations for turning the gear for the front side of the gear chamfer This phase is also described by classical mechanics laws. The axial force needed for turning ish2= \u221a(jp\u2212Ld\u2212dPF )2+(hd\u2212dB)2 \u00d7cosCb\u2212arctanA hd\u2212dB jp\u2212Ld\u2212dPFBD (24) Fax=AmaxeRr2 tan b+ hReRmTlosses r2 B f3+tan b 1\u2212f3 tan b where (31) dB=vaxt (25) Here, the negative sign means that turning is in the opposite direction to that of the angular velocityis the axial displacement of the sleeve of the gear" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003339_bfb0042513-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003339_bfb0042513-Figure1-1.png", + "caption": "Figure 1: Diagram of planar one-legged model used in simulations.", + "texts": [ + " The legs can be made into harmonic oscillators by introducing torsional springs at the hip joints. The resulting leg oscillations move the foot backward with respect to the hip during the stance phase, and forward in preparation for the next step during the flight phase. The objective of this study was to see if we could design a simple passive system that moved its legs with suitable trajectories for running. We implemented computer simulations of a planar one-legged model composed entirely of springs, masses, and linkages. The model is shown in Figure 1. We manipulated the running trajectories by tuning the natural frequency of the vertical bouncing motion to be a specific fraction of the natural frequency of the leg swinging oscillation, and by choosing initial conditions according to the running speed. We mafiipulated the parameters until phase plots of the variables indicated behavior that repeated on itself, one step after another. The observed running trajectories had a high degree of reentrance, with nearly no energy losses. The systems we consider are passive in that they are made up of springs, links, and masses, with no actuators or other sources of external energy" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003813_j.ijfatigue.2010.09.021-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003813_j.ijfatigue.2010.09.021-Figure4-1.png", + "caption": "Fig. 4. (a) The close-up views of a pair of roller and disk specimens showing the directionality of the surface roughness and (b) the measured surface roughness profiles (after run-in) of the roller-disk pair.", + "texts": [ + " Cylindrically ground specimens [39\u201345] are not considered here since the resultant circumferential machining marks (grooves) leads to the maximum roughness in the axial direction. It is desirable to have such grooves in the axial direction to be able to represent the contacts of the components such as gear applications since the orientation of the machining marks was shown to have substantial impact on RCF failure [45]. While the axial roller grinding techniques were reported by Patching et al. [50] and Alanou et al. [51], an alternate finishing method is devised here to simulate the shaved gear surface finishes on the roller and disk surfaces. Fig. 4a shows the close-up views of a pair of roller and disk specimens, showing the directionality of the surface marks. All the tests are performed using an automatic transmission fluid with its inlet temperature controlled at one of the two levels of 90 and 60 C. The ratio of the gears in Fig. 2b is such that the roller-disk pair operates at SR = 0.25. The disk speed is maintained at 2500 rpm to achieve a rolling speed of ur = 6.6 m/s. The surface hardness of the specimens is 59 HRC. A set of typical surface roughness profiles in the direction of rolling and sliding (x direction) are shown in Fig. 4b. These measurements were obtained using a surface roughness profiler (Talysurf, Taylor-Hobson). The upper and lower cut-off wavelength values of the surface profiler were set at 2.5 lm and 0.8 mm. A composite surface roughness value of about Rq \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 qr \u00fe R2 qd q 0:6 lm is achieved for each roller-disk pair where Rqr and Rqd are the root-mean-square roughness amplitudes of the roller and disk in the rolling direction, respectively. Before each test, a 1-h (350,000 roller cycles) run-in period is carried out at the half of the intended load and the same speed" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003670_978-3-642-82195-0-Figure1.14-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003670_978-3-642-82195-0-Figure1.14-1.png", + "caption": "Fig. 1.14. Vectors relevant for obtaining transformation matrix i-1A. for a sliding joint", + "texts": [ + " Thus, the transformation matrix between two adjacent link coordinate frames, for qi=O, has been determined. If joint i is a sliding one, the transformation matrix between systems i-1 i-1 0 Qi and Qi-1 does not depend on qi' so that Ai Ai holds. There- 16 fore, it is sufficient to determine matrix i-1A~ for a sliding kinema tic pair. It can be obtained in a manner completely analogous to the above described method (Equations (1.3.3) - (1.3.4)). The only differ ence is that vectors a. 1 . an.d~. 1 . are to be explicitly defined as _l- ,l l- ,l -+ kinematic parameters (perpendicular to e i ) (Fig. 1.14) but not to be computed from (1.3.2). While for a revolute joint these vectors determine the disposition of the links for qi=O, for a sliding joint this -+ -+ disposition has to be explicitly imposed, since vectors ~ii and r i - 1,i do not define this disposition anyhow. Once the vectors a. 1 . and a .. . ......1- ,1 II are selected, the transformation matrix i-1 A? l-1 A . is obtained from l l Equations (1.3.3) and (1.3.4). l Now we should determine the transformation matrix i-1 A . for an arbil trary qi for a revolute joint" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003623_robot.2009.5152390-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003623_robot.2009.5152390-Figure4-1.png", + "caption": "Fig. 4. X-4 Flight in Ground Effect.", + "texts": [ + " Initial tests on a gimbal to validate the attitude controller were reported previously [10]. The simplified plant and controller transfer functions are: G = 1.4343\u00d710\u22125(z\u22120.9916)(z+1)(z\u22120.9997) (z\u22120.2082)(z\u22120.9914)(z\u22121.038)(z2\u22121.943z+0.9448) (3) C = 400 ( 1 + 0.2 0.02 (z \u2212 1) + 0.3 (z \u2212 1) 0.02 ) (4) For testing with translational freedom the aircraft was suspended just above the ground at start-up. The rotors were held at idle when attitude controller was turned on, and then brought up to flight speed to carry the weight of the flyer (see Fig. 4). In this test the attitude control integral was not enabled, causing the flyer to stabilise at non-zero angles and drift across the test area. The X-4 flew at a height of approximately 0.4 m in ground effect and regulated its attitude within \u00b11 degree of equilibrium (see Fig. 5). For testing beyond ground effect the X-4 was flown tethered indoors. After engaging the attitude controller the suspended flyer was hoisted up 1.5 m into the air before bringing the rotors to flight speed. A pilot sent attitude reference commands to the flyer to keep it centered in the test area; the pilot did not stabilise the vehicle" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000059_j.addma.2020.101801-Figure16-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000059_j.addma.2020.101801-Figure16-1.png", + "caption": "Fig. 16. Schematic representation of the contour laser track and bulk laser track as a function of the strategies and of the offset in the (a) x-z plane and in the (b) xy plane.", + "texts": [ + " In the case of TW samples, factors influencing the roughness are also depending on the same two factors. The level of TED tends to decrease the roughness by increasing the melt pool size while increasing the offset reduces interactions between contours and bulk hatching melt pools, thus decreasing the roughness. Moreover, increasing the melt pool size decreases the offset and should then counteract the beneficial geometrical effect of large melt pools. However, the importance of those effects depends on the adopted strategy. Fig. 16 schematically represents the difference between both strategies. In BF strategy, the melt pools of the contours are influenced by the solidified melt pools of the bulk hatching. Indeed, the solidified bulk tracks impact the wetting of the melt pools of the contours. In the case of a larger offset, the interactions between the contour and bulk melt pools are less significant. However, increasing the offset also increases the amount of sub-surface porosities due to a bad overlapping [30,72] between the bulk tracks and the contour tracks, which is expected to be detrimental to the mechanical properties (particularly fatigue). Cracks can also easily initiate fracture in tensile tests and thus reduce the mechanical quality of the parts [40]. Micrographs of Fig. 16.(a) illustrate cross-sections of CF-TW and BFTW samples on which the bulk hatching and the contours of the last layer were not processed. In the case of the BF strategy, the solidified bulk tracks will disturb the melt pools of the contours. A large offset limits the impact of those solidified tracks and thus the roughness. As for the UTW samples, this can be observed by the contour melt pools orientation (dashed arrows in Fig. 16.a) of the last processed layer. In the case of the CF strategy, contour melt pools act as an \u2019overflow barrier\u2019. The offset has no more effect as long as the bulk TED level is equal or lower than the contour TED level. Indeed, for a small offset, the bulk hatching can re-melt the contours (Fig. 16.b). In this case, roughness increases since there are no more contours (Fig. 9, CF with a 0 \u03bcmoffset). Increasing the level of TED with a CF strategy decreases the level of O. Poncelet et al. Additive Manufacturing 38 (2021) 101801 roughness (Fig. 8.b) due to a geometrical effect. The same trend is observed in the case of the BF strategy when the offset is large enough. For smaller offsets, the trends are different because the increase of the melt pool size with the level of TED decreases the offset and thus increases the roughness (Fig. 8.a). For a large level of TED (above 220 J/ m), the positive geometrical effect overpasses the negative effect of the decreasing offset, thus reducing the level of roughness. Small variations of the solidified bulk melt pools in the case of a BF strategy, due to slight variations of some parameters (powder size and compaction, layers rotation, laser fluctuation.) [46,73] can induce an uneven side profile of the bulk hatching (Fig. 16.b). It impacts slightly the roughness since this uneven side profile disturbs the wetting behavior of the contour melt pools. It is worth noting that powder denudation [27,71] in BF strategy (Fig. 1.b) can also have a small impact on the contour melt pool geometry due to the induced slight lack of powder near the contour. The present study addressed the origin of the vertical roughness in LPBF AlSi10Mg alloy components. Three different structures have been considered to address the key factors impacting the level of roughness" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000202_j.mechmachtheory.2021.104330-Figure8-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000202_j.mechmachtheory.2021.104330-Figure8-1.png", + "caption": "Fig. 8. An example of the deployable grasping parallel mechanism. (a) The auxiliary sub-mechanism is denoted by v P x R x R u1 R u2 R. (b) Assembly uses the grasping sub-mechanism, the base, the platform, and two auxiliary sub-mechanisms. (c) The folded configuration of such a deployable grasping parallel mechanism.", + "texts": [ + " Finally, the structural characteristics of the auxiliary sub-mechanism in this case are: 1) there must be two or three successive revolute joints, i.e., ( i R j R) N , ( i R j R k R) N , u1 R u2 R, or u1 R u2 R u3 R, 2) the revolute joint(s), except those in the successive revolute joints, must be x R, and 3) the prismatic joint(s) must be v P or v1 P v2 P. An enumeration of such auxiliary sub-mechanisms is provided in Table 1 based on these structural characteristics. One example ( v P x R x R u1 R u2 R) is presented in Fig. 8 (a), which consists of one prismatic joint P a1 whose translational direc- tion is parallel to Y a Z a plane, two revolute joints whose axes are along X a -axis, and two revolute joints that are a 2R spherical sub-chain. Subsequently, a deployable grasping parallel mechanism is assembled using the grasping sub-mechanism, the base, the platform, and two auxiliary sub-mechanisms, as shown in Fig. 8 (b). Fig. 8 (c) illustrates the folded configuration of this mechanism. Additionally, such a mechanism has various deployable configurations and only one fully deployed configuration. When the whole mechanism is at full deployed configuration, the grasping sub-mechanism satisfies the condition that axes z 1 and z 6 (shown in Fig. 4 ) are coplanar with axes z 3 and z 4 , as shown in Fig. 5 (f). Several types of deployed configurations and the fully deployed configuration are also provided in Movie S1. Fully deployed configuration and the grasping configuration can be seen in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002483_02640410152006126-Figure5-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002483_02640410152006126-Figure5-1.png", + "caption": "Fig. 5. Aerodynamic force components. The four vectors V, D, Y and x lie in the plane perpendicular to L.", + "texts": [ + " Similarly, the drag, D, is characterized by the drag coe\u00fd cient, CD, and acts in a direction opposite to that of the translational velocity vector: D = -1 \u00b1 2 rCDAV V (3) where CD is also a function of the Reynolds number and ball roughness, and the other parameters are as de\u00ae ned above. In most previous studies, however, the lift reported was not only the Magnus force (i.e. perpendicular to the spin axis) but rather the sum of all force components perpendicular to the drag. Because of the asymmetric stitch pattern on the baseball, an additional force component, the s\u0300ide-force\u2019 Y, perpendicular to both the lift and drag, as shown in Fig. 5, generally exists. Because of the uncertainty in our ability to have the pitching machine throw exactly two- and four-seam fastballs, the side force could not be guaranteed to vanish. It was included in the model for completeness and so that its absence would not adversely a\u00fe ect the estimation of the lift coe\u00fd cient. In this paper, therefore, the aerodynamic force vector in equation (1) is written as FA = L + D + Y (4) D ow nl oa de d by [ G eo rg e M as on U ni ve rs ity ] at 1 4: 26 2 9 D ec em be r 20 14 The side-force, Y, is characterized by a third dimensionless side-force coe\u00fd cient, CY: Y = 1 \u00b1 2 rCYAV 2 L \u00b4 D |L \u00b4 D| (5) Notice that the cross-product term in equation (5) ensures that Y is mutually perpendicular to L and D" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003007_56.2077-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003007_56.2077-Figure1-1.png", + "caption": "Fig. 1. A contour following problem.", + "texts": [ + " l), then 1) move the end effector from its initial position a to point b in surface S; 2) move the end effector along a specified curve C in S from point b to point c so that it has a given specified contact force with S; 3) move the end effector from point c back to its initial position a. The motion of the manipulator consists of two parts: an unconstrained motion, where the end effector is not in contact with the constraint surface S (i.e., from point a to point b and from point c to point a in Fig. l), and a constrained motion, where the end effector is in contact with the constraint surface S (i.e., from point b to point c in Fig. 1). During the unconstrained motion, we have an open kinematic chain configuration. On the other hand, during the constrained motion, where the contact force must be considered, we have a closed kinematic chain configuration. For these types of Manuscript received August 27, 1986; revised March 19, 1987. This work was partially supported by the Air Force Office of Scientific Research under AFOSR Contract F 49620-82-COO89 and the Center for Research on Integrated Manufacturing (CRIM) at the University of Michigan" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003212_j.ijmecsci.2007.07.002-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003212_j.ijmecsci.2007.07.002-Figure2-1.png", + "caption": "Fig. 2. The finite element model of a profile-shifted spur gear. (a) Finite element meshment of plastic gear. (b) Detail of the contact region.", + "texts": [ + ", material, sliding-rolling ration at contact point, and lubricant between contact teeth, can affect the damping characteristics between engaged tooth pairs. Therefore, so far, no widely accepted damping ratio model exists. For simplicity, a viscous damping model with a constant damping ratio is employed in this work. Based on experimental results obtained by Quistwater and Dunell [29], the magnitude of damping ratio, z, is assumed with a value of 0.6 in this study. This study employs a finite element model for the profileshifted plastic gear (Fig. 2). The tooth width F is assumed as 12 times of the module m [30] in this study. The partial of the same plastic material cylinder (Fig. 2(b)), is employed to simulate the contact of the meshed tooth pair. Different cylinder radii are utilized in the finite element simulations in this study. The radii of the contact cylinders are calculated based on the radii of curvature of the engaged spur tooth at the corresponding contact points. The simulations access the gear materials of POM and Nylon 66 at an ambient temperature of 20 1C. Loading is applied at the operating pressure angle. The elastic\u2013 plastic model of the MARC finite element package is employed in tooth mesh stiffness analyses" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003835_tie.2008.2003196-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003835_tie.2008.2003196-Figure3-1.png", + "caption": "Fig. 3. Location of sensors on the rotor.", + "texts": [], + "surrounding_texts": [ + "A. Introduction Both nodal and modal reduction methods are based on reducing the number of equations in the physical system. We are going to build a new reduction methodology that needs a direct resolution of the equations of the model [10]. Therefore, the temperature of each node observed in the reduced model is a combination of the different boundary conditions weighted by transfer functions \u0398nodeobserved(s)= \u2211 X(s)\u03b8imposed(s)+ \u2211 Z(s)\u03a6imposed(s). (3) Our nodal model is linear (the exchanges by radiation are linearized). Equation (3) corresponds to the superposition principle of linear models applied in transient mode. As in the case of a state-space representation, we will talk in this new approach about observed nodes and no longer about conserved nodes." + ] + }, + { + "image_filename": "designv10_6_0003047_1.1767819-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003047_1.1767819-Figure1-1.png", + "caption": "Fig. 1 3-RRS mechanism", + "texts": [ + " Regarding the 3-RRS wrist, it is necessary to make the reader aware of the fact that, while this paper was under review, two other research groups @13\u201315# independently identified this type of wrist by using two different type synthesis techniques. So, today, the term new referred to the 3-RRS wrist has mainly the meaning of recently presented, whereas this author remains the first one who proposed it and the method used in this paper to address the study of the 3-RRS wrist still is original. The 3-RRS wrist is obtained by imposing some manufacturing and mounting conditions on a parallel mechanism with three degrees of freedom ~dof! that has three legs of type RRS ~Fig. 1!. Hereafter this mechanism will be called 3-RRS mechanism. In the next section a property of the rigid body motions will be demonstrated. Then, by exploiting this property, the mounting and manufacturing conditions that a 3-RRS mechanism has to encounter for being a spherical parallel manipulator will be enunciated. Finally the kinematic analysis of the 3-RRS wrist will be addressed and solved. For introducing the 3-RRS wrist the demonstration of the following statement is necessary: STATEMENT 1: If three distinct and not aligned points of a rigid body move on concentric spheres whose center does not lie on the plane located by the three points, then the rigid body must accomplish a spherical motion whose center is the center of the spheres", + " admits just the following solution q50 (8) Taking into consideration definition ~4!, Eq. ~8! becomes as follows P\u03075v3~P2C! (9) Finally, the dot product of Eq. ~9! and ~P2C! gives the following relationship P\u0307\u2022~P2C!50 (10) Since the P point is any point of the rigid body, Eq. ~10! states that any point of the rigid body moves on concentric spheres whose center is C, i.e., the rigid body accomplishes a spherical motion with center C. QED The 3-RRS Wrist The number of degrees of freedom ~dof number! of the 3-RRS mechanism ~Fig. 1! can be computed with the Gru\u0308bler equation: F56~n21 !2( j ~62fj! (11) where F is the dof number of the mechanism, n is the number of links and fj is the dof number of the j-th kinematic pair. The 3-RRS mechanism ~Fig. 1! is composed of eight links ~n58!, three spherical pairs (fj53) and six revolute pairs (fj51). Substituting these data into Eq. ~11! gives F53. Therefore the 3-RRS mechanism has three dof, i.e., is not overconstrained. Figure 4 shows a 3-RRS mechanism encountering the following mounting and manufacturing conditions: i. the revolute pair axes converge towards a single point; ~mounting and manufacturing condition! ii. the centers of the spherical pairs are not aligned; ~manufacturing condition! SEPTEMBER 2004, Vol" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000016_j.mechmachtheory.2020.104097-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000016_j.mechmachtheory.2020.104097-Figure1-1.png", + "caption": "Fig. 1. Landing and walking configurations of the ReLML.", + "texts": [ + " The paper is organized as follows: Section 2 introduces the structure, mechanism, and kinematics of the ReLML; next, Section 3 proposes the optimum dimension design strategy for this MMSO problem; Section 4 implements the optimization design of the walking leg execution mechanism; Section 5 implements the optimization design of the multi-mode trans- mission mechanism; Section 6 calculates the optimum dimensional parameters; in the end, Section 7 concludes the paper, summarizes main contributions, and discusses its potential effects. Fig. 1 illustrates the structure and parameter diagram of the ReLML, including two operation modes/configurations of landing and walking. The ReLML is constituted by one main body and four single legs. The single leg is an independent mechanical assembly attached to the structural frame of main body, and possesses the reconfigurable mechanism topolo- gies of landing leg and walking leg. And Fig. 2 illustrates the structure and mechanism diagram of the single leg in landing and walking configurations. The mechanism system of the single leg is constituted by metamorphic execution mechanism and multi-mode transmission mechanism: (1) The metamorphic execution mechanism has an integrated hybrid topology of ( R v U&2 R v U P b S ) \u2212 P b S , where P b denotes the buffering damper regarded as a passive prismatic pair actuated by the landing impact force, S denotes the spherical hinge, and R v denotes the metamorphic revolute hinge that is only active in walking mode while disabled in landing mode" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000477_lra.2021.3068115-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000477_lra.2021.3068115-Figure2-1.png", + "caption": "Fig. 2. Details of the robotic system. (a) The manipulator\u2019s motion states; (b) Assembling of the driver system.", + "texts": [ + " The wire ropes with flexible tubes, used for force transmission allow the driven system to be put far away from the manipulator to ensure the manipulator compact and light enough. There are six DOFs, including the DOFs for grasping with bending, the DOF for the rotational of the wrist, two DOFs for the manipulator\u2019s unfolding, and the translational DOF. The DOF configuration allows the manipulator to move and rotate vertically to the manipulator\u2019s axis and move along the axis. The motion states of the manipulator are shown in Fig. 2(a). The manipulator\u2019s stiffness is determined by the stiffness of joints 4 and 5. As shown in Fig. 2(b), the drive system can be divided into two parts in the consideration that the detachable structure is beneficial to replace the manipulator during the surgery. The reels used to drive the manipulators via wire ropes with flexible tubes are connected to the worm gears by the mechanical interface. The worm gears are driven by direct current (DC) motors (RE13, Maxon motor Inc.). The sliding blocks can move along Authorized licensed use limited to: University of Prince Edward Island. Downloaded on May 29,2021 at 19:13:45 UTC from IEEE Xplore" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003197_tec.2005.859964-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003197_tec.2005.859964-Figure4-1.png", + "caption": "Fig. 4. Location of sensors on the stator.", + "texts": [ + " The influence of these exchange coefficients on the whole thermal behavior of the motor is shown in Section V-B. 1) Thermal Implementation of the Machine: The temperature sensors used are negative temperature coeffiecient (CTN) thermistors of small size (diameter: 0.5 mm, length: 4 mm) and short response time (250 ms) [30]. They have a reference ohmic value of 10 k\u2126 at 25 \u25e6C. a) Implementation of the Stator: The stator is very well equipped: six sensors have been introduced in each angular sector (Fig. 4). Three angular sectors are implemented for each of the three particular sections of interest. b) Implementation of the Rotor: The rotor is implemented with nine thermistors (Fig. 5). The information is collected through a ten-track slip ring LITTON EC3848 [31]. 2) The Test Bench: The test bench includes the induction motor coupled to a direct current machine that can be used as a drive or a brake. The power supply of the machine is provided by an alternator on which the delivered frequency and tension can be separately controlled" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002788_a:1015221832567-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002788_a:1015221832567-Figure4-1.png", + "caption": "Figure 4. Postural Reflex Principle. Three types of symmetry are enforced for weight distribution. Diagonal\u2014Comparison of diagonal feet; Front-to-Back\u2014Comparison of front to back feet; and Side-to-Side\u2014Comparison of feet on left to feet on right side. The numbers near the feet denote the numbering of the feet.", + "texts": [ + " The equation for body posture adjustment is: \u03c4 d P\u0304 dt = \u2212P\u0304 + \u00b7 A B C Sfoot1 Sfoot2 Sfoot3 Sfoot4 (6) where A = [1 \u22121 \u22121 1], B = [1 1 \u22121 \u22121], C = [1 \u22121 1 \u22121], = \u03bb 0 0 0 \u03bb2 0 0 \u03bb3 , P\u0304 = [L Sw Tw] where \u03bb are small constants controlling the adaptation rate. The term P1 = L controls the lunge of the robot, P2 = Sw controls the side-to-side sway, and P3 = Tw controls the body twist bias. The intuition behind the matrix mapping the sensor commands to bias commands is given by reference to Fig. 4. During walking, C = 0. That is, twist compensation is switched off. This prevents the postural control mechanism from overriding the twist uCPGs. In addition to the ARRs, another class of computational module, an adaptive module (AM), is responsible for altering parameters of the ARR. The basic model for an AM is shown in Fig. 3. The AM has three components: (1) a forward model which uses an efference copy from a uCPG to predict sensory feedback, (2) a comparison of sensory feedback versus expected sensory feedback, and (3) a rule which uses the result of this comparison to modulate the uCPG in question", + " A comparison is made of the expected and the actual sensory signal. Based on the returning signal, the associated ARR is modulated to produce a different output. Below, we illustrate several AMs. 2.4.1. Twist Adaptive Module. This adaptive module acts with the ARR responsible for \u2018twist\u2019 movements of the body. A component of basic walking in animals is the sequential activation of the hypaxial muscles, responsible for twisting movements of the trunk in quadrupeds (Carrier, 1990, 1993). Referring to Fig. 4, the twist commands cause the trunk to rotate about its central axis. One of the effects of this motion is the transfer of weight to one set of diagonal feet and the unloading of the complementary diagonal set of feet. The components of the Twist Adaptive Module are given below. The forward model: dmTw+/\u2212 dt = \u2212mTw+/\u2212 + yTw+/\u2212 (7) MTw+/\u2212 = fh(mTw+/\u2212 \u2212 \u03c4Tw) (8) The comparison: eTw+ = fs(S f 1 + S f 3) \u00b7 MTw+ (9) eTw\u2212 = fs(S f 2 + S f 4) \u00b7 MTw\u2212 (10) The correction rule: ATw+/\u2212 = \u222b T 0 fs(eTw+/\u2212) \u2212 fs(Sv1 + Sv2) dt (11) ATw+/\u2212(0) = 0 where yTw+/\u2212 is the output of two ARR responsible for body twist", + " These experiments require progressively more adaptation to the environment and culminate in adaptive walking behavior. The robot learns to adjust key parameters of the CPG network to allow the robot to walk within minutes. The robot platform is a four-legged robot, \u201cGEO-II\u201d (Fig. 5). Sensors include a force sensor on each foot, and a gyro scope which senses body roll. The unique features of this robot include a flexible, three-degrees of freedom spine. This allows spinal movement including twist. A sketch of the basic structure of the trunk and legs is shown in Fig. 4. Model airplane servo actuators drive all axes. These servos are positional control devices. Geo II weighs 1.25 Kg. Computation is divided between an onboard processor, a 68HC11 based ServoX24 board by Digital Designs and Systems, Inc., and a dual Intel Pentium workstation. The ServoX24 board is responsible for generating command signals for the servos as well as A/D sampling of sensor signals. The workstation is responsible for computing the ARRs, the AMs, and reflexes modules. The workstation also hosts a graphical user interface" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002579_s0301-679x(01)00079-2-Figure8-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002579_s0301-679x(01)00079-2-Figure8-1.png", + "caption": "Fig. 8. An automotive gas turbine [37].", + "texts": [ + " Another technological need that provides challenges to tribology research is the development of high temperature engines. The second law of thermodynamics decrees that the wider the temperature range over which an engine operates, the more efficient it should, at least in theory, become. In practical terms this implies that the heat input stage of both gas turbine and crankcase engines should be designed to operate at the maximum possible temperature. In gas turbine engine technology, ceramic gas turbines are under development with inlet temperatures of 1350\u00b0C for automotive use (Fig. 8), [37] and 1700\u00b0C for supersonic/hypersonic aircraft [38], leading to bearing temperatures up to and possibly in excess of 300\u00b0C. In reciprocating engine technology, low heat rejection or adiabatic diesel engines are expected to reach 540\u00b0C top ring temperature [39]. Fig. 9 compares the predicted temperatures for such engines with those of water-cooled ones as a function of power output. The tribological challenge is to develop gas turbine bearings or diesel engine piston rings able to operate for long periods and with low friction at these very high temperatures" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000287_physrevapplied.15.064051-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000287_physrevapplied.15.064051-Figure3-1.png", + "caption": "FIG. 3. Simulation results of case i-a: (a) induced magnetic field and (b) Lorentz force density in the middle cross section of the molten pool at t = 120 \u03bcs. The white curves are the solid-liquid interfaces.", + "texts": [ + " Moreover, the magnitude of TECs can be estimated with Ohm\u2019s law [19,35], \u2016jTECs\u2016 \u223c \u03c3c(Sel \u2212 Ses) Tb \u2212 Ts \u03b4 , (29) where Sel, Ses, and \u03b4 are the Seebeck coefficients at the liquidus and solidus temperature, and the thickness of the molten pool. In these simulations, \u03b4 is about 50 \u03bcm. With the physical parameters in Tables V and VI, the estimated magnitude of the TECs is about 1.5 \u00d7 108 A/m2 matching with the current simulation results. To further analyze the effect of the Seebeck effect, the induced magnetic field, and Lorentz force density distribution in the middle cross section of the molten pool at t = 120 \u03bcs are given in Fig. 3. As convection in the induction 064051-5 equation (v \u00d7 B) in Eq. (19) is small, the main component of the induced magnetic field is the Seebeck-effectinduced magnetic field (bTECs). The intensity of bTECs is 1 \u00d7 10\u22125 T \u2212 1 \u00d7 10\u22124 T as shown in Fig. 3(a). Here bTECs is high on the solid-liquid interface, especially in the bottom of the molten pool, and decreases with the distance increase on both sides, which agrees with the laser welding simulation results by Chen et al. [19]. The induced magnetic field is the result by the outer product of \u2207Se and \u2207T where \u2207Se is zero in the same phase and not continuous on the solid-liquid interface. Moreover, the higher temperature gradient in the bottom of the molten pool leads to a larger induced magnetic intensity. In Fig. 3(b), the magnitude of the Lorentz force density in the molten pool ranges between 1 \u00d7 103 N/m3 and 1 \u00d7 104 N/m3. The Lorentz force is also higher in the bottom of the molten pool and the solid-liquid interface similar to the TECs. However, the Lorentz force in the upper part of the molten pool is much smaller than that in the bottom because the induced magnetic intensity is nearly zero in this region as shown in Fig. 3(a). Compared with the magnitude of the buoyancy force density (\u03c1gav(T \u2212 Tl) \u223c 1 \u00d7 103 N/m3), the Lorentz force is nonnegligible, although it is localized. The keyhole depths growth and z-direction recoil forces variation with time are given in Fig. 4 to study the effect of the Lorentz force in the laser melting process. In Fig. 4, both the keyhole depths and the z-direction recoil forces with and without the Seebeck effect share a similar trend as time increases. Before 50 \u03bcs, the molten pools are shallow with the keyhole depths being lower than 100 \u03bcm", + " 2 and the values of these variables are higher in the upper and bottom parts of the molten pool. The temperature gradients and electric currents in the four cases are about 1 \u00d7 108 K/m and 3 \u00d7 108 A /m2. It is the reason that the TECs (|\u03c3Se\u2207T| \u223c 108 A/m2) is much larger than the electric current by the convection (|\u03c3v \u00d7 B| \u223c 106 A/m2). In other words, the electric currents in the molten pool are mainly composed of the TECs due to the high-temperature gradient. The Lorentz force density distributions in Figs. 5(a4)\u2013 5(d4) are not like the result in Fig. 3(b) but similar to the distributions of the temperature gradient and electric current in Fig. 5. The Lorentz force densities are not only high in the bottom of the molten pool, but also strong in the whole molten pool. The magnitude of the Lorentz force densities in the inner region and surface of the molten pool is higher than that in the solid-liquid interface, similar to the distribution of electric current. Moreover, the magnitude of the Lorentz force density can reach 1.5 \u00d7 108 N/m3, which is about four orders higher than the result without external magnetic fields. To understand the Lorentz force density distributions, the intensity of induced magnetic fields in the middle cross sections of the molten pools are shown in Figs. 6(a) and 6(b). Although the intensities of induced magnetic fields are still 1 \u00d7 10\u22125 \u2212 1 \u00d7 10\u22124 T, the distribution of the induced magnetic fields are different from the simulation results without external magnetic fields in Fig. 3(a). The induced magnetic fields are not only high on the solid-liquid interface but also remarkable in the inner part of the molten pool, where the amplitude of the fluid velocity is higher as shown in Figs. 6(c) and 6(d). The convection induced magnetic field (bc) can be 064051-7 estimated with Ampere\u2019s law [31] and the intensity of bc is \u223c \u03bc0l\u03c3c|v||B0| = Rem|B0|, where l and |v| are the thickness and velocity of the fluid domain and Rem is the magnetic Reynolds number. With the values of l \u2248 50 \u03bcm, v \u2248 3 m/s, \u03c3c = 4" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002457_s0956-5663(03)00085-x-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002457_s0956-5663(03)00085-x-Figure2-1.png", + "caption": "Fig. 2. Assembly of NH4 selective electrode with microbial biomass.", + "texts": [ + " It was identified by MTCC and Gene Bank, Institute of Microbial Technology, Chandigarh as Bacillus sp. (shown in Fig. 1). For immobilization, the bacterial culture was centrifuged at 5000 rpm for 20 min at 4 8C and the pellet was retained. The optical density of the cell biomass, measured at 600 nm was set to 1.000 using PBS (pH 7.5). Aliquots of 1.5 ml cell biomass were filtered off on Whatman No.1 filter paper; the paper was dried and coupled to the body of the electrode with an \u2018O\u2019 ring to form the biocomponent of the biosensor (shown in Fig. 2). The growth profile of the microbe was studied and since it is a microbial system the minor variations in the activities of the probes was also studied. The stability of the microbial probe was compared with that of pure enzyme probe. The transducer was a potentiometer (Cyberscan-2500) in conjunction with a NH4 Ion Selective Electrode (ISE-Code No. EC-NH4-03) that detects the electrode potential developed across the membrane of the elec- trode when it comes in contact with ammonium ions released as a result of urea hydrolysis, forming a second generation biosensor" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002683_s0141-6359(00)00066-0-Figure5-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002683_s0141-6359(00)00066-0-Figure5-1.png", + "caption": "Fig. 5. The three-vee coupling slides on five constraints producing rotation about an instant center shown in the top view and also about an axis through the two seated balls.", + "texts": [ + " gen_mean(v, p) 5 H1 n O i 5 1 n uviu pJ1/p (11) Although not closely tied to a physical measure, Maxwell\u2019s criterion is simple to implement and it demonstrates techniques used in more specialized optimization criteria. It states that each constraint should be aligned to the local direction of motion allowed by the five other constraints, assuming that they remain engaged and are free to slide. To test this criterion, each constraint is released individually to discover the direction of motion at the released constraint compared to the actual constraint direction. This test is demonstrated in Fig. 5 on a symmetric three-vee coupling. The inner product (or dot product) between the direction of motion and the constraint direction provides a convenient scalar indicator of the alignment. The vector directions are given unit length so that perfect alignment produces a maximum inner product of one. There will be one inner product for each constraint, and the objective is to maximize all six. For this symmetric coupling, the inner product is the same for each of the six constraints and equal to cos(90\u00b0\u20132a), which is maximum at a 5 45\u00b0", + " Once a balanced optimum is found, finite element analysis can be used to improve the accuracy of the modal frequencies. Continuing the example of the symmetric three-vee coupling, a mass element will be placed at the center of stiffness and given principal moments of inertia equal to m Rm 2, where m is the mass and Rm is the radius of gyration. Eq. (12) gives the stiffness matrix, where k is the stiffness of each constraint and Rk is the radius to each constraint. The angle a is the parameter to optimize and is defined the same as before (see Fig. 5). The modal frequencies, in this case, are determined simply by dividing the diagonal elements of K by those of M with the results shown in Eq. (13). K 5 diag 1 3 3k sin2(a) 3k sin2(a) 6k cos2(a) 3kRk 2 cos2~a! 3kRk 2 cos2(a) 6kRk 2 sin2(a) 4 2 (12) v 5 S3k mD 1 2 3 sin(a) sin(a) 2 cos(a) g cos(a) g cos(a) 2g sin(a) 4 g 5 Rk Rm (13) Only a few degrees of freedom matter in the optimization depending on the radius ratio g. For example when g is small, the angular degrees of freedom will limit the modal frequencies", + "7 A simplifying step works under the assumption that the normal forces remain at the values calculated for equilibrium without friction. In effect, friction causes a nonrepeatability in the load vector required to bring the coupling to the ideal engagement point. This is the frictional force-moment vector, which is computed by transforming the six local friction forces to the base CS of the coupling and then adding. Multiplying the compliance matrix by this vector gives the nonrepeatability vector. For the symmetric three-vee coupling in Fig. 5, the dominant component of nonrepeatability at the center will be horizontal. Neglecting the other components and assuming the coupling is symmetrically loaded, Eq. (16) gives the nonrepeatability as a function of configuration, represented by a, and other terms m, P and k. The effect of the configuration is plotted in Fig. 6, which shows a minimum of 0.71 at a 5 58\u00b0. The estimate in Eq. (15), corresponding to a factor 1 in the figure, is somewhat conservative for the symmetric three-vee coupling having a nearly optimal vee angle", + " These are the six singular directions found for Maxwell\u2019s criterion and the ones used to sample the nonrepeatability of the coupling. The method used to compute the frictional forces is essentially the same as before except that the coefficient of friction is now a variable to be solved from the equation for the constraint not engaged, since its reaction force must be zero for the coupling to be on the verge of sliding.8 This procedure is repeated for each of the five remaining constraints, and the minimum value is typically used in the design optimization. When the symmetric three-vee coupling in Fig. 5 is loaded with a nesting force, a centering force develops tending to slide the coupling along the singular direction. The off-center vee transforms its share of the nesting force (assumed to be one-third in this example) into a centering moment about the instant center. Eq. (17) describes the centering force at the center of the coupling due to this moment as a function of the angle a and the coefficient of friction m. The limiting coefficient of friction corresponds to the threshold of sliding when the net centering force or moment is zero" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003764_s00170-010-2659-6-Figure8-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003764_s00170-010-2659-6-Figure8-1.png", + "caption": "Fig. 8 Von Misses residual stress; a long bead, b short bead, c spiral in, d spiral-out pattern", + "texts": [ + " It is predictable that changing the deposition pattern results in changing the temperature history of the process. The temperature contours of the part right after the last step of the deposition for different deposition patterns are shown in Fig. 7. As can be seen, the maximum temperature, just after turning off the laser, significantly drops below the melting temperature. This reduction is less in the short-bead pattern than in the other patterns. Different temperature histories have a direct effect on the residual stress of the part. Figure 8 indicates the distribution of Von Misses stress after the part cools to room temperature. Except for the spiral-in pattern where the maximum residual stress is at the surface of the cladding layer, for the other patterns, it is at the interface of the cladding layer and the substrate. The short-bead pattern shows the lowest maximum residual stress among the patterns. In order to compare the stress at the top surface of the cladding layer, Table 3 summarizes the minimum and maximum stresses along x and y and the Von Misses stress" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002683_s0141-6359(00)00066-0-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002683_s0141-6359(00)00066-0-Figure3-1.png", + "caption": "Fig. 3. The stiffness matrix K1 of the spring is expressed in terms of the local CS1. The goal is to express the stiffness matrix in terms of the base CS0. A collection of springs once represented in the same CS can be added together in series or parallel combinations.", + "texts": [ + " These two points of views have important practical value when dealing with sequential transformations and may be summarized with two simple rules [15]: Rule 1: post multiply to transform in body coordinates Rule 2: pre multiply to transform in base coordinates v0 5 T0/1 z T1/2 \u00b7 \u00b7 \u00b7 Tn21/n z vn 5 T0/n z vn (4) The [6 3 6] transformation matrix is derived from compatibility and equilibrium equations, which express the same geometric relationship, compatibility as a consistent relationship among displacements and equilibrium as a balance of forces. It is instructive to work through the example in Fig. 3, which shows one spring in what could be a parallel and/or series combination with many other springs. One end of the spring is grounded and the other is connected to a rigid link that extends to the base CS0. Movement of the link at CS0 causes the spring to deflect relative to CS1 as described by Eq. (5), the compatibility equations. Forces and moments developed in the spring at CS1 transfer to CS0 through the link as described by Eq. (6), the equilibrium equations. Both the compatibility equations and the equilibrium equations are readily expressed in terms of six-dimensional vectors" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003961_978-1-4419-7267-5-Figure5.3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003961_978-1-4419-7267-5-Figure5.3-1.png", + "caption": "Fig. 5.3 The structure of the Newton\u2013Euler inverse dynamics algorithm", + "texts": [ + " There we encountered the feature that spatial operator expressions can be evaluated using low order recursive algorithms. We take this approach to develop the O(N) Newton\u2013Euler inverse dynamics algorithm. 5.3 Inverse Dynamics of Serial-Chains 89 For the inverse dynamics problem, the hinge accelerations \u03b8\u0308 are assumed to be known. The spatial operator equations of motion in (5.21) map easily into Algorithm 5.2, which is referred to as the Newton\u2013Euler inverse dynamics algorithm for computing the inverse dynamics of the serial-chain. The structure of this algorithm is illustrated in Fig. 5.3. This algorithm is an O(N) computational procedure involving a base-to-tip recursion sequence to compute the spatial velocities and accelerations, followed by a tip-to-base recursion to compute the hinge forces. Algorithm 5.2 Newton\u2013Euler inverse dynamics algorithm\u23a7\u23aa\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23aa\u23a9 V(n+ 1) = 0, \u03b1(n+ 1) = 0 for k = n \u00b7 \u00b7 \u00b71 V(k) = \u03c6\u2217 (k+ 1,k)V(k+ 1)+H\u2217 (k)\u03b8\u0307(k) \u03b1(k) = \u03c6\u2217 (k+ 1,k)\u03b1(k+ 1)+H\u2217 (k)\u03b8\u0308(k)+a(k) end loop \u23a7\u23aa\u23aa\u23aa\u23aa\u23aa\u23a8 \u23aa\u23aa\u23aa\u23aa\u23aa\u23a9 f(0) = 0 for k = 1 \u00b7 \u00b7 \u00b7n f(k) = \u03c6(k,k\u2212 1)f(k\u2212 1)+M(k)\u03b1(k)+b(k) T(k) =H(k)f(k) end loop (5" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure4.3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure4.3-1.png", + "caption": "Fig. 4.3. The cross sections of segments", + "texts": [ + " Example. We consider a problem of designing a manipulator VE-2 (Fig. 4.2.a) having six degrees of freedom. It is intended for spot-welding tasks and some assembly tasks. Its kinematical scheme is arthropoid and shown in Fig. 4.2.b. Some manipulator parameters are adopted and given in Fig. 4.2.b,c. The other parameters have to be determined. Let us first consider the ques tion of segments geometry. Segments 2 and 3 are in the form of rectan gular tubes made of light alloy A\u00a3Mg3. The cross sections (Fig. 4.3.) are defined by Hx2 ' Hy2 and Hx3 ' Hy3 ' so these parameters have to be determined. The actuators which drive the joints S2' S3 are placed in manipulator base. The torques are transported to the corresponding joints where there are Harmonic Drive reducers. The reducers in joints S2' S3 have the masses of about 7kg and the mechanical efficiencies n = 0.8. It is necessary to choose the actuators which will drive the joints S2' S3. The manipulator is equipped with spring compensators for the joint S2", + " But, such speeds 256 257 are usually too high for practical application. Hence, we conclude that it is enough to perform the optimization with one value of execution time, the shortest one. That time corresponds to the largest operation speed which can be required from the device in its practical operation. Example 2. Let us again consider the arthropoid manipulator VE-2 (Fig. 4.2). It has been described in the example in 4.1. The problem is to choose the values of cross-section dimensions of segments 2 and 3 (Fig. 4.3). There are eight parameters defining these two cross-sections: hX2' Hx2 ' hY2' Hy2 ' h x3 ' Hx3 ' hy3' Hy3 \u00b7 In order to reduce the number of parame ters to be optimized we first introduce the constant ratios from Fig. 4.3. i.e. 0.9, 0.85, 0.9, 0.85 (4.3.1) But, there still remain four independent parameters. If we adopt 1 .5, 1.5 (4.3.2) then there are only two independent parameters: Hx2 and Hx3 . If our intention is to reduce the problem to one-parameter optimization, one possibility is to adopt Hx2 = HX3 which means that the two segments (2 and 3) are equal. We now perform the optimization for the reamining one independent parameter Hx2 . The manipulation task considered is described in the example in 4.1. (Fig", + " One should take care of the fact that if the number of parameters increases the procedure may become very time-consuming. Hence, we suggest two or three independent parameters. We think that in almost all problems we are interested in, the number of independent parameters can be reduced to two or three. Let us see an example. Example. We consider again the arthropoid manipulator VE-2 (Fig. 4.2). It was described in the example in 4.1. The problem is to choose the values of cross-section dimensions of segments 2 and 3. (Fig. 4.3). There are eight parameters defining these two cross-sections. In the example 2 in 4.3.1. the number of independent parameters was reducedby introducing the constant ratios (4.3.1) and (4.3.2). In that way there remain two independent parameters Hx2 and Hx3 ' In 4.3.1. the problem was further reduced to one-parameter optimization. It was first doneby considering the two segments (2 and 3) to be equal (Hx2 = Hx3 )' After that, the same was done in the other way by introducing the constant ratio between the two segments (Hx2 = 1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000262_j.mechmachtheory.2021.104299-Figure5-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000262_j.mechmachtheory.2021.104299-Figure5-1.png", + "caption": "Fig. 5. The three-dimensional finite element model of the housing.", + "texts": [ + " (3) can be expressed as T = [ cos \u03b2b sin \u03d5, \u00b1 cos \u03b2b cos \u03d5, \u2213 sin \u03b2b , r p sin \u03b2b sin \u03d5, \u00b1r p sin \u03b2b cos \u03d5, \u00b1r p cos \u03b2b , \u2212 cos \u03b2b sin \u03d5, \u2213 cos \u03b2b cos \u03d5, \u00b1 sin \u03b2b , r g sin \u03b2b sin \u03d5, \u00b1r g sin \u03b2b cos \u03d5, \u00b1r g cos \u03b2b ] (4) where \u03c6 = \u03b1 \u2213 \u03c8 . The \u201c+ \u201d in \u201c\u00b1\u201d and \u201c\u2212\u201d in \u201c\u2213\u201d denote anticlockwise rotation of the driving gear, and the \u201c\u2212\u201d in\u201c\u00b1\u201dand \u201c+ \u201d in \u201c\u2213\u201d refer to clockwise rotation of the driving gear. For the housing with large flexibility and complex structure, the three-dimensional finite element method and substructure technique are employed in order to considering the flexibility of housing, as shown in Fig. 5 . For each bolt hole, the six degrees of freedom of all nodes on its inner surface are constrained. For each bearing pedestal, all nodes on its inner surface are coupled, and then the six order stiffness matrix of four bearing holes is condensed by the substructure method. The stiffness matrix fully reflects the flexibility of the housing. When the models for the shaft element, bearing element, nonlinear contact element and housing element has been established, the stiffness matrix of the system can be assembled according to the finite element method [45] " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003835_tie.2008.2003196-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003835_tie.2008.2003196-Figure2-1.png", + "caption": "Fig. 2. Location of sensors on the stator.", + "texts": [], + "surrounding_texts": [ + "Our model results from the combination of two methods: a nodal method [1], [6], [7] which computes thermal transfers inside the active parts of the machine and a finite-volume method which models in detail the mechanical and thermal behavior of the fluid flow in the two internal cavities of the motor." + ] + }, + { + "image_filename": "designv10_6_0003117_70.246062-Figure7-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003117_70.246062-Figure7-1.png", + "caption": "Fig. 7. System behavior for the simulation in the presence of an obstacle.", + "texts": [ + " We chose p2 in (14) as p z o given by (25). We used a value of IC2 = 0.75. When the elbow comes close to the obstacle surface, the second term of the input in (12) tends to become very large. This is clear from the definition of the Lyapunovlike function V Z O . If the norm is greater than 3.0, the second term is proportionally reduced to have a norm of exactly 3.0. The elbow trajectory for the obstacle avoidance case is shown in Fig. 6. It is clear from Fig. 6 that the elbow avoids the obstacle. The system behavior is shown in Fig. 7 at eight intermediate stages. The convergence criterion was the same as in the first case and the convergence time was noted to be approximately 3.16 s. The actual time taken for the simulation was approximately 5 mins on a SUN 41260 computer. The successful utilization of nonholonomic redundancy is clear from Figs. 3, 5, and 7. The final configuration in each of these figures achieve the same end-effector position and orientation but the vehicle orientation and the joint variables are quite different from one another" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002484_1.2834121-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002484_1.2834121-Figure2-1.png", + "caption": "Fig. 2 Relation of the angles", + "texts": [ + " (7) will take the form of: (8) In the case of angular contact ball bearings, F^ is replaced by the deflection due to the preload. Equation (8) consists of a constant part and a variable part. From Fig. 1: L = re' (9) since the wavelength is the length of the inner race circumfer ence divided by the number of waves on the circumference. k = Inr N (10) Substituting Eq. (9) and Eq. (10) into Eq. (8): F, = Fo + F^sin (Nd') (11) Since the inner race is moving at the speed of the shaft and the ball center at the speed of cage, for the inner race waviness, 6' should be replaced with an angle 0, for the ith ball (see Fig. 2). = \u2022& + (a;,. - u),,)t + yi (12) If a point a on the circumference of the outer race and a point b at the ball center are assumed at the initial time and initial position at an angle 'd apart from a reference axis, as seen in Fig. 2, after the time t taken, the cage, i.e., the point b, will lag the shaft, i.e., the point a, and as a result of this, the (th ball will be at the angle of -{tot \u2014 wj). Hence the instantaneous height at the angle of interest: (F,), = Fo + F\u201e sin [N(^ + (w, - uj)t + yi)] (13) 2.2 Outer Race Waviness. In the case of outer race since the outer race is assumed to be stationary and the balls are rotating at the speed of cage, Eq. (13) will take the form of: (F,.),, = F\u201e + Fp sin [N(d + to J + yi)] (14) 2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002681_j.mechmachtheory.2004.04.003-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002681_j.mechmachtheory.2004.04.003-Figure1-1.png", + "caption": "Fig. 1. The traction drive CVTs: (a) half-toroidal; (b) full toroidal.", + "texts": [ + " For these reasons more promising solutions have to be found, and the toroidal traction drives may be one of these. They are being extensively investigated because of their high torque capacity, that makes them suitable for application in larger engine cars and even trucks. The most attractive typologies are the full-toroidal [10,11] and the half-toroidal traction drives [12\u201314]. The main components of these transmissions are the input and output discs, designed to create a toroidal cavity (see Fig. 1), coupled with an appropriate number of rollers. The high torque capacity of these transmissions is obtained by coupling together in a series scheme two or more single units [15\u201317]. Moreover the particular geometry of the toroidal traction drive makes it able to rapidly adjust its speed ratio to the request of the driver, thus improving the driving comfort [18\u201321]. Between the roller and the discs no metal\u2013metal contact occurs, the torque is transmitted by means of the shearing action of a special oil referred to as traction oil", + " The principal advantage of the proposed method with respect to other similar methodologies [30,31] consists of three points: the model is independent of the specific traction drive under consideration, the formulation presented does not require the determination of the traction curve by experiments performed on the given traction drive with the specific traction oil. The model is also able to take into account the influence of the spin motion on the mechanical efficiency and the traction performance of the variator. The main drawback is related to the large number of equations to deal with, that makes the overall computation time-consuming. Fig. 1 shows the main geometrical features of the toroidal variators. During the steady state operation of the CVT the swing center of the roller coincides with the cavity center O, and its axis of rotation is tilted of c. The tilting angle c (positive if clockwise directed) controls the distance r1 and r3 of the contact points A and B from the main axis of the variator, and, consequently, controls the ideal speed ratio srID \u00bc r3=r1. In the same Fig. 1, r12 \u00bc r23 \u00bc r0 represent radius of the toroidal cavity, that is also one of the two principal radii of curvature of the input and output discs. The quantity r11 is the second principal radius of curvature of the input disc, whereas r33 is the second principal radius of curvature of the output disc. Moreover r2 and r22 are the two principal radii of curvature of the roller with r22 < r12. The quantity e is the distance of the toroidal cavity from the disc axes, it is related to the aspect ratio k \u00bc e=r0 of the toroidal traction drive", + " When studying the toroidal traction drives, it is useful to define the input and output slip coefficients, usually referred to as creep coefficients Crin and Crout: Crin \u00bc jx1jr1 jx2jr2 jx1jr1 ; Crout \u00bc jx2jr2 jx3jr3 jx2jr2 \u00f03\u00de A small amount of creep must be always present to allow the transmission of torque. Besides the creep coefficients defined above, it is useful, for the next calculations, to introduce the following dimensionless geometric quantities (remember that r12 \u00bc r23 \u00bc r0, see also Fig. 1): ~r1 \u00bc r1 r0 \u00bc 1\u00fe k cos\u00f0h\u00fe c\u00de ~r3 \u00bc r3 r0 \u00bc 1\u00fe k cos\u00f0h c\u00de \u00f04\u00de By means of the creep coefficients and considering that srID \u00bc ~r3=~r1 it is possible to write the actual speed ratio sr \u00bc jx3j=jx1j as: sr \u00bc \u00f01 Crin\u00de\u00f01 Crout\u00de 1\u00fe k cos\u00f0h\u00fe c\u00de 1\u00fe k cos\u00f0h c\u00de \u00bc \u00f01 Crin\u00de\u00f01 Crout\u00desrID \u00f05\u00de and also define the speed efficiency mspeed of the variator as the ratio sr=srID: mspeed \u00bc sr srID \u00bc 1 Cr \u00f06\u00de where 1 Cr \u00bc \u00f01 Crin\u00de\u00f01 Crout\u00de stands for the global sliding coefficient between the output disc and input one" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002839_978-3-662-03845-1-Figure3.16-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002839_978-3-662-03845-1-Figure3.16-1.png", + "caption": "Fig. 3.16. (a) Macromolecular chains not adsorbed onto a wall. (b) Corresponding variation in the concentration c of macromolecular segments with distance s from the wall", + "texts": [ + " The same family of molecules can also stabilise the opposite systems, of water in-oil (W /0) type; by acting on the number of ethylene oxide links, we can adjust the Hydrophile-Lipophile Balance (HLB) of these molecules and adapt them to O/W and W /0 dispersions. It should not be thought that, because a polymer does not adsorb onto the particles in a suspension, it has no effect on the stability of a system. Indeed, if a macromolecule does not adsorb onto a surface, this means that the centres of mass of the macromolecules in the surrounding solution cannot come within a distance R of the wall (see Fig. 3.16a). Hence the concentration of macromolecule segments is lower close to the wall than further away in the solution (see Fig. 3.16b). We say there is depletion of the polymer. It is just as if the regions enclosing the particles were poor in polymer content, and their combined volume is far from being negligible, if the particles are sufficiently concentrated and have a large specific surface area. Even for the example described earlier of a rather dilute suspension (10 g/l) of particles of unit density and radius 100 nm, the volume from which a polymer of characteristic radius 50 nm would be excluded is 34 cm3 for 11 of suspension" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003545_j.ijmachtools.2009.08.010-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003545_j.ijmachtools.2009.08.010-Figure2-1.png", + "caption": "Fig. 2. The coupled stations.", + "texts": [ + " To transfer smoothly, the number of stations of both the outer rotor and the inner rotor must be identical. If it is necessary, virtual sections should be added to the dynamic model. The virtual section refers to the section whose length and mass are both zero, as shown in Fig. 1(b); the dashed circle and dashed line represent virtual sections added. For coupled stations, e.g. the 5th station in Fig. 1(b), the whole transfer matrix should be adjusted. The whole transfer matrix for coupled transfer element [18], as shown in Fig. 2, is as follows: fZgi\u00fe1 \u00bc \u00bdC i UI 0 0 UII \" # i zI zII ( ) i \u00bc \u00bdT ifZgi \u00f03\u00de The details of [C]i can be found in Appendix A. Starting from station 1 of the shaft in Fig. 1(b), with the help of Eqs. (2) and (3) fZgN\u00fe1 \u00bc \u00bdT N \u00bdT N 1 \u00bdT 1fZg1 \u00f04\u00de Defining the product of all element transfer matrices in the order given in the above equations as overall transfer matrix [A], Eq. (4) can be written as fZgN\u00fe1 \u00bc \u00bdA fZg1 \u00f04 1\u00de For free end in Fig. 1(b), at 1 and N+1 M\u00bc 0;Q \u00bc 0 Hence, it can be obtained from Eq" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003670_978-3-642-82195-0-Figure1.6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003670_978-3-642-82195-0-Figure1.6-1.png", + "caption": "Fig. 1.6. Manipulator link and its kinematic parameters", + "texts": [ + " Rodrigues formula approach The set of kinematic parameters Ki which are assigned to manipulator link Ci belonging to a simple open kinematic chain, has the form where ... ... ... Qi (qi1' qi2' qi3) - is a local coordinate frame attached to link i; R. 1. -+ -+ {rii , r i ,i+1} - the set of distance vectors expressed with respect to coordinate system Qi' assigned to link C i ; -+ ->- {ei , :i+1} - the set of unit vectors of joint axes by which link Ci is connected to links Ci - 1 and Ci +1 , expressed in coordinate system Qi' 9 An example of a manipulator link is shown in Fig. 1.6. Here ~ denotes that the corresponding vector is expressed in the local coordinate sys tem attached to link i. The local coordinate system is chosen in such a way that its unit vec->- ->- ->- tors Qi1' Qi2 and Qi3 coincide with main axes of inertia of the link, and its origin is positioned into the link mass center. The reasons for such frame assigment are its convenience for dynamic modelling of the mechanism, since in that case, the inertia tensor is always reduced to three main central moments of inertia", + " However, from the kinematic point of view, this is an arbitrary way of attaching the frame, since in a general case these axes do not coincide with the joint axis or a common normal between joint axes. This results in a more complex kine matic modelling than in Denavit-Hartenberg notation. However, it often happens that main axes of inertia are parallel to joint axis and to the common normal between the joint axes. In that case kinematic analysis in Rodrigues formula approach is also simplified. 10 Distance vectors which describe the manipulator link Ci are defined in ->- the following way (Fig. 1.6). Vector rii\" is a vector between center Zi of the joint i and the origin of coordinate frame Qi (mass center of ->- link i). Vector r i ,i+1 is a vector from the center Zi+1 of joint i+1 to the origin of coordinate frame Qi. Unit vector ~. corresponds to joint axis about (or along) which joint 1. -+ motion q. is performed. The notation e. denotes that it is expressed 1. 1. ->- with respect to the local coordinate frame Qi of link i. Vector ~i+1 represents vector of joint axis i+1 given with respect to the same coordinate frame Qi", + " Consider a simple open kinematic chain with n links. Each link is char acterized by two dimensions: the common normal distance a i (along the common normal between axes of joint i and i+1), and the twist angle Q i between these axes in the plane perpendicular to a i . Each joint axis has two normals to it a i _ 1 and a i (Fig. 1.16). The re lative position of these normals along the axis of joint i is given by d i \u00b7 Denote by 0ixiYizi the local coordinate system assigned to link i. We will first consider revolute jOints (Fig. 1.6). The origin of the coordinate frame of link i is set to be at the intersection of the com mon normal between the axis of joint i+1. In the case of intersecting joint axes, the origin is set to be at the point of intersection of the joint axes. If the axes are parallel, the origin is chosen to make the joint distance zero for the next link whose coordinate origin is defi ned. The axes of the link coordinate system 0i xiy i zi are to be se-+ lected in the following way. The zi axis of system i should coincide with the axis of joint i+1, about which rotation qi+1 is performed" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002596_(sici)1521-4109(199911)11:17<1293::aid-elan1293>3.0.co;2-2-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002596_(sici)1521-4109(199911)11:17<1293::aid-elan1293>3.0.co;2-2-Figure1-1.png", + "caption": "Fig. 1. Catalytic oxidation of hydrazine at a modi\u00aeed glassy carbon electrode in 0.15 M phosphate buffer (pH 7.5) a) without hydrazine and b) with 1.0 mM hydrazine at a scan rate of 25 mV s\u00ff1. c) as (a) and d) as (b) for bare glassy carbon electrode. e) as (b) for activated bare glassy carbon electrode.", + "texts": [ + "0 mM solution of hydrazine decreased around 2 %. These results permit us to conclude that the CFA modi\u00aeed electrode is suf\u00aeciently stable and can be considered as an electrode with reproducible responses. All experiments were carried out at ambient temperature. N2 bubbling was used to remove oxygen from the solution in the electrochemical cell. The electrochemical response of a caffeic acid modi\u00aeed glassy carbon electrode was previously reported and a mechanism was also proposed for electrode surface modi\u00aecation [27]. Figure 1 shows the cyclic voltammograms of the bare and caffeic acid modi\u00aeed glassy carbon electrode in the absence and presence of hydrazine. The caffeic acid modi\u00aeed glassy carbon electrode in 0.15 M phosphate buffer (pH 7.5), without hydrazine in solution, exhibits a well-behaved redox reaction (Fig. 1a). Upon the addition of 1.0 mM hydrazine, there is a dramatic enhancement of the anodic peak current and the cathodic peak current disappeared completely (Fig. 1b), which indicates a strong electrocatalytic effect. The anodic peak potential for the oxidation of hydrazine at CFA modi\u00aeed electrode is about 250 mV (Fig. 1b), while at the bare glassy carbon electrode no current is observed in the presence of hydrazine (Fig. 1d). The bare GC electrode is not reactive under these conditions while the activated bare GC electrode shows an anodic peak but at more positive potentials and with low peak current (Fig. 1e). This is in agreement with the fact reported in the literature [20, 29] that hydrazine oxidation is observed on GC electrodes only after special pretreatment of the surface. Figure 2 shows the dependence of the voltammetric response of CFA modi\u00aeed glassy carbon electrode on the hydrazine concentration. With the addition of hydrazine, there was an increase in the anodic current. Inset A of Figure 2 shows clearly that the plot of Ip versus hydrazine concentration constituted from two linear segments with different slopes, corresponding to two different ranges of substrate concentration" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000470_adom.202100053-Figure6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000470_adom.202100053-Figure6-1.png", + "caption": "Figure 6. Continuous photoactuation of a freestanding LCE-1 film at 120\u00a0\u00b0C by irradiation with LPUV light through a rotating polarizer (2\u00b0 s\u22121) (Movie\u00a0S4, Supporting Information). White arrows indicate the polarization direction of LPUV light. The angles are defined relative to the polarization direction in the first photograph. Intensity of LPUV light: 50\u00a0mW cm\u22122. Film size: 6\u00a0mm \u00d7 6\u00a0mm \u00d7 50\u00a0\u00b5m.", + "texts": [ + "[45] In this study, transcis-trans photoactuation and shape memory were achieved even at temperature above Tg with the aid of rearrangeable network. Adv. Optical Mater. 2021, 9, 2100053 www.advancedsciencenews.com \u00a9 2021 Wiley-VCH GmbH2100053 (6 of 7) www.advopticalmat.de In comparison with the order-disorder mechanism by trans-cis isomerization, the order-order transition by trans-cis-trans cycles is advantageous in inducing continuous motions. The continuous reshaping of a film can be induced by irradiation with UV light while rotating a polarizer (Figure\u00a06, Movie S4, Supporting Information). This motion is attributed to the constant realignment of mesogens and rearrangement of network structures. We demonstrated realignment and reshaping for poly siloxane LCEs by combination of photoalignment technique and exchangeable links. The alignment could be induced by irradiation with LPUV light through Weigert effect, which was memorized by rearrangement of network structures. The photoalignment in the surface of freestanding films leads to bending and shape memory" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000051_j.apm.2020.09.010-Figure19-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000051_j.apm.2020.09.010-Figure19-1.png", + "caption": "Fig. 19. Human interaction disturbance signals", + "texts": [ + "6 0 5 10 x 10-4 Fig. 20. Tracking errors with human interaction disturbances 0 1 2 3 4 5 6 7 8 9 10 -10000 -5000 0 5000 Time(s) C on tro l i np ut s (m N *m ) \u03c41 \u03c42 \u03c43 \u03c44 \u03c45 5 5.01 5.02 -500 0 500 1000 1500 5 5.02 5.04 -4200 -4000 -3800 Fig. 21. Control inputs with human interaction disturbances performance of the proposed strategy, simulations are carried out by applying a pulse signal at t = 5s as a sudden disturbance and a persistent random signal as the continuous disturbance in the simulation model. Fig. 19 gives the human interaction disturbance signals applied in the simulation. Fig. 20 presents the tracking errors of the 5 joints with the human interaction disturbances, the red rectangle frame marks out the errors disturbed by the random signal and the blue rectangle frame marks out the errors disturbed by the pulse signal. It can be seen that under the human interaction disturbances, the tracking errors can fast converge with satisfactory performance under the control inputs shown in fig. 21, which explains that the proposed control strategy is robust to the human interaction disturbances" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002576_28.968181-Figure7-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002576_28.968181-Figure7-1.png", + "caption": "Fig. 7. Drive system.", + "texts": [ + " 6 shows the operating area of the average torque and the instantaneous radial force of the test motor in the case where the advanced angle is changed from 0 to (7.5 ). The operating area of the test motor is the area surrounded with the point \u201ca,b,c,o.\u201d On the contrary, the area surrounded with point \u201co,b,c\u201d indicates the operating area in the case where the advanced angle is fixed at (7.5 ). It is evident that the operating area can be exceedingly enlarged by controlling the without fixing the . Fig. 7 shows the drive system of a bearingless switched reluctance motor. The calculator for controlling and is added to the system with a negative feedback loop as shown in Fig. 7. The calculator consists of the table of command value and precalculated with the flowchart as shown in Fig. 4 in order to reduce the sampling time of a digital signal processor. It is seen that the controller of the motor main winding currents is separated from the digital signal processor. Therefore, it is possible to realize the high-speed drive without the time delay in the control cycle of the motor main winding currents. The dimensions of the test motor are shown in Table I. Fig. 8 shows a model of the experimental system" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002459_s0963-8695(03)00011-2-Figure6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002459_s0963-8695(03)00011-2-Figure6-1.png", + "caption": "Fig. 6. Dynamic model of gear\u2013frame combination.", + "texts": [ + " This was necessary because the stiffness characteristics of the suspended gear teeth will be same when there is no fault present, but when one of the suspended gear teeth suffers from a crack (like a bending fatigue crack), the crack will open and close during vibration and the cracked tooth will exhibit non-linear stiffness variation. If a pre-load (which opens the crack) is applied, the effect of this non-linearity diminishes, and linear vibration assumptions can be made. A small mild steel plate was placed between the gear and the pre-load screw to prevent damage to the gear teeth. For simplified vibration analysis, both the gear and the frame can be considered as rigid bodies having lumped masses, and inertias located at their mass centres of gravity as shown in Fig. 6. The bodies can be considered to be connected to each other by four springs (k1; k2; ks; and ktor), where k1; k2; represent the equivalent translational spring effects of the two points of suspension, ks represents the equivalent stiffness of the pre-load fixing screw, and ktor represents the torsional spring effect of the pre-load screw during the relative rotational motion of the bodies. The equation of motion of the system can then be expressed in terms of the relative displacement, X\u00f0t\u00de \u00bc Xf\u00f0t\u00de2 Xg\u00f0t\u00de; and the relative rotation, u\u00f0t\u00de \u00bc uf\u00f0t\u00de2 ug\u00f0t\u00de; between the rigid bodies" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003135_j.conengprac.2006.09.001-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003135_j.conengprac.2006.09.001-Figure2-1.png", + "caption": "Fig. 2. Electromechanical system including mechanical imperfections.", + "texts": [ + " Backlash phenomenon is described by two independent mechanical parts, whose transmission is carried out via a dead zone, varying between 01 and 241. A spring system is placed between the two mechanical parts in order to deliver a smooth transmission. R. Merzouki et al. / Control Engineering Practice 15 (2007) 447\u2013457 449 On this test bench, one can measure input and output positions of the reducer part by using two incremental encoders of Fig. 1, where the relative load position is depending on friction between the gears in contact, as well as flexible transmission through a dead zone. Fig. 2 illustrates the simplified system schema of the real system. Let us consider that static friction is disregarded, then the mechanical model of the test bench, including the backlash is described by the following system Je:\u20acye \u00fe f e:_ye \u00fe C \u00bc u; Js:\u20acys \u00fe f s:_ys \u00bc N0:C; ( (1) Js, Je, f s, f e are, respectively, inertias and viscous frictions of reducer and motor parts which are identified experimentally. \u20acys, \u20acye, _ys, _ye are, respectively, accelerations and velocities of reducer and motor parts which are deduced by derivation of the measured input and output positions ys and ye. u, C, N0 are, respectively, control input torque, transmitted torque via the dead zone and reduction constant. Introducing the variables x1e \u00bc ye, x1s \u00bc ys, x2e \u00bc _ye, x2s \u00bc _ys, model (1) can be rewritten as _x1e \u00bc x2e; _x1s \u00bc x2s; _x2e \u00bc f e Je :x2e \u00fe u Je C Je ; _x2s \u00bc f s Js :x2s \u00fe N0:C Js : 8>>>>><>>>>: (2) Generally, modeling of the mechanical torque, transmitted through a dead zone and a flexible axis (see in Fig. 2), is given by a nonlinear and noncontinuous function of Fig. 3(b). Unfortunately, the noncontinuous characteristic of the transmitted torque around the contact areas, can make the system observation and control difficult. Thus, and in order to avoid this noncontinuous property, once thought of bringing a flexible bond inside the dead zone areas of the electromechanical system (see Fig. 3(a)). It describes a body1 trying to transmit motion to body2 via a dead zone of amplitude 2j0. The transmission will be correct when the two bodies are in contact (i" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000202_j.mechmachtheory.2021.104330-Figure9-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000202_j.mechmachtheory.2021.104330-Figure9-1.png", + "caption": "Fig. 9. Three configurations of the deployable grasping parallel mechanism shown in (a)\u2013(c) present the folded, fully deployed, and grasping configurations of this deployable grasping parallel mechanism, respectively. (d)\u2013(f) are the corresponding physical prototype.", + "texts": [ + " Additionally, such a mechanism has various deployable configurations and only one fully deployed configuration. When the whole mechanism is at full deployed configuration, the grasping sub-mechanism satisfies the condition that axes z 1 and z 6 (shown in Fig. 4 ) are coplanar with axes z 3 and z 4 , as shown in Fig. 5 (f). Several types of deployed configurations and the fully deployed configuration are also provided in Movie S1. Fully deployed configuration and the grasping configuration can be seen in Fig. 9 (b) and (c), respectively. This model is also demonstrated by presenting the corresponding configurations of the physical prototype in Fig. 9 (d)\u2013(f). Besides, this deployable grasping parallel mechanism has other deployed configurations, after which it also can carry out the grasping motion, which can be seen in Movie S1. The standard base of constraint-screw system for the auxiliary sub-mechanism is S r a = { S r a1 = (0 , 1 , 0 , 0 , 0 , 0) T } , (43) which denotes a constraint force along X a -axis. The standard base of motion-screw system for the auxiliary sub-mechanism is S a = \u23a7 \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23a8 \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23a9 S a1 = ( 1 , 0 , 0 , 0 , 0 , 0 ) T S a2 = ( 0 , 1 , 0 , 0 , 0 , 0 ) T S a3 = ( 0 , 0 , 1 , 0 , 0 , 0 ) T S a4 = ( 0 , 0 , 0 , 1 , 0 , 0 ) T S a5 = ( 0 , 0 , 0 , 0 , 0 , 1 ) T \u23ab \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23ac \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23aa \u23ad " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure9.1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure9.1-1.png", + "caption": "Fig. 9.1 Fabricated four-layer DP-RE type ECF micromotor", + "texts": [ + " New Microactuators Using Functional Fluids 93 To improve performance of an ER microactuator that is a fluid microactuator with ER microvalves, the mathematical model of the ER valve, flexible ER valve, and so on were proposed and developed. Also, microvalves using MRF were proposed and developed. 5. Development of high output power piezoelectric micropumps As a micro fluid power source, high output power piezoelectric micropumps using fluid inertia effect in a pipe and the one using resonance drive were proposed and developed. 6. Applications of the developed actuators To realize high output power DP-RE type ECF micromotors (Fig.9.1), the several electrode configurations are investigated as in Fig.9.2. The experimental results implies the ECF micromotor possibly generates 130 W/kg or higher in millimeter scale. In addition, we are also developing micrometer scale motors using MEMS technologies. 4. Development of microactuators using ERF/MRF 94 Shinichi Yokota, Kazuhiro Yoshida, Kenjiro Takemura and Joon-wan Kim We are developing a novel gyroscopes using ECF. This is called an ECF liquid rate gyroscope shown in Fig.9.3. This gyroscope measures a drift flow of the ECF jet, which is occurred due to Coriolis force" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003742_1.4000277-Figure10-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003742_1.4000277-Figure10-1.png", + "caption": "Fig. 10 Overview of fi", + "texts": [], + "surrounding_texts": [ + "Fig. 7 Ball-raceway contact in rigid model \u201eFv=0\u2026\n011102-4 / Vol. 132, JANUARY 2010\nDownloaded From: http://tribology.asmedigitalcollection.asme.org/ on 01/27/2016 Terms\nsi = s0 cos 0 \u2212 ci cos ci \u2212 ri cos ri 2 + s0 sin 0\n\u2212 ci sin ci \u2212 ri sin ri v 2 1/2 6\nin which the positive sign of the radical sign is for i=1,2 and the negative sign is for i=3,4. The contact angle i is expressed as\ncos i = s0 cos 0 \u2212 ci cos ci \u2212 ri cos ri\nsi 7\n4.2 Hertzian Deformations and Ball Loads. The total Hertzian contact deformation ij of the jth ball in the ith raceway groove can be expressed as\nij = cij + rij = si \u2212 m0 \u2212 C xij 8\nwhere C xij is the crowning drop of the carriage at the location of the jth ball in the ith raceway groove.\nFrom the Hertzian theory, cij and rij are given by 7\nage deformations\nTransactions of the ASME\nof Use: http://www.asme.org/about-asme/terms-of-use", + "w b t\nw\nF i\nJ\nDownloaded Fr\ncij = CcijQij 2/3, rij = CrijQij 2/3 9\nhere Ccij and Crij are the coefficients of the deformations, given y the following equations 7 . Hereinafter, suffixes c and r refer o carriage and rail, respectively\nCcij = 2K\nc\n3 1\n8 3 E 1 \u2212 2 2 c\n10\nCrij = 2K\nr\n3 1\n8 3 E 1 \u2212 2 2 r\nhere E is the Young\u2019s modulus, is the Poisson\u2019s ratio, c and r are the curvature sums for the carriage and rail, respectively, 2K / c and 2K / r are coefficients, which are determined\nig. 9 Positions of raceway groove curvature centers in flexble model\nournal of Tribology\nom: http://tribology.asmedigitalcollection.asme.org/ on 01/27/2016 Terms\nby the auxiliary values cos c and cos r, respectively 8 . The auxiliary values cos c and cos r are given by\ncos c = 1\nrc c , cos r =\n1\nrr r 11\nThe curvature sums for the carriage c and rail r are given by\nc = 4\nd \u2212\n1 rc , r = 4 d \u2212 1 rr 12\nFrom Eqs. 8 \u2013 10 , the ball load Qij can be written as\nQij = si \u2212 m0 \u2212 C xij Ccij + Crij 3/2\n13\n4.3 Theoretical Expressions for Vertical Stiffness by Flexible Model. The static balance of the vertical forces of a linear bearing can be written as\nj=1\nn\nQ1j sin 1j + Q2j sin 2j \u2212 Q3j sin 3j \u2212 Q4j sin 4j = FV\n14\nwhere n is the number of the loaded balls in a raceway groove. For a linear bearing with in-phase ball arrangement under a preload and a vertical load FV, the following relationship exists\nQ1j = Q2j, Q3j = Q4j 15 Substituting Eq. 15 into Eq. 14 , the following equation is obtained\n2 j=1\nn\nQ1j sin 1 \u2212 Q3j sin 3 = FV 16\nThe following theoretical expression for the vertical stiffness by the flexible model is derived from the above\nKVf = dFV\ndv =\nd\ndv 2 j=1\nn\nQ1j sin 1 \u2212 Q3j sin 3 17\nNote that Q1j, Q3j, 1, and 3 in Eq. 17 are the functions of the deformations of the carriage and rail, and the vertical displacement v of the carriage, as shown in Eqs. 6 \u2013 13 .\n4.4 Deformations of Carriage and Rail. In the calculation of the vertical stiffness by the flexible model, estimations of the deformations of the carriage and rail are required. In this study, these deformations were calculated by using the FEM software COSMOSWORKS .\nThe overview and cross section of the FE model for calculating the deformations of the carriage and rail are shown in Figs. 10 and 11, respectively. In the FE model, a block was attached to the carriage and the rail was fixed to the ground with bolts. To model the carriage, block, and rail, a solid element was chosen in COS-\nnite element model\nJANUARY 2010, Vol. 132 / 011102-5\nof Use: http://www.asme.org/about-asme/terms-of-use", + "M a u\nr g t t g p q a\nw e r\nu p\n0\nDownloaded Fr\nOSWORKS. Since the cross section of the test bearings is bilaterlly symmetrical, as shown in Fig. 3, a symmetrical FE model is sed, as shown in Figs. 10 and 11.\nIn the FE analysis, if the concentrated forces, which are the eaction forces of the ball load Qij, are applied to the raceway rooves of the carriage and rail, the deformations at the points of he concentrated force applications are overestimated. To prevent hose overestimations, the reaction forces acting on the raceway rooves of the carriage and rail were modeled by the uniform ressures qic and qir, respectively. The areas under the pressures ic and qir are shown in Fig. 12. The uniform pressures qic and qir re given by\nqic = 1\naicL1 j=1\nn\nQij, qir = 1\nairL1 j=1\nn\nQij 18\nhere L1 is the carriage length, ai is the major axis of the contact llipses of the ith ball and raceway grooves, and the suffixes c and refer to the carriage and rail, respectively. If there is no restraint to the carriage in the FE model under the niform pressures qic and qir, the FE analysis shows carriage itching, which occurs due to the inevitable calculation errors. To\n11102-6 / Vol. 132, JANUARY 2010\nom: http://tribology.asmedigitalcollection.asme.org/ on 01/27/2016 Terms\nprevent this, a certain area of the upper surface of the carriage was restrained to six degrees of freedom, as shown in Fig. 11.\n4.5 Calculation Procedure of Vertical Stiffness Using Flexible Model. The vertical stiffness calculation flow chart, using the flexible model, is shown in Fig. 13. The detailed calculation procedure is as follows:\nStep 1. The groove radii rc and rr of the carriage and rail, the carriage length L1, the crowning drop of the carriage C xij , the reference ball diameter d0, the oversize 0 of balls, the nominal contact angle 0, the number n of the loaded balls in a raceway groove, the Young\u2019s modulus E, the density , and the Poisson\u2019s ratio are given. Then, the distance s0 Eq. 4 between the raceway groove curvature centers Oci and Ori, the reference distance m0 Eq. 5 between the raceway groove curvature centers, and the coefficients Ccij and Crij Eq. 10 of the deformations are calculated. Step 2. The vertical load FV is given. Step 3. The contact angle i, the ball load Qij, and the vertical displacement v are assumed. Step 4. The major axes aic and air of the contact ellipses, and uniform pressures qic and qir Eq. 18 are calculated. Step 5. Constant pressures qic and qir are applied to the carriage and rail. The deformations ci and ri, and their directions ci and ri are calculated by FE analysis. In the FE analysis, the outward carriage deformations are also calculated. Step 6. The vertical displacement v Eqs. 6 , 13 , and 16 of the carriage is calculated. Step 7. If the vertical displacement v obtained in Step 6 matches the assumed values v, then go to Step 9, otherwise, go to Step 8. Step 8. Using the calculated values of the deformations ci and ri, their directions ci and ri, and the vertical displacement v, the contact angle i Eq. 7 , and the ball load Qij Eqs. 6 and 13 are calculated. Then the calculated values of v, i, and Qij are adopted as new assumed values of themselves and return to Step 4. Step 9. The vertical displacement v obtained in Step 7 is the determined value for the set up condition of the vertical load FV. By repeating the Steps 2\u20138 for the numerous values of the vertical load FV, the calculated characteristics of the vertical load-displacement in the flexible model are obtained. Step 10. From the calculated characteristics of the vertical loaddisplacement in Step 9, the calculated vertical stiffness KVf Eq. 17 in the flexible model is calculated.\nIn the above calculation procedure, the following material constants for the test linear bearings and block were used: Young\u2019s modulus E=206 GPa, Poisson\u2019s ratio =0.3, and density =7800 kg /m3.\nressures qic and qir\nTransactions of the ASME\nof Use: http://www.asme.org/about-asme/terms-of-use" + ] + }, + { + "image_filename": "designv10_6_0003961_978-1-4419-7267-5-Figure7.1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003961_978-1-4419-7267-5-Figure7.1-1.png", + "caption": "Fig. 7.1 Structure of theO(N) AB Algorithm 7.1 for serial-chain forward dynamics", + "texts": [ + " The second sweep is a base-to-tip recursion that uses the \u03bd(k), and other terms computed in the first sweep, to compute the hinge and spatial accelerations for all the links. Referring back to the parallels with time-domain, optimal filtering discussed in Sect. 6.4, the steps in the tip-to-base recursion are analogous to the steps in an optimal filter recursion for computing state estimates. Similarly, the steps in the base-to-tip Step 4 recursion are analogous to the steps in an optimal smoother recursion for computing smoothed state estimates. The Steps 1 and 2 sweeps shown in the illustration of the forward dynamics algorithm in Fig. 7.1 compute the kinematic velocity dependent Coriolis and gyroscopic terms for all the bodies in base-to-tip recursions. This pair of sweeps can be combined into a single base-to-tip sweep. The AB algorithm recursions are shown as Steps 3 and 4 in the figure. 7.2 Forward Dynamics 127 The AB algorithm has O(N) computational cost because the cost of each of the steps in the above algorithm is fixed, and the steps are carried outn times during the course of the algorithm. The AB algorithm the fastest forward dynamics algorithm for systems with greater than 6\u20138 bodies" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003742_1.4000277-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003742_1.4000277-Figure4-1.png", + "caption": "Fig. 4 Outward carriage deformation measuring method", + "texts": [ + " Specifically, the difference v\u2212v0 between the vertical displacement v under a certain vertical load FV and the initial vertical displacement v0 was detected by using electric comparators A-C. In this paper, the measured vertical displacement was the average of the three measurements from electric comparators A-C. Substituting the measured vertical load and the measured vertical displacement into Eq. 1 , the measured vertical stiffness KV was obtained as KV = dFV dv = d FV \u2212 FV0 d v \u2212 v0 1 2.3 Carriage Deformation Measurements. The outward carriage deformation measuring method is shown in Fig. 4. First, as shown in Fig. 4 a , the unloaded carriage width width of the removed and unloaded carriage was measured by a digital micrometer. In Fig. 4, Oc\u2212xczc are the coordinates indicating the measurement points of the carriage width, and the mark \u201c \u201d shows the measurement points. Next, as shown in Fig. 4 b , the loaded carriage width width of the carriage with the rail under a preload and a vertical load FV was measured. The deformations of the carriage were obtained by subtracting the unloaded carriage width from the loaded carriage width. 3 Experimental Results 3.1 Vertical Stiffnesses. The measured characteristics of the vertical load-displacement are indicated by solid lines in Fig. 5. Also, in Fig. 5, the vertical load-displacement characteristics, calculated by the conventional rigid model 6 , are indicated by broken lines", + "org/about-asme/terms-of-use Journal of Tribology Downloaded From: http://tribology.asmedigitalcollection.asme.org/ on 01/27/2016 Terms 3.2 Carriage Deformations. The typical measured deformations of the carriages in the test linear bearings under a preload and a vertical load, are shown in Fig. 6. In Fig. 6, the positive and negative signs of the carriage deformations indicate that the side faces of the carriage are deformed outward and inward, respectively. In Fig. 6, xc and zc are the same as those in Fig. 4. It is clear from Fig. 6 that the side faces of the carriage deform outward. The deformations of the side faces of the carriages are smaller at the top zc=3 mm , and increased toward the bottom zc=27 mm . These deformations have a tendency to be greater under either a larger preload or a smaller vertical load. In addition, under a certain value of zc, these deformations are not significantly affected by the longitudinal location xc of the carriage. 4 Flexible Model 4.1 Distance Between Raceway Groove Curvature Centers of Carriage and Rail" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002484_1.2834121-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002484_1.2834121-Figure4-1.png", + "caption": "Fig. 4 The reference axes", + "texts": [ + " The deflection for each ball can then be calculated from Eq. (3). Having calculated the deflection for the /th ball in its contact direction, the force in the same direction (W,) can easily be found. This force can be split into two components in the radial (W\u201e) and axial (W\u201ei) directions for angular contact ball bearings. Hence the force in the X direction is: Wx. = Wr. cos e, (18) where 5, is the angle between the X axis and the axis of the \u00abth ball and this angle is a combination of different angles as shown in Fig. 4. Three sets of reference axes are described as shown in Fig. 4. The first one (X, Y, and Z) is fixed in space and the X axis is vertically downwards in the gravitational force direction. Axes X, y and z (not shown in Fig. 4), move with the rotor but do not spin with it. The second set of the axes (u, v and w) can be defined arbitrarily in the space. It is considered stationary with the cage turning relative to it. In our case the u axis has an off-set angle of i9 anti-clockwise from the X axis. The last set (Xc, yc and Zc) has its origin at the shaft center but is rotating at cage speed w .\u0302. Thus, at time t, it is at angle uij from the fixed u axis. If the angle between two adjacent balls is defined as 7, it will be: r = 2n (19) position is now found easily since it is fixed with respect to the xyz set: 9, = d + Luj + iy where the cage speed LV^ is (Harris, 1991): 1 cos a d,n 1 , '^b 1 H cos a d,\u201e (20) (21) 2", + " (24)) is obtained using the Runge-Kutta iterative method since they are nonlinear and the direct substitution technique does not hold for them. The details of the computational solution of the equations can be found in the previous papers (AktUrk etal., 1992; 1994; 1997; 1998). 3 Results and Discussion In order to study the effect of waviness in a more detailed form, the angular contact ball bearing employed in this paper was reduced to a radial ball bearing for the time being and modeled as in Fig. 5. The angles and reference axes were set as in Fig. 4. The off-set angle in Fig. 5 is an arbitrary reference point on the cage. The contact stiffness coefficient between the balls and the raceways were considered to be linear and constant. Balls were radially preloaded in order to ensure the continues contact of all balls and the raceways, since otherwise a chaotic behavior might be observed (Gad et al , 1984b). The preloaded deflection for each ball. So, was assumed to be 5 fim. The center of the inner race is shifted 2 fim in the x direction and 2 /MI in the y direction with respect to the outer race center" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003545_j.ijmachtools.2009.08.010-Figure12-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003545_j.ijmachtools.2009.08.010-Figure12-1.png", + "caption": "Fig. 12. Schematic diagram of the test rig for measurement of stiffness at the location of spindle nose.", + "texts": [ + " In contrast, when the bearing\u2019s gyroscopic effects and centrifugal force are included in the dynamic model, as the rotational speed increases, the dynamic stiffness of spindle decreases obviously, due to the softened bearing stiffness. Furthermore, when the spindle passes the critical speeds, the dynamic stiffness of the spindle, without considering bearing\u2019s gyroscopic effects and centrifugal force, is much bigger than that of the spindle with the bearing\u2019s gyroscopic effects and centrifugal force considered. For the verification of the proposed double-rotor model, a set of test rig has been designed to test the dynamic stiffness at the spindle nose, as shown in Fig. 12. An unbalanced mass is mounted at spindle nose to generate an exiting force during the rotation of spindle. The displacement of the spindle nose is detected by an eddy current sensor and the displacement signal is sampled by a signal acquisition unit (AZ308R), then the sampled signal is analyzed by the CRAS V7.0 software and the out-of-balance response at the spindle nose is obtained. The dynamic stiffness at the spindle nose is as follows: K \u00bc meo2 jxj where m is the mass of the unbalanced mass, jxj the amplitude of the displacement at the spindle nose" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure3.25-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure3.25-1.png", + "caption": "Fig. 3.25. Constraint permitting no relative motion", + "texts": [ + " 1 32) The matrix G which transforms the reaction components (eq. (3.4.33)) is G r ---~----~----~----~--~~:~~~-+--~~:~~~-~--~~~~~~ j (3.4.133) I I I I 0(3 x 1) : 0(3 x1): h : s : ~ (6x5) Now all the elements of the dynamic model (3.4.35) are determined and the model can be solved. 3.4.10. Constraint permitting no relative motion We consider a manipulator having the gripper connected to the ground (or to an object which moves according to a given law) in such a way that no relative motion is possible (Fig. 3.25). In this case the constraint can be expressed in the form. f 1 (t) , (3.4.136a) 199 e = f4 (t) , (3.4.136b) This problem makes sense for six d.o.f. manipulators only. However, even in that case there are no free parameters since nr = n-6=6-6=0. The second derivative of (3.4.136a,b) gives If we wish to write this relation in the form (3.4.25), it is clear that the reduced position vector and the reduced Jacobian do not exist. The reduced adjoint matrix is (3.4.137) The reaction force and reaction moment have three independent components each" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003605_0169-2607(85)90002-1-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003605_0169-2607(85)90002-1-Figure3-1.png", + "caption": "Fig. 3. Definition of movement characteristics measuring the translational and angular velocities of the sperm head. V c and V A are the translational velocities along the true curvilinear and averaged paths, respectively. ~'Jc is the angular velocity along the curvilinear path.", + "texts": [ + " If a centroid is found within the specified range, it is connected with the last detected centroid using linear interpolation. Once the set of successive positions of sperm heads is established (i.e. the paths), analysis of the kinematics of swimming trajectories can be performed. In general, sperm cell trajectories are not straight. Fig. 2 presents typical paths of human seminal spermatozoa. Measures of swimming speed along a cell's trajectory and the degree of straightness in the swimming path are of considerable biological interest. We compute three measures of translation swimming speed (Fig. 3). The 'curvilinear' velocity, V c, for each cell is defined as the distance per unit time between successive positions of each centroid in the cell's path. The 'straight line' or rectilinear velocity, VsL, is defined as the distance between the first and the last centroid of a path divided by the total elapsed time. We also compute an 'average' velocity, V A, which is based upon a curvilinear, spatially averaged path of the sperm. This measure is obtained using a running, multicentroid weighted average [20]. The instantaneous angular velocity, ~2, along the sequence of centroids is also computed (Fig. 3). In analogy with determination of the translational velocity, the angular velocity is obtained with respect to the true curvilinear path ($2c) and also with respect to the average path (~2A). All computations of instantaneous velocities are based upon a three-point centered difference scheme. The values of Vc, Va and, in some instances, VSL, thus measure the vigor of sperm translation. The movement char- acteristics VsL/V c, V a / V c, VsL/V a, ~2 c and ~2 a reflect the geometry of cell swimming trajectories" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure2.57-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure2.57-1.png", + "caption": "Fig. 2.57. Manipulator UMS-1V", + "texts": [ + " Thus the driving actuator for the joint S4 is not necessary. Let us now discuss the driving torques in the joints S2 and S3' These torques are very large due to large manipulator weight and the heavy payload. In such cases the compensation is usually applied. The hydro or pneumatic compensators may be used or sometimes even active compen sation. 114 2.8.3. Example 3 This example deals with the anthropomorphic manipulator UMS-1V - vari ant with 5 degrees of freedom. The manipulator is shown in Fig. 2.57. The joints S2 and S3 are powered by 23 FRAME MAGNET MOTORS, 2315-P20-0, produced by INDIANA GENERAL. The reduction ratio is N = 100, and the reducer mechanical efficiency n = 0.8. The maximal characteristic (pm _ nm) i.e. the maximal torque depending on motor rotation speed max is obtained by an experiment and it is shown to be almost a straight line (Fig. 2.58). The characteristic differs from a straight line only in the region of slow speeds. If this region is not especially inter esting from the standpoint of constraint violation, we may use a straight line aproximation and in such a way save some computer memory" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003122_robot.2003.1242230-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003122_robot.2003.1242230-Figure1-1.png", + "caption": "Fig. 1. The Clavel\u2019s Delta Robot", + "texts": [ + "00 02003 IEEE 4116 three degree of freedom Delta robot. In 1988, R. Clavel developed the prototype of this robot at the Lausanne Federal Polytechnic Institute. 2. Inverse geometric model The following elements are the elements of. the topological structure of one of the three kinematic closed chains of the manipulator, respectively: an engine, an active revolute joint, an intermediary mechanism with four revolute links that connect four bars, which are parallel two and two, and finally a passive revolute link connected to the moving platform (fig. 1). Let Oxego (Ta) he a fix Cartesian frame. A three degrees of freedom Delta manipulator is moving with respect to this reference frame. The manipulator has three legs. The elements of these legs have known dimensions and masses. One of the three active elements of the robot is the first body of the leg A. This is a homogenous crank, which rotates about the axis A,z; with the angular velocity oh and the angular acceleration &,\", . It has the length A, A , = I: , the mass m; and the tensor of inertia j t " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000495_j.wear.2021.203963-Figure12-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000495_j.wear.2021.203963-Figure12-1.png", + "caption": "Fig. 12. Preload test bench.", + "texts": [ + " As we can see, both the fractal parameters of the rail raceway and carriage raceway showed a slight decrease after the running test. Therefore, in the preload degradation model, the input fractal parameters of the rail raceway are approximated as (1.9259 + 1.9108)/2 = 1.91834 and (4.0612 + 3.6492)/2\u00d7 10\u2212 7 = 3.8552\u00d7 10\u2212 7 m, respectively, and the fractal parameters of the carriage raceway are approximated as (1.9216 + 1.9104)/2 = 1.9163 and (4.1144 + 3.9838)/2\u00d7 10\u2212 7 = 4.0491\u00d7 10\u2212 7 m, respectively. The LRG DA45CL is tested on two specially designed test benches to obtain the degraded preload. Fig. 12 shows the preload test bench, which is comprised of a linear motor, two aerostatic slideways, an aerostatic moving platform, and a Futek LSB302S pull pressure sensor. Due to the carriage of the tested LRG is connected with the work table through the pull pressure sensor, the carriage can therefore move reciprocally along the rail and the aerostatic slideway when the worktable is driven by the linear motor. The preload can then be obtained through the drag force measured by the pull pressure sensor, which was measured in triplicate in both the forward and backward travels" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003457_20080706-5-kr-1001.00138-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003457_20080706-5-kr-1001.00138-Figure3-1.png", + "caption": "Fig. 3. Pitch motion.", + "texts": [ + " Roll motion and Altitude: The roll motion of the vehicle is regulated by the difference in the angular velocity of rotors (see Fig. 2). The altitude is controlled by increasing or decreasing the thrust of the rotors. 978-3-902661-00-5/08/$20.00 \u00a9 2008 IFAC 803 10.3182/20080706-5-KR-1001.3881 Pitch motion: The advantage of this configuration is the addition of an extra mass, besides the ones of the rotors, which is placed down enough to provide a weightbased torque, obtaining then, a pendular damped effect (naturally stable), see Fig. 3. To counteract this pendular motion, the rotors tilt parallel (at the same time) in opposite sense of the pitch motion maintaining the upwards position, emulating a mobile pivot, and moreover behaving as damping factor. Yaw motion: The yaw motion is driven via the rotors\u2019 differential tilting generating the required torque to provoke a rotation (see Fig. 4). Let I={iIx , jIy , kI z } denote the right handed inertial frame, B={iBx , jBy , kB z } denotes frame attached to the body\u2019s aircraft whose origin is located at its center of gravity (see Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000326_j.mechmachtheory.2021.104264-Figure26-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000326_j.mechmachtheory.2021.104264-Figure26-1.png", + "caption": "Fig. 26. Planetary gear (a) vibration shape of the fourth dominantly elastic-body mode at 5850 Hz (mode 22) and (b) associated elastic-body nodal diameter components of the ring gear (black bars) and planet gears (gray bars) from FE/CM simulation.", + "texts": [ + " The combination of a force and torque input simulates the effect of the shaker mounted along the ring-planet line of action in experiments and excites modes with rotational and translational motion. The discrete-body curves show dynamic response primarily in the gear modes below 40 0 0 Hz that are also evident in Figs. 20 and 21 , and expected from prior research [53] . The discrete-body curves do not show a significant peak anywhere near 5860 Hz (mode 22). On the other hand, the elastic-body curve in Fig. 25 shows resonance at 5850 Hz, which indicates elastic-body vibration of the planet gear in this mode. Fig. 26 shows the planetary gear vibration shape and associated nodal diameter components in the fourth elastic-body mode from the FE/CM model. The simulation shows that planet elastic-body vibration is much more prominent than ring elastic-body motion in this mode. The two nodal diameter component of the planet gear dominates the response. The most prominent component of the ring gear, the one nodal diameter component, is discrete-body motion. Comparing the vibration shape from FE/CM simulations in Fig. 26 to the experimental shapes in Figs. 23 and 24a is not practical because the most dominant motion in simulations \u2013 elastic-body motion of the planet gear \u2013 is not measurable in experiments. The ring gear, however, provides an opportunity for comparison. Experiments show more elastic-body ring gear motion ( Fig. 24 b) but FE/CM simulations indicate more discrete-body motion ( Fig. 26 b). Comparing the vibration shape of the fourth dominantly elastic-body mode in Fig. 26 to the first three in Figs. 17 and 19 reveals the qualitative difference between ring-dominant elastic-body modes (numbers 19\u201321) and the planet-dominant elastic-body mode (number 22). Similar to the other dominantly elastic-body modes, the 5860 Hz mode contains both discrete-body and elastic-body motion. The mode shape is characterized by the following attributes, given in order of prominence: \u2022 Significant two nodal diameter elastic-body deformation of the planet gears, \u2022 Elastic-body deformation and discrete-body motion of the ring gear, \u2022 Rotational discrete-body motion of the planet gear, \u2022 Increased translational discrete-body motion of the planet gear at higher torque, and \u2022 Carrier translational discrete-body motion at higher torque" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003415_0250-6874(89)87037-4-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003415_0250-6874(89)87037-4-Figure1-1.png", + "caption": "Fig . 1 . Schematic diagram of the micro planar electrode . (a) Photoresist film ; (b) working electrodes; (c) counter electrode ; (d) sapphire substrate .", + "texts": [], + "surrounding_texts": [ + "298\nvariety of physiological fluids [1, 4 - 7] . At present most of them are based on the use of glucose oxidase (GOD) to catalyse glucose oxidation, producing gluconolactone and hydrogen peroxide . It is common to detect the change of concentration of either oxygen or hydrogen peroxide electrochemically for the determination of glucose concentration . There are some disadvantages of these types of glucose sensors for in vitro monitoring in whole blood and plasma ; variations of dissolved oxygen may cause fluctuations on the electrode response and the dynamic range of glucose detection is decreased by the lack of dissolved oxygen . Human blood glucose concentration is normally about 4 - 6 mM, but it may increase to more than 30 mM in the condition diabetes mellitus . On the other hand, ordinary dissolved oxygen in blood is estimated at only 2 .2 mM and is insufficient to oxidize the total blood glucose [8] . Therefore the upper limit of linearity for the current response becomes depressed to a level insufficient for the direct measurement of blood glucose [5, 8 ] .\nMediators other than oxygen for electron transfer have been used to overcome these disadvantages . Many kinds of electron mediators have been reported so far, and include hexacyanoferrate(III) [9], a range of organic dyes [10], quinone derivatives [11], ferrocene derivatives [12, 13] and some phenazinium ions [14] . The electron mediator used for medical glucose sensors has to fulfill many requirements such as stability, availability and low toxicity. From these points of view, ferrocene derivatives (Fecp 2R) were excellent electron mediators between the reduced form of GOD and the electrode, as shown by the following scheme :\nglucose + GOD(ox) -> gluconolactone + GOD(red) (1)\nGOD(red) + 2Fecp2R+ - > GOD(ox) + 2Fecp2R + 2H+ (2)\n2Fecp2R\n2Fecp2R+ + 2e (3)\nImmobilization of an enzyme and a mediator on electrodes is the major subject in the development of micro glucose sensors . Electropolymerization techniques facilitate modification of each electrode among an array of electrodes constructed on a substrate . Polypyrrole (PPy) has recently attracted much attention on account of its excellent properties [15 - 19] . A recent report describes that GOD molecules are enveloped into PPy in the case of electropolymerization [20] . The trapped GOD retains its catalytic activity for glucose oxidation . This GOD-trapped PPy electrode has, however, some weak points when considering applications to a micro glucose sensor for clinical use ; a long time is required to obtain a steady current in amperometric determination of glucose ; immobilization of an electron mediator is difficult on PPy together with GOD ; the current response usually decreases after a week or so .\nThis paper describes the construction of ferrocene-mediated micro glucose sensors using PPy-modified electrodes, and the subsequent characterization test .", + "Experimental\nApparatus Micro gold electrodes as shown in Fig . 1, with two working electrodes\nand a counter electrode, were prepared by the photolithographic method [2] . Titanium was first sputtered onto the sapphire wafer to improve the adhesion of gold . Then a gold layer ( ;:4-1 \u00b5m thick) was deposited on the wafer by sputtering . The gold layer was patterned by etching with KI/I 2 solution (KI :I2 :H20 = 20 :5 :22 by weight) . The patterned gold layer was covered by a negative photoresist, except the electrodes and the bonding parts . It is possible to make these electrodes much smaller by using semiconductor fabrication techniques, but in this series of experiments we used the illustrated size of electrodes for ease of handling . Amperometric measurements and electropolymerization were conducted with a PGR-902 Polarolyzer (TOA Electronics Ltd .) and a HA104 potentiostat/galvanostat (Hokuto Denko Co .) respectively in threeelectrode cells . All potentials are referred to the saturated calomel electrode (SCE) . A scanning electron microscope (5-415, Hitachi Ltd .) was employed for observing the PPy surface structure .\nReagents Pyrrole was purchased from Wako Pure Chemical Ind . Ltd. and 1,1'- dimethylferrocene (DMFe) was purchased from Tokyo Kasei Ind . Ltd . Glucose oxidase (EC 1 .1 .3 .4 type II Aspergillus niger), supplied by Sigma Chemical Co ., had an activity of 27 500 units/g . All other reagents were purchased from Wako Pure Chemical Ind . Ltd .\n299", + "300\nThe composite solution for glucose determinations contains 50 mM potassium phosphate buffer (pH 7 .0) and 0 .1 M KCI . 0 .5 M D-glucose solution was prepared fresh every two weeks using this buffer solution .\nProcedure PPy-modified electrodes were prepared by electropolymerizing in\naqueous solutions of 0.1 M pyrrole and 0 .1 M KCl as the supporting electrolyte for two minutes at room temperature, unless otherwise indicated . Immobilization of GOD was performed by adsorbing on PPy films as follows. The PPy-modified electrodes were dipped into GOD aqueous solution (50 mg GOD/ml H20) overnight in a refrigerator at 4 \u00b0C, rinsed in distilled water for 30 seconds and dried in a desiccator .\nThese GOD-adsorbed electrodes were dipped into dichloromethane solution of 1% DMFe and 2% polyvinylbutyral (PVB) for 10 s, and then dried in air. DMFe was trapped into the PVB matrix around the adsorbed GOD on the PPy film. The electrodes were stored in potassium phosphate buffer at 4 \u00b0C when not in use .\nThe electrodes were immersed in 10 ml of the buffer solution with a platinum counter electrode and SCE and were potentiostatted at fixed potential against SCE during the determination of glucose concentration . The temperature of the buffer solution was controlled at 25 - 40 \u00b0C by circulating water of fixed temperature in the jacket of the vessel.\nResults and discussion\nDetermination of glucose using H 202 electrodes GOD-adsorbed PPy-modified electrodes (GOD/PPy electrodes) without\nDMFe were tested for glucose determination based on H 202 detection . In air-saturated buffer solution the GOD/PPy electrode was operated potentiostatically at 0.7 V and output current was monitored after injection of glucose . A rapid increase in current was observed and steady-state currents were obtained within one minute . This result indicates that GOD could be adsorbed onto the PPy electrode, retaining glucose oxidation activity. Figure 2 shows the calibration curve for these electrodes . This sensor did not have a large enough determination range to monitor the glucose in diabetic blood directly. The saturation of the current response at 15 mM glucose concentration seemed to be due to insufficient dissolved oxygen . To extend the dynamic range of glucose detection, a semipermeable-type membrane that restricts only the permeation of glucose has been generally used by attaching it over the enzyme electrode. However, this method has disadvantages such as retardation of response time and reduction of current response . Moreover, these GOD/PPy electrodes were unstable above 0 .6 V (versus SCE). The PPy films were thus damaged by high potentials and exposure to H2O2 during the determination of glucose [15] . Therefore PPy electrodes based on the detection of H 2O2 are not suitable for stable micro glucose sensors ." + ] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure3.38-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure3.38-1.png", + "caption": "Fig. 3.38. The second impact", + "texts": [ + "37) we have to solve the equations (3.4.177) and (3.4.178) defining the cylindrical hole and the cylindrical peg. While the peg is moving towards the hole there is no real solution to this equation system. The impact happens when this system has one real so lution only. Thus, in each iteration the system has to be solved nume rically. In the next time interval (T 2 ) the motion of the peg is constrained. It is a surface-type constraint, the one discussed in Para. 3.4.12. Then the second impact happens (point A2 in Fig. 3.38a or A1 in Fig. 3. 38b) . After this second impact the motion of the manipulator is subject to two-d.o.f. joint constraint (Para. 3.4.7). However, if there are large perturbances, the motion after the second impact cannot be considered in this way but it is subject to two constraints of surface type (Fig. 226 3.39a).cylindrical joint constraint (two d.o.f) can'be used when the axis of the peg (*) is close enough to the hole axis (**) (see Fig. 3. 39b) \u2022 The problem of friction and jamming was considered in Para" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000144_j.matpr.2021.03.016-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000144_j.matpr.2021.03.016-Figure2-1.png", + "caption": "Fig. 2. Schematic of EBM [7].", + "texts": [ + " SLM eliminates the need of welding and riveting and also the use of mold which will ensure reduction of the design as well as the production time [6]. A schematic of SLM is shown in Fig. 1. In EBM, the generated electrons from an electron gun are accelerated using a potential difference and focused with the help of an electromagnetic lens, scanned as per the embedded CAD model, metal powder is raked on to the build platform, selectively melted and the build platform is lowered for successive layer building [6]. A schematic of EBM is shown below in Fig. 2. A vacuum environment must be created in the building chamber so as to eliminate the chances of interaction between gas and electron beam, otherwise the surface finish of the EBMed part will be very poor [7]. Generally the parts produced using EBM shows more density as compared to its SLM counterparts [8] but shows more surface roughness, less ultimate tensile stress and yield stress and almost similar hardness [9]. In WAAM process, 3D parts are built by metal weld bead deposition in layer by layer using the welding methods like GMAW, GTAW and PAW which generally have high deposition rates [10]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002716_j.ijmachtools.2005.01.014-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002716_j.ijmachtools.2005.01.014-Figure4-1.png", + "caption": "Fig. 4. Prism dimension and hatch orientation designed for orthogonal experiment. (a) 3D-view and dimension description of experimental prisms. (b) Hatch orientation of each layer varies 1208 to improve component qualities.", + "texts": [ + " Hence it is significant to study the effect of the specific energy on the cross-section shapes of the Ni alloy cladding layer on low carbon steel substrate by single-track cladding with different laser processing parameters. The parameters used in this experiment are shown in Table 1. (2) An orthogonal experiment was carried out to reveal the comprehensive effects of the optimized laser processing parameters. During the experiment, an orthogonal parameters array as shown in Table 2 was applied respectively to fabricate nine hexagon prisms whose dimension is shown in Fig. 4(a). Each prism was built six layers with the specific combination of process parameters. In order to avoid the possible defects appearing at the same place in each layer, the hatch orientation in each layer changed 1208 with the previous layer, as shown in Fig. 4(b). Other parameters are shown in Table 3. (3) Ni alloy samples were manufactured with optimal parameters to examine the process feasibility. Fig. 5 is the result of the single-track cladding experiment. The laser energy input of the process can be e 1 meters for single-track cladding r power 1500, 2000, 2500, 3000, 3500 (W) velocity 3, 5, 7, 9, 11 ( mm sK1) eter of laser spot 2 mm owder, character Ni\u201324Cr\u20134Si\u20132.5B\u20133Fe\u20132.5Mo\u20130.6C (wt%) K140/C320 mesh der feed rate 5.8 g minK1 ying gas, flow rate Ar, 8 L minK1 trate Low carbon steel plate, 10 mm thickness where P is the laser power (W), D is the diameter of the laser spot (mm), S is the scan velocity (mm sK1)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000058_j.triboint.2020.106785-Figure7-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000058_j.triboint.2020.106785-Figure7-1.png", + "caption": "Fig. 7. (a) The specially designed loading ring; (b) photo of the assembly of loading ring, test bearing and instrumented bearing; (c) measuring strain at all roller positions when the roller 0 was loaded.", + "texts": [ + " The data acquisition systems and DC control unit are integrated with a computer for real time measurement of strain response and load as well as controlling the motor. According to the measurement principle, the load distribution in a bearing can be calculated from the strain measurement once compliance matrix is determined. In order to obtain the compliance matrix, a loading ring was specially designed to apply the force on one specific roller position while the strains at all interested roller positions are measured as shown in Fig. 7. Compliance matrix components k\u03b1\u2212 \u03b2 can be obtained as follows k\u03b1\u2212 \u03b2 = \u0394\u03b5\u03b1\u2212 \u03b2 \u0394P\u03b2 (5) where \u03b5\u03b1\u2212 \u03b2 is the measured strain at the positions of roller \u03b1 when the load P\u03b2 applied to the roller \u03b2. The contribution of self-weight has been removed from the applied load. As shown in Fig. 7(c), when the load P0 is applied to the roller 0, \u03b5\u03b1\u2212 0 (\u03b1 represents 3L, 2L, 1L, 0, 1R, 2R, 3R) can be measured. With the increasing of P0, the change of \u03b5\u03b1\u2212 0 is recorded. Then the compliance matrix components k\u03b1\u2212 0 can be obtained by Eq. (5). The loading ring is kept not to rotate in order to ensure that the loading roller is located at the bottom and in the line of the loading direction of applied load. Other compliance components k\u03b1\u2212 \u03b2 can be obtained similarly by moving the corresponding roller under the specially designed load ring" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000058_j.triboint.2020.106785-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000058_j.triboint.2020.106785-Figure2-1.png", + "caption": "Fig. 2. Finite element models with (a) general housing, (b) instrumented housing.", + "texts": [ + " A bearing of 17 cylindrical rollers SKF NU 2214 ECM was used in our study. The specification of the bearing is shown in Table 1. The whole bearing geometry was downloaded from the freely accessible SKF component database. According to the SKF rolling bearing catalogue, this bearing owns normal radial internal clearance with a range of 0.040\u20130.075 mm [25]. However, for the simplicity of the simulation, no internal clearance was considered in this bearing geometry. Only the contact in the bottom half of bearing was modeled to reduce the computational cost as shown in Fig. 2. Besides, the cage was removed to reduce the number of contact surfaces. The relative displacement between adjacent rollers is limited by constraining the degree of freedom of the roller in the T (tangential) and Z (axial) directions. The outer ring is tied to a bearing housing of cylindrical tube shape with the thickness of 14 mm. The general housing without notches and the instrumented housing with notches were modeled respectively as shown in Fig. 2. For the instrumented housing, the groove depth of the notch is 2 mm and the Table 1 Specifications of test bearing. Bearing model NU2214ECM Bearing outside diameter 125 mm Bearing bore diameter 70 mm Pitch diameter 98.5 mm Radial Clearance Normal [25] Roller diameter 15 mm Roller length 22 mm Contact angle 0\u25e6 Number of rollers 17 Y. Hou and X. Wang central angle corresponding to the notch is 10.0\u25e6. There exist two pairs of rolling contact interfaces in the bearing, i.e. one between the inner ring and rolling element and the other between the rolling element and outer ring" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002878_s0043-1648(97)00076-8-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002878_s0043-1648(97)00076-8-Figure4-1.png", + "caption": "Fig. 4. Dynamic model of a high speed angular contact ball bearing.", + "texts": [ + " (12)) using the method presented in [ 15] (see Appendix D) the load-displacement correlations of the beating are given by: Fr=8r(Kr+iH~); F,,=~$,,(K,,+iH,,); M=~p(K, .+iH, . ) (13) where: \u2022 6r, 6a, q~ are the displacements between bearing rings on radial, axial, and angular directions, respectively; \u2022 Kr, K=, Km are the overall rigidities acting in phase with displacements on radial, axial, and angular directions, respectively, \u2022 Hr, H=, H,~ are the overall hysteretic dampings acting in quadrature. ,-- From these considerations, for a high speed angular contact ball bearing under a complex load, the dynamic model presented i~ Fig. 4 was proposed. 3. Dynamie model validation The validation of the proposed dynamic model was achieved by a theoretical and experimental analysis of the dynamic state of a test grinding machine main spindle ( Fig. 5) in controlled conditions of speed, bearings preload, and load. The level of the transversal vibrations of the main spindle having a major influence on the quality surface in the grinding process was co~sidered in research [ 1,3]. Consequently, were determined both theoretical and experimental amplitudes of the transversal vibrations of the test main spindle offset grinding wheel in controlled conditions of speed for various values of bearings preload Fp, and test force Fs that simulates main grinding force (see Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure14.3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure14.3-1.png", + "caption": "Fig. 14.3 Process of needle electrode fabricated by micro EDM", + "texts": [ + " In our study we made several electrode patterns to investigate experimentally how is the strength of the ECF jet influenced by the type of electrodes and gaps. Some kind of the novel needle electrode with the micro pins for the cylindrical ECF pump is fabricated by a micro Electrical Discharge Machine (micro EDM). The micro EDM has a manufacturing potential as the most precise and convenient way of such precise and complicated electrode. The processing procedure of the positive electrode by the micro EDM is illustrated in Fig.14.3. At first a rod electrode is formed to a cuspidate needle electrode by a wire electro-discharge grinding (WEDG) method [9]. Next step the cuspidate electrode with negative polarity is fed into a plate electrode to make a sharp edged groove or hole. The groove or hole array pattern is repeatedly formed according to the configuration of the array pins of the needle type electrode. The polarity of a new thick rod electrode is then reversed, and the new rod electrode is fed into the plate electrode on the grooves or holes" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003715_tps.2010.2076355-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003715_tps.2010.2076355-Figure4-1.png", + "caption": "Fig. 4. Electromagnetic-force analysis on the PM when the PMs are in different positions of the slot. (a) PMs are in the centerline of slot. (b) PMs are not in the centerline of slot.", + "texts": [ + " If the PM locates in the centerline of the PM slot, the magnetic path for the two sides of the PM is symmetric, and the amplitude of the electromagnetic force on the surface of BC and CD is equal, but the direction is opposite. If the PM locates in the noncenterline of the PM slot, the direction is also opposite, but the amplitude is not equal; the difference is the pressure of the frictional force. According to the relationship of acting and reacting forces, we obtain the electromagnetic force on the PM, which is shown in Fig. 4. We use the finite-element method (FEM) to calculate the electromagnetic force when the PM is in different positions in the slot. We define the variable L as the distance between the PM and the slot; the force is shown in Fig. 5. The electromagnetic force increases with decreasing s, and the magnitude is smaller when L is wider. The direction of the electromagnetic force is 270\u25e6 approximately, which means that the force points toward the central shaft. The frictional force due to pressure of the PM against the sides of the slot is nearly zero, so it is neglected" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002565_s0043-1648(03)00338-7-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002565_s0043-1648(03)00338-7-Figure4-1.png", + "caption": "Fig. 4. Relations between global and local co-ordinate system for left and right tooth flank.", + "texts": [ + " (12) will be very small compared to 1 (see Section 6), thus we can assume that this term is equal to zero. With this assumption, we get t\u0302 o inj = t\u0302 v inj, n\u0302 o inj = n\u0302 v inj (13) and as a consequence, the vertical location of the instantaneous centre of rotation will be constant and the same for the right and left flank. The following relation will now obtain [4] rwi cos\u03b1wt = ri cos\u03b1t (14) Fig. 3 shows the teeth of gear one and two and their rigidly connected co-ordinate systems. The two global parameters \u03c61 and \u03c62 define the rotations of the gears. A global co-ordinate system Sa inj (see Fig. 4) is introduced to determine the position of a point defined by \u03d5inj in the contact region. This co-ordinate system is located at the instantaneous centre of rotation I and the ya inj axis has the same direction as the normal vector n\u0302 o inj (and therefore parallel to the line of action). The co-ordinate transformation from So inj to Sa inj involves one rotation about the gear axis and one translation from the gear centre to I. An auxiliary global co-ordinate system Sr inj is applied such that Or inj coincides with Oo inj and Sr inj and Sa inj have the same orientation of their co-ordinate axes. The co-ordinate transformation from So inj to Sr inj is rep- resented by the matrix equation r r inj(\u03d5inj, \u03b8inj) = M ro injr o = xr inj yr inj = ri sin(\u03d5inj + \u03b8inj)\u2212 (ri\u03d5inj \u2212 1 2 s \u2217 inj) cos\u03b1t cos(\u03d5inj + \u03b8inj \u2212 j\u03b1t) ri cos(\u03d5inj + \u03b8inj)+ (ri\u03d5inj \u2212 1 2 s \u2217 inj) cos\u03b1t sin(\u03d5inj + \u03b8inj \u2212 j\u03b1t) (15) where M ro inj = [ cos \u03b8inj sin \u03b8inj \u2212sin \u03b8inj cos \u03b8inj ] (16) We determine from Fig. 4 that \u03b8inj(\u03c6i) = \u03c6i + (\u22121)i\u03c4in+ \u03c0(1 + 1 2j)+ j\u03b1wt (17) where \u03c4i = 2\u03c0/zi is the angular pitch. The co-ordinate transformation from Sr inj to Sa inj is represented by the matrix equa- tion ra inj(\u03d5inj, \u03b8inj) = dar inj + r r inj = ri sin (\u03d5inj + \u03b8inj)\u2212 (ri\u03d5inj \u2212 1 2 s \u2217 inj) cos\u03b1t cos(\u03d5inj + \u03b8inj \u2212 j\u03b1t)+ jrwi cos\u03b1wt ricos (\u03d5inj + \u03b8inj)+ (ri\u03d5inj \u2212 1 2 s \u2217 inj) cos\u03b1t sin(\u03d5inj + \u03b8inj \u2212 j\u03b1t)\u2212 rwi sin \u03b1wt (18) where dar inj = [ jrwi cos\u03b1wt \u2212rwi sin \u03b1wt ] (19) Finally, we have n\u0302 a inj = n\u0302 r inj(\u03d5inj, \u03b8inj) = M ro injn\u0302 o inj = [ j cos(\u03d5inj + \u03b8inj \u2212 j\u03b1t) \u2212j sin(\u03d5inj + \u03b8inj \u2212 j\u03b1t) ] (20) In the last decade, there has been a growing interest in wear simulation of gears [5\u201313]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002627_physreve.70.061411-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002627_physreve.70.061411-Figure3-1.png", + "caption": "FIG. 3. Perturbation to measure rs1\u2212rc' 2 /K3d\u22121. Again the conelike arrows represent the orientation of the magnetization while the flat arrow represents the direction of the perturbation.", + "texts": [ + " Therefore we determine the limiting cases for either setting k' or ki to zero first, lim k'\u21920 lim ki\u21920 xg2g2 = r , s97d lim ki\u21920 lim k'\u21920 xg2g2 = r 1 \u2212 rc' 2 /K3 . s98d Because we discussed the autocorrelation function of the transverse momentum density, Eqs. (97) and (98) give the inertia of the gel against velocity perturbations along the planes with a normal vector either perpendicular or parallel to the preferred direction, respectively. In the first case the usual inertia (Fig. 2) due to mass can be measured while in the second case (Fig. 3) an increase of the inertia can be observed. The inverse susceptibility matrix of the other three components is obtained in the same manner and reads 061411-7 xij \u22121 =1 1 r 0 + iM0c'ki 0 1 r + iM0cik' \u2212 iM0c'ki \u2212 iM0cik' M0 2sK2k' 2 + K3ki 2d 2 , s99d where i , jP hg1 ,g3 ,dm2j. We again obtain the static susceptibilities by inverting this matrix: xg1g1 = rfsK2k' 2 + K3ki 2d \u2212 ci 2k' 2 rgN\u22121, s100d xg3g3 = rfsK2k' 2 + K3ki 2d \u2212 c' 2 ki 2rgN\u22121, s101d xg1g3 = c'kicik'r2N\u22121, s102d xg1dm2 = ic'kirM0 \u22121N\u22121, s103d xg3dm2 = icik'rM0 \u22121N\u22121, s104d xdm2dm2 = M0 \u22122N\u22121, s105d with N= sK2k' 2 +K3ki 2d\u2212rc' 2 ki 2\u2212rci 2k' 2 " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003117_70.246062-Figure5-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003117_70.246062-Figure5-1.png", + "caption": "Fig. 5. System behavior for the simulation in the presence of joint limits.", + "texts": [ + " We therefore place an upper bound on the norm of the second term. When the norm is greater than 3.0, the second term is proportionally reduced to have a norm of exactly 3.0. The gain and the saturation for the primary Lyapunov-like function discussed in Section IV-A was used concurrently. Fig. 4 shows the trajectory of the joint variables for the simulation in the presence of joint limits only. It can be seen from Fig. 4, which is very different from Fig. 2, that none of the joint limits has been violated. The system behavior is shown in Fig. 5 at eight different intermediate stages. The convergence criterion was kept the same as in the first case, and the time for convergence was noted to be approximately 1.5 s. The actual time taken for the simulation was approximately 2.5 mins on a SUN 4/260 computer. C. End-Effector Trajectory Planning in Presence of Obstacles Finally we simulated the case in the absence of joint limits but in the presence of an obstacle. The same initial and desired configurations given by (26) and (27) were used" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000229_j.mechmachtheory.2021.104529-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000229_j.mechmachtheory.2021.104529-Figure1-1.png", + "caption": "Fig. 1. Gear tooth geometry of profile-shifted spur gear in case I.", + "texts": [ + " Considering the modifying method, we can calculate addendum as ha,i = ( h\u2217 a + pi \u2212 \u0394q ) mn, (i= p, g) (4) where subscript i represents the pinion and gear, h\u2217 a is the addendum coefficient, pi denotes the modification coefficient, \u0394q is the addendum modification coefficient, and can be expressed by \u0394q = pp + pg \u2212 q, where q is the center distance modifying coefficient. In the following subsections, the TVMS model of the profile-shifted spur gear is analyzed and discussed according to the two cases of design parameter setting. If the root circle is smaller than the base circle, the gear tooth geometry can be described in Fig. 1. The tooth profile starts from the J. Wang et al. Mechanism and Machine Theory 167 (2022) 104529 addendum circle and ends at the root circle, where the profile is an involute curve between the addendum circle and the base circle, while the rest is the transition curve. Based on the gear tooth geometry, the geometrical parameters utilized to analyze the stiffness components can be formulated as follows, h = Rb[(\u03c61 +\u03c62)cos\u03c61 \u2212 sin\u03c61] (5a) hx = { Rbsin\u03c62 + rf \u2212 \u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305 rf 2 \u2212 (x \u2212 d1) 2 \u221a , 0 \u2264 x < d1 Rb[(\u03c62 \u2212 \u03c6)cos\u03c6 + sin\u03c6], d1 \u2264 x \u2264 d (5b) d = Rb[(\u03c61 +\u03c62)sin\u03c61 + cos\u03c61] \u2212 Rf cos\u03c63 (5c) d1 = Rbcos\u03c62 \u2212 Rf cos\u03c63 (5d) x = { Rb[cos\u03c6 \u2212 (\u03c62 \u2212 \u03c6)sin\u03c6] \u2212 Rf cos\u03c63, \u2212 \u03c61 \u2264 \u03c6 < \u03c62 ax\u03c6 + bx,\u03c62 \u2264 x \u2264 \u03c63 (5e) where \u03c63 = arcsin(h1 /Rf ), ax = d1 /(\u03c63 \u2212 \u03c62) and bx = d1\u03c63 /(\u03c63 \u2212 \u03c62)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure4.25-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure4.25-1.png", + "caption": "Fig. 4.25. A 9 d.o.f. manipulator UMS-E", + "texts": [ + " They can be placed in manipulator column and their torques transported to corresponding joints. The same holds for reducers. Let as make an important remark. The choice procedures proposed are exact i.e. they are based on the complete dynamic models of both mecha nism and actuators. Such a procedure is expecially suitable for high speed manipulation where dynamic effects of robot are imDortant. But, the methodology can also be used for low speed manipulation since it is general. 290 291 4.5.4. Examples Example We consider the arthropoid manipulator UMS-E (Fig. 4.25) designed to carry loads up to 60 kg. It is a redundant manipulator having nine de grees of freedom. It is originally designed for hydraulic drives. Here we are going to choose electromotors and thus the example is rather hypothetic. The manipulation task consists in carrying the payload of 60 kg mass along the trajectory AoA1A2 (Fig. 4.26) keeping all the time its ini tial orientation. On each straight-line part of this trajectory the velocity profile is trapezoidal with the acceleration time being 20% of 292 transport time (ta =0,2T)", + " Since we want our actuator to operate without the reducer we choose a stronger assembly: hydraulic -4 2 cylinder KNAPP Z 9.40/25 having A = 12.6\u00b710 m, m = 2.65 kg, and MOOG servovalve 76-103 having k /c 1 = 4.22.10- 5 m3 /s/rnA, k 9.04.10-11 5 q c m /Ns. For this assembly the interval for reduction ratio is [N 1 , N2 ] [0.76, 1.88] and it contains N=l. Thus this assembly can operate with out the reducer. Example 3 This example illustrates the choice of rotary hydraulic actuator. Let us consider again the manipulator UMS-E (Fig. 4.25) and the manipula tion task from Example 1. We choose again the actuator for the joint S5 but this time it is a rotary hydraulic actuator. The maximal torque is P5c tain v' 2n 3 m 2507.4 Nm. By adopting ~Pn 70 bar we ob- We now adopt the motor PRVA PETOLETKA*) 145-7000 having V'/2n = 433.12010-6 m3 . *) The largest Yugoslav industry for hydraulics and pneumatics. 297 m m / The critical pOint is QK = 2258.7 W, DOK '\" 2612.5W s. Relation (4.5.75) gives V > 79.79 litre/min. We adopt MOOG servovalve 72-154 having sn Vsn 95 litre/min i 200 rnA max For the reduction ratio we obtain [N 1 , N21 = (0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003521_j.conengprac.2007.04.008-Figure6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003521_j.conengprac.2007.04.008-Figure6-1.png", + "caption": "Fig. 6. Propulsive force in the horizontal plane.", + "texts": [ + " (6) the first term denotes the torque of the propulsive force due to the main rotor, the second term refers to the torque of the friction force, and the torque of gravity force is shown in the third term. dOv dt \u00bc lmF v\u00f0ov\u00de Mfric;v \u00fe g\u00bd\u00f0A B\u00decos av C sin av Jv , (6) where A \u00bc mt 2 \u00femtr \u00femts lt; B \u00bc mm 2 \u00femmr \u00femms lm, C \u00bc mb 2 lb \u00femcblcb , Fv\u00f0ov\u00de \u00bc kfvpjovjov for ovX0; kfvnjovjov for ovo0; ( (7) dav dt \u00bc Ov. (8) The mathematical model of the remaining parts of the system in horizontal plane is described in Eqs. (9)\u2013(11) (see Fig. 6). In Eq. (9) the first term is the torque of propulsive force due to the tail rotor, the second term implies the torque of the friction force, and the third term refers to the torque of the flat cable force that is completely nonlinear and can be obtained by point-by-point measurement. Fig. 7 shows the torque of the friction force that covers viscous, coulomb and static frictions: dOh dt \u00bc ltFh\u00f0oh\u00decos av Mfric;h Mcable\u00f0ah\u00de D cos2 av \u00fe E sin2 av \u00fe F , (9) where av \u00bc cte, D \u00bc mm 3 \u00femmr \u00femms l2m \u00fe mt 3 \u00femtr \u00femts l2t , E \u00bc mb 3 l2b \u00femcbl2cb; F \u00bc mmsr 2 ms \u00fe mts 2 r2ts, Fh\u00f0oh\u00de \u00bc kfhpjohjoh for ohX0; kfhnjohjoh for oho0; ( (10) dah dt \u00bc Oh" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003670_978-3-642-82195-0-Figure2.4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003670_978-3-642-82195-0-Figure2.4-1.png", + "caption": "Fig. 2.4. A scheme of forward recursive relations", + "texts": [ + " This is due to the fact that there are no multi plications (or additions) between matrices (or vectors) which are the functions of the same joint coordinates. This will not be the case with the Jacobian matrix computation. 2.2.4. Forward recursive symbolic relations In this subsection we will derive forward recursive relations which yield symbolic expressions for the elements of transformation matrices \u00b0Ti , i=1, .\u2022\u2022 ,n. They ensure optimal evaluation of the elements of these matrices. We will derive these symbolic relations starting from the general for ward recursive relation (2.2.7), outlined in Fig. 2.4. 75 Let us assume that the matrix \u00b0Ti _1 has already been evaluated, and that joint i is revolute. According to equations (2.2.7) and (2.2.1) we can write cosq i -sinqicoso.i sinqisino.i aicosqi \u00b0T. 0 sinqi cosqicoso.i -cosqisino.i aisinqi (2.2.56) ~ Ti - 1 0 sino.i d. coso.. ~ ~ 0 0 0 l6 (a redundant manipulator), then the discussion is rather complicated. Six d.o.f. of the gripper are enough for all manipulation tasks. So the tasks for manipulators with n>6 usually contain some additional requirements which are not imposed on the gripper but on the manipulator as a whole (for instance, that a manipulator bypasses some obstacle in the work ing space). Hence, for solving the task geometry, not only the gripper d.o.f. but the d.o.f. of the manipulator as a whole are also important. An extensive discussion on kinematics with exact answers about the conditions for the disappearance of some d.o.f. will not be given here. So we shall restrict out consideration to the cases when there are no singularities. Let us be more precise. For a manipulator with n < 6 d.o.f. we shall assume that its gripper also has n d.o.f.: for a mani pulator with n>6 d.o.f. we shall assume that its gripper has six d.o.f., i.e., the maximal possible number. It is an important fact that this assumption holds for almost all practical problems. For instance, when 45 imposing a task on a certain manipulator we always take care about avoiding the singularity points, i.e., we choose the trajectories which can be performed. Keeping in mind the above assumption, we shall simply talk about degrees of freedom, regardless of whether the whole manipu lator, or its gripper only, is concerned. The following consideration will be restricted to mechanisms having one d.o.f. joints only. This means that number of segments equals the number of d.o.f. We now derive the so-called general algorithm for dynamic analysis. It is a basis for the development of a new algorithm which covers some typical classes of manipulation tasks and is more suitable for users. 2.4.1. General algorithm for dynamic analysis Let us consider a manipulator as an open chain of rigid bodies, without branches, as shown in Fig. 2.15. Let the manipulator have six d.o.f. ~ -----~ Fig. 2.15. Manipulator as a kinematic chain The last body (segment) of the chain represents the manipulator gripper, i.e., in the phase of transferring some work object, the last segment is the gripper and object combined. Thus, the manipulation task can usu ally be considered as a prescribed motion of a rigid body (the last segment) in space. In the develop ment of the general simulation algo rithm, one started from the fact that a rigid body motion can, in the most general way, be prescribed by means of a known initial state, and a known time function of the center of gravity acceleration (or of some other point on the segment) ~(t), and a known time-function of the an gular acceleration ~(t) of the body. Such an approach is justified because for many manipulation tasks these values can easily be prescribed. For instance, gripper center of gravity motion is usually prescribed quite easily by means of the trajectory and the velocity profile. Thus, we will now describe the algorithm (considering the manipulation task) in terms of ~(t) and ~(t), i.e., these are the input values [23, 24]. So, in matrix notation (2.4.1) 46 where w designates a 3x1 matrix corresponding to vector w, likewise for E and all other vecotrs in the sequel. NOw, it is clear why we in troduced the notation Xa=X (see (2.2.5), (2.2.6)). It is due to the fact that E is not the second derivative of any coordinates. In Para. 2.3. when the c.-a. method for model formation was described, it was shown how the matrices n, e, r, ~ were derived and calculated, so that it holds: nq + e, (2.4.2a) rq + ~. (2.4.2b) The matrices are calculated from the recursive expressions for veloc ities and accelerations of segments. There are no indices in the equa tions (2.4.2a,b). w is the acceleration of gripper c.o.g. and E is the angular acceleration of the gripper. The matrices n, e, r, ~ are cal culated recursively during the formation of dynamic model. In each it eration they correspond to the new segment. At the end of model foDffing procedure these matrices correspond to the gripper. This is the reason that no indices are used with these matrices. The vectors wand E hold for the gripper and are expressed in the cor responding body-fixed coordinate system. In the external coordinate system it holds w A6 rl q + A6e A6 r q + A6~ (2.4.3a) (2.4.3b) where A6 is the transition matrix of the gripper system. These two ex pressions can be combined (2.4.4) J A to give (2.4.5) (6x1) where the Jacobian and the adjoint matrix are (2.4.6) The internal (generalized) accelerations are now q It should be exphasized that this approach to the Jacobian is very suitable. When we carry out the c.-a. model forming procedure then we have the matrices n, e, r, ~ calculated. So, we immediately have the Jacobian and the adjoint matrix with no additional calculation. Equations (2.4.2) - (2.4.6) hold for the gripper c.o.g. If motion of some other gripper point is prescribed instead of its c.o.g. then the Jacobian matrix is changed. Let us consider a point A determined by a vector p c;A (Fig. 2.16). Then, for the acceleration it holds 47 where p designates the matrix 0 -P3 ~21 P ~ ~3 0 -P1 -P2 P1 0 (2.4.8) (2.4.9) which corresponds to the vector ~ = {P1 , P2' P3} and is used to form the vector product by matrix calculus. If we introduce (2.4.2) into (2.4.8) instead of wand E , we obtain c g g tn-pO i:i + e - p~ + k (2.4.10) or (2.4.11) where * n n - pr, * e e - p~ + K (2.4.12) After transition to the external coordinate system and combination with (2.4.3b) it follows 48 Hence the new Jacobian and the new adjoint matrix are J A , A (rl-pr) g = rl' , A (0-P+k) g ~ 0' (2.4.13) (2.4.14 ) It was said that this algorithm had the manipulation task input in terms of accelerations. There are some algorithms which use the task input in terms of velocities. Then . => q The Jacobian is the same as in (2.4.4), (2.4.14). It may seem to someone that the prescription of external velocity (X) is more suitable than the prescription of acceleration (Xa = X). As we have chosen the acce~ eration input, here are some reasons, justifying such an approach. If the velocity input is used, then we obtain q and it is necessary to perform numerical differentiation in order to compute q which is ne eded for the calculation of drives P. The numerical differentiation is still an undesirable procedure. On the other hand, the manipulation task is very often given by a trajectory and a velocity profile along it. The velocity profile in fact means the acceleration. Special con veniences appear in some practical cases. The most common velocity pro file is the triangular and the trapezoidal one (Fig. 2.17). It can be seen that the corresponding accelerations are constant and thus very easy for prescription. This acceleration approach will be worked out in the sequel. This general algorithm is sometimes extremely convenient. Suppose a manipulation task in which a 6 d.o.f. manipulator should move an object from the point A to B (Fig. 2.18) along the straight line keeping all the time the initial orientation of the object. The velocity profile is assumed to be triangular. Let the execution time be T. First, we ha- ve to prescribe the initial state q(to ) = qO, q(to ) = O. In order to prescribe the linear motion of the object in terms of acceleration it is enough to give: o - ->- be unsuitable because of the input w, E. For a manipulator motion from one position to another it is necessary to define ~(t) and t(t). While ~(t) can easily be defined, definition of orientation change in terms ->- of E may be difficult. Since our intention is to make the algorithm more convenient for the users, we make some further elaboration of the task-input procedure. We now search for the three parameters which define the orientation of the gripper (or of a rigid body in general) in a convenient way. The most common parameters defining the body orientation are Euler's angles but they are inconvenient for definition. Such orientation definition does not follow from the functional motion of manipulator and these angles can hardly be measured. So, we choose another set of angles (8, ~, ~) defining the orientation (Fig. 2.19). Let us notice that this orientation definition understands one direction (b) and the angle of rotation around this direction. Such approach will be shown to be very convenient because it really follows from the functional movements of 51 manipulators in practical operation. However, this angle representa tion sometimes results in some singularity problems but it is the price we have to pay for simple handling of the algorithm. These problems and the way of avoiding them will be discussed later. (bl Fig. 2.19. Definition of orientation In practice, we meet manipulators with different numbers of d.o.f. (most often: 4, 5 or 6 d.o.f.). They are intended for different classes of manipulation tasks. Hence, we now analyze the need for a certain number of d.o.f. and their use in certain classes of tasks [22, 26]. Let us first define more precisely some notions which will be used: P06~t~on~ng means moving some given point of the last segment to some desired point in the working space, i.e., the motion of that point of the last segment along a prescribed trajectory according. to a pre scribed motion law. Full on~entat~on of a body in space means an exactly determined angular position of the body with respect to the external space. It can also be considered in the following way: some given body axis (or some arbi trary fixed direction on the body) coincides with ~ prescribed direc tion in the space and the rotation angle around this direction is also prescribed. The term total orientation is used also. Pant~al o~ientat~on of a body only means that the given body-fixed di rection concides with the prescribed direction in space (which can be changeable according to some law). The difference between the partial and the total orientation is shown in Fig. 2.20. In Fig. 2.20(a), (b) the task of transferring a container with liquid is shown. In case (a) it is only important that the axis (*) is vertical and so it is the case of partial orientation. In case (b) not only the direction (*) but also the direction (**) is impor tant. For the given direction (*) the direction (**) may be replaced by angle ~. Hence, the case (b) represents the total orientation. Fig. 2.20(c), (d) shows something analogous but for assembly tasks. 52 We now consider two examples which demonstrate that the orientation representation chosen (direction and angle) really follows from prac tical manipulation tasks. Fig. 2.21. presents a task of spraying pow der along a prescribed trajectory. The task reduces to the need to realize the motion of an object (container) along the trajectory (a) (i.e. positioning) and along the trajectory the container should rotate around the direction (b) according to the prescribed law W(t). So, the orientation representation in terms of one direction and the rotation angle directly coincide with the functional motion of manipulator. In this case the choice of the direction is different from that in Fig. 2.20(a), (b) because of different manipulation tasks. The next example represents screwing a bolt in (Fig. 2.22). Let us now analyze the need for a certain number of d.o.f.: To solve the positioning task, which is a part of every manipulation task, three d.o.f. are needed. 53 To solve the positioning task along with the task of partial orienta tion, five d.o.f. are necessary. To solve the positioning task along with the task of full orientation, six d.o.f. are necessary. Manipulators with four, five and six d.o.f. will be considered here. In order to obtain a simple handling algorithm we derive a special adapting block for each manipulator class (4, 5 or 6 d.o.f.). This is due to the fact that these manipulators are dedicated to different classes of manipulation tasks and each class of tasks is suitable for definition in its own way. Even in one class (for instance manipula tors with 6 d.o.f.) the task may be defined in a few different ways. Thus, the adapting blocks enable a user to apply the task definition which is most suibable (in his opinion) to his manipulator and to the task which has to be performed. He does it by choosing one of the adap ting blocks which is already incorporated in the algorithm or he may even program its own adapting block. Let us define the generalized position vector X \u2022 It represents a set g of parameters which define the position of a manipulator. This vector is of dimension n (n = number of d.o.f.). It may be chosen to equal the internal coordinates (Xg = q) or the external coordinates (Xg = X) or 54 it may be mixed (X contains some internal and some external coordi g nates). Each adapting block operates with its special position vector and we choose the most suitable one. This position vector X repreg sents some generalization, for it is used instead of external coordinates vector X. The aim of each adapting block is to compute q which is necessary for the calculation of driving forces and torques. This computation of q is performed by means of Jacobian method or sometimes more directly. Anyhow, q is computed starting from X which has to be known. g .~ '1b) ~ L.--~T-- Fig. 2.22. Screwing a both in We here present these adapting blocks. But before that we have to derive some mathematical transfor mations which are common for most adapting blocks. At the beginning of 2.4.2. it was said that the set of angles 8, ~, ~ (Fig. 2.19) was chosen to define the total orientation of a body. In order to make easier the later derivation of adapting blocks we now give some transformations. Let us introduce a new Cartesian coordinate system which corresponds to the chosen set of angles (8, ~, ~). This system is obtained from the external one in the following way: rotation is first made around the z-axis (angle 8), and then around the new y-axis in the negative sense (angle ~); finally, the rotation around the new x-axis represen~ the angle ~ (Fig. 2.23). This system will be called the orientation system. Let us notice that the x-axis of such system coincides with the previously introduced direction (b). Let A be the transition matrix of the orientation system. Then A (2.4.15) where 55 [ co,e -sine :]. [ c~,o 0 -'~nol Ae sine cose A 4J 0 0 sln4J 0 COS4J [ : 0 -,:n.] A = coslj! (2.4.16 ) lj! sinlj! coslj! Let us find the first and the second derivatives of the transition matrix A Ae A4J Alj! + Ae A4J Alj! + Ae A Alj! (2.4.17) 4J A Ae A4J Alj! + Ae A4J Alj! + Ae A Alj! + 4J + 2A e Alj! + 2Ae Alj! + 2Ae (2.4.18 ) A4J A A Alj! 4J 4J where aAe aAe 2 Ae 8, Ae e a Ae 82 as as + --- ae 2 aA . aA4J a 2 A \u00b72 4J ijJ + ___ 4J A4J alP 4J, A alP 4J (2.4.19) 4J a4J 2 aAlj! aAlj! a 2 A \u00b72 Alj! lj!, 1\\lj! ~ar alj! iP + alj!2 lj! and aAe [-'in8 -cose o ] a 2 A [ -co'S sine ~ ] cose -sine o , e -sine -cose as ~ 0 0 0 0 0 aA4J [ -,:no 0 -CO'O] a 2 A [ -c:'o 0 'ino] 0 o , 4J 0 o (2.4.20) alP ---;-;;T cos4J 0 -sin4J -sln4J 0 -cos4J aAlj! [: 0 -c~'\u00b7l a 2 A [: 0 o ] -sinlj! ~ -coslj! sinlj! alj! alj!2 coslj! -sinlj! -sinlj! -coslj! 56 Introducing (2.4.19) and (2.4.20) into (2.4.18) one obtains: CAe CA ()A A 8 4l .. + A A ~ ijj as A4l Alji + Ae 3(j) Alji4l + e 4l ()lji \"-v----' \"-v----' '---v-----' Fe F Flji 4l ()2 A 82 ()2 A \u00b72 ()2 A \u00b72 + e A Alji + Ae 4l Alji + Ae A ~a7 --2- 4l lji + 4l 4l ') ()4l ()lji'. G So (2.4.21) reduces to .. A (2.4.22) The matrices Fe' F4l , Flji are determined by (2.4.21), (2.4.20), (2.4.16). Let it be noticed that the orientation coordinate system has no direct relations with the previously introduced b.-f. system. Let us now de rive the adapting blocks. The Jacobian matrices which appear in dif ferent adapting blocks are different. But, they will be always marked by the same letter J. 2.4.3. Manipulator with four degrees of freedom The first block (block 4-1). For a manipulator it is possible to cho ose a position vector to be equal to the internal coordinates vector. For a 4 d.o.f. manipulator it is 57 x g q (2.4.23) Thus if X is given it means that q is given and no calculation is ne-g eded. Such an approach understands that the motion is prescribed directly in terms of internal coordinates. This approach may simply be used for some configurations such as the cylindrical manipulator (Fig. 2.24) . The second block (4-2). A manipulator with 4 d.o.f. solves the posi tioning task by using three d.o.f., while the remaining one performs operations frequently sufficient for many practical manipulation tasks (Fig. 2.24). Hence we choose a generalized position vector X g (2.4.24) where (x, y, z) represent the Cartesian coordinates of some point of the gripper. Thus the manipulation task is defined via positioning plus one internal coordinate which is given directly. From (2.4.13) and (2.4.14), it follows that: 58 w rl' + 8' (2.4.25 ) For prescribed Xg [x y z q4 l , (2.4.25) represents a system of 3 equa tions with 3 unknowns Q1' Q2' Q3. After solving these equations the whole vector q = [q1 q2 q3 q4lT becomes known. This approach is closer to the essence of practical manipulation tasks. For better understanding consult the example in 2.8.1. Other possibilities. Depending on the form of the desired trajectory, in some cases it is suitable to prescribe positioning in cylindrical or spherical coordinates (Fig. 2.25). Let us first consider the cylindrical coordinate system (p, a, z). -+ Projected onto the axes of such a system, acceleration w has the form w p -2 pa , w a w Z and further, the following Cartesian projections are obtained: w x w cosa p w y i.e. the acceleration vector is w z (2.4.26 ) (2.4.27) w = [w w W]T x Y z 59 (2.4.28) NOw, vector (2.4.28) together with (2.4.27), (2.4.26) is used in eq. (2.4.25) instead of w = [x Y z)T in order to compute q1' Q2' Q3' For the computation of w by using (2.4.26) and (2.4.27), it is neces sary to know p, a, z and also p, p, a, ~. Only p, a, z, Q4 appear as input values. So, during the recursion from one time instant to anoth er, the values of p, p, a, a are calculated by integration together with integration over the generalized coordinates. If a spherical coordinate system (r, a, S) is considered, then the ac celeration projected onto the corresponding axes has the form w r w a 2 -2 rcos Sa 2~~cosS + racosS - 2r~~sinS - -.. - 2 Ws 2rS + rS + rsinScosSa or, in the Cartesian system w x w y so the acceleration vector is (2.4.29 ) (2.4.30) (2.4.31 ) The vector (2.4.31) together with (2.4.30), (2.4.29) is now used in (2.4.25) instead of w = [x Y z)T. As input data r, a, S, q4 appear and r, r, a, ~, S, ~ are obtained by integration. 2.4.4. Manipulator with five degrees of freedom The first block (block 5-1). The first possibility is to prescribe the manipulator motion directly in terms of internal coordinates. Then 60 x g q So, Xg i.e. q represent directly the input values (2.4.32) The second block (5-2). A manipulator with 5 d.o.f. solves the posi tioning task along with the task of partial orientation. The positioning will be treated in external Cartesian coordinate sys tem (x, y, z), so these coordinates will be included in the position vector Xg . Let us now discuss the problem of partial orientation. Some given grip per axis (i.e. some arbitrary fixed direction on the gripper) has to coincide with the prescribed direction in external space. In order to define a direction on the gripper we use a unit vector fi, where the tilde shows that the vector is expressed via projections onto the axes .... of the corresponding body-fixed system. So, the unit vector fi determines the direction with respect to the gripper b.-f. system. It is constant and represents the input value. The direction in external space will be prescribed by two angles e and ~ (Fig. 2.26). The angles determine the direction with respect to the external system. These two directions have to coincide. Let us point out that the b.-f. system and the external system need not coincide. Fig. 2.26. presents the de termination of a direction with respect to the b.-f. and to the exter nal coordinate system. Hence, the position vector is x g For posi tioning we use (2.4. 13), (2.4. 1 4) i . e \u2022 w n' q + 8' Dimensions of these matrices are: n' (3 x 5), 8' (3xl), q (5Xl). (2.4.33) (2.4.34) In the sequel we shall use transition matrices. Let Ag be the transi tion matrix of the gripper b.-f. system and let A be the transition matrix of the orientation coordinate system. Since the x-axis of the + orientation system coincides with the direction (b) the unit vector h can be expressed in the orientation system via projections [1 0 OlT. + So, the vector h can be expressed in the external system as (2.4.35) The second derivative is 62 (2.4.36 ) Introducing (2.4.22) into (2.4.36), one obtains (2.4.37) The matrix product Fe [1 0 O]T represents the first column of matrix Fe' Let us mark this column by f e1 . The first column of F~ is f~1 and the first column of F~ is f~1' Let it be noticed that f~1 = O. So, from (2.4.37) it follows or f e\u00b7\u00b7 f .. + G[1 OO]T e1 + ~1~ + G[1 OO]T If we introduce the notation u = G[1 OO]T then Dimensions of matrices are: h (3 x1), v (3 x 2), u (3 x1). (2.4.38) (2.4.39 ) (2.4.40) (2.4.41) On the other hand, the first and the second derivative of vector h may be expressed as . h t xh + t:; x(~ xh) g g g -+-+ -+ -+ -+ -hXE + W x(w xh) g g g were index g indicates the gripper. In matrix form -hE + a ~ g (2.4.42) (2.4.43 ) (2.4.44 ) ->- where h is analogous to (2.4.9) and a 63 ~ x(~ xh). The vector h expres g g sed in external system is obtained from one of these two expressions h A h g or h Expression (2.4.3b) or (2.4.13) gives A roo + A g q g Introducing (2.4.46) into (2.4.44) one obtains or where r' -hA rq = g r'q + <1>' -hA r = g hA + a = g <1>' -hA + a g (2.4.45) (2.4.46) (2.4.47) (2.4.48) (2.4.49) Dimensions of matrices are: h (3x1), r (3x5), r' (3x5), (3 X 1), <1>' (3 xl), q (5 x 1 ) , a (3 x 1 ), Ag (3 x 3) . Combining (2.4.41) and (2.4.48), it follows v~:J +u r' q + <1>'. (2.4.50) (2.4.50) represents a set of three equations which should be solved for two unknowns: e and ~. The left minimal inverse (the generalized inverse) [27] of matrix v is LM (vTv)-1 v T v (2.4.51 ) Now [:J vLMr' q + vLM('_u) \"---v--\" (2.4.52) r\" <1>\" or introducing r\" , <1>\" 64 r\" q + q,\" (2.4.53) Dimensions of matrices are: v LM (2x3), r\" (2x5), q,\" (2 x1), q (5 x1). NOw, equations (2.4.34) and (2.4.53) can be written together in the form x if [ ~:, ] [ 0' ] z q + q,\" 8 (2.4.54) Ii> or X Jq + A g (2.4.55) where the Jacobian and the adjoint matrix are J [ ~:, ] A [ ::.] (2.4.56) Dimensions of matrices are: Xg (5 x1), q (5 x1), J (5 x5), A (5 x1). Further procedure is as given in the general algorithm (2.4.57) It is evident that X, if, z, 8, Ii> have to be the input values. S, e, ~, ~ which are also needed for calculation are obtained by integration starting from the previous time instant. This integration is performed together with the integration over generalized coordinates. h also ap pears as input value. When we first introduced the angles S, ~ (in 2.4.2) we said that this approach may somet~mes result in some singularity problems. From Fig. 2.19. it is evident that if ~ ~/2 then the angle S cannot be defined (Fig. 2.27). In that case fS1 0 and the rank of matrix v is equal to 1. Hence the left minimal inverse v LM cannot be computed because of singularity problem. This singularity is called virtual singularity. 65 The adjective \"virtual\" is used to distinguish such singularity from the previously mentioned true singularity. In the case of true singu larity a manipulator really cannot move and rotate in all directions because of the loss of one d.o.f. In the case of virtual singularity no d.o.f. is lost and the manipulator can perform any motion. Such virtual singularity follows from the mathematical apparatus applied. z (b) ~ ~/2 8 undefined y x At the end we mention the possibility of defining the positioning in cylindrical or spherical coordinates. It can be done in a way analo gous to that explained for 4 d.o.f. manipulators. 2.4.5. Manipulator with six degrees of freedom The first block (block 6-1). As in the case of 4 and 5 d.o.f. we may choose position vector Xg = q and prescribe directly internal acceler ations ij1, ... ,ij6. The second block (6-2). In this case the manipulation task is defined in the following way: we prescribe positioning and partial orientation and also one internal coordinate directly, namely q6(t). Since positi oning is defined by x, y, z and partial orientation (one direction) by 8, ~, the generalized position vector is x g (2.4.58) It should be explained why this block is incorporated in the algorithm i.e. when it is suitable. To solve the desired position and partial orientation (one direction) five d.o.f. are needed. With most manipu- 66 lators the sixth d.o.f. is rotational and designed so that its axis of rotation coincides with the longitudinal axis of the gripper and the working object (Fig. 2.28). So by directly prescribing the correspond ing co~rdinate q6(t), the rotation of the working object around its axis is also prescribed (Fig. 2.28). The procedure of derivation of this block is similar to the procedure applied to 5 d.o.f. manipulators. In an analogous way we obtained equa tion (2.4.54) i.e. x y z [ 8' ] ,p\" (2.4.59) But the dimensions of matrices are now different: q (6 x 1), n' (3 x 6), 8' (3x1), r\" (2 x6), ,p\" (2 x 1). If we wish to obtain the Jacobian form, then (2.4.60) 8 ~ ______ ~y~ ______ -J) J 67 q can now be computed by the inverse of the 6x6 Jacobian matrix (2.4.61 ) Since verse Z, (i, q6 of iP, is given we can simplify this calculation and avoid the in the 6x6 matrix. Let us consider equation (2.4.59). If x, y, q6 (i.e. Xg) are input values, then (2.4.59) represents the system of 5 equations which should be solved for the 5 unknowns Q1' Q2' Q3' Q4' q5\u00b7 It is clear that the 5x5 matrix inverse now appears. The third block (6-3). A manipulator with 6 d.o.f. solves the positi oning task along with the task of total orientation. Positioning will be treated in external Cartesian coordinate system (x, y, z), so these coordinates will be included in the position vec tor Xg. Let us now discuss the problem of total orientation. When we consider the example in Fig. 2.20(b) we conclude that with the total orientation not only the direction (*) but also the direction (**) is important. So the total orientation may be considered in terms of two directions. Leter, we shall show that for the one direction given, the other is replaced by the rotation angle ~. Let us introduce the two directions: the main direction (b) and the auxiliary one (c). These directions are perpendicular to each other (Fig. 2.29). Let us first define these directions with respect to the gripper. For :t- ... such definition unit vectors hand 5 are used (Fig. 2.29). These vectors are expressed in the gripper b.-f. system. They are constant and represent the input values. In order do define the two directions (b), (c) with respect to the external system we use the three angles 6, ~, ~ (Fig. 2.29). The two directions on the gripper should coincide with the two directions in the external space. It should be pointed out that the gripper b.-f. system and the external system need not coincide. Hence, the generalized position vector is x = [x y z e ~ ~lT (2.4.62) g For positioning we use (2.4.13), (2.4.14) Le. 68 w Il'q + 0' Dimensions of matrices are: q (6x1), Il' (3x6), 0' (3 x 1). (2.4.63) Let A be the transition matrix of the gripper b.-f. system and A the g transition matrix of the orientation system. Since the x-axis of the orientation system coincides with the direction (b) the unit vector h can be expressed in the orientation system via projections [1 0 O]T. So, the vector h can be expressed in the external system as (2.4.64) From Figures 2.23 and 2.29 we conclude that the z-axis of the orienta->- tion system coincides with the direction (c). Hence the unit vector s can be expressed in the orientation system via projections [0 0 l]T and in the external system 69 (2.4.65) The following transformations are similar to those derived in the second block of 2.4.4. but they will be shortly repeated here. The second derivative of (2.4.64) gives By combining this relation with (2.4.22) one obtains (2.4.66) or (2.4.67) where fSl is the first column of matrix FS and f~l is the first column of F~. The first column of F~ is f~l = O. If we introduce the notation v h = [f Sl f~l]; (2.4.68) then (2.4.69) Dimensions of matrices are: h (3 x l), v h (3 x 2), u h (3 x l). In a way analogous to that in the second block of 2.4.4. one obtains . h -+ -+ w xh -+ g g g equation (2.4.71) becomes (2.4.71 ) (2.4.72) E r~q + ~ (2.4.73) where r' h -hA r ~ g h' = -hA + a h ~ g (2.4.74) Dimensions of matrices are: E (3 x1), q (6 x1), r (3 x6), r~ (3x6), (3 x 1), h (3 x 1), a h (3 x 1), Ag (3 x3). Combining (2.4.69) with (2.4.73) V h [:] + uh = rhq + h (2.4.75) Since v h is of dimensions (3 x2), system (2.4.75) is solved for [8 ~lT by using the left minimal inverse (2.4.76 ) Now (2.4.77) where <1>\" = vLM('_U ) h h h h (2.4.78 ) Dimensions of matrices are: v~M (2 x 3), r h (2 x6), h (2 x 1), q (6 x1). Now, for the vector s it follows from (2.4.65) that s (2.4.79 ) 71 By using (2.4.22) in (2.4.79) one obtains [ 001 8 + F lP (2.4.80) The matrix product Fe[O 0 1]T represents the third column of matrix Fe. Let this column be marked by f e3 . The third column of FlP is f lP3 and the third column of F~ is f~3. Thus (2.4.80) gives If we introduce the notation then v\" s + v\" ~ + u s s Dimensions of matrices are: s (3 x 1), Analogously to (2.4.70) one obtains ~ ->- ->- s Wg x s :>- ->- ->- ->- x (~ x~) s -s x E + W g g g and in the matrix form 5 -SE = g + as v' s u s G[O 0 1]T (3x 2) , v\" s (3 x 1 ) , u s (2.4.81 ) (2.4.82) (2.4.83 ) (3x 1) \u2022 (2.4.84) (2.4.85) where ~ = ~ x(~ x~), and the vector ~ in the external system is ob-s g g tained from one of these two expressions s = or s = (2.4.85a) If we introduce (2.4.72) into (2.4.85) it follows s (2.4.86) where 72 r I S -sA r\u00b7 = g , ~' s -sA ~ + a = g s (2.4.87) Dimensions of matrices are: 5 (3x1), q (6 x1), r (3 x6), r~ (3 x6), ~ (3 x1), ~~ (3 x1), as (3 x1). Combining (2.4.83) with (2.4.86) Let us now introduce (2.4.77) into (2.4.88) to obtain or v\" ~ s + u s v\" ~ = (r I -v I r\" ) q + ~ I - V I ~\" - u s s sh s sh s (2.4.88) (2.4.88a) (2.4.89) (2.4.89) represents a system of three equations which should be solved for ~. The left minimal inverse of v\" is s Now where v\"LM s ( \"T ,,) -1 \"T v v v s s s r\" = v\" LM (r I -v I r \" ) s s s s h ' (2.4.90) (2.4.91) LM ( ) ~\" = v\" ~ I -v I ~\" -u s s s sh s (2.4.92) Dimensions of matrices are: v~,LM (lx3), r~' (lx6), ~~' (lx1), q (6x1). Now, equations (2.4.63), (2.4.77) and (2.4.91) can be written together in the form x z [nl] [e l] r h q + ~h r\" ~\" s s (2.4.93) 73 or Xg Jq + A (2.4.94) where the Jacobian and the adjoint matrix are ~;~ 1 ~ 8'1 J A = ~h r\" ~\" s s (2.4.95) Dimensions of matrices are: Xg (6x1), q (6x1), J (6 x6), A (6 x1). The accelerations can now be calculated (2.4.96) It is evident that X, y, z, e, ~, ~ have to be the input values. 8, 8, ~, ~, ~, ~ are obtained by integration from the previous time instant. h, s also appear as input. The discussion on virtual singularities presented in the second block of 2.4.4. also holds here. During the derivation of the adapting blocks (the second block in 2.4.4. and the second and the third block in 2.4.5.) we have used the unit :t- :tvectors h, s to define the directions on the gripper. These vectors are expressed in the gripper b.-f. system. They are constant and represent the input values. But we can conclude from the derivation presented that these vectors are not necessary. The vectors fi, ~ are used only for the calcula~ion of ~, ;. From (2.4.45) and (2.4.85a) we see that the .... .... vectors h, s can be obtained by using the orientation system and thus :t- :twithout using h, s. Let us explain this. If the position of a manipulator is known (e.g. known q) and if the directions (b), (c) are known in the external system (e.g. known 8, ~, ~) then the relative orienta tion of these two directions with respect to the manipulator gripper is completely determined. Hence, determination of this relative orien tation by defining fi, ~ is unnecesary (superfluous). So, why do we still :t- :t. \u2022 \u2022 \u2022 use vectors h, s7 It was sald that the values of q, q, 8, S, ~, ~, ~, ~ in each time instant are obtained by integration from the previous time instant. Hence, in the initial time instant to all these values have to be prescribed. One possibility is to prescribe x, y, z, S, ~, 74 ~ in this initial time instant and compute q(to ) (for simplicity we assume that the manipulator starts from a resting position so all ve locities i.e. all first derivatives are equal to zero). But, in this approach we face the problem of calculating the internal coordinates q for known external coordinates X, i.e. q = n- 1 (X). In Para. 2.2. it was said that such procedure was very extensive and undesirable. Hence we use another approach. We prescribe q in the initial time instant (i.e. z ~ q(t )) and also h, s. Now the values of 8, ~, ~ are obtained by simple o * ~ calculation. This approach using h, s also offers a possibility of better visual relation with the task. Let us explain it by an example. If a manipulator has to move an object in an assembly task (Fig. 2.30) then the longitudinal axis (b) of the object and the perpendicular one (c) are essential. In order to define which directions on the gripper z ~ are important we use h = {O, 1, O}, s = {-1, 0, O}. In this way we de- fine directly the relative orientations of directions (b), (c) with respect to the gripper. From the standpoint of visual relation with the task we consider this approach to be more convenient than the de finition of relative orientations in terms of absolute position of the manipulator and the absolute orientations of (b), (c) with respect to external system. Anyhow, these two approaches are both possible, and the user will choose one of them. For better understanaing of this block consult the example in 2.8.4. 2.4.6. Velocity profiles and practical realization of adapting blocks 75 In the paragraphs dealing with the derivation of adapting blocks it was said that each block uses its special generalized position vector Xg which represents set of parameters defining a manipulator position. Theinternal and the external coordinates may appear as the elements of Xg . If a manipulator has n d.o.f. then the generalized position vector is of dimension n. Let Pl' P2, ..\u2022 ,Pn be parameters defining a manipu lator position. Then the generalized position vector is (2.4.97) It was explained that an adapting block operates in such a way that for some time instant it calculates q on the basis of known Xg . Hence Xg is needed in each time instant. The algorithm also uses the values of the parameters and their first derivatives. It does not hold for all para meters but only for those defining the gripper orientation (e.g. 8, ~, . w). For genera:ity we say that Xg , Xg are also needed in each time instant. Xg and X in some time instant are computed by integration g - starting from the previous time instant. Thus, X for each time instant . g represents the input. In order to start the time iterative procedure we also need the initial values of Xg ' Xg i.e. Xg(to )' Xg(to )' The procedure described is completely general and can be used for any trajectory. But, for some given manipulation task it is not so easy to find the values of X in a series of time instants. Hence, we develop . g a subroutine which prepares these data for some typical manipulation tasks. We consider manipulator motions where Xg changes from one given value to another with the triangular or trapezoidal velocity profile. The triangular profile for one of parameters is shown in Fig. 2.31a. We define this profile by a constant acceleration and deceleration: 4l1Pi 4(p~nd _ p~tart2 a. 1. 7 T2 (2.4.98) Now \u00b0ri t < T/2 (tEAB) p. (t) 1. -a. t > T/2(tEBC) 1. (2.4.99) 76 The algorithm operates with discretized time. Let the interval T be di vided into 60 subintervals ~t by using a series of time instants to' t 1 , .\u2022. ,t60 . Let Pi~ be the acceleration in time instant t~. Now, in discretized form: ={ ai' ~ 0, 1, ... ,29 PH -ai~ ~ 30, 31, ..\u2022 ,59 (2.4.100) D ta p.=p~tart T p.=p~nd 1 1 1 1 Fig. 2.31b. Trapezoidal profile of parameter velocity Repeating the procedure (2.4.100) for each parameter one obtains Xgfor all time instants. This is done and stored in the computer memory be fore starting the time-iterative algorithm. Thus only the starting and the terminal position of manipulator together with the execution time have to be prescribed (i.e. xstart, xend , T). The number of subintervals g g (it has been assumed to be 60 here) can be changed as wished. Let us explain what this triangular profile means in practice. If Xg=q then each internal coordinate changes between the two given values with constant acceleration and deceleration. Let us now consider another case: Xg [x y z 6 ~ ~]T. Then the triangular velocity profiles for parameters x, y, z produce straight-line motion of the gripper with ... the triangular profile of gripper velocity v g \u2022 Rotations 6, ~, ~ also follow such a profile. The trapezoidal velocity profile is shown in Fig. 2.31b. Such motion is sometimes called the motion with constant velocity because the velocity is constant over the longest part of the trajectory. For such motion 77 one has to prescribe the initial and the terminal p~nd, i=1, \u2022\u2022\u2022 ,n) together with the execution time 1 . t. (. start POS1 10n 1.e. Pi T and the accelera- tion (deceleration) time tao The subroutine procedure computes the constant value of acceleration: a. 1 end start Pi - Pi and the values of Pi' i=1, ... ,n: ail t -< t a i\\ (t) { 0 \u2022 ta -< t -< T - -a. : t > T - t 1 a (2.4.101) (t E AB) t (t E Be) a (2.4.102) (t E eO) If Xg = [x y z 8 ~ ~], then the trapezoidal velocity profiles for pa rameters x, y, z produce straight line motion of the gripper with the + trapezoidal profile of gripper velocity v g . We have discussed the two most common velocity profiles. Let us notice that the initial and terminal velocities equal zero. Some additional subroutines can be prepared for any other desired profile. In order to obtain a more general algorithm we consider a trajectory which consists of several segments each of them being of triangular or trapezoidal type. Let there be m segments of trajectory i.e. let a ma nipulator move sequentially into m given points A1 , \u2022\u2022. ,Am starting from the initial point Ao (Fig. 2.32). 2.32. Manipulator trajectory So, it is first necessary to pre scribe the number of points m. Then we prescribe the positions of divi sion points A1 , A2 , ..\u2022 ,Am in terms of Xg1 , Xg2 ' ..\u2022 'Xgm Now if a tran sition Ak _1+Ak is of triangular type then Tk is prescribed and if it is of trapezoidal type then Tk, t~ are prescribed (k is\u00b7 not exponent but upper index). Special indicators are used to define the profile of each transition. For the trapezoidal profile the value of the indicator is 1 and for the triangular profile 78 the value is 2. Let it be noticed that in the case of triangular and trapezoidal profiles a manipulator stops in each point A1 , \u2022\u2022\u2022 ,Am. There is another transformation incorporated in the algorithm. It was said that e, ~, ~ have to be prescribed in each point Ai' in order to define the directions (b), (c) with respect to the external space. But it is sometimes easier to determine the external projections of the + + corresponding vectors hand s then determine the angles e, ~, ~. In that case we prescribe h, ~ (with respect to external system) in each division point A1 , \u2022\u2022\u2022 ,A and there is a subroutine which computes e, ~, + m ~. Prescription of h is equivalent to the prescription of a plane per + pendicular to h. At the end of 2.4.5. it was explained that there are two possibilities for the initial point Ao. For that point we can prescribe X and comgo pute the initial position q(to ) necessary for the algorithm start. In order to avoid the extensive calculation q = n- 1 (X ) we suggest that g the initial state be directly prescribed and then simply calculated X n(q). It is due to the fact that manipulators usually start from g some well known starting position so q(to )' q(to ) can easily be determined. If sometimes the determination of q(to )' q(to ) is complicated then we suggest to start the algorithm from some new initial point in which the state is known and move the manipulator towards the old ini tial point which is now the first point in the sequence. The trajectory described is not completely general but is general enough for the aim of the algorithm. It covers most manipulation tasks in prac tice. Anyhow the algorithm can be generalized by developing and incor porating some additional trajectory-input subroutines." + ] + }, + { + "image_filename": "designv10_6_0003276_1.2336803-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003276_1.2336803-Figure4-1.png", + "caption": "FIG. 4. Geometry of a thin viscous rope. The Cartesian coordinates of the rope\u2019s axis relative to an arbitrary origin O are x s , t , where s is the arc length along the axis and t is time. The rope\u2019s radius is a s , t . The unit tangent vector to the axis is d3 s , t x , and d1 s , t and d2 s , t d3 d1 are material unit vectors in the plane of the rope\u2019s cross section. The Cartesian unit vectors ei are fixed in the reference frame rotating with an angular velocity equal to the angular frequency of steady coiling.", + "texts": [ + " Because our goal is to perform a linear stability analysis of steady coiling, we write the equations in a reference frame that rotates with angular velocity e3 relative to a fixed laboratory frame. The Einstein summation convention over repeated indices or subscript/superscript pairs is assumed. Greek indices range over the values 1 and 2 only. Latin indices range over the values 1, 2, and 3 except for the Euler parameters qi, in which case i=0, 1, 2, and 3. The quantity ijk is the usual alternating tensor. Finally, derivatives with respect to arc length along the rope axis are denoted by primes. Figure 4 shows the geometry of an element of a thin viscous rope. Let x s , t be the Cartesian coordinates of a point on the rope\u2019s axis, where s is the arc length along it and t is time, and let di s , t be a triad of orthogonal unit vectors ticle is copyrighted as indicated in the article. Reuse of AIP content is subje 139.184.30.132 On: Tue, 1 defined at each point on the axis. The tangent vector to the axis is d3, and d1 and d2 d3 d1 are material vectors normal to the axis that follow the rotation of the fluid" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000190_tro.2020.3047053-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000190_tro.2020.3047053-Figure1-1.png", + "caption": "Fig. 1. CardioMag, a large-scale eight-electromagnet eMNS.", + "texts": [ + " Downloaded on May 19,2021 at 19:47:09 UTC from IEEE Xplore. Restrictions apply. expense of intractable computation times associated with solving the governing electromagnetic boundary-value problems. In this work, we restrict our study to mathematical models, and more particularly models, which can be obtained from magnetic field data rather than from a priori information about a MNS. We primarily focus our efforts on eMNS with stationary electromagnets. When appropriate, we use data from the CardioMag [10] shown in Fig. 1, a clinical-size eMNS with eight electromagnets, because it exhibits most of the properties that render modeling an eMNS complex, namely a large workspace, a large number of electromagnets, and nonlinear magnetization. In this article, we contrast methods that are based on mathematical interpolation, and assume that the magnetization is linearly related to electromagnet currents and that the measurements are error free, described in Section III, from models that are fit to data using error minimization techniques, described in Section IV" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000474_s00170-020-06432-1-Figure15-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000474_s00170-020-06432-1-Figure15-1.png", + "caption": "Fig. 15 a The system of monitoring equipment. b 1\u20134, the location of flashes; 5, the location of chamber lights (reproduced from [50], Copyright (2017), with permission from Elsevier)", + "texts": [ + " The device can well evaluate the thermal history of forming and associate with forming quality. Abdelrahman et al. [50] described a device for monitoring fusion defects of powder bed by using optical imaging technology, as shown in Fig. 16. The system is equipped with a 36.3 megapixel DSLR camera (Nikon D800E) with an image size up to 7360 \u00d7 4912 pixels. The device with multiple flash modules is installed in the cabin of EOS M280, which can obtain images after powder scattering and laser exposure. Four photos are taken by flash 1\u20134 (the position of flash is shown in Fig. 15) after repainting, and one photo is taken when indoor lighting is turned on. The acquired image is segmented by the binary template. The intentional defects are designed into the parts at different positions, and then, the defects are detected automatically. The results showed that the accuracy is high. The laser may be affected by the characteristics of the lens in the Lagrange coordinate system when using coaxial monitoring. The laser is easily affected by the angle and distance when using paraxial monitoring, even if the strong signal is received in the Eulerian reference frame" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002663_mssp.2000.1345-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002663_mssp.2000.1345-Figure1-1.png", + "caption": "Figure 1. Unconstrained rigid body.", + "texts": [ + " The equations of motion for an unconstrained rigid body written down for an arbitrary reference point A are [1}3] 0888}3270/01/010189#23 $35.00/0 ( 2001 Academic Press mrK A !mr AC ]u5 \"f A !mu](u]r AC ) (1a) mr AC ]rK A #H A )u5 \"t A !u](H A )u) (1b) where m is the mass; rK A the vector of translational accelerations; r AC the vector from point A to centre of gravity C; u the vector of angular velocities; f A , t A the vectors of external forces, torques and H A the inertia tensor with respect to point A. We now introduce a global inertial reference frame G (x, y, z) and a local body-\"xed reference frame \u00b8 (m, g, f) (see Fig. 1). The transformation of quantities a (accelerations, forces) from global (G) into local (L) coordinates can be described via the orientation matrix B (matrix of Bryant angles, successive rotation about the angles t i , [1}3]): am ag af \" c 2 c 3 !c 2 c 3 s 2 c 1 s 3 #s 1 s 2 c 3 c 1 c 3 !s 1 s 2 s 3 !s 1 c 2 s 1 s 3 !c 1 s 2 c 3 s 1 c 3 #c 1 s 2 s 3 c 1 c 2 a x a y a z (2) hij hgggggggigggggggj hij aL B aG where s i , c i are sine, cosine of Bryant angle t i (i\"1, 2, 3). If the gravitational acceleration g is assumed to point in the negative z-axis direction, equations (1a) and (1b) can be rewritten using matrix notation as m 0 0 0 m 0 0 0 m , m 0 f AC " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002513_026404197367137-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002513_026404197367137-Figure2-1.png", + "caption": "Figure 2 Illustration of the ball during contact. In the left-hand diagram (time = t0), the ball has just touched the surface and may be sliding. The middle diagram shows the impulsive force due to friction that is applied to the ball. The right-hand diagram (time = t1) shows the ball just before losing contact with the surface. The impulsive frictional force has stopped the ball from sliding.", + "texts": [ + " When the ball bounced on either the torus or the backboard, it was assumed that the component of the speed of the ball\u2019s centre of mass which was perpendicular to the surface was reduced by the square root of this fraction: vn(t1) = - \u00ce kvn(t0); k = 1.3 + r 1.8 - r (4) The component of the velocity of the ball\u2019s centre of mass which is tangential to the surface is coupled with the spin through the assumption that, at time t1, the ball is not sliding on the surface: (t1)rb = v t(t1) (5) Applying a suitable impulse to the ball when it contacts a surface (Fig. 2) yields two equations: mvt(t0) + F(t1 - t0) = mv t(t1) (6) I (t0) - F(t1 - t0)r = I (t1) (7) Using the inertial properties of a hollow sphere (I = m 2 3 r2 b) and equations (5), (6) and (7), the solutions D ow nl oa de d by [ E as te rn K en tu ck y U ni ve rs ity ] at 0 7: 46 1 8 M ar ch 2 01 3 for the departing tangential speed and spin can be derived: v t(t1) = 1 5 (3v t(t0) + 2 (t0)rb) (8) (t1) = 1 5r (2 (t0)rb + 3v t(t0)) (9) A computer program simulated a ball release 4 m behind (l = 4 m) and 1 m below (h = 1 m) the centre of the hoop: (y, z) = (-4, -1)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002647_tcst.2002.806450-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002647_tcst.2002.806450-Figure1-1.png", + "caption": "Fig. 1. ROCSAT-3 satellite on-orbit configuration.", + "texts": [ + "ndex Terms\u2014Linear matrix inequality (LMI), nonlinear control, spacecraft attitude control. I. INTRODUCTION THE ROCSAT-3 program is to develop a constellation of six low-earth orbiting satellites for operational weather prediction, space weather monitoring, and climate research. Each ROCSAT-3 satellite is a micro satellite of approximately 40 kg in weight. Fig. 1 gives a schematic representation of the ROCSAT-3 spacecraft. The ROCSAT-3 payload system, called Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC), will have three primary payloads: 1) advanced GPS receiver; 2) tiny ionospheric photometer; and 3) tri-band beacon transmitter. The operation scenario of the ROCSAT-3 is illustrated in Fig. 2. The ROCSAT-3 attitude determination and control system (ADCS) is designed to be pitch momentum biased with the boom structure nadir pointing" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003508_tac.2008.2009615-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003508_tac.2008.2009615-Figure3-1.png", + "caption": "Fig. 3. Experimental Furuta pendulum system.", + "texts": [ + " Taking the derivative of both sides of this equation with respect to where Thus, the following equation is obtained: Express the quantity from that equation Then for the inequality (12) to be true, the following should hold: (13) Then for the real part of , we can write (14) Representing the transfer function in the exponential format and taking the derivative with respect to leads to the following inequality: (15) or finally to formula (11). Therefore, the stability of the periodic motion is determined just by the slope of the phase characteristic of the plant, which must be steeper than a certain value for the oscillation to be asymptotically stable. In this section, we present experimental results using the laboratory Furuta pendulum, produced by Quanser Consulting Inc., depicted in Fig. 3. It contains a 24-Volt DC motor that is coupled with an encoder and is mounted vertically in the metal chamber. The L-shaped arm, or hub, is connected to the motor shaft and pivots between 180 degrees. At the end, a suspended pendulum is attached. The pendulum angle is measured by the encoder. As described in Fig. 3, the arm rotates about axis and its angle is denoted by while the pendulum attached to the arm rotates about its pivot and its angle is denoted as . The experimental setup includes a PC equipped with an NI-M series data acquisition card connected to the Educational Laboratory Virtual Instrumentation Suite (NI-ELVIS) workstation from National Instrument. The controller was implemented using Labview programming language allowing debugging, virtual oscilloscope, automation functions, and data storage during the experiments" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002682_1.1843161-Figure13-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002682_1.1843161-Figure13-1.png", + "caption": "Fig. 13 Contact between normally crossing cylinders: \u201ea\u2026 geometry of cylinders; and \u201eb\u2026 the contact ellipse", + "texts": [ + " The midplane distributions of the pressure, film thickness, and oil temperature in the middle layer of the film (Z50.5) together with the corresponding Newtonian results are presented in Fig. 12. Although the pressure, the depth of the dimple, and the oil temperature decrease when t0 decreases, the differences between non-Newtonian solutions and the Newtonian solution are not very large. It can be concluded that, the effect of non-Newtonian behavior on the dimple is small. For normally crossing cylinders shown in Fig. 13~a!, let the lower cylinder be cylinder a, its tangential velocities along x and y directions are ua and va , respectively; similarly, the upper cylinder is cylinder b, its tangential velocities along x and y directions are ub and vb , respectively. It is obvious that this problem is a point contact one and the contact ellipse is shown in Fig. 13~b!. Different from the usual point contact problem, in the current problem the contact has velocities both along x and y directions. It is assumed that each cylinder rotates independently without axial motion, i.e., ua50 and vb50, so that the slide-roll ratios along x and y directions are always equal to 22.0 and 2.0. The global entrainment velocity is not along x and y directions but has an angle between the x axis. The generalized Reynolds equation for this problem is more complicated than that in Refs" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002837_physrevlett.84.1631-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002837_physrevlett.84.1631-Figure4-1.png", + "caption": "FIG. 4. Front propagation along a helix. Two possible modes are (A) crankshafting and (B) speedometer cabling.", + "texts": [ + " To estimate front velocities involving helical shapes (below), note that the essential physics of this result is a balance between the power generated from the transition to the less energetic twist state, Ptw DV c, and the power lost due to rotational drag, Prd R zrv 2ds zr DV 2jc2, where v DV c is the axial rotation rate and DV V1 2 V2, giving c DV zr DV 2j. While inertial and viscous front propagation naturally lead to rotation of the unstable helix, there are two types of motion that allow this: crankshafting, in which one helix rigidly pivots about the axis of the other, and speedometercable motion where each helix rotates about its own axis (Fig. 4) [2]. Here we outline simple scaling arguments for these dynamics; a more detailed discussion is presented elsewhere [8]. In a viscous fluid, we might expect the mode requiring the least power dissipation to be favored. The dissipation P is simply the integrated product of the force per length and the velocity. For crankshafting, Pcr z v 2L3 sin2 a 3, while for speedometer-cable motion Psp z R2v2L, where L is the total arclength of the moving segment. Crankshafting dominates unless R L sin a 2 \u00f8 1, in which case speedometer-cable motion takes over" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002756_0278364904047393-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002756_0278364904047393-Figure2-1.png", + "caption": "Fig. 2. Rear foot at toe-off, and front foot at heel-touch.", + "texts": [ + " The first coordinate q1 will be assumed to remain constant during the SSP, namely t \u2208 [t i , t t ] , q1(t) = \u03c0 \u2212 \u03b2, (2) while in the DSP, the vector q in eq. (1) is subjected to closure constraints that can be written as (see Figure 1 for the notations) at Universitats-Landesbibliothek on December 31, 2013ijr.sagepub.comDownloaded from t \u2208 [t t , t f ] , { C1(q(t)) \u2261 Oi 1A t 6 \u00b7 X0 \u2212 L+ = 0 , (3) C2(q(t)) \u2261 Oi 1A t 6 \u00b7Y0 = 0, (4) \u2208 [t t + \u03b5, tf ] , C3(q(t)) \u2261 \u03c6(q(t)) = 0. (5) In eq. (2), \u03b2 is the angle of the foot triangle at the tip Bi 6 (Figure 2). ConstraintsC1 andC2 in eqs. (3) and (4) specify the Cartesian coordinates of the contact point At 6 of the heel of the front foot. In eq. (3), L and denote the step and foot lengths, respectively. In eq. (5), \u03c6 represents the inclination angle of the front foot with the ground; \u03b5 is a short duration, after which the front foot remains flat on the ground, as specified by the constraint C3. In the following, constraints such as eqs. (3), (4), and (5) will be put together in the vector-valued function Ch defined as Ch(q) = (C1(q), " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000280_j.matdes.2021.109843-Figure15-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000280_j.matdes.2021.109843-Figure15-1.png", + "caption": "Fig. 15. 3D distribution (the Y 0 half) of aB and b for the 3000 W FL case.", + "texts": [ + " And there is no significant difference in a-lath thickness between the two cases. In other words, the laser power 3000 W helps in increasing the aB fraction without increasing the a-lath thickness. Besides, as it can be seen in Fig. 12, the forming surface of the 3000 W case is flatter than the 2500 case. Therefore, the laser power 3000 W helps in increasing the forming stability during the multi-layer deposition. The laser power 3000 W is the optimal processing parameter. The 3D distribution (the Y 0 half) of aB and b for the 3000 W FL case is shown in Fig. 15. The main constituent phases are aB and b. In the additive part, the capacity of heat dissipation makes different phase fractions. At the center, the fraction of aB is around 0.8 and the fraction of b is around 0.2. At the ends, the fraction of aB is around 0.5 and the fraction of b is around 0.5. Similar to what has been stated in the SL cases, the predicted b fraction seems larger. Take all the above SL and FL cases into consideration. The DCPM used in the research shows accuracy in prediction phase fractions and a-lath thickness during WLAM" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002580_s002211200300689x-Figure11-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002580_s002211200300689x-Figure11-1.png", + "caption": "Figure 11. Finite venetian blind locomotor dragging a body.", + "texts": [ + " It is not clear from figure 7 what asymptotic behaviour is obtained for the oscillating Oseenlet, although the higher power is suggested. We emphasize that the nonlinear term in (7.4a) is needed to reach equilibration. This is the reason for our claim that the bifurcation to reciprocal flapping flight is necessarily accompanied by departure from the Stokesian realm of locomotion. These general arguments have their counterpart in the venetian blind model, but since the problem is linear in \u03c3 (see Appendix B), the only nonlinearity can come from a modification of the model by the addition of a passive element producing drag, see figure 11. Then if Re\u03c9 > Re\u03c9c we have \u3008D\u3009 = DB , where DB is the dimensionless drag of the attached body. Once supercritical, DB = C Ref Re2 \u03c9 (Re\u03c9 \u2212 Re\u03c9c), (7.8) where C is a positive constant. In our dimensionless formulation, in the Stokesian realm, body drag would be K\u03bdLUf for some positive constant K or in dimensionless form KRef /Re2 \u03c9 per unit area of blind. Thus K = C(Re\u03c9 \u2212 Re\u03c9c) and Ref remains undetermined. We must then modify the drag law by a nonlinear correction, DB = KRef / Re2 \u03c9(1 + \u03b1Ref ), \u03b1 > 0, (7" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000146_s40684-021-00348-1-Figure6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000146_s40684-021-00348-1-Figure6-1.png", + "caption": "Fig. 6 Conditions of the simulations for assessing (left)\u00a0displacement and (right)\u00a0stress", + "texts": [ + " For ease of analysis, it is assumed that the finger just has isotropic material properties from a combination of multiple 3D printed layers in different directions. As shown in Fig.\u00a05, the experiments and simulations exhibited similar displacements, with an error range of 0.04\u20130.2\u00a0mm. Therefore, the reliability of determined mechanical properties was sufficient. The values are listed in Table\u00a01. Modeling and simulation were executed with CATIA V5 software. In the simulations, the displacement of each finger and the stress on the object were measured. To simulate displacement, the bottom of the finger was fixed, as shown in the left part of Fig.\u00a06, and a uniformly distributed load with a total magnitude of 10\u00a0N was imposed on the surface 1 3 contacting the object. A distributed, rather than concentrated, load was applied to assess the overall deformation of the finger. In the stress simulation, the maximum stress that a finger would exert on a steel bar while gripping was obtained by applying a uniformly distributed load of 10\u00a0N to the fingertip. As shown in the right part of Fig.\u00a06, the bottom of the finger was clamped, and a steel bar was fixed in position. The bar was 55\u00a0mm from the base of the finger, as is typical when gripping an object. After the finger deformed, the maximum displacement does not always occur at the fingertip with respect to the structure geometry. Nevertheless, as the gripping of the object was strongly influenced by the displacement of the fingertip, the displacement of the fingertip was considered as the main result, as well as the stress exerted on a steel bar" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure2.42-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure2.42-1.png", + "caption": "Fig. 2.42. Components of linear deviation", + "texts": [ + " we distinguished two sorts of linear joint and introduced the corresponding indicators Pi (relation (2.5.6)). ->- NOw, the length R,i of a segment (between the two joints) is 1. 1 n. 1 1 1+ -+ +-+ -+ r i i + siP i q i e i + r i , i + 1 + s i + 1 (1 -p i + 1 ) q i + 1 e i + 1 (2.5.24) For standard form segments, with the zi-axis of b.-f. system placed along the cane, it holds ->- 'k:. 1 (2.5.25) For the gripper and its point A the length is defined as (2.5.26) ->- Calculation of deformations. Linear deviation u i consists of three or two components (Fig. 2.42) depending on whether the segment \"i\" is elastic or rigid: ->- ->-eR, ->- ->- u i _ 1+ui +~i_1XR,i' ->- ->- -t u. 1 +~. 1 xx,. 1- 1- 1 k . e1 k . e1 (2.5.27) o ->-eR,. h 1 f h 1 u i 1S t e component resu ting rom tee astic deformation of segment \"i\". For the angular deviation one obtains 1 ->- ->-eR, k ->- ~i-1+~i ' ei ~i (2.5.28) ->- ~i-1 k ei 0 h h ->-eR, results f th 1 . d f f t were t e component ~i rom e e ast1c e ormation 0 segmen \"i\". 92 Relations (2.5.27) and (2.5.28) make possible the recursive calculation -+ -+ -+-+ of deviations u i and ~i starting with Uo = 0, ~o = O" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000208_j.matdes.2021.109725-Figure19-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000208_j.matdes.2021.109725-Figure19-1.png", + "caption": "Fig. 19. Tensile properties for orientations perpendicular (X-Y plane) and parallel (Y-Z plane) to the vertical build direction in post solution heat treated LPBF Haynes 282 at 850 C.", + "texts": [ + " dicular (X-Y plane) to the vertical build direction in post solution heat treated LPBF Haynes 282. The more isotropic mechanical behaviour found in the post solution heat treated material, as indicated by the hardness tests, is further supported by tensile tests at 850 C on round cylindrical specimens extracted from both the parallel (Y-Z) and perpendicular (X-Y) planes to the vertical build direction. This can be seen in relation to the 0.2% proof stress and ultimate tensile strength values displayed in Fig. 19, where the samples taken perpendicular to the primary build orientation offer a marginally superior tensile performance, although the difference across the two alternative orientations would be considered to lie within the natural variation of tensile data. A marginal increase is again observed in elongation values as the parallel orientation is seen to exhibit a slightly more ductile response. This may be a remnant of the build orientation, however this variation is small in the context of the overall values of elongation which encouragingly exceed 30% in both the parallel and perpendicular orientated materials" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003926_1077546307080026-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003926_1077546307080026-Figure4-1.png", + "caption": "Figure 4. Pitting stages used in the experiments.", + "texts": [ + " In such cases, a pitting fault may occur in time on the tooth surfaces on which a higher load is experienced. Simulated surface pits were introduced on some of the pinion gear teeth using an electro-erosion machine, as shown in Figure 3, and were intended to replicate a pitting failure, initiating on a single tooth and then developing over the neighbouring tooth surfaces. First, a circular pit (whose diameter and depth are approximately 0.7 mm and 0.1 mm respectively) was seeded onto a single tooth surface as shown in Figure 4(b). This gear tooth, called the centre tooth, was positioned such that it came into mesh at approximately 300 pinion rotation. After that, in order to represent the progression of the fault, the number of defective teeth was increased to five and additional pits were introduced as shown in Figure 4(c) (5 pits total on the centre tooth, 3 pits on the adjacent two teeth, and 1 pit on each of the other two teeth). In the third stage, the severity of fault was increased by once more doubling the number of pits on these teeth. For the final stage of fault development, the number of pits was doubled again, and the surface of the centre tooth was completely covered by severe pitting marks as shown in Figure 4(e). at UNIVERSITE LAVAL on May 10, 2015jvc.sagepub.comDownloaded from at UNIVERSITE LAVAL on May 10, 2015jvc.sagepub.comDownloaded from During the tests, the speed of test pinion was set to 2678 rpm, giving a fundamental tooth meshing frequency of 1294 Hz for the first stage, and 420.7 Hz for the second stage. The vibration and positioning signals were sampled at 15 kHz and stored on a computer. The raw vibration data was continuously collected over 1338 pinion rotations and the frequency domain approach (Futter, 1995) was used to determine the residual vibration" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003742_1.4000277-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003742_1.4000277-Figure3-1.png", + "caption": "Fig. 3 Vertical displacement measuring points", + "texts": [ + " 2 were used. A vertical load FV was applied to the carriage of the test linear bearings through a block, load cell NMB: C2M1-500 K, Kanagawa, Japan using a universal testing machine Shimadzu Corporation: DSS-25T, Kyoto, Japan , while the rail was fixed to the bed with bolts. The vertical load FV varied from 12.6 N to 2000 N. The lowest value of FV, which is 12.6 N, was the initial load FV0, which was sum of the weights of the carriage and the block. The vertical displacement measuring points are shown in Fig. 3. JANUARY 2010, Vol. 132 / 011102-110 by ASME of Use: http://www.asme.org/about-asme/terms-of-use T t w m 0 Downloaded Fr he vertical displacement was measured using electric comparaors A-C Feinpr\u00fcf: 1318, G\u00f6ttingen, Germany at three points here the block is attached to the carriage. The vertical displaceent was measured with reference to the initial vertical displace- 11102-2 / Vol. 132, JANUARY 2010 om: http://tribology.asmedigitalcollection.asme.org/ on 01/27/2016 Terms ment v0 under the initial vertical load FV0", + " The overview and cross section of the FE model for calculating the deformations of the carriage and rail are shown in Figs. 10 and 11, respectively. In the FE model, a block was attached to the carriage and the rail was fixed to the ground with bolts. To model the carriage, block, and rail, a solid element was chosen in COS- nite element model JANUARY 2010, Vol. 132 / 011102-5 of Use: http://www.asme.org/about-asme/terms-of-use M a u r g t t g p q a w e r u p 0 Downloaded Fr OSWORKS. Since the cross section of the test bearings is bilaterlly symmetrical, as shown in Fig. 3, a symmetrical FE model is sed, as shown in Figs. 10 and 11. In the FE analysis, if the concentrated forces, which are the eaction forces of the ball load Qij, are applied to the raceway rooves of the carriage and rail, the deformations at the points of he concentrated force applications are overestimated. To prevent hose overestimations, the reaction forces acting on the raceway rooves of the carriage and rail were modeled by the uniform ressures qic and qir, respectively. The areas under the pressures ic and qir are shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000472_j.wear.2021.203685-Figure8-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000472_j.wear.2021.203685-Figure8-1.png", + "caption": "Fig. 8. Sliding distances of a pinion and a gear.", + "texts": [ + " The sliding distance presented by Flodin and Andersson [31] is described as follows ( Sp ) r\u2192r+1 = Sap \u20d2 \u20d2 \u20d2 \u20d2 v2 v1 \u2212 1 \u20d2 \u20d2 \u20d2 \u20d2 (21) ( Sg ) r\u2192r+1 = Sag \u20d2 \u20d2 \u20d2 \u20d2 v1 v2 \u2212 1 \u20d2 \u20d2 \u20d2 \u20d2 (22) H. Wang et al. Wear xxx (xxxx) xxx where Sap and Sag are the moving distances of the pinion and gear from position r to position r+1, respectively. v1 and v2 are respectively the tangential velocities of the contact points on the pinion and gear. The coordinate transformation method presented in Ref. [42] is applied to this work. As depicted in Fig. 8, in the initial coordinate system X1O1Y1, origin O1 is on the pinion\u2019s center, and X1-axis passes through the two centers of the gear pair. In the transformed coordinate system X2B2Y2, origin B2 is set on the approach point, and X2-axis is set along the line of action (LOA). Then, from r to r+1 (r = 1, 2, 3, \u2026, R-1), the moving distance of the gear drive is expressed as (Sa)p,g = \u20d2 \u20d2 ( Y2(p,g) ) r+1 \u2212 ( Y2(p,g) ) r \u20d2 \u20d2 (23) In accordance with Eqs. (21) and (22), the sliding distances of point and gear are respectively written as ( Sp ) r\u2192r+1 = \u20d2 \u20d2 ( Y2p ) r+1 \u2212 ( Y2p ) r \u20d2 \u20d2 \u20d2 \u20d2 \u20d2 \u20d2 v2 v1 \u2212 1 \u20d2 \u20d2 \u20d2 \u20d2 (24) ( Sg ) r\u2192r+1 = \u20d2 \u20d2 ( Y2g ) r+1 \u2212 ( Y2g ) r \u20d2 \u20d2 \u20d2 \u20d2 \u20d2 \u20d2 v1 v2 \u2212 1 \u20d2 \u20d2 \u20d2 \u20d2 (25) Euler\u2019s method is used to integrate Eq", + " At the microlevel, a small roughness value between contact surfaces may cause a large change in contact pressure. H. Wang et al. Wear xxx (xxxx) xxx The geometry, operation, and wear parameters that are used in the wear prediction of a spur gear drive are indicated in Table 4. Assuming that the initial profile of the pinion and gear is standard involute (\u03ba = 0), in accordance with Eq. (17), the initial load-sharing factor \u03b10 is shown in Fig. 13(a). Along LOA, the positive direction is from approach point B2 to recession point B1 and the origin is set on the pitch point (Fig. 8). Given the mesh stiffness of spur gears is time varying, along with LOA, the initial load-sharing factor increases at the first double-tooth contact, equals to 1 at the single-tooth contact, and decreases at the second double-tooth contact. On the basis of Eq. (19), the load of a contacting gear tooth pair is considerably determined by the load-sharing factor because the total load has not changed. As described in Fig. 13(b), the variation tendency of contact force is the same as the variation trend of the load-sharing factor" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure18.18-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure18.18-1.png", + "caption": "Fig. 18.18 Gyro-sensor and its equivalent circuit", + "texts": [ + "16, and the maximum efficiency is approximately 4 to 6%. The difference in the characteristics by the rotation direction and several problems must be improved by the structural modifications. However, it is found that a potentiality of the single crystal ultrasonic motor which consumes low power exists. We also investigated a new motor, the operation principle of which depends on a vibratory gyro. Figure 18.17 shows the disk-type vibratory gyro, and its basic principle is shown by the equivalent circuit in Fig.18.18. By inputting the moments M1 and M2 and considering the phase difference between them, the moment M3 is generated and rotates the rotor. This motor is referred to herein as the gyromoment motor (GMM). [9, 10] A number of GMMs are shown in Figs. 18.19 and 18.20. The CW and CCW rotation of the rotor can be determined easily by setting the phase difference between the moments M1 and M2. The driving method of the electromagnetic-type GMM is shown in Fig.18.21, which shows the directions of rotor rotation for the driving methods" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000389_s10846-021-01325-1-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000389_s10846-021-01325-1-Figure1-1.png", + "caption": "Fig. 1 Schematic of a quadrotor", + "texts": [ + " Section 5 discusses closed\u2013loop stability and the results on performance evaluation and comparison of the proposed controller with NDI design are presented in Section 6. In the same section, Monte\u2013Carlo simulation and experimental results are presented. Lastly, Section 7 concludes this work. 2Mathematical Model and Problem Formulation Mathematical model of a plus (+) configured rigid quadrotor with symmetrical axis as derived using Newton\u2013Euler formulation [15] is discussed in this section. The quadrotor, shown in Fig. 1, consists of four motors mounted at the end of four arms and are responsible for causing motion in horizontal and vertical plane. The vertical motion of the quadrotor is generated by collective thrust produced by all the four motors by increasing or decreasing the speed of the rotors evenly at the same instance. When a motor rotates, it generates reaction torque in the plane perpendicular to the force vector in the direction opposite to the rotation of motor and therefore, if all the four rotors rotate in the same direction, it will result in generation of constant yaw motion throughout the flight" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure4.4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure4.4-1.png", + "caption": "Fig. 4.4. Manipulation task", + "texts": [ + " The torques are transported to the corresponding joints where there are Harmonic Drive reducers. The reducers in joints S2' S3 have the masses of about 7kg and the mechanical efficiencies n = 0.8. It is necessary to choose the actuators which will drive the joints S2' S3. The manipulator is equipped with spring compensators for the joint S2. Thus, the parameters to be determined are: cross section dimensions of segments 2 and 3, and parameters of actuators S2 and S3' and finally, the reduction ratio. 247 The manipulator is tested on the assembly task shown in Fig. 4.4. The object should be moved along the trajectory AoA1A2A3. The velocity pro file on each straight-line part of the trajectory is triangular. The changes in orientation are also shown in Fig. 4.4. The execution time is T = T1 + T2 + T3 The manipulat~r starting position is given in Fig. 4.2.b. The constraint is that the position error due to elastic deformations be smaller than u = 0.002 m. p The design (i.e. determination of parameters) is carried out by using the design game procedure. The procedure started with the initial cross section dimensions: Hx2 = 0.25m, Hy2 = 0.13m, Hx3 = 0.16m, Hy3 = O.OSm. We first choose the 2kW D.C. motors as the actuators for the joints 52' 53. Catalog parameters (stall torque P~ and no-load rotation speed n~) m m m m ", + "3. i.e. 0.9, 0.85, 0.9, 0.85 (4.3.1) But, there still remain four independent parameters. If we adopt 1 .5, 1.5 (4.3.2) then there are only two independent parameters: Hx2 and Hx3 . If our intention is to reduce the problem to one-parameter optimization, one possibility is to adopt Hx2 = HX3 which means that the two segments (2 and 3) are equal. We now perform the optimization for the reamining one independent parameter Hx2 . The manipulation task considered is described in the example in 4.1. (Fig. 4.4). The stress constraint and the constraint of elastic deformation are imposed. We require that the position error due to elastic deformation be smaller than 0.002m. The optimization by using the binary search gives the optimal value of opt the parameter Hx2 : Hx2 0.22m. The other dimensions follow from (4.3.1), (4.3.2): Hx2 = HX3 = 0.22m, Hy2 = Hy3 = 0.147, hx2 =hx3 = 0.187, h 2 = h 3 = 0.132. For these dimensions the energy consumption y. y is E = 2509 J. 258 We suppose that the assumption about equal segments (2 and 3) was not quite suitable for it is probably far from the best ratio between two segments" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003055_0094-114x(94)90024-8-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003055_0094-114x(94)90024-8-Figure4-1.png", + "caption": "Fig. 4. The workspace of the manipulator when 3 DOF are provided by changing its leg lengths.", + "texts": [ + " In order to determine the values of X0~, Y0~ and Z0, we can write the following system of the equations {[(e., + Xo, )2 + (e.~ + Yo, ~,,2 R2 }' + (e:, - zo, )2 = 2 - 15.6, ( 1 9 ) where Px,= Lxlx. + Lv, y . + Lz, z . . P~ = Mx=x. + MrlY~I + MzlZ~l. Pzl = Nxl x . + N).Iy. + Nzl z . . i = 6 . 7 . 8 . Then this reverse problem has the same solution as for case (i) above. (ii) Assume that the 3 DOF of the manipulator are provided by changing only the lenghts 1~.6, 14.7 and lsj. In this case the sliders remain stationary (Fig. 4). For such a manipulator the workspaces generated by the joints 6, 7 and 8 are three planes which are perpendicular to the base and pass through the joints 3, 4 and 5 and the OZ axis respectively. The trace equations of these planes in the XO Y plane are A,x + B,y = 0, (i = 3, 4, 5) (20) where Ai -- cos ~,, and B~ = cos ~, are the direction cosines of the normals to these planes. In order to locate the top joints 6, 7 and 8 on each of these planes firstly the values for the coordinates x6 and z6 are specified" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure32.1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure32.1-1.png", + "caption": "Fig. 32.1 Photo of micro ultrasonic motor", + "texts": [ + " To achieve these features, we used a shape memory alloy actuator driven by an optical source and a flexible displacement sensor using piezoelectric polymer. The optical waveguide in the actuator and the flexible displacement sensor were deposited using a paste injection system. 32.2.1 Micro Ultrasonic Motor and Sensor The micro servo motor consists of a micro ultrasonic motor and a micro encoder. Each device uses a piezoelectric vibrator and a micro magnetic resistive sensor. 32.2.1.1 Micro Ultrasonic Motor Configuration The micro ultrasonic motor is shown in Fig.32.1. This motor is the cylindrical type micro ultrasonic motor and uses a cylindrical piezoelectric vibrator [2\u20134]. The motor consists of a rotor, bearing, piezoelectric vibrator, and glass case. The rotor is joined to the output shaft and is made of stainless used steel. The bearing is made of poly (tetrafluoroethylene) (PTFE). The vibrator and the bearing are supported by a glass case. The glass case has a diameter of 1.8 mm and a height of 5.8 mm. To generate traveling waves, four divided electrodes are located on the outer surface of the piezoelectric vibrator" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003546_ac00283a032-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003546_ac00283a032-Figure1-1.png", + "caption": "Figure 1. Absorption spectra of (1) the Ti-PAPS-H O2 system and, (2) PAPS at pH 7.0: [Ti(IV)] and [PAPS], 2 X 10- P M; [H202], 1 X", + "texts": [ + " The solution was cooled to room temperature and the absorbance was measured at 539 nm. For the control assay, a solution containing the same constituents as the above was prepared, except that the glucose solution, instead of serum, was added. Determination of Hydrogen Peroxide. When hydrogen peroxide was added to the Ti-PAPS reagent a t pH ca. 1.0, a 0 1985 American Chemical Society 0003-2700/85/0357-1107$01.50/0 10-5 M. sharp peak appeared at A,, 539 nm due to the formation of the Ti-PAPS-H202 complex, as shown by curve 1 in Figure 1. With the addition of hydrogen peroxide, constant absorbance values were obtained within a few minutes at 37 O C and remained virtually unchanged over a period of 24 h at room temperature. The absorbance at 539 nm was proportional to the concentration of hydrogen peroxide. The composition of the complex was confirmed by Job's method: only a 1:l:l complex was found to form in the solution containing Ti(IV), PAPS, and hydrogen peroxide. Though the structure of the Ti(IV)-PAPS-H202 is still uncertain, the most probable one which can be presumed at present is shown below" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure2.6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure2.6-1.png", + "caption": "Fig. 2.6. (a) \"Specificity\" of (i-l)-th segment on the upper end", + "texts": [ + " That angle may be regarded as the angle between the projections of the -> -> vectors -r i - 1 i and r ii onto the plane perpendicular to the joint axis ~ i (F ig. 2.4): A particular case occurs when ~ .. I Ie. or~. 1 . I Ie .. Then, the angle ~~ ~ ~-,~ ~ of rotation may not be considered in the previous way. If ~. 1 . I Ie. ~-,~ ~ 29 we call it the \"specificity\" of the (i-1)-th segment on the upper end. -** -+ -+* -+ Then we introduce a unit vector r. 1 . perpendicular to e. (r. 1 .~e.) ~* ,~ ~ ~-, ~ ~ (Fig. 2.6a). Further, the vector t. 1 . is used instead of ~. 1 . for 1- ,1 -+ -+ 1- ,1 determining the generalized coordinate q .. If r .. I Ie. we call it the ~ ~~ ~ \"specificity\" of the i-th segment on the lower end. Then we introduce -+* -+ -+* -+ a unit vector r ii perpendicular to e i (rii~ei) (Fig. 2.6b) and use it -+ instead of r ... ~~ -+* r .. 11 -+ -+ e. r.. Ci ~~~t:~~~~ __ ~l~ ____ ~l~l __ ~ (b) \"Specificity\" of i-th segment on the lower end The definition of generalized coordinate in the case of \"specificity\" is shown in Fig. 2.7. The existence of \"specificity\" has to be given to the algorithm via special indicators. If Sj is a linear joint, then the corresponding generalized coordinate 30 q. is defined as a relative linear displacement along the joint axis 7 J e i.e. q. = I~I (Fig. 2.5)", + " Thus, in each iteration the system has to be solved nume rically. In the next time interval (T 2 ) the motion of the peg is constrained. It is a surface-type constraint, the one discussed in Para. 3.4.12. Then the second impact happens (point A2 in Fig. 3.38a or A1 in Fig. 3. 38b) . After this second impact the motion of the manipulator is subject to two-d.o.f. joint constraint (Para. 3.4.7). However, if there are large perturbances, the motion after the second impact cannot be considered in this way but it is subject to two constraints of surface type (Fig. 226 3.39a).cylindrical joint constraint (two d.o.f) can'be used when the axis of the peg (*) is close enough to the hole axis (**) (see Fig. 3. 39b) \u2022 The problem of friction and jamming was considered in Para. 3.4.7 and 3.5. Rectangular problem. A rectangular assembly task is shown in Fig. 3.40. Such a manipulation task requires six d.o.f. manipulators since the total orientation of working object is needed. 3.6.3. Constraint permitting no relative motion We consider the final phase of an assembly task (Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000467_j.ast.2021.106564-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000467_j.ast.2021.106564-Figure1-1.png", + "caption": "Fig. 1. RCS distribution.", + "texts": [ + " . Reaction control systems The operating characteristic of the RCS is discrete that turn the zzle switch on or off according to the commands provided by e control system. The RCS has only two states: \u20181\u2019 represents on d \u20180\u2019 represents off. When the RCS turned on, it can provide fixed ntrol torque on the body axis. In this paper, the RCS is designed the arrangement of X-33 reference the article [15]. For this case, only consider the 20 ideal jets which are primary. The RCS disbution is shown in Fig. 1, while the parameters are shown in ble 1. \u03c2 \u2208 3\u00d720 is a matrix and the element of the control torque , j (i = 1,2,3, j = 1,2, \u00b7 \u00b7 \u00b7,20) is provided by the j-th RCS on e i-th axis. T rcs \u2208 20\u00d71, where T rcs is a binary number (0 or 1) ich refers to the k-th RCS state. The magnitude of the RCS torque is calculated as Ml = \u23a1 \u23a3 F R1U + F R2U + F R4U + F L2D +F L3D + F L4D \u2212 F R2D \u2212 F R3D \u2212F R4D \u2212 F L1U \u2212 F L2U \u2212 F L4U \u23a4 \u23a6 \u00b7 rl (13) Mm = \u23a1 \u23a3 F R1U + F R2U + F R4U \u2212 F L2D \u2212F L3D \u2212 F L4D \u2212 F R2D \u2212 F R3D \u2212F R4D + F L1U + F L2U + F L4U \u23a4 \u23a6 \u00b7 rm (14) Mn = [ F R1R + F R2R + F R3R + F R4R \u2212F L1L \u2212 F L2L \u2212 F L3L \u2212 F L4L ] \u00b7 rn (15) where Ml , Mm , Mn are the rolling, pitching and yawing torque, respectively, rl , rm , rn are the rolling, pitching and yawing arm, respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003815_j.mechmachtheory.2009.06.001-Figure23-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003815_j.mechmachtheory.2009.06.001-Figure23-1.png", + "caption": "Fig. 23. Defective generators with an exceptional mobility.", + "texts": [ + " A product of two factors is a 2D subgroup and the product of the other two factors is another subgroup, which is dependent with respect to the first subgroup. In other words, the intersection of the two 2D subgroups is a 1D subgroup. From the list of products of dependent subgroups [5], we obtain only two possible situations, namely, C1. [{H(A1, u, p1)}{H(A2, u, p2)}][{H(A3, u, p3)}{H(A4, u, p4)}] = {C(A1, u)}{C(A3, u)} if A2 e line (A1, u) and A4 e line (A3, u). We have {C(A1, u)} \\ {C(A3, u)} = {T(u)}. Hence, if two axes are collinear, then, the other two axes must not be collinear. For instance, the open chain of Fig. 23a is a defective chain for the generation of X-motion. The subgroups {C(Ai, u)} with either (i= 1 or 3) or (i= 1 and 3),can also be generated by PH or HP arrays (PR or RP when the pitch is zero) if the P is parallel to the H axis (R axis). These defective generators are shown in Fig. 23b\u2013f. It is noteworthy that a defective X generator happens when a revolute pair arbitrarily replaces any screw in these generators. C2. [{H(A1, u, p1)}{H(A2, u, p2)}][{H(A3, u, p3)}{H(A4, u, p4)}] can be equated to {C(A1, u)}{T(Pl)} with {C(A1, u)}\\{T(Pl)} = {T(u)}; in this case, the plane Pl of vectors s3, s4 is parallel to u. Consequently, if two screws are coaxial, then the plane of two P pairs must not be parallel to the screw axis. The chain in Fig. 24a shows this kind of defective generator" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000210_tie.2021.3075886-Figure6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000210_tie.2021.3075886-Figure6-1.png", + "caption": "Fig. 6: The mechanisms of CTRUAV\u2019s maneuvers.", + "texts": [ + " The key geometric dimensions of the CTRUAV prototype are depicted in Fig. 5, where lb is the distance from the rear rotor to the CoG of CTRUAV in direction Xb, l f and ls are the distance from the coaxial tilt-rotor modules to CoG in directions Xb and Yb, respectively. The tilt axis of the coaxial rotors coincides with XbYb plane of the bodyfixed frame B, which means the distance from the tilt axis to CoG in directions Zb is zero. The overall mechanisms of the CTRUAV\u2019s maneuvers are illustrated in Fig. 6, which are achieved by varying the thrusts and tilt angles of the rotors. III. DynamicModeling To design the control strategy for the CTRUAV prototype, its dynamic model is derived. We first define the generalized coordinates based on the two reference frames described in Fig. 1 as follows: q = [\u03be> \u03b7>]> \u2208 R6, where \u03be = [x y z]> \u2208 R3 Authorized licensed use limited to: University of Saskatchewan. Downloaded on July 07,2021 at 16:22:54 UTC from IEEE Xplore. Restrictions apply. 0278-0046 (c) 2021 IEEE" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000195_j.oceaneng.2021.108660-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000195_j.oceaneng.2021.108660-Figure1-1.png", + "caption": "Fig. 1. The path following depiction of underactuated MSV.", + "texts": [ + " However, in many cases, due to the limitation of cabin space and cost, Doppler log may not be installed, or the sensor may fail or be polluted by noise, resulting in inaccurate measurement value. In this case, the simplest way to obtain the ship speed information is to conduct numerical differentiation on the measured value of ship position. However, if there are noise signals in the position measurements, the differential operation will amplify these noise signals, which will greatly affect the path tracking accuracy of underactuated surface ships. The path following depiction is given in Fig. 1 as below. The path parameter is denoted by \u03b8. To obtain the path following error, a new reference coordinate system is introduced, i.e., SerretFrenet (SF) coordinate system. The origin of SF coordinate system is chosen as an arbitrary point PF(\u03b8) on the predefined path, thexaxis and yaxis of SF coordinate system are tangent and normal to the path. The SF coordinate system and the inertial coordinate system differ by \u03c8F which expressed as \u03c8F = atan2(y\u2032 F ,x \u2032 F)with (\u22c5) \u2032 F = \u2202( \u22c5)/\u2202\u03b8. P = (x,y)denotes the vessel\u2019s position in inertial coordinate system as shown in Fig. 1, PF = (xF , yF)is defined as the position of the motional target point along the predefined path in inertial coordinate system. The path following error equation established in the SF coordinate system is written as follows: [ xe ye ] = [ cos \u03c8F sin \u03c8F \u2212 sin \u03c8F cos \u03c8F ][ x \u2212 xF y \u2212 yF ] (3) where xe denotes the along-track error and yedenotes the cross-track error. By solving the time differential of (3), we can obtain the location tracking error dynamic equation described in SF coordinate system as below: [ x\u0307e y\u0307e ] = \u23a1 \u23a3 u cos(\u03c8 \u2212 \u03c8F) \u2212 v sin(\u03c8 \u2212 \u03c8F) + \u03c8\u0307Fye \u2212 \u03b8\u0307 \u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305 x\u2032 2 F + y\u2032 2 F \u221a u sin(\u03c8 \u2212 \u03c8F) + v cos(\u03c8 \u2212 \u03c8F) \u2212 \u03c8\u0307Fxe \u23a4 \u23a6 (4) Consider the underactuated MSV model (1) and (2) under the condition of unknown external disturbances, unknown dynamic and unavailable velocity, the control target of the paper is to drive the vessel to track the desired planar path at the constant surge velocity within finite time through designing the guidance law and output feedback path following control law" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000053_icra40945.2020.9197524-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000053_icra40945.2020.9197524-Figure3-1.png", + "caption": "Fig. 3: Configuration of the robotic arm.", + "texts": [ + " No hard constraints on inputs are considered in this paper; therefore, the input constraint set is set to be U = Rnu . First of all, unlike a general multirotor, our UAM\u2019s additional freedom in the robotic arm should be carefully managed to avoid a crash between the multirotor airframe and the robotic arm. To ensure this self-collision avoidance, following constraints are devised: S3 z \u2264 0 S4 z \u2264 0 dz \u2264 0 (8) where S3, S4, and d are position vectors of the 3rd servomotor, the 4th servomotor, and the end-effector of the robotic arm described in FB while having their origins at OB as in the Fig. 3, and the subscript z in \u2217z denotes the third component of a vector \u2217. Since OB is assumed to be centered at the CoM of the multirotor, and these vectors are all described in FB , the above constraints imply that the robotic arm must always stay below the airframe of the multirotor. Note that all three position vectors S3, S4, and d are a function of H which can be derived with forward kinematics; therefore, these constraints can be formulated only with system states. The second constraint, which is avoiding collision with the door, is constructed as follows: nTD(Rtd) \u2265 RA max \u03b8 { nTD ( Rt [ cos \u03b8 sin \u03b8 0 ]T)} (9) In equation (9), the left-hand side indicates the shortest distance between the CoM of the UAM and the door surface, and the right-hand side quantifies the distance between the CoM of the UAM and the multirotor\u2019s airframe closest to the door surface" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003917_tvcg.2007.70431-Figure6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003917_tvcg.2007.70431-Figure6-1.png", + "caption": "Fig. 6. (a) Shape vectors Di are orthogonal to each edge and directed inward. (b) The foot Ji is the barycenter of points Qj and Qk with coefficients cot j and cot k, whereas pseudofoot point J?i has barycentric coordinates cot j and cot k.", + "texts": [ + " Any point X \u00bc \u00f0x; y\u00deT in the rest triangle TP can be parameterized with its barycentric coordinates i\u00f0X\u00de such that x y 1 2 4 3 5 \u00bc P1x P2x P3x P1y P2y P3y 1 1 1 2 4 3 5 1 2 3 2 4 3 5 \u00bc jPj E: \u00f07\u00de The inverse relation defines the barycentric coordinates of any point X 2 TP given that the triangle is not degenerate: 1 2 3 2 4 3 5 \u00bc D1x D1y 0 1 D2x D2y 0 2 D3x D3y 0 3 2 4 3 5 x y 1 2 4 3 5 \u00bc jDj X; \u00f08\u00de where . Di is the ith shape vector of triangle TP , and . 0 i is the ith barycentric coordinate of the origin of the coordinate frame. Shape vectors Di are the gradient vectors of the barycentric coordinates i (the shape functions), and they play a key role in the discretization of the membrane energy. Those vectors are directed along the inner normal (independently of the triangle orientation) and are of length 1=hi, hi being the altitude of Pi (see Fig. 6a). This can be translated with the following geometric relation: Di \u00bc 1 2AP \u00f0Pi 1 Pi 2\u00de?; \u00f09\u00de where i j \u00bc \u00f0\u00f0i 1\u00fe j\u00demod 3\u00de \u00fe 1 and X? \u00bc \u00f0 y; x\u00deT is the orthogonal of vector X. Another important fact is that each pair of shape vectors \u00f0Di;Dj\u00de is the covariant basis of the contravariant basis made by the two vectors \u00f0Pi 1 Pi 2\u00de and \u00f0Pj 1 Pj 2\u00de: 4\u00f0AP \u00de2\u00f0Di Dj\u00de \u00bc \u00f0Pi 1 Pi 2\u00de \u00f0Pj 1 Pj 2\u00de 1 : Thus, for i 6\u00bc j and for all vector a 2 IR2, we have the following two relations: a \u00bc\u00f0a Di\u00de\u00f0Pi 1 Pi 2\u00de \u00fe \u00f0a Dj\u00de\u00f0Pj 1 Pj 2\u00de; a \u00bc\u00f0a \u00f0Pi 1 Pi 2\u00de\u00deDi \u00fe \u00f0a \u00f0Pj 1 Pj 2\u00de\u00deDj: 1", + " Applying the Rayleigh-Ritz analysis, we consider that the triangular surface should evolve by minimizing its membrane energy, therefore along the opposite derivative of that energy with respect to the nodes of the system, that is, the deformed positions Qi: FTRBS i \u00f0TP \u00de \u00bc @W\u00f0TP \u00de @Qi T \u00bc X j6\u00bci kTPk 2lk\u00f0Qj Qi\u00de \u00fe X j 6\u00bci \u00f0cTPj 2li \u00fe cTPi 2lj\u00de\u00f0Qj Qi\u00de: \u00f015\u00de We can provide a geometric interpretation of that force, if we consider the two points Ji and J?i in the deformed triangle TQ. The first point Ji is the foot of Qi also defined as the barycenter of points Qj and Qk with coefficients cot j and cot k. The second point J?i is a pseudofoot point defined as the barycenter of points Qj and Qk with coefficients cot j and cot k (see Fig. 6b). With those two additional points, the force can be written as FTRBS i \u00f0TP \u00de \u00bc \u00f0 \u00fe \u00del2i trE 4AP \u00f0Qi J?i \u00de \u00fe 8AP l2i \u00f0Qi J?i \u00de L2 i \u00f0Qi Ji\u00de : The force is clear zero if TQ \u00bc TP since we then have trE \u00bc 0 and J?i \u00bc Ji. It is also important to note that if the rest triangle TP is obtuse in j or k, then the point J?i is not in the segment \u00bdQj;Qk that can be the cause of instabilities. This expression is somewhat similar to the altitude springs used by Bridson et al. [36] to prevent the collapse of tetrahedra" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003715_tps.2010.2076355-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003715_tps.2010.2076355-Figure1-1.png", + "caption": "Fig. 1. Rotor structure of the VMRPMSM. (a) The rotor structure. (b) The prototype rotor.", + "texts": [ + " In addition, whether the converter can provide sufficient current to the PMSM is also questionable because the current and the voltage of the converter are always finite. Using the analysis of FW principles, a scheme of a variable magnetic reluctance PMSM (VMRPMSM) based on field adjustment is presented. The new PMSM has the advantages of adapting different loads by the automatically adjustable magnetic flux and becomes an excellent competitor in drive systems for electric vehicles. The stator of a fractional 18-slot winding is the same as the general structure of a PMSM. The rotor shown in Fig. 1 is composed of a PM slot, main and secondary PMs, and a nonmagnetic conductor. The repulsive force between the main PM and the secondary PM can help them contact gently when they are very close in one PM slot. As the motion of the PMs occupies part of the rotor space, four pole pairs are necessary to provide enough air-gap magnetic density to ensure torque density at low speed. The shape of the outer boundary of the rotor is changed to optimize the air-gap magnetic-density waveform [5]. As shown in Fig. 1, the main PMs are in the initial position when the speed is less than or equal to the base speed. 0093-3813/$26.00 \u00a9 2010 IEEE The centrifugal force on the main PMs increases when the speed increases above the base speed. The magnets then move outward along the PM slot until the centrifugal force and electromagnetic force reach a balance. The effective magnetic flux provided by the main PMs decreases as their distance from the central shaft increases because the reluctance of the flux path increases", + " In this way, air-gap FW is implemented. The position of the PM in the PM slot determines the reluctance of the path through which the flux produced by the PM passes. This, in turn, affects the flux density B in the air gap. At the same time, the net force on the PM determines its position along the gap. Hence, it is necessary for us to analyze the force on the PM. These forces include the electromagnetic force, the centrifugal force, friction, and the gravitational force. We choose main PM #1 (Fig. 1) as the object whose motion is to be analyzed. We assume the following: 1) The mass of the main PM is distributed homogeneously; 2) the smoothness of the PM is uniform over its surface, and the coefficient of the dynamic friction is equal to the coefficient of static friction; and 3) the effect of the gravitational force is negligible. For the machine discussed in Section VI, the gravitational force is 0.174 N for one PM, but the centrifugal and the electromagnetic forces are 11.37 and 11.55 N, respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure24.10-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure24.10-1.png", + "caption": "Figure 24.10 is the bottom view of the designed 6-8 spherical stepping motor when the output shaft is at the vertical position. The positions of the permanent magnets and the coils (4,4\u2019), (5,5\u2019) and (6,6\u2019) are same as Fig.24.9. Therefore, when I supply three phase sinusoidal currents to the armature coils (4,4\u2019), (6,6\u2019) and (5,5\u2019), the rotor will rotates around the output shaft in the same direction as Fig.24.9. When I supply three phase sinusoidal currents to the armature coils (1,1\u2019), (2,2\u2019), (3,3\u2019) and (4,4\u2019), (6,6\u2019), (5,5\u2019) simultaneously, the output torque will be doubled.", + "texts": [ + " The permanent magnets are positioned at every 90 degrees around the output shaft and North Poles and South Poles are positioned alternately. The pairs of coils (1,1\u2019), (2,2\u2019) and (3,3\u2019) are positioned at every 120 degrees around the output shaft. The relationship between the permanent magnets and the armature coils is similar to that of the conventional three Actuator with Multi Degrees of Freedom 287 phase planer stepping motor with two pairs of permanent magnets. Therefore, when I supply three phase sinusoidal currents to the armature coils (1,1\u2019), (2,2\u2019) and (3,3\u2019), the rotor will rotates around the output shaft. Fig. 24.10 Bottom view Fig. 24.11 Tilt view 288 Tomoaki YANO Figure 24.11 is the view of the designed 6-8 spherical stepping motor from the direction of the arrow. One of the iron cores is just under the armature coil 245. The position of the armature coil 245 is the center of the triangle formed from coil2, coil4 and coil5. The positions of the permanent magnets and the coils (2,6\u2019), (5,24\u2019) and (4,25\u2019) are same as Fig.24.9. Therefore, when I supply three phase sinusoidal currents to the armature coils (2,6\u2019), (5,24\u2019) and (4,25\u2019), the rotor will rotates around coil245" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure3.41-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure3.41-1.png", + "caption": "Fig. 3.41. Final phases of assembly tasks", + "texts": [ + "cylindrical joint constraint (two d.o.f) can'be used when the axis of the peg (*) is close enough to the hole axis (**) (see Fig. 3. 39b) \u2022 The problem of friction and jamming was considered in Para. 3.4.7 and 3.5. Rectangular problem. A rectangular assembly task is shown in Fig. 3.40. Such a manipulation task requires six d.o.f. manipulators since the total orientation of working object is needed. 3.6.3. Constraint permitting no relative motion We consider the final phase of an assembly task (Fig. 3.41a). In the phase of insertion we face the rectangular assembly problem. But, in this final phase the working object is fixed and no relative motion is possible. 227 Another example is shown in Fig. 3.41b. When the first two screws are screwed-in the object becomes fixed and no relative motion is possible. The theory covering these problems is explained in Para. 3.4.10. 3.6.4. Practical problems of bilateral manipulation Assembly tasks. Two most interesting tasks with bilateral manipulation are cylindrical and rectangular assembly tasks (Fig. 3.42). The whole discussion on cylindrical assembly task given in Para. 3.6.2 can be applied to bilateral manipulation. Case of no relative motion. The connection of the two grippers can be such that no relative motion is permitted" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000326_j.mechmachtheory.2021.104264-Figure6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000326_j.mechmachtheory.2021.104264-Figure6-1.png", + "caption": "Fig. 6. Ring gear accelerometer configuration in experiments (coinciding with elastic node locations in the finite element/contact mechanics model). The key accelerometers #5, 10, and 11 used in frequency response plots are highlighted.", + "texts": [ + " The literature and our experiments show that this accelerometer configuration is sufficient to capture general motion of the ring gear provided the ring is approximately inextensible [55] . Hidaka [45] and Botman [56] claim that ring gear motion is primarily characterized by radial elastic-body deformation. Nevertheless, to test this assumption, accelerometers were positioned radially and tangentially on the ring gear. Fig. 5 shows the vibration response of these two components in steady state at 60 0 0 Hz. The radial component is an order of magnitude larger than the tangential component. Consequently, our subsequent measurements consider only the radial vibration component. Fig. 6 notes ring gear accelerometer numbers and highlights key locations used to identify elastic-body vibration in experiments. More than one accelerometer location is needed to identify all elastic-body modes because certain ones may have a node of zero vibration amplitude near any given accelerometer. The accelerometer numbers used coincide with node locations in the finite element/contact mechanics model (e.g. accelerometer #5 in experiments and node #5 in the finite element/contact mechanics model are both in the twelve o\u2019clock position on the ring gear)", + " Discrete-body translational motion of a gear body is illustrated by the position of a solid red circular body shifted away from its nominal position, which is indicated by a dotted black line. The mass center trajectory of planet discrete-body translational motion is given by a (usually ovular) solid black line. The discrete-body rotation is indicated by the angle of a solid red radial line on the displaced body circle. This line extends from the planet center, so it will always connect to the mass center trajectory. The nominal rotational position is always indicated by a black dotted horizontal line. Elastic-body motion is depicted by blue dots (accelerometer locations in Fig. 6 ) connected by a spline interpolated thick red line. We are only able to obtain this data experimentally for the ring gear. In finite element modeling \u2013 without limitations on sensor placement \u2013 we also do this for the excited planet gear. There are not enough data acquisition channels to measure all discrete-body and elastic-body degrees of freedom in experiments simultaneously. Only planet one (excited by the modal shaker in Fig. 2 b) discrete-body motion is acquired when measuring the full elastic-body motion of the ring gear", + " More detail regarding the combined FE/CM model and computational efficiency of this technique is contained in [25] . A planar model is sufficient for the present spur planetary gear. The model predicts discrete-body vibrations of all gear components for direct comparison to the experiments for these degrees of freedom. The software outputs the deflection of any specified node. We use this tool to obtain the elastic deformation of 16 nodes on the ring gear coinciding with the experimental accelerometer locations in Fig. 6 . Eventually the elastic-body motion of the excited planet also drew interest, so 16 nodes (with #1 pointed toward the sun gear in the \u2212x p direction and numbered counterclockwise) are also probed around this gear body, as illustrated in Fig. 7 . The FE/CM model uses boundary conditions that simulate experimental conditions. Numerical values are contained in [53] . The rotational stiffnesses of the sun gear and carrier shafts (obtained analytically and by finite element analysis) are applied to the rotational degrees of freedom of those components, although our prior work [53] shows that these parameters do not affect the frequency range of current interest", + "\u201d Modes in the latter category have a significant portion of energy associated with elastic-body vibration, so we call them \u201cdominantly elastic-body modes.\u201d There is no quantitative criterion to distinguish modes in the two categories noted, except moderately elastic-body modes have enough discrete-body motion that a lumped-parameter model identifies them, albeit incompletely, with reasonable accuracy, while dominantly elastic-body modes are missed by the analytical model. Fig. 9 shows the experimental frequency response in the radial direction of the ring gear using the three accelerometer locations identified in Fig. 6 . Three locations are used in the plot because different locations around the ring gear demonstrate each resonant peak better than others due to the nature of elastic continuum deformation. A given accelerometer location may exhibit maximum elastic-body deflection (if near an anti-node) or zero deflection (if close to a vibration node). The vertical dashed line around 3600 Hz in Fig. 9 separates the region of previously-studied \u201cgear modes\u201d (in [53,54] ) to the left and modes not previously identified to the right", + " The gear modes were thought to be accurately described in terms of discrete-body motion only, and past publications focused on discrete-body motion of the planets, sun gear, and carrier. There are, in addition to the gear modes below 3600 Hz, four more frequency response peaks at higher frequency not previously identified because they exhibit elastic-body motion, primarily in the ring gear. The 5860 Hz mode (number 22 in Table 2 ) also features planet elastic-body motion, as we will describe. Fig. 10 shows the FE/CM simulation results of essentially the same data. Node/accelerometer location #11 is not used (it is right next to #10, see Fig. 6 ). Additionally, planet gear data helps identify the highest mode (5850 Hz in this figure). Planet gear motion is dominant in experiments in this mode too. Natural frequencies and relative amplitudes in the experiments and FE/CM model are remarkably similar. Table 2 compares the natural frequencies in Figs. 9 and 10 . The mode numbers start at 13 because the first 12 modes were previously identified as \u201cfixture modes\u201d with predominant strain energy in the shafts and supporting bearings [53] . All natural frequencies in Table 2 agree within 6% error, and 70% of them agree within 3% error" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure4.7-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure4.7-1.png", + "caption": "Fig. 4.7. Scheme of manipulation task", + "texts": [ + " This tube can be pulled out of the second segment up to 0.8 m. This results in the segment being 1.2 meters long. Thus the cross-section dimensions of this segment remain to be chosen. The cylindrical tube cross-section is defined by the outside radius (R) and the inside radius (r), as shown in Fig. 4.5b. In order to reduce the number of independent parameters we adopt the constant ratio ~ = r/R 0.85. Thus there remains only one parameter to be optimized. It is the outside radius R. Let us define the manipulation task. It is shown in Fig. 4.7. The working object has to be moved along the trajectory AoA1A2 with a triangular velocity profile on each straight-line part. We adopt: T2 = 2T1 where T1 is the execution time T(Ao+A1 ) and T2 = T(A1+A2 ). We perform the optimization with several different values of the total execution time (T = T1 + T2) in order to check whether the results depend on this ex ecution time. Each optimization is performed by using the binary search procedure. The results obtained are shown in Fig. 4.8. The binary search has been carried out for eight values of T: 4" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000545_jestpe.2021.3055224-Figure8-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000545_jestpe.2021.3055224-Figure8-1.png", + "caption": "Fig. 8 Radial air-gap flux density waveforms of a doubly cylindrical machine with three conductor layouts from 2D FEA and their approximations using winding functions.", + "texts": [ + " Though one may lose sight of the exact spatial distribution of currents and fluxes, the MMF drop and magnetic field distribution in the air gap can be determined with great simplification by introducing the winding function. The classical winding function theory requires at least one side of the air gap to be smooth, so that the air-gap flux density waveform Bg(\u03d5, t) can be obtained from the air-gap MMF immediately by neglecting the MMF drop in iron cores, as shown by the agreement between the FE-predicted air-gap flux density waveforms and the approximations by using winding functions in Fig. 8. If both sides of the air gap are non-uniform, or there is flux barrier/short-circuited coils near the air gap, the air-gap flux density waveform Bg(\u03d5, t) will not be derived from the air-gap MMF directly because Bg(\u03d5, t) depends on not only the air-gap MMF distribution but also the flux paths. In order to address this issue and inspired by the derivation of the winding function concept, the authors contributed to the field of electric machinery by proposing the general air-gap field modulation theory [26]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002863_02640410410001730179-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002863_02640410410001730179-Figure1-1.png", + "caption": "Figure 1. Three-segment model of the golf swing (adapted from Campbell and Reid. 1985)", + "texts": [ + " However, Jorgensen (1970, 1994) improved the double pendulum model by allowing for horizontal and vertical (but not angular) acceleration of the \u2018\u2018hub\u2019\u2019. Jorgensen\u2019s model showed improved fit with the swing of low-handicap golfers, and he concluded that translation of the \u2018\u2018hub\u2019\u2019 played an important role in generating torque and thus clubhead speed. Campbell and Reid (1985) produced a three-segment planar model that incorporated trunk rotation (about the spine) in addition to shoulder and wrist action (Figure 1). They then used this model to perform optimization and maximization of driving performance. Sprigings and Neal (2000) also used a planar three-segment model (Figure 2), but incorporated more realistic muscle dynamics to investigate optimal limb sequencing and delay times for maximal clubhead speed. The results showed that correctly timed wrist torques could produce gains in clubhead speed. The major supposition of all of these previous models has been that golf is a planar activity with trunk rotation, arm swing and clubhead motion all remaining in the same plane throughout the downswing" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000220_tmech.2021.3075478-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000220_tmech.2021.3075478-Figure2-1.png", + "caption": "Fig. 2. Experimental setup of Linear motor", + "texts": [ + " In addition, by innovatively designing the adaptive law, the proposed control scheme achieves the asymptotic tracking even when the unknown disturbances always exist, while the asymptotic tracking is only achieved when the disturbances die out or the bounded stability can be ensured by the results in [28], [42]. Importantly, by employing an event-triggered mechanism, this scheme also has additional advantages in reducing the system communication resources significantly. To illustrate the theoretical results, the following linear motor setup produced by Akribis company as shown in Fig. 2 is considered to verify the proposed control scheme. This setup communicates with the computer via EtherCAT network, and the control algorithm is implemented through TwinCAT 3.0 software. The position and velocity signals are transmitted to computer from servo drivers by means of the linear optical encoders. The dynamic model of this setup is described as My\u0308 = u\u2212By\u0307 \u2212AfSf (y\u0307) + Fd (62) where the state variables are given by the displacement y, and velocity y\u0307 respectively, whereas u is the control input" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002538_j.jsv.2003.06.003-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002538_j.jsv.2003.06.003-Figure1-1.png", + "caption": "Fig. 1. Model of tire treadband: a circular cylindrical shell with simply supported edges.", + "texts": [ + " By the superposition of the basis functions, the forced response of the system can be obtained when the system is driven by a point harmonic force at a fixed location in the reference frame. Since a single basis function is associated with only one natural frequency, a basis function coefficient can be found by solving a single ordinary differential equation. In addition, the wave number decomposition procedure [1] has been applied to the resulting forced responses, thus allowing the dispersion relations for a rotating shell to be represented from the viewpoint of a fixed observer so that they can be easily compared with the dispersion relations for a stationary shell. Fig. 1 shows a cylindrical shell model of a tire treadband: the shell is assumed to rotate about a fixed axis coincident with the origin of the reference co-ordinate system. Note that the local co-ordinate system, attached to the treadband, rotates with the treadband and that the reference co-ordinate system is fixed. In the present analysis, the effects of inflation pressure and rotational stiffening were accounted for through resultant in-plane residual stresses. However, static deformation of the shell due to either inflation or rotation was neglected, i" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure3.19-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure3.19-1.png", + "caption": "Fig. 3.19. Relative translation", + "texts": [ + " Axis x is along h*, z is along s , and Ys along ~ = s xh \u2022 s s If we connect the gripper to the moving object, as shown in Fig. 3.17, ~ ~* then h (on the gripper) has to coincide with h (on the object) and * accordingly Xs coincides with xs. This means that e * e , * We note that the relative translation occurs along x . s* with respect to axis xs. coordinate of gripper point A * and Zs coordinates of point A --*- o A s --* A A equal zero it holds that (3.4.86) Let u 1 be the * Since the Ys (3.4.87) (see Fig. 3.19). Thus u 1 defines the relative translation. +* +* + Relative rotation is performed around.h (note h =h) and is defined by (3.4.88) If a six d.o.f. manipulator (n=6) is considered, u 2 is a free parameter * since ~ can be changed as we wish (~ is given by (3.4.85\u00bb. But, with a five d.o.f. manipulator (n=5) the angle ~ is not free but it follows from xA' YA' zA' e, ~, and hence, u 2 is not a free parameter. Let us now define the reduced position vector determining the position relative to the joint constraint" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003281_027836498600500206-Figure7-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003281_027836498600500206-Figure7-1.png", + "caption": "Fig. 7. Simulation of singularity 2.", + "texts": [ + " (25), ~6, equals zero if where Thus singularities occur if any of the three factors in ~6 becomes equal to zero. The three determined singularities in motion may be interpreted kinematically as follows: 1. The first singularity with E = 0 is shown in Fig. 6. Point 0(i) is located on axis d-d, which is parallel to the z(i) axis. Point 0(~) may trace out a line on the surface of the cylinder of radius s 12, and the parameters of motion d~ila and d~3z4 become dependent. 2. The second singularity in motion occurs with cos \u00c7p23 = 0, when axes a-a, b-b, and c-c lie in parallel planes (Fig. 7) and the lines of the shortest distances between axes a-a and b-b, c-c and b-b coincide with each other. Links 3 and 4 are rigidly connected. Link 2 and the assembly of links 3 and 4 are movable at the indicated position, while links I and 5 and all other links of the manipulator are at rest. 3. The third singularity occurs with sin \u00c7p45 = 0 (Fig. 8). At this position, axes a-a and b-b are aligned, and links 4 and 5 can be rotated as one rigid body while other links are at rest. 6.3. PROCEDURE OF COMPUTATION Using equations of singularities Eq" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003002_robot.1997.606774-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003002_robot.1997.606774-Figure2-1.png", + "caption": "Figure 2: Base coordinates.", + "texts": [ + " We give the definition of the metrology or base frame and the end link frame exclusively; the definition of the intermediate frames can be found in for example [7]. The non-geometric parameters include only the joint offsets, since in most closed-loop calibration methods the gains are difficult to estimate [6]. 3.1.1 Definition of the Base Frame There are two cases for the definition according to whether the first robot axis is parallel with or perpendicular to the plane. We show the definition for the first case using DH parameters. In order to handle the problem easier, let\u2019s number the base frame as -1 (Figure 2). There is a problem with finding frame origins 00 and 0-1, because there is no constraint on the location of the endpoint on the plane. Assuming that we can apply DH parameters for frame 1 , the first definitive point is the intersection of the common normal 51 with the first rotation axis ZO. This intersection is a good choice for 00, which then sets dl = 0. Project 0 0 to the plane to set 0 - 1 and z-1. Since the first robot axis is nearly parallel to the plane, z-1 and zo are nearly perpendicular, and their common normal 20 is well defined", + " However 31 92 the maximum likelihood estimate is obtained by minimizing the following chi-square function: we noticed that this configuration yielded a serious observability problem in case of the Puma 560 robot. 3.1.2 Because the orientation of the end link frame does not play a role, only three parameters out of the four are needed. We can choose z, to be parallel with zn-l; this :sets a, = 0. 3.2 The Identification Procedures 3.2.1 Nonlinear Least Squares Optimization Relative to the -1 frame (Figure 2), the plane constraint on the end link frame can be expressed by the calibration equation: Definition of the End Link Frame p; = 0 After substituting the forward kinematics (3) of the robot and linearizing the equation, we get: Api = 0 - f ( # k ) = &'A# where is the basis for the iterative update of parameters. contains the third component of f i . This equation 3.2.2 Implicit Loop Method The Implicit Loop Method is based on the unification of open and closed-loop methods: the closure of kinematic loops by end-effector measurements or by constraints are considered equivalent [12]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002644_1.1398289-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002644_1.1398289-Figure1-1.png", + "caption": "Fig. 1 Rigid rotor supported by a pair of ball bearings", + "texts": [ + " But his model could not explain the nonlinear load-deflection effect because it could not include the change of the relative position between the rolling elements during rotation. Aktu\u0308rk et al. @8,9# proposed a vibration model of a ball bearing with waviness considering three degrees of freedom. They could not explain ball bearing vibration due to the effects of angular motion. This research presents a nonlinear model to analyze the ball bearing vibration resulting from the waviness in the rigid rotor supported by two or more ball bearings considering five degrees of freedom, as shown in Fig. 1. The proposed model can calculate the angular vibration as well as the translational vibration of the rotor supported by two or more ball bearings with waviness. Numerical results of this research are validated with those of prior researchers. This research also characterizes the vibration frequencies resulting from the various kinds of waviness existing in rolling elements, the harmonic frequencies resulting from the nonlinear load-deflection characteristics of the ball bearing and the sideband frequencies resulting from the waviness interaction of the ball bearing", + " Because the phase angle of ball waviness in contact with the outer race is 180 deg ahead of the ball waviness in contact with the inner race, the ball waviness due to the interaction of two surfaces can be defined as follows: u j5( l51 O C jlFcos~ lvbt1g j l!1cosH lvbS t1 p vb D1g j lJ G , (6) where vb , C jl , and g j l are the spinning frequency of the ball, the amplitude of ball waviness and the initial phase angle of ball waviness, respectively. The contact force of the ball bearing supporting a rotating system acts along the contact angle, and its angle can be defined by the positive or the negative angle, as shown in Fig. 1. The equations of motion of a rigid rotor can be expressed in terms of the mass center so that the position vectors of the inner and outer groove radius center of the j th ball, Ri j and Ro j , should be defined with respect to the mass center of a rotating system consistently, as shown in Fig. 4. They can be expressed as follows: RW i j5Ri cos c j \u0131W1Ri sin c jW1aikW (7) RW o j5Ro cos c j \u0131W1Ro sin c jW1aokW . (8) The azimuth angle of the j th ball in x-y plane c j , can be expressed with the rotating frequency of the cage", + " Applying these forces and moments to the force and moment equilibrium conditions, the equations of motion can be derived as follows: mx\u03081Fx50 my\u03081Fy50 mz\u03081Fz50 Izu\u0308x1IrVu\u0307y1M x50 Journal of Tribology rom: http://tribology.asmedigitalcollection.asme.org/ on 01/28/2016 Term Izu\u0308y2IrVu\u0307x1M y50, (28) where m, Ir , Iz , and V is the mass of a rotor, the radial mass moment of inertia, the polar mass moment of inertia and the rotating speed of a rotor, respectively. 5.1 Analysis Model and Numerical Procedure. This research investigates the ball bearing vibration resulting from the waviness in a rigid rotor supported by a pair of ball bearings, as shown in Fig. 1. The analysis model has a pair of inner-race rotating type of ball bearings, and it has the negative and positive contact angles at the left and right ball bearings, respectively. The span center of the ball bearings is assumed to coincide with the mass center in the sections 5.2 and 5.3. Tables 1 and 2 show the specification of the spindle system and the ball bearing. Waviness amplitude in the rolling elements is assumed to be 0.531026 m, and the ratio of the waviness amplitude and the elastic compression of a ball is about 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003135_j.conengprac.2006.09.001-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003135_j.conengprac.2006.09.001-Figure1-1.png", + "caption": "Fig. 1. Electromechanical test bench.", + "texts": [ + " In this paper, the matrix dimensions in the persisting condition are reduced by using only unknown parameters in the regressor structure. The remainder of this paper is organized as follows. The next section describes the electromechanical test bench. Section 3 describes the backlash modeling and Section 4 presents the developed super-twisting observer to estimate the disturbing backlash torque and the dead zone amplitude. Sections 5 and 6 present simulation and experimental results, respectively. Conclusion is given in Section 7 and at last, the algorithm convergence proof is given in the Appendix. The test bench presented in Fig. 1 has been developed to identify some mechanical imperfections. All of this development is given in Merzouki and Cadiou (2005). It represents an electromechanical system made up of a motor reducer involving an external load. The motor part is actuated by a DC motor delivering a relative important mass torque. This test bench presents built-in mechanical imperfections as friction, backlash and elasticity and allows to vary their amplitudes. Coulomb friction is represented by a contact of various components of the system with different rigidities", + " Viscous friction depends on the lubricant viscosity, contained between surfaces in contact. Backlash phenomenon is described by two independent mechanical parts, whose transmission is carried out via a dead zone, varying between 01 and 241. A spring system is placed between the two mechanical parts in order to deliver a smooth transmission. R. Merzouki et al. / Control Engineering Practice 15 (2007) 447\u2013457 449 On this test bench, one can measure input and output positions of the reducer part by using two incremental encoders of Fig. 1, where the relative load position is depending on friction between the gears in contact, as well as flexible transmission through a dead zone. Fig. 2 illustrates the simplified system schema of the real system. Let us consider that static friction is disregarded, then the mechanical model of the test bench, including the backlash is described by the following system Je:\u20acye \u00fe f e:_ye \u00fe C \u00bc u; Js:\u20acys \u00fe f s:_ys \u00bc N0:C; ( (1) Js, Je, f s, f e are, respectively, inertias and viscous frictions of reducer and motor parts which are identified experimentally", + " (25) is written as follows: _cDa \u00bc cDaG 1t _Gt \u00fe z\u03042jTGt, (26) using the equalities of Gt given above, the dynamic expression to compute cDa is given by _cDa \u00bc \u00bd cDaj\u00fe z\u03042 jTGt. (27) A dynamic form to find Gt is _Gt \u00bc GtjjTGt. (28) The use of Eqs. (27) and (28) ensures the asymptotic convergence of cDa to Da. These equations allow to identify the real values of the parameters K and j0. For the simulation tests, a variable velocity trajectory tracking is carried out in the system model set up of Fig. 1. After the injection of a sinusoidal control signal, see Fig. 7, the corresponding simulation constants are given in Table 1. The value of g represents a nominal value taken from the experimental test bench. For input velocity estimation of Fig. 8, one can notice a good performance of the estimation with an asymptotic convergence of the error in Fig. 9. Then, the input position estimation deduction of Fig. 10 shows that the position estimation error goes also to zero (see Fig. 11). Similarly, the state Fig", + " Also, due to reconstruction of the system states Fig. 18. Estimation of input velocity signal. 0.5 0.1 0.05 0 -0.05 -0.1 0 2 4 6 8 10 Time (sec) 12 14 16 18 20 E st im at ed in pu t v el oc ity e rr or e (r ad /s ) Fig. 19. Input velocity estimation error. R. Merzouki et al. / Control Engineering Practice 15 (2007) 447\u2013457454 via the considered observers, the disturbing position hysteresis has been well identified as shown in Fig. 17. Experimental tests have been done on the electromechanical test bench (see Fig. 1) described in Section 2, with the observer parameters given in Table 2. Only two states are measured, corresponding to positions of the motor axes (input position) and reducer part (output position). The proposed observers reconstruct input and output velocities of backlash phenomenon from the already performed input and output position measurements. Fig. 18 shows the real input velocity signal (continuous line) and its estimation through the corresponding observer (dotted line), where the estimation error converges to zero with less variations Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002559_0278364904047389-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002559_0278364904047389-Figure1-1.png", + "caption": "Fig. 1. Coordinate convention of SLIP with pitching dynamics. In the text, the COM coordinates are parametrized by Cartesian coordinates, i.e., y = \u03b6 sin(\u03c8) and z = \u03b6 cos(\u03c8). In flight, the leg angle \u03c6 is in general a function of time and of the SLIP\u2019s liftoff state: \u03c6(t, x0).", + "texts": [ + " We are motivated in part by the need to explain and control the remarkable performance of RHex, an autonomous hexapedal running machine whose introduction has broken all prior published records for speed, specific resistance, and mobility over broken terrain (Saranli, Buehler, and Koditschek 2001). When RHex is properly tuned it exhibits sagittal plane center of mass (COM) The International Journal of Robotics Research Vol. 23, No. 10\u201311, October\u2013November 2004, pp. 979-999, DOI: 10.1177/0278364904047389 \u00a92004 Sage Publications trajectories well modeled by the spring loaded inverted pendulum (SLIP; Altendorfer et al. 2001), depicted in Figure 1. Indeed, this reflects the machine\u2019s bio-inspired origins, since animal (Blickhan and Full 1993) and human (Schwind 1998) runners exhibit sagittal plane COM trajectories similarly well described by the SLIP model. Moreover, the introduction by Raibert (1986) of the first dynamically stable running robots embodied the literal SLIP morphology. Thus, while other interesting hybrid Hamiltonian models of robotics are likely to be amenable, we focus the development of our new analytical method on variations of the SLIP running model", + " As a final observation that we will require below (in Appendix A), note that if Theorem 3 has been shown to hold for S\u03b1 = G\u03b1 \u25e6F\u03b1; it also holds for reverse time flow maps of the formS\u03b1 = F\u03b1\u25e6G\u03b1: LEMMA 3. If S\u03b1 = G\u03b1 \u25e6 F\u03b1 is an involution, then S \u2032 \u03b1 = F\u03b1 \u25e6G\u03b1 is an involution, too. Proof. S \u2032 \u03b1 \u25e6 S \u2032 \u03b1 = F\u03b1 \u25e6G\u03b1 \u25e6 F\u03b1 \u25e6G\u03b1 = (G\u03b1 \u25e6G\u03b1) \u25e6 F\u03b1 \u25e6G\u03b1 \u25e6 F\u03b1\ufe38 \ufe37\ufe37 \ufe38 =id \u25e6 G\u03b1 = G\u03b1 \u25e6G\u03b1 = id . In this section we establish the specifics of the SLIP models considered in this paper. They are listed in terms of the categories: geometry, trajectories, control, and potential forces. Geometry. The 3DoF sagittal plane SLIP model is shown in Figure 1. It shows a rigid body of mass m\u0303 and moment of inertia I\u0303 with a massless springy leg with rest length \u03b6\u03030 attached at a hip joint that coincides with the COM. The strength of gravity is g\u0303. The approximation of a leg with zero mass avoids impact losses at touchdown and simplifies the control. For convenience, all of the following expressions are formulated in dimensionless quantities, i.e., t = t\u0303 \u221a g\u0303 \u03b6\u03030 , y = y\u0303 \u03b6\u03030 , y\u0307 = \u02d9\u0303y\u221a \u03b6\u03030 g\u0303 , at NORTHERN ARIZONA UNIVERSITY on June 11, 2015ijr.sagepub", + " The flight vector field reads f\u03022(\u0302x) = ( y\u0307, z\u0307, \u03b8\u0307 , 0,\u22121, 0 ) (16) whose analytic flow is trivially computed as f\u0302 t 2 (\u0302x0) = y0 + y\u03070t z0 + z\u03070t \u2212 t2 2 \u03b80 + \u03b8\u03070t y\u03070 z\u03070 \u2212 t \u03b8\u03070 . (17) Solving eq. (7) with f\u03022, the diagonal linear involutive time reversing symmetry G\u03022 of eq. (16) is not uniquely defined and is given by G\u0302\u2213 2 = diag(\u22131, 1,\u22131,\u00b11,\u22121,\u00b11) . (18) As will become clear later in the next section, in order to define a stride map as in eq. (4), the time reversal symmetries should match for stance and flight, hence G\u0302\u2212 2 = G\u03021 =: G\u0302 is chosen. The threshold function h2 for a general leg placement parametrized by the angular trajectory \u03c6(t, x\u03020) (see Figure 1) becomes zero when the toe touches the ground h2(\u0302x0, t) = z(t)\u2212 cos(\u03c6(t, x\u03020)) (19) and implicitly defines the control input t2(\u0302x0). If \u03c6 depends on x\u03020, the liftoff coordinates, feedback control is employed. The design of the function \u03c6 constitutes the control authority in our SLIP model. Poincar\u00e9 section. A SLIP stride consists of stance and flight, therefore its stride map should be written as S\u0302 = F\u03022 \u25e6 F\u03021. The end of the stance phase is characterized by the liftoff event, detected by the threshold equation h1; the end of flight is characterized by the touchdown event, detected by the threshold equation h2", + " Because we exploit in this paper the factorization of R into stance and flight phase, it is natural to work in \u201cliftoff coordinates\u201d, i.e., on the Poincar\u00e9 section P; hence, the feedback variables are naturally assumed to be taken at the \u201ceasily detected\u201d liftoff event as noted in S1. We appraise in Section 3.3.1 the alternative choice of working formally in apex coordinates (not to be confused with the physically unattractive choice of taking the sensory feedback measurements at the apex event). Criteria S2 and S3 can be addressed by rewriting the leg angular trajectory \u03c6 that is defined in an inertial frame (see Figure 1) as \u03c6(t, x0) = \u03c6C(t, C(x0))\u2212 \u03b8(t). (36) The second term in eq. (36) indicates that \u03c6C is specified with respect to the SLIP\u2019s body frame, as will be the case in all 3DoF SLIP models in this paper. For 2DoF SLIP models, \u03b8 is not defined and this term is absent. It is not possible to distinguish S3(iii), \u201cquality\u201d (i.e., inertial versus non-inertial frame based) in the 2DoF setting, since by its very geometry, body frame coordinates cannot be introduced. On the other hand, the additional body pitch degree 9", + " Note that this feedback control cannot be modeled straightforwardly in our simplified SLIP system because of the masslessness of the leg. at NORTHERN ARIZONA UNIVERSITY on June 11, 2015ijr.sagepub.comDownloaded from of freedom of the 3DoF SLIP model allows this distinction to be made. A leg angle trajectory that only uses sensing with respect to the body reference frame S3, can be modeled by the following output map CB( \u03c6B0 \u03c6\u0307B0 ) = ( arccos(z0)+ \u03b80 \u2212 z\u03070\u221a 1\u2212z2 0 + \u03b8\u03070 ) = CB(x0) (37) where \u03c6B0 is the leg liftoff angle with respect to the body normal (see Figure 1) and \u03c6\u0307B0 is the leg\u2019s angular velocity at liftoff measured in the body frame. Specifying this trajectory in the body frame yields \u03c6(t, x0) = \u03c6CB (t, \u03c6B0 , \u03c6\u0307B0)\u2212 \u03b8(t). (38) In summary, the 3DoF SLIP model allows the distinction of the \u201cquality\u201d of sensing required for a particular control input which in turn enables an assessment of the \u201ccost\u201d of control. In this section, we observe that deadbeat control of a 2DoF or 3DoF SLIP model requires the Jacobian of a real-analytic return map to be globally singular, not just at the control target fixed point x\u0304 but in a neighborhood U\u0304 x\u0304 of the reduced Poincar\u00e9 section X ", + " Figure 3(d) is reminiscent of KAM-tori of area-preserving two-dimensional mappings (see Moser 1973). However, as can be seen in Figure 4, the phase space volume is not preserved away from the fixed point x\u0304 for k = 1. In Appendix C we invoke reversibility (Sevryuk 1986) in place of area-preservation to show that the numerically observed neutral stability for the leg recirculation scheme with k = 1 is expected. In this final example application, we address the full 3DoF SLIP model with pitching dynamics depicted in Figure 1 that will be the basis for a RHex inspired running monoped in Altendorfer, Koditschek, and Holmes (2004). We develop two central results. First, we characterize the (unique) body frame sensor model (37) required to achieve singular control and characterize the resulting globally singular return map Jacobian. Secondly, comparing the number of available design parameters of this SLIP model to the dimension of the reduced Poincar\u00e9 section, we exclude the possibility of deadbeat control. We want to investigate the possibility of deadbeat control with a leg angle trajectory of the form (38) \u03c6(t, x0) = \u03c6CB (t, \u03c6B0 , \u03c6\u0307B0)\u2212 \u03b8(t), i" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002683_s0141-6359(00)00066-0-Figure9-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002683_s0141-6359(00)00066-0-Figure9-1.png", + "caption": "Fig. 9. Orthographic and isometric views of one LRU. The arrows numbered 1\u20136 represent the six constraints that support the assembly. The arrows are proportional to the reaction forces.", + "texts": [ + " This concept for the NIF requires many hundreds of large kinematic couplings to handle LRUs with the transportation canister and to mount them within the laser structures. The kinematic mount between the LRU and laser structure, although based on three vees, deviated from our experience sufficiently to motivate an optimization using the limiting coefficient of friction. Fig. 8 shows this design on a prototype LRU, which is temporarily separated from the support structure to show the kinematic mount. The basic configuration of the kinematic mount is a three-vee coupling with one widely spaced vee at the top and two vees near the bottom. Fig. 9 shows the locations and orientation of the six constraints in four different views. Configuring the mounting points to lie in a vertical plane gives the most favorable aspect ratio and accommodates the dense packing of LRUs. Furthermore, finite element analysis showed that the torsional mode of the frame would be a limitation to vibrational stability, assuming zero friction in the constraints. Placing the instant center of the upper vee near the principal axis of the LRU reduces the inertia in the torsional mode and increases the frequency" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure8.1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure8.1-1.png", + "caption": "Fig. 8.1 Designed model of actuator operation with magnetic circuit", + "texts": [ + " Thus, this X-ray exposure stage makes it feasible to form three-dimensional (3D) structure such as spiral coil patterns [6-8]. With this technique, it was possible to fabricate high aspect ratio coil line structures. An electromagnetic type actuator including a magnetic circuit was designed with the aid of calculated by simulation. The simulation was carried out varying the aspect ratio of the coil lines. For the design of the magnetic circuit, we used the type known as an \u201copen frame solenoid\u201d, which is open at the sides as shown in Fig.8.1 [6,7]. For the material of the magnetic core (fixed core and plunger) and the shield parts (yoke) we used the nickel iron alloy Permalloy 45, because it has the largest permeability of the soft magnetic metals. Therefore, it can generate a strong magnetic field with a very small electric current. When a voltage is applied to the coil, a magnetic flux is formed in a gap, which deforms the magnetic field and produces a suction force on the plunger. An acrylic pipe with an outside diameter of 5 mm and an inside diameter of 3 mm was used as the base material for coil lines fabrication", + " This figure shows that the copper layer was grown up from the bottom of grooves, completely filling the high aspect ratio structures. Isotropic chemical etching of copper using E-process-W etchant was performed until only the copper in the grooves remained, thus forming the coil lines. The pipe rotation mechanism was also used to rotate the acrylic pipe in the etchant to ensure uniform pipe surface etching. From this result, we produced coil lines by copper etching until the protrusions of groove structures were exposed, as shown in Fig.8.8. We also built a measurement system, as shown in Fig.8.1, in order to measure the suction force of the designed electromagnetic type actuator. This system is a very Development of a New Nano-Micro Solid Processing Technology 85 simple structure and it is easy to change the coil [7], as shown in Fig.8.9. The gap between the plunger and the fixed core was adjusted by an XY stage. Figure 8.10 shows a comparison of the theoretical values by simulation and actual measurement of the suction force generated by a coil with 30 m width and an aspect ratio of 2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003593_0301-679x(84)90093-8-Figure7-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003593_0301-679x(84)90093-8-Figure7-1.png", + "caption": "Fig 7 Schematic diagram o f modif '~d ehd test rig f o r fu l ly f looded testing. A - video camera system, B - microscope, C - loading system, D - splash guard, E - transparent cover, F - thermal insulation, G - steel ball, H - glass disc, I - stirrer, J - heating system, K - test fluid, L - sealed roller bearing", + "texts": [ + " The authors have studied three o/w emulsion systems, with properties shown in Table 4, and which fall into two categories: fluids B and C can be used with a hard water supply, but fluid A requires a softer water source. The emulsifying oils were supplied in concentrated form for mixing with water. Thus, 5/95 o/w emulsion was prepared in the laboratory by slowly adding the required amount of emulsifying oil (5% by weight) to distilled water at room temperature using a Silverson L2R mixer at a rotating speed of about 800 r/min over 20-30 minutes. Elastohydrodynamic film thickness tests were carried out under fully flooded conditions. A schematic diagram of the test rig is shown in Fig 7. This arrangement eased emulsion supply problems and prevented evaporation from the surface. It is also much more representative of a fully flooded pump than the drip-feed commonly employed in optical work. No optical films were observed for three 5/95 dilute emulsions at any time during two hours of running at constant speed of about 3 m/s over a temperature range of 20-60\u00b0C. Thus it can be concluded that no ehd films of more than 0.1 tan thick form in such circumstances. The removal of chromium from the rubbing track was noted to Table 4 Properties of emulsifying oil Emulsifying oil for Maximum acceptable Refractive dilute 5/95 o/w hardness of water index emulsions A ~ 250 mg/I 1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure2.44-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure2.44-1.png", + "caption": "Fig. 2.44~ pm - nm diagrams", + "texts": [ + " We have also adopted some value of the reduction ratio. All the calculations refer to some defined manipulation task with a pre scribed execution time. Test 1. We can find the pm - nm characteristic of the chosen motor max in the catalog. It is the diagram of maximal torque depending on motor r.p.m. If the diagram is not given directly, it can be constructed from the data given in the catalog. In manipulator systems, we often use m m permanent magnet D.C. motors. For such motors the Pmax - n characteristic has a polygonal form (straight lines in Fig. 2.44). In the cata log we find sometimes the value of maximal motor torque (corresponding to the point A in Fig. 2.44) and the maximal rotation speed (point B in Fig. 2.44). These two values define the maximal characteristic (we 97 assume a straight line). Let the value of maximal torque for nm+O (point m m A) be marked by PM and let the value of rotation speed for P +0 (point B) be marked by n~. The torque P~ is often called stall torque, and the rotation speed n~ is called no-load speed. When this speed is expressed in terms of r.p.m. then it is marked by n~ and if it is expressed in terms of rad/s then we mark it by w~. The straight line maximal charac teristic between P~ and n~ will be proved in paragraph 4.5.1. It should be said that there is sometimes a difference between the real value of maximal torque (P~r) and its theoretical value (P~); the real value of pMm is less than pmM. In such a case the maximal characteristic pm _nm r. max has an upper bound P~r (point C in Fig. 2.44a). This characteristic defines the feasible domain. The real pm - nm characteristics must be wholly within this domain. The calculation of pm - nm characteristic was explained in 2.5.1. In each iteration a new point of the diagram is obtained. The algorithm checks whether it is within the permissible do main. If it is, a new iteration starts, and if it is not, the algorithm signals that there is a violation of the constraint. The constraint considered follows from the mathematical model of D.C. actuator", + " If we neglect rotor acceleration effects and friction term, motor output torque is (2.6.2) where CM is the constant of torque. Combining (2.6.1) and (2.6.2) one obtains u - (2.6.3a) If rotation speed is expressed in terms of r.p.m. (nm 60 \u00b7m 271 q ) then (2.6.3b) Let us introduce the constraint of maximal input voltage u max Then, from (2.6.3) it follows m n m ~ (2.6.4) m umaxCM m where PM = R is stall torque and nM 60 u max . -- ---- lS no-load speed. 271 CE This constraint of maximal input voltage can be represented by a strainght line in pm - nm plane ((1.) in Fig. 2.44b). We use this con straint in the quadrants I and III of the pm - nm plane. For the quad rants II and IV we introduce the constraint of maximal rotor current in order to keep this current smaller than the stall current value: Iii..; iM (2.) in pm u max h . .. d b h' 1 l' --R--.T lS constralnt lS represente y a orlzonta lne - nm plane (Fig. 2.44b). Finally, we introduce the constra- int of maximal allowed speed n max ((3.) in Fig. 2.44b), for instance n max m nM\u00b7 If viscous = umax / (CE friction is not neglected RBc + ---C ). B is the viscous M c m then no-load speed becomes wM friction coefficient. This modi- fied constraint is represented by dotted line in Fig. 2.44b. An example is shown in Fig. 2.44a.Straight lines represent the con straint pm _ nm. It can be concluded that the pm - nm diagrams spread max 99 when the working speed increases, i.e., the execution time T decreases. For T = 5s and T = 4s the diagrams are wholly within the permissible domain. It means that the actuator chosen can produce manipulator work at this speed. For T = 3s the diagram extends beyond the permissible domain i.e. the constraint is violated. It means that the motor cannot produce manipulator work at that speed", + " Test of a hydraulic actuator Testing of a hydraulic actuator can be done in a way similar to the test of a D.C. electromotor. The algorithm for dynamic analysis comput es the characteristic of driving torque (or force) p versus internal velocity q (rotational or translational). In the case of rotational joint r.p.m. (n) is usually used instead of q. This characteristic is compared with the maximal capabilities of the actuator. With the D.C. motor these maximal capabilities were defined by a linear maximal cha racteristic P:ax - nm (Fig. 2.44). With the hydraulic actuator this appears to be rather different. Maximal torque (or force) is not cou pled strongly with actuator speed. Theoretically, the torque does not depend on motor speed. For instance, with the rotational hydraulic ac tuator the torque can be expressed as m V' P = ~p 2n where ~p is differential pressure and V'is the unit volume (per one full revolution). The maximal torque pm follows directly from the max maximal difference in pressure and has a constant value with respect to motor speed", + " 252 It should also be said that we do not optimize the parameters of all segments. Some segments are completely determined by the constructive solutions adopted. We shall explain this fact in more detail in the example, but let us say here that, for instance, the actuators chosen determine completely the segments which form the gripper (the last three segments if a six d.o.f. manipulator is considered). We may say that there usually exist one or two segments which should be optimized. If a cylindrical (Fig. 2.44) or spherical (Fig. 4.6) manipulator is in question, there is usually one main segment forming the manipulator arm and this is the one to be optimized. With anthropomorphic (Fig. 2.53) or arthropoid (Fig. 4.2) manipulators there are two main segments which form the manipulator arm and which should be optimized. We can make some further simplifications in order to reduce the number of parame ters to be optimized. The lengths of segments can be considered as known since they directly follow from the reachability conditions im posed" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000026_acsami.0c17518-Figure7-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000026_acsami.0c17518-Figure7-1.png", + "caption": "Figure 7. Assembly and movement of the snake-shaped structure. (A) Schematic of parts and assembly. (B) Assembly process of the chain structure in the auxiliary workshop. (C) Swing and (D) curling of the chain structure. (E,F) Changes in the angle of each joint during swinging and curling.", + "texts": [ + " The successful assembly and transmission of gears indicate that the integrated assembly method using bubble robots may play an important role in the production of integrated functional microstructures. 2.6. Assembly and Movement of the Snake-Shaped Structure. In addition to the fixed connection forms considered so far, a chain structure similar to a snake can also be assembled by a bubble microrobot using microparts. Unlike the microparts connected by tail\u2212socket joints, the microparts connected by shaft\u2212hole joints can rotate with respect to each other during movement. As shown in Figure 7A, microparts with double shafts or holes are designed and manufactured. The diameter of the shaft is 50 \u03bcm, and the pitch is 220 \u03bcm. The diameter of the holes is 60 \u03bcm, and the pitch is 120 \u03bcm.When the shaft is inserted into the hole, it can rotate freely in the hole. Conversely, the hole can rotate around the shaft. The assembly process of the four parts in the auxiliary workshop is shown in Figure 7B. After a pair of microparts is connected by a shaft\u2212hole joint, this set of parts is pushed out of the workshop. Then, bubble robots assemble two additional parts to form another set. Finally, the two sets of parts are integratively assembled to form a snake-shaped chain structure composed of four microparts. Owing to the nature of shaft\u2212hole joints, the assembly can swing and curl flexibly like a snake, as shown in Figure 7C,D and Movie S6. In the process of swinging and curling, each part can be rotated and the angle of each joint can be changed. The parts are numbered as 1\u22124, and the joints are marked as \u03b212, \u03b223, and \u03b234. The solid lines represent the position of each part, and the solid line circles represent the position of the shaft\u2212hole joint. The dashed lines and circles represent the previous or initial https://dx.doi.org/10.1021/acsami.0c17518 ACS Appl. Mater. Interfaces XXXX, XXX, XXX\u2212XXX G positions of the parts and joints, respectively. The arrows indicate the direction of the movement of part 4. The bubble robot drives part 4 directly, so part 4 can be regarded as the driving part and parts 1\u22123 can be considered as the driven parts. The change in the joint angles over time is shown in Figure 7E,F. During the swinging process shown in Figure 7C,E, \u03b212 remains almost unchanged and the rotation mainly occurs between parts 3 and 4. \u03b234 fluctuates between 20 and 25 s, which is caused by the return error of the stage. During the curling process, the angle of each joint changes considerably, as shown in Figure 7D,F. Unlike during the swinging process, the change in the joint angle of parts 2 and 3 is the smallest during the curling process. This is due to the fact that part 2 is relatively short, and \u03b223 cannot change when parts 1 and 3 are in contact. Initially, \u03b212 is less than 180\u00b0. Finally, all the joint angles are greater than 180\u00b0, which indicates the realization of curling. In both the processes, all the joints show good rotation performance, and the movement of the snake-shaped chain structure is very flexible" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003232_10402009108982033-FigureI-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003232_10402009108982033-FigureI-1.png", + "caption": "Fig. I-Sliding optlcal EHD device.", + "texts": [], + "surrounding_texts": [ + "in conjunction with a sliding point contact device. The Hertzian contact is formed by a stationary 1R transparent disc (sapphire o r diamond) loaded against a rotating steel ball. IR radiation is focused into the contact using the FTIR microscope system and this is reflected at. the lubricandsteel . . interface and collected by the microscope optics for analysis by the IR detector. Spectra can be taken of discrete areas of the contact, typically 75-200 pm in diameter, the area being defined by the aperture used. For most spectra in this study an aperture of 100 pni diameter was employed. A variable temperature sliding EHD device was designed for this work and is shown in Fig. 1. T o ensure that the contact is fully flooded the steel ball is immersed in a controlled temperature lubricant bath. The sliding EHD device is mounted on an X-Y-Z micropositioning table directly underneath the FTIR microscope and the microscope is focused through the vertical movement of the table. The horizontal table gives a total of 25 mm movement in both X and Y directions with 10 pm resolution, and in this way the entire contact area, inlet and exit regions can be examined. The Hertzian contact is defined by the formation of inter- D ow nl oa de d by [ M os ko w S ta te U ni v B ib lio te ] at 1 3: 11 1 0 N ov em be r 20 13 l'crcncc I'ringes clue to the high refractive index of the IR winclow so that the relative position of the target spot is ;iccuraicly known. T h e range of test conditions employed in this sti~cly is s i~~iiniar ized in Table 2. I)cpcncling upon the wavelength range required, either s:il)l)hirc o r cliamond windows were employed. Sapphire ;ibsorl)s I R above 5 p111 which means that its use is limited to the 2 to 5 pnl range. This region includes the strong C-H strclcli b;~ncls associated with hydrocarbon basestocks. Dia~ l l o n d ciun be i~secl over the entire mid-1K range of 2 to 4 0 pnl, though some loss o r resolution is experienced in the 4 lo 5.5 p m range. Reflection losses a r e also greater than li)r s ;~pphirc clue to the very high refractive index of dia111onc1. 'l'hc clii~mond window was only used where inforI I I ; IL~OI) W;IS rcqi~ired from the region above 6 pm. Tlnc s1)cctromcter used was a FTIR instrument with 3600 c l a ~ ; ~ slation ancl Spectra Tech IR Plan microscope. 'I'his spectrometer is a single beam system so that sample spcctr;i must be ratiocd against a background spectrum to remove s p i ~ r i o i ~ s absorption bands d u e to 1R optics and ;~tmospIicrc. Background spectra were usually taken from the cliamoncl o r sapphirelsteel interface a t the middle of the static, lo:tdcd Hcrvzian contact. Absorption bands d u e to the C I ~ ; I I I I O I I C I wcre also substantially reduced by this method, although this clepends upon the position o f the sample area ; I I I ~ t he i l l t ~ r l i ~ c i i ~ l oil film thickness. T o obtain a full Hertzi;~n profile, spectl.ii were taken at 50 p m overlapping intervals ;)long the contact center line, parallel to the direction of 111otion as shown schematically in Fig. 2. Typically, twelve TABLE 2-TEST CONDITIONS U ED I N SLIDING RIG Hertzian width Load Maximum Hertzian pressure Sliding speed Bulk oil temperature Static specimens: sapphire disc diamond disc type I1 Sliding specimen: M52 100 steel ball spectra sample 20-72 N 0.8-1.5 GPa 0-2.5 ms-' 20-100\u00b0C 25.4 mm diameter (R1 1.6) 3 mm diameter (RI 2.4) 25.4 mm diameter size 1 OOpm - Sliding Fig. ?-Geometry of EHD contact. readings could be taken from the inlet to the exit region. Table 3 lists the test lubricants and additives studied. LUBRICANT PRESSURE STUDY In a preliminary test of the feasibility of the method, the rig was r u n using a synthetic hydrocarbon base oil (PAO) to examine infrared pressure shifts in a n E H D contact. Infrared spectra from the inlet, Hertzian and exit regions of a sapphirelsteel contact sliding a t 0.1 m/s a r e given in Fig. 3. Only the C-H stretch region 3100-2800 cm-I is shown. T h e intensity of the peaks can be related to oil film thickness a n d can be seen to decrease passing from the inlet to the Hertzian contact. In the exit, although the film g a p is large, the amount of oil present is reduced d u e to cavitation. Static calibration of the dependence of absorbance on film thickness suggests that E H D films down to 8 0 n m can be detected, as indicated in Fig. 4. This result has been applied to an operating contact where central film thickness was measured as a function o f sliding speed both optically a n d by 1K absorbance and , as can be seen in Fig. 5 there is excellent agreement between the two methods. Careful examination of Fig. 3 reveals that the position of the peak a t 2923 cm-I , attributed to the asymmetric C-H (CH*) stretch vibration, shifts towards higher frequencies in the high pressure region. Such pressure shifts a r e well documented in both the Raman ( l l ) , (12) and IR (14) literature a n d Raman shifts have been used by other workers to generate pressure profiles within the E H D contact (12). > Calibration of peak shift-pressure dependence is usually done by ruby fluorescence measurements (14), but this was D ow nl oa de d by [ M os ko w S ta te U ni v B ib lio te ] at 1 3: 11 1 0 N ov em be r 20 13 In Lubro Studies of Lubricants in EHD Contacts Using FTIK Absorption Spectroscopy flg. 3--infrared spectra from sliding EHD contact. Average film thicknesslnm Fig. 4-Calibration of absorbancemim thickness. Load : 20N Oil temperature 20\u00b0C Ball sliding speed mls Fig. &Measured central oil film thickness. not possible in this study. The frequency shift was measured as a function of load for the low speed case and the shift was found to increase linearly with pressure calculated from Hertzian theory. A secondary pressure scale (15) was also used to calibrate this shift for a limited number of tests. A small amount of sodium nitrate powder was incorporatetl in the test fluid and the two pressure shifts, that of the C-H and of the antisymmetric stretch of the nitrate ion were compared. When the actual pressure was calculated from the nitrate shift using an expression given by Klug ant1 Whalley (15), reasonable agreement between the two nieth- - ods was found. By measuring the C-H stretch frequency shift at different positions in the contact it was possible to determine the pressure profile experienced by the lubricant in its passage across the contact. This is shown in Fig. 6 which also includes a film thickness profile plotted directly from the peak intensity. The latter is approximate, neglecting any thermal effects which might also contribute to absorption variations, but does appear to give a sensible film thickness profile. The shape of the pressure profile accords quite well with profiles obtained by microtransducers (16) or EHD theory, although the sampling diameter using this infrared method is LOO coarse to permit a pressure spike to be resolved. For this application, Raman is a more appropriate spectroscopic tool because of its finer spatial resolution. ANTIWEAR ADDITIVE FILM WORK Work using optical interferometry has demonstrated that some phosphorus-containing antiwear additives, notably the dialkyl and diary1 phosphonates, can form thick reacted films within EHD contacts at elevated temperatures. Most of the evidence has come from optical interferometric nieasurement of increased EHD film thicknesses (2), and there has been no direct confirmation of the chemical composition of the EHD film in the contact, nor of the relative contri- D ow nl oa de d by [ M os ko w S ta te U ni v B ib lio te ] at 1 3: 11 1 0 N ov em be r 20 13 - 1.2 Apermrc 1OOpm ball sliding speed 0.25 ms-I INLI7I' Resolution 4cm-I oil temps 25 OC 1:XT load 2ON _ 1.0 baseslock P A 0 - 0.8 2 0 U - 0.6 \"3 t _ 0.4 - 0.2 H&m width Fig. 6--Pressure profile from C-H shift for a sliding EHD contact. biitioli to the film from the basestock and additive compotlclits. 111 the current work therefore, infrared spectroIlictry has been employed to monitor the composition of tlcvcloping plivsphonate films in an EHD contact. Kcsults for one phosphonate antiwear additive bis(t-octyl phcnyl) pl~osphonate (BOPP) are presented. The lubricant ~lsccl was 3 percent wlw BOPP in PA0 basestock and the sliding speccl was 0.3 nis-I. Spectra were taken from the center of tlic rubbing contact at regular intervals during a test to monitor film build-up. I;ilm clcposition was initially observed in the outlet region 01' tllc contact as a gelantinous precipitate and, as each test prvccccI~cl, i~ltcrkrornctric color changes were observed in the central region indicating that film growth was occurring. I7igi1rc 7 shows a series of spectra taken from the center of' ;I sliclil~g coiltact during a test at 80\u00b0C. Figure 7(a) is at the st;lrt of the test and 7(b) and (c) are after 10 and 30 ~ni~rutcs running respectively. It can be seen that there is r;~picl growth of an absorption peak at 1 100 cm- ' , char;rctcristics of a P=0-M inorganic moiety (17). Figure 8 summari~cs ~ h c growth in absorbance of two peaks, the C-H strctcli at 2933 cm- and the P = 0-M vibration peak at 1100 cm-I, labcled hydrocarbon and reacted film respectively, at two different bulk oil temperatures 60\u00b0C and 80\u00b0C (iiote that ~ l i c abscissa time scales are different). Although it is not possible to directly compare the absolute absorbance v;~lucs, the rc:~ctccl film can be seen to grow faster at higher tclnI)el;tturcs. 'I'he figure shows that the growth of the P=0M pc;~k lijllows a similar pattern to that observed for film tliicklicss using optical interferometry, with an apparent intluctivll period followed by accelerating film development (2). It is noteworthy that the absorptions due to C-H and I'=O-M both rise during tests indicating that the quantity of both in the film is increasing with time. There are two pvssiI)l~ ~ ~ p l i ~ ~ i a t i o ~ i ~ for the ncrease in the C-H absorb; I I I C ~ : i t is either due to hydrocarbon groups associated with tlic rcactccl layer, or an increasing quantity of oil is being tr;~pl~ctl within the film as rubbing proceeds. 3% bis Cctyl phenyl phorphonat in synlhclic hydmcarbn Test conditions: buk oil mpanuc 8WC load .?ON sliding rpcd 0.3ds Figure 9 helps to answer this question. It shows two spectra taken at the end of the 80\u00b0C test just before and just after the ball was halted. When sliding ceases, the C-H absorption peak almost disappears but the P=O-M peak remains. It can thus be concluded that the antiwear film is composed primarily of inorganic material based on phosphorus, oxygen and metal. However the presence of the material promotes the entrainment of oil into the contact, increasing the EHD separation. SHEAR ALIGNMENT IN EHD CONTACTS The strain rates in the inlet and center of concentrated contacts are very high, typically lo6 to 10' s-I, and it is likely that many molecules align or otherwise attain a non- D ow nl oa de d by [ M os ko w S ta te U ni v B ib lio te ] at 1 3: 11 1 0 N ov em be r 20 13 In Lubro Studies of 1,ubricants in EHD Contacts Using FTIR Absorption Spectroscopy 253 0. 3% bir Octvl phenvl phol~honalc I --lo.Scan condi~tonr 128 scans 8crn.1 reralvlion 2OOprn a p c n m specua r2 Tcrt cond!l6anr: buk o ~ l tcrnpenlurc 80'C lord 20N Fig. 9-IR spectra of BOPP reacted films In an EHD contact. random spatial arrangement under these conditions. Such alignment is often used to explain shear thinning effects found with high n~olecular weight polymers and solutions (18). Lauer has produced some evidence of molecular alignment in EHD and hydrodynamic contacts (7), (19) using infrared emission and transmission-absorption spectroscopy respectively. The 1K micro-reflectance technique has been used to study shear alignment in the inlet and Hertzian regions of a sliding EHD contact. A KKS-5 I R polarizer inserted in the microscope allows spectra to be sampled at two polarizations, parallel, (11) and perpendicular, (I) to the line of flow, both parallel to the contact plane. Dichroic 1K spectra, the ratios of band absorbances for the two polarizations, can Due to the low sliding speeds necessary to avoid starvation, the EHD film thickness was very low and it was not possible to detect the soap structure within the contact. 1R spectra are therefore confined to the inlet and outlet regions. IR spectra from the inlet region of a sliding, diamond on steel, EHD contact are shown in Fig. 10 for three different speeds, at a polarization parallel to the direction s f sliding. The intensities of the band at 1582 cm-' associated with the soap structure can be seen to increase relative to the bands at 1458 and 1378 cm- ' , which are primarily due to the base oil. If spectra are taken at perpendicular polarization, the inverse effect is observed. This is indicative of alignment of the carboxylate (COO-) bands with increasing shear rate. Previous work using hydrodynamic shear device and transmission dichroic IR spectra has shown that alignment of the soap structure occurs at relatively low shear rates and that this can be related to viscosity loss (21). In those hydrodynamic tests, spectra were run in a dual beam instrument at polarizations parallel and perpendicular to the flow direction so that true dichroic ratios, (paralleVperpendicular absorbance), could then be calculated directly. The antisymmetric stretch vibration of the carboxylate group was found to align with flow, the dichroic ratio reaching a limiting value of 1.75 at a shear rate of approximately lo3 s-I. In Fig. 11, IR unpolarized spectra are shown from both the inlet and exit regions. Changes in the composition of the grease can be seen to occur as it passes through the contact. The spectrum from the exit region is taken from reveal molecular alignment in polynler systems (20). Three simple systems, grease, polyphenylether (5P4E) and VI polymer solution have been studied, each of which has been shown in previous work to undergo shear alignment. 1 Background spectra were taken frorn the center of the 3 loaded Hertzian contact at each polarization so that ab< sorption bands due to the polarizer substrate were removed. b) o m 4 mls w Apcnurc 256 r a n s ~ r e s . ~ O C ~ I I I 8 cm-l c) 0 023 mls e One disadvantage of this method is that the background Polariscr II to sliding dimt ion spectrum needs to be rerun for each change of polarization, 0.1 which makes measurement of the absolute dichroic ratio for a particular band difficult. For tht: EHD results presented in this paper the relative absorbances of bond vibrations are measured for each polarization, so that some estinlation of alignment effects may be made. Simple Grease A simple grease, composed of lithium soap thickener, \"\" IRW 17W 1501 IW IMO antioxidant and mineral oil base stock has been studied. wavcnumbcr ~ ~ - 1 Band positions and assignments are summarized in Table 4. Fig. 10--Polarized IR spectra from EHD inlet for simple grease. TABLE BANI) POS~TIONS AN11 ASSI~NMENTS FOR GREASE Sl'ECIXA COO- asym. stretch COO- asym. stretch C-H (CH2) C-H (CH3) COO- sym. stretch COO- sym. stretch C-H (CH3) soap structure soap structure base oiVsoap base oiVsoap soap structure soap structure base oil sym. scissors D ow nl oa de d by [ M os ko w S ta te U ni v B ib lio te ] at 1 3: 11 1 0 N ov em be r 20 13 0.0057 Ws. 2ON. 200pm apcnurc 256 scans. 8 cm.1 rcs. A Flg. 11-IR spectrum from the Inlet and exit reglons for a simple grease. Fig. 12-IR transmission spectrum polypheynlether (5P4E). a c lcp~s i t in the wake of the cavitated oil film 250 p n ~ downstream fro111 the contact center. It is essentially that of the soap s t r~ lc turc alonc. Polyf)h~!wyl elher 51J4E . . I he lul~ricating properties of bis-(bisphenoxy-phenoxy)Ixnzenc, 51'4E, hitve been extensively studied in recent years, ancl its rhcological behavior within EHD contacts is well cha~~ctc r izcc l . In addition, Lauer and coworkers (8), ( I I ) , (19) have stucliccl its nlolecular response using IK emission and transmission spectroscopy. Polarization studies have in- I'he positioning of the polarizer in this study is such that for both orientations, parallel a n d perpendicular, enhanced absorption for vibrations parallel to the sliding surfaces is likely to occur so that any orientation o f the benzene rings should be reflected as a relative change in the intensity of the in-plane and out-of-plane absorptions with shear. Figure 13 shows two polarized IR spectra, both taken from the inlet region (250 p m in front of the contact center) a t 0 a n d 0.27 ms-I. In the shearing case, the intensity of the in-plane bands has increased relative to the out-of-plane. T h e ratio of the absorbance of a n in-plane band (1480) to . . clicatccl that flow alignment of n~olecules occurs a t high a n out-of-plane o n e (690) gives a n estimation of the degree shear rates. of alignment. T h e change of relative alignment with contact 17igure 12 is an IK transmission spectrum for 5P4E, Sam- position is summarized for o n e test in Table 6 and can be pled on a K13r window. Band positions and assignments a r e seen to increase as the Hertzian zone is approached. Presummarizccl in 'I'ablc 5. T h e bands can be grouped into vious work using transmission dichroic measurements for two broad classifications; vibrations that a r e respectively a hydrodynamic shear device has shown similar orientation p;\";illcl ancl perpendicular to the plane of the benzene ring. effects (21). .I'AHI.E 5-BANI) I'OSI~I'IONS A N D ASSIC:NMEWI'S FOR 5P4E a C-C in-plane stretch y C-1.1 our-ollplane delbrma~ion 4 out-of-plane defornl;~lion p C-1-1 in-plane tlefornl;~tion BANI) POSI-I'ION cm- I 1590 1480 1310 1266 1213 1170 1141 1075 988 969 856 770 755 690 ASSIGNMENI' a C-C a C-C a C - 0 asym. a ring-0 sym. p C-H mono sub. p C-H meta sub. y C-H mcta sub. y C-H mono sub. y C-H meta sub. y C-H meta sub. y C-H mono sub. 4 C-C mono/nieta sub. COMMENT in-plane vibration out-ol-pl;unc vibration D ow nl oa de d by [ M os ko w S ta te U ni v B ib lio te ] at 1 3: 11 1 0 N ov em be r 20 13 In Lubro Studies of Lubricants in EHD Contacts Using FTIR Absorption Spectroscopy 255 173)on-1 lbramnor CrOlmnPMA 10% vlw PMA .ddiuvc in HVI D u Y r r k 200 pm apcnwc. 20N. 250 pm fmm ccnuc of conlact 256 scans. 8 cm-l ms. Spccrn x l Polariscr II lo sliding in conlac1 plane b) 0.275 ds t I in-lllanr vibrations 1 0.5 0 0 IRW 14W Km wavcnumbcr cm-1 Fig. 13-Polarized IR spectra from EHD Inlet for 5P4E. Polymer Viscosity-Index Improver ~ ' A H I . E 6-DEC;KEE OF ALIGNMENT OF 5P4E I N EHD CONI'ACI'" + ] + }, + { + "image_filename": "designv10_6_0002514_robot.2001.933055-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002514_robot.2001.933055-Figure1-1.png", + "caption": "Figure 1 : Stewart-Gough parallel robot", + "texts": [ + " In previous work, the identifiable parameters of parallel robots are derived by intuition. In the case of serial robots, the identifiable parameters are computed from a QR decomposition of the analytical observation matrix [12]. We propose to extend this method for parallel robots even in the case where the identification Jacobian matrix cannot be obtained analytically. 2. Description of the robot The parallel robot studied here is composed of a fixed base and a movable platform connected with six legs of motorized variable length (Figure 1). The base connections are composed of Universal joints (U-joints) and the platform connections are composed of Spherical joints (S-joints). The centers of the U-joints and S-joints are respectively denoted by A, and B, (i = 1 to 6). We suppose that the U-joints are composed of two revolute and intersecting joints, while the S-joints are composed of three intersecting revolute joints. The configuration of the parallel robot is given by the (6x1) vector L representing the leg lengths A,B, for i=l, " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000033_tec.2020.2965180-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000033_tec.2020.2965180-Figure2-1.png", + "caption": "Fig. 2. Predicted flux flow patterns (a) without excitation and (b) with excitation.", + "texts": [ + " \u2022 Higher reliability: In contrast to the PM synchronous motors (PMSMs), in which the PMs are embedded in the rotor structure, in the proposed PM-assisted motor the PMs are located in the stator. This feature not only increases the output torque of the proposed PM-SRM, but also enhances its reliability in contrast to the PMSMs. \u2022 Flux adjusting capability of the PMs: The embedded PMs reduce the saturation level in the stator poles and yoke. In other words, the stator core becomes less saturated than the PM-less counterpart of the PM-SRM at the same excitation currents. This unique feature of the PM-SRM is proved in the following section. Figure 2a illustrates the predicted flux flow patterns of the PMs under the non-excitation condition. When the coils are not excited, the flux of the outer PMs, \u03d5pm1 and inner PMs, \u03d5pm2 do not enter the air-gaps and flow through the stator back-irons. Once the coils are excited, , as shown in Fig. 2b, the flux generated by the outer PMs tends to pass through the stator poles rather than the stator yoke, hence, it weakens the flux density in the stator yoke and enhances the flux density in the stator poles and air-gap. Besides, the flux of the inner PMs traverses through the small stator teeth and the air-gaps rather than the stator poles and yoke. Therefore, it lessens the flux density in the stator pole and increases the flux of the air-gaps. To recap, both the inner and outer PMs enhance the air-gap flux density, the outer PMs increase the flux density of the 0885-8969 (c) 2019 IEEE" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure26.3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure26.3-1.png", + "caption": "Fig. 26.3 EAP actuator with the five layer structure. Left: the left and the right layers are chosen to be the electrodes (case I). Right: the middle and the right layers are chosen to be the electrodes (case II)", + "texts": [ + " This is the standard method for analyzing the deformation of the three layer actuators. However, the absolute values of C and A or even the sign of those cannot be determined separately by this method. For the actuator that we studied, we know that C A >0, which means that the expansion rate of the cathode is larger than that of the anode. In order to determine if the cathode and the anode are expanding or contracting, we used a five layer actuator and the experimental measurement was combined with a symmetrical analysis (see Fig.26.3). The five layer actuator is fabricated in the same method as the three layer actuator except that it has three electrode layers and two separator layers in the order electrode-separator-electrode-separatorelectrode. By using the five layer actuator, we can induce the stress on the electrode layers in an asymmetrical fashion in contrast to the three layer actuator. Let us consider the following two cases. In case I, the left and right electrode layers are chosen to be the electrode layers. The middle layer is electrically left open (see Fig.26.3, Left). This structure is similar to that for the three layer structure: it is symmetric with respect to the plane parallel to the layers and placed at the center of the actuator. By flipping the sign of the electrical potential of the two electrode layers, it should behave in a similar fashion to the three layer structure, both electrically and mechanically, except that the elastic property of the middle layer is different. Therefore, when the left layer is chosen to be the anode and the right layer the cathode, the five layer actuator will bend towards left, in the same way as the three layer actuator. There are three possibilities for this to happen; 1. C> A>0 (both the cathode and the anode expand), 2. C>0> A (the cathode expands and the anode contracts), and 3. 0> C> A (both the cathode and the anode contract). We cannot distinguish which 308 Kenji Kiyohara, Takushi Sugino, and Kinji Asaka of the three actually occurs only by measuring the motion of this actuator. In case II, the middle and right electrode layers are chosen to be the electrode layers (see Fig.26.3, Right). The left layer is electrically left open. Unlike in case I, this structure has a different symmetry from that of the three layer structure: it is not symmetric with respect to the plane parallel to the layers and placed at the center of the actuator. By measuring the motion of this actuator when the sign of the electrical potential is flipped, we are able to distinguish the three possibilities above. For possibility 1, C > A >0, the actuator should bend toward left, regardless of the choice of the cathode and the anode out of the middle and right electrode layers" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002883_027836499501400304-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002883_027836499501400304-Figure1-1.png", + "caption": "Fig. 1. Overhead view of a SCARA-type manipulator visually tracking. If a constant transformation between the camera and object is desir-ed, and the object continues to move in the -X direction, the manipulator will soon reach a singularity, and the system will fail.", + "texts": [ + " When visually tracking an object with an eye-in-hand system, it is also important that the manipulator maintains a configuration that allows motion in all directions of possible object motion without requiring extremely large joint velocities from any actuator, because the future motion of the object is either unknown or imprecisely known. This also requires that the manipulator should not be near singularities. Typically, when visually tracking objects with an eyein-hand system it is necessary to constrain the allowable tracking region to regions of the workspace where there is no danger that the manipulator passes near kinematic singularities or joint limits. This often places extreme limitations on the trackable workspace. Consider the visual tracking system shown in Figure 1. If a constant transformation between the camera and object is desired and the object continues to move in the -X direction, the manipulator will soon reach a singularity and the system will fail. Had the hand-eye system been initially started from a different configuration, the external singularity would have been reached either sooner, if the camera was initially placed nearer the object, or later, if the camera started farther from the object. However, if the system employs knowledge of the manipulator\u2019s configuration to improve the configuration using any redundancies that may exist, the tracking region can be greatly extended" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003237_tmech.2006.886254-Figure6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003237_tmech.2006.886254-Figure6-1.png", + "caption": "Fig. 6. Mechanics of stable pushing.", + "texts": [ + " We first show a condition for the object motion where the object remains in contact with both the hands of the robot. We assume that the friction force between the object and the floor acts through an effective center of friction (ECOF) proposed in [19], [20].1 The velocity of the object at ECOF is antiparallel to the frictional force. We impose three assumptions: 1) the friction coefficient of both the hands are same; 2) the forces are acting on the object balance; and 3) the friction distribution between the object and the floor is known. As shown in Fig. 6(a), the relative motion between the hands and the object does not occur if the line of action is strictly 1In [20], the same physical quantity is defined as the equivalent center of friction. included inside the friction cone and if the line of action passes strictly inside the contact segment including both hands [19]. As shown in Fig. 6(b), by considering the instantaneous center of rotation (COR), we can obtain a necessary condition for the object to be in contact with the hands [20]: Step 1: For a given position of the COR, calculate the position of the ECOF. Step 2: Rotate the area of the line of action, obtained in Fig. 6(a), for \u00b190\u25e6. Step 3: If the COR is included in the area obtained in Step 2, the object will keep contact with the hands. In this paper, we control the force that the hands apply to the object. Although the object will rotate if the forces of both the hands are different, it is difficult to precisely control the rotational motion of the object. Next, we consider the condition where the robot does not fall down by rotating about an edge of the support polygon. The foot does not rotate if the ZMP is strictly included inside the support polygon" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003729_9780470612231.ch6-Figure6.26-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003729_9780470612231.ch6-Figure6.26-1.png", + "caption": "Figure 6.26. Cross-section of miniature TI-SPR instrument", + "texts": [ + " The resonant angle at which coupling occurs is essentially dependent on the refractive index at the surface of the sensor. As a result, changes in the refractive index or mass will change the resonant angle corresponding to signal increases as mass increases and signal decreases as mass decreases. 6.6.1.6. Miniature TI-SPR sensor The miniature TI-SPR device was first released in 1996 by Texas Instruments, and consists of an LED, a polarizer, a thermistor allowing correction due to temperature changes and two 128 silicon photo diode arrays (Figure 6.26). These components are mounted on a single platform using conventional semiconductor-based opto-electronic manufacturing techniques. The platform is encapsulated in an epoxy resin molding structure. Changes in mass are related to changes in the resonant angle and this change is measured by the photodiode array. The width of light produced by the light emitting diode is controlled by the polarizer and reduces the emission of transverse electric radiation. Under conditions of TIR the wedged shaped beam is directed onto a linear photo diode array by a mirror" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure9.2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure9.2-1.png", + "caption": "Fig. 9.2 Electrode patterns of rotor plates", + "texts": [ + " New Microactuators Using Functional Fluids 93 To improve performance of an ER microactuator that is a fluid microactuator with ER microvalves, the mathematical model of the ER valve, flexible ER valve, and so on were proposed and developed. Also, microvalves using MRF were proposed and developed. 5. Development of high output power piezoelectric micropumps As a micro fluid power source, high output power piezoelectric micropumps using fluid inertia effect in a pipe and the one using resonance drive were proposed and developed. 6. Applications of the developed actuators To realize high output power DP-RE type ECF micromotors (Fig.9.1), the several electrode configurations are investigated as in Fig.9.2. The experimental results implies the ECF micromotor possibly generates 130 W/kg or higher in millimeter scale. In addition, we are also developing micrometer scale motors using MEMS technologies. 4. Development of microactuators using ERF/MRF 94 Shinichi Yokota, Kazuhiro Yoshida, Kenjiro Takemura and Joon-wan Kim We are developing a novel gyroscopes using ECF. This is called an ECF liquid rate gyroscope shown in Fig.9.3. This gyroscope measures a drift flow of the ECF jet, which is occurred due to Coriolis force" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003295_rob.4620060605-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003295_rob.4620060605-Figure2-1.png", + "caption": "Figure 2. General representation of a robot link-obstacle pair", + "texts": [ + " The basic strategy that we shall adopt for obstacle avoidance is somewhat similar to the one proposed in Ref. 5 ; however, our approach to obstacle avoidance is different and more general because we implement this strategy within the configuration control framework. The strategy may be summarized as follows: If any point on the robot enters the SO1 of any obstacle, the robot redundancy is utilized to inhibit the motion of that point in the direction toward the obstacle. Note that this strategy is simple and intuitively appealing. Figure 2 shows a general robot link i of length I, and a general obstacle j and associated SOI, in three-dimensional space. Define (X\u2018) , , E R3 to be the position of the criticd point on link i relative to obstacle j (measured in the robot base frame), where the critical point ij is that point on link i currently at a minimum distance from obstacle j . Here i = 1,2 , . . . , n and we assume that there are k obstacles, so that j = 1,2 , . . . , k . Let (Xo), E R3 and (r,,), denote the position of the center and the radius of obstacle j , respectively", + " In constructing an algorithm to locate active critical points, it is important to note that the locations of the critical points vary during the robot task and must be continually updated. Thus the algorithm used to locate these critical points must be computationally efficient. We proceed by first locating all of the critical points (the points on each link closest to each of the obstacles) and then determining which (if any) of these critical points are within obstacle SOIs and are therefore active. Referring to Figure 2, we define XI E R3 to be the location of joint i relative to the base frame, a,, E RC to be the distance measured along link i from joint i to critical point i j , pl, = (XO)] - XI, and el = (Xt+* - X,)/lz. These definitions as shown in Figure 2 may be used to derive the following recursive algorithm for computing the location of all active critical points: 1 I* = e:pIJ = - 1 - - if alJ S O then alJ = 0 (17) if aIJ r l , then all = l, if ( L ' ~ ) ~ , < ( r , , ) , then ( X C ) , is an active critical point, (20) otherwise it is not active. 730 Journal of Robotic Systems- 1989 Calculation of E,, 6, and J, Having located the active critical points using the algorithm (17)-(20). the constraint vector (16) may be readily constructed from definition (15)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002908_robot.2004.1308903-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002908_robot.2004.1308903-Figure4-1.png", + "caption": "Figure 4. Change of Altitude Errol", + "texts": [], + "surrounding_texts": [ + "Keywords: UA V, aulonomoys navigation, fuz&ogic control\nI. INTRODUCTION The paper objective is to demonstrate fuzzy-logic based autonomous navigation and control of small manned - unmanned aerial vehicles as shown in Fig. 1. Given an aerial vehicle dynamic model, a two-module fuzzy logic controller is derived that allows any such vehicle: i) to fly through specified waypoints in a 3-D environment repeatedly, ii) to perform trajectory tracking, and, iii) to duplicate I follow another aerial vehicle\u2019s trajectory.\nThe implementation framework utilizes MA T U B S standard configuration and the Aerosim Aeroriautical Simulation Block Set that provides a complete set of tools for rapid development of detailed 6 degrees-of-freedom nonlinear generic manned / unmanned aerial vehicle models (which may be customized through parameter files), including, among others, the Aerosoride UAV and the Nuvion general-aviation airplane) [I I].\nThe two-module fuzzy logic controller is composed of the altitude module, and the latitude-longitude module; an\n0-7803-8232-3/04/$17.00 02004 IEEE 4041\nadditional error-calculating box is also designed for fuzzy controller parameter tuning and flight adjustment purposes.\nThe proposed approach is modular and general; it is applicable to all types of aerial vehicles with minor control module adjustments, provided that the respective dynamic model is known or it may be derived. Further, the derived hmework is also suitahle for VTOL navigation and control. However, as a fM step, only the class of small manned aerial vehicles is considered in this paper.\nThe rest of this section presents related research, while Section I1 discusses details of the proposed fuzzy logic controller. Section I11 presents the simulation environment and describes the modules developed in MATLAB, essential for simulation studies. Section IV includes results, while Section V concludes the paper.\nA. Related Research\nThere exist several approaches related to navigation and control of UAVs; representative research includes neural networks [I], non-linear adaptive control [2], fuzzy logic [3], 161, neuro-fuzzy control, fuzzy logic and evolutionary or genetic algorithms [4], [IO], feed-forward plus PD feedback control [5] and controllers implementing feedback linearization and adaptive neural networks [9]. In addition, there exist intelligent control systems like the CIRCA-I1 [7] that utilizes real-time artificial intelligence and control theory to design an integrated UAV control system, and WITAS [PI. a long-term basic research project its purpose being the development of technologies and functionalities leading to a fully autonomous UAV.\n11. FUZZY LOFIC CONTROL SYSTEM The proposed fuzzy logic controller configuration is shown in Fig. 2. The aerial vehicle controller is of Mamdan-type, designed and tested on the North American Navion model; the same design may be applied to any UAV model.\nThe two fuzzy logic controller modules are responsible for altitude control and latitude-longitude control; when combined, they may adequately navigate the aerial vehicle. All input and output linguistic variables have a fmite number of linguistic values with membership functions empirically defined after exhaustive simulation studies.", + "The altitude fuzzy logic controller has three inputs: a) altitude error, b) change of altitude error, and, c) airspeed. The altitude error is the difference between the desired altitude and the current altitude of the airplane. The change of altitude error indicates whether the, aerial vehicle is approaching the desired altitude or if it is going away &om it. The airspeed is the current speed of the vehicle, Outputs are the elevators command and the throttle command, responsible for the decent and accent of the aerial vehicle.\n1\n08-\n06\n0 4\n0 2 -\n0 .a\nAEP I(EN\n'\n-\n-\n.a3 .rm :io0 o im 2m a3 KO\nLinguistic yalues representing 'the linguistic variable altitude error are: {Alfifude-Error-Negative (AEW Ahirude-Emor-Sfable (AES), Alfifude-Emor-Posifive (AEP)). Linguistic values corresponding to the linguistic variable change of altitude error are: {Negofive-Change .(NC), sfable : (S), posifive-change (PC)}. Linguistic values that represent the linguistic variable airspeed are: (Small-Airspeed (SA), ~ ~ .Medium-Airspeed (M), Big-Airspeed (BA)). Theu corresponding membership functions are shown in Fig. 3 to 5 , respectively.\nLinguistic values that descrihe the output linguistic variable elevator are: {Negafive-Elevafor WE), Sfable-Elevalor (SE), Positive-Elevator (PE)] with membership functions shown in Fig. 6. . .", + "Linguistic values representing the Linguistic variable throttle command are: {Low-Throftle (LT), Medium-77rottle (MlJ High-E+roftle (HT)}, as shown in Fig. 7.\n(A), Righf (R), Too-Right (TR with membership function shown in Fig. 10.\nFigure7. monk\nThe latitude-longitude controller has as inputs the heading error and the change of heading error. The heading error is the difference between the desired and the actual heading of the airplane. The output is the roll angle of the airplane.\nThe linguistic values that describe the input linguistic variable heading error are: fCecester-I(CI). Too-Right (TR). Righ! (R), Ceriter (C), Left (L), Too-Lefl (TL), Ceitfer-2 ( U ) } . The heading error membership function is shown in Fig. 8.\nFigureS. Heading\nThe change of heading error linguistic values are: {Negafive N, Stable (5'). Posifive (P)} as shown in Fig. 9.The output variable linguistics values are: {Too-Left (TL), Lefi (L), Ahead\n111. MATLAB MPLEMENTATION ENVIRONMENT A simulated environment in MATLAB has been implemented. The Aerosim Block Sef has been extensively used.\nThe derived flight controller model is shown in Figure 11. It consists of six subsystems represented as Sirnulink blocks, also shown in Fig. 1 1.\nAircraft model: It is provided by the Aerosim Block Sec in this case, the American Navion is used." + ] + }, + { + "image_filename": "designv10_6_0002720_1.1541628-Figure5-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002720_1.1541628-Figure5-1.png", + "caption": "Fig. 5 Spatial Chain 4P-4R with Partitioned Mobility.", + "texts": [ + " Furthermore, if Ha(i , j) is contained in any of the intersecting subgroups, there are two possibilities, either Ha(i , j)5$e% or not. It should be Transactions of the ASME shx?url=/data/journals/jmdedb/27745/ on 03/24/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F noted that the possibility of Ha(i , j)5B is precluded since Hc(i , j) and Hcc(i , j) are subgroups and the identity e must belong to both. Hence ePHa(i , j)5Hc(i , j)\u00f9Hcc(i , j). A very simple example of a kinematic chain with partitioned mobility will now be presented. Consider the 4P-4R chain shown in Fig. 5. The prismatic pairs generate the subgroup TR3, of spatial translations, while the revolute pairs generate the subgroup, SO(3)Q , of rotations around the fixed point Q. The smallest subgroup of E(3) that contains all the elements representing the relative displacements of any pair of links of the chain is E(3) itself. However, if one considers the relative displacements of link 5 with respect to link 1, it follows that, see Fanghella and Galletti @34#, Lc~5,1!5Ne@Hc~5,1!#5Ne@TR3# and Lcc~5,1!5Ne@Hcc~5,1", + " Thus, the mobility of the chain requires the satisfaction of some additional conditions involving link lengths and link angles and all the links are paradoxical links of class 2. If the chain is movable, it is called a paradoxical chain obtained from a trivial chain or paradoxical chain class 2. It is well known that the only movable linkage obtained from a four revolute spatial chain, that does not degenerate into a simpler chain; i.e. a planar or spherical linkage, is the Bennett linkage. Consider, again, the 4P24R kinematic chain showed in Fig. 5. This mechanism was considered in Section 3; there, it was found that links 1 and 5 are links that partition the mobility of the chain and the kinematic chain has partitioned mobility. Notwithstanding, if one considers, for example: \u2022 Links 1 and 2, they are trivial links and the kinematic chain is a trivial one. \u2022 Links 1 and 8, they are trivial links and the kinematic chain is a trivial one. \u2022 Links 1 and 6, they are exceptional links and the kinematic chain is an exceptional one. It should be noted that in all cases the mobility of the chain is F52" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002582_s0094-114x(99)00045-2-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002582_s0094-114x(99)00045-2-Figure3-1.png", + "caption": "Fig. 3. The troque adjustment coupling.", + "texts": [ + " Besides, it makes the computation possess high time resolution in the high frequency range, so this method is more suitable to detect the fault signal. This study will apply wavelet transform to diagnose the fault from the vibration signals for the gear transmission system. The experiment equipment used throughout this paper is shown schematically in Fig. 2 It consists of four gears (two pinions with 50 teeth and the other two gears with 150 teeth) and a permanent magnet DC motor. The torque adjustment coupling as shown in Fig. 3 connects the two shafts into one axle. The ends of the axle are connected with two pinions. Another axle that has two gears on the ends is connected to a motor through a timing belt transmission. The torque in the gear test equipment may be adjusted by shifting the relative phase of the elements in the coupling. The advantage of utilizing this coupling is explained in details as follows. In conventional gear test experiment, the torque on gears is given by external loading, such as a magnetic brake" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002663_mssp.2000.1345-Figure7-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002663_mssp.2000.1345-Figure7-1.png", + "caption": "Figure 7. Principle of run-down method.", + "texts": [ + " However, the identi\"cation procedure can be automated and time requirements are very low since all 10 inertia parameters are identi\"ed simultaneously. The accuracy of the results is medium according to one single test presented in [3]: the deviations of mass and centre of gravity location are $3%, the deviations of moments/products of inertia are $(10}15)%. 4.2.1.2. Run-down method. The moment of inertia about a speci\"ed rotation axis can be identi\"ed by run-down testing [3]. Here the test specimen is rotated about a speci\"ed axis with changing rotational velocity (Fig. 7). The rotational acceleration and the torque about the rotation axis are measured and can subsequently be converted to a moment of inertia [16]. The mechanical system is mounted such that rotation axis and z-axis of the inertial frame coincide. The f-axis of the body \"xed frame is chosen co-linear to the z-axis of the inertial frame (Fig. 7). Due to these restrictions the third row of equations (3b) yields equation (16) if no external forces except for the bearing forces act. H Aff cKA\"+ i tfP i . (16) If only the known motor/brake torque t MB acts on the test specimen and if the rotational acceleration is measured, the moment of inertia about the rotation axis can be calculated from H Aff\" t MB cK A . (17) An expression similar to equation (17) can be found if the rotation axis is equal to the x- or y-axis of the inertial frame and if the rotation axis passes through the centre of gravity" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003983_j.wear.2009.06.017-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003983_j.wear.2009.06.017-Figure4-1.png", + "caption": "Fig. 4. Mapping of a fixed tooth surface grids onto Q(r,z) plane.", + "texts": [ + " This results in (I + 1) \u00d7 (J + 1) grid oints at which pressure time histories and sliding distance must e computed on both pinion and gear surfaces. Since the tooth surfaces of hypoid gear are generated by a formng or generating process with the complex machine settings and utter parameters, the surface geometry cannot be described in losed form, but rather must be obtained numerically. In order to implify this problem, spatial Cartesian coordinates, x, y and z of rid points are projected on a plane Q(r,z) as shown in Fig. 4. The xtremes of the tooth surface A are projected to Q(r,z), where the ectangle B maps the tooth surface A. Likewise, all the grid nodes n the tooth surface A are also projected to Q(r,z). The Cartesian oordinate values in the gear reference coordinate system Xg are obtained by using the curvilinear surface parameters of each grid node on both surfaces that are provided by the contact model. Use of the coordinate system Q(r,z) for wear simulation simplifies the analysis as well as presentation of the wear profiles" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure32.4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure32.4-1.png", + "caption": "Fig. 32.4 Schematic and photograph of micro servo motor using micro magnetic resistive sensor", + "texts": [ + " The maximum starting torque was estimated to be 5.5 Nm when the driving voltage and the preload were 40 Vp-p and 1.0 mN, respectively. As can be seen, the starting torque values peaked when the applied voltage values were over 30 Vp-p. 378 Takefumi KANDA 32.2.1.3 Micro Encoder and Servo Motor The micro encoder for detecting the rotating condition, which is generated by the micro ultrasonic motor, was created by using a micro magnetic resistive sensor. A schematic of the micro encoder is shown in Fig.32.4. The shaft driven by the micro motor is connected with the magnetic drum, which has a magnetic slit pattern. The magnetic resistive sensor detects the magnetic pattern on the drum. The minimum magnetic pattern pitch is 40 m from the resolution of the sensor. Therefore, when the magnetic drum has a diameter of 2.3 mm, the angular resolution is estimated to be 2\u00b0. In our evaluation, there were 10 magnetic patterns and the pattern pitch was 0.43 mm. The output 2-phase signal values from the magnetic resistive sensor are plotted in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002639_0168-874x(93)90075-2-Figure13-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002639_0168-874x(93)90075-2-Figure13-1.png", + "caption": "Fig. 13. Pressure distribution obtained from experimental investigation at 5150 N vertical load and 2.0 bar internal pressure IN/ram2].", + "texts": [ + " Deformed cross-section of the tire at 10 mm contact displacement (= 1305 N) and 2.0 bar internal pressure. Undeformed ]III Deformed / ~ I i r - - ~ 't . . . . . . . . . Undeformed / / Deformed /~?f, /f//A~ Fig. 9. Deformed cross-section of the tire at 20 mm contact displacement (- 3052 N) and 2.0 bar internal pressure. Fig. 10. Deformed cross-section of the tire at 32 mm contact displacement (-= 5233 N) and 2.0 bar internal pressure. tained pressure distributions at three different stages of contact: 10 mm ( - 1305 N), 20 mm ( - 3052 N) and 32 mm (-= 5233 N). Figure 13 contains the result from an experimental investigation of the pressure distribution of a tire with smooth tread at 5150 N vertical load. With regards to the axial direction, a comparison with Figure 12 (c) illustrates the remarkably good agreement between the numerically and the experimentally obtained distribution of the contact pressure. The stress concentration observed along the edge of the contact region agrees reasonably well with the respective experimental result. With regards to the distribution along the circumferential direction, however, the agreement is not so good" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003972_1.2823085-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003972_1.2823085-Figure4-1.png", + "caption": "Fig. 4 Geometry of the melt pool", + "texts": [ + " These considertions, however, are attributed from that fact that the level of odel nonlinearity decreases when particular parametric arrangeent is considered e.g., combining two separate nonlinear terms uch as L2 2 /dp 2 to one individual term such as L2 /dp n . The parametric gray-box model is then presented by h\u0307 + h = 3 2 m\u0307 w0 db dp 1 + h t db tan cos n k v t 3 here h\u0307 is the derivative of the clad height m/s , m\u0307 is the powder ow rate kg/s , is the powder density kg /m3 , h0 and w0 are he steady state values of the clad height and width m , respecively see Fig. 4 , dp is the powder jet diameter m , is the ngle between the nozzle and the laser beam, db is the laser beam iameter see Fig. 5 , and , n, and k are unknown parameters that re identified through experimental analyses. Using the experiental results and the recursive least squares method, the model arameters are identified offline. The experimental tests are se- ournal of Manufacturing Science and Engineering om: http://manufacturingscience.asmedigitalcollection.asme.org/ on 01/29 lected with different processing parameters; therefore, a domain is obtained for each of the model parameters, which can be expressed as kmin k kmax min max nmin n nmax 4 Figure 6 shows the experimental results of the process transient response resulting from a random step in the scanning speed" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure4.13-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure4.13-1.png", + "caption": "Fig. 4.13. Torque-speed characteristics depending on reduction ratio", + "texts": [ + " The torque-speed characteristics can also be expressed in the plane (nm, pm), where pm is the necessary motor torque and nm is the motor rota tion speed. Since the motor acts through the reducer, it is Nn, P nN 267 (4.5.1) where N is the reduction ratio and n is the mechanical efficiency of the reducer. The constraint is represented by the maximal characteris tic of the motor pm - nm i.e. maximal motor torque depending on ro-max tat ion speed. It has already been said (Para. 2.6.1) that this maximal characteristic is a nearly straight line. Fig. 4.13a shows the neces sary characteristic P-n and the maximal characteristic Pmax - n (both in (n, P) plane) for two values of the reduction ratio N. The necessary characteristic does not depend on N but the maximal characteristic does. Fig. 4.13b shows the same relations but in (nm, pm) plane. Now the necessary characteristic does depend on N and the maximal one does not. In both figures we see that for the ratio N1 the test is positive, i.e., the motor is suitable, and for N2 the constraint is violated and the test is negative. So, we conclude that motors and reducers should be determined together. But, while the choice of motors is simply a matter of selection from the ones offered, the reduction ratio is chosen in an optimal way enabling the maximal operation speed", + " We now choose the motor having the least Tmin , i.e., allowing the greatest operation speed. Let us now discuss the data about the motors which should be given to the computer. This depends on the tests imposed. If the power require ments are tested then the data about motor power are necessary. If the torque-speed characteristic is tested then it is necessary to give the maximal characteristic pm - nm. Since this characteristic is almost max a straight line it is enough to give two values: p~ (point A in Fig. 4.13b) and n~ (point B). p~ is the maximal motor torque corresponding to nm+O and n~ is the maximal rotation speed corresponding to pm+O. p~ m is often called stall torque and nM is called no-load speed. Ifexpresm sed in terms of rad/s no-load speed is marked by wM. When the real value of maximal torque (P~r) is less than P~ it is then necessary to prescribe P~r (Fig. 4.13b). If power-dynamic power characteristic is tested then the computer needs p~, rotor resistance and inertia moment (Rr and J r ), and the constants of torque and electromotor force (CM, CE). Finally, if overheating test is to be made then nominal motor torque pm is needed. nom Systematic selection procedure. Although the checking method previous ly desribed can sometimes be very suitable, it does not allow a sys tematic choice of the most appropriate motor. Hence, besides this checking method we propose a systematic sel~ction method based on power analysis" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure9.6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure9.6-1.png", + "caption": "Fig. 9.6 Integrated cells with serial and parallel", + "texts": [ + " The tank membrane and the fiber-reinforced tube are arranged to be a bicylindrical structure. Then the actuator could be a cell, easy to be integrated. When the ECF jet is generated, the inner pressure of the fiber-reinforced tube increases, resulting in making the artificial muscle cell contract. The fabricated cell with 13.5 mm \u00d7 14 mm generates contraction of 1.2 mm. The ECF micro artificial muscle cell developed here is suitable for integrating in combinations in series and parallel as shown in Fig.9.6, to obtain desired output force and displacement. 96 Shinichi Yokota, Kazuhiro Yoshida, Kenjiro Takemura and Joon-wan Kim New Microactuators Using Functional Fluids 97 Another application is an ECF micro finger shown in Fig.9.7. A finger tube has three chambers as in the figure, and each of them is connected through an ECF jet generator. Namely, the ECF can actively be moved from one chamber to the others. Then, the finger tip moves in 3D space. A large model prototype with 4.5 mm in diameter was developed and the above-mentioned principle was experimentally confirmed" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003024_s0022-460x(03)00358-4-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003024_s0022-460x(03)00358-4-Figure3-1.png", + "caption": "Fig. 3. Transmission.", + "texts": [ + " This angle can now be determined from cos gg \u00bc ggffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0Rp;tip r\u00de2 sin2 \u00f0kp \u00fe t\u00de \u00fe \u00f0a \u00f0Rp;tip r\u00de cos \u00f0kp \u00fe t\u00de\u00de2 q : \u00f011\u00de The contact normal has the slope a \u00bc kg \u00fe gg t; \u00f012\u00de and the lever arms for the normal force in the contact point are hg;n \u00bc gg; \u00f013\u00de hp;n \u00bc a cos a hg;n: \u00f014\u00de The overlap d; which corresponds to the deformation in the contact point, is d \u00bc gg \u00f0gg \u00fe kg \u00fe tan a0 a0 Gg tan gg\u00de \u00fe r; \u00f015\u00de and the lever arms for the friction forces in the contact point are hg;f \u00bc gg tan gg r \u00fe d; \u00f016\u00de hp;f \u00bc hp;n tan \u00f0a\u00fe kp \u00fe t\u00de \u00fe r: \u00f017\u00de The last possibility of contact is between the involute flank of the pinion and the tip rounding of the gear. The deformation and the lever arms for this case can be obtained by shifting the notations p and g in Eqs. (7)\u2013(17) at the same time as the direction of the rotation is shifted (G- G). The transmission which will be analyzed is shown in Fig. 3. The gear set is coupled to external systems, which are reduced to one stiffness and one inertia at each side of the gear set. The gears are mounted on linear elastic bearings with the stiffnesses cp and cg while the external inertias are mounted on stiff bearings. The transmission is driven by the torque Mdrive and is braked by the torque Mbrake: Loading the parts will, of course, give rise to elastic deformations. Also resisting forces due to the deformation velocity will however occur. This damping is assumed to be viscous, which implies that the torque on the gears can be expressed as Mp \u00bc c1 \u00f0G1 Gp\u00de \u00fe d1 \u00f0 \u2019G1 \u2019Gp\u00de; \u00f018\u00de Mg \u00bc c2 \u00f0Gg G2\u00de \u00fe d2 \u00f0 \u2019Gg \u2019G2\u00de: \u00f019\u00de An arbitrary contact between the gears is shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003619_s0263574708004268-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003619_s0263574708004268-Figure1-1.png", + "caption": "Fig. 1. Model of a planar biped in midair.", + "texts": [ + " To ensure such control, we envision the adaptation of the Reaction Null-Space method introduced in the previous section. The support foot/feet play the role of a \u201cbase,\u201d while the rest of the links of the biped play the role of the \u201cmanipulator\u201d in the equation of motion (1). \u2021 This follows directly from the well-known fact that the pseudoinverse-based particular solution has a minimum norm. As an illustrative example, we consider a simple three-link planar model in the sagittal plane, comprising the foot, the lower body (leg), and the upper body (see Fig. 1). The joint at the foot is the ankle joint (angle \u03b81), the other joint is the \u201chip joint.\u201d The equation of motion of the three link model can be written as follows:[ Hf Hf l HT f l H l ] [ \u03bd\u0307 \u03b8\u0308 ] + [ cf cl ] + [ gf gl ] = [ 0 \u03c4 ] + [ JT fp JT ] [ f n ] (8) where \u03b8 \u2208 2 Joint angle vector \u03bd \u2208 3 Foot velocity (angular speed incl.) H l \u2208 2\u00d72 Leg and upper body inertia matrix Hf \u2208 3\u00d73 Foot inertia matrix Hf l \u2208 3\u00d72 Inertia coupling matrix cl \u2208 2 Velocity dependent nonlinear joint torque cf \u2208 3 Velocity dependent nonlinear wrench at the foot gl \u2208 2 Gravity joint torque gf \u2208 3 Gravity wrench at the foot \u03c4 \u2208 2 Joint torque vector" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002497_b005995l-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002497_b005995l-Figure2-1.png", + "caption": "Fig. 2 Overview and cross-sectional views of the microbial electrode tip. (1) PVA\u2013SbQ microbial layer; (2) electroplated gold working electrode; (3) electroplated gold counter electrode; (4) electroplated gold layer; (5) electrically insulating solder resist ink layer; (6) electrical contacts; (7) basal glass\u2013epoxy plate.", + "texts": [ + " fluorescens was grown under aerobic conditions on a shaking incubator (Takasaki Scientific Instruments, Japan) at 130 rpm for 20 h in 200 ml of LB medium (1.0 g of NaCl, 2.0 g of Bacto Triptone, and 1.0 g of yeast extract). After growth, the cells were harvested by centrifugation at 8000 rpm for 10 min and washed three times with a 10 mM phosphate buffer (pH 7.0, 5 \u00b0C). The cell suspension was finally adjusted to an absorbance (A580) of 30 using a phosphate buffer (10 mM, pH 7.0) and stored at 5 \u00b0C. Fig. 2 shows overview and cross-sectional views of the microbial electrode tip. The procedure for preparing the base of the sensor tip (15 3 40 mm) is as follows. Working and counter electrodes were formed by etching the copper laminate layer on the basal glass\u2013epoxy plate and electroplating the surface with gold (6 3 38 mm). Finally, the areas of the electrodes (3 3 7 mm) and electrical contacts (1 3 7 mm) were then defined by coating the remaining area of the electrode with electrically insulating solder-resist ink (PSR-4000 Z26, Taiyo Ink, Japan)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003670_978-3-642-82195-0-Figure1.16-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003670_978-3-642-82195-0-Figure1.16-1.png", + "caption": "Fig. 1.16. Denavit-Hartenberg kinematic parameters for a revolute kinematic pair", + "texts": [ + " A correlation between these two kinematic modelling tech niques, with respect to generality, complexity and convenience for dy namic modelling have been discussed in [10) in detail. Let us now consider how link coordinate systems are assigned to links 21 by this method, together with kinematic link parameters which are here introduced. Consider a simple open kinematic chain with n links. Each link is char acterized by two dimensions: the common normal distance a i (along the common normal between axes of joint i and i+1), and the twist angle Q i between these axes in the plane perpendicular to a i . Each joint axis has two normals to it a i _ 1 and a i (Fig. 1.16). The re lative position of these normals along the axis of joint i is given by d i \u00b7 Denote by 0ixiYizi the local coordinate system assigned to link i. We will first consider revolute jOints (Fig. 1.6). The origin of the coordinate frame of link i is set to be at the intersection of the com mon normal between the axis of joint i+1. In the case of intersecting joint axes, the origin is set to be at the point of intersection of the joint axes. If the axes are parallel, the origin is chosen to make the joint distance zero for the next link whose coordinate origin is defi ned", + " The zi axis of system i should coincide with the axis of joint i+1, about which rotation qi+1 is performed. The -+ xi aXis will be aligned with any common normal which exists (usually the normal betwen axes of joint i and i+1) and is directed from jOint i 22 to joint i+1. In the case of intersecting joint axes, the ~. axis is ~ chosen to be parallel or antiparallel to the vector cross product -+- -+ -+ -+-+ -+ zi_1 xz i' The Yi axis satisfies xixY i = zi' The joint cOOrdin!te qi fO~ a revolute joint is now defined as the an gle between axes x i _1 and xi (Fig. 1.16). It is zero when these axes are parallel and have the same direction. The twist angle a i is mea-... ... ... sured from axis zi_1 to zi' i.e. as a rotation about xi axis. Let us now consider prismatic joints (Fig. 1.17). Here, the distance d i becomes joint variable qi' while parameter a i has no meaning and is set to zero. The origin of coordinate system corresponding to the sliding joint i is chosen to coincide with the next defined link origin. The ~. ... ~ axis is aligned with the axis of joint i+1", + " The computer program for manipu lator UMS-3B, obtained by the software package is also given. 2.2.1. Backward and forward recursive relations This kinematic analysis will be based on Denavit-Hartenberg's kinematic notation, presented in Subsection 1.3.2 in detail. For the sake of clear ness, we will here repeat the expressions for homogeneous transforma tion matrices i-1 Ti between two adjacent link coordinate frames. If joint i is a revolute one, and link coordinate frames are assigned to the links according to the procedure presented in Subsection 1.3.2 (Fig. 1.16), the homogeneous transformation between systems i and i-1, is given by cosq i -sinqicosCti sinqisinCti aicosqi i-1 sinqi cosqicOSCti -cosqisinCti aisinqi (2.2.1) T. l. 0 sinCti cosCti d. l. 0 0 0 where: qi - is the rotation angle in joint i, measured between axes x i _ 1 and xi (Fig. 1.16); Cti - the twist angle between joint axes zi_1 and zi measured in the direction of axis a i - the common normal distance between joints i and i+1; 57 d i - the distance along joint axis zi-1 between the origin of system (i-1) and the point of intersection of joint axis zi-1 with the common normal between axes zi-1 and zi\u00b7 The upper (3x3) submatrix of i-1 T . transforms vectors expressed in 1 system i into vectors expressed in system i-1. The last column of matrix i-1 T . is the position vector between the origins of systems i and i-1, 1 expressed also with respect to system i-1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002601_3477.865178-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002601_3477.865178-Figure1-1.png", + "caption": "Fig. 1. Five-link biped model: m is the mass of link i; r is the length of link i; a is the distance between the center of mass of link i and the lower joint of link i.", + "texts": [ + " This paper was recommended by Associate Editor S. Lakshmivarahan. The author is with the Institute of Maritime Technology, National Taiwan Ocean University, Keelung 20224, Taiwan, R.O.C. (e-mail: jgjuang@imt.ntou.edu.tw). Publisher Item Identifier S 1083-4419(00)06721-2. In order to demonstrate the proposed learning scheme, the walking machine BLR\u2013G1 robot [10] is used as the simulation model. This robot consists of five links, a body, two lower legs, and two upper legs, with two hip joints and two knee joints as shown in Fig. 1. This robot introduced in [10] has no feet (no ankle). A steel pipe at the tip of each leg is used to maintain the lateral balance. Thus, the motion of the robot is limited to only the sagittal plane (X\u2013Z plane). Since there is no foot, no ankle torque can be generated; the biped locomotion can be only indirectly controlled by using the effect of gravity (inverted pendulum). The ground condition is assumed to be rigid and nonslip. The biped always keeps only one leg in contact with the ground. The contact is assumed to be a single point" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003815_j.mechmachtheory.2009.06.001-Figure25-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003815_j.mechmachtheory.2009.06.001-Figure25-1.png", + "caption": "Fig. 25. Defective generators with two adjacent coaxial H or R pairs.", + "texts": [], + "surrounding_texts": [ + "The famous Delta robot [20] implements successfully hinged parallelograms in three limb chains that are generators of three X-motions. Various potential applications of X-motion generators with parallelograms are going to be elucidated in further works. In fact, circular translation and rectilinear translation are not the same motion. The opposite bars of a 1-dof hinged parallelogram can move while remaining parallel. Hence, the coupling between two opposite bars generates relative 1-dof circular translation that is a 1D manifold contained in the 2D subgroup of planar translation; the plane is the one of the parallelogram. Consequently, for a small motion, a hinged parallelogram is equivalent to a prismatic pair. Replacing all P pairs by hinged parallelograms, we obtain all possible X-motion generators including hinged parallelograms; these generators are shown in Figs. 6\u20138. Flattened parallelograms are singular and must be avoided. When only one P pair for each of the generators shown in Fig. 4 is replaced by one hinged parallelogram, Figs. 9 and 10 are readily obtained. Here, we must notice that the four generators, (III9) PRRPa, (III11) PHHPa, (III12) HPPaH and (III14) RPPaR in Fig. 10 are cancelled out because they have architectures that are equivalent by kinematic inversions to chains shown in Fig. 9. PaPaRHIII1( ) ( III2 PaPaRR) PaPaHH)III3( Figs. 11\u201313 are generators of X-motion obtained by the replacement of the two P pairs in chains of Fig. 5 by two hinged parallelograms. Likewise, Figs. 14\u201316 are X-motion generators derived by replacing only one P pair in each generator of Fig. 5 with one hinged parallelogram. That way, we obtain a total of eighty-two chains having at least one parallelogram, noticing that the kinematic inversion of each of these foregoing chains is also an adequate chain for generating X-motion. 4. Defective X-motion generators A defective chain for generating X-motion arises from the permanent singularity of the chain. Then the chain does never generate the desired X-motion. Such a phenomenon is not properly a singularity. As a matter of fact, singular means specific of special poses of the chain. However, such an abuse of language has some practical interest because the same geometric condition may yield transitory or permanent failure in the generation of X-motion. Clearly, open chains obtained from the trivial or exceptional 4-bar 1-dof closed chains with 1-dof Reuleaux pairs by splitting in two parts for any one link are defective X-motion generators. Using group dependency, we can derive all possible cases of defective chains for the generation of Schoenflies motion. In general, the singularity happens iff the following set equation fH\u00f0N1;u; p1\u00degfH\u00f0N2;u; p2\u00degfH\u00f0N3;u; p3\u00degfH\u00f0N4;u;p4\u00deg \u00bc fEg \u00f010\u00de does not imply the set equations fH\u00f0N1;u; p1\u00deg \u00bc fH\u00f0N2;u; p2\u00deg \u00bc fH\u00f0N3;u; p3\u00deg \u00bc fH\u00f0N4;u; p4\u00deg \u00bc fEg: \u00f011\u00de which are solved iff the helical motion angles are equal to zero. Here, the subset of displacements represents variations of position from the home posture. The absence of displacement necessarily belongs to the set of feasible displacements. Set Eq. (10) is the mathematical model of a mechanism obtained from the open chain pictured in Fig. 1 by welding the distal bodies i and j on a fixed frame. Such a closed-loop mechanism generally cannot move and, then, the open chain of Fig. 1 effectively generates X-motion. If a link in the closed mechanism can move, then the generator of X bond is defective or permanently singular. Two kinds of singularities may happen; the undesired motion either has only infinitesimal amplitude or can have finite amplitude. The detection of undesired infinitesimal motion is done through the study of a possible linear dependency of the four twists. This topic will be studied in another work. On the other hand, group theory is a fruitful tool for PPPR)b(PPPH)a( Pl Pl Fig. 22. Defective generators with three coplanar P pairs. the characterization of finite motion. Beyond the trivial and exceptional cases that are explained through the group dependency of displacement subsets, only four paradoxical cases were definitely established by Delassus [19]. Myard\u2019s work [24] is also devoted to the study of paradoxical closed chains with five or six revolute pairs, which are beyond the subject of our paper. In spite that special exceptional chains have been misled to be paradoxical ones in [25], the paradoxical mobility still cannot be explained only by the group dependency, which does not require the use of the Euclidean metrics. The paradoxical chains of Delassus can yield passive motion with finite amplitude. This kind of singularity will be confirmed in further work. Neglecting the paradoxical mobility, which is transitory in an open chain, a link of the previous mechanism can move permanently iff two open sub-chains generate two dependent kinematic bonds, the intersection of which is not {E}. In order to avoid the defective generators, the following cases must be considered: Case A. In set Eq. (10), a product of three factors is equal to a 3D subgroup of {X(u)} and the fourth 1D factor is included in this subgroup. Referring to Fig. 17, if the four pitches are equal, then \u00bdfH\u00f0A1; u; p\u00degfH\u00f0A2; u; p\u00degfbiH\u00f0A3; u; p\u00deg \u00bc fY\u00f0u; p\u00deg and fH\u00f0A4;u; p\u00deg fY\u00f0u; p\u00deg implies [{H(A1, u, p)}{H(A2, u, p)} {H(A3, u, p)}] {H(A4, u, p)} = {Y(u, p)}{H(A4, u, p)} = {Y(u, p)} \u2013 {X(u)}. Hence, this chain fails in generating Schoenflies motion for any pose and, in other words, it is a defective chain for the generation of X-motion. The four pitches must not be all equal. Pitches may be equal to zero but not all zeros. When four pitches are zeros, the chain generates the planar gliding motion, {Y(u, 0)} = {G(u)}. By the same token, one can demonstrate that if two screw pitches are equal, then two P pairs must not be perpendicular to u. For instance, two chains of Fig. 18 actually generate the 3-dof pseudo-planar motion rather than 4-dof X-motion. Furthermore, if three screw pitches are equal and one P pair is perpendicular to the parallel H axes, as shown in Fig. 19, these chains are trivial chains of a subgroup of pseudo-planar motion and never generate X-motion. One additional defective generator, a series of four prismatic pairs that generates {T} instead of {X(u)}, is displayed in Fig. 20 for completeness. Case B. A product of two factors is a 2D subgroup and one among the other two factors is included into this subgroup. For example, p1\u2013p2; A2 2 line\u00f0A1; u\u00deor\u00f0A1A2\u00de u \u00bc 0 ) fH\u00f0A1; u; p1\u00degfH\u00f0A2; u; p2\u00deg \u00bc fC\u00f0A1; u\u00deg; A3 2 line\u00f0A1; u\u00de ) fH\u00f0A3; u; p3\u00deg fC\u00f0A1; u\u00deg ) \u00bdfH\u00f0A1; u; p1\u00degfH\u00f0A2; u; p2\u00deg {H(A3, u, p3)}{H(A4, u, p4)} = {C(A1, u)}{H(A3, u, p3)}{H(A4, u, p4)} = {C(A1, u)}{H(A4, u, p4)} \u2013 {X(u)}. Hence, three axes must not be coaxial. Fig. 21a shows such a defective chain with three coaxial H pairs. The subgroup {C(A1, u)} can also be generated by PH or HP arrays (PR or RP when the pitch of H is zero) if the P is parallel to the H axis (R axis). Fig. 21b\u2013f shows other defective X-motion generators being in this situation, in which the replacement of any screw H by revolute R yields a defective X-generator chain, too. In Fig. 22, the cases with three prismatic pairs that are parallel to a plane are defective generators of X-motion and must also be avoided. Case C. A product of two factors is a 2D subgroup and the product of the other two factors is another subgroup, which is dependent with respect to the first subgroup. In other words, the intersection of the two 2D subgroups is a 1D subgroup. From the list of products of dependent subgroups [5], we obtain only two possible situations, namely, C1. [{H(A1, u, p1)}{H(A2, u, p2)}][{H(A3, u, p3)}{H(A4, u, p4)}] = {C(A1, u)}{C(A3, u)} if A2 e line (A1, u) and A4 e line (A3, u). We have {C(A1, u)} \\ {C(A3, u)} = {T(u)}. Hence, if two axes are collinear, then, the other two axes must not be collinear. For instance, the open chain of Fig. 23a is a defective chain for the generation of X-motion. The subgroups {C(Ai, u)} with either (i= 1 or 3) or (i= 1 and 3),can also be generated by PH or HP arrays (PR or RP when the pitch is zero) if the P is parallel to the H axis (R axis). These defective generators are shown in Fig. 23b\u2013f. It is noteworthy that a defective X generator happens when a revolute pair arbitrarily replaces any screw in these generators. C2. [{H(A1, u, p1)}{H(A2, u, p2)}][{H(A3, u, p3)}{H(A4, u, p4)}] can be equated to {C(A1, u)}{T(Pl)} with {C(A1, u)}\\{T(Pl)} = {T(u)}; in this case, the plane Pl of vectors s3, s4 is parallel to u. Consequently, if two screws are coaxial, then the plane of two P pairs must not be parallel to the screw axis. The chain in Fig. 24a shows this kind of defective generator. It is a defective chain with a passive exceptional mobility. Once more, the subgroup {C(A1, u)} can also be generated by PH or HP arrays (PR or RP when the pitch is zero) when the P is parallel to the H axis (R axis), as shown in Figs. 24b and c. Here, special cases of Fig. 22 are discarded for simplicity. Case D. If two adjacent pairs generate the same 1D subgroup, then, obviously, the open serial chain generates a 3D manifold included in the 4D subgroup {X(u)}. The required four DOFs of a generator of X-motion are not achieved. Hence, two adjacent H or R pairs must not be coaxial with the same pitch and two adjacent P pairs must not be parallel. Moreover, in a PPP subchain two non-adjacent P pairs that are parallel remain parallel, what must be avoided, such as Fig. 26g. Chains belonging to this case are shown in Figs. 25 and 26, in which R pairs can replace H pairs. To sum up, the defective X-motion generators are briefly tabulated in Table 3. These open chains have passive internal 1- dof mobility: the connectivity is 3 instead of 4. Moreover, their inversions are also defective chains for generating X-motion." + ] + }, + { + "image_filename": "designv10_6_0003082_cdc.1994.411460-Figure8-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003082_cdc.1994.411460-Figure8-1.png", + "caption": "Figure 8: Nature of zero dynamics", + "texts": [ + " There is thus a one-to-one correspondence between solutions (zr(t), u,(t)) of system (3) and arbitrary maps xr(t). Remark 1 The above relations correspond to a pendulum of length f [7], and as noticed in [2] the flat output has been x known (but for other reasons) to mechanicians for a long time 0 as the Huygens center of oscillation. Remark 2 No general method to check that a system is flat is known, but it is often possible to find as here a flat output by physical reasoning. 0 To conclude, we depict the nature of zero-dynamics for different choice of outputs in figure 8. If we consider as output a point, fixed to the aircraft body and located above the solid line, then the equilibrium point, (&,,&) := (0,O) of the zero dynamics is a center. Below the solid line the equilibrium point becomes a saddle (nonminimum phase). Along the solid line the system is degenerate, except at H which is a flat output and we have a trivial case of no zero dynamics. 4 The control scheme As another consequence of its flatness, the IS system is fully linearizable by (dynamic) feedback" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003815_j.mechmachtheory.2009.06.001-Figure17-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003815_j.mechmachtheory.2009.06.001-Figure17-1.png", + "caption": "Fig. 17. The defective generator with four identical pitches.", + "texts": [ + " This kind of singularity will be confirmed in further work. Neglecting the paradoxical mobility, which is transitory in an open chain, a link of the previous mechanism can move permanently iff two open sub-chains generate two dependent kinematic bonds, the intersection of which is not {E}. In order to avoid the defective generators, the following cases must be considered: Case A. In set Eq. (10), a product of three factors is equal to a 3D subgroup of {X(u)} and the fourth 1D factor is included in this subgroup. Referring to Fig. 17, if the four pitches are equal, then \u00bdfH\u00f0A1; u; p\u00degfH\u00f0A2; u; p\u00degfbiH\u00f0A3; u; p\u00deg \u00bc fY\u00f0u; p\u00deg and fH\u00f0A4;u; p\u00deg fY\u00f0u; p\u00deg implies [{H(A1, u, p)}{H(A2, u, p)} {H(A3, u, p)}] {H(A4, u, p)} = {Y(u, p)}{H(A4, u, p)} = {Y(u, p)} \u2013 {X(u)}. Hence, this chain fails in generating Schoenflies motion for any pose and, in other words, it is a defective chain for the generation of X-motion. The four pitches must not be all equal. Pitches may be equal to zero but not all zeros. When four pitches are zeros, the chain generates the planar gliding motion, {Y(u, 0)} = {G(u)}" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002802_ip-cta:20020236-Figure6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002802_ip-cta:20020236-Figure6-1.png", + "caption": "Fig. 6 Moclel of n two-link rohotic nicinipulutor", + "texts": [ + " When holding the condition IsiI>s!, it can be seen that the control law is the same as the proposed FSMC. However, the amount of hitting control in region 1s; I < s! is dominated by the grade of the membership function of NZ, that is, the hitting control could be attenuated by the grade of NZ. 6 Simulation results Here, we demonstrate the proposed FSMC by the tracking control of a two-link robotic manipulator with two degrees of freedom in the rotational angles described by angles ql and q2, as shown in Fig. 6. The aim is to produce some torque signals that create a sliding motion in the phase plane for each link. The dynamic equations describing the motion of the robotic system are derived by the Lagrange scale function L(q, q) [32], and are defined to be L(q, 4) = T(q , 4) - U(Y3 4) (35) where T(q, q) and U(q, 4 ) are the total kinetic and potential energy. respectively, q = [ql q2]? The Lagrange equation has the form where z = [ z l z2ITcR2 is the vector of the externally applied torques along the directions of their corresponding generalised coordinates q" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000209_j.jmst.2021.03.008-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000209_j.jmst.2021.03.008-Figure3-1.png", + "caption": "Fig. 3. Details of the DED (Directed energy deposition) experiments: (a) schematic of the copper/steel bimetal specimen fabrication and the cross-section specimen; (b) configuration of the horizontally combined bimetal tensile specimens; (c) configuration of the vertically combined bimetal tensile specimens; (d) dimension feature of the tensile specimen.", + "texts": [ + " ence, in our experiment, after two-layer fabrication, the processng parameters for steel were adopted to fabricate the remaining ayers of coating (shown in Table 4 ). The processing parameters or DED steel on the steel substrate were obtained from previous esearch [31] . It should be noted that the vertically combined cop- er/steel bimetal tensile specimens were fabricated on the thick u-Cr substrate with dimensions of 135 mm \u00d7 180 mm \u00d7 40 mm. T i o i t ( o m c E O f m t n c s A s c o he preparation process for the copper/steel bimetal is illustrated n Fig. 3 . The metallographic specimen and tensile specimen were cut ff from the bimetal structure using electric discharging machinng, as illustrated in Fig. 3 . The Cu-Cr substrate and DED stainless ensile specimens were also prepared. The cross-section specimen Fig. 3 (a)) was mechanically polished and then etched by a solution f 5 g FeCl 3 , 10 mL HCl, and 100 mL H 2 O at room temperature. The icrostructure was observed by the Motic AE20 0 0Met optical miroscope (OM), and the scanning electron microscopy (SEM, ZEISS VO 18) equipped with an energy dispersive spectrometry (EDS, Fig. 2. The starting stainless steel powder: (a) xford X-Max 50) system. The element distribution of the interace was detected by an electron probe microanalyzer (EPMA, Shi- adzu EPMA-8050 G)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003204_tmag.2007.893631-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003204_tmag.2007.893631-Figure1-1.png", + "caption": "Fig. 1. Schematic diagram of the six-slot/four-pole PMSM.", + "texts": [ + " Different from conventional windings, the six-slot stator windings cannot produce symmetrical magnetomotive force (MMF) under the four poles, and more harmonics exist in the air gap, which will increase the torque ripple and noise. In this paper, the finite-element method (FEM) is used to optimize the rotor from the aspects of magnetic-pole embrace, magnetic bridge, and magnetic-pole eccentricity to obtain better air-gap magnetic field distribution and torque curves [6]\u2013[11]. The schematic diagram of the PMSM is shown in Fig. 1, and the main parameters are shown in Table I. As to PMSM, both the amplitude and distribution of the air-gap magnetic field will be affected by the changing of the magnetic-pole embrace, which will further influence the average torque and torque ripple. With the volume of the permanent magnets kept unchanged, the magnetic-pole embrace varies from 0.67 to 0.92 by the step of 0.05, and the torque curves are obtained by time-stepping FEM. From the torque analysis, the average torque and torque ripple can be obtained, which are shown in Table II" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure2.23-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure2.23-1.png", + "caption": "Fig. 2.23. Set of angles determining the total orientation", + "texts": [ + "19) was chosen to define the total orientation of a body. In order to make easier the later derivation of adapting blocks we now give some transformations. Let us introduce a new Cartesian coordinate system which corresponds to the chosen set of angles (8, ~, ~). This system is obtained from the external one in the following way: rotation is first made around the z-axis (angle 8), and then around the new y-axis in the negative sense (angle ~); finally, the rotation around the new x-axis represen~ the angle ~ (Fig. 2.23). This system will be called the orientation system. Let us notice that the x-axis of such system coincides with the previously introduced direction (b). Let A be the transition matrix of the orientation system. Then A (2.4.15) where 55 [ co,e -sine :]. [ c~,o 0 -'~nol Ae sine cose A 4J 0 0 sln4J 0 COS4J [ : 0 -,:n.] A = coslj! (2.4.16 ) lj! sinlj! coslj! Let us find the first and the second derivatives of the transition matrix A Ae A4J Alj! + Ae A4J Alj! + Ae A Alj! (2.4.17) 4J A Ae A4J Alj! + Ae A4J Alj" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003072_0022-3093(96)00191-3-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003072_0022-3093(96)00191-3-Figure2-1.png", + "caption": "Fig. 2. Schematic of a Clark polargraphic electrode used to measure the concentration of oxygen in solution. The oxygen electrode consists of an A g / A g C 1 reference electrode and a Pt electrode, both immersed in a KC1 solution and in contact with the sample chamber through an oxygen-permeable membrane [2].", + "texts": [ + " (CH2COO)~- CH~COOH ,= CH3COO- HO2CCO 2 H ~ - OOCCOO- 282 J.M. Miller et al. / Journal of Non-C~stalline Solids 202 (1996) 279-289 In the case of catalase, solution assays were designed to determine the effect of methanol on the activity of the protein. The relative enzymatic activity of catalase was determined by measuring the rate of oxygen evolution from the decomposition of hydrogen peroxide using a YSI \u00ae Model 53 biological oxygen meter. This oxygen monitor uses a Clark-type polargraphic electrode (Fig. 2) which, when submerged in a suitable liquid, measures a current proportional to the dissolved oxygen partial pressure. The solution assay of catalase followed a procedure outlined by Maehly and Chance [22] and Beers and Sizer [21]. In a suitable test tube, one in which the oxygen electrode fit snugly, 5.5 ml of deionized water was mixed with 40 I*1 of 5 X 10 -9 M bovine liver catalase (Sigma Chemical) dissolved in 0.05 M phosphate buffer (pH 7.00). While continuously stirring the solution, the oxygen electrode was inserted so that the tip was completely submerged" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003003_tmag.2004.843349-Figure13-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003003_tmag.2004.843349-Figure13-1.png", + "caption": "Fig. 13. Eddy-current distribution model for thermal analysis.", + "texts": [ + " This alternative variation of heat flux and the respective time duration are is sequentially stored in an LS file, and the transient thermal simulation is run. The results of simulation showing temperature rise from 0 to 10 000 s at stator is shown in Fig. 12. 2) Thermal Analysis Considering Eddy-Current Loss: The core loss distribution in SRM is another considerable factor for heat production. Before the boundary conditions are set as detailed in this paper for thermal analysis, an iron loss analysis has to be performed to take into account the core loss distribution. Fig. 13 depicts the results of eddy-current loss distribution as obtained by FEA [15]. The thermal analysis made on this model will be a simulation considering copper loss and eddy-current loss. The results of simulation conducted on this model, showing temperature rise from 0 to 7200 s at stator, for the continuous load of 7 A, is shown in Fig. 14, which indicate that the steady-state temperature is attained at 356 K, whereas without considering the eddy-current loss, it was 350 K. 3) Thermal Analysis Considering Fins: The temperature rise of the electric machines is kept under permissible limits by providing fins" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003047_1.1767819-Figure6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003047_1.1767819-Figure6-1.png", + "caption": "Fig. 6 3-RS structure", + "texts": [ + " The inverse position analysis of the 3-RRS wrist is the determination of the actuated joint coordinate values compatible with a given platform orientation. In the implementation of these two problems the base point C can be also considered fixed in the platform since the platform accomplishes spherical motions with center C. Direct Position Analysis. Since the actuated joint coordinates have to assume given values, the revolute pairs adjacent to the base can be considered locked. If the actuated revolute pairs are locked, the 3-RRS wrist becomes the 3-RS structure shown in Fig. 6. Therefore the DPA reduces to find the possible assembly configurations of the 3-RS structure. The closure equations of the 3-RS structure can be written as follows @Rbp p~Ai2C!1b~C2Bi!# 25hi 2 i51,2,3 (12) where Rbp is the rotation matrix that transforms the vector components measured in Sp into the vector components measured in Sb and the left-hand superscript p or b added to a vector indicates the reference system, Sp or Sb respectively, the vector is measured in. Expanding Eqs. ~12! yields the following relationships ~see Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003853_978-3-540-30301-5_17-Figure16.11-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003853_978-3-540-30301-5_17-Figure16.11-1.png", + "caption": "Fig. 16.11a,b Cart\u2013table model [16.37]", + "texts": [ + "22) This is the reason why p was named as zero-moment point. Nevertheless, one must note that the frictional force creates a nonzero vertical moment (16.21) in the general case. \u03c4z = 0 . (16.23) With given robot dynamics and motion, we can calculate or predict the resulting ZMP by using Newton\u2019s law. To distinguish this from the original ZMP defined in the former subsection, we will use the term computed ZMP as in the paper of Vukobratovic\u0301 et al. [16.3] Simple Case Let us start with an extremely simple mechanism. Figure 16.11a illustrates a walking robot and its simplified model, which consists of a running cart on a massless table. The cart has mass M and its position is (x, zc) corresponds to the center of mass of the robot (Fig. 16.11b). Also, the table is assumed to have the same support polygon as the robot. In this case, the torque \u03c4 around the point p is given by \u03c4 = \u2212Mg(x \u2212 p)+ Mx\u0308zc , (16.24) where g is the acceleration due to gravity. Using the zero-moment condition of \u03c4 = 0, the computed ZMP of this cart\u2013table model is obtained as p = x \u2212 zc g x\u0308 . (16.25) From this equation, we can observe two fundamental facts about the computed ZMP. 1. When the acceleration of the cart is zero, the ZMP corresponds to the projection of the CoM: p = x", + " Nagasaka et al. proposed an efficient real-time method that is also applicable to running and jumping motion [16.43]. Harada et al. proposed another efficient real-time method that can be used when pushing an object during walking [16.44]. Pattern Generation Using Preview Controller In this subsection, we will describe the method proposed by Kajita et al. [16.37]. Its stability and possible expansions are well discussed by Wieber [16.29]. For the simplicity, let us use the cart\u2013table model of Fig. 16.11 again, but this time, we take the jerk of the cart as the system input u, ... x = u . (16.42) In this way, the ZMP equation (16.25) can be translated into a strictly proper dynamical system as d dt \u239b \u239c \u239d x x\u0307 x\u0308 \u239e \u239f \u23a0 = \u239b \u239c \u239d 0 1 0 0 0 1 0 0 0 \u239e \u239f \u23a0 \u239b \u239c \u239d x x\u0307 x\u0308 \u239e \u239f \u23a0+ \u239b \u239c \u239d 0 0 1 \u239e \u239f \u23a0u , (16.43) p = ( 1 0 \u2212zc/g ) \u239b \u239c \u239d x x\u0307 x\u0308 \u239e \u239f \u23a0 . For this system, we can design a digital controller that lets the system output follow the reference input as u(k) = \u2212Gi k\u2211 i=0 e(i)\u2212 Gx x(k) , (16.44) e(i) := p(i)\u2212 pd(i) , where Gi is the gain for the ZMP tracking error, Gx is the state feedback gain, and x := [xx\u0307 x\u0308] " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003439_j.neucom.2007.06.019-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003439_j.neucom.2007.06.019-Figure1-1.png", + "caption": "Fig. 1. Two-link robotic manipulator.", + "texts": [ + " The adaptive multi-model SMC using soft computing for robotic manipulators is presented in Section 4. The simulation results to demonstrate the effectiveness of the proposed control scheme are given in Section 5. Finally, Section 6 presents some concluding remarks. In the absence of friction or other disturbances, the dynamic equation of an n-link rigid robotic manipulator system can be described by the following second-order nonlinear vector differential equation M\u00f0q\u00de\u20acq\u00fe B\u00f0q; _q\u00de _q\u00fe G\u00f0q\u00de \u00bc u (1) where q \u00bc [q1,y,qn]T is an n 1 vector of joint angular position, as shown is Fig. 1, for a two-link robot manipulator, _q \u00bc \u00bd_q1; . . . ; _qn T and \u20acq \u00bc \u00bd \u20acq1; . . . ; _qn T are n 1 vectors of corresponding velocity and acceleration, respectively, u is an n 1 vector of applied joint torques (control inputs), M(q) is an n n inertial matrix, B\u00f0q; _q\u00de is an n n matrix of coriolis and centrifugal forces and G(q) is an n 1 gravity vector. The inertial matrix M(q) is symmetric and positive definite and it is bounded as a function of q; m1IpM(q)pm2I. The matrix described by _M\u00f0q\u00de 2B\u00f0q; _q\u00de is a skew symmetric matrix, that is xT[ _M\u00f0q\u00de 2B\u00f0q; _q\u00de] x \u00bc 0, where x is an n 1 nonzero vector" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003670_978-3-642-82195-0-Figure1.10-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003670_978-3-642-82195-0-Figure1.10-1.png", + "caption": "Fig. 1.10. Reference coordinate system", + "texts": [ + " For qi*O, the distance between these points equals is the vector between point Zi at link Ci _ 1 and the mass link Ci . Therefore, it depends on qi + r .. 11 +0 I .. 11 where ~~i is the distance between Zi and 0i for qi=O. ->- qi\u00b7 Vector r ii center of (1.3.1) Beside the local coordinate frames attached to the links, a reference, 12 fixed coordinate system Oxyz is to be assigned. With respect to this system external coordinates describing manipulation tasks, are defined. This system is usually positioned at manipulator base (Fig. 1.10). Its origin need not coincide with the center Z1 of the first joint, so ->- that a distance vector r 1 between these points has to be defined. This o ->- vector, or more exactly, its axis e 1 serves as a reference for defining the zero value of joint coordinate q1 in the same manner as vector ->- ->- ->- r. 1 . when defining joint coordinate q .. If r 1=0 or r 1 is colinear 1- ,.!, 1 0 0 with e 1 , an auxilliary vector has to be introduced, in the same way as ->- it was described for vector r. 1 " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure28.4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure28.4-1.png", + "caption": "Fig. 28.4 5Nm-Class CMRFC", + "texts": [ + " At the same time, it is necessary to note not only the structure but also the material, especially MRF itself. Generally speaking, particles whose diameters are more than 1/10 of the distance of a gap are not ensured to be filled sufficiently in it. Because commercial MRFs consist of micron-size particles (1~10 m), there is a possibility of becoming the obstacle of steady performance. In this study, therefore, we also try to develop new MRF with nanoparticle. On the basis of the multi-layer structure mentioned above, we developed 5NmClass CMRFC. Figure 28.4 shows appearance and cross-sectional view of it. Table 28.1 shows specification data of the 5Nm-Class CMRFC. Basic characteristics tests were conducted for this device. During tests, input part of the clutch was fixed and output part was rotated by a servo-motor with constant speed of 1 rad/s. Figure 28.5 (a) shows static torques of the device. White circles show experimental data and black squares show theoretical values. We can calculate estimation torque of the MRF devices with magnetostatic analysis" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003670_978-3-642-82195-0-Figure2.6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003670_978-3-642-82195-0-Figure2.6-1.png", + "caption": "Fig. 2.6. An illustration of the forward recursive relations for joints with parallel axes", + "texts": [ + "87) can be efficiently utilized in evaluating the Jacobian oJ with respect to the base reference sys tem, so that the total savings in that case are considerable (see Sub section 2.4.3). Let us now consider the computation of the homogeneous transformations corresponding to revolute joints with parallel axes, according to the forward recursive relations. As before, we will denote the serial number of the joint whose axis (axis zk_1) is the first in the series of parallel axes by k, while the last joint with the parallel axis will be designated by K. We will also assume that the axes are adopted to have the same direction, so that ai=O, i=k,k+1, .\u2022\u2022 ,K-1 (Fig. 2.6). 83 By postmultiplying homogeneous transformations, starting from the base o 0 0 0 out to link k, we can obtain matrices T1 , T 2 , \u2022\u2022. , Tk _ 1 , Tk . Instead of computing \u00b0Tk +1 according to \u00b0Tk +1 = \u00b0Tk kTk +1 , we will first obtain the product of matrices corresponding to parallel joints, and then o premultiply the resultant matrix by Tk _ 1 \u2022 Accordingly, the recursive relations have the following form 1 eE, the line advances in the A direction.", + "texts": [ + " Surface tensions of a few liquids Water Glycerol Formamide Thiodiglycol Methylene iodide Aroclor 1242 ( trichlorobiphenyl) 1-Bromonapthalene Tricresyl phosphate Hexachloropropylene 1,1-Diphenylethane t-Butyl napthalene Dicyclohexyl Bis-(2-ethylhexyl) orthophthalate Squalane Hexadecane Tetradecane Dodecane Decane Octane Surface tension mJm- 2 72.6 63.4 58.2 54.0 50.8 45.3 44.6 40.9 38.1 37.7 33.7 32.8 31.3 29.5 27.6 26.7 25.4 23.9 21.8 Fig. 1.2. Soap film on a rectangular frame. A force 2')' (')' per interface) is exerted per unit length of the moveable side 4 1. Droplets: Capillarity and Wetting known as the triple line (cf. Fig. 1.3). Young's Relation (Fig. 1.3a) angle with the liquid interface is called the contact angle BE' If the three phases present are solid/liquid/air, the equation describing the balance of forces pro jected in the plane of the solid surface, known as Young's relation, is: iSG = i cos BE + iSL . rSB = rAB cos BE + rSA . The vertical component is balanced by the elastic force due to deformation of the solid, whose amplitude is microscopic (of the order of A). If B is not equal to BE Young's forces are unbalanced and its contact line moves (Sect. 1.2.7). Neumann's Triangle (Fig. 1.3b) \"fAG + \"fBG + \"fAB = 0 . 1.2 The Players and the Rules of the Game 5 There is a pressure discontinuity across a curved interface. Consider the ex ample of an oil droplet (0) in water (W) (Fig. l.4a). The droplet is spherical, so as to reduce its surface energy. Letting R be the radius, and displacing the o /W interface through dR, the work done by capillary forces and pressure is given by: dW = - PodVo - PwdVw + ,owdA , where dVo = 4nR2dR = -dVw is the volume increase and dA = 8nRdR the area increase of the droplet", + " However , rubbing the glass with a piece of potato, and b 10 1. Droplets: Capillarity and Wetting breathing on it again, condensation droplets no longer appear and the water totally wets the glass; starch deposits, which are hydrophilic, have made the glass wettable. Viscosity TJ, Capillary Speed V* = '\"'( /TJ When describing the dynamics of wetting, we must analyse the motion of the contact line. At rest, the contact angle is ()E. When the contact line is moving at speed U, the contact angle is the dynamical angle ()d (see Fig. 1.3). If ()d > ()E, the capillary force ['\"'(SA - ('\"'( cos ()d + '\"'(sd 1 is positive and the line moves forward (U > 0). If ()d < ()E, the line moves backwards (U < 0). The dynamical equation of the line is the relation ()d = ()d(U). It is found by writing down the equilibrium condition between: (a) the driving force Fd . This pulls the liquid wedge front along and is just the unbalanced Young force: Fd = '\"'(SA - b cos ()d + '\"'(sd = '\"'((cos ()E - cos ()d) . In the limit of small angles, Fd can be expanded as 1 (2 2) Fd ~ 2'\"'( ()d - ()E " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000299_s11071-021-06364-9-Figure9-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000299_s11071-021-06364-9-Figure9-1.png", + "caption": "Fig. 9 Equivalent physical model of PMSM main drive system with electromagnetic effect", + "texts": [ + " The corresponding is electromagnetic damping changes dramatically, and the amplitude decreases rapidly with the frequency increase in the low-frequency range, but the amplitude decreases slowly in the high-frequency range. 3.2 The influence of PMSM magnetic field on the system nature characteristics In order to analyze the influence of torsional electromagnetic stiffness and electromagnetic damping on the gear transmission system nature characteristics, the torsional vibration model of the motor\u2013gear system is changed as shown in Fig. 9. Jm, J1 are the inertia moment of the rotor and gear 1, hm and h1 are the torsion angle, and Ka and Ca are the torsional stiffness and torsional damping of the motor shaft, respectively. The undamped free vibration equation of the PMSM main drive system and gear transmission system is: Jmh 00 m \u00fe Ka hm h1\u00f0 \u00de \u00bc Km 0 hm\u00f0 \u00de MX 00 \u00fe Kn \u00fe Kt \u00fe Kr \u00fe Ke\u00f0 \u00deX \u00bc 0 ( \u00f025\u00de After considering the electromagnetic effect, the modal equation and natural frequency of the coupling system can be expressed as: Table 1 Main parameters of electromechanical coupling system Parameter Symbol Value Unit Parameter Symbol Value Unit Pole pairs p 8 Flux linkage wf 3" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000499_j.surfcoat.2021.127492-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000499_j.surfcoat.2021.127492-Figure4-1.png", + "caption": "Fig. 4. (a) Photographic images and (b) schematic of friction measurement.", + "texts": [ + " The contact angle was measured using drop shape analyzer (DSA25, KR\u00dcSS Instruments) to estimate the adhesion of stainless steel on human skin. Approximately 2 \u03bcL of water was dropped on a surface more than five times at room temperature, and the average contact angle between the surface and the droplet was used to examine the stick\u2013slip phenomenon between human skin and stainless steel parts. Friction tests were conducted using a friction coefficient tester (FPT\u2013F1, Labthink) to measure the friction coefficients of the parts, as shown in Fig. 4a. Fig. 4b presents the friction tester and the method in a schematic form. A silicon sheet in contact with the as-built surface was used to evaluate the surface quality, because the resultant surface characteristic and compression resistance of human skin are almost identical to the silicon sheet. Thus, the touch sensation, in terms of the stick\u2013slip phenomenon on the surface, was quantitatively analyzed based on the friction coefficient and the F\u2013d curves. Friction coefficients were calculated using the equation, \u03bc = F/P, where normal force P is 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000474_s00170-020-06432-1-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000474_s00170-020-06432-1-Figure1-1.png", + "caption": "Fig. 1 Schematic overview of the SLM machine (reproduced from [3], Copyright (2010), with permission from Elsevier)", + "texts": [ + " The deflection direction of the laser beam is controlled by the galvanometer and f-\u03b8 field mirror to reach any position in the forming area. The tools and fixtures are eliminated since the laser beam and metal powder are used as manufacturing tools, and the advantages of the short production cycle, high material utilization rate, and low cost by using SLM [1]. In theory, SLM can form any complex part and realize personalized customized service. SLM molding parts can be widely used in medical, mold, aerospace, ship, automobile, and other fields [2]. The schematic diagram of SLM equipment is shown in Fig. 1. After decades of development, SLM has made great progress and can meet the manufacturing of complex 3D parts in most commercial fields. However, the quality of the SLM parts is far from the commercial standard. SLMmanufactured metal parts are difficult to be applied in actual production without post-processing, especially in the medical and aerospace fields with challenging quality and certification requirements. One of the main standards is that the manufacturing accuracy and forming quality related to the size required by the final product are not up to the standard" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002839_978-3-662-03845-1-Figure7.34-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002839_978-3-662-03845-1-Figure7.34-1.png", + "caption": "Fig. 7.34. Stages in the manufacture of a bioriented hollow object", + "texts": [ + " Even poly( ethylene glycol terephthalate), which is imper meable to air, is not suitable when processed in this way. In order to make bottles impermeable to carbon dioxide, bioriented poly (ethylene glycol terephthalate) is used. Indeed, biorientation implies that crys talline domains, impermeable to carbon dioxide, develop in the two directions. This reduces passage of the gas to just the amorphous regions. Diffusion paths become tortuous and long, thereby reducing permeability. This is achieved by first producing a pre-form, consisting of a tube closed at one end (see Fig. 7.34). The pre-form is made by injection, as described in the next section. The pre form is then reheated to a temperature just above glass transition and inflated 258 7. Polymer Materials by gas injection. This forces it onto the cold mould. Because of the significant change in size (a factor of 3 or 4 in each direction), the large deformation rate and the moderate temperature used, a high degree of biorientation is obtained. Indeed, polymer chain flow cannot occur in these conditions. Unfortunately, biorientation is perturbed if we attempt to make a flat bottom for such bottles" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure33.1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure33.1-1.png", + "caption": "Fig. 33.1 Driving principle of the ultrasonic micro motor", + "texts": [ + " Taking these points into account, the present paper proposes a new concept [1, 2] in which a coil type stator contacts on a cylindrical rotor directly, hence, the structure becomes very simple and can realize miniaturization. Four different types of ideas and prototypes are proposed, manufactured and tested their fundamental performances. 1 Yuji FURUKAWA President ofthe Polytechnic University Japan 2 Tomoyuki KAGA Current Graduate Course Students, Tokyo University of Agriculture and Technology 3 Kenji MAKITA, Tetsuro WADA, Akihei NAKAJIMA Former Graduate Course Students, Tokyo University of Agriculture and Technology Yuji FURUKAWA ,1 Tomoyuki KAGA2, Kenji MAKITA3, Tetsuro WADA3 and Akihei NAKAJIMA3 388 Fig.33.1 (a) shows schematic diagram of the developed ultrasonic micro motor. The prototype consists of an external vibrator, waveguide, stator and rotor. Waveguide made of stainless steel thin wire receives ultrasonic vibration from the vibrator that is attached to one end of it (hereinafter, the waveguide is described as an arm part of coil) and propagates the vibration to the coil type stator. At the micro contact points between the outer surface of stator and the inner surface of rotor, rotational force acts toward helical direction, consequently, both a radical and axial driving force acts on the rotor as shown in Fig.33.1 (b). The details of mechanism are as follows. The micro frictional force works opposite to the forward direction of progressive wave at the contact points always. In addition, the frictional force is influenced by the axial direction of the coil as shown in Fig.33.1 (c). Therefore, the rotor receives both a rotary and aaxial force at the same time. Y. FURUKAWA, T. KAGA, K. MAKITA, T. WADA and A. NAKAJIMA Development of Ultrasonic Micro Motor with a Coil Type Stator 389 Fig.33.2 shows the structure of fabricated motor where a Langevin type ultrasonic vibrator is applied. The one end of the arm is fixed on a XYZ Y stage which is set under the vibrator and pressed to the tip of vibrator. The progressive flexural wave propagates along the waveguide to the coil type stator", + " The rotor is covered with a cylindrical case and supported axially and radially by fitting one end of the case with the stopper. The foil and case are made of stainless steel and TI polymer respectively in order to give enough heat and wear resistance. When an ultrasonic vibration is applied to the arm, a progressive wave propagates along with a waveguide and reaches to the foil type stator, and the rotor is driven at small contacts between the rotor and stator according to the principle described in Fig.33.1. Y. FURUKAWA, T. KAGA, K. MAKITA, T. WADA and A. NAKAJIMA Development of Ultrasonic Micro Motor with a Coil Type Stator 395 In order to check the effect of rotor/stator arrangement on a rotational direction of motor, two different combinations were prepared, where the rotor is set outside of stator or inside. However, both of them rotated to the same direction of propagation of progressive wave and was opposite to the former ultrasonic motor described in Section 33.3 and 33.4. Table 33.5 compares the rotational speed of coil type and foil type stator" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000038_j.engfracmech.2020.106874-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000038_j.engfracmech.2020.106874-Figure1-1.png", + "caption": "Fig. 1. (a) Near-net-shaped AM 17-4 PH SS samples. Schematics showing MC(T) specimens with (b) transverse (TAB; THT) and (c) longitudinal (LAB) notches as well as (d) dimensions of specimen with beveled holes and location of remote back-face strain gage.", + "texts": [ + " Nomenclature c Crack length, mm cn Initial EDM notch length, mm C Load reduction rate, mm\u22121 da/dN Crack-growth rate, m/cycle E Modulus of elasticity, GPa F Stress-intensity boundary-correction factor h Initial EDM notch height, mm K Stress intensity factor, MPa\u221am Kc Fracture toughness, MPa\u221am Kmax Maximum stress intensity factor, MPa\u221am Ncp Number of pre-cracking cycles Pmax Maximum applied remote load, kN Pmin Minimum applied remote load, kN R Stress ratio Ra Surface roughness, \u00b5m w Width of specimen, mm \u03b1 Constraint factor \u0394K Stress intensity factor range, MPa\u221am \u0394Keff Effective stress intensity factor range, MPa\u221am (\u0394Keff)th Effective stress intensity factor range threshold, MPa\u221am \u0394Kth Threshold stress intensity factor range, MPa\u221am \u03c3ut Ultimate tensile strength, MPa \u03c3ys Yield stress (0.2% offset), MPa parallel and perpendicular to the build direction). Commercially-available, gas-atomized (under argon) 17-4 PH stainless steel (SS) powder (3D Systems) \u2013 with 80% of its particle size distribution below 22 \u00b5m \u2013 was utilized in this study to fabricate samples using an LPBF system (3D Systems ProX 100). Optimized process parameters, reported in [33], were chosen for fabricating 17-4 PH SS rectangular blocks under inert argon atmosphere, as shown in Fig. 1(a). All the rectangular blocks were manufactured in the same direction with a height of 48.8 mm, width of 58.8 mm, and thickness of 6.35 mm. Modified compact, MC(T), specimens were extracted from these blocks (see for example ASTM E647-15 [26]), using electrical discharge machining (EDM). In order to consider the effect of material anisotropy on the FCG behavior, two sets of MC(T) specimens were made by changing the initial notch orientation: (i) crack propagation direction perpendicular to the build direction (i.e. transverse crack) and (ii) crack propagation direction parallel to the build direction (i.e. longitudinal crack), as shown in Fig. 1(b) and 1(c), respectively. For MC(T) specimens with a transverse crack, duplicate sets of samples were manufactured and subjected to solution annealing for 30 min at approximately 1040 \u00b0C, air cooling (AC) to room temperature (Condition A) and age hardening heat treatment for 1 h at 482 \u00b0C, followed by AC (Condition H900 or peak-aging). Thus, a total of three sets of AM 17-4 PH SS were taken into account: (i) MC(T) specimens with a transverse crack in as-built condition (TAB), (ii) MC(T) specimens with a longitudinal crack in as-built condition (LAB), and (iii) heat-treated MC(T) specimens with a transverse crack (THT)", + " However, after heat treatment, the yield stress and ultimate tensile strength of AM 17-4 PH SS became comparable to that of wrought material in the peak-age (H900) condition. This is due to the formation of fine, coherent precipitates in the martensite matrix during the peak-aging (i.e. at 450\u2013510 \u00b0C), causing the material to become significantly harder with higher tensile strengths [38]. MC(T) specimens had a width (w) of 40.6 mm, an initial EDM notch height (h) of ~0.4 mm and notch length (cn, measured from the pin-hole centerline) of ~12.2 mm, as illustrated in Fig. 1(d). The specimens were the same as a standard C(T), except the pinholes which were were located further from the notch than the standard specimen. The stress-intensity factor (K) and back-face strain (BFS) relations for the modified and standard C(T) specimens were compared with the ASTM E647 equations [26]. The calculations indicated that the standard K solution and BFS equations [26] can be used for the MC(T) specimens, since the K values were within\u00b12% and BFS values were within 1.4% for c/w \u2265 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003670_978-3-642-82195-0-Figure1.13-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003670_978-3-642-82195-0-Figure1.13-1.png", + "caption": "Fig. 1.13. Vectors relevant for obtaining transformation matrix", + "texts": [ + " l' assigned to two adjacent i-1 l- i-1 3x3 links. Denote this matrix by Ai. Matrix AiER depends on kinematic parameters of the links and, for a revolute joint, on joint co ordinate qi. We will first consider the case when joint i is a revolute one. In order to determine matrix i-1 Ai for any value of joint coordinate qi' we will first compute this matrix for qi = 0, and then, by using the result obtained and Rodrigues formula we shall gain the desired matrix. i-1 0 Consider links Ci _ 1 and Ci when qi = 0 (Fig. 1.13). Denote by Ai the i-1 A . for a revolute jOint l matrix which transforms vectors expressed in the coordinate system of link i into the vectors expressed in system Qi-1. For that we will use conditions of the type ->- i-1 0 .+ v Ai v .+ ->- 15 where v is a vector in system Qi and v is the same vector expressed . i-1 0 with respect to system Qi-1' Evidently, for comput1ng Ai we need to know three linearly independant vectors expressed with respect to both the systems. Let us find three such vectors. The vector which is known with certainty with respect to both the sys.+ ->- terns is the unit vector of the joint axis, i.e. vectors e. and e. are 1 _1 known (defined as kinematic parameters of the kinematic chain) . Besides, from the definition of projections of vectors -+ ->- note by a;; and a. 1 . ...L..L 1- ,1 ~he jOin~ coordinate it follows that, for qi=O, r ii and I i - 1 ,i are antiparallel (Fig. 1.13). De unit vectors corresponding to these projections. They are, evidently, obtained as ->- a .. 11 ;;.x(~ .. x;;.) 1 11 1 ->- ->- (1.3.2) Since vector r ii is known with respect to system Q., a .. is also known . .+ . 1 11 ->- with respect to Qi , 1.e. a ii 1S determined by (1.3.2). vector a!-1,i is, however, known with respect to Q;-1' i.e. (1.3.2) gives as a. 1 .. -+ -+..L -+ ..... 1- ,1 Note that vectors a .. and a. 1 . are perpendicular to e .. Therefore, we ->- ->- 11 .1- ,1 .1 i-1 0 can select eixa i as the th1rd vector needed for comput1ng Ai' Thus, we have ->- i-1 0'+ e" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure3.12-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure3.12-1.png", + "caption": "Fig. 3.12. Mechanism with the gripper subject to a surface-type constraint", + "texts": [ + " 166 n-1( ) ->- ->-L r' -r + k=i kk k,k+1 and ->- dMi then we obtain the form (3.4.1). -> r' nn ->- + p riO o , (3.4.4) s.=O ~ (3.4.5) s. =1 ~ This extension was necessary since the constraints produce reaction force and reaction moment acting on gripper. These reactions will be determined so that the constraints are satisfied. 3.4.2. Surface-type constraint Let us consider an n-d.o.f. manipulator and impose the constraint that the point A of the gripper cannot move freely but is forced to be on a given surface (Fig. 3.12). The immobile surface is defined by h(x, y, z) o (3.4.6) An iterative approach to this problem is given in [8]. Here, we derive another, noniterative one. 167 If we introduce reaction force -> -> FA R no (3.4.7) where -> IFAI, -> Ilh(xA, YA' zA) R n 0 IVhl (3.4.8) and Ilh f out MA, i.e.: (3.4.10) The constraint (3.4.6) can be written in the form of velocities. By differentation: o (3.4.11 ) The next derivation produces the acceleration form o (3" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003162_50008-0-Figure7.37-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003162_50008-0-Figure7.37-1.png", + "caption": "FIGURE 7.37 Lamellar thermocouple suitable for the measurement of flash temperature.", + "texts": [ + " A conventional thermocouple embedded in the contacting material is unsuitable for the measurements because the temperature rise is confined to the surface. The only way that a thermocouple can be used with accuracy is if a lamellar thermocouple is attached to the surface. A lamellar thermocouple is made by depositing on the surface successive thin films approximately 0.1 [~m] thick of insulants and two metals. The specialized form of thermocouple required to measure flash temperatures is illustrated schematically in Figure 7.37. ELASTOHYDRODYNAMIC LUBRICATION 349 Surface temperature profiles within an EHL contact determined by infra-red spectroscopic measurements [56]. The lamellar thermocouple requires elaborate coating equipment for its manufacture and is not very durable against wear. The measurement of surface temperature can be a very difficult experimental task and for most studies it is more appropriate to estimate it by calculating the range of surface temperatures that may be found in the particular EHL contact" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure3.1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure3.1-1.png", + "caption": "Fig. 3.1 Principle of movement of 1-DOF device", + "texts": [ + " The author has proposed AZARASHI (Seal) Mechanism and made a 3-DOF device [5]. Though the mechanism has smaller number of controlled devices, it can move with micrometer order steps in the x-, yand -directions. 1 Katsushi FURUTANI Department of Advanced Science and Technology, Toyota Technological Institute 20 Katsushi FURUTANI In this article, the principle and performance of AZARASHI Mechanism are introduced. Then, a driving method of a piezoelectric actuator with current pulses is introduced. Finally some applications of AZARASHI mechanism are described. Fig.3.1 shows a moving principle of a 1-DOF device [6, 7]. The 1-DOF device put on a base consists of Friction devices A and B connected by Extension device. vice A applies a constant frictional force and Friction device B is controlled by an on-off action. The following relation must be satisfied: Brightness of Friction devices indicates strength of a frictional force. Friction de- AZARASHI (Seal) Mechanism for Meso/Micro/Nano Manipulators 21 OnOff FFF C (3.1) where FC is a constant frictional force at Friction device A, and FOn and FOff are frictional forces in the cases of clamping and releasing, respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000155_j.jmapro.2021.04.041-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000155_j.jmapro.2021.04.041-Figure2-1.png", + "caption": "Fig. 2. Schematic of the fabricated part.", + "texts": [ + " The selected laser powers are 920 W, 743 W, 485 W, and the scan speeds are 25 mm/s, 40 mm/s, 40 mm/s, respectively. The laser power has three levels, and the scan speed has two levels. The main reason for the selection of these process parameters is to investigate the effect of process parameters such as scan speed and laser power on residual stress while other parameters such as layer height, hatching space, and scan path are kept the same. The deposited layer thickness for all the samples is 250 \u03bcm, and hatch spacing is 105 \u03bcm. A bi-directional continuous scan path is used. Fig. 2 illustrates schematic of the fabricated samples. X-ray diffraction (XRD) technique (PANalytical Empyrean multipurpose X-ray diffractometer equipped with Cu \u2212 K\u03b1 radiation) is used to measure the residual stress of the specimens using the sin2\u03a8 method [54,55]. The E. Mirkoohi et al. Journal of Manufacturing Processes 68 (2021) 383\u2013397 coordinate and location of measured points are listed in Table 5. For each point through the height of samples the residual stress is measured two times and the results were averaged" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000161_j.optlastec.2021.107337-Figure7-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000161_j.optlastec.2021.107337-Figure7-1.png", + "caption": "Fig. 7. Schematic illustration of the local inert gas shielding at the nozzle tip (adapted from [22]).", + "texts": [ + " The strengthening but volatile elements such as magnesium [20] will be partially vaporized, as observed in the experiment and shown in Fig. 5(e-f). The Mg content in the remelted layer is lower than that in the un-remelted layer. The higher value measured on the top surface is considered to be the result of the Mg-rich soot that was generated during the DED process and has covered the sample surface. The melt pool is locally protected by the powder conveying gas (Ar) and an additional shielding gas (Ar) stream, as shown in Fig. 7. Cuboids were fabricated with different shielding gas flow rates to observe the influence of inert gas shielding on the build quality. Four laser powers were used: 450, 500, 550 and 600 W. As shown in Fig. 8, both large (greater than approx. 100 \u00b5m) and small (less than approx. 50 \u00b5m) pores are seen in the cross-sections of samples fabricated with the lower (3.6 l/ min) shielding gas flow rate. Such large pores no longer appeared in samples fabricated with higher shielding gas flow rates, but only small dispersed pores remain" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure2.28-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure2.28-1.png", + "caption": "Fig. 2.28. Rotation of working object around its axis", + "texts": [ + " Since positi oning is defined by x, y, z and partial orientation (one direction) by 8, ~, the generalized position vector is x g (2.4.58) It should be explained why this block is incorporated in the algorithm i.e. when it is suitable. To solve the desired position and partial orientation (one direction) five d.o.f. are needed. With most manipu- 66 lators the sixth d.o.f. is rotational and designed so that its axis of rotation coincides with the longitudinal axis of the gripper and the working object (Fig. 2.28). So by directly prescribing the correspond ing co~rdinate q6(t), the rotation of the working object around its axis is also prescribed (Fig. 2.28). The procedure of derivation of this block is similar to the procedure applied to 5 d.o.f. manipulators. In an analogous way we obtained equa tion (2.4.54) i.e. x y z [ 8' ] ,p\" (2.4.59) But the dimensions of matrices are now different: q (6 x 1), n' (3 x 6), 8' (3x1), r\" (2 x6), ,p\" (2 x 1). If we wish to obtain the Jacobian form, then (2.4.60) 8 ~ ______ ~y~ ______ -J) J 67 q can now be computed by the inverse of the 6x6 Jacobian matrix (2.4.61 ) Since verse Z, (i, q6 of iP, is given we can simplify this calculation and avoid the in the 6x6 matrix" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003962_978-3-540-30301-5_3-Figure2.1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003962_978-3-540-30301-5_3-Figure2.1-1.png", + "caption": "Fig. 2.1a,b Pl\u00fccker basis vectors for motions (a) and forces (b)", + "texts": [ + " Suppose that v is a 3-D vector, and that v = (vx, vy, vz)T is the Cartesian coordinate vector that represents v in the orthonormal basis {x\u0302, y\u0302, z\u0302}. The relationship between v and v is then given by the formula v = x\u0302vx + y\u0302vy + z\u0302vz . This same idea applies also to spatial vectors, except that we use Pl\u00fccker coordinates instead of Cartesian coordinates, and a Pl\u00fccker basis instead of an orthonormal basis. Pl\u00fccker coordinates were introduced in Sect. 1.2.6, but the basis vectors are shown in Fig. 2.1. There are 12 basis vectors in total: six for motion vectors and six for forces. Given a Cartesian coordinate frame, Oxyz , the Pl\u00fccker basis vectors are defined as follows: three unit rotations about the directed lines Ox, Oy, and Oz, denoted by dOx , dOy, and dOz , three unit translations in the directions x, y, and z, denoted by dx , dy, and dz , three unit couples about the x, y, and z directions, denoted by ex , ey, and ez , and three unit forces along the lines Ox, Oy, and Oz, denoted by eOx , eOy, and eOz " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000146_s40684-021-00348-1-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000146_s40684-021-00348-1-Figure3-1.png", + "caption": "Fig. 3 Parallel\u00a0(left) and switching mechanism (center) and centric\u00a0(right) gripping methods", + "texts": [ + " The fully threaded bolt connected to the stepper motor drives a moving plate up or down according to the rotation of the motor (ball-screw mechanism). Since the fingers are connected to the moving plate through the support, the fingers also move as the moving plate moves up and down (Fig.\u00a02b). In addition, two connected gears connected to the servomotor are also connected to two of the three fingers through a fixture. When the servomotor rotates, the gears rotate to change the relative angles of the two fingers (Fig.\u00a03). Thus, the posture of one finger remains the same, but the gripping method can be switched by changing the posture of the other two fingers. The working part grips the object according to the movement and deformation of the fingers. The object Fig. 2 a Modeling of gripper and b the designed gripping mechanism 1 3 used to test the centric gripping method is assumed to be spherical, with a diameter of 1\u20138\u00a0cm. The coupling part has a bolt to fix the gripper to the support, and there is space to store the stepper motor and electric wires" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003764_s00170-010-2659-6-Figure7-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003764_s00170-010-2659-6-Figure7-1.png", + "caption": "Fig. 7 Temperature distribution of the cladding layer in Kelvin right after the last deposition step; a long bead, b short bead, c spiral in, d spiral out", + "texts": [ + " \u2013 The reference temperature for computing the thermal strain for the substrate and deposited material is the room temperature and melting temperature, respectively. \u2013 The Z direction at the bottom of the substrate is subjected to zero constrained movement. It is predictable that changing the deposition pattern results in changing the temperature history of the process. The temperature contours of the part right after the last step of the deposition for different deposition patterns are shown in Fig. 7. As can be seen, the maximum temperature, just after turning off the laser, significantly drops below the melting temperature. This reduction is less in the short-bead pattern than in the other patterns. Different temperature histories have a direct effect on the residual stress of the part. Figure 8 indicates the distribution of Von Misses stress after the part cools to room temperature. Except for the spiral-in pattern where the maximum residual stress is at the surface of the cladding layer, for the other patterns, it is at the interface of the cladding layer and the substrate" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003289_j.optlastec.2006.09.008-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003289_j.optlastec.2006.09.008-Figure1-1.png", + "caption": "Fig. 1. Scheme of a typical laser track with its main geometric characteristics: clad height H and clad width W. clad. angle, a \u00bc 180 2 arctan\u00f02H=W \u00de [1].", + "texts": [ + " The experiments were carried out with a coaxial laser cladding system consisting of a 6 kW continuous CO2 laser (Rofin Sinar model RS 6000 RF), a three-axis CNCcontrolled table (Balliu model Maxicut) with work volume 1.25 0.6 0.6m3, a powder feeder and a coaxial cladding head. After the tests the samples were sectioned transverse to the clad track and polished successively with SiC paper with several granulometry in water. The samples were then etched with Nital (2%). The geometry of the clad track was studied by shop microscopy, with 30 magnification and 1 mm resolution. Fig. 1 shows the scheme with a typical cross section of one laser track and defines the main geometrical quantities usually used for laser track characterization: clad height (H) and clad width (W). The clad angle (a) can be calculated by the following expression [1]: a \u00bc 180 2 arctan 2H W (1) with, H the clad height and W the clad width. Response surface methodology (RSM) is the procedure for determining the relationship between various parameters with the various machining criteria and exploring the effect of these process parameters on the coupled responses [8]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003853_978-3-540-30301-5_17-Figure16.3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003853_978-3-540-30301-5_17-Figure16.3-1.png", + "caption": "Fig. 16.3 Compass model", + "texts": [ + " Indeed, this interesting piece of work was not really followed up, but was surely the inspiration for many researches on cyclic systems. Among these, purely passive walkers have largely been considered, and we will now provide some insight into this area. The aim of this section is to present some basic facts and concepts related to passive walking. Many more details may be found in the literature, for example Part B 1 6 .2 in [16.1, 4, 6] among others. The issues considered here are mainly taken from [16.7]. We use the simplest possible model (Fig. 16.3), an unactuated symmetric planar compass descending a slope of angle \u03c6. Masses are pinpoint, and telescopic massless legs are only a way of ensuring foot clearance. Several assumptions underlie the model. Among these, let us mention that the swing phase is assumed to be slipless, and that the double stance phase, during which the swing and support leg are exchanged, is instantaneous. The related impact is slipless and inelastic. We define (following the notation in Fig. 16.3): \u23a7 \u23a8 \u23a9 \u03bc = mH m ; \u03b2 = b a x = [q, q\u0307] = [qns, qs, q\u0307ns, q\u0307s] . (16.1) The swing-stage equations of the robot, similar to those for a frictionless double pendulum, can be written in the form of Lagrangian dynamics H(q)q\u0308 +C(q, q\u0307)q\u0307 + 1 a \u03c4g(q) = 0 , (16.2) where H(q) = ( \u03b22 \u2212(1+\u03b2)\u03b2 cos 2\u03b1 \u2212(1+\u03b2)\u03b2 cos 2\u03b1 (1+\u03b2)2(\u03bc+1)+1 ) , C(q, q\u0307) = ( 0 \u2212(1+\u03b2)\u03b2q\u0307ns sin(qs \u2212qns) (1+\u03b2)\u03b2q\u0307s sin(qs \u2212qns) 0 ) , \u03c4g(q) = ( g\u03b2 sin qns \u2212[(\u03bc+1)(1+\u03b2)+1]g sin qs ) , where 2\u03b1 is the inter-leg hip angle. The specificity of this system with respect to, for example, manipulation robots, is that we have to complete the continuous dynamics with equations describing the step transition" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000068_tie.2021.3057002-Figure11-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000068_tie.2021.3057002-Figure11-1.png", + "caption": "Fig. 11. Prototype and Temperature Measuring Position.", + "texts": [ + " The permanent magnet temperature measured by the NTC sensors that embed at certain locations inside the permanent magnet slot, and the temperature of the permanent magnet is tested as soon as the motor stopped. In order to reduce the temperature difference between the measured one when rotor just stopped and the practical case while machine rated operating, a brake, which could stop the rotor quickly, is achieved by the co-connected load machine. The temperature measuring positions in motor are shown in Fig. 11. In Fig.11, the specific locations of temperature measurement points are given, where the Test1 and Test4 thermistors are located at the permanent magnet near the fan end. The Test2 and Test5 thermistors are located at the axial center position of the permanent magnet. The Test3 and Test6 thermistors are located at the permanent magnet near the axle stretch end. The Test7 thermistor is located at the stator end windings near the fan end. The Test8 thermistor is located at the stator end windings near the axle stretch end" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003767_07ias.2007.202-Figure12-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003767_07ias.2007.202-Figure12-1.png", + "caption": "Fig. 12. Temperature control setup", + "texts": [ + " With the observer, the flux variation according to not only temperature variation but also manufacturing tolerance can be compensated by the proposed scheme. V. EXPERIMENTAL RESULTS In the experiment, a dynamo system in Fig. 11 is installed with the IPMSM and the Induction Machine (IM). The machine parameters of the tested IPMSM are shown in Table 1. An iron hood covered by glass fiber is installed upon the IPMSM to insulate the motor thermally. And, a heating resistor which is operated by the auto-temperature controller is installed inside the hood, in Fig. 12 . To stabilize the system in the thermal sense, the IPMSM was heated and the temperature of IPMSM has been maintained at the preset temperature for a while. A highly accurate torque sensor is installed between IPMSM and IM, and the IPMSM is operated in torque control mode while the IM is operated in speed control mode. Let us first examine problems in conventional torque control method caused by changes in temperature. Comparing the result of applying the current reference at 30[ ] to IPMSM at 30[ ] and IPMSM at 110[ ], it can be seen that as the temperature changes the accuracy of the torque control decreases" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002434_s1044-5803(03)00091-3-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002434_s1044-5803(03)00091-3-Figure1-1.png", + "caption": "Fig. 1. Schematic diagram of lase", + "texts": [ + " Although the density of these materials allows considerable savings in weight and, hence, in fuel consumption, inmost cases, it is necessary tomodify the basic form of the metal. This can be done by laser surface treatment. The aim of this work is to analyze the microstructural and hardness variations throughout samples of an aluminum copper alloy (Al\u201315 wt.% Cu) submitted to a laser surface remelting treatment. The analysis procedure consisted of scanning electron microscopy (SEM) characterization and microhardness tests in resolidified and unmelted substrate regions. 2. Experimental procedure The laser surface remelting process is illustrated schematically in Fig. 1. A continuous 1-kW CO2 laser was used for the experiments in this study. The specimens were prepared by melting pure components in a graphite crucible and pouring the melt into a mould that promoted unidirectional solidification. The ingots were sectioned on a plane parallel to the direction of heat extraction, and the examination of specimen microstructures revealed a dendritically solidified structure with segregation. Before the laser treatment, the specimens were polished using 1200 grit SiC paper to ensure uniform finishing. The laser machine operated at a power of 1 kW and the laser beam travelled at speeds of 500 and 800 mm/min. The specimens were sectioned transverse to the direction of the laser trace (ZY plane of Fig. 1) and were prepared by conventional metallographic techniques. The sections were etched in a solution of 10% NaOH in distilled water for 15 s and were subsequently analyzed using SEM. Microhardness tests were performed on the cross sections using a microhardness testing system connected to an image processing system Neophot 32 and Leica Q-500 MC to measure the hardness indentations. The purpose of the microhardness tests was to document the variation of strength along the different microstructural zones as a function of the heat treatment induced by the variation of the laser beam speed" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000326_j.mechmachtheory.2021.104264-Figure8-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000326_j.mechmachtheory.2021.104264-Figure8-1.png", + "caption": "Fig. 8. Experimental planet gear with duplex cylindrical roller bearing. The bearing outer race is the planet gear body, and the inner race is the solid planet pin (not shown).", + "texts": [ + " Only discrete-body motion was studied in previous work comparing experiments and finite element simulation, so the outer race of the ring gear and inner race of all external gears were defined rigid in [53] . That constraint must be lifted in light of the elasticbody vibration, but these surfaces are far from free. The experimental ring gear is restrained from elastic-body deformation by the snugged bolts holding it to the fixtures and a close slip fit with the fixture inner radius surface. The planet gears are restrained from elastic-body deformation by the distributed radial stiffness of their bearings shown in Fig. 8 . Without any consideration of these stiffness factors, the FE/CM model drastically underestimates natural frequencies with significant elastic-body deformation. The elastic-body support stiffness of the ring gear and planet gears just mentioned is accommodated primarily by adjusting the elastic modulus of the mesh elements at the boundaries noted. The ring gear and planet gear rim meshes (sufficiently away from the tooth elements) in the FE/CM model each have four rows of elements. The stiffness resisting elastic-body deformation of the ring gear in the fixtures was captured by increasing the elastic modulus of the outermost row of ring gear elements by one order of magnitude, identified iteratively to bring FE/CM results into agreement with experiments", + " The mode shape is characterized by the following attributes, given in order of prominence: \u2022 Significant two nodal diameter elastic-body deformation of the planet gears, \u2022 Elastic-body deformation and discrete-body motion of the ring gear, \u2022 Rotational discrete-body motion of the planet gear, \u2022 Increased translational discrete-body motion of the planet gear at higher torque, and \u2022 Carrier translational discrete-body motion at higher torque. While some elastic-body motion of ring gears is generally expected \u2013 especially for thin ring gears \u2013 observation of planet elastic-body motion is more surprising, particularly with the bearings in Fig. 8 and a solid shaft inner race (not shown). These planet gears are not intentionally thin or compliant; they are similar in design to production helicopter gears and supported by production helicopter bearings. Planetary gear vibration research and, in our industry interactions, practical design pays little attention to elastic-body vibration of planet gears, but this research reveals that to be a misguided assumption in applications that may achieve higher mesh frequencies that trigger vibration of higher natural frequency modes (e" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003628_s11044-008-9121-7-Figure6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003628_s11044-008-9121-7-Figure6-1.png", + "caption": "Fig. 6 Closed chain", + "texts": [ + " In fact, the Newton\u2013Euler method usually requires large computation time, since it needs the computation of all the internal reactions of constraint of the system, even if they are not employed in the control law of the manipulator. On the other hand, the Lagrangian formulation is based on the computation of the energy of the whole system with the adoption of a generalized coordinate framework. These computations are unnecessary when the theory of screws and the principle of virtual work are used systematically. Figure 6 shows a closed chain in which a body n of mass mn and centroidal inertia matrix In is under the action of gravitational and inertial forces. In addition, the body n is supporting an external force fe and an external torque \u03c4e . The velocity state Vn = [\u03c9n vn]T and the reduced acceleration state An = [\u03c9\u0307n an \u2212\u03c9n \u00d7vn]T describe the motion of rigid body n taking its mass center as representation point, in other words, vn and an are, respectively, the translational velocity and acceleration of the mass center" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000278_tbme.2021.3083580-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000278_tbme.2021.3083580-Figure1-1.png", + "caption": "Fig. 1. (A) The full exoskeleton assembly for a unilateral system. The assembly includes the knee and ankle joints where the knee joint is powered by the actuator and the ankle joint is an articular joint. (B) The isometric view of the actuator assembly with the main components labeled. The red dotted lines indicate the load path of the power transmission between the actuator and the user. (C) Configuration of the actuator and a torque sensor for the actuator benchtop testing. (D) Steady-state measured torque values with various current inputs (circles). The dotted line shows the theoretical trend calculated based on the torque constant of the motor. (E) Step response of the actuator (50% of the maximum torque) under benchtop setting (commanded torque \u2013 dotted line, measured torque \u2013 solid line). (F) The bode plot of the actuator performance under benchtop setting in response to sinusoidal commanded torque profiles.", + "texts": [ + " This hypothesis is based on the ability of the user to adjust the assistance in real-time. PM provides the user the most control over the assistance, and BT provides the least since the assistance profile is fixed for the controller. IM falls between BT and PM as the assistance profile is adjusted based on the knee joint angle, so the user can adjust the magnitude of assistance but only based on a strict torque-angle relationship. A. Mechatronic Design The one degree of freedom robotic knee exoskeleton was designed to assist the flexion and extension of the knee joint (Fig. 1A and 1B). We prioritized the design criteria to minimize the overall weight of the device, which is directly correlated to the metabolic cost penalty due to the added mass to the user\u2019s body [32]. Our exoskeleton system employs a quasi-direct drive similar to previous knee exoskeleton systems [15-17]. While our design has comparable performance compared to the previous knee exoskeletons with the quasi-direct drive mechanism, this design is the first bilateral, autonomous, robotic knee exoskeleton with the quasi-direct drive mechanism that had its performance evaluated during human locomotion", + " The electrical current was controlled (PI closed-loop control) by an open-source VESC motor controller using an analog signal input. A forcesensitive resistor was placed at the user\u2019s heel for each leg to detect the heel-contact. All inputs and outputs of sensors and the motor controller were integrated by a custom-made printed circuit board (PCB), and a microprocessor (myRIO 1900, National Instruments, USA) was used to control the device with a control-loop rate updating at 200 Hz. The characterization of the actuator performance was performed on a benchtop setting (Fig. 1C). During testing, the actuator housing and the end effector were statically mounted on a frame with an external torque sensor (Transducer Techniques, CA) coupled in series. We performed step response testing by commanding various electrical current inputs to validate the linearity of the actuator response. The steady-state result indicated a linear relationship (R 0.99) between the commanded current and the measured torque (Fig. 1D). As shown with an exemplary step response result (Fig. 1E), illustrating a 50% of the actuator torque output (8.7 Nm), the steady-state response of the measured torque yielded approximately 8.56 Nm, indicating about 1.6% deviation from the theoretical value. This slight deviation of steadystate measured torque compared to the theoretical value (while it only occurred in the high torque command region) may have resulted from the motor hysteresis due to thermal loss. To validate this heat loss more systematically, we conducted thermal testing by commanding the maximum torque", + " As the conventional exoskeleton assistance does not require a peak torque to be applied for more than a couple of hundred milliseconds during the gait cycle, our result assured that our actuator output can reliably provide assistance without overheating. Lastly, we conducted torque bandwidth testing using a sinusoidal torque input in various frequencies (ranging from 0.1 ~ 20 Hz). For each sinusoidal input, we set the peak torque with 90% of the actuator's maximum capability. Our test result showed that our actuator\u2019s torque bandwidth was 17 Hz which was computed by taking a -3dB magnitude decay point from a generated bode plot (Fig. 1F). B. Controller Design 1) Biological Torque Controller (BT) Similar to previous biological torque controllers designed for the hip and the ankle joints, the BT for this study was designed to closely follow the profile of the knee joint moment during the early stance phase of incline walking [23, 31]. The parabolic-shaped assistance profile provided active knee extension assistance for the first 30% of the estimated gait cycle with its peak reaching 30% of the peak biological knee moment occurring during incline walking, about 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002768_tnn.2004.836198-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002768_tnn.2004.836198-Figure1-1.png", + "caption": "Fig. 1. System configuration: three inverted pendulums on three carts connected by springs and dampers.", + "texts": [ + " Notice that the upper bound for the adaptation gain has in the numerator, while the lower bound has in the denominator. Therefore, can be selected sufficiently large to ensure that . Remark 6.4: The adaptive laws in (25) are based on gradient descent and use sigma modification term for preventing the parameter drift. One can alternatively use the projection based adaptive algorithm to ensure boundedness of the RBF weights by definition [35]. We consider three identical inverted pendulums mounted on carts, as depicted in Fig. 1. The carts are connected by springs and dampers. In each subsystem, we assume that the position of the cart and the angle of the pendulum are measured and the cart is regulated by input forces . The equations of motion for the system are given as follows: (42) (43) (44) (45) (46) (47) where , , are input forces to the carts (N), is the mass of the cart (kg), is the mass of the rod (kg), is the distance from the pivot on the cart to the center of gravity of the rod (half of full length)(m), is the moment of inertia of the rod with respect to its center of mass , is the gravitational acceleration m/s , is the spring constant (N/m), is the damping constant s/m , , are interconnection forces due to springs and dampers" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002667_s0141-0229(00)00210-6-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002667_s0141-0229(00)00210-6-Figure1-1.png", + "caption": "Fig. 1. Schematic design of sensor: a, platinum wire; b, glass; c, teflon cap; d, PVA membrane.", + "texts": [ + " The solution was left at 225\u00b0C for 16 h then thawed at 4\u00b0C for 8 h. This process was repeated five times; finally, the resulting sponge-like discs were carefully washed three times with a 0.1 M phosphate buffer (2 ml, pH 8.0) for 24 h at 4\u00b0C. The working electrode was a platinum wire (0 .5 mm diameter), which was polished with alumina powder to ensure a flat surface and sealed in a glass tube. The active sensor was formed by a membrane disc, placed on the electrode surface, and fixed with a teflon cap with a 3 mm hole (Fig. 1). When not in use, the membranes were stored at 4\u00b0C in a 0.1 M phosphate buffer at pH 8.0. The mechanical properties of the membranes permitted their easy replacement and use. Free and immobilized ChO activities were determined spectrophotometrically. The assay mixture containing 2 ml choline chloride solution (30 mM in a 20 mM Tris buffer, pH 8.0), 20 ml 4-aminoantipyrine solution (1% m/v), 40 ml of phenol solution (1% m/v), 100 ml POD (100 purpurogallin U ml21) was incubated at 25\u00b0C for 5 min in a spectrophotometer" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003729_9780470612231.ch6-Figure6.16-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003729_9780470612231.ch6-Figure6.16-1.png", + "caption": "Figure 6.16. (a) Schematic of a QCM (b) Photo of bare QCM", + "texts": [ + " The absorption of these solvents would change in the mass of the polymer, which would be then seen as a change in the fundamental frequency of the quartz to which it was bound. GC coatings were the first coatings used due to their excellent sorption properties and the pre-existing knowledge of their applications. When the acoustic wave travels through the bulk of the crystal, the sensor is called a bulk acoustic wave (BAW) device and when the wave travels along the surface of the crystal, it is called a surface acoustic wave (SAW) device. Figure 6.16 shows a typical quartz crystal microbalance (QCM), which is a specially cut quartz wafer supported between two gold electrodes which generates a bulk acoustic wave through the crystal. If an uncoated QCM (A) with a fundamental frequency of FA is coated with a polymer (B), the fundamental frequency of the QCM will drop to FB (Figure 6.17). When this coated QCM is then exposed to a vapor (C), some of the vapor will be absorbed into the polymer coating and will change the mass of the crystal, and hence its fundamental frequency" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure2.36-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure2.36-1.png", + "caption": "Fig. 2.36. Boundary conditions on the last segment", + "texts": [ + " 5 '\" 9) and (2 .. 1 ) offer the possibility of recursive calculation of total forces and moments in manipulator jolnts. The boundary conditions for this backward recursion are -> Fend, (2.5.12a) +1 (2.5.12b) and they are shawIl in Fig~ 1.36. ... F _ and enc:! are the forc(J and the moment the manipulator produces if in contact with some object on the gTound. (:fig. ~36a). If the last segment of the manipulator is free (not in contact with the groundl f niellt if written in b~-f. systems~ + Fend o? = 0 (Fig. 2.36b). Let us now consider a rotat.ional joir!t S1. In that jOint, tilcre is the driving torque 1 (with the directi.on along ), react moment (perpendi.cular ~i)' and the reaction force (Fig. 2.37a \" If the joJnt linear, tllen there is a driving force (along ;. t.he rf..:act ion 51 is force FHi {perpendicular + ~ to. \u20aci) f and the reaction lTlOTllent\" acting on the i-th segment (Fig. 2. 7bi. fI'hu2, tl~e tot.al forCE': in joint Si is: ->- , 1 r F + R:L s p, i. l (2\" 5\" 13) and t.he tot,al moment The reaction force can now be computed as 85 86 -+ s" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000285_j.optlastec.2021.107277-Figure8-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000285_j.optlastec.2021.107277-Figure8-1.png", + "caption": "Fig. 8. Temperature distribution of the molten pool during simulation under laser power of 1500 W and scanning speed of 0.01 m/s at different times: (a) 0.5 s, (b) 1.0 s, (c) 1.5 s, (d) TiAlSi alloy converted from TiAlSi powder.", + "texts": [ + "1 mm hexahedron elements on TiAlSi powder bed was used to improve the calculation accuracy. The 304 stainless steel substrate and HAZ were given the coarser mesh to enhance computational efficiency. The powder layer elements were transformed into alloy elements among the computational progress. The laser cladding craft was successfully executed by the program exhibited in the flow chart (Fig. 7). As to improve the deposition rate of the powder in the process in which the powder was pre-laid on the substrate surface, the thickness of powder layer was about 0.4 mm. Fig. 8 provides the temperature field cloud chart of the single-track cladding under the condition that laser power of 1500 W and scanning speed of 0.01 m/s. The heat source energy was appeared as gaussian distribution. Temperature evolution was presented in the simulation process. The energy was concentrated in a small area and spread around. It can be seen from Fig. 8(a\u2013c) that the maximum temperature of the molten pool is proportional to time. The temperature selection judgment mechanism can well help us to distinguish between melted and unmelted elements. The black line in the picture is the dividing line between melted and unmelted areas. Fig. 8(d) exhibits the morphology of cladding layer. Due to the exponential attenuation of energy along the Z axis orientation, the energy distribution was more uniform along the X and Y axis orientation. Therefore, the energy can hardly convey to the interface of the powder layer and substrate to melt them when the laser power is comparatively low. In other words, the high laser power will lead to a high dilution rate and wettability, which will significantly reduce the coating height. C. Shen et al. Optics and Laser Technology 142 (2021) 107277 To further understand the effect of laser power on the geometric shape of the coating, several measurement points were placed at the boundary of the cross-section to detect the temperature evolution during laser cladding process" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003060_s0956-5663(01)00269-x-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003060_s0956-5663(01)00269-x-Figure1-1.png", + "caption": "Fig. 1. Schematic diagram displaying the enzyme and electrode reactions involved in the detection of phenolic compounds at composite tyrosinase electrochemical biosensors.", + "texts": [ + " The comparison of capabilities of the amperometric composite tyrosinase biosensors are illustrated in this work by their response to different phenolic compounds (phenol, catechol, 4-chloro-3-methylphenol, 4-chloro-2- methylphenol, 4-chlorophenol, 2,4-dimethylphenol, 2,3- dimethylphenol, and 3,4-dimethylphenol), most of them included in the EPA pollutant list, in a phosphate buffer working solution. The enzyme reaction involves the catalytic oxidation of these compounds to the corresponding quinones, and the electrochemical reduction of these quinones was employed to monitor this reaction (Fig. 1). 2.1. Apparatus, electrodes and electrochemical cells Experiments were performed on a Metrohm (Herisau, Switzerland) 641 VA potentiostat connected to a Linseis (Serb, Germany) L6512 recorder. The electrochemical cell was a BAS (W. Lafayette, IN, USA) Model VC-2 cell with a BAS RE-1 Ag/AgCl/KCl (3 M) reference electrode and a platinum wire auxiliary electrode. Other apparatus used were a Metrohm 628- 10 rotating electrode connected to a E-510 Metrohm potentiostat, and a 728 Metrohm magnetic stirrer" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003625_tmech.2008.2010935-Figure12-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003625_tmech.2008.2010935-Figure12-1.png", + "caption": "Fig. 12. Comparison of design parameters (Ro = 76.2 mm).", + "texts": [ + " (19) For the layout in Table IV where m = 10, and thus, K(\u2208 R 3\u00d710) K = [( \u21c0 K1 + \u21c0 K13) ( \u21c0 K2 + \u21c0 K14) \u00b7 \u00b7 \u00b7 ( \u21c0 K17 \u2212 \u21c0 K20 \u2212 \u21c0 K21 + \u21c0 K24)]. (19a) Two sets of simulation results are given here to illustrate the effects of pole sizes on the magnetic torque and the inverse torque model of the orientation stage. 1) Effect of Pole Size on the Magnetic Torque: Observations in Fig. 4 suggest that both small ar and L (for a given ao ) have a significant effect on the increase in the z-component magnetic fluxes, and hence, on the compact design of a spherical motor. The effect can be illustrated with the example in Fig. 12 and Table V, where two pole sizes of a spherical motor are compared. Design 1 (D1) simulates the torque between the rotor PM and stator EM of the SWM [9], where L \u2265 1, while design 2 (D2) models that of the 3-DOF orientation stage (Fig. 10) with the same outer radius Ro = 76.2 mm. In D2, both the PM and EM have a much smaller L of 0.2 and 0.3, respectively, and as a result, the rotor PM (embedded in the \u201csocket\u201d) has a 1.4 times larger rotational radius than that of D1. The EM in Table I is used for D2 and repeated here for ease of comparison" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003670_978-3-642-82195-0-Figure1.22-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003670_978-3-642-82195-0-Figure1.22-1.png", + "caption": "Fig. 1.22. Vectors relevant for the Jacobian computation", + "texts": [ + " the refe rence point is the manipulator end-effector tip and the translational velocity of this point with respect to the base reference system is considered), is to use recursive relations (1.3.11), (1.3.17), i.e. according to 0+ R. ~,o 0+ Rn+1 . ,~ o ,(i) Jo i=2, ..\u2022 ,n 0+ 0 i-1+ Ri - 1 ,0 + Ai - 1 Ri ,i-1 ' i=2, ... ,n 0+ 0+ Rn +1 ,0 - Ri,o 0+ 0+ e i x Rn +1 ,i - for revolute joints 0+ e i - for sliding joints 0, (n) ] ER3xn J c (1 .5.23) 42 The relations are the most appropriate for Rodrigues formula approach, i-1+ where joint axes e i are arbitrary unit vectors with respect to coordinate systems (i-1) (Fig. 1.22). However, the joint axes ~i are most frequently colinear with one of the axes of the link coordinate system. In this case matrix-vector product o i-1+ Ai - 1 e i requires no floating-point operations. The computation of the vector cross product can be similarly eliminated, as will be de scribed in the text to follow, for Denavit-Hartenberg kinematic nota tion. In Denavit-Hartenberg kinematic notation the joint axes coincide with + zi-1 axes of link coordinate systems, so that ~i-1 = [0 0 1]T holds" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002726_0045-7906(94)90021-3-Figure10-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002726_0045-7906(94)90021-3-Figure10-1.png", + "caption": "Fig. 10. These configurations resulted from using the pseudoinverse and the optimal kinematic fault tolerant inverse on the test trajectory described in Fig. 8 up to the positions shown. Circles delineate the remaining reachable workspace should a particular joint fail while the manipulator is at this configuration. The shaded regions are reachable by the manipulator from these configurations irrespective of which joint fails. The configuration resulting from the pseudoinverse clearly does not possess a high degrec of fault tolerance since a failure of the third joint would cause the manipulator to immediately be unable to proceed along the path.", + "texts": [ + " On the other hand, even though the direction of the trajectory changes at times t = 20 and t = 40, no significant discontinuity in the norm of the joint velocity occurs since approximately equal ratios of f and ~ are necessary both before and after the turn. The above discussion shows that the optimal kfm inverse results in well-conditioned configurations, however, the real benefits of using the optimal kfrn inverse over the pseudoinverse become apparent when one considers operation after a joint failure. To evaluate the performance of each inverse after a failure, all possible single joint failures are simulated to occur at t = 75 (x = [0, 1] r) on the test trajectory. The resulting failure configurations for both of the inverses are shown in Fig. 10 along with the remaining path which is indicated with a bold line. First, consider locking the first joint while the second two joints remain usable. The remaining region of the workspace that is reachable by the resulting manipulator for both cases is a circle of radius 2 m centered at the end of the first link and is indicated with a dotted line. Note that in the pseudoinverse case, a portion of the remaining trajectory lies outside of the new workspace boundary while in the resulting optimal kfm configuration the entire remaining path is reachable by the failed manipulator", + " It should be clear that if the third joint fails in this configuration the manipulator will immediately lose it's ability to track the desired path. In summary, if either the first or third joint fails, only the configuration resulting from using the optimal kfm inverse would be able to complete the task while if the second joint fails neither of the resulting configurations allow the task to be completed. For any given configuration, the region of the workspace that remains reachable under all three of the possible single joint failures in the manipulator is the guaranteed reachable workspace. In Fig. 10 the guaranteed reachable workspaces are shaded for both of the configurations that result at t = 75 from using the two different inverses. Since the optimal kfm inverse function maximizes the minimum singular value of the Jacobians resulting from failures, and because the minimum singular value is a measure of the distance from a singularity, the optimal kfm inverse function keeps the manipulator away from what would be singularities if a failure were to occur. Since workspace boundaries are by definition singular configurations, using the optimal kfm inverse insures that the manipulator will be in a configuration that is away from a workspace boundary should a joint fail" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003511_rsta.2006.1913-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003511_rsta.2006.1913-Figure1-1.png", + "caption": "Figure 1. A simple model of a stick insect leg. Each leg can be modelled as a manipulator with three hinge joints, resulting in 3 degrees of freedom (d.f.). From the body towards the foot, the joints are called the thorax\u2013coxa joint (TC), the coxa\u2013trochanter joint (CT) and the femur\u2013tibia joint (FT). The joint axes (solid arrows) account for protraction/retraction of the coxa (Pro/Re), depression/levation of the trochanter and femur (Dep/Lev), and flexion/extension of the tibia (Flx/Ext). The joint of the foot and the foot itself are neglected for simplicity. Each step cycle can be divided into two states: the stance movement on the ground (dashed arrow) and swing movement through the air (dotted arrow). The state transitions occur at the anterior extreme position (AEP) and posterior extreme position (PEP).", + "texts": [ + " This behaviour requires a higher degree of sensitivity with respect to the ever-changing properties of the environment and needs a control system that is able to intelligently react to this information. As we are interested in studying the principles underlying autonomy and decision-making in neuralmotor control, we therefore decided to concentrate on stick insects, which will be the main subject in the rest of this article. (f ) Modelling autonomous walking by behaviour-based, distributed ANNs In a walking insect, at least three joints per leg have to be controlled (figure 1): the thorax\u2013coxa joint (TC-joint); the coax\u2013trochanter joint (CT-joint); and femur\u2013tibia joint (FT-joint). The CT- and FT-joints are simple hinge joints with 1 d.f. Phil. Trans. R. Soc. A (2007) corresponding to levation/depression of the femur and extension/flexion of the tibia, respectively (figure 1). The TC-joint, which connects the leg to the body, is more complex, but most of its movement can be modelled by the rotation around a slanted axis. The two Euler angles that define the axis of protraction/retraction of the leg vary only little during normal walking (Cruse & Bartling 1995) and can be assumed constant. Thus, an insect has to control 18 joints in total, which, owing to their simplicity, result in an equal number of d.f.. In principle, there are two equally sensible ways of modelling hexapod locomotion based on biological findings", + " Similar rules have been found for the walking crayfish (Cruse 1990) and cats (Cruse & Warnecke 1992). The core of WALKNET consists of a set of six single-leg controllers, each of which is built by a number of distinct modules that are responsible for solving particular subtasks. Some of these modules might be regarded as being responsible for the control of special \u2018microbehaviours\u2019; for example, a walking leg can be regarded as being in one out of two mutually exclusive states, namely performing a swing or a stance movement (figure 1). During stance (or power stroke), the leg maintains ground contact and is retracted to propel the body forward, while supporting the weight of the body. During swing (or return stroke), the leg is lifted off the ground and moved in the direction of walking, to touchdown at the location where the next stance should begin. Owing to the rhythmicity of insect gaits (e.g. Wilson 1966) and the alternating activation of antagonistic motor neuron groups in reduced preparations (e.g. Bu\u0308schges et al. 1995), the two states of the step cycle of each leg are often treated as two phases of the same central motor pattern", + " As yet, it is unknown to what extent such modulation is a cause or rather a result of the corresponding changes in leg kinematics. (a ) Swing movements are mechanically uncoupled, regulated and targeted Controlling a swing movement is easier than controlling a stance movement, because a leg in swing is mechanically uncoupled from the environment and, owing to its small mass, essentially uncoupled from the movement of the other legs. Therefore, whatever a leg does during a swing movement, it has virtually no impact on the movements of the other legs. According to figure 1, each stick insect leg can be modelled as a manipulator with 3 d.f. of rotation. As physiological experiments have shown that each one of these d.f. may show only a weak neural coupling to the two others (Ba\u0308ssler & Bu\u0308schges 1998), the neural control network must have at least three pairs of motor outputs, one for each pair of antagonistic muscles per leg joint. For simplicity, each pair of these motor outputs is modelled in WALKNET as a single floating-point variable, allowing both negative and positive output" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002420_robot.1999.770005-Figure7-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002420_robot.1999.770005-Figure7-1.png", + "caption": "Fig. 7 Lower-limb's motion divided into 5 types of step", + "texts": [ + " But notice that we can plan the lower-limb motion arbitrarily, while we can only decide the trunk trajectory due to consideration of the dynamical condition of balance of the robot. We are able to make and classify various kinds of motion patterns after fiom the observation explained below. 4.1.1 Classification of unit patterns of the lower-limb By defining a step of back-and-forth walking as a unit pattern, we classified the motion of each leg into five types of step motion in consideration of the locomotive motion velocity (gait attribute per step) as shown in Fig.7. Basically, we realized the human-follow motion by the combination of these types of step motions. To prevent unstability in the trajectory of the trunk (explained in the next section), caused by an excessive change of moment around the ZMP, we decided that the lower-limb unit patterns must be performed mutually in the direction of the arrow in Fig.7. The connection rule for the unit patterns is shown in Fig.8. 4.1.2 Classification of unit patterns of the trunk We planned the trunk trajectory to compensate for the moment generated by the lower-limb motion planned above. It has been noted that in classifying unit patterns of the trunk, the dynamics of the trunk motion should be considered. We can deform the equation of moment balance around the pitch and roll axis (Eq.6 & 7) as below: where@ (t> and VI (t> are known variables in the equation Here, we simply discuss the trunk motion around the pitch axis" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003287_tbme.2005.851530-Figure11-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003287_tbme.2005.851530-Figure11-1.png", + "caption": "Fig. 11. Keyframes of the foot rotation.", + "texts": [ + " The only variables used for optimization in the frontal plane are and . APPENDIX III CALCULATING THE JOINT ANGLES USING INVERSE KINEMATICS As we have already defined trajectories of the COM and angular momentum, the next step is to calculate kinematic parameters that satisfy these trajectories. Inverse kinematics is used for this purpose. At first, positions and rotational trajectories of the feet, which are defined here as and , are calculated using footstep data specified in advance. As shown in Fig. 11, four keyframes of the support foot are specified. The data include postures of the foot at initial contact, initial full contact, heel rise, and toe-off. The - component of the velocity of the motion of the foot of the swing leg when it is lifted from the ground is calculated by where is the step length. The final velocity of the motion of the foot when it comes into contact with the ground is set to zero. The trajectory of the swung foot is calculated by interpolating the keyframes with a cubic spline curve" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000562_j.mechmachtheory.2021.104380-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000562_j.mechmachtheory.2021.104380-Figure3-1.png", + "caption": "Fig. 3. Mechanism approximation of slender flexible links.", + "texts": [ + " Likewise, the compliance c 1 will be much smaller than c 2 and c 3 , such that the bending effect about the x -axis, related to t 1 , can also be neglected. Therefore, in the proposed method, for each segment, only t 2 and t 3 are retained in the elastic approximation linkage to reproduce the effects of bending about y -axis and torsion about z -axis. As a result, a spatial hyperredundant mechanism with 2 n elastic revolute joints will be generated to approximate the elastostatics behavior of the slender flexible link, as shown in Fig. 3 . (Here, n is the number of discretized segments.) In the proposed method, the product-of-exponential (POE) formulation [50] is adopted to analyze the kinematics of the hyper-redundant approximation mechanism. As shown in Fig. 3 , two reference frames, namely the spatial frame { S } and the tip frame { T } , are constructed at the base and the tip end of the spatial hyper-redundant mechanism. Then, the pose of the link tip can be obtained as g st (\u03b8) = exp ( \u0302 \u03b61 \u03b81 ) \u00b7 \u00b7 \u00b7 exp ( \u0302 \u03b6N \u03b8N ) g st, 0 (3) where \u02c6 \u03b6i \u2208 se (3) , i = 1 , \u00b7 \u00b7 \u00b7 , N, denote the twists (in 4 \u00d7 4 standard representation) of the elastic revolute joints in home configuration. \u03b8 = [ \u03b81 , \u00b7 \u00b7 \u00b7 , \u03b8N ] T \u2208 R N\u00d71 represents the displacement vector of the corresponding joint variables" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002513_026404197367137-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002513_026404197367137-Figure1-1.png", + "caption": "Figure 1 Illustration of the three variables: angle of release ( a ), speed of release (v) and spin ( ). Angle of release varied from 45 to 65\u00a1 , speed from 7.0 to 7.8 m s- 1, and tangential velocity from r = -2 m s- 1 (forespin) to r = +2 m s- 1 (backspin). Parameters in the model are also illustrated: the height of ball release (measured from the centre of the hoop), h = 1 m; the horizontal length of ball release (measured from the centre of the hoop), l = 4 m; the radius of the basketball, rb = 0.121674 m; the radius of the hoop, rh = 0.234250 m.", + "texts": [ + " Keywords : Basketball, free throw, optimal trajectory. Successful free throw shooting is required for all basketball players, regardless of position. The objective of the shooter is to shoot a basketball (circumference 0.749-0.780 m) through a horizontally oriented hoop (inside radius 0.225 m; thickness radius 0.0085- 0.0100 m) whose centre is 3.05 m above the \u00af oor and 4.225 m in front of the free throw line (Pocock, 1992). The ball is released with an angle of release ( ), speed (v) and spin ( ) (Fig. 1; for nomenclature, see Appendix 1). The optimal trajectory, which is dependent upon the shooter, can be de\u00ae ned as the trajectory which maximizes the probability of a successful shot when it is attempted. If the optimal trajectory is currently not used, its adoption could increase the success of free throw shooting. A 69% success rate for free throw shooting has been reported for men\u2019s college basketball in the USA over 20 consecutive seasons (Krause, 1991). The optimal trajectory of the basketball free throw has been quantitatively addressed in several studies *Address all correspondence to Gordon R", + " 2) yields two equations: mvt(t0) + F(t1 - t0) = mv t(t1) (6) I (t0) - F(t1 - t0)r = I (t1) (7) Using the inertial properties of a hollow sphere (I = m 2 3 r2 b) and equations (5), (6) and (7), the solutions D ow nl oa de d by [ E as te rn K en tu ck y U ni ve rs ity ] at 0 7: 46 1 8 M ar ch 2 01 3 for the departing tangential speed and spin can be derived: v t(t1) = 1 5 (3v t(t0) + 2 (t0)rb) (8) (t1) = 1 5r (2 (t0)rb + 3v t(t0)) (9) A computer program simulated a ball release 4 m behind (l = 4 m) and 1 m below (h = 1 m) the centre of the hoop: (y, z) = (-4, -1). We chose l = 4 m to \u00ae t the personal observation that the shooter extends his arms beyond the 4.225 m free throw line in all shooting techniques. A value, h = 1 m, corresponds to a backspin overhead shooter with a height of approximately 1.6 m (Vaughn and Kozar, 1993), or a taller shooter using a forespin, underhand technique (personal observation). There were three input variables to the computer program: the angle ( ), speed (v), and spin ( ) at release (Fig. 1). In all cases, the parameters used to describe the hoop, backboard and ball were chosen as midway between the extrema used for Olympic tournaments and world championships (Pocock, 1992). Speci\u00ae cally, the following parameters were \u00ae xed: radius of ball = rb = 0.7645 m/(2 ) ~ 0.122 m; radius of hoop = rh = 0.234 m; radius of hoop\u2019s rim = rt = 0.009 m; radius of hoop\u2019s rim + radius of ball = r = 0.131 m. The computer program incrementally adjusted angle, speed and spin and calculated both those combinations which resulted in a successful shot and the sequence of rim or backboard bounces" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002531_s0167-2789(99)00153-0-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002531_s0167-2789(99)00153-0-Figure2-1.png", + "caption": "Fig. 2. Strains in two symmetry breaking transformations: (a) isotropic to uniaxial (backbone anisotropy parameter r > 1), (b) cubic to tetragonal.", + "texts": [ + " The latter exhibit domains and soft deformations modes just like the former, and through similar mechanisms (rearrangement of twinned martensitic variants). For crystalline solids, the symmetry breaking transformations of interest involve parent phases with discrete crystallographic symmetry, and they deliver only a finite number of distinct product phases. For a cubic to tetragonal transformation, for example, there are three preferred states of distortions describing the product phases, corresponding to three uniaxial stretches Uni , i = 1, 2, 3, along unit vectors ni parallel to the edges of the cubic cell of the parent phase (see Fig. 2). Since superimposed rigid body rotations leave the energy invariant, each of the three uniaxial stretches defines an energy \u201cwell\u201d, and the stress-free (or \u201cnatural\u201d) states of the product phase are defined by the union of these wells, namely, by a set of the form K = \u222a3 i=1SO(3)Uni , where SO(3) is the group of rotations in R3. Viewed from this perspective, nematic elastomers provide us with an infinite dimensional version of the last formula, namely, K = \u222an\u2208S2 SO(3)Un, where S2 is the unit sphere in R3" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003670_978-3-642-82195-0-Figure1.8-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003670_978-3-642-82195-0-Figure1.8-1.png", + "caption": "Fig. 1.8. Joint coordinate of a revolute kinematic pair", + "texts": [ + " Distance vectors r ii and r i _ 1 i are chosen to correspond to the selected joint center Zi. Denote by r~. and ~~ 1 . the projections of these vectors onto the plane IT .. 1.1. 1.- ,1. ->- ->- 1. The joint coordinate q. is the angle between vectors -r~ 1 . and r~. 1. 1.- ,1. 1.1. (Fig. 1.7). The situation when these two vectors coincide corresponds to the zero value of joint coordinate qi. A more detailed scheme of vectors defining the joint coordinate qi for a revolute kinematic pair is presented in Fig. 1.8. Here, points 0i_1 and 0i denote mass centers 11 of links Ci _1 and Ci , respectively. ->- ->- Let us now consider a special case when either r i - 1 ,i or r ii is colinear with ~ .. In that case the projection of this vector onto the plane 1 ->- perpendicular to joint axis e i is not defined, so that the above definition of joint angle can not be applied. Then, it is necessary to in ->- troduce an auxilliary vector which is not colinear with e i , whose pro->- jection will determine joint angle qi. For example, if r ii is colinear with ei one can adopt vector qi1 or qi2 (Fig. 1.8) instead of ~ii' so that its projection determines the zero value of qi. The jOint coordinate for a sliding joint is defined in the following way. The center Zi of joint i lies on joint axis and is defined by the ini tial point of vector ~. 1 . (Fig. 1.9). One should select a point 1- ,1 Zi belonging to link Ci on the joint axis, which cojncides with Z. for 1 qi=O. For qi*O, the distance between these points equals is the vector between point Zi at link Ci _ 1 and the mass link Ci . Therefore, it depends on qi + r " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002555_s0304-8853(03)00324-x-Figure5-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002555_s0304-8853(03)00324-x-Figure5-1.png", + "caption": "Fig. 5. Skewed rotor.", + "texts": [ + " Considering the relative position between permanent magnets and armature, the relation b \u00bc y\u00fe a is satisfied. Thus the Fourier expansions of \u00f0hm=\u00f0hm \u00fe g\u00f0y; a\u00de\u00de\u00de2 is expressed as hm hm \u00fe g\u00f0y; a\u00de 2 \u00bc G0 \u00fe XN n\u00bc1 Gn cos nz\u00f0y\u00fe a\u00de: \u00f09\u00de Substituting Eqs. (9), (5) and (4) to Eq. (1), the cogging torque can be expressed as follows: Tcog\u00f0a\u00de \u00bc pzLFe 4m0 \u00f0R2 2 R2 1\u00de XN n\u00bc1 nGnBr\u00f0nz=2p\u00de sin nza; \u00f010\u00de where LFe is the axial length of armature, R1 the outer radius of armature, R2 the inner radius of stator yoke. Fig. 5 shows the skewed rotor. When there exists skewing, the distributions of B\u00f0y; a\u00de at different axial positions are not the same. If B\u00f0y; a\u00de at the axial position L is expressed as B\u00f0y; a;L\u00de; the coenergy within the motor is W \u00bc 1 2m0 Z V B2\u00f0y; a;L\u00de dV \u00bc R2 2 R2 1 2m0 Z LFe 0 Z 2p 0 B2\u00f0y; a;L\u00de dy dL: \u00f011\u00de If the skew angle corresponding to the axial length of armature LFe is Nsy1; the skew angle corresponding to axial position L is L=LFeNsy1: Thus the expansion of \u00f0hm=hm \u00fe g\u00f0y; a\u00de\u00de2 is as follows: hm hm \u00fe g\u00f0y; a\u00de 2 \u00bc G0 \u00fe XN n\u00bc1 Gn cos nz y\u00fe a\u00fe L LFe Nsy1 : \u00f012\u00de Substituting Eqs" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003212_j.ijmecsci.2007.07.002-Figure6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003212_j.ijmecsci.2007.07.002-Figure6-1.png", + "caption": "Fig. 6. Experimental results for wear depth along the path of contact at different running cycles (Tsukamoto [18]). (a) Driving gear. (b) Driven gear.", + "texts": [ + " Generally, the tooth separation in high speed metal gear pair may cause serious nonlinear problems, as mentioned in Kahraman [35]. However, due to the flexibility of POM and Nylon, no tooth separation was observed during the engagement process. Simulation results shown in Figs. 4 and 5 also indicate that no tooth separation exists in the engagement cycle for the POM\u2013 POM and Nylon\u2013Nylon tooth pairs. To eliminate the unnecessary and misleading, the \u2018\u2018no backlash\u2019\u2019 assumption is acknowledged in the study. Fig. 6 presents the variation of cumulative wears on gears 1 and 2 along the contact path. For gear 1, numerical results demonstrate that one peak point of the cumulative wear moves gradually from IP toward LPSTC as the number of running cycles increases. The second wear peak is located initially near HPSTC and then shifts gradually toward FP. A similar wear pattern exsits for gear 2. These numerical results are consistent with experimental findings obtained by Tsukamoto for a POM/POM gear pair [14]. The variation of tooth profiles introduced via the cumulative sliding wear effect can affect the variation of the contact loads along the contact path" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000563_j.triboint.2021.107106-Figure9-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000563_j.triboint.2021.107106-Figure9-1.png", + "caption": "Fig. 9. Cutting planes used to evaluate results from the CFD models for the DGBB (left) and RNRB (right).", + "texts": [ + " Others have reported lower values for the percentage of fluid drag loss caused by the inner race in CRBs (~32%) [11] and tapered roller bearings (~37%) [13] It is worth noting, however, that the fluid shear at the inner race caused by the relative difference between inner race rotation (faster) and roller/cage rotation (slower) integrated over the length of high aspect ratio needle rollers will certainly result in higher inner race viscous torque when compared to a similar cylindrical roller. To further investigate the sources of fluid drag losses in the CFD simulations, bearing cage wall shear stress and fluid velocity were plotted for the highest and lowest Reynolds number operating conditions. Fig. 9 illustrates the planes used to plot the velocity vectors and streamlines for each bearing. As suggested by fluid drag loss distribution in Fig. 8, the DGBB cage wall shear stress increases with Reynolds number. Fig. 10 indicates minimal shear stress on the DGBB cage at low Reynolds number and a unique shear stress pattern on the cage wall at high Reynolds number. Shear stress contours for the highest Reynolds number tested in Fig. 10 highlight a kidney-shaped region of high stress at the edge of the stamped-style DGBB cage pocket near the pressure outlet" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002942_physreve.67.051702-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002942_physreve.67.051702-Figure1-1.png", + "caption": "FIG. 1. Experimental setup and a typical fiber seen in microscope with the illustration of the main parameters of the fibers. The curvature radius of the neck of the fiber is r, the diameter is D, and the length of the fiber is L. The speed of the pulling was in the range of 0,v,0.1 mm/s.", + "texts": [ + " The fiber-drawing device used in our experiments consists of two needles with micro-positional accessories built on a \u00a92003 The American Physical Society02-1 hot stage ~HS1 from Instec. Inc.! that allows temperature regulation with 0.1 \u00b0C precision. A drop of a liquidcrystalline material is placed on top of the needles when they touch each other. The distance between the pins can be varied by micrometer screws in two directions with speed up to 0.1 mm/s. Optical observations of the suspended liquidcrystal bridges and fibers are carried out by a polarizing mi- 05170 croscope ~BX60 from Olympus! equipped with a color charge-coupled device camera. ~Fig. 1!. The molecular structures and the phase sequences of the materials studied by us are shown in Fig. 2. For small strains, the materials behave similar to Newtonian fluids, i.e., as the distance between the needles increases, they develop concave shapes with the decreasing curvature radius. Typically at D;15\u201320 mm, a homogeneous elongation deformation occurs and the diameter of the filament remains constant, provided that the fluid reservoirs at the end plates have enough materials. On further increasing the length, the diameter is decreasing in about 1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002878_s0043-1648(97)00076-8-Figure6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002878_s0043-1648(97)00076-8-Figure6-1.png", + "caption": "Fig. 6. Test rig and measurement chain.", + "texts": [ + " The level of the transversal vibrations of the main spindle having a major influence on the quality surface in the grinding process was co~sidered in research [ 1,3]. Consequently, were determined both theoretical and experimental amplitudes of the transversal vibrations of the test main spindle offset grinding wheel in controlled conditions of speed for various values of bearings preload Fp, and test force Fs that simulates main grinding force (see Fig. 5). The theoretical amplitudes were determined by the transfer matrix methyl [20]. The experimental validation of the theoretical results obtained was achieved on a test rig schematically presented in Fig. 6. The test main spindle was mounted on a concrete bed insulated from surrounding environment by rubber dampers to remove possible external disturbances and is driven through belt transmissions by an electric motor. The amplitudes of the transversal vibrations of the test main spindle offset grinding wheel were measured by a Bmel & Kjaer measurement chain: accelerometer type 2431, condit':oning amplifier type 2626, frequency analyser type 2113, level recorder type 2305. A comparison between theoretical and experimental results obtained is preserlted in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003471_j.fss.2009.09.012-Figure7-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003471_j.fss.2009.09.012-Figure7-1.png", + "caption": "Fig. 7. Schematic of electromechanical system.", + "texts": [ + "9, \u22120.2] 2(0) = [ 21(0), 22(0), 23(0), 24(0), 25(0)] = [0.5, 0.2, \u22120.2, 0.3, 0.4] The simulation results are shown in Figs. 1\u20136. Figs. 1 and 2 show the trajectories of x1 and x2, respectively. The trajectories of parameter p\u03021, p\u03022 and control input u are shown in Figs. 3 and 4. The trajectories of parameter vectors 1 and 2 are depicted in Figs. 5 and 6. Example 2. To further show the effectiveness of the proposed adaptive fuzzy controller, we consider the electromechanical system which is shown in Fig. 7. The dynamics of the electromechanical system is described by the following equation [7]:{ Mq\u0308 + Bq\u0307 + N sin(q) = I L I\u0307 = V \u2212 RI \u2212 K Bq\u0307 (102) where M = J K + mL2 0 3K + M0 L2 0 K + 2M0 R2 0 5K , N = mL0G 2K + M0L0G K , B = B0 K J is the rotor inertia, m is the link mass, M0 is the load mass, L0 is the link length, R0 is the radius of the load, G is the gravity coefficient, B0 is the coefficient of viscous friction at the joint, q(t) is the angular motor position (and hence the position of the load), I (t) is the motor armature current, and K is the coefficient which characterizes the electromechanical conversion of armature current to torque" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003542_28.2871-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003542_28.2871-Figure1-1.png", + "caption": "Fig. 1 Portion of induction-machine magnetic equivalent circuit with radial slot leakage permeances neglected.", + "texts": [ + "NTRODUCTION OR explanation of the simplifications that are the topic of F this paper, it is useful to repeat in short steps some facts from the magnetic equivalent-circuit description of electric machines. This procedure is derived in detail in [I] . The initial point is the representation of the induction machine in the manner shown in Fig. l . For each machine the three types of permeances can be defined for the circuit of Fig. 1. Permeances independent of the angle between the stator and rotor and of the fluxes through them-these elements represent stator and rotor leakage paths and are denoted by letter CJ. Permeances dependent on the angle between the stator and rotor but independent of fluxes through them-these are the air-gap permeances. Permeances independent of the angle between the stator and rotor but dependent on fluxes through them-these elements represent the iron core. They are shaded to emphasize their nonlinear character", + " The author is with the Department of Electrical Engineering, The University of Akron, Akron, OH 44325. IEEE Log Number 8717328. and Ghru in Fig. 4 in [2] can be set equal to zero. Furthermore, this assumption leads to canceling the matrices Alz, ,421 , Aw, and A43 defined in [2]. This means that the system of machine node potential equations defined by equation (3.1 .) in [2] can be split into three subsystems. The solution procedure of these subsystems takes less time and memory than for the original one. One must keep in mind that flux tubes defined by means of Fig. 1 allow only radial direction of fluxes in teeth and only tangential direction of fluxes in yokes. This means that for the case when flux in the machine is not distributed as assumed in the preceding (e.g., when flux densities are high above magnetizing curve knee), different shapes of flux tubes should be defined to keep accuracy. The node potential equations that were defined by equation (3.1 .) in [2] now can be written as AIlPl= -42,s (1) 0093-9994/88/0300-0308$01 .OO 0 1988 IEEE OSTOVIC: MAGNETIC EQUIVALENT-CIRCUIT MODELING 309 bs and, finally, the torque is n o a0 ;", + " One can see the increase of the rotor flux magnitude at speeds for which there is a smaller screening effect of the rotor cage. At the same time the rotor flux becomes almost dc, which is expressed by its nearly fixed position on the rotor periphery. Starting in the Opposite Direction To illustrate the effects of a change of direction of the stator air-gap field, a computation (which resulted in the next few OSTOVIC. MAGNETIC EQUIVALENT-CIRCUIT MODELING 31 I graphs) was carried out. One can see that all traveling waves in the machine have changed their direction, without any other change (compare Fig. 10 to Fig. 5 ; Fig. 1 1 to Fig. 7; Fig. 12 to Fig. 8; and Fig. 13 to Fig. 9). Reversing from - ns).,,chr to ns).,,chr The purpose of the figures in this paragraph is to illustrate the behavior of the machine in its complete operation range. Fig. 14 represents the speed-versus-time curve whereas Fig. 15 gives the rotor tooth flux change for the same transient. Although Fig. 15 hardly needs any further explanation, a few words about it are appropriate. At the very beginning of the transient, while the speed is near to -n,ynchr, the field starts to penetrate into the rotor teeth" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure25.10-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure25.10-1.png", + "caption": "Fig. 25.10 Structure of Segment-structured Cr/DLC film", + "texts": [ + " It seemed that the mask during DLC deposition influenced the shape of the segments. Therefore, the deposition technique without the mask was required for the new method. On the other hand, the distribution of the projections was required for the friction drive of the motor and easy process can have advantage. It is known that adhesion strength between chromium and DLC film as well as that between LiNbO3 substrate and chromium. According to the strength, we proposed segment-structured chromium films under DLC (S-Cr/DLC) film as shown in Fig.25.10. The stator transducer with the film is denoted as \u201cS-Cr/DLC film stator.\u201d In this configuration, enough adhesion strength can be acquired. The deposition mask is not required during the DLC deposition. Additionally, the deposition of segment-structured Cr is easy process, as mentioned below. Figure 25.11 shows fabrication process of S-Cr/DLC film stator. At first, chromium film and aluminium film were deposited on the LiNbO3 substrate by vacuum evaporation process, and a resist layer was coated on the aluminium film (Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000046_j.addma.2020.101357-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000046_j.addma.2020.101357-Figure3-1.png", + "caption": "Fig. 3 Boundary conditions", + "texts": [ + " The molten pool surface shape is determined by calculating the optimum Lagrange multiplier so that the volume increment per unit calculation step is equal to the volume of the droplet supplied from the wire. After the calculation is finished, the welding torch is moved with consideration of the amount of movement per calculation step. This series of calculations is repeated until the welding torch moves from the deposition start position to the end position. The shape of the deposited metal can be simulated by the above processes. In this study, a bead-on-plate test was simulated. Fig. 3 shows the simulation model. The substrate size was 150 x 150 x 5 mm, and the bead length was 100 mm. The calculations of the temperature field and the surface shape, expressed as differential equations (2) and (3), are conducted by the finite difference method (FDM). Rectangular parallelepiped, that is, hexahedron, elements are applied to solve Equation (2). Moreover, rectangular elements are applied to solve Equation (3). The element size differed with the location. The minimum element size was 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002527_pu2003v046n04abeh001306-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002527_pu2003v046n04abeh001306-Figure3-1.png", + "caption": "Figure 3. Rigid body on a plane.", + "texts": [ + " For an elementary description of the motion, however, this model has frequently been used [3 \u00b1 6, 8 \u00b1 10, 12]. As a model for the rattleback we consider here a heavy rigid body that rolls without slipping on a horizontal plane. The absence of sliding can be treated as a nonholonomic constraint placed on our system. This constraint simply means that the velocity of the point of contact is zero, that is, v x r 0 ; 1 where r is the position vector of the point of contact, Q, with respect to the center ofmass,G; and v andxare the velocity of the center of mass and the angular velocity of the body (Fig. 3). In what follows, all vectors are assumed to refer to a body-fixed coordinate frame. Using the balance of linear momentum and the balance of angular momentum relative to the point G (see Fig. 3), we get (with respect to the body-fixed frame) the following equations d dt mv mv x\u00ffmgc N ; 2 d dt Ix Ix x r N : Here,N is the normal force acting on the body at the point of contact Q, c is a unit vector pointing vertically upwards, m is themass of the body, g is the acceleration due to gravity, and I is the inertia tensor referenced to the center of mass. Using the constraint equation (1) and the first equation of (2), we eliminate v and N from (2) and, thus, obtain _Ix mr _x r mr x _r Ix x m x; r x r mgr c : The angular momentum of the body relative to the point of contact Q is M Ix mr x r : 3 Then, using the equations governing the behavior of the unit vector c in the body-fixed frame, we represent the equations of motion in the form [8] _M M x m_r x r mgr c ; _c c x : 4 Herex should be expressed as a function ofMwith the use of (3)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000495_j.wear.2021.203963-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000495_j.wear.2021.203963-Figure4-1.png", + "caption": "Fig. 4. Contact between the rolling element and raceway surfaces.", + "texts": [ + " [23], the contact area between two rough surfaces can be obtained as Aij(b\u2212 n\u2019) = \u222b aL 0 n(a)ada = D 2 \u2212 D aL (7) where n(a) refers to the number of the asperities with the truncated area over than a, which satisfies the power-law distribution [18] and can be obtained as n(a) = DaD/2 L /2aD/2+1; the fractal parameter D denotes the complexity (fractal dimension) of the rough surface; aL is the maximum contact area of the asperity which is related to another fractal parameter G, with G denoting the characteristic length scale of rough surface. It is worth mentioning that, Eq. (7) is only applicable for characterizing the interaction between the surfaces of two flat contacts, while for LRGs, the contact mode between the rolling elements and raceway changes into the interaction between two curved contacts as shown in Fig. 4. In the feed direction, the raceway surface is flat and the rolling element surface is curved as shown in Fig. 4(a), while in the vertical feed direction, both the two surfaces are curved as shown in Fig. 4(b). This contact mode leads to a decrease of n(a). Therefore, a contact coefficient specifically for the two curved rough surfaces in the LRG is introduced as \u03bb= ( Sh S )Xh (8) where Sh denotes the theoretical Hertz contact area; S denotes the projected area of the rolling elements on the raceway surface with S = \u03c02Rr\u22c5arcsin(r /R)/180; Xh denotes the sum of the principal curvatures of the two curved, rough surfaces with Xh = 1/r \u2212 1/R. Accordingly, the contact coefficient \u03bb can be rewritten as \u03bb= [ Sh \u03c02Rrarcsin(r/R)/180 ] ( 1 r\u2212 1 R ) (9) According to the Weierstrass-Mandelbrot (W-M) function [20], the two-dimensional profile curve of the raceway surface can be characterized as z(x)=G(D\u2212 1) \u2211\u221e n=n1 cos 2 \u03c0\u03b3nx \u03b3(2\u2212 D)n ; 1 < D < 2;\u03b3 > 1 (10) where \u03b3n represents the spectrum of rough surface, n1 denotes minimum sample rate, \u03b3n1 \u2248 1/L with L representing the sampling length", + " S(\u03c4)=C\u2019G2(D\u2212 1)\u03c4(4\u2212 2D) = 1 N \u2212 n0 \u2211N\u2212 n0 i=0 ( zi+n0 \u2212 zi )2 (14) where C\u2019 = \u0393(2D \u2212 3)sin[(D \u2212 1.5)\u03c0]/(4 \u2212 2D)ln\u03b3, and \u0393()is the gamma function. In the real number domain, \u0393(x) = \u222b+\u221e 0 tx\u2212 1e\u2212 tdt. Take logarithm on both sides of Eq. (14), the following relationship can be obtained as lgS(\u03c4)= (4 \u2212 2D)lg\u03c4 + lgC\u2019 + 2(D \u2212 1)lgG (15) According to Eq. (15), we can obtain the fractal parameter D and G as D= 4 \u2212 k 2 (16) lgG= b \u2212 lgC\u2019 2(D \u2212 1) (17) where k and b are 4-2D and lgC\u2019 + 2(D \u2212 1)lgG, respectively. C.-G. Zhou et al. Wear 482\u2013483 (2021) 203963 As shown in Fig. 4, for a certain rolling element, the sum of the load Q\u2019 ij(b\u2212 n\u2019) acting the asperities is balanced by the contact load Qij(b\u2212 n\u2019) acting on the rolling element. Therefore, the following relationship can be obtained as Qij(b\u2212 n\u2019) =Q\u2019 ij(b\u2212 n\u2019) = \u03bb \u222b aL 0 Pp\u2019 n(a)da (18) where aL denotes the maximum contact area of all the asperities; Pp\u2019 denotes the load of each asperity in different contact states, e.g., the complete plastic deformation (p\u2019 is p), the elastic-plastic deformation (p\u2019 is ep), and the elastic deformation (p\u2019 is e); Qij(b\u2212 n\u2019) can be obtained by Eq" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002663_mssp.2000.1345-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002663_mssp.2000.1345-Figure4-1.png", + "caption": "Figure 4. Principle of suspension method.", + "texts": [ + " Time requirements are low to medium since only the mass and two coordinates of the centre of gravity can be identi\"ed simultaneously. No references were found in the literature rating the accuracy of the identi\"cation results. The suspension method yields the centre of gravity location of the test specimen as geometric information [5, 12]. Here the test specimen is successively suspended at several points, e.g. by a wire. The intersection point of all wire lines depicts the centre of gravity location (Fig. 4). In order to identify the centre of gravity location at least two suspension points are necessary. The suspension method is safe if the suspension is secure and it is also approved in industry. The necessity for suspending the mechanical system can limit the applicability and an adapter may be required. Skill requirements of the testing personal are basic. The only hardware demand is a suspension wire while no software is needed. Time requirements for testing and data processing are medium to high (if an adapter is required) while the accuracy of the results is low" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002484_1.2834121-Figure5-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002484_1.2834121-Figure5-1.png", + "caption": "Fig. 5 Numbering of rolling elements, total net force, phase angle and off-set angle", + "texts": [ + " (24)) is obtained using the Runge-Kutta iterative method since they are nonlinear and the direct substitution technique does not hold for them. The details of the computational solution of the equations can be found in the previous papers (AktUrk etal., 1992; 1994; 1997; 1998). 3 Results and Discussion In order to study the effect of waviness in a more detailed form, the angular contact ball bearing employed in this paper was reduced to a radial ball bearing for the time being and modeled as in Fig. 5. The angles and reference axes were set as in Fig. 4. The off-set angle in Fig. 5 is an arbitrary reference point on the cage. The contact stiffness coefficient between the balls and the raceways were considered to be linear and constant. Balls were radially preloaded in order to ensure the continues contact of all balls and the raceways, since otherwise a chaotic behavior might be observed (Gad et al , 1984b). The preloaded deflection for each ball. So, was assumed to be 5 fim. The center of the inner race is shifted 2 fim in the x direction and 2 /MI in the y direction with respect to the outer race center. For different off-set angles the total net force and the angle between the net force and the x axis (phase angle) as seen in Fig. 5 were recorded. This procedure of observing the total net force and the phase angle (Aktiirk and Gohar, 1998) was applied to a bearing with a wavy outer race surface in order to study the resulting force variation due to waviness. Since the inner ring rotation is diffi cult to model in this manner, the inner ring waviness was not studied with this model. The waviness amplitude was set to 2 //m and the number of waves round the outer race circumference was varied for a bearing with 8 balls. The total net force and phase angle changes were recorded, as shown in Fig", + " However, the total net force and phase angle still change m times (m is the number of balls). When the number of balls and the number of waves are equal, the change in the phase angle is negligible. This was also experimentally observed by Wardle and Poon (1983) and Wardle (1988). Since the balls and the waves are in phase, the vibrations produced will be important. If the change in the phase angle is investigated in detail, minute changes may be observed as shown in Fig. 7. The jump from 0 to 90 degrees disappears and as the system suggest (see Fig. 5) the phase angle is almost steady at 45 degrees. For 9 waves in Fig. 6 the system behaves almost like the system with 7 waves but this time shift occurs from 0 to 90 degrees and then it decreases almost linearly to 0 degrees again. Continuing increasing the number of waves first to 10 and then to 11 causes almost the same sort of effect in a opposite sense to the increasing of the number of waves from 4 to 6. When the number of waves are 11, 12, or 13 the change in the total net force and phase angle are small" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000229_j.mechmachtheory.2021.104529-Figure6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000229_j.mechmachtheory.2021.104529-Figure6-1.png", + "caption": "Fig. 6. Schematic representation of the dynamic model of the gear and pinion set.", + "texts": [ + " To understand the effect of profile-shift on the operation performance of the gear system, it is necessary to study the TVMS and dynamic response of individual profile shift and compound profile shift separately. The research framework can be illustrated in Fig. 5. Based on the TVMS of the profile-shifted spur gear, the vibration responses and the statistical features can be extracted by the lumped mass model. In this paper, a six degrees of freedom dynamic model of the gear and pinion system is generated, as shown in Fig. 6. For spur gears, since the meshing stiffness affects the gear pair plane and not the axial vibration, only the motions along the action line, perpendicular to the action line, and rotation are considered. In this model, the x-axis is aligned with the action line of the gear and pinion set. To simplify the analysis, we consider a perfect profile without wear for the gears. The end of the shaft is connected with the bearings, assumed by the parallel spring-damping unit. The governing equations of the dynamic system can be written as, mpx\u0308p + cbx\u0307p + kbxp = \u2212 Fm (15a) mpy\u0308p + cby\u0307p + kbyp = \u2212 Ff (15b) Ip\u03b2\u0308p = \u2212 FmRb,p \u2212 Tp (15c) mgx\u0308g + cbx\u0307g + kbxg = Fm (15d) mgy\u0308g + cby\u0307g + kbyg = Ff (15e) Ig\u03b2\u0308g = \u2212 FmRb,g \u2212 Tg (15f) where mp,g and Ip,g are the mass and moment of inertia of the pinion and gear, respectively, cb and kb are the bearing damping and stiffness, accordingly, Tp and Tg are the driving torque and load torque, and Fm and Ff are the meshing force and friction force, respectively, which can be expressed by Fm = k(t) [ xp \u2212 xg +Rb,p\u03b2p +Rb,g\u03b2g \u2212 e(t) ] + cm [ x\u0307p \u2212 x\u0307g +Rb,p\u03b2\u0307p +Rb,g\u03b2\u0307g \u2212 e\u0307(t) ] (16a) J" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002715_j.actamat.2004.09.039-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002715_j.actamat.2004.09.039-Figure1-1.png", + "caption": "Fig. 1. (a) Sample configuration and axis labels. (b) 3D AFM observation of a nickel 320 nm thick film on a polycarbonate substrate. A slight depression is visible near the edges of the wrinkle.", + "texts": [ + " The results are then compared with in situ atomic force microscopy (AFM) observations of nickel thin films deposited on polycarbonate substrates. The samples were made of nickel thin films (Young s modulus Ef = 200 GPa and Poisson s ratio mf = 0.312) of various thicknesses (50, 110 and 320 nm) deposited on a polycarbonate substrate (Es = 2.4 GPa, ms = 0.37) using an ion beam sputtering method. The experiments are carried out by using an AFM interfaced with a compression machine. The system allows in situ AFM observations of the film evolution during the compression of the substrate along the (Ox) axis (see Fig. 1(a) for axis configuration). During the compression, external stresses Dr1 xx are thus generated in the film. The notation 1 is introduced to distinguish the loading prescribed far from the blister from the local values of stress in the film rxx(x). The stress computed in the substrate is characterized by the superscript s. The increment of stress is hence added to the initial residual stress ri to give a total stress in the film r1 xx \u00bc Dr1 xx \u00fe ri. As ex- pected [12], the straight-sided structures arise perpendicularly to the compression axis above a critical stress (Fig. 1(b)). The general shape of the buckling patterns, as well as the height of the wrinkles, can be followed at each step of the compression, providing a post-critical dependence of the buckling mode as a function of the stress r1 xx . The delaminated regions of the film are assimilated to rectangular strips of infinite length and width 2b. The width 2b is derived from the delamination and strongly depends on the film thickness h. No crack extent is considered in the calculation which is carried out in the plane strain hypothesis" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002651_robot.1991.131641-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002651_robot.1991.131641-Figure2-1.png", + "caption": "Figure 2. Stewart Platform", + "texts": [ + " ] 26= (s6 x Z6)T In Section IV, the equations developed here will be used to compute symbolic formulations for the prototype parallel manipulator kinematics. 'h end-effector Fioure 1. Parallel Manioulator Geometrv A. Hardware To investigate the basic characteristics of the parallel manipulator, a prototype manipulator was constructed (see Figure 9 for a photograph). The configuration of this manipulator is somewhat different from the usual Stewart platform configuration. In the Stewart platform, the link connection points on the base and the mobile are located on a circle centered at the middle of the base and the mobile as shown in Figure 2. In Figure 2, rh is the end-effector radius, h h is the center post height, and rb is the base radius. In our prototype manipulator, the link connection points are located on two concentric circles as shown in Figure 3. In The manipulator consists of six legs, a fixed base, and a movable end-effector. Each link is actuated by a 3 watt DC motor through a bevel gear and a rack-pinion. The gear ratio is 1:128 and the pinion diameter is 19.2 mm. This results in a maximum unloaded link velocity of 61 mm/s. Each link is supported by a two DOF gimbal at the base and by a universal joint at the end-effector" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002839_978-3-662-03845-1-Figure7.33-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002839_978-3-662-03845-1-Figure7.33-1.png", + "caption": "Fig. 7.33. Different stages in extrusion blow moulding of a hollow object", + "texts": [ + " This produces a polymer sheath which is inflated with air and stretched at the same time. Inflation induces a transverse orientation, whilst vertical stretching induces a longitudinal orientation. A cooling ring causes the polyethylene to crystallise and fixes this biorientation. The results obtained in this way can be assessed by considering the strength of the plastic bags we fill with provisions at the supermarket cash desk. Bottle Blowing Plastic bottles are manufactured by extrusion followed by blowing (extrusion blow moulding), as shown in Fig. 7.33. A certain length of tube is extruded (the parison) and a mould applied. The latter obturates the bottom end of the parison. Air pressure is supplied inside the parison, forcing the melt onto the cold mould and hence giving it its final shape. In this process, the orien- tation conferred upon the polymer is low. This is because the polymer melt flows before it can orient itself (there is almost no network effect due to en tanglement). Bottles for flat water and cooking oil are made in this way from poly( vinyl chloride), and orange juice bottles from polyethylene" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003772_s0022112078001354-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003772_s0022112078001354-Figure1-1.png", + "caption": "FIGURE 1. Similarity between pipe and channel for Stokeslet fields.", + "texts": [ + " The model we use is an infinite number of cilia, whose bases are equally spaced on a flat plate, with all cilia on the same x2 line beating completely synchronously and identically, see 0 2. This yields a flow which is periodic in the x2 direction. An infinite 24 F L M 06 sequence of cilia lined identically on top and bottom plates at fixed x2 are to be compared with a finite number of equally spaced cilia attached to the circumference of a tube, all the way around it. The similarity of flow in a pipe and channel can be seen in figure 1 , where equal-strength Stokeslets are pointing into the paper a t the crosses. Each wedge in the pipe is periodically repeated, and on the wedge \u2018walls\u2019 we have the normal velocity equal to zero. This wedge (shaded area in pipe) is to be compared with a parallelepiped with the bottom wall at x3 = 0, and the top \u2018wall\u2019 at x3 = 4H (shaded area in channel). If Stokeslets are close to the wall and densely packed those two regions (wedge and parallelepiped) are very much alike. As Stokeslets get more and more dense, we approach an axisymmetric flow in the pipe, and a two-dimensional flow in the channel", + " We assume these Stokeslets are all of equal strength and pointing in the x1 direction. Clearly the total contribution from this sequence is a periodic velocity field in the x2 direction with period b. Moreover their sum is a solution for the flow due to a Stokeslet at (&, t2, &,) pointing in the x1 direction, inside a parallelepiped the walls of which are given by x, = 0, x3 = H , x2 = c2 + i b , x2 = t2 - i b , with no-slip conditions on x3 = 0, and x, = H , and zero normal velocity on x2 = t2 f i b . This parallelepiped repeats itself, see figure 1. Summing for the flux, we get zero flux in each of the above parallelepipeds. Indeed if we have to solve for a Stokeslet inside a tube of arbitrary cross-section, then we also impose the condition that, as x1 -+ f 03, u -+ 0. The flux is bounded by the maximum velocity multiplied by the cross-sectional area (which is finite) and since u --f 0, we must have zero flux, by incompressibility, in general. By this argument we must have zero flux in each parallelepiped, and the solution there is given by the sum of the infinite sequence of the identical Stokeslets", + " Liron Thus this sequence of Stokeslets raises the pressure from a constant value - A at rl = -00 to a value + A , at rl = + 00, and the total pressure rise is 2A. One should note again the parallelism between this result and the pressure due to a Stokeslet (or finite number of Stokeslets situated on a cross-section) in a pipe. If we have a Stokeslet in a pipe pointing in the z direction (see figure 3)) then this Stokeslet will raise the pressure from some constant - B a t x = -00, to + B a t z = +a, Liron & Shahar (unpublished work). Let us look at the pipe, or one parallelepiped of figure 1. To get the flux, one integrates the downstream velocity due to the contribution of all Stokeslets, over the pipe cross-section, plus the Poiseuille flow. Let us look at an infinite periodic sequence of Stokeslets of unit strength all pointing downstream, as shown in figure 3. Let u(x, xi) be the velocity at a point x due to the Stokeslet at xi in the x direction. The flux due to this line of Stokeslets is Q = Q 1 + Q2 , A being the cross-section of the pipe. Q1 is the flux due to the Stokeslet solutions, and Qz is the flux due to the Poiseuille flow" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure34.1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure34.1-1.png", + "caption": "Fig. 34.1 Slider for a standing wave-type, self-running, ultrasonically-levitated sliding table: (a) configuration of the slider, and (b) flexural vibration mode at 35 kHz predicted by FEA", + "texts": [ + " First, the standing-wave-type ultrasonically levitated slider for a self-running sliding stage was investigated, and the noncontact straight backand-forth motion of the slider was aimed. The motivation of this linear slider was the use for a compact-size noncontact 2D stage without guide rails which the conventional ultrasonically levitated table requires. The generation of acoustic streaming is necessary for most noncontact ultrasonic motors. The goal was to realize a standing wave-type ultrasonic noncontact slider for a linear stage with a simple and thin structure. The configuration of the slider is shown in Fig.34.1. The standing wave-type levitated slider consists of an aluminum plate (30.0\u00d710.0\u00d71.0 mm3) and a PZT plate (10.0\u00d710.0\u00d71.0 mm3). The polarization of the PZT plate is in the thickness direction, and the two components were bonded using epoxy and the mass of the slider was 1.62 g (52.9 N/m2). By applying the input voltage to the PZT, flexural vibrations can be generated along the aluminum plate at frequencies ranging from 20 to 100 kHz (Fig.34.1(b)). The slider on the flat substrate can be levitated in the vertical direction (z-direction) by the acoustic radiation force radiated from the plate of the slider when the slider gravity and the radiation force are balanced. When the vibration distribution along the plate is asymmetric in the length direction (x-direction), the acoustic field in the air gap between the flat substrate and the levitated slider will also be asymmetric, and acoustic streaming will be induced along the air gap in the length direction", + " Self-Running Non-Contact Ultrasonically Levitated Stage 407 We propose the ultrasonically levitated 2D stage, in which the four self-running linear sliders are integrated to a base plate, and the vibrations of these four sliders will control the thrust of the 2D stage in the four directions, i.e., positive x-, y-, and negative x-, y-directions. To isolate the performances of each embedded slider, the four sliders with different lengths were designed to have different resonance frequencies. The lengths of these sliders were determined via the FEA. The FEA was performed with a single slider shown in Fig.34.1 (a) having the different length. No fixing condition was applied in the slider model while four sliders will be connected via a 1-mm-thickness rectangular base plate. Figure 34.7 shows the relationship between the slider length and the resonance frequency of the vibration mode A calculated by the FEA. With the slider length of 25 to 30 mm, the lower resonance frequencies of the mode A can be obtained with the larger slider length. From the experimental result shown in Fig.34.4, the resonance frequency of the vibration mode B was approximately 1 kHz higher than that of the mode A" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002644_1.1398289-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002644_1.1398289-Figure2-1.png", + "caption": "Fig. 2 Race waviness model", + "texts": [ + " This research also characterizes the vibration frequencies resulting from the various kinds of waviness existing in rolling elements, the harmonic frequencies resulting from the nonlinear load-deflection characteristics of the ball bearing and the sideband frequencies resulting from the waviness interaction of the ball bearing. The geometrical imperfections of the ball bearing are classified as periodic waviness and localized defect on the surface of rolling elements. The geometrical imperfections of a ball bearing can be modeled as a sinusoidal function to express the waviness of peri- s of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F odic lobes, and the localized defects can also appropriately be expressed by the combination of the several sinusoidal functions. Figure 2 shows the waviness of the inner and outer races along the locus of the groove radius center. The inner race waviness in contact with the j th ball can be defined along the locus of the inner groove radius center as follows: Ai cos@2l~v i2vc!t12p~ j21 !/Z1a i# , (1) where l, Ai , vc , v i , Z, and a i are the waviness order and amplitude, the rotating frequencies of the cage and the inner race, the number of the ball and the initial phase angle of waviness, respectively. In Eq. ~1!, v i2vc is the relative rotating frequency of the inner race with respect to the cage, and the negative sign represents the counter clockwise rotation of the ball bearing" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003715_tps.2010.2076355-Figure9-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003715_tps.2010.2076355-Figure9-1.png", + "caption": "Fig. 9. No-load magnetic-flux distributions of the VMRPMSM. (a) s = 11 mm. (b) s = 0 mm.", + "texts": [ + " Only the excitation of the PM is present when the VMRPMSM is operated in a no-load mode. The no-load magneticdensity distributions are absent when the distance s is a maximum and a minimum value. The magnetic flux visually describes the space distribution of the magnetic field. The variable-density degree represents the strength or weakness of the magnetic field. The denser the magnetic flux is, the stronger is the magnetic field. We can see that the density of the magnetic-flux distribution with s = 0 mm is weaker than the distribution with s = 11 mm (see Fig. 9). The results indicate that the value of s is smaller, the magnetic flux is weaker, and the magnetic field is weaker. The comparison of the no-load air-gap magnetic-density waveforms is shown in Fig. 10. The waveform of the no-load air-gap magnetic density is proximately a sinusoidal wave. The magnitudes of the fundamental wave with s = 11 mm and s = 0 mm are from 0.737 to 0.414 T, which reduces by 43.8%. The experimental data are from 0.72 to 0.4 T, which reduces by 44.4%. This indicates that the VMRPMSM can realize the function of FW" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003562_09544062jmes700-Figure7-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003562_09544062jmes700-Figure7-1.png", + "caption": "Fig. 7 (a) Load carrier, (b) platform, and (c) entire set-up used for dynamic test", + "texts": [ + " This decrease in sensitivity affected the sensor\u2019s accuracy over time. It is believed that the decrease in sensitivity contributed to the high accuracy and curved surface errors that were measured for this sensor. A novel set of tests were designed to examine the response of the sensors under a dynamic load. The authors have not found similar tests in literature. Sensors were placed under one of the three legs of a load carrier (described in section 2.2.5) which rested on top of a platform, as shown in Fig. 7. The platform was fixed to an electromagnetic shaker for vertical excitation, with stability provided by restricting the motion of two of the legs (Fig. 7(b)). With this set-up, onethird of the total static and dynamic load applied to the carrier was directed through the test sensor via the 6-mm diameter cylindrical leg. Sinusoidal loads were applied to the sensor at frequencies of 15, 60, and 100 Hz, such that the 6.3 kg load achieved nominal maximum peak accelerations of 2.4, 4.8, and 7.1 m/s2 measured by an accelerometer (accuracy error of 1\u20132 per cent over the frequency range used) placed on the load carrier just above the pressure sensor. The load applied through the sensor follows readily from the product of the mass and the accelerometer measurement" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002546_41.824133-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002546_41.824133-Figure3-1.png", + "caption": "Fig. 3. Approximate phase diagram of surface PM synchronous motor.", + "texts": [ + " The loss minimization condition is derived in Section IV and its implementation with SC and LMC in controlled scheme is described in Section V. The experimental results are presented in Section VI. Finally, in Section VII, the implementation of the LMC in a current-controlled scheme is briefly presented. In Fig. 2, the per-phase equivalent circuit of the PM synchronous motor is given in the p.u. system. In this circuit, the effects of iron and stray losses are ignored. The phasor diagram in synchronously rotating - reference frame is illustrated in Fig. 3. Since the resistance of the stator winding is very small [9], the respective voltage drop could be neglected. The stator current is resolved into the respective and -axis components. The excitation current is aligned with the axis. The and -axis components of stator voltage are given, respectively, by (1) (2) and (3) Furthermore, the - and -axis components of magnetizing current are given, respectively, by (4) and (5) Finally, the electromagnetic torque of the motor is given by (6) The main losses on the PM synchronous motor are the following" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003885_la801907x-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003885_la801907x-Figure2-1.png", + "caption": "Figure 2. Snapshots of cilium bending due to an oscillatory force applied to the cilium\u2019s free end. The cilium is attached to the substrate with an angle of R ) 45\u00b0, the dimensionless force amplitude is A ) 10, and the sperm number is Sp ) 3. Snapshots a and c show two limiting positions of the cilium oscillation: stretched in the vertical direction and touching the substrate, respectively. Snapshots b and d show intermediate positions when the cilium moves in the downward and upward directions, respectively. The color shows the strain in the solid, and the arrows represent the direction and magnitude of the fluid velocity.", + "texts": [ + " Herein, we alter f and a to vary the oscillatory regimes of the beating cilia. Given that the cilium\u2019s moment of inertia is I) b4/12, the dimensionless force amplitude A ) 1/3aL2/EI represents the ratio between the amplitude of the driving force and the bending rigidity of a cilium. We consider relatively large amplitudes Ag 1; consequently, for sufficiently slow oscillations where the viscous dumping is weak, the cilium touches the bottom wall when the force is directed downward and is stretched in the vertical direction when the force is directed upward (Figure 2). At these limiting positions, further increases in the force cause only slight changes in the cilium geometry. We find that the cilium geometry is strongly affected by the viscous forces from the surrounding fluid. These forces are proportional to the cilium velocity and thus depend on the oscillation frequency. The dimensionless sperm number Sp ) L(\u03c2\u22a5\u03c9/EI)0.25 characterizes the relative importance of the viscous force and the bending rigidity of the cilium EI; here, \u03c2\u22a5)4\u03c0\u00b5, is the viscous drag coefficient and \u03c9 ) 2\u03c0f is the angular velocity of the cilium\u2019s undulations", + " Our aim is to identify the oscillatory regimes where the cilia can effectively pump the surrounding fluid. In a low-Reynoldsnumber environment, time-irreversible motion is required to induce a net fluid flow. Obviously, extremes in the sperm number are not favorable for inducing the pumping of fluid, with small Sp leading to periodic oscillations and large Sp completely suppressing the cilia\u2019s motion. For intermediate Sp, however, the effects of the fluid viscosity and cilium bending rigidity are of comparable importance, and time-irreversible motion can emerge (Figure 2) that causes a net fluid flow in the channel. Our simulations indeed indicate that there is a net fluid flow in a range of Sp between 1.5 and 6 (Figure 3a).35 Here, we use a scale (28) Ladd, A. J. C.; Kinney, J. H.; Breunig, T. M. Phys. ReV. E 1997, 55, 3271\u20133275. (29) Buxton, G. A.; Care, C. M.; Cleaver, D. J. Model. Simul. Mater. Sci. 2001, 9, 485\u2013497. (30) We assign a value of k/2 to those springs that are located on the cilia surfaces and k/4 to the springs at the edges. We also set the LSM masses equal to m/2 and m/4 for nodes at the surfaces and edges, respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003162_50008-0-Figure7.4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003162_50008-0-Figure7.4-1.png", + "caption": "FIGURE 7.4", + "texts": [ + " Frictional forces are the inevitable result of sliding and cause a shear stress to act along the interface, as shown in Figure 7.3. The frictional stress acting at the interface is balanced by rotating the planes of principal stresses through an angle '~)' from their original positions when frictional forces are absent. The magni tude of the angle '~)' depends on the frictional stress ~tq acting at the interface according to the relation: t) = 1 / 2 c o s - l ( k t q / k ) The variation with depth below the interface of the principal shear stress '~max' for a cylinder and the plane on which it slides is shown in Figure 7.4. The contours show the principal shear stress due to the combined normal pressure and tangential stress for a coefficient of friction/~ = 0.2 [9]. It can clearly be seen that as friction force increases, the maximum shear stress moves towards the interface. Thus there is a gradual increase in shear stress acting at the interface as the friction force increases. This phenomenon is very important in crack formation and the subsequent surface failure and will be discussed later. Elastic bodies in contact deform and the contact geometry, load and material properties determine the contact area and stresses" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure3.13-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure3.13-1.png", + "caption": "Fig. 3.13. Two examples.of a moving surface", + "texts": [ + "21) This additional force is introduced in (3.4.17) and the new model ob tained: [ I 1 WI-OF (n -llVA ) I 0 0 -:-1------~------ [ -~-l [-~-l' [~~-l (3.4.22) We have dealt here with surface-type constraint but any constraint can be considered in a similar way. However, there appear problems when a nonstationary constraint is considered (e.g. a moving surface). One idea is to express such a constraint in the form: h(x, y, z, t) = O. But, this representation does not cover some important cases of surface motion (Fig. 3.13). If there is no friction, such a motion of the surface (Fig. 3.13) causes + no problems. But, if the friction is considered, then vA in (3.4.20), (3.4.21) becomes the relative velocity and the motion of surface be comes of main importance and produces many problems. In order to avoid all the problems mentioned we propose another meth odology based on independent parameters. 170 3.4.3. Independent parameters representation - general methodology In Para. 2.4 the generalized position vector Xg was introduced. It con sisted of n independent parameters determining manipulator position" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure2.30-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure2.30-1.png", + "caption": "Fig. 2.30. A gripper carrying a screw", + "texts": [ + " But, in this approach we face the problem of calculating the internal coordinates q for known external coordinates X, i.e. q = n- 1 (X). In Para. 2.2. it was said that such procedure was very extensive and undesirable. Hence we use another approach. We prescribe q in the initial time instant (i.e. z ~ q(t )) and also h, s. Now the values of 8, ~, ~ are obtained by simple o * ~ calculation. This approach using h, s also offers a possibility of better visual relation with the task. Let us explain it by an example. If a manipulator has to move an object in an assembly task (Fig. 2.30) then the longitudinal axis (b) of the object and the perpendicular one (c) are essential. In order to define which directions on the gripper z ~ are important we use h = {O, 1, O}, s = {-1, 0, O}. In this way we de- fine directly the relative orientations of directions (b), (c) with respect to the gripper. From the standpoint of visual relation with the task we consider this approach to be more convenient than the de finition of relative orientations in terms of absolute position of the manipulator and the absolute orientations of (b), (c) with respect to external system" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003003_tmag.2004.843349-Figure8-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003003_tmag.2004.843349-Figure8-1.png", + "caption": "Fig. 8. Meshed 3-D model of SRM in FEA scenario with the boundary conditions specified.", + "texts": [], + "surrounding_texts": [ + "1) Simulation Procedure and Results: The transient thermal analysis, in which the temperature varies with respect to time, is simulated for different duty cycles. The setting up of boundary conditions has certain steps to be followed using \u201cload step\u201d (LS) files. The value of is set on the meshed model of excited stator poles according to the load pattern. For instance, consider the intermittent load as shown in Fig. 11. The load step (LS) files are sequentially created to take care of the changes in and the respective time period, using solution\u2014time-step\u2014sub-step command. The execution of this command will require the respective values of changing load and time, which has to be systematically input. Finally, write LS command will be used to write the above sequence of LS files as a single file to perform transient thermal analysis. The command outres, all, all must be given before simulation to make the final result of th LS file as the starting values for the th LS file. An example of intermittent load is considered for illustration (Fig. 11). The ON and OFF periods are 900 s each. The heat flux, in W/m , is proportional to 7 A at all the ON periods. It is zero at all the OFF periods. This alternative variation of heat flux and the respective time duration are is sequentially stored in an LS file, and the transient thermal simulation is run. The results of simulation showing temperature rise from 0 to 10 000 s at stator is shown in Fig. 12. 2) Thermal Analysis Considering Eddy-Current Loss: The core loss distribution in SRM is another considerable factor for heat production. Before the boundary conditions are set as detailed in this paper for thermal analysis, an iron loss analysis has to be performed to take into account the core loss distribution. Fig. 13 depicts the results of eddy-current loss distribution as obtained by FEA [15]. The thermal analysis made on this model will be a simulation considering copper loss and eddy-current loss. The results of simulation conducted on this model, showing temperature rise from 0 to 7200 s at stator, for the continuous load of 7 A, is shown in Fig. 14, which indicate that the steady-state temperature is attained at 356 K, whereas without considering the eddy-current loss, it was 350 K. 3) Thermal Analysis Considering Fins: The temperature rise of the electric machines is kept under permissible limits by providing fins. It is possible to increase the heat energy transfer between the outer surface of the machine and the ambient air by increasing the amount of the surface area in contact with the air. Fins are the corrugations provided throughout the outer surface of the frame. When fins are provided on the outer frame of the machine, as shown in Fig. 15, the surface area of heat dissipation gets increased, thus effecting the heat dissipation. It is of the kind called radial fin with rectangular profile. In order to increase the fin effectiveness, various possible combinations of fin dimensions are to be considered. Steadystate thermal analysis has to be carried out for each combination. The fin dimension which produces the least steady-state temperature rise is usually selected for the end product. Table I is the summary of steady-state thermal analysis performed on varying fin dimensions. The fin with a thickness of 2 mm and a length of 3.5 mm is declared for the end product as it produced the least steady-state temperature of 329.893 K. Figs. 16 and 17 respectively represent the results of steady-state and transient thermal analyses on the SRM with radial fins." + ] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure2.65-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure2.65-1.png", + "caption": "Fig. 2.65. Internal velocities q", + "texts": [], + "surrounding_texts": [ + "In this paragraph we discuss briefly the organization of input to the dynamic analysis algorithm from the standpoint of some specific fea tures of the algorithm. Fig. 2.47. presents a block scheme of algorithm input. Let us explain this scheme. The first set of indicators (LB i ) serves to define algorithm printout. There are several dynamic variables and characteristics which can be calculated (Para. 2.5.) and, thus, which can be printed. We use the indicators LBi to define which of these dynamic characteristics will be printed. 105 The indicators LCi define the set of tests. Thus, we choose the tests by using these indicators. On the basis of these two sets of indicators (LB and LC) the algorithm itself decides what should be computed in order to give the required prints and to perform the required tests. The configuration input contains the definition of geometry and iner tial properties. Some other parameters are also defined, for instance the cross section inertial moment if stress or deformation analysis is required. This input block allows the choice of standard-form segments. A set of indicators is used to determine the segment which has a stan dard form and which form it is. For a standard-form segment the algo rithm itself computes the segment mass, inertial tensor, cross section inertial moments etc. on the basis of the input dimensions of standard form and the input data on material. If the actuators tests or torque - r.p.m. prints are required, then the catalog characteristics of actuator and reducers are needed. Spe cial indicators are used to define which actuators have to be tested. If stress or elastic deformation analysis (the corresponding tests or prints) is required, some properties of segments material must be known (e.g. Young's modulus, maximal permitted stress, etc.). A set of indi cators is used to define which segments are considered elastic, and another set to define which segments have to be stress-tested. Manipulation task input has been discussed in 2.4. and the correspon ding input file will be explained through examples in 2.8. 2.S. Examples In this paragraph we present several examples illustrating the opera tion of the algorithm for dynamic analysis. We demonstrate the use of adapting blocks, the calculation of various dynamic characteristics and some testings. The first example (2.8.1) deals with a 4 d.o.f. 106 manipulator. In (2.8.2) and (2.8.3) two 5 d.o.f. manipulators are con sidered. Finally, in (2.8.4) we present an example of a manipulator with 6 d.o.f. 2.8.'. Example' We consider a cylindrical manipulator UMS-2V - variant with 4 d.o.f. The external look and manipulator data are presented in Fig. 2.48a. This figure also shows the choice of generalized coordinates (internal coordinates) q\" q2' q3' q4 and the adopted b.-f. systems. The kinematic scheme of manipulator is shown in Fig. 2.48b. The minimal configuration consists of one rotational (q,) and two linear (q2' q3) degrees of fre ed?m. With this 4 d.o.f. variant, the gripper is connected to the min imal configuration by means of a rotational joint (q4). Manipulation task. The manipulator carries a 3kg mass working object. The moments of inertia of the working object are Ix4 = Iy4 = Iz4 = 0.0' kgm2 (with respect to the corresponding b.-f. system). The object is to be moved along the trajectory Ao A, A2 A3 (Fig. 2.48b). Every part of the trajectory (Ao+A\" A,+A2 , A2+A3 ) is a straight line. Object ro tation for the angle TI/2 has to be performed on the trajectory part Ao+A\" and the backward rotation (- \u00a5) on the part A,+A2 \u2022 The complete scheme of manipulation task is shown in Fig. 2.48b. We have to notice a few things. If a cylindrical manipulator has to reach the points Ao ' A\" A2 , A3 , it usually follows the trajectory rep resented by a dashed line in Fig. 2.49. This is done because of sim plier control synthesis. In this example we have chosen straight line motion betwen two points (full line in Fig. 2.49) in order to demon strate the algorithm possibilities. Triangular velocity profile is adopted. Adapting block 4-2 is suitable for this manipulation task because it T = [x y z q4 l Now, let us discuss the\u00b7 in-uses the position vector X g put values. The manipulator has to move to points Ao ' A\" A2 , A3 one after another, so m = 3. In the starting point Ao we give the initial state q(to ) = [0 -D.' -0.2 OlT, q(to ) = O. In the point A, we give the value of position vector Xg(A,) = Xg , = [0.57 D.' 0.6 TI/2lT and also the time interval in which motion from the previous point is performed T T' = '.5s. Analogous values have to be given for points A2 , (Ao+A,) 107 108 A3 . Thus the input list for the definition of manipulation task is: 110 Results. We now present some results obtained by means of the dynamic analysis algorithm. The trajectory in the state space is shown first. Fig. 2.50. presents the time history of internal coordinates q and Fig. 2.51. presents the same for internal velocities q. The next figure (Fig. 2.52) shows the corresponding time history of the driving forces and torques in manipulator joints. 2.8.2. Example 2 Let us consider the arthropoid manipulator having 5 degrees of freedom. It has been designed for manipulation with heavy loads. The minimal configuration consists of three rotational d.o.f. (q1' q2' q3) and the gripper is connected to the minimal configuration by means of two ro tational joints (q4' q5). The external look, manipulator data, the cho ice of generalized (internal) coordinates, and the adopted b.-f. sys tems are shown in Fig. 2.53. 111 Manipulation task. The manipulator has to move a 250 kg mass object along the trajectory Ao A1 A2 A3 (Fig. 2.54). Every part of the trajec tory (Ao+A\" A1+A2 , A2+A3 ) is a straight line. The velocity profile on each part is triangular. The complete scheme of manipulation task, i.e. the initial position, the trajectory of object motion and the changes in object orientation, is shown in Fig. 2.54. It can be concluded that in this task the partial orientation only is necessary. Thus, this ma nipulation task consists of positioning along with partial orientation, so five d.o.f. are enough. It is evident from the manipulation task scheme (Fig. 2.54) that the direction (b) is the most important. In order to define the direction :1: (b) with respect to the gripper we use the unit vector h = {a, 1, O} (expressed in the gripper b.-f. system 06x6Y6z6). The two angles 8, ~ define the direction (b) with respect to the external system Oxyz. We T use the adapting block 5-2, so the position vector is X =[x y z 8 ~l . g The nubmer of points to be reached is m = 3. The initial position is defined by q(to ) = [0 -n/6 -4n/6 -n/6 OlT. Now, the input list defining the manipulation task is: m 3 Indicator of adapting block 2 Indicators for profiles 222 Initial position q(to ) 0 -n/6 -4n/6 -n/6 0 Xg1 = [x Y z 8 ~]A1 1.5 1.5 0 0 0 T1 = ~Ao+A1) 3. X = g2 [x y z 8 ~]A2 0 2 0.8 n/2 0 T2 = T(A1+A2) 3. X = g3 [x y z 8 ~]A3 1.5 0 0 0 0 T3 = T(A2+A3) 4.5 112 h if(b) Manipulator data Segment-i 1 2 3 4 mi[kg] - 125 98 1 0 2 31 Ixi[kgm ] - 26 0.05 2 I . [kgm ] - 31 26 0.05 yl 2 Izi[kgm ] 15 2.8 2.8 0.05 Length[m] 0.4 1 .5 1.5 0.2 * working object included Fig. 2.53. An arthropoid manipulator * 5 270 38 3 38 0.2 Results. Fig. 2.55. presents time-histories of the internal coordina tes q and Fig. 2.56. presents the corresponding time histories of driving torques in manipulator joints. In performing the task the manipulator consumed 15660 J of energy. From the manipulator configuration and the manipulation task (Figs. 2.53, 2.54) it is clear that the joint S4 does not play an active role. Hence we may consider a manipulator with no drive in that joint (P4=0). In that case the manipulator gripper would behave like some kind of a pendulum. In order to avoid large oscillations we may apply some pas sive amortization. Thus the driving actuator for the joint S4 is not necessary. Let us now discuss the driving torques in the joints S2 and S3' These torques are very large due to large manipulator weight and the heavy payload. In such cases the compensation is usually applied. The hydro or pneumatic compensators may be used or sometimes even active compen sation. 114 2.8.3. Example 3 This example deals with the anthropomorphic manipulator UMS-1V - vari ant with 5 degrees of freedom. The manipulator is shown in Fig. 2.57. The joints S2 and S3 are powered by 23 FRAME MAGNET MOTORS, 2315-P20-0, produced by INDIANA GENERAL. The reduction ratio is N = 100, and the reducer mechanical efficiency n = 0.8. The maximal characteristic (pm _ nm) i.e. the maximal torque depending on motor rotation speed max is obtained by an experiment and it is shown to be almost a straight line (Fig. 2.58). The characteristic differs from a straight line only in the region of slow speeds. If this region is not especially inter esting from the standpoint of constraint violation, we may use a straight line aproximation and in such a way save some computer memory. Here, we work with the original characteristic without approximation. The manipulator has to move a container with liquid along the trajecto- .- N M q L(') o..o..o..c...o.. \\ l. .. _ .. .......... ,.'-1 III lI) <:t' \" (Y') f- N c:( III (Y') \" N f- \\ 1\\ --------~--~~~:~~:~L-\u00b77 ~ o o \"1 o o ,. o o o '\" , o 0 lI) <:r- I I o o rp o (Y') I ,._. : .'. I ,,: o 0 o 0 ~ -. o o o lI) , o 0 N ~ , I .~ 9 o o o <:r-, o , .....\u2022 / .-.~.~. o o \"'1 o \"7 .. o 0 o 0 N (Y') \" I o o o r o 0 N (Y') I' I o o <:r I' o o o 9\" o ., o o lI) I' o lI) I' III (Y') \" f- o 115 . 0. 4 pm M r \\ \u2022 -1 . --- / .... ..r Ao ~ 0. 2 0. 1 \u2022\u2022 .\u2022 \u2022 : ..:- =:: :: I .... .. , ~ 1 0 . ~ ... :; .- -~ .. , . ~ .. , I I 1 . 2. pm m ax \\ m - n ~ (c o n st ra in t) T = 3 .2 5 I 3. F ig . 2 .6 3 . D ia g ra m s pm - nm (t o rq u e . v s . r. p .m .) fo r jo in t 5 2 4 . nm [1 0 3 r .p .m J rv a 121 122 123 profile. The execution time is T Some of the results are shown in Figs. 2.70. and 2.71. Time histories of internal coordinates q and torques P are given in the figures. In performing the task the manipulator consumed 1263 J of energy. No re sistance to the insertion is considered. 124 125" + ] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure4.28-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure4.28-1.png", + "caption": "Fig. 4.28. Manipulation system UMS-3B", + "texts": [ + "iQin-t, CY /:-I1:N REDUCER SE:LEr:TIOt~ BEGINS (.joint No.5) FEASIBLE INTERVAL FOR REDUCTION RATIO IS: [288.2 A74.5 J Select reducer ~nd typp the reducticn ratio rFl0.~J:300. P-n TEST IS POSITIVE AND MOTOR REDUCER AS&fM~LY JS f:.K. Is reduc\",;- ? lacRd in .joint [Y /NJ: Y T8pe the reducer mass <81> [Fl0.5J:9. Fig. 4.27. Example of choice comunication 293 294 Example 2 This example illustrates the procedure for the choice of electro hydra ulic actuators. We consider the cylindrical six d.o.f. manipulator UMS-3B (Fig. 4.28) Let us discuss the choice of electrohydraulic actuator for the second joint (degree of freedom q2). It is a rotational joint driven by a dylinder with translatory piston motion. Nonlinear dependences between the linear and angular variables are solved in the dynamic analysis 295 algorithm. The manipulation task consists in moving the spraygun from the point Ao to the point A1 (Fig. 4.28) keeping all the time its initial orien tation in space. The motion is performed with trapezoidal velocity profile with the transport time T = 0.625 s and the acceleration time ta = 0.2T 0.125 s. It means that the mean velocity is vm = 0.8 m/s and the maximal velocity is vmax = 1 m/s. The dynamic analysis algorithm gave the Fm_im diagram and the Qm_DQm diagram as shown in Figs. 4.29 and 4.30. From the Fm_im diagram the maximal value of force is Fm = 5163.3 N. We c decided to use MOOG servovalve having 6Pn = 70 bar" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000494_j.msea.2021.141493-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000494_j.msea.2021.141493-Figure1-1.png", + "caption": "Fig. 1. (a) Additively manufactured block and the coordinate system. (b) Laser scanning strategy. (c) Dimensions of the dog-bone specimen for tensile tests. All dimensions shown are in mm. (d) Tensile specimens with the loading direction perpendicular to the laser scanning direction. (e) Tensile specimens with the loading direction parallel to the laser scanning direction.", + "texts": [ + " An in-house developed DED system was used to produce AM samples. The system is equipped with a YLS4000CL fiber laser. The powder is transported by argon gas flux and delivered to the deposition region through a coaxial nozzle. The entire process is carried out in Ar environment to avoid oxidation during deposition. Process parameters include laser power P = 600 W, laser spot diameter d = 1.2 mm, hatch spacing \u0394Y = 0.7 mm, layer thickness \u0394h = 0.2 mm, and laser scanning speed V = 480 mm/min. A block of dimensions of 65 mm \u00d7 32 mm \u00d7 12 mm, shown in Fig. 1 (a), was fabricated via the DED system. The back-and-forth laser scanning strategy was employed as shown in Fig. 1(b). The block was sectioned into flat tensile specimens using wire electrical discharge machining. The thickness of specimens is 1.8 mm, and specimen dimensions are illustrated in Fig. 1(c). Two types of tensile specimens with the loading direction perpendicular or parallel to the laser scanning direction, denoted by S\u22a5 and S\u2016 respectively as shown in Fig. 1(d) and (e), were prepared to investigate the mechanical anisotropy of AM specimens. To characterize local deformation behavior, the microscope ex-situ DIC technique following the procedures applied in Ref. [51] is used in the present study. Before performing DIC imaging, a random pattern with an appropriate scale and resolution is needed to cover the sample surface for image correlation analysis. In this work, the etching method was used as an effective patterning method, using a solution comprising 15 ml HCl and 5 ml diluted HNO3 for 15s", + " Engineering stress versus strain curves of the specimens S\u22a5 and S\u2016 are compared in Fig. 4. The yield strengths of S\u22a5 and S\u2016 specimens are 420 MPa and 445 MPa, respectively. The ultimate strength and elongation of the S\u22a5 specimen are 520 MPa and 60%, and those of the S\u2016 specimen are 558 MPa and 50%, respectively. The S\u2016 specimen shows higher strength and lower elongation than the S\u22a5 specimen. The mechanical anisotropy associated with the loading direction in relation to the build direction (see Fig. 1 for orientation reference) has been reported in Refs. [15\u201317], highlighting the important role of grain morphology and orientation. In the present study, we note that the mechanical anisotropy in relation to the scan direction is comparable to that in relation to the build direction. When a sample is plastically L. Chen et al. Materials Science & Engineering A 820 (2021) 141493 deformed under uniaxial tension, more barriers for dislocation motions are encountered for the S\u2016 specimen due to the high angles between the loading direction and boundaries of columnar grains (see Fig", + " 2(b)), leading to the higher strength of the S\u2016 specimen than that of the S\u22a5 specimen. The presence of grain boundaries, on the other hand, tends to reduce elongation by providing a preferential path for damage accumulation [16]. Additionally, a few other sources can contribute to the observed differences in mechanical responses. Recall that Fig. 2 has revealed substructure colonies. Substructure and its spatial distribution might come into effect, which will be discussed later. The thermal history during manufacturing is different between the two specimens (refer to Fig. 1 for illustration of the difference in deposition paths), possibly altering the dislocation content. Lastly, void growth and flaw-induced fracture affect ductility, as discussed below. Fractographs performed on the S\u22a5 and S\u2016 specimens are presented in Fig. 5, showing ductile fracture preceded by substantial plastic deformation. Cleavage fracture exists in a few local areas as titled flat planes, shown in Fig. 5(a), explaining lower ductility compared to the wrought 316L. A few mild tear ridges appear on the fracture surface as shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003204_tmag.2007.893631-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003204_tmag.2007.893631-Figure2-1.png", + "caption": "Fig. 2. Shape of the eccentric magnetic pole.", + "texts": [ + " The data of Table V show that the reduction rates of the average torque are at quite close range, but those of the torque ripple change notably, which can reach the peak value at the magnetic-bridge width of 0.9 mm. Based on the compromise principle, 0.9 mm can be regarded as the optimum point of the magnetic-bridge-width choice. By further analysis, the aberrance rates of the air-gap magnetic field with the magnetic bridge width of 1 and 0.9 mm are respectively 26.43% and 24.23%, which also shows the performance improvement. The eccentric magnetic-pole shape is adopted, as shown in Fig. 2. O is the center of the magnetic-pole outside arc, O\u2019 is the center of the magnetic-pole inside arc, and is the thickness of the eccentric magnetic pole, which changes with the angular position. Owing to the use of the eccentric magnetic pole, the air-gap magnetic field can be more close to the sine wave and the cogging torque can be reduced. The machine is further optimized with the investigation of the magnetic-pole eccentricity. The eccentric distance, which is the distance between O and O\u2019, varies from 0 to 2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003255_09544070d21604-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003255_09544070d21604-Figure1-1.png", + "caption": "Fig. 1 Main parts of a gearbox transmission", + "texts": [ + "eywords: manual gearbox, synchronization, second bump, numerical simulation 1 INTRODUCTION 1. To make the angular velocity difference between the synchro hub and the gear to be engaged at Manual car gearbox synchronizers are complicated zero. This task is called \u2018synchronization\u2019. mechanical structures. They ensure the connection 2. To prevent gear changing when there is a of three main parts of the transmission (Fig. 1; see difference of angular velocity. This task is called also Fig. 30). The synchronized side of the trans- \u2018interdiction\u2019. mission is made up of the disengaged plate clutch, 3. To move the synchro sleeve between the synthe input shaft of the gearbox, and the connected chronizing splines. gears. The synchronizing side is composed of mech- 4. To allow power transmission when gear changing anical parts up to the wheels of the car. The gear- occurs. changing mechanism consists of forks and shafts moved either by actuators or by hand", + " Variations in the angular velocity difference are As the dynamical behaviour of these three mech- usually obtained by conical friction clutches, while anical parts is complicated to simulate, owing to the the power transmission is usually done by spline large number of elements involved, it is not easy coupling. One, two, or three conical surfaces are to study the entire gear-changing process in detail. considered, depending on the torque transmitted. The following study considers only synchronizer Clearly, a wide variety of technical solutions exists behaviour, with the four following aims. but the same types of problem are found. In this paper, the Borg\u2013Warner-type synchronizer with one conical surface clutch is considered (Fig. 1). Note also* Corresponding author: INSA-Lyon, Ge\u0301nie Industriel, Ba\u0302t. Jules that only three centring mechanisms are taken intoVerne, 20 Av. Albert Einstein, Villeurbanne Cedex, F-69621, France. email: daniel.play@insa-lyon.fr account. D21604 \u00a9 IMechE 2006 Proc. IMechE Vol. 220 Part D: J. Automobile Engineering at SUNY MAIN LIBRARY on March 12, 2015pid.sagepub.comDownloaded from 2 STATE OF THE ART effects of different linings on cone surfaces and the effects of grooves on the synchro ring conical Although synchronizers have been used since the surface", + " Changing is done quickly and shift filtered and do not appear in the measurements; hence, they are considered as maximum peak valuescomfort is good. Unfortunately, the probability of such cases is also low because of spline geometry in the simulation. In the case of the test-bench numerical environ-and medium-size second bump force peaks are usually observed. ment, the behaviour of one synchronizer is simulated. The synchronizer can be set to threeAn analysis of measured second bump data confirms the previous description. From a study of the geometrical positions: successively, position P1, neutral, and position P2 (Fig. 1). As in real test bench,occurrences, a peak force occurrence diagram can be drawn. The measured data are obtained by sampling power losses are different for positions P1 and P2. Synchronizer data come from measurements on reallong duration tests. Peak values are gathered into D21604 \u00a9 IMechE 2006 Proc. IMechE Vol. 220 Part D: J. Automobile Engineering at SUNY MAIN LIBRARY on March 12, 2015pid.sagepub.comDownloaded from synchronizers. It is supposed that every relative in the simulated case. Simulations fit well with the measured data in this case" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003026_physreve.65.040903-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003026_physreve.65.040903-Figure1-1.png", + "caption": "FIG. 1. Model problem. A naturally straight but flexible rod, initially parallel to the z axis, with one end held fixed with zero moment at x5b , y50, z50. We seek the steady-state shape when the end of the rod is forced to rotate in the x-y plane about the z axis at frequency vB .", + "texts": [ + " Thus, in the body-fixed frame, there are two kinds of flows that contribute to bundling: the flow due to frame rotation, and the swirling flows set up by each individual filament. Here we focus on the flow due to rotation of the bodyfixed frame; the swirling flows and interactions among flagellar filaments will be treated in a separate publication @8#. Our treatment is in the spirit of Machin @9#, who used a similar approach to argue that eukaryotic flagella could not be passive elements driven by motors at the cell body ~see also Ref. @10#!. *Electronic address: Thomas_Powers@brown.edu 1063-651X/2002/65~4!/040903~4!/$20.00 65 0409 Figure 1 illustrates the model problem. For simplicity, replace the helices with straight but flexible rods of length L, rotated with the frequency vB about the cell body axis of symmetry, z. Let b denote the distance between the axis of the unstressed rod and the z axis. Since the body is about a micron across, and flagellar filaments are typically six to ten microns long, we suppose b!L . We also disregard the rotational disturbance flow arising from the no-slip condition at the cell body. In the body-fixed frame, this disturbance flow reduces the net rotational flow near the body", + " Finally, we focus our attention on the contribution to flagellar filament wrapping due to body rotation, and not the flows set up by the individual rotating filaments, by ignoring the hydrodynamic interactions among the rods. Thus, it suffices to consider the shape of a single rod. During runs, the left-handed flagellar filaments turn counterclockwise ~when viewed from outside the cell!, and the body turns clockwise ~when viewed from behind, i.e., from the distal end of the bundle!. When our model filament is turned about the body-rotation axis z in this same sense ~clockwise when viewed from the positive z-axis, see Fig. 1!, it forms a right-handed shape ~e.g., see Fig. 2 and note that the proximal end x/L5b50.1 is in the plane z50, and the distal end with x near 0 has positive z coordinate!. Furthermore, two left-handed helices rotating about their respective axes with proximal ends held stationary will lead to a flow \u00a92002 The American Physical Society03-1 which also tends to wrap the helices around each other in a right-handed manner @8#. Thus, the body-rotation effect treated here and the swirling flow effect treated in Ref", + " The ratio of these two torques is O\u201e(a/b)2(L/l )@ log(L/a) 11/2#\u2026. For the representative values L510 mm, a 04090 '10 nm, and b'1 mm, this ratio is small even if L/l '10. Therefore, we disregard rotational drag and twist strain. To find the bending force per unit length, note that since b!L , the displacement of any rod element will also be small. Thus, the elastic energy is well approximated by the quadratic expression E5 1 2 AE F S ]2x ]z2 D 2 1S ]2y ]z2 D 2Gdz , ~2! where x and y are as in Fig. 1, and A is the bend modulus @15#. Since the variation in rod shape is rapid for sufficiently high rotation rate, even for small b, this approximation eventually fails and must be replaced by the full geometrically nonlinear elastic rod energy. As we discuss below, the rotation rates of interest are small enough for Eq. ~2! to hold. The variational derivative of Eq. ~2! yields the elastic bending force per unit length: 2dE/dr'52A]4r' /]z4, where r' [x x\u03021y y\u0302. To leading order for b!L , the motion of the rod is purely perpendicular to the rod centerline, yielding the equation of motion @9# z'S ]r' ]t 2v'D52A ]4r' ]z4 , ~3" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure22.9-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure22.9-1.png", + "caption": "Fig. 22.9 Operation of sheet-like curved type muscle", + "texts": [ + " Further, considering the pinch force of the general male is about 20N to 25N, this glove is effective in assisting the pinch operation. Pneumatic Rubber Artificial Muscles and Application to Welfare Robotics 261 22.6 Elbow Power Assist Wear A sheet-like curved type pneumatic rubber artificial muscle is newly developed to realize a thin rubber muscle. By using this muscle, a power assist wear assisting the bending motion of the elbow is developed [4]. 22.6.1 Sheet-Like Curved Type Rubber Artificial Muscle It is composed of the rubber tube sandwiched between upper and lower two sheets sutured surroundings as shown in Fig.22.9. The end of rubber tube is sealed, the other is piped to the pressure control valve. By using the elastic sheet (fabric rubber) extending only to the axial direction of two sheets, when the rubber tube is pressurized, the extending operation in the axial direction is obtained. Three kinds of operations can be achieved by making the difference in the amount of extension of both sheets due to the difference in the number of sheets or the elasticity of the sheets. Fig.22.9(a) shows the case of using same numbers of sheet in both sides. Since the amounts of extension are same, the linear extension in the axial direction is caused. When there is difference in the number of upper and lower sheets, the difference in the amounts of extension causes the extension and curved motion as shown in Fig.22.9(b). In Fig.22.9(c), the material not to extend in the axial direction (nylon band) is used in the upper sheet, only the curved operation occurs by pressurizing the rubber tube. Due to the combination of these operations, the power assist smoothly along the human body movement can be obtained. 262 Toshiro Noritsugu, Masahiro Takaiwa and Daisuke Sasaki Figure 22.10 shows the operation of manufactured artificial muscle. The artificial muscle used for the elbow power assist wear is 350mm in the total length, and 100mm in the width" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003384_20.278859-Figure6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003384_20.278859-Figure6-1.png", + "caption": "Fig. 6 - 100-Line Fimte-Element Flux plot ( 0 = 60') Showing Equal Two-F'hase Excitation", + "texts": [ + " The effective permeability is given by 1 (6) 1 - p(WN = F - 3 B ) *$/A) ' where H is magnetic field strength, B is flux density, Cp is magnetic flux through the element and A is the circuit element area. The remaining saturable reluctances are given by lsc Rsc = 6 p(Cpsc/Asc) Asc ' (7) where lrp is the rotor pole length, Arp is the rotor pole area, lrc is the average rotor core length, Arc is the rotor core area, lsp is the stator pole length, Asp is the stator pole area, lsc is the average stator core length and Asc is the stator core area. Note that although the rotor core reluctance length between adjacent poles is 1/6 rather than 1/4, tooth base flux spreading (Fig. 6) makes this effectively correct . III. SATURABLE MATERIAL MODEL There are several ways to model saturable materials[3]. The most straight-forward method which still gives fairly accurate results and stable circuit mesh solutions is where p i , P2and r are constants. This can be extended with more power terms as required. Using Eqn. 11, Eqn. (6) becomes (12) 1 Pi + P2 ICp/Al(r-l) p(Cp/N = IV. CIRCUIT MESH SOLUTION The circuit mesh for fig. 1 results, making use of two pole symmetry, in a matrix equation of the form R(O,Cp/A) 'P - M = 0 (13) where R is reluctance - 9x9, CP is flux - 9x1, M is excitation - 9x1 and 0 is zero - 9x1", + " The unexcited phase fluxes follow the finite-element trend with significant error which could be reduced by refining the mesh in the stator pole area as described above. However, this error does not significantly affect the ability of the model to accurately predict the results of multiple phase at a time excitation because the dominant effect is core saturation and not pole-to-pole and pole-to-core leakage. Note that the major effect is in the range 180 to 360\u00b0 where adjacent rotor poles overlap the excited stator poles as shown in Fig. 6. This is where multi-phase currents would flow under high-speed motoring or generating conditions. VI. THREE-DIMENSIONAL EHXClX Three-dimensional effects can be accounted for by decreasing the pole to core reluctance to account for endwinding leakage and by decreasing the airgap reluctance to account for leakage between the rotor and stator ends. VII. CONCLUSIONS The new switched reluctance motor magnetic equivalent circuit model with mutual coupling and multi-phase excitation successfully predicts the magnetic behavior of an SRM with multiple phase at a time excitation" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003628_s11044-008-9121-7-Figure5-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003628_s11044-008-9121-7-Figure5-1.png", + "caption": "Fig. 5 The limb of a 3-CPS parallel manipulator with its infinitesimal screws", + "texts": [ + " The kinematics of open serial chains using screw theory is the basis of this subsection; for a detailed explanation of it the reader is referred to [42\u201344]. Consider the 3-RPS parallel manipulator shown in Fig. 1. In order to satisfy the rank of the Jacobian matrix spanned by the infinitesimal screws of the limbs of the mechanism, the parallel manipulator is modeled as a 3-CPS manipulator (CPS = Cylindrical + Prismatic + Spherical), in which the translational displacements of the cylindrical joints are null. Figure 5 shows the infinitesimal screws of one limb of the 3-CPS parallel manipulator. With this consideration, the velocity state 0V1 O = [0\u03c91 0v1 O ]T and the reduced acceleration state 0A1 O = [0\u03c9\u03071 0a1 O \u2212 0\u03c91 \u00d7 0v1 O ]T of the moving platform, body 1, with respect to the fixed platform, body 0, can be obtained, respectively, in screw form through any of the i-th limbs, i \u2208 {1,2,3}, of the parallel manipulator as follows 0V1 O = [ 0\u03c91 0v1 O ] = 5\u2211 j=0 j\u03c9 i j+1 j $j+1 i (9) and 0A1 O = [ 0\u03c9\u03071 0a1 O \u2212 0\u03c91 \u00d7 0v1 O ] = 5\u2211 j=0 j \u03c9\u0307 i j+1 j $j+1 i + $Liei (10) where \u2022 0\u03c91 and 0\u03c9\u03071 are the angular velocity and acceleration of the moving platform, \u2022 0v1 O and 0a1 O are the velocity and acceleration of a point O fixed to the moving platform which is instantaneously coincident with a point of the fixed platform, \u2022 k\u03c9 i k+1 and k\u03c9\u0307 i k+1 are the joint velocity and acceleration rates of body k + 1 with respect to the adjacent body k, both in the same limb" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002958_la060167r-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002958_la060167r-Figure4-1.png", + "caption": "Figure 4. Randle\u2019s equivalent circuit.", + "texts": [ + " The metal pad and the gold wire were covered with silicone glue in such a way that only the surface covered with HRP was exposed to the electrolyte when it was used as a working electrode. Characterization by Impedance Spectroscopy. Impedance spectroscopy is a powerful tool for studying the interface properties of surface-modified electrodes. An AC-modulated small signal voltage is applied to the electrochemical cell, and the AC current response is recorded as a function of the modulation frequency. The resulting complex impedance of the electrochemical cell can be represented by the simple equivalent circuit shown in Figure 4 The different elements of the circuit correspond to the resistance of the solution (RS), a capacitive element (CD), which in some cases can be described as a double layer capacitance, and two other elements related to the charge-transfer processes. RCT, the electron-transfer resistance, dominates in the case of kinetic limited processes. The Warburg impedance (ZW), a frequency dependent term, represents the resistance to the mass transport of electroactive species, dominating in the case of diffusionlimited kinetics. The Nyquist diagram of the complex impedance represents the imaginary versus the real part of the impedance. In general, for the equivalent circuit of Figure 4, the Nyquist plot will show a semicircle and a linear region. The semicircle at higher frequencies corresponds to an electron-transfer-limited process, and the linear portion at lower frequencies corresponds to the diffusion-limited process. We have measured the nonfaradaic impedance of the NCD electrode when no redox species was present in the electrochemical cell. In this situation, any contribution from the Warburg impedance can be neglected. The corresponding plot is shown in Figure 5A. The experimental data (open symbols in Figure 5A) have been fitted with a model (simulation data as solid symbols in Figure 5) based on the equivalent circuit of Figure 4, assuming no contribution from the Warburg impedance. The value of the electron-transfer resistance for the case of the unmodified NCD electrode is RCT \u2248 5500 \u2126. After modification of the electrode surface with the TFA molecules, RCT shows a conspicuous increase (RCT \u2248 59 000 \u2126) as can be seen in Figure 5B. The resistance increment indicates that the organic layer acts as an insulating barrier that hinders the current flow to the electrode. Figure 6 shows the Nyquist plot of the protein-covered electrode. In the high-frequency region, a new contribution to the total impedance is visible. In the case of the protein-modified electrode, the simple equivalent circuit of Figure 4 cannot describe the complex situation, which is schematically shown in Figure 7. The presence of the enzyme will modify the properties of the molecules beneath, adding new capacitive terms. Remarkable in Figure 6 is that the protein modification introduces a component with very low resistance to electron-transfer: the RCT of the high-frequency component is about 400 \u2126. As discussed below, this low resistive path results from the direct charge transfer between the enzyme\u2019s redox group and the electrode surface" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002524_s0165-0114(99)00180-3-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002524_s0165-0114(99)00180-3-Figure1-1.png", + "caption": "Fig. 1. Switching of SMC. (a) Sliding condition in two-dimensional planes. (b) Sliding condition of chatting and boundary layer. (c) Sliding condition of fuzzy switching.", + "texts": [ + " A fuzzy system is a collection of fuzzy IF\u2013THEN rules of the form: R( j): IF x1 is A j 1 and : : : and xn is Ajn THEN y is Bj: (7) By using the strategy of singleton fuzziBcation, product inference and center-average defuzziBcation, the output of the fuzzy system y(x)= \u2211l j=1 y j( \u220fn i=1 Aji (xi))\u2211l j=1 \u220fn i=1 Aji (xi) ; (8) where Aji (xi) is the membership function of linguistic variable xi, and yj is the point in R at which Bj achieves its maximum value (assume that Bj (yi)= 1). By introducing the concept of fuzzy basic function vector !(x), (8) can be rewritten as y(x)= \"T!(x); (9) where, \"=(y1; : : : ; yl)T, !(x)= (!1(x); : : : ; !l(x))T; !j(x)= \u220fn i=1 Aji (xi)\u2211l j=1 \u220fn i=1 Aji (xi) : (10) The concepts of fuzzy SMC (Fig. 1a), Lyapunov synthesis (Fig. 1b) and fuzzy SMC with fuzzy switching (Fig. 1c) are similar. They apply FS to approximate the system dynamics and use a stable Hurwitzian polynomial as reference dynamics. The idea of fuzzy SMC is to use (crisp) switching around the sliding surface to reduce the eHect of disturbances. Lyapunov synthesis does not specially address the eHect of disturbance in its design. Fuzzy SMC with fuzzy switching, which provides a smooth transition between diHerent level of disturbance around sliding surface, uses a fuzzy system to approximate the crisp switching to avoid chattering and steady state error", + "(x), (22) \"\u0307g=\u2212 r2eTPb!(x)uI (23) Fuzzy SMC with fuzzy switching \"\u0307f =\u2212 r1s!(x), (15) \"\u0307g=\u2212 r2s!(x)uI , (16) \"\u0307h=\u2212 r3s+(s) (27) Summary of control laws Fuzzy SMC uI = 1 g\u0302(x; t) ( n\u22121\u2211 i=1 kie(i) \u2212 f\u0302(x; t) \u2212(D + ) sgn(s) + x(n)d ) (6) Lyapunov Synthesis uI = 1 g\u0302(x; t) ( n\u22121\u2211 i=1 kie(i) \u2212 f\u0302(x; t) + x(n)d ) (18) Fuzzy SMC with fuzzy switching uI = 1 g\u0302(x; t) ( n\u22121\u2211 i=1 kie(i) \u2212 f\u0302(x; t)\u2212 h\u0302(s; t) + x(n)d ) (24) The sliding control law (6) is discontinuous across the sliding surface s(t) and leads to chattering (Fig. 1b). Chattering is undesirable because it involves high control activity and may excite highfrequency dynamics. A thin boundary layer neighbouring the sliding surface: B(t)= {x: |s(x; t)|6,} (28) which makes the control changes continuously within this boundary layer and will lead to smoothing out of the chattering (Fig. 1b). SpeciBcally, we change the control law (6) to u= n\u22121\u2211 i=1 kie(i) \u2212 f\u0302(x; t) + x(n)d \u2212 (D + ) sat(s=,); (29) where the saturation function sat(s=,) is deBned as sat(s=,)= \u22121 if s=,6\u22121; s=, if \u22121\u00a1s=,61; 1 if s=,\u00bf1: (30) Wang et al. in Part I [10], proposed a soft (fuzzy, h\u0302(s|\"h)) switching, to replace the crisp switching sgn(s) to avoid chattering, to replace boundary layer sat(s=,) to reduce the steady state error. h\u0302(s|\"h) can be regarded as a series of BL which linked nonlinear smoothly with FS (Fig. 1c). The initialization of the switching term can be selected to be boundary layer which is a linear switching and continue to update the switching term h\u0302(s|\"h) to reduce the steady-state error. In this section, we propose a fuzzy SMC with state bounded supervisory controller and parameter projection. The key in this approach is to design an appended second-level supervisory nonfuzzy controller to guarantee stability in a supervisory fashion [11,12] (Fig. 3). The state x is uniformly bounded, that is |x(t)|6Mx, \u2200t\u00bf0, where Mx is a constant given by the designer" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003425_978-3-540-30301-5_34-Figure33.5-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003425_978-3-540-30301-5_34-Figure33.5-1.png", + "caption": "Fig. 33.5 Intelligent assist device: the simplest form of upper-extremity enhancers for industrial applications. The IAD can follow a worker\u2019s high-speed maneuvers very closely during manipulations without impeding the worker\u2019s motion.", + "texts": [ + " Upper-extremity exoskeletons were designed based primarily on compliance control [33.26\u201329] schemes that relied on the measurement of interaction force between the human and the machine. Various experimental systems, including a hydraulic loader designed for loading aircrafts and an electric power extender built for two-handed operation, were designed to verify the theories (Fig. 33.3 and Fig. 33.4). The intelligent assist devices (IAD) are the simplest non-anthropomorphic form of the upper-extremity systems that augments human capabilities [33.30, 31]. Figure 33.5 illustrates an intelligent assist device (IAD). At the top of the device, a computer-controlled electric actuator is attached directly to a ceiling, wall, or an overhead crane and moves a strong wire rope precisely, and with a controllable speed. Attached to the wire rope is a sensory end-effector where the operator hand, the IAD, and the load come into contact. The end-effector includes a load interface subsystem and an operator interface subsystem. The load interface subsystem is designed to interface with a variety of loads and holding devices" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003262_j.humov.2006.09.005-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003262_j.humov.2006.09.005-Figure1-1.png", + "caption": "Fig. 1. Experimental setup.", + "texts": [ + " Six college baseball players in Juntendo University, Chiba, Japan, volunteered for the experiment (mean age = 20.8 years; mean height = 1.74 m; and mean weight = 73.0 kg). They have played baseball for eleven years, starting with a little league championship tournament, and are currently playing in a college baseball league in Tokyo, Japan. All of them were right-handed hitters. After the experimenter had explained the purpose and procedure of the experiment, each participant signed an informed consent form. The whole setup of the experiment is depicted in Fig. 1. Two force platforms were fixed on the ground in a batter\u2019s box to record GRFv during hitting movements (Fig. 1). The size of the force platforms should be large enough for the participants to take their hitting stances and make a stepping motion toward the direction of a pitch. Therefore, a pilot examination of the stance widths and stepping lengths of the participants was conducted. It revealed that the mean stance width was 0.53 m (range 0.39\u20130.73 m), while the mean stepping length was 0.35 m (range 0.15\u20130.56 m). Based on these measurements, the sizes of force platforms were determined as 0.71 m by 0.56 m for the front foot and 0", + " The linearity between the applied force and the measure of the strain gauges was confirmed by a linear regression analysis for each of the platforms (mean r2 = .98). Force signals obtained from the strain gages were amplified by a dynamic strain amplifier (DPM-8H with a frequency response: DC to 5 kHz and a sensitivity switch set at 1000 \u00b7 10 6 le, Kyowa Electronic Instruments Co., Tokyo, Japan). A pitching machine (ZMA-581, Toa Sports Machine, Tokyo, Japan) was placed on a pitcher\u2019s mound, which was 18.44 m away from the force platforms in accordance with the distance between a pitcher\u2019s plate and a home plate (Fig. 1). Balls were projected by the machine as shown in Fig. 1. Two microphones were placed on the ground immediately below the pitching machine and immediately behind the batters to record the sounds of the ball projection from the pitching machine and the ball\u2013bat contact, respectively, through an audio-amplifier. The sound signals were used to identify the time of the ball release from the pitching machine and of the ball\u2013bat contact. These sound signals and the force signals from the platforms were registered by a computer through an analogue-to-digital conversion with the sampling frequency of 1 kHz" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002579_s0301-679x(01)00079-2-Figure7-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002579_s0301-679x(01)00079-2-Figure7-1.png", + "caption": "Fig. 7. A commercial toroidal traction drive [31].", + "texts": [ + " In transmissions, one area fraught with tribological complications is the application of toroidal traction drives. Continuously variable transmissions (CVTs) offer significant energy-saving by enabling crankcase engines to operate closer to their optimum performance level over a full driving cycle. At present, most vehicle CVTs in use are belt drives and these are limited in torque capability to use in relatively low capacity engines. CVTs based on counterformal contact, in particular with a toroidal geometry (Fig. 7) [31], offer higher torque capability and could thus be used in largerengined cars and even trucks. From the tribology research point of view, there are currently two main challenges posed by traction drives. One is to produce lubricants able to provide high friction or \u2018traction\u2019 over the wide temperature and pressure range experienced in EHD contacts. Most conventional lubricants reach a limiting EHD traction coefficient at high pressures and strain rates of about 0.03 to 0.06, falling to between 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003286_bf01175968-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003286_bf01175968-Figure1-1.png", + "caption": "Fig. 1. The fixing of a rectangular prisma, a By means of seven point-contacts, b The example given by Thompson and Taft", + "texts": [ + " The necessity of the condition follows from the fact that if, out of any two normals, the sense of one of them is reversed, their mutual opposition about the screw defined by the other five normals is lost. Fig. l a shows the fixing of a rectangular prism by means of seven pointcontacts. The locations shown in the figure refer to a numerical example with Y l = 3 , z l = 2 ; Y 2 = 1, z 2 = 4 ; x a - - ~ 4 , z a = 5 ; x 4 = 1, z4--~ 1 ; x s = 1.5, y5----2; x~ = 3.5, Y6 = 2.5 ; xv = 1, Y7 = 1.5. The equilibrating forces in the absence of applied forces are also shown; all of them are positive as required. Fig. 1 b shows schematically the example given by Thompson and Taft [3]. Contacts 2 and 3 are in a vee groove; Mong the z-axis; contacts 1 and 7 are parallel to the y-axis; contacts I f the normals are so chosen that some of them (six or less) are linearly dependent, the number of contacts needed will be more than tha t given by the foregoing analysis (see sections 5, 6). If the body shape is however such tha t linear dependence between six or less number of normals is unavoidable, the degree of freedom cannot be reduced to nil by any number of contacts" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000232_j.ymssp.2021.108403-Figure7-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000232_j.ymssp.2021.108403-Figure7-1.png", + "caption": "Fig. 7. Dynamic model of planetary gear trains.", + "texts": [ + " Complexity of the acquired signals X. Liu Mechanical Systems and Signal Processing 166 (2022) 108403 would be further enhanced by this effect. To simulate the actual vibration signals collected by transducers installed on the housing of planetary gearbox, in this study, a resultant vibration signal model is developed by considering the multiple source vibration and the transfer path as well as the background noise. To gain the vibration source signals, a nonlinear dynamic model is developed for planetary gear trains, as shown in Fig. 7. \u2018s\u2019 denotes sun gear, \u2018r\u2019 denotes ring gear, \u2018c\u2019 denotes carrier, \u2018pn\u2019 denotes N planet gear. Herein, oxy is a rotating coordinate system fixed on the geometric centre of the carrier. Each component i (i = s, r, c, pn) has two translational motions (xi, yi) and one torsional motion (ui). The bearing element of each component is modelled as a virtual springdamping unit with stiffness kij and damping cij (j = x, y, u). Each gear mesh pair is represented as a nonlinear displacement function f(\u03b4in) (i = s, r; \u03b4in denotes the relative displacements along the action lines of gear pairs) with time-varying stiffness (krn, ksn) and damping (crn, csn)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000492_j.jmst.2021.04.004-Figure7-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000492_j.jmst.2021.04.004-Figure7-1.png", + "caption": "Fig. 7. (a) Schematic diagram of the actuating delay time experiment. (b) High-speed images from the movement of the magnet to the movement of S-LMD and H-LMD. (c) Schematic diagram of the wheel model. (d) Actuating process of the wheel. The wheel was placed on a glass substrate and actuated by a magnet.", + "texts": [ + " The resistance force F h and f may increase faster than the magnetic driving force F m so the elocities of the droplets decreased as the size increased. The highst average actuating velocities for the H-LMD and S-LMD were .45 cm/s and 4.08 cm/s when the size was 4 \u03bcL. The H-LMD had arger actuating velocity, which indicated that it had better mag- etic controllability than the S-LMD. Additionally, the actuating delay time and the offset distance f the H-LMD and S-LMD were also measured. For the measure- ent, the magnet was placed underneath the glass substrate and he testing droplet was located directly above the magnet ( Fig. 7 a). he actuating delay time was defined as the time interval between t t t a 0 d w a S f t s s n m p t r d s d s w ( a t t c p p 3 t t t w f he movement of the magnet and the droplet. The start times of he magnet and the testing droplet were noted as t 0 and t 1 , respecively, and the delay time was calculated by t 1 \u2212 t 0 . In Fig. 7 b, the ctuating delay time for the H-LMD and S-LMD were 0.58 s and .83 s respectively. In addition, the offset distance d , defined as the istance from the center of the droplet to the center of the magnet hen the droplet started to move, could also be used to describe nd quantify the magnetic controllability of the two droplets. The -LMD had an offset distance of 5.94 mm, while it was 5.27 mm or the H-LMD ( Fig. 7 b). The H-LMD had smaller actuating delay ime and shorter offset distance than the S-LMD because of the trong magnetism and it was easier to be attracted by magnets, howing the high sensitivity and low time delay under the mag- etic field. It is noteworthy that the droplet is always at the edge of the agnet when following the magnet movement during the testing rocess because the magnetic field at the edge of the magnet is he largest according to Fig. 6 d. The static friction force and the esistance moment caused by the deformation of the droplet hinered the movement of the droplet. In order to overcome the re- istance moment, a longer offset distance was required to drive the roplet to roll [36] . Due to the small actuating delay time and the hort offset distance, the H-LMD was used as the driving motor for heeled robots ( Fig. 7 d). A double nozzle high precision 3D printer Flashforge, ltd., China) was utilized to print the wheel model with diameter of 3 cm and the H-LMD (8 \u03bcL) was placed at the botom of the wheel inside ( Fig. 7 c). A magnet was used to actuate he H-LMD, which changed the center of gravity for the wheel and aused the wheel to roll forward (Movie S4). The entire moving rocess was untethered, which meant that the H-LMD exhibited romising revolutionary uses and good magnetic maneuverability. .6. Application of the droplets in a micro-valve Based on the above study, the H-LMD was magnetically conrollable with a better elasticity and mechanical robustness than he S-LMD. These properties enabled it to be applied in the inegrated microfluidic devices, such as micro-valve [ 37 , 38 ]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure9.9-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure9.9-1.png", + "caption": "Fig. 9.9 FERMA (Flexible ER MicroActuator)", + "texts": [ + " Through experiments, the electrode sizes and flow channel height were optimized to have a high output power. The maximum flow rate and pressure of 5.5 cm3/s and 7.2 kPa were obtained. New Microactuators Using Functional Fluids 99 We are developing microactuators using ER microvalves. The ER microvalve controls the ERF flow by the apparent viscosity change due to the applied electric field through fixed electrodes. To realize soft microactuators for medical applications and so on, an FERMA (Flexible ER MicroActuator) that has an FERV (Flexible ER Valve) was proposed and developed as shown in Fig.9.9. An FERV based on flexible SU-8 cantilever structures and the novel MEMS fabrication process was proposed. The FERV shown in Fig.9.9(b) was successfully fabricated with 5 mm length, 2.4 mm width and 0.2 mm thickness and the sufficient flexibility was confirmed. It was experimentally confirmed that the static characteristics are independent from the bending. Furthermore, an FERMA using the FERV was fabricated and tested. Also, we have proposed an inherently robust ER microactuator against disturbance as shown in Fig.9.10. The microactuator consists of a pair of movable and fixed parallel plate electrodes with variable gap length and an upstream restrictor" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003788_978-1-4020-5967-4-Figure12-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003788_978-1-4020-5967-4-Figure12-1.png", + "caption": "FIGURE 12. Combination of compound pulleys to move a weight of 1000 talents with a force of 5 talents. Drachmann\u2019s drawing above (The Mechanical Technology, p. 87) is from Ms B; the figure below is from Heronis Alexandrini opera, vol. II, p. 156.", + "texts": [ + " A similar point follows for the screw, since it is just a twisted wedge; again, it is a crucial assumption that the number of turns of the screw in a given time remains the same (in the text above: \u201cthe turning of the screw many times takes more time than a single turn\u201d). In the case of both wedge and screw, then, it is clear that Heron\u2019s understanding of the phenomenon of slowing up involves a comparison between machines of different mechanical advantage; moreover, this comparison assumes that the moving forces in the two machines travel at the same speed. Such a comparison between moving forces also underlies Heron\u2019s account of slowing up in the case of the compound pulley (Mechanics 2.24, Fig. 12; since the Ms figure is not very clear, the following refers to the figure in Heronis Alexandrini opera). Specifically, Heron notes that in order to lift a weight of 1000 talents at over the distance , a force of 200 talents exerted at must be pulled through 5 times the distance (since each rope in the 5-pulley system must be pulled over a distance ). Similarly, a force of 40 talents exerted at must be pulled through 5 times the distance of the force at (since in order to move the rope at by a certain distance, the rope at must be pulled through 5 times that distance)", + ", R\u2032 F1 F2 D2 D1 where D1 and D2 are the distances covered by the moving forces, travelling at a constant speed, in different times.49 Now the operation of the compound pulley can also be analyzed in a way that leads to a different understanding of the phenomenon of slowing up. On this view, the comparison is between the moving force and the weight moved, rather than between two different moving forces. If the moving force is smaller than the weight, it will cover more distance than the weight in any given time (e.g., in Fig. 12 during the time in which the force at moves a certain distance, the weight at will move 1/5 of that distance). Thus the moving force travels more quickly than the weight; in this sense, the \u201cslowing up\u201d that occurs in the machine is the result of the weight moving more slowly than the force that moves it. At any given time the ratio of the distance covered by the moving force to that covered by the weight will be the inverse of the ratio of the force to the weight, i.e., R\u2032\u2032 F1 F2 D2 D1 where F2 equals the weight" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000033_tec.2020.2965180-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000033_tec.2020.2965180-Figure1-1.png", + "caption": "Fig. 1. Configuration of the proposed PM-SRM with two sets of PMs.", + "texts": [ + " This paper presents a new PM-assisted switched reluctance motor (PM-SRM) with two sets of inner and outer PMs embedded between the end teeth of the neighboring poles and inside the connecting yoke of the adjacent modules, respectively. The configuration of the proposed PM-SRM is introduced. The operating principle is analyzed based on the magnetic circuit model (MCM) of the motor. The motor characteristics are obtained and compared with those of PM-less SRM, 6/5 and 12/8 SRMs, and 6/5 and 12/8 HRMs. Finally, the PM-SRM is prototyped and the experimental results are carried out to validate the simulation results. The configuration of the proposed PM-SRM is shown in Fig. 1. It is composed of three magnetically-disconnected modules with four teeth per stator pole. The rotor consists of twenty-five teeth. The main flux sources are concentrated coils wrapped around the stator poles and six small PMs are embedded between the neighbouring modules as auxiliary flux source, all of which have the same magnetization direction as depicted with arrows. Employing both multiple teeth structure and PMs provide meritorious features as: \u2022 Multiple teeth per pole: The electromagnetic torque of an SRM, Tem, with n teeth per stator pole can be written as [26], [28]: Tem = Iph\u222b 0 N2 phIph\u00b50nlrs 2g di = n" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003425_978-3-540-30301-5_34-Figure33.20-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003425_978-3-540-30301-5_34-Figure33.20-1.png", + "caption": "Fig. 33.20 The exoskeleton hip degrees of freedom (back view). Only the rotation axis does not pass through the human hip ball and socket joint. The adjustment bracket is replaceable to accommodate various sized operators", + "texts": [ + " It is natural to design a 3-DOF exoskeleton hip joint such that all three axes of rotation pass through the human ball-and-socket hip joint. However, through the design of several mockups and experiments, we learned that these designs have limited ranges of motion and result in singularities at some human hip postures. Therefore the rotation joint was moved so it does not align with the human\u2019s hip joint. Initially the rotation joint was placed directly above each exoskeleton leg (labeled \u2018alternate rotation\u2019 in Fig. 33.20). This worked well for the lightweight plastic mockup, but created problems in the full-scale prototype because the high mass of the torso and payload created a large moment about the unactuated rotation joint. Therefore, the current hip rotation joint for both legs was chosen to be a single axis of rotation directly behind the person and under the torso (labeled \u2018current rotation\u2019 in Fig. 33.20). The current rotation joint is typically spring loaded towards its illustrated position using sheets of spring steel. Like the human\u2019s ankle, the BLEEX ankle has three DOFs. The flexion/extension axis coincides with the human ankle joint. For design simplification, the abduction/adduction and rotation axes on the BLEEX ankle do not pass through the human\u2019s leg and form a plane outside of the human\u2019s foot (Fig. 33.21). To take load Part D 3 3 .8 off of the human\u2019s ankle, the BLEEX ankle abduction/adduction joint is sprung towards vertical, but the rotation joint is completely free", + " To minimize the hydraulic routing, manifolds were designed to route the fluid between the valves, actuators, supply, and return lines. These manifolds mount directly to the cylinders to reduce the hydraulic distance between the valves and actuator, maximizing the actua- tor\u2019s performance. The actuator, manifold, and valve for the ankle mount to the shank, while the actuators, manifold, and valves for the knee and hip are on the thigh. One manifold, mounted on the knee actuator, routes the hydraulic fluid for the knee and hip actuators. Shown in Fig. 33.26, the BLEEX torso connects to the hip structure (shown in Fig. 33.20). The power supply [33.47\u201349], controlling computer, and payload mount to the rear side of the torso. An inclinometer mounted to the torso gives the absolute angle reference for the control algorithm. A custom harness (Fig. 33.27) mounts to the front of the torso to hold the exoskeleton to the operator. Besides the feet, the harness is the only other location where the user and exoskeleton are rigidly connected. Figure 33.26 also illustrates the actuator, valve, and manifold for the hip abduction/adduction joint" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002692_02783649922066394-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002692_02783649922066394-Figure4-1.png", + "caption": "Fig. 4. Cusp-type singularity and its projection into leg space. Three assemblies coalesce P . A candidate never-special motion is shown from A1 to A3.", + "texts": [ + " Because of this the linkage is readily displaced in the direction of lost constraint, and this is identified with the acquisition of transitory freedom. Should three assemblies coalesce, the linkage relies on thirdorder constraints and the propensity to wobble, now cubic, is much greater. If double coalescence is intolerable because the linkage structure is too poorly conditioned to be useful, triple coalescence is more so. This argues that triply coalesced assemblies are pernicious and best avoided, or better still, \u201cdesigned out\u201d by judicious dimensioning. Figure 4 provides a more fundamental interpretation of triple coalescence and suggests why it gives a sufficient prerequisite for never-special motions. Here the fold of Figure 3 has been folded. When C (the configuration space) is projected into leg space, the branch locus cusps at the point P . Points inside the cusp, e.g., A\u2032, have three local pre-images (assemblies) inC; points outside it have one; and atP the three assemblies coalesce. This \u201cfolding of the fold set\u201d is known as a cusp-type singularity (Poston and Stewart 1978; Bruce and Giblin 1992), and eq. (24) amounts to a crude form of the versal unfolding of this singularity. By diffeomorphism, eq. (24) could be brought into model form (for instance, see Bruce and Giblin\u2019s work (1992)), although we do not pursue this here. We make the following observations based on Figure 4: \u2022 The triple coalescence at P allows the linkage to negotiate a special configuration in moving between two assemblies having the same leg lengths. A candidate motion is any that encircles P (e.g., that from A1 to A3). \u2022 A trajectory passing though the special configurationP has det ( \u22020 \u2202\u03b8 ) = 0 at P . Note, however, that det ( \u22020 \u2202\u03b8 ) will take the same sign on either side of this special configuration if the trajectory remains on upward-facing regions. Innocenti and Parenti-Castelli (1998) report that they have observed this phenomenon in numerical investigation", + " \u2022 Hunt and Primrose (1993) describe an imagined procedure wherein an in-parallel actuated device is moved very close to a special configuration and the actuators then locked. Ill-conditioning of the structure together with compliance in the ball-socket joints and leg rods allows it to be \u201cpopped\u201d through to the nearby assembly. Near a triply coalesced assembly it is possible to \u201cpop\u201d between the three nearby assemblies in the same imagined way, but we should not expect to be able to cycle through them, moving from one to the next in a cyclic sequence. One assembly will be central, e.g.,A2 of Figure 4, so that in popping between the other two, here A1 and A3, it will usually be visited. Objections to Figure 4 because it is dimensionally inconsistent with the spaces C for the linkages of Figures 1 and 2 are best reconciled by viewing doubly and triply coalesced assemblies via their codimension, rather than their dimension, making recourse to the accepted notion that objects with the same codimension have similar properties (see, e.g., Poston and Stewart (1978)). In Figure 4, C is a surface; the fold set corresponding to first-order degeneracy is of codimension 1; and the cusp at P , where there is second-order degeneracy, has codimension 2. While the configuration space C for the planar device has dimension 3, sets of interest (folds and cusps) have codimensions 1 and 2 consistent with Figure 4 (similarly for the octahedral manipulator). Provided we don\u2019t go beyond corank 1, second-order degeneracy, Figure 4 is valid if we think of it as describing a two-dimensional slice of C where, say, all but two of the leg rods are fixed. Whitney (1955) showed that the projection of a surface to a plane always splits into folds and cusps, but nothing more complex. We expect then that for small perturbations of the fixed leg lengths, the topological structure of nearby branch-loci slices are, ordinarily, at Univ Politecnica De Valencia on June 3, 2015ijr.sagepub.comDownloaded from preserved. A change in the structure of a slice of the branch locus indicates higher order degeneracies of eq" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003729_9780470612231.ch6-Figure6.13-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003729_9780470612231.ch6-Figure6.13-1.png", + "caption": "Figure 6.13. Schematic diagram of evanescent waves and detection at the sample surface", + "texts": [ + " Some chemical and biochemical reactions emit their own light \u2013 chemiluminescence or bioluminescence. This can be used to measure the concentration of some specific analytes under certain conditions. The major advantage of this phenomenon is that no light source is required. 6.4.1.1. Evanescent wave sensors When light propagates in an optical fiber or waveguide (see Figure 6.12) under conditions of total internal reflection, a fraction of the radiation extends a short distance from the guiding region into the medium of lower refractive index that surrounds it (see Figure 6.13). This so-called evanescent field can interact with molecular species in close proximity to the fiber core e.g. in the cladding of the optical fiber itself. The motivation for embracing this evanescent wave (EW) approach is due to a number of advantages it offers: \u2013 It is easy to miniaturize and no coupling optics are required. \u2013 It is possible to discriminate between surface and bulk effects by controlling the launch optics. \u2013 Sensitivity can be higher when compared to bulk optic approaches. \u2013 Highly absorbing or highly scattering media are suited to this technique because the effective path length is so small and scattering does not interfere to the same extent", + " SPR biosensors Several biosensors have been developed based on the phenomenon of SPR which allows the detection of biomolecular interactions in \u201creal time\u201d. The principle behind SPR is described in the context of BIAcore for convenience. At an interface between two media of different refractive indices (e.g. glass and water), light coming from the side of the higher refractive index is partly reflected and refracted. Above a certain critical angle of incidence, the light is totally internally reflected and no light is refracted across the interface between the two surfaces of different refractive index \u2013 see Figure 6.13. Under total internal reflection (TIR) conditions, an electromagnetic field component called the evanescent wave penetrates into the medium of lower refractive index a short distance in the order of one wavelength. As the evanescent wave moves further away from the interface into the lower dense medium, the wave decays exponentially. If the interface between the media is coated with a thin layer of metal (in the case of BIAcore, this metal layer is gold) containing electron clouds at the surface and the passage of the evanescent wave through this metal layer causes the plasmons to resonate, this results in a quantum mechanical wave known as a surface plasmon" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003815_j.mechmachtheory.2009.06.001-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003815_j.mechmachtheory.2009.06.001-Figure1-1.png", + "caption": "Fig. 1. A general generator of X-motion.", + "texts": [ + " If A G and B G, that is, A and B are subsets of G, then, from the closure of product in the group, it implies AB # G. When the group H has a dimension and the subsets also have a dimension, dim AB = dim G leads to AB = G. The equality is generally valid only in a neighborhood of the identity. Consequently, the Schoenflies subgroup can be generated by many serial arrays of kinematic pairs. The following set equality can be regarded as a generic expression of the decomposition of the 4D subgroup {X(u)} into a product of four 1D subgroups, which are generated by the 1-dof Reuleaux pairs [15], as shown in Fig. 1. PPRHIII1( ) III2( PPRR) III3( PPHH) PPHR( )III4 III5( PRPR) III6( PRPH) PHPR(III7) PHPHIII8( ) III9( PRRP) III10( )PRHP III11( PHHP) fX\u00f0u\u00deg \u00bc fH\u00f0N1;u;p1\u00degfH\u00f0N2;u;p2\u00degfH\u00f0N3;u;p3\u00degfH\u00f0N4;u;p4\u00deg \u00f09\u00de In set Eq. (9), one, two or three of the factors {H(Ni, u, pi)} may be replaced by a 1D subgroup {T(si)} of translation parallel to the unit vector si, provided that the vectors si are linearly independent. One, two or three pitches may also be equal to zero. Obviously, set Eq. (9) is valid in a neighborhood of the identity E if and only if (iff) the product in its right side is a 4D manifold; else the product as well as the open chain of Fig. 1 are singular. The detection of transitory singularity is out of the scope of this paper. Actual achievements of {X(u)} mechanical generators can be obtained by placing in series kinematic pairs represented by subgroups of {X(u)}; a serial arrangement of four 1-dof kinematic pairs without intermediate link having passive motion makes up a mechanical generator of the subgroup {X(u)}. What has to be noticed is that a 4-R chain is obviously defective for generating {X(u)} because such a chain has a redundant internal mobility and generates fG\u00f0u\u00deg fX\u00f0u\u00deg", + " In general, the singularity happens iff the following set equation fH\u00f0N1;u; p1\u00degfH\u00f0N2;u; p2\u00degfH\u00f0N3;u; p3\u00degfH\u00f0N4;u;p4\u00deg \u00bc fEg \u00f010\u00de does not imply the set equations fH\u00f0N1;u; p1\u00deg \u00bc fH\u00f0N2;u; p2\u00deg \u00bc fH\u00f0N3;u; p3\u00deg \u00bc fH\u00f0N4;u; p4\u00deg \u00bc fEg: \u00f011\u00de which are solved iff the helical motion angles are equal to zero. Here, the subset of displacements represents variations of position from the home posture. The absence of displacement necessarily belongs to the set of feasible displacements. Set Eq. (10) is the mathematical model of a mechanism obtained from the open chain pictured in Fig. 1 by welding the distal bodies i and j on a fixed frame. Such a closed-loop mechanism generally cannot move and, then, the open chain of Fig. 1 effectively generates X-motion. If a link in the closed mechanism can move, then the generator of X bond is defective or permanently singular. Two kinds of singularities may happen; the undesired motion either has only infinitesimal amplitude or can have finite amplitude. The detection of undesired infinitesimal motion is done through the study of a possible linear dependency of the four twists. This topic will be studied in another work. On the other hand, group theory is a fruitful tool for PPPR)b(PPPH)a( Pl Pl Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000131_j.matcom.2020.12.030-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000131_j.matcom.2020.12.030-Figure1-1.png", + "caption": "Fig. 1. Three-dimensional structure and geometrical model of a WMR.", + "texts": [ + " (3) Numerical simulations and comprehensive comparisons with the existing ZNN models for the trajectory racking control of WMR further demonstrate the robustness and effectiveness of the proposed RZNN model. . Problem statement In this section, we first present the three-dimensional structure and geometrical model of a WMR, and then its orresponding inverse kinematic model is introduced. For the purpose of better understanding, the three-dimensional structure and geometrical model of a WMR is resented in Fig. 1. As seen from Fig. 1(a), a WMR consists of a movable base platform and a six-joint manipulator, nd its geometrical model is presented in Fig. 1(b). The notations in Fig. 1(b) are presented below. (1) Po: center point of the movable base platform circle, its coordinate is (Xo, Yo, Zo). (2) Pm : manipulator location on the movable base platform, its coordinate is (Xm , Ym , Zm). W c w w (3) d: projection distance between the center point Po and the location of the manipulator Pm . (4) b: radius of the movable base platform circle. (5) r: radius of the driving wheels. (6) \u03c6: heading angle of the movable platform, and \u2022 \u03c6 is the heading velocity. (7) Q: hypothetical point which the movable base platform rotates around", + " Activation functions Formulations Linear activation function (LAF) \u03c4 (x) = x Power activation function (PAF) \u03c4 (x) = xk k > 3 and k is an odd integer Bi-power activation function (BPAF) \u03c4 (x) = (1\u2212exp(\u2212\u03be x))/ (1 + exp(\u2212\u03be x)) \u03be > 1 Power-sigmoid activation function (PSAF) \u03c4 (x) = \u23a7\u23a8\u23a9x p, |x | \u2265 1 1 + e\u2212\u03be \u2212 e\u2212\u03be x 1 \u2212 e\u2212\u03be + e\u2212\u03be x , otherwise Hyperbolic sine activation function (HSAF) \u03c4 (x) = (exp(\u03be x)\u2212exp(\u2212\u03be x))/2 \u03be > 1 Sign-bi-power activation function (SBPAF) \u03c4 (x) = (|x | k +|x | 1/k )sgn(x)/2 0 < k < 1 Based on the above discussion, the IKP can be illustrated that the desired path need to be tracked by the endffector of the WMR is given in advance, the corresponding joint and wheel trajectories are required to be generated. n this work, we will focus on designing a new RZNN model for solving the IKP, and the proposed RZNN model ill be introduced in the next section. . Robust zeroing neural network (RZNN) model In this section, we propose a new RZNN model for solving the IKP of the WMR in Fig. 1, and the proposed ZNN model for solving the IKP of the WMR reaches fixed-time convergence noise suppression simultaneously. First, we define a vector-valued error function to monitor and control the process of the IKP of the WMR. E(t) = rmd (t) \u2212 rm(t) (5) Here, rmd (t) \u2208 Rm is the desired path to be tracked, and rm(t) is the actual path of the end-effector of the WMR, nd ei (t) stands for the i th element of E(t). As seen from Eq. (5), the IKP of the WMR is converted to enforce ach element ei (t) of E(t) converging to 0", + "025*exp(\u2212t) Based on Lemma 1, the bounded time ti of the i th subsystem can be directly obtained as: ti \u2264 1 \u03bbbk ( b a )1/p ( 1 + 1 pk \u2212 1 ) The upper bound convergence time of RZNN (9) attacked by a DNDN is obtained as: tb = max(ti ) \u2264 1 \u03bbbk ( b a )1/p ( 1 + 1 pk \u2212 1 ) Based on the above analysis, we can conclude that the RZNN model (9) attacked by a DNDN converges to he exact solution of IKP of the WMR in fixed time tb, and tb is also irrelevant to the initial state of the dynamic system. \u25a0 It is worthy to point out that Theorems 1\u20133 demonstrate that the proposed RZNN not only has the ability to converge to the exact solution of IKP of the WMR in fixed time tb, but also rejects interference and noises, and hese are two important improvements of the original ZNN model. . Simulations and comparisons In this section, simulation results of a WMR with its three-dimensional model presented in Fig. 1 are investigated o demonstrate the robustness and effectiveness of the proposed RZNN model (9) in dynamic noise-polluted nvironment for solving the IKP of the WMR. Part A is the simulation and analysis of the RZNN model. For omparison, part B is simulation and analysis of the original ZNN model. .1. Wheeled mobile robot (WMR) path tracking via RZNN model in noise-polluted environment In this section, the end-effector of the WMR is expected to track a windmill-shaped trajectory task. During the xecution of this task, i" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000062_012121-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000062_012121-Figure4-1.png", + "caption": "Figure 4. Universal working body. a) is a complete view; b) the paw of the cultivator; c) a cultivator with a slot; 18 - holder; 19 - wing; 20 - blade; 21 - slot; 22 - a cultivator; 23 - the curvature of the cultivator; 24 - toe paws; 25 - slotter; 26 - ledge;27 - base plates.", + "texts": [ + " The main section is located in the middle and contains a bar, transport and support wheels, and hydraulic cylinders for servicing the side sections. The front frame of the main section is designed in the same way as the frames of the side sections. The second frame is with one post and paw. The rear frame is made with four tines, a needle grinder and a tine harrow. The needle chopper and harrow work the soil to a depth equal to the cultivation depth. ERSME 2020 IOP Conf. Series: Materials Science and Engineering 1001 (2020) 012121 IOP Publishing doi:10.1088/1757-899X/1001/1/012121 Figure 4 shows a universal working body of the tillage unit, which consists of a cultivator paw and its holder, two wings with a fused blade located on the outer surface along the edge of the wings. On the joint line of the paw wings, a through slot is made for a saber-shaped working body (a ripper with a slotter), made with the curvature of the cutting edge in the direction of movement, and an indent from the toe of the paw. The length of the slot is half the length of the paw wing and the width is 2-3 mm" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003670_978-3-642-82195-0-Figure1.11-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003670_978-3-642-82195-0-Figure1.11-1.png", + "caption": "Fig. 1.11. Arthropoid robot", + "texts": [ + " Its origin need not coincide with the center Z1 of the first joint, so ->- that a distance vector r 1 between these points has to be defined. This o ->- vector, or more exactly, its axis e 1 serves as a reference for defining the zero value of joint coordinate q1 in the same manner as vector ->- ->- ->- r. 1 . when defining joint coordinate q .. If r 1=0 or r 1 is colinear 1- ,.!, 1 0 0 with e 1 , an auxilliary vector has to be introduced, in the same way as ->- it was described for vector r. 1 .. 1- ,1 13 An illustration of the vectors defining manipulator links for a typical industrial robot presented in Fig. 1.11, is shown in Fig. 1.12. Here, the origin of the reference coordinate frame coincides with the center ->- .->- Z1 of the first joint, resulting in r 01 =0. Besldes, r 11 is parallel to ->- '11' ->-, d ->-, e 1 \u00b7 So, two aUXl lary vectors r 01 an r 11 are introduced in order to define position when q1=0 (the case when the vectors become antiparal lel). In Fig. 1.12 the arthropoid robot is shown in its initial confi guration, when all joint coordinates are equal to zero. Kinematic para meters of all the links are listed in Table 1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000338_j.msea.2021.141355-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000338_j.msea.2021.141355-Figure2-1.png", + "caption": "Fig. 2. The tensile specimens design scheme for tensile tests. (a) Schematic diagram, and (b) geometry of tensile specimens in mm.", + "texts": [ + " Chemical compositions were analyzed using the D8 ADVANCE X-ray diffractometer (XRD), and the scanning angle ranged from 20\u25e6 to 100\u25e6 in 2\u03b8 with a scanning rate of 5.0\u25e6/min. In addition, the elemental distributions of deposited layers were identified using the energy dispersive spectrometer (EDS). The HVS-1000 Vickers micro-hardness tester was used to measure the micro-hardness distribution of deposited layers and substrate along the building direction, with the load of 5 N and the dwell time of 10 s. The specimen was machined into dog-bone shaped samples for tensile test, its specific size and schematic diagram were shown in Fig. 2. The tensile test was carried out at room time (RT) of 27 \u25e6C using a double column electronic universal testing machine with the video extensometer. The fracture morphologies were characterized by SEM. For the wear resistance test, the specimens were sectioned into the same size of 25 \u00d7 25 \u00d7 7 mm3 and then polished their top surfaces by buffing machine. SiN ball counterparts with a diameter of 6 mm were used as grinding materials and the wear test was performed at RT by HT1000 universal friction and wear equipment" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003283_095440705x34757-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003283_095440705x34757-Figure2-1.png", + "caption": "Fig. 2 The teeth contact model", + "texts": [ + " With reference to giventhe models for the dynamics of the unsynchronized gear pairs usually consider the presence of an over- helical involute gear pairs, many numerical simulations have been conducted to test the influencesall term accounting for dissipative effects, such as friction in bearings or hysteresis, neglecting the of the above parameters on gear rattle noise reduction.effects caused by the oil inserted between the meshing gear teeth. The goal of this article is to present a theoretical model for better understanding of the influence of 2 MOTION EQUATION the damping effects owing to the oil film between the impacting teeth of an unladen gear pair on the Figure 2 shows a scheme of a 1 DOF model of an unladen meshing gear pair in which gear 1 representsgear rattle phenomenon. The effect owing to the oil inserted between the meshing teeth could be the driving gear. When the teeth are in contact [Figs 2(a), (c), and (e)] the presence of an elastic forceappreciable, especially in the dead space when the gear teeth are separated but approaching each other is assumed, but during the approach phase, when D17704 \u00a9 IMechE 2005Proc. IMechE Vol. 219 Part D: J. Automobile Engineering the teeth are separated [Figs 2(b) and (d)], the force pair in Fig. 3 characterized by a total contact ratio of 2.93 is reported. The stiffness is consequently theis a non-linear damping force owing to a pure squeeze oil effect. The contact can occur either on sum of n functions which are shifted by a transverse base pitch (X z ). Following Cai [3] the ith functionthe driving side [Figs 2(a) and (e)] or on the driven side [Fig. 2(c)]. K i (X) has the expression Under such an hypothesis, the motion equation of the rattling gear can be written as Ki(X )=kp expACa KX\u2212eXz /21.125e a X z K3B (2) mx\u0308+F(x, x\u0307)+ fr=\u2212mX\u0308, where e and e a are the total contact ratio and with the transverse contact ratio respectively, and X z is the transverse base pitch. For a complete meshing F(x, x\u0307)=GK(X )x, if |x| b S(x)x\u0307, if |x|\u220f(b\u2212hmin) (1) cycle, X starts from 0 and ends at eX z . The term k p represents the stiffness at the pitch point, which where m is the mass of the driven gear, x=r 2 h 2 \u2212r 1 h 1 depends on the tooth parameters as well as the C ais the relative displacement between the teeth, coefficient" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002545_s0165-0114(01)00038-0-Figure10-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002545_s0165-0114(01)00038-0-Figure10-1.png", + "caption": "Fig. 10. The inverted pendulum system.", + "texts": [ + " 8(b) shows the state x2(t) and its desired trajectory y\u0307m(t)= cos(t). Fig. 9 shows the phase-plane trajectory of the controlled DuJng system. The control results show chattering phenomenon since the proposed method employs switching function in the control algorithm. As can be seen from the Ggures, the proposed controller can achieve both regulation and tracking for the given nonlinear system in the presence of uncertainty. Consider the problem of balancing an inverted pendulum on a cart, as shown in Fig. 10. The dynamic equations of the pendulum are [29] x\u03071 = x2; x\u03072 = g sin(x1)\u2212 amlx22 sin(2x1)=2\u2212 a cos(x1)u 4l=3\u2212 aml cos2(x1) ; (28) where x1 is the angle in rad of the pendulum from the vertical axis, x2 is the angular velocity in rad=s1; g=9:8m=s2 is the acceleration due to gravity, m=2:0 kg is the mass of the pendulum, a=(m + M)\u22121; M =8:0 kg is the mass of the cart, 2l=1:0m is the length of the pendulum, and u is the force applied to the cart. Since the dynamic equations of the nonlinear system is available, a TS fuzzy model used to approximate this system can be manually calculated by simple linearization method" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002831_3477.558842-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002831_3477.558842-Figure2-1.png", + "caption": "Fig. 2. Configuration of the forearm boundary singularity for PUMA manipulator.", + "texts": [ + " One is the boundary singularity [19] with b d4C3 a3S3 = 0 (19) and the other is the interior singularity [19] with i d4S23 + a2C2 + a3C23 = 0: (20) From (19), the condition for boundary singularity is equivalent to 3 = 92:6864 or 272:6864 . However, as far as the working 0 J11 = d4S1S23 a2S1C2 a3S1C23 d2C1 d4C1C23 a2C1S2 a3C1S23 (d4C23 a3S23)C1 d4C1S23 + a2C1C2 + a3C1C23 d2S1 d4S1C23 a2S1S2 a3S1S23 (d4C23 a3S23)S1 0 d4S23 a2C2 a3C23 d4S23 a3C23 (15) 0 J21 = 0 S1 S1 0 C1 C1 1 0 0 (16) and 0 J22 = C1S23 C1C23S4 S1C4 C1C4C23S5 S1S4S5 + C1S23C5 S1S23 S1C23S4 + C1C4 S1C4C23S5 + C1S4S5 + S1S23C5 C23 S23S4 C23C5 S23C4S5 : (17) space of PUMA manipulator is concerned, 3 = 272:6864 is unreachable. Referring to Fig. 2, it can be seen that the boundary singularity happens when the wrist point is located on the x2 axis. In this configuration, the tasks in x2 direction and z2 direction are dependent. This key point can also be identified by viewing the linear velocity of the wrist in coordinate 2 as 2 VW = 2 R0 0VWx 0VWy 0VWz = 2VWx 2VWy 2VWz = 2 J11 _ 1 _ 2 _ 3 (21) where 2R0 is the rotation matrix which transforms the components expressed in coordinate 0 into those expressed in coordinate 2. Then, 2J11 will have the following structure 2 J11 = 2 R0 0 J11 = 0 0 0 0 (22) where \u2019s represent some values other than zero. From (22), it is not obvious about which direction is the singular one. In order to identify the singular direction easily, one more rotation is needed. See Fig. 2, where a new coordinate system (xb;yb; zb) is defined. The orientation between coordinate system (x2;y2; z2) and (xb;yb; zb) is b R2 = cos 0 sin 0 1 0 sin 0 cos with = tan 1 d2 D and D = d4S23 + a2C2 + a3C23: Then b J11 = b R2 2 J11 = 0 0 0 0 0 : (23) From (23), obviously, the singular direction of the forearm boundary singularity is in the xb direction. In other words, in this configuration, the Wrist cannot have a linear movement in the xb (singular) direction (see Fig. 2). As for the interior singularity, referring to Fig. 3, it happens when the Wrist locates at the y1-z1 plane. Then, one of the axes in z1, or z2, or y3 can be chosen as the singular direction. Here, the direction in y3 is chosen. Therefore, when the interior singularity occurs, J11 viewed in coordinate 3 becomes 3 J11 = 3 R0 0 J11 = 0 0 0 : (24) From (24), the linear singular direction of the forearm interior singularity is clearly in parallel with y3 axis. If both boundary and interior singularities are encountered, then 3 = 92:6864 and 2 = 90 " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003009_978-3-642-50995-7_21-Figure8-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003009_978-3-642-50995-7_21-Figure8-1.png", + "caption": "Fig. 8. Aeronautical Systems Modeled Using ADAMS", + "texts": [ + " Other automotive systems often modeled, but not shown, include windshield wipers, convertible top mechanisms, sunroof retraction devices, controlled seating systems, quick-disconnect fueling apparatus, door and window mechanisms, trunk and hood articulation systems, and differential gearing assemblies. Aeronautical systems provide perfect applications (see Refs. [13,14]) for ADAMS since, by design, they typically undergo large overall motions involving coupled rotations and translations. A few select aeronautical systems modeled by ADAMS are illustrated in Figure 8. These include prop-driven aircraft, rotorcraft (helicopters), and jet aircraft whose dynamic performance is predicted during take-off, flight, and landing maneuvers in order to insure stability, absence of flutter characteristics, and proper durability. Modeled subassemblies include landing gear and flexible rotor-blade/bucket assemblies, as shown, as well as guidance and control systems, ailerons and rudders, turbine and impellers, hatch and safety systems, and weapon system release mechanisms" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003670_978-3-642-82195-0-Figure2.3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003670_978-3-642-82195-0-Figure2.3-1.png", + "caption": "Fig. 2.3. An illustration of the backward recursive relations", + "texts": [ + " These relations are directly utilized in the program implementation of the software package for symbolic kinematic model generation. In this chapter we will introduce the following notation for the ele ments of the transformation matrices iT. J Tj i 11 Tji12 Tji13 Tji14 iT. Tji21 Tji22 Tji23 Tji24 (2.2.29) J Tji31 Tji32 Tji33 Tji34 0 0 0 This notation is suitable from the standpoint of program implementation of the algorithm. 67 We will start from the general backward recursive relation (2.2.5), graphically outlined in Fig. 2.3. Let us first consider the case when joint i is a revolute one. If matrix iTn has already been evaluated, the matrix i-1 Tn is, according to (2.2.1) and (2.2.5), given by cosq i -sinqicosai sinqisinai aicosqi i-1 T sinqi cosqicosai -cosqisinai aisinqi iT (2.2.30) n n 0 sina. cos a. d. 1. 1. 1. 0 0 0 1- e i \u2022 A linear joint Sj (Fig. 2.5) allows a relative translation along -> an axis determined by a unit vector e j \u2022 Ci ' Cj and quadrats are used to mark the centers of gravity (c.o.g. in the sequel) of each segment in the figures in the text. si' Sj are in dicators determining the type of joints: to, 1 , if Sk is a rotational joint if Sk is a linear joint. ------~B (2.3.3) Fig. 2.3. Open kinematic chain without branching 28 The prescription of the configuration will be discussed later", + " Thus the maximal rota s tion speed nm is determined by the maximal flow. Now, the feasible max domain in the pm_nm plane has a rectangular form. We also notice the nominal point nominal r.p.m 2.46a. have a with the corresponding values of nominal torque pm and nom nm . For a real actuator the characteristics of Fig. nom slightly different form (Fig. 2.46b); for instance, the maximal torque is not independent but decreases a little with the ro tation speed. The maximal rotation speed also shows a small difference. The characteristics from Fig. 2.4 6b. correspond to an existing ac tuator and are taken from catalog. pm nom -------, Test of a hydraulic actuator is now similar to the test of a D.C. motor. If the pm_nm (or P-q) characteris tic computed by means of dynamic analysis algorithm lies wholy wit hin the feasible domain then the test is positive. If the character istic violates the constraint i.e. I I I I I I nmmax nm extends beyond the domain then the Fig. 2.46a. Theoretical form of the permissible do main 3D 40 50 300 250 200 nominal point 150 100 50 test is negative" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002390_41.847898-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002390_41.847898-Figure4-1.png", + "caption": "Fig. 4. A two-degrees-of-freedom robot arm.", + "texts": [ + " The weights of the context network are updated based on the backpropagation algorithm [12]. The final update rules for this network are 'zj = X h2 hz y hj (38a) $ji = X h2 hj hi $ji 2ji (38b) ji = X h2 hj ( hi $ji) 2 3ji (38c) where > 0 is the learning rate, is the data set over which the network has been trained, and hz =wh z yhz (39a) hj = X h2 hz 'zj y h j : (39b) The proposed law was tested in simulation by controlling the position of the first joint of a two-degrees-of-freedom robot arm, depicted in Fig. 4. The joint was driven by a dc motor connected to it by a reduction gearbox (N = 1 : 10). The selected dc motor was the E-541 from Electro-Craft Corporation, Minneapolis, MN, which has the following nominal parameters: Rm = 2:31 ; Lm = 6:67 mH; KE = 10:96 V/kr/min; KT = 14:83 oz in/A; Jm = 0:005 oz in s2; and Dm = 0:15 oz in/kr/min. The equations representing the dynamic movement of the arm and the dynamic response of the dc motor can be found in [13] and [14], respectively. The whole system was modeled by two feedforward ANN\u2019s, as was described in Section V" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002831_3477.558842-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002831_3477.558842-Figure3-1.png", + "caption": "Fig. 3. Configuration of the forearm interior singularity for PUMA manipulator.", + "texts": [ + " 2, where a new coordinate system (xb;yb; zb) is defined. The orientation between coordinate system (x2;y2; z2) and (xb;yb; zb) is b R2 = cos 0 sin 0 1 0 sin 0 cos with = tan 1 d2 D and D = d4S23 + a2C2 + a3C23: Then b J11 = b R2 2 J11 = 0 0 0 0 0 : (23) From (23), obviously, the singular direction of the forearm boundary singularity is in the xb direction. In other words, in this configuration, the Wrist cannot have a linear movement in the xb (singular) direction (see Fig. 2). As for the interior singularity, referring to Fig. 3, it happens when the Wrist locates at the y1-z1 plane. Then, one of the axes in z1, or z2, or y3 can be chosen as the singular direction. Here, the direction in y3 is chosen. Therefore, when the interior singularity occurs, J11 viewed in coordinate 3 becomes 3 J11 = 3 R0 0 J11 = 0 0 0 : (24) From (24), the linear singular direction of the forearm interior singularity is clearly in parallel with y3 axis. If both boundary and interior singularities are encountered, then 3 = 92:6864 and 2 = 90 . In this case, J11 viewed in coordinate 2 becomes 2 J11 = 2 R0 0 J22 = 0 0 0 0:149 0:865 0:434 0 0 0 (25) Therefore, the linear singular directions of the forearm boundary and interior singularities are in parallel with x2 and z2 axes" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002721_rob.10099-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002721_rob.10099-Figure2-1.png", + "caption": "Figure 2. The three basic types of kinematic pairs.", + "texts": [ + " It is also well known that the relative velocities, proportional to the relative infinitesimal displacements, between a pair of rigid bodies connected by these types of kinematic pairs form one-dimensional subalgebras, and therefore subspaces, of the Lie algebra, e(3), of the Euclidean group. Furthermore, these subalgebras are denoted by (1) revolute joint, VR AR s\u0302 ;r s\u0302 e 3 , (12) (2) screw or helical joint, VH AH s\u0302 ;r s\u0302 hs\u0302 e 3 , (13) (3) prismatic joint, VP AP 0 ; s\u0302 e 3 , (14) where s\u0302 is a unit vector along the kinematic pair axis, r is the position vector from any point along the kinematic pair axis to a point arbitrarily chosen as the origin, and h is the pitch of the screw axis. For a graphical explanation of the joint parameters, see Figure 2. Furthermore, for conciseness sake, any one of these subspaces of the Lie algebra of the Euclidean group will be denoted by V1 or, when necessary, by A1 . It is possible, now, to advance a formal definition of the infinitesimal mechanical liaison or infinitesimal bond of a pair of adjacent bodies in an open kinematic chain. Definition 9: Let i and j be a pair of arbitrary rigid bodies in an open kinematic chain. Then the infinitesimal mechanical liaison or infinitesimal bond, between i and j, denoted by V(i ,j), is defined as the set of all possible velocities of the rigid body j with respect to the rigid body i" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003654_s0022-460x(81)80143-5-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003654_s0022-460x(81)80143-5-Figure4-1.png", + "caption": "Figure 4. Enlargement of the arbitrary small segment (Ss) of table path from Figure 3. Convention: positive velocity downwards.", + "texts": [ + " The weighting due to ball velocity is thus visualized more clearly. As the ball velocities become very large the trajectories approach the vertical, and the weighting towards the upward (negative) velocities becomes less. In the limiting case when the trajectories are exactly vertical (infinite ball velocity) no shadow zones are prossible and the velocity-derived weighting ceases. Only in this case is the distribution of Wt the Gaussian distribution. Consider now an arbitrary small segment 8s of the table path in Figure 3. This segment is shown enlarged in Figure 4. Let the table velocity be w in this segment. The ball velocity is tt (constant). A measure of the probability of impact as a function of the table velocity w is required. The subsequent analysis follows that of Feng and Graft [12] who considered the impact of a sphere against the end of a rod which was vibrating sinusoidally. The probability of the segment 8s being intercepted by the ball is proportional to 8~/84>. Now 84> = 8~ + 8r, and 8r = 8x/u, but 8 = w84>. Combining these three expressions and rearranging gives 8~184> = 1 - wlu" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000340_j.jmbbm.2021.104552-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000340_j.jmbbm.2021.104552-Figure1-1.png", + "caption": "Fig. 1. Additively manufactured bone plate: (a) CAD model (b) assembly of as-prepared plates (c) after stress relieving (d) after milling.", + "texts": [ + " Ti-6Al-4V bone plates were printed using the Renishaw AM400 laser melting system at the Auckland University of Technology, New Zealand, with the processing parameters as listed in Table 1. Alloy powder of the following composition was used for fabricating the bone plates: 6.00 \u00b1 0.50% Al, 4.00 \u00b1 0.50% V, Fe \u2264 0.25, O \u2264 0.13, C \u2264 0.08, N \u2264 0.05, H \u2264 0.012, and balance Ti (by mass). In one fabrication schedule, a total of five plates were built of the following dimensions: 70 mm length, 17.5 mm width with the holes (for fitting screws) of radius 2.8 mm, and thickness 3 mm. The schematic design of the plate is shown in Fig. 1. Zaxis is considered as the build direction throughout this study. Bone plates were stacked in two columns of five plates each on the build plate. The surfaces of the bone plates were covered with support structures for easy separation after fabrication. Post-fabrication, plates were subjected to heat treatment in a furnace filled with Argon gas for stress relief. The temperature was increased to 730 \u25e6C over 1 h and then held for 2 h. The furnace was powered off, and the furnace door was opened when the temperature dropped below 400 \u25e6C", + "9 mm height and 2.9 mm diameter was scanned. The porosity visualization was done using the AVIZO software. Images were collected at 1.125 \u03bcm voxel size. For phase identification, X-ray diffraction (XRD) analysis was performed using Panalytical X\u2019Pert PRO Diffractometer with Cu K\u03b1 (\u03bb = 1.54 \u00c5) radiation at 40 kV and 30 mA. Scanning was done in the range of 2\u03b8 from 30\u25e6 to 120\u25e6 with a step size of 0.033\u25e6 and a scan speed of 0.0106\u25e6/s. XRD scanning was done on both XY and XZ surfaces of the AM and HT bone plates (Fig. 1). Bulk texture measurement was performed in an X-ray texture goniometer based on Schulz reflection geometry (Rigaku Smartlab XRD) with Cu-K\u03b1 source at 45 kV and 30 mA on XY surface. All samples were prepared by standard metallographic procedures followed by electropolishing (Struers LectroPol 5) at 40 V in an electrolyte with a composition of 60 ml perchloric acid, 360 ml butoxy ethanol, and 600 ml methanol. Samples for optical microscopy, scanning electron microscopy, and electron backscatter diffraction (EBSD) were prepared by standard metallographic procedures followed by electropolishing" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003425_978-3-540-30301-5_34-Figure33.15-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003425_978-3-540-30301-5_34-Figure33.15-1.png", + "caption": "Fig. 33.15 Sagittal plane representation of the exoskeleton in the single stance phase. The torso includes the combined exoskeleton torso mechanism, payload, control computer, and power source", + "texts": [ + " The above discussion motivated the design philosophy using a 1-DOF system. An exoskeleton, as shown is a system with many degrees of freedom and therefore implementation of the controller needs further attention. Below we extend the above control technique to the single support phase only. Refer to [33.38] and [33.39] for more details associated with multivariable control. In the single support phase, the exoskeleton system is modeled as the seven-DOF serial link mechanism in the sagittal plane shown in Fig. 33.15. The inverse dynamics of the exoskeleton can be written in the general form as: M(\u03b8)\u03b8\u0308 +C(\u03b8, \u03b8\u0307)\u03b8\u0307 + P(\u03b8) = T +d , where \u03b8 = (\u03b81\u03b82 . . . \u03b87) and T = (0, T1T2 . . . T6) . (33.16) M is a 7 \u00d7 7 inertia matrix and is a function of \u03b8, C(\u03b8, \u03b8\u0307) is a 7 \u00d7 7 centripetal and Coriolis matrix and is a function of \u03b8 and \u03b8\u0307, and P is a 7 \u00d7 1 vector of gravitational torques and is a function of \u03b8 only. T is the 7 \u00d7 1 actuator torque vector with its first element set to zero since there is no actuator associated with joint angle \u03b81 (i. e., angle between the exoskeleton foot and the ground); d is the effective 7 \u00d7 1 torque vector imposed by the pilot on the exoskeleton at various locations. According to (33.14), we choose the controller to be the exoskeleton inverse dynamics scaled by (1\u2212\u03b1\u22121) , where \u03b1 is the amplification number T = P\u0302 + (1\u2212\u03b11)[M\u0302(\u03b8)\u03b8\u0308 + C\u0302(\u03b8, \u03b8\u0307)\u03b8\u0307] , (33.17) C\u0302(\u03b8, \u03b8\u0307, P\u0302(\u03b8) and M\u0302(\u03b8) are the estimates of the Coriolis matrix, gravity vector, and the inertia matrix, respectively, for the system shown in Fig. 33.15. Note that (33.17) results in a 7 \u00d7 1 actuator torque. Since there is no actuator between the exoskeleton foot and the ground, the torque prescribed by the first element of T must be provided by the pilot. Substituting T from (33.17) into (33.16) yields, M(\u03b8)\u03b8\u0308 +C(\u03b8, \u03b8\u0307)\u03b8\u0307 + P(\u03b8) = P\u0302(\u03b8)+ (1\u2212\u03b1\u22121)[M\u0302(\u03b8)\u03b8\u0308 + C\u0302(\u03b8, \u03b8\u0307)\u03b8\u0307]+d . (33.18) In the limit when M(\u03b8) = M\u0302(\u03b8), C(\u03b8, \u03b8\u0307) = C\u0302(\u03b8, \u03b8\u0307), P(\u03b8) = P\u0302(\u03b8), and \u03b1 are sufficiently large, d will approach zero, meaning the pilot can walk as if the exoskeleton did not exist" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002744_0302-4598(95)01846-7-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002744_0302-4598(95)01846-7-Figure4-1.png", + "caption": "Fig. 4. Effect of repeated cycles on the stability of P3MT grown on Pt on the response towards 1 mM NADH (in 0.01 M Na2SO 4) solution: curve a, cycle 1; curve b, cycle 100; I, anodic; II, cathodic.", + "texts": [ + "1 M in concentration in nano-pure water. b Peak differences from those measured in glassy carbon and Pt electrodes. c Buffer I: 5 mM NaeHPO4, 5 mM NaH2PO 4 and 0.1 M NaCI. electrolyte. However, the reversibility vs. irreversibility shown in Figs. 3 and 4 cannot be explained at this stage of the present work. The highest catalytic effect was observed with the use of buffer I. The stability of the polymer film was examined by repeatedly cycling the electrode within a narrow potential window as shown in Fig. 4. The usual adverse adsorption effect onto the electrode which resulted in the fouling of its surface and the significant attenuation of the voltammetric current signal was not observed. The anodic peak current values Ipa correlate linearly with the square root v l / 2 of the scan rate for all the electrolytes used, indicating that the charge transfer process is controlled mainly by solution mass transport as illustrated in Fig. 5. Moreover, the peak potential Era exhibited a positive linear shift with the logarithm of the scan rate indicating the irreversible nature of the electrode reaction" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003863_10402004.2010.512117-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003863_10402004.2010.512117-Figure2-1.png", + "caption": "Fig. 2\u2014Thermal network of thrust ball bearing, inner race lubricated.", + "texts": [ + " In order to address this issue with regard to parameter uncertainties, a specific study on CD was undertaken based on experimental measurements in a wind tunnel for several adjacent balls as is the case in a bearing. The fraction of lubricant in the air X is then adjusted based on the experimental and numerical global power losses and the corresponding expression for the drag force is compared with the classic formula obtained by Parker and Signer (13). Finally, it is demonstrated that, for highspeed applications, rolling forces must be included in any realistic modeling attempt. The test machine described in Fig. 2 is composed of one driving shaft supported by two preloaded angular-contact ball bearings fixed to a rigid housing. The outer ring of the test bearing on the driven shaft (in grey in Fig. 2) is mounted in a separate housing equipped with strain gauges to measure the bearing friction torque. The driven shaft is mechanically isolated from the driving shaft by revolute and prismatic joints in order to eliminate any force or moment transfer. The test bearing is one of an Xmounted pair and it is loaded via a hydraulic jack imposing a controlled axial thrust on the outer ring of the other bearing of the pair. Jet lubrication is employed and the lubricant is conveyed to the inner races by grooves on the driven shaft and then splashed by centrifugal effects to lubricate and cool down the bearings" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003770_s00138-006-0066-7-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003770_s00138-006-0066-7-Figure1-1.png", + "caption": "Fig. 1 Schematic of the laser cladding process", + "texts": [ + "eywords Laser cladding \u00b7 Trinocular CCD-based optical detector \u00b7 Image processing \u00b7 Recurrent neural network \u00b7 Perspective transformation Laser cladding is an advanced laser material processing technique, which has been used in manufacturing, part M. Iravani-Tabrizipour \u00b7 E. Toyserkani (B) Department of Mechanical and Mechatronics Engineering, University of Waterloo, 200 University Avenue West, Waterloo, ON, Canada N2L3G1 e-mail: etoyserk@uwaterloo.ca repair, rapid prototyping of functional components, and coating for a decade. In this process, a laser beam melts both powder particles and a thin layer of the moving substrate to create a layer (clad) on the substrate with a thickness ranging from 0.1 to 2 mm as shown in Fig. 1. For part fabrication or prototyping using this technique, similar to other layer-based techniques, a threedimensional CAD solid model is used to produce a part without intermediate steps. This approach to produce a mechanical component in a layer-by-layer fashion allows industry to fabricate a part with features that may be unique to laser cladding technique. These features include a homogeneous structure, enhanced mechanical properties, deposition of multiple materials and production of complex geometries" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure3.1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure3.1-1.png", + "caption": "Fig. 3.1. Open and closed chain in an assembly manipulation task", + "texts": [ + "11)-(2.3.18)) when forming the expres sion for S. So, we conclude that such an approach allows a better adap tation of model forming procedure to the system considered. Chapter 3: Closed Chain Dynamics In Chapter 2 we derived an algorithm which solved the complete dynamics of manipulation robots. Let us note that the algorithm considered a manipulator as an open kinematic chain. This fact restricts the set of manipulation tasks which can be analyzed. Let us consider a peg-in-the -hole assembly task (Fig. 3.1). In such a task the manipulator changes its configuration. In the phase of transferring the object it is an open kinematic chain (Fig. 3.1a) and in the phase of insertion a closed chain since its last segment is connected to the ground by means of a joint permitting one translation and one rotation (Fig. 3.1b) There is another reason for studying closed chains. There exist some special manipulator configurations which contain closed chains (Fig. 3.2). Thus, in order to solve their dynamics in any manipulation task one has to solve closed chains. Recently, certain efforts have been made towards solving the closed 151 chain dynamics. Paragraph 3.2. provides a short review of these results. What is common to most of these approaches to closed chains is their generality. The methods are derived so as to cover a general kinematic scheme containing arbitrary open or closed chains", + " We consider two cases of closed chains interesting for practice. The first case appears in some special robot mechanisms which are designee to contain closed chains (e.g. manipulator of Fig. 3.2 or ASEA robot). The second case appears in assembly manipulation for instance, or to be more general, this case refers to any manipulation task in which the gripper is not allowed to more freely but its motion is subject to some constraints resulting from the interaction with the environment. An illustration is given in Fig. 3.1. This case also covers the prob lems of bilateral manipulation. 152 Let us also mention the third case of closed chains. These are problems of biped gait in double support phase or multilegged walking mechines, but they will not be discussed here. Paragraph 3.3 discusses the first case and 3.4 the second. These two paragraphs develop the theory which is necessary for the solution of concrete problems. Paragraph 3.6 is devoted to the actual problems of constrained gripper motions. Paragraph 3.4 discusses the theoretical and practical aspects of con strained gripper motion. The dynamic models of such robot motions are derived. These models can be used to obtain the solutions either to the direct or to the inverse dynamic problem. These solutions assume that the constrains imposed on gripper motion are satisfied at anytime instant. Thus the initial conditions also satisfy the constraints. Let us consider the peg-in-the-hole assembly task (Fig. 3.1) in which an open chain becomes closed when the peg enters the hole. The models derived in 3.4 are valid when the peg has already entered the hole. Thus, the problem of insertion still remains to be solved. It usually involves the impact which ens~res the initial conditions which satisfy the insertion constraints. Paragraph 3.5 is devoted to the solution of this problem. This paragraph will briefly describe the main results achieved in closed chain dynamics. The method [1] represents a general theory for formulating dynamic equations for robots of arbitrary configuration", + " discussed the theoretical aspects of constrained gripper motions. The dynamic models of such robot motions were derived. In the discussion of model solution it was assumed that the initial state sat isfies the constraints imposed. Let us consider two time intervals T1 and T2 . In the interval T1 the gripper is not subject to any constraint. It is a free motion when the robot is not in contact with the constraint. If a peg-in-the-hole assembly problem is considered, the interval T1 represents the phase in which the peg is moved towards the hole (Fig. 3.1a). We can calculate the nominal dynamics in this time interval in such a way that the peg comes into the hole without any collision, i.e., that the terminal state of interval T1 satisfies the constraint. In the interval T2 the peg is inserted into the hole. The terminal state of T1 becomes the initial state for T2 . The constraint is imposed and the chain is closed. In the nominal dynamics calculation we prescribe this insertion and the reactions (for instance we prescribe reactions to equal zero)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003961_978-1-4419-7267-5-Figure3.7-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003961_978-1-4419-7267-5-Figure3.7-1.png", + "caption": "Fig. 3.7 Illustration of nodes on a serial-chain system", + "texts": [ + "2 on page 162 extends the \u03c6 operator and related recursions to more general multibody systems such as tree-topology systems, where the link numbering can be arbitrary and the \u03c6 and \u03c6\u2217 operators are not necessarily triangular. Robotic multibody systems typically have distinguished frames of interest (also referred to as nodes) that need to monitored and/or controlled. The end-effector frame is an example of such a node for robotic arms and is generally located on 54 3 Serial-Chain Kinematics the outer-most link. As illustrated in Fig. 3.7, these nodes may not coincide with the body frames or the hinge frames. Also, a body can have none to multiple such nodes. In this section, we explore the Jacobian operators that define the differential relationship between the generalized velocities of the system and the spatial velocities of such distinguished nodes. Since individual bodies can have multiple nodes, we introduce the notation O i k to denote the ith node on the kth link. The number of nodes on the kth body is denoted nnd(k). A single end-effector frame located on link 1 would be denoted O 0 1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003234_1.1809637-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003234_1.1809637-Figure1-1.png", + "caption": "FIG. 1. Principle of laser polishing.", + "texts": [ + " Unlike laser polishing, conventional abrasive polishing techniques have limitations that include low polishing rate, difficulty in process automation, difficult to polish a welldefined area, high consumable cost, waste disposal issues, etc. Laser polishing is a single step process that can be used to polish selected areas and complex three-dimensional surfaces. The objective of the present work is to study the effect of laser remelting on surface properties such as topography, roughness, reflectance, hardness, and corrosion resistance of 304 stainless steel. The principle of laser polishing is shown in Fig. 1. The laser pulse melts the tops of the surface irregularities and a) Electronic mail: tuananh_mai@yahoo.com 1042-346X/2004/16(4)/221/8/$22.00 221 Downloaded 20 Nov 2012 to 139.184.30.132. Redistribution subject to LIA successive pulses produce the desired level of remelting in the impingement area. In the molten state, the initial rough profile on the surface is smoothed out under the force of surface tension and gravity. The irradiation time must be longer than the material viscous damping time to allow a proper material flow" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002527_pu2003v046n04abeh001306-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002527_pu2003v046n04abeh001306-Figure4-1.png", + "caption": "Figure 4. The real parts of the characteristic exponents for rotational motion about the vertical axis for different relations between the principal moments of inertia: (a) I1 5, I2 6, I3 7, and condition 1 is fulfilled; (b) I1 4, I2 5, I3 6, and condition 1 is not fulfilled (m 1, g 100, a1 9, a2 4, h 1, d 0:2).", + "texts": [ + " Let E be the energy value corresponding to o . This Lemma clearly shows that for d 6 0 the stability of the rotation depends on its direction (clockwise or counterclockwise). This fact discriminates nonholonomic systems from Hamiltonian systems. In addition, for the rotational motion to be stable the distribution of mass within the body must satisfy the condition FGD > 0, and the angular velocity must be sufficiently large. There exist bodies whose rotational motions in both directions are unstable. In Fig. 4, graphs of the real parts of the eigenvalues are shown. In diagram (a), the `geometrodynamical' condition 1 is satisfied, while in diagram (b), condition 1 is not satisfied. These graphs indicate that, at energy values E for which o0 < o , an unstable rotation about the vertical axis always exists, and the solutions tend to this motion as t! \u00ff1. A typical phase portrait of the Poincare\u00c2 map for a paraboloid (E > E ) is shown in Fig. 5. All trajectories wind onto the stable, steady rotational motion for t! 1 and on the unstable rotation for t! \u00ff1. Simulations have shown that there are no other attractors in the phase space. In Ref. [5], it was shown that in the vicinity of the critical frequency, as the stability is lost o0 > \u00ffo , o0 \u00ffo , the Andronov \u00b1Hopf theorem on the birth of a cycle can be applied. In the vicinity of the rotation about a vertical axis, a stable limiting cycle arises. This cycle corresponds to a periodic solution of (4). Figure 4a indicates that, for o0 < o , o0 o and with the direction of time reversed, the theorem on the birth of a cycle applies again. This is called a reverse Hopf bifurcation [the same result follows from the reversibility of (11)]. The results of simulations presented in Fig. 6 clearly show that, for t! 1, in addition to the (stable) Karapetyan cycle, two other stable cycles appear (these two cycles persist as well when the physical parameters are slightly disturbed). The appearance of these additional cycles can hardly be predicted analytically", + " Next, we present the results of numerical simulations of the above-described three-dimensional map for various values of the energy. Two models, an ellipsoid and a paraboloid, are considered. The ellipsoid model is more complex because it admits overturns of the body. For the simulations, we set the following dimensions (both for ellipsoid and paraboloid) I1 5 ; I2 6 ; I3 7 ; m 1 ; g 100 ; 17 for the paraboloid (7) we assume a1 9, a2 4, h 1 and for the ellipsoid, b1 3, b2 2, b3 1. In both cases, the principal radii of curvature at the point r1 r2 0, r3 1 are equal; the stability is described by Fig. 4a, the critical value of the energy E is 1300, and the frequency of rotation about the vertical is o 18:516 . . . Here, lengths are measured in centimeters, masses in kilograms, and times in 10\u00ff1=2 s. A preliminary numerical analysis shows that the whole set of feasible energies Emin;1 , where Emin mgh 100, can be divided into five regions within which the dynamics is similar for various E. I. E > E . In the phase space, only rotation about the vertical in one direction is possible. This rotation is asymptotically stable (the map has a regular attractor; Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002418_cdc.2001.980200-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002418_cdc.2001.980200-Figure2-1.png", + "caption": "Figure 2: Compass gait biped robot", + "texts": [ + " Because the characteristic multipliers mi are the eigenvalues of the linear map DP(x*), they determine the stability of the Poincarb map P(xk), and hence the stability of the periodic solution. Three cases are of importance: 1. All mi lie within the unit circle, i.e., Im,l < 1,Vi . The map is stable, so the periodic solution is stable. 2. All mi lie outside the unit circle. The periodic solution is unstable. 5 Example 5.1 Model A model of the compass gait biped robot is discussed in detail in [3, 61. A summary is included here for completeness. The biped robot can be treated as a double pendulum, with point masses m H and m concentrated at the hips and legs respectively. Figure 2 provides a schematic representation and identifies other important parameters, lengths a and b, and incline angle y. The robot configuration is described by the support angle 0, and the non-support angle O n S . The dynamic equations describing the robot can be written (26) n / f ( s ) e + ~ ( ~ , 4 ) e + ~ g ( ~ ) 1 = o where 0 = [ena Os]'. The state vector is therefore 2: = IS, 8, e,, B,]' t R4. The matrices of (26) are given by, where 0, = 0, -On,, (3 = b/a , p = mH/m, and g = 9.8 is the gravitational constant" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003038_diacare.17.5.387-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003038_diacare.17.5.387-Figure1-1.png", + "caption": "Figure 1\u2014Schematic diagram of hollow-fiber probe andflow-cell with a needle-type glucose sensor for extracorporcal glucose measurement in the miniaturized subcutaneous tissue glucose monitoring system based on microdialysis sampling method. A: Hollow-fiber probe. In an inner cannula, the perfusate is transported to the tip of the probe, diffused through the dialysis membrane, and the dialysate then comes out through an outlet cannula. B: Sensor flow-cell.", + "texts": [ + " With a single dialysis hollow-fiber probe, subcutaneous tissue glucose concentrations can be monitored continuously for up to 4 days without any in vivo calibrations and for 7 days by introducing in vivo calibrations in healthy and diabetic volunteers. RESEARCH DESIGN AND METHODS Development of the system The miniaturized extracorporeal monitoring system consists of a microdialysis hollow-fiber probe, a flow-cell with a needle-type glucose sensor for extracorporeal sensing, a precision microroller pump, and a monitoring system. A microdialysis Cuprophan hollow-fiber probe (Fig. 1A) was used with a molecular cutoff of 50,000 dalton (regenerated cellulose dialysis hollow-fiber membrane, inner diameter: 0.20 mm; outer diameter: 0.22 mm; length: 15 mm; AM-Neo-2000H, Asahi Medical, Tokyo, Japan). The microdialysis hollow-fiber probe was steadily perfused with isotonic saline solution (0.15 M NaCl in water) using a microroller pump (RA-20GM-CA20-06, Sayama Precision, Sayama, Japan) at a flow rate of 120 fiVh. The perfusate is transported through an inlet cannula (polyimide coated fused-silica tube, outer diameter 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003815_j.mechmachtheory.2009.06.001-Figure20-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003815_j.mechmachtheory.2009.06.001-Figure20-1.png", + "caption": "Fig. 20. A defective generator with four prismatic pairs.", + "texts": [ + " By the same token, one can demonstrate that if two screw pitches are equal, then two P pairs must not be perpendicular to u. For instance, two chains of Fig. 18 actually generate the 3-dof pseudo-planar motion rather than 4-dof X-motion. Furthermore, if three screw pitches are equal and one P pair is perpendicular to the parallel H axes, as shown in Fig. 19, these chains are trivial chains of a subgroup of pseudo-planar motion and never generate X-motion. One additional defective generator, a series of four prismatic pairs that generates {T} instead of {X(u)}, is displayed in Fig. 20 for completeness. Case B. A product of two factors is a 2D subgroup and one among the other two factors is included into this subgroup. For example, p1\u2013p2; A2 2 line\u00f0A1; u\u00deor\u00f0A1A2\u00de u \u00bc 0 ) fH\u00f0A1; u; p1\u00degfH\u00f0A2; u; p2\u00deg \u00bc fC\u00f0A1; u\u00deg; A3 2 line\u00f0A1; u\u00de ) fH\u00f0A3; u; p3\u00deg fC\u00f0A1; u\u00deg ) \u00bdfH\u00f0A1; u; p1\u00degfH\u00f0A2; u; p2\u00deg {H(A3, u, p3)}{H(A4, u, p4)} = {C(A1, u)}{H(A3, u, p3)}{H(A4, u, p4)} = {C(A1, u)}{H(A4, u, p4)} \u2013 {X(u)}. Hence, three axes must not be coaxial. Fig. 21a shows such a defective chain with three coaxial H pairs" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure18.1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure18.1-1.png", + "caption": "Fig. 18.1 (a) Construction of a stator vibrator and (b) vibration mode and operating principle", + "texts": [ + " Therefore, we herein consider ultrasonic motors that use a thin annular plate stator vibrator that vibrates in the non-axisymmetric ((1,1)) mode, in which a single vibrating element is arranged. This type of ultrasonic motor has a simple structure and is easier to position around a rotating shaft than a rectangular plate-type ultrasonic spindle motor having similar output power [1]. The stator vibrator using an annular plate was designed by the finite element method analysis (ANSYS), as shown in Fig.18.1(a). The total thickness of this stator vibrator is 0.6 mm. Its vibration modes, including the movement of a vibratingpiece arranged in the plate, are shown in Fig.18.1(b). The stator vibrator is composed of piezoelectric ceramics in the form of an annular plate to which thin metal plates are bonded to the upper and lower surfaces, and the electrodes are formed by two piezoceramic sections. Poling in the two sections is in the thickness direction, but in opposite directions in each section. Therefore, by applying a driving electric voltage of the same phase to each electrode, the non-axisymmetric ((1,1)) mode shown in Fig.18.1(b) can be generated. At the same time, the vibrating-piece has a flexural displacement with phase difference from the non-axisymmetric ((1,1)) mode, as shown in the figure, so that an elliptic motion is generated at the tip of the vibrating-pieces. Such a motion causes the rotor to rotate by a friction force. This stator vibrator had a resonance frequency of 172 kHz and an input admittance of 163 mS. The stator vibrator is positioned on the measurement apparatus shown in Fig.18.2 and is supported by four screws at ends of T-type bars on both sides of the vibrator" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002721_rob.10099-Figure10-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002721_rob.10099-Figure10-1.png", + "caption": "Figure 10. A linkage that is simultaneously an exceptional linkage, a trivial linkage and a linkage with partitioned mobility.", + "texts": [ + " (43), and it follows that F f i dim Ac 1,5 dim Acc 1,5 dim Aa 1,5 8 4 4 3 3. (48) One practical application of this multi-loop spatial linkage is as a three-dimensional translating platform, where the input can be conveniently located in the three helical pairs, which can be conveniently replaced by revolute or prismatic pairs that connect the base with each of the connecting legs. In fact, it can be stated that exceptional linkages are the simplest but complete parallel mechanisms. Example 4: Consider the eight-link spatial linkage shown in Figure 10. The first four prismatic joints, with arbitrary directions, generate the subalgebra p3 associated with the subalgebra of spatial translations. Similarly, the last four revolute joints, with intersecting axes, generate the subalgebra s, associated with the subalgebra of spherical displacements. Then, it should be clear that Ac 1,5 p3 and Acc 1,5 sQ . Thus Aa 1,5 p3 sQ 0 . Hence, links 1 and 5 are links that partition the mobility of the kinematic chain, and the kinematic chain has partitioned mobility" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000019_j.ymssp.2020.107373-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000019_j.ymssp.2020.107373-Figure4-1.png", + "caption": "Fig. 4. Modelling of the single teeth of a spline.", + "texts": [ + " Thus, the force can be calculated by f i \u00bc Kb d\u00f0 \u00de3=2 \u00bc Kb xcosui \u00fe ysinui c0\u00f0 \u00de3=2 H xcosui \u00fe ysinui c0\u00f0 \u00de \u00f06\u00de where Kb is the Hertz contact stiffness, and H x\u00f0 \u00de represents Heaviside function. Therefore, the bearing force and contact force components in x and y directions can be expressed as F \u00bc XNb i\u00bc1 f i \u00bc XNb i\u00bc1 Kb xcosui \u00fe ysinui c0\u00f0 \u00de3=2 H xcosui \u00fe ysinui c0\u00f0 \u00de h i cosui \u00f07\u00de Fx \u00bc XNb i\u00bc1 f icosui \u00bc Fcosui Fy \u00bc XNb i\u00bc1 f isinui \u00bc Fsinui \u00f08\u00de The meshing stiffness of a spine pair is based on the Weber energy method [36,37], which is also called the material mechanics method. It is assumed that the tooth is a non-uniform cantilever beam, as shown in Fig. 4. The effective length is Le, which is equal to the distance from the base pointM to the addendum circle. The effective length of the tooth is divided into a series of rectangular elements along the axis of symmetry, denoted by the symbol i. Fj is the load transmitted by any point j, and dj is the deformation of a single tooth in the Fj direction at point j. The gear deformation consists of three parts of elastic deformation: 1, the bending deformation, shear deformation, and axial compression deformation of the tooth portion; 2, the base deformation of the transition fillet connected to the gear teeth; and 3, the contact deformation between the tooth causing the contact stress" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002863_02640410410001730179-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002863_02640410410001730179-Figure4-1.png", + "caption": "Figure 4a. Angel (a) of upper body and arm (left-arm) plane to Z Axis, showing club \u2018\u2018below\u2019\u2019 plane. Figure 4b. Angle (b) of upper body and arm (left-arm) plane to target line (parallel to X axis). Position shown would result in a negative angle.", + "texts": [], + "surrounding_texts": [ + "position data were used in the present study, and the fact that the limb motion takes place at lower frequencies, 50 fields per second was deemed appropriate. Also, only accurate (to target line) sequences in which the ball and clubhead appeared to be coincident at impact were used, so as to minimize clubhead position errors around ball contact. While 50 fields per second made the exact moment of impact difficult to assess, by using clubhead and ball velocities from previous literature (Sprigings & Neal, 2000), typical digitizing errors could be estimated. This resulted in timing errors of approximately 1.5 ms if ball and club appeared coincident on the video. As the time of impact in golf is 5 ms (Cochran & Stobbs, 1968), this was deemed acceptable. It was therefore possible to identify one sequence for each golfer in which ball and clubhead appeared coincident at impact and had been rated as being along the target line by golfer and experimenter.\nEach sequence started at the first observed motion of the clubhead during the backswing and continued until ten fields after impact. Even though only the downswing (from reversal of clubhead direction at the top of the backswing until impact) was used for the planar analysis, this ensured that there were sufficient data before and after the period of interest for post-digitizing smoothing. The anatomical landmarks, club markers and ball were digitized in every field by the same operator using the Ariel Performance Analysis System running on a Viglen Contender 700 microcomputer with a 17 inch monitor. Three-dimensional object space coordinates were obtained from the 2 twodimensional images using a direct linear transformation (Abdel-Aziz & Karara, 1971; Karara, 1980). Coordinates were then smoothed using a Butterworth fourth-order reverse filter with a cut-off\nfrequency of 10 Hz for the body landmarks and 20 Hz for the club handle, bottom of the club shaft, clubhead centre and ball. These frequencies were chosen by visual inspection of the frequency spectrum for each point.\nThree segments were defined. First, the left shoulder girdle segment was bounded by the 7th cervical vertebra and the left glenohumeral joint centre. Second, the left arm was defined as being between the left glenohumeral and left wrist joint centres. Finally, the club segment linked the left wrist joint centre and clubhead. The vertex and 3rd metacarpophalangeal joint were not included in any analysis, and were solely used to assist in identification of segments. The base of club handle and bottom of shaft markers were also not included in the subsequent planar equations, but were used solely for calculation of digitization accuracy (see below).\nThe equation of a plane was calculated by entering the three-dimensional coordinates of the 7th cervical vertebra, left glenohumeral and left wrist joints into a Microsoft Excel spreadsheet. This plane (\u2018\u2018left-arm plane\u2019\u2019) containing the left shoulder girdle and left arm segments was given in the form ax + by + cz + d = 0, where a, b, c and d represent coefficients of the standard plane equation (Smyrl, 1978).\nThis plane was projected onto the yz and xz reference planes. The angles of these projections to the z reference axis (aligned on the ground at 908 to the target line) and the target line (parallel to the x axis) were then computed. The former gave the inclination of the left-arm plane to the horizontal (a), and the latter (b) provided information on the relationship of the left-arm plane to the target line (an angle of 08 showing that left-arm plane and target line were parallel). These angles are shown in Figures 4a and 4b. The consistency of these angles was then assessed by examining angle \u2013 time plots for the whole of the downswing phase. If the left-arm plane remained constant throughout this period as suggested in previous models, it would be expected that these two angles (a and b) would not change.\nThe perpendicular distance of the clubhead centre from the left-arm plane (Smyrl, 1978) was computed, giving an objective measure of whether the clubhead lay in the same plane, and therefore if the downswing could be considered planar as assumed by previous studies.\nDigitizing accuracy was defined as the difference between known locations and reconstructed positions (Challis, 1997). This was determined in two ways. First, 16 known test points (independent of the control points) evenly distributed on the calibration frame were digitized for 10 fields and the root mean square error between object and unsmoothed image\nD ow\nnl oa\nde d\nby [\nU PM\n] at\n1 1:\n32 2\n4 D\nec em\nbe r\n20 14", + "coordinates were calculated. Second, the calculated club shaft length (as defined as the distance between the unsmoothed digitized data for the club handle and the bottom of the club shaft) from one sequence of 60 fields was compared with a real measured value (to an accuracy of+ 1.0 mm) of club shaft length.\nTo estimate digitizing precision (Challis, 1997), one sequence was digitized six times and the unsmoothed data from each digitization were then used to calculate the left-arm plane. \u2018\u2018Typical errors\u2019\u2019 (Hopkins, 2000) were calculated for the two plane angles and the clubhead distance, showing the precision of each of the computed variables. Typical error was used because it has been pointed out (Hopkins, 2000) that other measures, such as limits of agreement, are too large as a reference range for making a decision about a change in a participant\u2019s measurements.\nFinally, coordinate data were also output to Virtual Reality Modelling Language files running on Cosmo Player software (Computer Associates, Islandia, NY, USA) to aid three-dimensional visualization of the left-arm plane, clubhead position and reference axes.\nThe root mean square error of the 16 static test points were 7.1 mm, 9.8 mm and 5.1 mm for the x, y and z directions respectively, representing 0.4%, 0.5% and 0.3% of the calibrated volume. The mean club shaft length calculated from the digitized data was 687.5 (s = 19.4) mm, compared with a real measurement of 696 mm, giving a mean error of 8.5 mm (1.2%) and a root mean square error of 20.1 mm (2.9%).\nRepeated digitization of one sequence gave typical errors of+ 4.18 and+ 2.88 for the angle between the left-arm plane and the z axis (a) and target line (b) respectively, and+ 0.07m for the clubhead distance from the left-arm plane. These represented 8.5%, 8.0% and 11.5% respectively of the range in these variables for the sequence digitized.\nAngle of left-arm plane to horizontal (a)\nThe angle between the left-arm plane and the horizontal (z axis) is shown in Figure 5. Initial (top of backswing) angles were between 1268 and 1468 for the different players. All golfers then decreased the angle throughout the downswing, until at impact the mean angle was 1028 (range 98 \u2013 1088). This indicated that the left-arm plane \u2018\u2018steepened\u2019\u2019 during the downswing. Four golfers continued to decrease their angle through impact, but participants 2 and 3 increased their angles slightly before impact. Player 5 showed a decrease throughout the latter half of his downswing, but then maintained a constant angle from 60 ms before impact until ball strike.\nAngle of left-arm plane to target line (b)\nThe angle between the left-arm plane and the target line is shown in Figure 6, with a value of 08 indicating alignment between the left-arm plane and intended target line. Four of the golfers (participants 1, 4, 5 and 6) started the downswing with the left-arm plane aligned at an angle of greater than 08 (range 0 \u2013 108), indicating very slight anticlockwise (from above for a right-handed\nD ow\nnl oa\nde d\nby [\nU PM\n] at\n1 1:\n32 2\n4 D\nec em\nbe r\n20 14", + "player) plane rotation past the target line. In all four cases, this was followed by a clockwise rotation of approximately 258 (range 22 \u2013 348) during the first half of the downswing. However, three golfers started with large negative left-arm plane to target line angles (clockwise) at the start of the downswing and a slight increase during the first half of the downswing. During the second half\nof the downswing (from approximately 100 ms before impact until ball contact), all participants increased the left-arm plane to target line angle (anticlockwise rotation). At impact, four golfers had obtained positive angles (rotation \u2018\u2018past\u2019\u2019 the target line) of 28 to 338, but the other three had not managed to rotate the left-arm plane to the target line (798 to \u2013 28).\nFigure 5. Angle (a) of upper body and arm (left-arm) plane to horizontal (Z axis) throughout downswing. Participant numbers are followed by handicap in brackets\nFigure 6. Angle (b) of upper body and arm (left-arm) plane to horizontal (X axis) throughout downswing. Participant numbers are followed by handicap in brackets\nD ow\nnl oa\nde d\nby [\nU PM\n] at\n1 1:\n32 2\n4 D\nec em\nbe r\n20 14" + ] + }, + { + "image_filename": "designv10_6_0003808_j.jsv.2007.05.053-Figure16-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003808_j.jsv.2007.05.053-Figure16-1.png", + "caption": "Fig. 16. Torsion bar for free vibration experiment.", + "texts": [ + " Parameters that are difficult to determine include tire stiffness, clutch and band friction characteristics, torque converter output torque and system damping, to name some. An experiment was developed to simultaneously excite low-frequency free vibration of the vehicle driveline and high-frequency transient vibration from impacts. On the test rig, the automatic transmission is placed in park (grounding the rigid body motion). To apply the load a \u2018torsion bar\u2019 has been rigidly attached to each wheel rim (Fig. 16). An electromagnetic release mechanism is attached to the end of the torsion bar. On each side up to 20 kg of mass is evenly loaded onto the bar via the electromagnets. Turning off the power to the electromagnets releases the weights, freeing the stored potential energy. (The masses are dropped onto thick rubber pads to minimise vibration transmitted through the floor and test beds to the powertrain system.) The loading twists the driveline from the wheels up to the ARTICLE IN PRESS A.R. Crowther et al" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003391_0076-6879(88)37005-9-Figure6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003391_0076-6879(88)37005-9-Figure6-1.png", + "caption": "FIG. 6. Enzyme reactor electrode for measurement of sucrose and glucose using an immobilized invertase reactor and a GOD electrode.", + "texts": [ + " Part of the hydrogen peroxide formed in the GOD reaction inside the membrane is consumed by the HRP-catalyzed conversion of bilirubin, and the anodic current is decreased depending on the bilirubin concentration. The slope of the calibration curve is 0.8/xA/mM/cm 2 between 0.005 and 0.05 mM bilirubin. For successive measurements of glucose and disaccharides, the GOD electrode described may be combined with enzymatic disaccharide hydrolysis catalyzed by an immobilized disaccharidase in the measuring cell. For sucrose determination, invertase is used. The enzyme is fixed on silk which is then installed on a rack mounted under the lid of the measuring cell (Fig. 6). Before the immobilized invertase is immersed in the measuring solution, the endogenous glucose concentration of the sample is determined. Addition of the sample causes a current increase of the GOD-covered electrode which is completed after 30 sec. At this time the immobilized invertase is inserted in the stirred solution, catalyzing the splitting of sucrose into D-fructose and a-D-glucose which spontaneously mutarotates to form fl-D-glucose. The rate of fl-D-glucose formation depends linearly on the sucrose concentration in the measuring cell up to 10 mM" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure14.9-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure14.9-1.png", + "caption": "Fig. 14.9 Fabricated micro ECF pump modules", + "texts": [ + " Comparing to the original electrode with one pin and hole electrode, the isomorphic pair of electrodes shown in Fig.14.5, have much potential to supply the output pressure by the ECF jet. The magnitude of the output pressure in the case of the six pins and holes type of electrode has a maximum potential to generate the strong ECF jet in our experiments. Design and Fabrication of Micro Pump for Functional Fluid Power Actuation System 161 According to the experimental results of pumping performance, the prototype of the cylindrical micro pump module as shown in Fig.14.9 is designed and fabricated. A chassis of the pump is fabricated at one process by a 3D optical rapid prototyping method; a micro stereolithography system. Figure 14.10 shows a comparison between the output pressure of the previous developed planar ECF pump [8] and the developed cylindrical ECF pump. The magnitude of the output pressure in the case of the cylindrical ECF pump is much larger than one in the case of the planar ECF pump. The size of the cylindrical ECF pump is much smaller than the planar ECF pump, volume ratio of 1/12" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003457_20080706-5-kr-1001.00138-Figure6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003457_20080706-5-kr-1001.00138-Figure6-1.png", + "caption": "Fig. 6. The T-Phoenix UAV.", + "texts": [], + "surrounding_texts": [ + "In this section, we present the real-time experimental results obtained when applying the proposed controllers, (24) , (18) , (25) and (47) to the T-Phoenix UAV (see Figures 6)." + ] + }, + { + "image_filename": "designv10_6_0002450_10402009608983585-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002450_10402009608983585-Figure1-1.png", + "caption": "Fig. 1-Film thickness measurement in a rolling point contact.", + "texts": [ + " Mode of replenishment These areas are addressed in this paper. The aims of this study therefore, were two-fold to measure lubricant film thickness under starved conditions at realistic bearing operating temperatures and to correlate these results with those of lubricant reflow around the contact. EXPERIMENTAL Test Conditions and Materials Lubricant film thickness has been measured for a rolling point contact at three bulk temperatures: 20\u00b0, 50' and 80\u00b0C. A diagram of the test device is shown in Fig. 1. Thin film optical interferometry was used to measure film thickness in the center of the contact. This method has been described in earlier papers (12). It is capable of measuring films in the range 2-300 nm with a resolution of 2 nm. The bearing contact is simulated by a steel ball loaded and driven in nominal pure rolling by a rotating glass disc. The underside of the disc is coated with a chromium semireflective film overcoated by silica. The experimental test conditions are summarized in Table 1", + " D ow nl oa de d by [ Y or k U ni ve rs ity L ib ra ri es ] at 1 7: 52 0 2 Ja nu ar y 20 15 Starvation and Reflow in a Grease-Lubricated Elastohydrodynamic Contact 703 V1 u I bulk grease I E I I 1 I TIME m E R of DISC REVOLUTIONS (a) Fig. ll-Flow balance in grease lubrication. mechanisms were identified: inlet displacement of lubricant ;~ncl cross or squeeze flow from the contact. The reflow meclianis~n in grease lubrication is more complex as it depends l~potl oil release from the grease and its availal~ility close to the crlritact; hence, it is time dependent. Diffel-cnt regimes can be identified depending upon the doniinant flow mechanisms, as Fig. 1 1 demonstrates. After the initial charge of grease, the bulk is rapidly pushed away from the track producing gross starvation of the inlet (I) . Grease that has passed through the contact in the initial overrolling is shear degradccl arid cleposited in the rolling track as thickencr/oil glonicratcs and inlu reflow . , . , . , . , . , 0 50 100 150 200 2.50 300 350 400 NUMBER of DlSC REVOLUTIONS (b) free base oil. This accords with the view expressecl by Scarlett (2) of a highly worked grease layer deposited in the track" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000511_j.addma.2021.102277-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000511_j.addma.2021.102277-Figure3-1.png", + "caption": "Fig. 3. (a) Machined specimens geometry tested using MTS Minibionix servo-hydraulic machine; (b) as-built specimens geometry tested using Zwick Roell Z250 SE machine for RT test and Zwick Roell Z050 TH servo-hydraulic testing machine for HT test in TEC-Eurolab.", + "texts": [ + " Ten measurements were done in different areas of the polished surface of the sample. The uncertainty for microhardness measurement was calculated as standard deviation on the measurement. Four different specimen types were produced in order to evaluate mechanical properties with tensile-test: vertical and horizontal (specimen axis respectively parallel and perpendicular to the building direction) machined specimens, vertical as-built specimens, and finally samples of pure Mo produced using conventional production routes. Two kinds of geometries were designed. The first one (Fig. 3(a)) was optimized for the testing at the Department of Industrial Engineering (University of Padua, Padova, Italy), while the second geometry (Fig. 3 (b)) for the tests at room temperature (RT) and high temperature (HT), in collaboration with TEC-Eurolab (TEC-Eurolab Srl, Campogalliano (MO), Italy). Vertical and horizontal specimens, of both geometries, were additively manufactured using optimized process parameters in order to obtain fully dense components. Once the production process was completed, the samples were removed from the platform by EDM. Then, specimens produced according to the design of Fig. 3(a) were machined in order to obtain homogeneous surface finishes and to eliminate distortions caused by the production process. These vertical and horizontal specimens are named as \u201cAM.m.V\u201d and \u201cAM.m.H\u201d, where \u201cAM.m\u201d indicates \u201cadditively manufactured.machined\u201d, while \u201cV\u201d and \u201cH\u201d stands for \u201cVertical\u201d and \u201cHorizontal\u201d, respectively. The third type is an additively manufactured vertical specimen, produced according to the design of Fig. 3(b), which has been tested as built at RT and HT (600 \u25e6C). In the following, this type of specimen will be called \u201cAM.asb.V\u201d and \u201c600\u25e6C_AM.asb.V\u201d, respectively, where \u201cAM.asb\u201d stands for \u201cadditively manufactured.as built.\u201d. The parameters used for specimens production were P = 150 W, hd = 0.04 mm, v = 750 mm/s, and t = 0.02 mm. Finally, the fourth type of samples was produced according to geometry of Fig. 3(a), starting from a ground and annealed bar with an initial diameter of 10 mm, produced by Plansee. In the following, the Plansee bar is named as \u201cG-A bar.m\u201d which indicates \u201cGround-Annealed bar.machined\u201d. For each test series, five samples were obtained and three of them were tested for mechanical properties evaluation. A MTS Minibionix servo-hydraulic testing machine having a load capacity of 15 kN equipped with a MTS TestStar IIm controller, has been adopted to perform tensile static tests on machined, i.e. \u201cAM.m.V\u201d and \u201cAM.m.H\u201d, and \u201cG-A bar.m\u201d specimens. A displacement rate equal to 0.3 mm/min has been applied under displacement control in agreement with ASTM E8/E8M \u2212 16a Standard [40], which suggests a crosshead speed equal to 0.015 mm/mm/min of the original length of reduced parallel section, i.e. 20 mm (see Fig. 3(a)). The uniaxial MTS extensometer Model No. 632.29 F-30 having gauge length of 5 mm has been adopted. The MTS controller acquired the applied load from the load cell of the testing machine and the strain from the extensometer during each static test. A Zwick Roell Z250 SE testing machine having a load capacity of 250 kN and being equipped with a testControl II controller, has been adopted to perform tensile static RT tests on \u201cAM.asb.V\u201d specimens. A strain rate equal to 0.015 mm/mm/min has been applied under strain control in agreement with ASTM E8/E8M \u2212 16a Standard [40] (see Fig. 3(b)). The makroXtens HP100 extensometer Model No. 083939 with gauge length set at 24 mm has been adopted to measure the strain The Zwick Roell controller acquired the applied load from the load cell of the testing machine and the strain from the extensometer during each static test. A Zwick Roell Z050 TH testing machine having a load capacity of 50 kN and being equipped with a testControl II controller and an hightemperature furnace (1250 \u25e6C, Model No. 1029795), has been adopted to perform high-temperature (HT) tensile static tests on \u201c600\u25e6C_AM.asb. V\u201d specimens. A displacement rate equal to 0.15 mm/min has been applied under displacement control in agreement with ASTM E20\u201321 [41], which suggests a crosshead speed equal to 0.005 mm/mm/min of the original length of reduced parallel section, i.e. 32 mm (see Fig. 3(b)). The laserXtens 2\u2013120 HP/TZ high-temperature extensometer Model No. 1061538 has been adopted to measure the strain. Each specimen was heated before the static test up to 600 \u25e6C in one hour and then temperature was kept constant for 30 min before starting the test. The temperature was monitored before and during the static test by adopting three thermocouples attached to the sample. The samples were tested in as built condition (except for grip section which have been threaded), and the final geometry is reported in Fig. 3(b). Again, load and strain have been acquired by the Zwick Roell controller from the load cell and the extensometer, respectively, for each tested specimen. The production of refractory metals as W and Mo is particularly affected by powder morphology. For instance, Zhou et al. [42] fabricated W samples with part density of 16 g/cm3 starting from powder with irregular shape. Still with regard to W production by LPBF, a comparison between powders of different shapes was studied by Yang et al. [43]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003742_1.4000277-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003742_1.4000277-Figure1-1.png", + "caption": "Fig. 1 Test linear bearing", + "texts": [ + " ournal of Tribology Copyright \u00a9 20 om: http://tribology.asmedigitalcollection.asme.org/ on 01/27/2016 Terms the carriage and rail is introduced and the theoretical expressions of the vertical stiffnesses using the flexible model are presented. Later, comparison of the experimental results with calculated results is carried out and the reliability of the flexible model is confirmed. 2 Experiments 2.1 Test Linear Bearings. The test linear bearings used in the experiment were linear guideway type \u201cnonrecirculating\u201d ball bearings, as shown in Fig. 1. Each test linear bearing consists of a rail, a carriage, a retainer, and balls. Each test linear bearing had four rows and the ball groupings were retained in phase by a retainer. All of the test linear bearings were preloaded with oversized balls. The preloads of the test bearings were light and medium. The specifications of the test linear bearings are shown in Table 1. 2.2 Vertical Stiffness Measurements. For the vertical stiffness measurements of the test linear bearings, the test rig and measurement apparatus shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure2.76-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure2.76-1.png", + "caption": "Fig. 2.76. A rotational joint", + "texts": [ + " The second approach is oriented to calculation of this friction torque. It will be described through the example of rolling bearings. First we restrict our consideration to calculation of torques for known motion since the inverse calcula tion in the presence of static friction would be rather complex. In .... .... Para. 2.5.3. it was shown how the total force FSi and total moment MSi in joint Si are calculated. We now consider one mechanism joint, a ro tational one, consisting of two rolling bearings (Fig. 2.76). Note that the joint index \"i\" is omitted in Fig. 2.76. and will also be omitted in the following discussion. .... .... After calculation of MS and FS the reaction moment is found in the form (2.10.4) The projection -+- -+- of MS onto the axis e represents the sum of driving tor.... que P. and .... l Mfe). Now: -+- -+- -+- friction torque Mf . Let Mf be the module of vector Mf (Mf = Pi = (MS\u00b7~) - Mfsgn(q) (2.10.5) Let the reaction moment MR be substituted by two forces (Fig. 2.77). 138 From Fig. 2.77. it follows that Mf2 can be computed by [31] d Mfl = llFeLl 2' We compute the equivalent loads for bearings [30]: FeLl' FeL2 \u00b7 Then the friction torques Mfl and (2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000232_j.ymssp.2021.108403-Figure20-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000232_j.ymssp.2021.108403-Figure20-1.png", + "caption": "Fig. 20. Healthy and worn sun gears. (a) healthy, (b) with light surface wear, (c) with medium surface wear and (d) with heavy surface wear.", + "texts": [ + " 18, the components of the test system include a motor, an encoder, a planetary gear gearbox, a fixed-shaft gearbox, a magnetic brake, a brake controller, a data acquisition system and a computer. The planetary gearbox in this test rig has the same parameters as the example system applied in the numerical simulation. The layout of the acceleration transducer on the housing of the planetary gearbox is displayed in Fig. 19. In the present study, the experimental tests are performed under four conditions: a healthy sun gear, a sun gear with light surface wear, a sun gear with medium surface wear and a sun gear with heavy surface wear, as shown in Fig. 20. The light surface wear, the medium surface wear and the heavy surface wear on the sun gear are used to simulate the different gear wear status, X. Liu Mechanical Systems and Signal Processing 166 (2022) 108403 which can be represented as GWSI, GWSII and GWSIII, respectively. GWS0 represents the healthy status. The experimental tests are conducted under motor rotation frequency of 3 Hz and magnetic brake load of 12.2 N\u22c5m. The waveforms of the experimental acceleration signals of the planetary gearbox in four conditions are depicted in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000377_j.jmrt.2021.01.030-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000377_j.jmrt.2021.01.030-Figure1-1.png", + "caption": "Fig. 1 e Schematic diagrams of (a) additive manufacturing devi measuring device.", + "texts": [ + " An alcohol-based paint containing TiC nanoparticles with different mass fractions was painted onto the surface of the deposition layer, as described by Bermingham [17]. The chemical compositions of the 2219 Al alloy, and 2319 fillerwire are summarised in Table 1. Before testing, the oxide film on the surface of the 2219 substrate was removed using a wire brush and surface cleaning using acetone. The AM process was performed using a Magic 5000 Job G/F Fronius AC power source with an automatic wire feeder, a sixaxis Fanuc robot with a welding torch, a clamping device with water-cooling system, and a surface coating device (Fig. 1(a)). The test parameters were set using a control display unit: the current, deposition speed, and wire feeding speed were 110 A, 0.2 m/min, and 2.0 m/min, respectively. The mass fraction of coated TiCnps with a radius of c. 40 nm was 0.5 wt.%, 1.0 wt.%, 1.5 wt.%, 2.0 wt.%, respectively, in which the mass fraction was controlled by the coating speed. Ultra-high-purity argon (99.999%) was adopted as a shielding gas, and the flow rate thereof was 15 L/min. The temperature variation during solidification of the deposited layer was measured by a thermocouple with a measurement frequency of 100 Hz (Fig. 1(b)). After WAAM processing, the samples were sectioned on the plane normal to the direction of travel of the arc, polished with an automatic polishing machine, and etched using a highly diluted Keller\u2019s reagent. The tensile strength of the samples was measured using a material testing machine (Instron-5967, Instrand) at a tensile cross-head displacement rate of 0.5 mm/min. Microstructure and elements distribution were analysed by scanning electronmicroscopy (SEM,MERLIN Table 1 e Nominal chemical compositions of the materials (wt Material Si V Mg Fe Mn 2219 alloy 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003055_0094-114x(94)90024-8-FigureI-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003055_0094-114x(94)90024-8-FigureI-1.png", + "caption": "Fig. I. The 6 DOF in-parallel manipulator.", + "texts": [], + "surrounding_texts": [ + "Meek. Mack. Tkeory Vol. 29. No. I. pp. 115-124. 1994 0094-114X/94 $6.00 + 0.00 Printed in Great Britain. All rilhts n~xrved Copyrtlght ~ 1993 Pergamcm Prum lad\nA FORWARD AND REVERSE DISPLACEMENT ANALYSIS OF A 6-DOF IN-PARALLEL MANIPULATOR\nRASIM I. ALIZADE and NAZIM R. TAGIYEV Department of Robotics. Azcrbaidzhan Technical University. Narimanov Ave. 25, 360602.\nBaku. Azerbaidzhan\nJOSEPH DUFFY Center for Intelligent Machines and Robotics. Mechanical Engineering Department.\nUniversity of Florida. Gainesville. FL 32611. U.S.A.\n(Received !0 October 1991: received for publication 6 October 1992)\nAbetract--A kinematic analysis ofa 6 degree of freedom (IX)F) parallel manipulator which has three legs. mounted on moving sliders is described. Therefore. the 6 D O F are provided by the sl ider displacements and by changing the leg lengths. This manipulator structure provides a large functional workspuce. A forward displacement analysis is performed by using a decomposition method and reduces to the one non-linear equation solution by using an interaction method. Two distinct reverse displacement analyses are given. A manipulator workspace determination and a method for the specification of the platform position in space.\nI. INTRODUCTION\nIn the last few years parallel mechanisms have received much attention because they can be used as industrial robots. Parallel mechanisms are well suited for use in situations where there is a need for accuracy and rigidity. Basically, some types of manipulator are based on the mechanism, which has been called the Stewart Platform[I-5]. Many researchers have investigated the reverse displacement problem, that is inherently simple for the parallel mechanisms. At the present time there are few articles [6-8] which have investigated in closed-form the forward displacement problem. In these articles 6 DOF mechanisms are investigated. However, in this mechanism 3 DOF are provided by the slider displacements and another 3 DOF are provided by changing hydraulic cylinder leg lengths. The main advantage of this manipulator, compared with the Stewart Platform type is the capability to produce pure rotation.\n2. FORWARD DISPLACEMENT ANALYSIS\nConsider a mathematical model of the manipulator illustrated by Figs 1 and 2. Moving and stationary right handed coordinate systems O~ X~ Y~ Z, are introduced. The origin of the moving system O, is located at the center of the platform and the axes O, X, and O, Y, are in its plane. The axis O~ Y, is chosen to pass through joint 7 and the axis O, X, is chosen to be parallel to the side 6-7. The cosines of the constant angles between the vectors, which are labeled with subscripts are d,. n : d,. n = d,o.,3 ffi 0. The length of the sides of the platform are labeled I,~,, tu. lu.\nThe hydraulic cylinder lengths 13.6,14.7,1sa and the angles \u00a2h,~02, \u00a2~3 are the generalized coordinates of the manipulator. The angles Oh, \u00a2~2 and \u00a2h are formed by respectively the axes OX, O Y and the radius R2 which connects the center O, and the corresponding base joint.\nThe formulation of the forward displacement analysis is as follows. Given the generalized coordinates Oh, ~02, ~03, 13.6, 1,.7 and 15.,, it is required to determine the platform position in space.\nThe platform position will be determined by the direction cosines of the moving axes and the coordinates of the center Or.\nuwr ~l- , ! 15", + "The following system of the equations describes the mathematical model of the manipulator\n/.~ (x3 - x6 ) + M ' ,@3 - Y6) + .,V, (z3 - z6) = i ~ , d L , , ; ( i )\n(X 7 -- X6) 2 4\" 0'7 - -Y6) 2 4\" (:7 -- :6 ) 2 =/62.7, (2)\n/~(x4 - xT) + M,(Y4 - )'7) + N,(:4 - :7) = 14.Td,.u; (3)\n(x, - x,)* + O's -y7)2 + (:s - y 7 )2 = 12,; (4)\nL,o(X5 - xs) + MIo(Y5 - Y s ) 4- N.o(Z5 - Is) : is.sdto.,3; (5)\n(xs - x6) 2 + (Ya - y ~ ) 2 + (*l - *6Y = 1~,; (6)\n('~3 - - X6) 2 \"j\" (Y) - - Y6) 2 4\" (\"3 - - Z6) 2 ---- 1~.6; (7)\n(x4 - XT)= + (y, - y7)2 + (:4 :7)= 2 . - - : 14.';, ( 8 )\n(xs - xs)* + (Ys - Ys) 2 + (*, - zs) 2 : l|.s; (9)\nwhere the coordinates of the joints 6, 7 and 8 are unknown parameters. In order to determine the unknown parameters the decomposition method which is given in detail in [10] is used. Following this method in order to determine the coordinates of joints 6, 7 and 8 we can use modules COR3P and COR3 [10]. However, it is necessary to introduce one additional equation into the system of equations (!)-(9). This equation expresses a variable distance between any of the three sliders and the platform joint, for example, 14.s\n(x, - x~) 2 + (y, - y6) 2 + (z, - *6)' ffi 1~, ffi ~2. (10)\nApplying the decomposition method to the system of equations (I, 7, 10), (3, 8, 2) and (9, 6, 4) using two modules COR3P and one module COR3 step by step determine the coordinates of the", + "joints 6, 7 and 8. After introducing all the unknown parameters into equation (5) we will obtain a non-linear equation,\nF(x, A) = 0, (! l)\nwhere A is the vector of the mechanism constant parameters. Equation (I I) is solved for 0 by using one of the iteration methods. Then by introducing this value of 0 and employing the algorithm mentioned above determine coordinates of the joints 6, 7 and 8. Finally, the direction co~nes of the moving axes and the coordinates of the point O, can be determined.\nIn order to define the inclination angles of the hydraulic cylinders we can use the following expression\n#, .. arccos(LjL, + M/Mk + NjN,),\nwhere i-- 1,2,3;j = II, 12, 13 and k =20,21,22. In addition, there are some limits of the inclination angles for each specific manipulator assembly, which is given by\n#,~,, ~ #, ~< #,~,. (12)\nIt is necessary to check this inequality at each position of the manipulator." + ] + }, + { + "image_filename": "designv10_6_0002460_s0890-6955(00)00103-6-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002460_s0890-6955(00)00103-6-Figure3-1.png", + "caption": "Fig. 3. Heat transfer model of the cylindrical assembly. (a) Press\u2013fitted cylindrical structure. (b) Bondgraph model of heat transfer in cylindrical stucture.", + "texts": [ + " Bond graph models of the spindle system shown in Fig. 2 are presented in Figs. 3\u20135, and the basic elements of the bond graph are listed in Table 1. Instead of employing the finite element method which needs more complexity and computing efforts, the lumped method can be applicable [4,5]. In order to model the contact structure, the thermal contact resistance element is considered as follows. The bond graph model of the press-fitted cylindrical structure between the inner ring and the outer ring shown in Fig. 3(a) is suggested in Fig. 3(b), with a modulated thermal contact resistance M\u0307R\u0307c and the active bond element [10]. The initial negative clearance di generates the initial contact pressure Pc in the contact surface of two combined rings. As temperature gradients along the radial direction vary in accordance with operating time and conditions, the resultant thermal deformation causes change in the negative clearance and the contact pressure is subsequently changed. The contact pressure Pc is a very important factor in the thermo-elastic system because it determines thermal and dynamic properties such as preload, stiffness, damping factor and thermal conductivity" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002839_978-3-662-03845-1-Figure1.6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002839_978-3-662-03845-1-Figure1.6-1.png", + "caption": "Fig. 1.6. The two wetting scenarios: S < 0, partial wetting (non-zero contact angle BE); S > 0, total wetting", + "texts": [ + " Capillary phenomena involve two different pressures: capillary pressure and hydrostatic pressure. The capillary length h;-I is defined by equating the Laplace pressure ,h; with the hydrostatic pressure pgh;-I, so that h;-I = {fg. For water, , = 72 mJ m- I , p = 103 kgm-3 , 9 = 10 ms-2 and we find h;-I = 2.7 mm. For most liquids, h;-I rv 1 mm. On distance scales s \u00ab h;-I, gravity can be neglected and the system considered as being in a state of weightlessness. If, on the other hand, s \u00bb h;-l, gravitational effects predominate. When a droplet is placed on a substrate (Fig. 1.6), there are two possible scenanos: (a) Partial wetting: in equilibrium, the droplet forms a blob shape charac terised by a contact angle BE. (b) Total wetting: the droplet spreads out. The parameter distinguishing between these two scenarios is the spreading parameter S, which measures the energy difference between the bare substrate ('SA) and the substrate covered with a film of liquid ('SL + ,): 8 1. Droplets: Capillarity and Wetting If S > 0, the energy ofthe bare substrate is greater, and the liquid will cover it (total wetting)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002953_i2004-10041-1-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002953_i2004-10041-1-Figure1-1.png", + "caption": "Fig. 1. Sketch of the experimental configuration. The main quantities defined in the text are indicated in the figure. The darker section, limited by R\u2217, indicates the membrane region, under azimuthal compression, where wrinkling might occur.", + "texts": [ + " In Section 3, in addition to measurements of the length and the amplitude of wrinkles, we test the number of wrinkles by varying the size of the pulling circle, the pulling central force and the membrane tension. In Section 4 we introduce the basis of our theoretical model and we contrast it with our experimental results. For the sake of continuity the complete description of our semi-analytical calculations is developed in the appendix. Finally, our main conclusions are presented in Section 5. Aiming to mimic the contraction of a cell attached to a stretched membrane, we consider the geometry sketched in Figure 1. The circular membrane is pulled toward the center along a circle (radius r0). We denote ur(r0) = \u2212\u03b4 the imposed radial displacement. In order to account for the initial stretching of the membrane, we impose the displacement ur(R) = \u03b2 along the large outer radius, R. In the following, we denote u(r, \u03b8) the horizontal-displacement field and \u03b6(r, \u03b8) the out-of-plane displacement of the membrane. The general set of equations governing the equilibrium shape of the membrane is given in the appendix. If the mechanical situation is stable with respect to the buckling of the membrane (\u03b6 = 0), taking into account the imposed deformation, one shows easily that the horizontal-displacement field reduces to ur, which obeys \u2206ur = 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure3.21-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure3.21-1.png", + "caption": "Fig. 3.21. Decomposition of reactions", + "texts": [ + "103) I I * I * O(3x1) : O(3x1) : s(3x1) : ~(3X1) (6x4) Now, all the elements of the dynamic model (3.4.35) are determined and the model can be solved. Friction effects. We remember that the relative motion of the gripper ~ with respect to the joint connection is defined by u 1 = A A and u = * 2 = 1jJ - 1jJ \u2022 ... Let us find the friction force. We substitute the reaction moment MA -+ -+ -+-+ by two forces FM1 , FM2 , and the reaction force FA by two forces FF1' ... FF2 (Fig. 3.20). The lengths ~1 and ~2 are shown in Fig. 3.21a,b and they are defined as * if U1+LL (Fig. 3.21a). Now: 191 ->- R,2 ->- ->- R,1 ->- FF1 R,1+R,2 FA' FF2 R,1+R,2 FA (3.4.104) and ->- ->- ->- ->- ->- hXMA ->- hXMA FM1 R,1+R,2 , FM2 - R,1 +R,2 (3.4.105) The total forces are ->- ->- ->- ->- ->- ->- F1 FF1 + FM1 , F2 FF2 + FM2 (3.4.106) These forces determine the position of gripper points A; and A; which are in connection with the cylindrical constraint (Figs. 3.21, 3.22). ->- ->- The friction forces Ff1 and Ff2 act in these points. The absolute values of these friction forces (Pf1 and Pf2 ) are ~lp1 I 192 and ~IF21" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003815_j.mechmachtheory.2009.06.001-Figure26-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003815_j.mechmachtheory.2009.06.001-Figure26-1.png", + "caption": "Fig. 26. Defective generators with two parallel P pairs.", + "texts": [ + " 22 are discarded for simplicity. Case D. If two adjacent pairs generate the same 1D subgroup, then, obviously, the open serial chain generates a 3D manifold included in the 4D subgroup {X(u)}. The required four DOFs of a generator of X-motion are not achieved. Hence, two adjacent H or R pairs must not be coaxial with the same pitch and two adjacent P pairs must not be parallel. Moreover, in a PPP subchain two non-adjacent P pairs that are parallel remain parallel, what must be avoided, such as Fig. 26g. Chains belonging to this case are shown in Figs. 25 and 26, in which R pairs can replace H pairs. To sum up, the defective X-motion generators are briefly tabulated in Table 3. These open chains have passive internal 1- dof mobility: the connectivity is 3 instead of 4. Moreover, their inversions are also defective chains for generating X-motion. The paper is devoted to the primitive generators of Schoenflies motion, also called X-motion for conciseness. A set {X(u)} of X-motions with a given vector u orienting the axes of its feasible rotations is endowed with the algebraic structure of a four-dimensional Lie group" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003659_tmag.2008.2001450-Figure6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003659_tmag.2008.2001450-Figure6-1.png", + "caption": "Fig. 6. General schematic diagram of a BLDC motor with slots.", + "texts": [ + " Upon substituting back the constants and into (11) and using (4) and (1), the air radial and tangential components of the air-gap field distribution are obtained as follows: (14) (15) where when the field distribution in the air gap is given by (16) (17) where This model has been applied to three-phase slotless BLDC motor with radial, parallel, sinusoidal magnitude, and sinusoidal angle magnetization. The parameters of the motor taken are The results obtained by our model and the FEM are shown in Fig. 2 for radial magnetization, Fig. 3 for parallel magnetization, Fig. 4 for sinusoidal angle magnetization, and Fig. 5 for sinusoidal amplitude magnetization. In the case of a slotted stator (Fig. 6) the magnetic field is changed throughout the air gap and magnet region due to presence of slots. The change in the magnetic field due to slotting is a function of distance from the slots. The influence of slots is minimum at the magnet and rotor iron interface, whereas the greatest influence of slots is experienced at the stator surface. Besides this the slotting is a function of saturation of the ferromagnetic material used in the rotor and stator. Since saturation effect is very difficult to describe analytically, it has been ignored in the present analysis" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003231_b609137g-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003231_b609137g-Figure1-1.png", + "caption": "Fig. 1 (A) The enzyme/MWCNT/polysulfone screen-printed thickfilm electrochemical detector, top view; (B) Cross section of the detection area of enzyme/MWCNT/polysulfone screen-printed detector; (C) schematic drawing showing structure of HRP/MWCNT/ PS composite; (a) polycarbonate substrate, (b) insulator layer, (c) HRP/MWCNT/polysulfone conducting composite, (d) silver contact for the working electrode, (e) carbon ink contact layer.", + "texts": [ + " Preparation of carbon/polysulfone screen-printed electrode. The amperometric sensors used in the present investigation consisted of a single working screen-printed electrode deposited onto polycarbonate (PC) substrate. Silver ink acting as a conductive layer was printed and cured in a furnace at 60 uC overnight. Carbon paste ink was printed and cured at the same temperature overnight. A nonconductive isolating ink was applied and cured at 60 uC overnight. The reaction area of the working electrode was 20 mm2. Fig. 1 shows a schematic of the structure of MWCNT/PS screen-printed electrode. The carbon/polysulfone composites were prepared as follows. The MWCNTs or graphite suspension was mixed with the 7.5% wt25 PS\u2013DMF solution for 10 min under continuous stirring. The mixed ratios (carbon/PS-DMF suspension) were 6.5, 9.6, 12.5, 15.0, 17.6 wt%. Serigraphy is applied to print the composite onto the reaction region of 12 working electrodes. The electrodes were then immersed into bidistilled water for the phase inversion during 5 min and rinsed for 1 min and then the electrodes were dried at room temperature" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure17.1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure17.1-1.png", + "caption": "Fig. 17.1 Microrobot driven by artificial micro cilium", + "texts": [ + " Recently high performance micro machines such as micro mobile machines which can move and work in human body or micro conveyers which can transport a cell or a DNA are strongly required. In order to obtain excellent mobility for these micro machines, it may be effective to arrange a lot of micro actuators and to cooperatively drive them. In the natural field, a paramecium drives its cilia to generate progressive wave and moves in water. If we can fabricate artificial micro cilium actuators in group, we will obtain high performance micro mobile robot as shown in Fig.17.1. Thus the authors have aimed to develop artificial micro cilium actuators in group[1] which are composed of \u2018a piezoelectric pipemorph actuator\u2019[2]. This actuator was composed of a thin metallic needle as an internal electrode, piezoelectric ceramics layer surrounding the needle and multiple external electrodes on the 1 Nobuyuki IWATSUKI and Koichi MORIKAWA Department of Mechanical Sciences and Engineering, Graduate School of Science and Engineering Tokyo Institute of Technology 190 Nobuyuki IWATSUKI and Koichi MORIKAWA piezoelectric thin film" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002461_70.478428-Figure6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002461_70.478428-Figure6-1.png", + "caption": "Fig. 6. The multisteering system, showing the virtual axles that must be added to convert the system into multiinput chained form.", + "texts": [ + " The derivatives of these inputs should not appear in the coordinate transformation. In order to increase the relative degree of $1 with respect to the other steering inputs, n1 virtual axles will be added in front of each steering axle for j E (2, e . . , m}. The virtual inputs are temporarily denoted by 123, the angular velocities of the axles at the front of each virtual chain. After continuing similarly for 42, . a , +m-l, y, a total of n3 virtual axles will have been added in front of the j th steerable axle, as has been sketched in Fig. 6. Now there are the same number of passive axles between an axle 0: on the chain and any (virtual) steerable axle, and this is the same as the number of passive axles between the axle Qq and the front steering wheel 6;. After these virtual axles have been added, the jth steering train now contains n3 axles, of which only n3 - n3-1 are real (physical). The only axles which are considered as steerable in this formulation are the first axles of each virtual extension, or 6; for j E { 1, .... m}. The state variables that have been introduced, which correspond to the angles of these virtual trailers, are denoted by Q: f o r j E (2, + " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003197_tec.2005.859964-Figure5-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003197_tec.2005.859964-Figure5-1.png", + "caption": "Fig. 5. Location of sensors on the rotor.", + "texts": [ + " 1) Thermal Implementation of the Machine: The temperature sensors used are negative temperature coeffiecient (CTN) thermistors of small size (diameter: 0.5 mm, length: 4 mm) and short response time (250 ms) [30]. They have a reference ohmic value of 10 k\u2126 at 25 \u25e6C. a) Implementation of the Stator: The stator is very well equipped: six sensors have been introduced in each angular sector (Fig. 4). Three angular sectors are implemented for each of the three particular sections of interest. b) Implementation of the Rotor: The rotor is implemented with nine thermistors (Fig. 5). The information is collected through a ten-track slip ring LITTON EC3848 [31]. 2) The Test Bench: The test bench includes the induction motor coupled to a direct current machine that can be used as a drive or a brake. The power supply of the machine is provided by an alternator on which the delivered frequency and tension can be separately controlled. A NORMA D6200 power analyzer collects the electric and mechanical data of the studied machine. The temperatures shaft housing end winding iron bracket rotor shaft housing end winding iron bracket rotor \u22121" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure11.4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure11.4-1.png", + "caption": "Fig. 11.4 Fabricated micromirror. Schematic drawing of the micromirror for illustrating the effect of the tension inside the torsion bar for suppressing the vertical displacement", + "texts": [ + " The factor t3 shows that decreasing t is effective for decreasing k . The proximity patterning without using the stepper will give the minimum size of a few m. As for the deposited film, the thickness of ~100 nm can be used as the structure. The spring constant from eq. (11.2) is 1.4x10-11 Nm/rad by setting values of G, l, w, and t as 80 GPa, 200, 4, and 0.3 m, respectively. For obtaining larger spring constants for other displacement, tension is applied to the torsion bar. As seen from the inset of Fig.11.4, the tension works against the vertical displacement of the mirror. The tensile stress 0 inside SiN film can be 760 MPa [6]. The tension 0wt is 910 N. This value is quite large compared to the driving force of about 7 nN in our actuator design. The thin film torsion bar is softest in the vertical direction. The vertical spring constant kz is expressed as follows [7]. )5,3,1(, 12 21 1 ,1 2 0 4 3 n l nk wtkkEwtl k n oddn nn z (11.3) There are terms correspond to the factors due to the elasticity E (290 GPa) and the stress 0", + " 2 5335 2 33 0 1091023 )( 8 1 wttwtw l Ewttw l k stretch (11.4) 122 Minoru SASAKI The first term corresponds to stretching against the stress 0. The second nonlinear part corresponds to the elastic stretching. The dominant part is the first term having the value of 3.1x10-12 Nm/rad when the mirror rotation is small (<6.6 rad). This is 22% of the spring constant estimated from eq (11.2). The tension is fundamentally perpendicular to the rotational displacement inside the torsion bar. The increase of the spring constant is minimized. Figure 11.4 shows the fabricated micromirror. The dimensions of the torsion bar is 200x4x0.3 m3. The structures of the thin film torsion bar and the vertical comb drive actuator are realized by combining the isotropic and the anisotropic Si plasma etching. Figure 11.5 shows the mirror rotation angle as a function of the driving voltage. The thickness of the comb finger is 10 m. The rotation angle reaches 7.3O at 5 V. The comb gap is 4 m in the lateral direction. The curve is smooth showing a nearly linear relation", + " Electrostatic actuators have the lower risk of temperature increase, since they consume little power and generate the negligible heat. As for a disadvantage, the magnitude of the electrostatic force is rather small compared to other actuation forces. As described before, the thin film torsion bar with the tension can realize High-Performance Electrostatic Micromirrors 123 the low-voltage driving. Although SiN film generates a large tensile stress, it is an insulating material. A metal overlayer is necessary for constructing the electrostatic actuator. Au/Cr metals are deposited as shown in the inset of Fig.11.4(a). The temperature characteristics are found to be poor. For example, the mirror rotation angle is 4.3O at 5 V at room temperature (17 OC). At 60 OC and 5 V, the mirror rotation angle decreases to 1.3O. This can be attributed to the differing CTEs of the materials used in the torsion bar. Realizing the tense thin film torsion bar with Si material having the same CTE with that of Si substrate will be ideal. Many actuators have been fabricated using crystalline (c-) Si or polycrystalline (poly-) Si on Si substrate", + " The tensile stress is generated by the crystallization of amorphous (a-) Si. Figure 11.6 shows the fabricated micromirror using the tensile poly-Si film [8]. poly-Si thin film torsion bar 150 m114 m Fig. 11.6 Fabricated micromirror and the magnified image of the torsion bar. The inset shows the lateral cross-section of the thin film torsion bar. The width of the torsion bar is 5 m 124 Minoru SASAKI The surface roughness is 0.006-0.055 m Ra. The device surface is smoother compared to that (0.10-0.58 m Ra) of the previous device shown in Fig.11.4. This is attributed to the chemical inertness of poly-Si against HF vapor used in the sacrificial SiO2 layer etching. Figure 11.7 shows the mirror rotation angle measured at different temperatures. This mirror rotates by 4.0O at 15 V. The curves almost overlap each other. When the temperature increases up to 100 OC, the fluctuation of the rotation angle increase is 0.14O. This corresponds to 3 % of the stroke and the sensitivity of 1.7x10-3 O/OC. The rotational spring becomes softer at higher temperature" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003865_j.actaastro.2010.10.017-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003865_j.actaastro.2010.10.017-Figure1-1.png", + "caption": "Fig. 1. Geometry of orbit motion of spacecraft.", + "texts": [ + " For a detailed assessment of the system performance under the proposed control strategy, the results of numerical simulations incorporating the effects of various system parameters are examined in Section 4. Finally, the conclusions of the present study are stated in Section 5. The investigation is initiated by formulating the complete nonlinear equations of motion of the rigid spacecraft to develop a mathematical model that facilitates the design of nonlinear control methodologies. The proposed system comprises a rigid spacecraft in an elliptical planar trajectory with the Earth\u2019s center at one of its foci (Fig. 1). An Earth centered inertial (ECI) frame denoted by I-XIYIZI (Fig. 1), has its origin located at the center of the Earth, with the ZI-axis passing through the celestial North pole, the XI-axis directed towards the vernal equinox, and the YI-axis completing the right-handed triad. Next, we define a local vertical local horizontal (LVLH) orbital reference frame L-x0y0z0 with its origin always at the center of mass of the spacecraft. The nodal line represents the reference line in orbit for the measurement of the true anomaly (eccentric orbit) or angle y (circular orbit)", + " 2. The corresponding plots of sliding surfaces and angular velocity are given in Fig. 3. With no external disturbances acting on the spacecraft, the motion of the system reaches the sliding surface Su=0 in finite time which can be analytically determined using the following relation: tr r JSu\u00f0t0\u00deJ 2pZ orbitsr0:5 orbit \u00f068\u00de where Z\u00bc 1:3 from Table 2. The angular velocity of the spacecraft is stabilized to ox \u00bcoy \u00bc 0 and oz \u00bc 0:0011 rad=s. According to the coordinate frames selected as shown in Fig. 1 the spacecraft z-axis is normal to the orbit plane and therefore oz would be equal to the orbital rate (when e=0). Next we consider the case where there is no actuation available on the yaw axis (Case II). It is clearly evident in Fig. 4 that the control algorithm given by Eq. (27) fails to stabilize the yaw motion motion of the spacecraft with Ug \u00bc 0. The reason for uncontrollable rotation of the spacecraft about its x-axis can be analytically determined from the zero-dynamics of the yaw equation of motion" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000232_j.ymssp.2021.108403-Figure18-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000232_j.ymssp.2021.108403-Figure18-1.png", + "caption": "Fig. 18. Planetary gearbox test rig.", + "texts": [ + " As can be observed from Fig. 17, the healthy status and the gear wear accumulation status with various severities are separated correctly by using the proposed fault indicators, which has good clustering performance. Therefore, the methodology proposed in this X. Liu Mechanical Systems and Signal Processing 166 (2022) 108403 study can effectively assess the gear wear status of the planetary gear train. In this section, a set of experimental tests are conducted to validate the numerical simulation results. As shown in Fig. 18, the components of the test system include a motor, an encoder, a planetary gear gearbox, a fixed-shaft gearbox, a magnetic brake, a brake controller, a data acquisition system and a computer. The planetary gearbox in this test rig has the same parameters as the example system applied in the numerical simulation. The layout of the acceleration transducer on the housing of the planetary gearbox is displayed in Fig. 19. In the present study, the experimental tests are performed under four conditions: a healthy sun gear, a sun gear with light surface wear, a sun gear with medium surface wear and a sun gear with heavy surface wear, as shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002627_physreve.70.061411-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002627_physreve.70.061411-Figure1-1.png", + "caption": "FIG. 1. Sketch of experimental setup. The conelike arrow represents the magnetization of the uniaxial gel while the flat arrows represent the external force.", + "texts": [ + " Our system differs qualitatively from the isotropic ferrogels by the macroscopic variables associated with relative rotations. These variables describe, as already mentioned, the relative rotations between the orientation of the magnetization and the polymer network. In this section we discuss an effect associated with these variables. We apply a constant shear flow and determine the change of magnetization. We assume that the direction of the frozen-in magnetization in the uniaxial ferrogel is parallel to the x direction while the shear is applied in the x-y plane as sketched in Fig. 1. Furthermore we assume spatial homogeneity. In this case the dynamic equations for the momentum density and the scalars r , s, and c are satisfied automatically. Contributions due to magnetostriction effects are neglected. These effects are of higher order in the variables [cf. Eqs. (19) and (14)] while we focus on linear effects. These assumptions reduce the set of dynamic equations to ]tMi + Xi = 0, s56d ]tV\u0303i + Zi = 0, s57d ]teij + Yij = 0. s58d Now we need to find the relevant expressions for the quasicurrents" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000285_j.optlastec.2021.107277-Figure6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000285_j.optlastec.2021.107277-Figure6-1.png", + "caption": "Fig. 6. Model geometry and grid: (a) isometric view, (b) elements with different attributes from top view (c) cross-section view of the model.", + "texts": [ + " conductivity of powder material can be summarized as: kp = ka (1 \u2212 \u03c4)nm \u03c0 as Rn (14) where ka is the thermal conductivity of TiAlSi alloy, \u03c4 is the porosity of TiAlSi powder, nm is the coordination number, as is the sintering neck radius of powder, and Rn is the average radius of powder. The melting point of TiAlSi is about 800 \u25e6C. Fig. 5 illustrates the physical properties of TiAlSi powder and its alloy. The concise 3D transient model was applied to simulate the experiment process at the fundamental of the assumptions above. The established model is shown in Fig. 6. The model was only half-built because it was symmetrical along the laser scanning orientation, which effectively reduced computation. During the simulation, the element type Solid 70 was used for TiAlSi powders, TiAlSi alloys and 304 stainless steel substrates. Given the statistics, the entire geometry was cut into 414,324 elements, of which 32,000 elements were used for TiAlSi powders, and the remaining was occupied by 304 stainless steel substrates. Flow chart of single-track numerical simulation is exhibited in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure2.68-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure2.68-1.png", + "caption": "Fig. 2.68. Arthropoid manipulator GORO-80", + "texts": [ + " We can see that the trapezoidal velocity profile enables faster moving up (Ao +A1) compared with the triangular profile. 118 With the triangular profile T(Ao~A1} = 1.2 s is not posible and with the trapezoidal profile even T(Ao~A1} = 1 s is posible. One can conclude that with this manipulator and this manipulation task the trapezoidal profile is more convenient, because the actuator capabilities are used in a more efficient way (Fig. 2.67). 2.8.4. Example 4 In this example we present the manipulator GORO-80 having six rotatio nal degrees of freedom. Fig. 2.68a, shows the external look,Fig. 2.68b. shows the kinematical scheme, and in Fig. 2.68c. there is a table with the manipulator data. The manipulation task is shown in Fig. 2.69. The initial position of manipulator (Ao in Fig. 2.69) is given in 2.68b. Working object has to be inserted into a hole as shown in Fig. 2.69. First, the object is moved from Ao into a position A1 . Keeping in mind the form of the object and the hole, it is clear that the total orientation is necessary. It is shown in Fig. 2.69 via two directions (b) and (c) i.e. via two vec~ ~ tors hand s. Now insertion is performed" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002790_robot.1990.125962-Figure6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002790_robot.1990.125962-Figure6-1.png", + "caption": "Figure 6. A Two Link Manipulator", + "texts": [ + " Note that at point g, the forward integration uses the maximum acceleration while the backward integration follows the limit curve instead of the maximum deceleration. In the above algorithm we make use of the limit curve. However, if computation time is to be minimized, there is no need to compute the velocity limits in order to determine if the trajectory crosses the limit curve, or to find the critical points. (16) dim V. EXAMPLES Several examples are presented to demonstrate the robustness of the modified algorithm and to show the existence of singular critical points and critical arcs. In these examples, the two link manipulator shown in Figure 6 with the parameters given in Table 1 is used. Icl = 0.5 m 11 = 1.0 m mi = 1 kg I1 = 0.08 Kg-m2 Ti = 1 N-m Ic2 = 0.5 m 12 = 1.0 m m2 = 1 kg I2 = 0.08 Kg-m2 T2 = 1 N-m The zero inertia lines in joint space of the two link manipulator are shown in Figure 7. These lines are drawn for various angles, integrating Equation (14) for i=1,2. Also shown in Figure 7 is a path tangent to one of the zl lines. The point of tangency, marked by a square, is a critical point. The same path and the manipulator are shown in Cartesian space coordinates in Figure 8" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003208_978-3-642-79069-0-Figure3.3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003208_978-3-642-79069-0-Figure3.3-1.png", + "caption": "Fig. 3.3. The three main parts of a horizontal starch gel electrophoresis apparatus (all parts made of Perspex). Top-frame (positioner) to position the comb used to produce a number of trays into which the samples can be applied. The assembled positioner is mounted on the gel mould immediately after the starch gel has been poured into the mould; middle-gel mould; bottom-buffer tray", + "texts": [ + " As the starch solution cools, it solidifies forming an opalescent gel which can be used as separation medium. The following descriptions are limited to the horizontal mode of starch gel electrophoresis since the vertical version is seldom used. The solubilized starch is cast in a gel tray, the set- up of which can be very simple, con sisting of a thick glass plate on which a frame of PlexiglasR (PerspexR) of variable hight and size is attached with a little vacuum grease [28]. A more solid set-up is demonstrated in Fig. 3.3. It consists of a bridge-like tray. The bottom ends of each side of the tray are covered with a strip of Perspex being attached with self-adhesive tape. Then the tray is placed on a horizontal level and filled with gel until the liquid stays about 1 mm above the tray. Afterwards it is covered with a frame into which a slot former (comb) can be inserted while the starch is stillliquid (Fig. 3.3). After the starch solution has solidified into a gel, removal of the template will leave trays in the gel in which the samples can be placed. The teeth of the comb must be long enough to penetrate about 1 mm of the gel tray bottom. The dimensions of the teeth of the comb determine the volume of the solution which can be filled into the sample slots. The sample volume in a slot can be varied to make banding patterns either darker or lighter using combs of 1 to 2 mm thickness. There are other sample application methods in addition to the use of slot formers: cuts may be made in the gel with a razor blade or knife, and small filter paper strips, into which sample solution has been soaked, may be inserted into the cuts, or else the whole starch block may be cut perpendicularly to the migration direction of proteins into a 1/5 and 4/5 sized part", + " For most enzymes the buffer systems are continuous which means that the same buffer ions in the gel and the electrode vessels are used, though the gel buffer is usu ally ten times less concentrated than the electrode buffer. Buffer systems are named discontinuous if gel and electrode buffer are different in their composition. A discon tinuous system has been used, e. g., to separate nucleoside phosphorylase isozymes of human erythrocytes. Electrode buffer solutions should be fresh if small buffer re servoirs are used (Fig. 3.3). Iflarger buffer volumes are used the buffer may be taken two to four times. But in this case it is essential to mix anodal and cathodal buffer and check the pH-value before starting a new experiment. The main function of the buffer is to keep the pH within the separation medium constant. The extent to which the pH is altered is directly related to the voltage gra dient, the current and the duration of electrophoresis. Buffers function at optimum rate efficiency when the desired pH is close to the pK-value of the buffering substance, and when they have an appropriate ion strength and stability", + " Another method is to soak sample solutions into small pieces of filter paper (Whatman NO.3 MM, or, if heavier loading is wanted, Whatman No. 17 filter paper) of the size 2 X 8 mm and insert these into the gel with the aid of tweezers and a small piece of razor blade. The sample inserts should be well-spaced and not allowed to protrude above the surface of the gel. The samples are usually applied to the prospec tive cathodal end since most enzymes behave chemically as anions at the pH-values of commonly used buffer systems (Chap. 6) [1- 3, 26, 28]. When using the gel tray shown in Fig. 3.3 the slot former is taken out of the gel and the covering Perspex plate removed from the gel. Then the samples are applied. Before the gel tray containing the applied samples is placed into the electrophoretical apparatus, approximately 180 ml of buffer are filled in each electrode vessel. Except for a few enzymes, both buffer trays contain the same buffer solutions (Chap. 6). When using the gel tray shown in Fig. 3-3 no wicks are needed to link the starch gel with the electrode buffer because the ends of the gel dip directly into the cathodal and anodal buffer. Electrophoresis is carried out in a cold room or a refrigerator at 4 - 8 DC but leaving the power supply outside the cooling device. The voltage gradients and the times of electrophoresis depend on the buffer systems used and some of the most often applied conditions have been compiled in Chap. 6. The voltage is adjusted to the appropriate level by taking measurements directly across the ends of the gel at the start of the experiment using a voltmeter" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002544_robot.1989.100155-Figure5-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002544_robot.1989.100155-Figure5-1.png", + "caption": "Figure 5 . Manipulator Path I.", + "texts": [ + " The function S, (S) defines the Limit Curve required by the algorithm to find the optimal switching points as discussed in Reference [6]. Also, any manipulator velocity profile which is higher at any point than the Limit Curve in the S - S phase plane will cause the vehicle to lose its footing or saturate one or more joint actuators. IV. AN EXAMPLE The technique is applied to a typical system whose parameters are given in Table I. The manipulator path for the first case considered, Case I, is shown in Figure 5 . The path is represented in the software implementation by straight lines and circular arcs [12]. The system's tendency to tip is relatively low since the manipulator does not carry a payload and the vehicle is relatively heavy. The Limit Curve and time optimal trajectory calculated for this case are shown in Figure 6. The minimum-time necessary for the manipulator to complete this movement is 1.4 seconds, compared to approximately 3.4 seconds required by a conventional motion plan that uses constant velocity and acceleration path segments also shown in Figure 6" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003670_978-3-642-82195-0-Figure1.1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003670_978-3-642-82195-0-Figure1.1-1.png", + "caption": "Fig. 1.1. Model of a manipulator with n links and n joints", + "texts": [ + " The complexity of the inverse kinematic problem, together with various approaches to ob tain its solution, will be considered, too. 1.2. Definitions In this section we will introduce some basic notations and definitions relevant for manipulator kinematics formulation. We will be concerned with the manipulator structure, link, kinematic pair, kinematic chain, the joint coordinate vector and its space, the external coordinate vector and the external coordinate space, direct and inverse kinematic problems and redundancy. 2 Let us consider the model of a robot mechanism shown in Fig. 1.1. The model consists of n rigid bodies which represent mechanism links. These links are interconnected by revolute or prismatic (sliding) joints, having rotational and translational motion, respectively. The mechanical structure of the mechanism, represented by an arranged n-tuple (J 1 , ... ,Jn ), will be termed as manipulator structure, where for each iEN = {l, ... ,n}, JiE{R, T}. Here R stands for a revolute joint and T for a prismatic one. For example, the manipulator structure RTTRRR stands for a mechanism with 6 joints, where the second and third joints are sliding, and the remaining joints are rotational" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure3.4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure3.4-1.png", + "caption": "Fig. 3.4. Mechanism with a kinematic parallelogram", + "texts": [ + " We also solve the nonlinear dependence between l l l * the joint driving torque Pi and the cylinder force Pi [9]. The solution to all these dependences is included in the dynamic analysis al gorithm in the form of a special subroutine. Let us consider another example of a mechanism containing a closed chain. It is the mechanism shown in Fig. 3.2. For this scheme which contains a kinematic Daralleloqram there is no simple approximative '55 solution. The mechanism has to be considered as a closed chain. The kinematic scheme of such a mechanism is given in Fig. 3.4. Let us define the direct branch (solid line in Fig. 3.5). Such a simplified mechanism has n de~rees of freedom (d.o.f.) and we define n generalized coordi nates q, , ... ,qn' It is an open chain and we may use the method from Para. 2.3 to form the dynamic model. In fact we find the matrices wd , vd which determine the acceleration energy (2.3.35) and the left hand side of Appel's equations (see eq. (2.3.36)). The upper index \"dO in dicates that the direct branch is consider only. 156 Let us now add the segments 2' and 2\" which close the chain (Figs" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003770_s00138-006-0066-7-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003770_s00138-006-0066-7-Figure2-1.png", + "caption": "Fig. 2 Schematic view of trinocular optical CCD-based detector", + "texts": [ + " Incorporating the vision system into a robot with higher degree of freedom (e.g., greater than 5) calls for a critical selection of cameras\u2019 locations with respect to robots\u2019 end-effector to prevent any possible collision. 3. Image processing is computationally intensive; hence, this approach cannot provide a high frequency feedback signal compared to various analogue sensors such as photo-transistors. In order to address these challenges, a trinocular optical CCD-based detector was designed as shown in Fig. 2. Three digital cameras with resolution 659 \u00d7 494 pixels were considered to monitor the process zone, in which an interference filter with bandwidth of 700 \u00b1 40 nm plus a neutral filter with optical density value of 4 were used. Also, a set of magnification lenses from Sony with number of SPT-M124-17 is incorporated into each camera to magnify the process zone. The polar angles between the cameras were 120\u25e6 and the horizontal angle between one individual camera and the substrate plane was set to 15\u25e6 as shown in Fig. 2. The cameras were connected to digital frame grabbers within a PC equipped with a QNX real-time operating platform. The images were initially pre-processed within the frame grabber to be chopped to the size of 352 \u00d7 350 pixels. The images were cut to the lower size for further computational analysis. This task was performed within the frame grabber. The images were then sent to a feature tracking algorithm for extracting the clad height. The feature tracking algorithm includes: 1. Image selection, 2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure6.6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure6.6-1.png", + "caption": "Fig. 6.6 Schematic of silicon XY-microstage containing Moonie amplification mechanism, and the working principle of the Moonie amplification mechanism", + "texts": [ + " These values are approximately 10 times smaller than those estimated value from device design. 61 The reason of this discrepancy relies on the large stiffness of the beam supporting the stage. Recent deep reactive ion etching of Si is well developed; therefore, a Si-PZT hybrid XY-microstage with novel design are fabricated and evaluated. In this stage, Si is used as a base material and stacked PZT actuators are used to drive the stage. The design of the proposed XY-microstage driven by stacked PZT actuators with Moonie amplification mechanisms [11] is shown in Fig.6.6. This design consists of two movable structures arranged so that movement in both the X and Y directions are controlled by actuators. The Moonie amplification mechanism will amplify the stroke of stacked PZT actuators for the respective directions. The center stage is supported by two sets of support beams, and can be actuated by the Moonie amplification mechanism. In addition, the center stage is placed in the movable outer frame, which is also supported by support beams and can be actuated by another Moonie amplification mechanism. The stage is made of a Si substrate with a size of 20\u00d720\u00d70.4 mm. Silicon is chosen as a base material as it is preferable to metals due to its material properties such as inelasticity, hardness and small thermal expansion. Furthermore, the use of silicon will lower the cost on the basis of batch production. As shown in Fig.6.6, the Moonie mechanism is based on four beams arranged in a \u201cdiamond\u201d configuration in order to drive translation along one axis [12]. The four beams are connected by rounded hinge with radius r. The basic amplification factor of the Moonie mechanism can be calculated by the following equation. COT SIN COSM factor W LAMP , (6.2) where AMPfactor is the amplification factor, LM is the half length of the Moonie mechanism in the expansion direction, W is the half height of the Moonie mechanism and Moonie angle is the angle between the diamond rhombic direction and the longitudinal direction of the actuator" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure3.22-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure3.22-1.png", + "caption": "Fig. 3.22. Determination of friction forces", + "texts": [ + " ->- ->- The friction forces Ff1 and Ff2 act in these points. The absolute values of these friction forces (Pf1 and Pf2 ) are ~lp1 I 192 and ~IF21. The forces act in the directions opposite to the relative velocities of points Ai, Ai. Each velocity has two components: longi tudinal (along h) and tangential (along T). Thus, the relative veloci ties of Ai and Ai with respect to cylindrical constraint are (3.4.107) -+ -+ where R is the radius of the cylinder, and T1 , T2 are tangential unit -+ -+ vectors in points Ai, Ai (Fig. 3.22). The vectors T1, T2 can be found as NOw, the friction forces are (3.4.108 ) -+ -+ where v 1ro and v 2ro are unit vectors: ... ..,. ... v 2ro = v2r/lv2rl -+ Each friction force has a longitudinal (F~) and a tangential component ... (F t ) : 193 -u ->- ->- ->-->- -)1iF2icosa ->- -)1i F 2 i 1 ->- FQ,2 (Fn-h)h h h 0-2 2-2 u 1 +R u 2 ->- ->- ->- ->- -)1iF1 isina ->- R~2 ->- F t1 (Ff1 -T1 )T1 T1 -)1i F1 i T1 );2 2-2 u 1 +R u 2 - ->- ->- ->- ->- -)1iF2isina ->- ->- RU 2 ->- Ft2 (F n -T 2 )T 2 T2 -)1i F 2 i T2 0-2 2-2 U1+R u 2 These forces can be arranged in a different way to find the total lon gitudinal friction force: -> and the total friction moment (scalar value) around h: ->- ->- (3" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002692_02783649922066394-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002692_02783649922066394-Figure1-1.png", + "caption": "Fig. 1. The octahedral manipulator, so called because its 12 triangular faces define an octahedron. The platform triangle B1B2B3 moves relative to a fixed-base triangle A1A2A3. Double-ball-joint-ended rods between platform and base serve as six connecting \u201clegs.\u201d", + "texts": [ + " They call such motions \u201csingularity-free evolutions\u201d; here we call them \u201cnever-special assembly changing motions\u201d (or just \u201cnever-special motions\u201d) to emphasize that the platform body remains fully constrained throughout the motion. Wenger and Chablat (1998) give an explanation of these never-special assembly changing motions via notions of characteristic surfaces and uniqueness domains. The purpose of this paper is to develop a deeper understanding of how never-special assembly changing motions arise. We focus on the octahedral or 3\u20133 manipulator, shown in Figure 1, because we see its fully triangulated form as the best starting point for practical parallel-manipulator design. But our development is given dually for the simpler 3\u20133 planar-motion device in Figure 2, and in Sections 7 and 9 we use this device to illustrate some key points. Much is already known about the octahedral manipulator. A detailed description of its geometry and special configurations have been given (Hunt and McAree 1998). Methods for solving the forward kinematics of this device are described by several authors, including Nanua, Waldron, and Murthy (1990), Charentus and Renaud (1989), Merlet (1992), and McAree and Daniel (1996), all of which either state or prove that, with the leg lengths fixed, there are as many as 16 different ways of assembling the linkage as a structure", + " We aim (1) to show why three assemblies coalescing enables the platform to undertake never-special motions, (2) to explore sufficient conditions for triple coalescence, and (3) to consider whether the possibility of these motions might be \u201cdesigned out\u201d by appropriate specialization. Though we do not consider connections with other in-parallel actuated arrangements, several of our observations also have valid interpretations in the broader setting of those devices also. Our interest in these questions arises from our use of an adaptation of Figure 1 as the input device for a force-reflecting telerobotic system (McAree and Daniel 1996; Daniel and McAree 1998). In this role, the linkage functions as a six degree-of-freedom joystick that a human operator moves arbitrarily. A slave arm (typically a serial robot) connected to the input device by computer mimics motions made by the operator, enabling interaction with objects in a remote environment. If we are to track the moving platform unambiguously, using only leg-length sensors, the device must not undertake never-special motion", + " We stated this in a previous work (McAree and Daniel 1996), where we described a forwardkinematic solution for tracking the moving platform. We thank Jean-Pierre Merlet of the Institut National de Recherche at Univ Politecnica De Valencia on June 3, 2015ijr.sagepub.comDownloaded from en Informatique en Automatique (INRIA) at Sophia Antipolis for a computer-generated counterexample that demonstrated the claim to be wrong. This stimulated our interest in the problem. Suppose the locations of the double ball-socket joints at A1, A2, and A3 of Figure 1 are known. We let 8 be the product space of leg-rod lengths L \u2261 (L1, L2, . . . , L6) and \u03b8 \u2261 (\u03b81, \u03b82, \u03b83), where the \u03b8i are dihedral angles between (nonadjacent) leg-triangles A1B2A2, A2B3A3, and A3B1A1, and the base-triangle A1A2A3. Note that specifying a location of the platform determines the leg-rod lengths and the angles \u03b8i uniquely. But these nine parameters are not independent. The fixed distances between points Bi amount to three constraints that restrict physical assemblies to a (9 \u2212 3 =) 6-D configuration space C in 8", + " (8) has full rank, the legrod motion1L resulting from the motion v can be written 1L = \u2212\u03b5 2 2 \u22020 \u2202L + \u03b5 vT \u2202 201 \u2202\u03b8 \u2202L ... \u22121 vT \u2202 201 \u2202\u03b8 2 v ... = \u2212\u03b5 2 2 ( I \u2212 \u03b53+ \u03b5232 \u2212 . . . )(\u22020\u22121 \u2202L )vT \u2202 201 \u2202\u03b8 2 v ... , where 3 = ( \u22020\u22121 \u2202L )v \u2202 201 \u2202\u03b8 \u2202L ... , \u2248 \u2212\u03b5 2 2 \u22020\u22121 \u2202L vT \u2202 201 \u2202\u03b8 2 v ... . (9) For every motion \u03b5v satisfying this expression, there exists a complementary motion \u2212\u03b5v in the opposite direction that also satisfies it. As \u03b5 goes to zero, these two assemblies, one for either side of the special configuration, come together. To generalize this conclusion to Figure 1, we start by expressing the rank-2 matrix \u22020 \u2202\u03b8 via its singular value decompo- sition; i.e., \u22020 \u2202\u03b8 = 3\u2211 i=1 \u03c3iuivTi , \u03c33 = 0, \u03c31 \u2265 \u03c32. (10) (Note we use row-column notation to index elements of ui and vi : ui = (u1i , u2i , u3i ).) Suppose we alter the legs while keeping the angles \u03b8 fixed so that the imagined platformtriangle distortion10 occurs only in the direction u3 corresponding to no first-order constraint, and let the magnitude of this distortion be \u03bb having order O(\u03b52) or higher. The equilibrating motion 1\u03b8= \u03b51v1 + \u03b52v2 + \u03b53v3 is of order O(\u03b5) in direction v3, and O(\u03b52) or higher in directions v1 and v2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002663_mssp.2000.1345-Figure6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002663_mssp.2000.1345-Figure6-1.png", + "caption": "Figure 6. Test robot according to [3, 15].", + "texts": [ + " The accuracy of the results is very high. Typical deviations according to [8, 9, 14] are $(0.01}0.5) mm. 4.2.1.1. Measurement robot method. Only one method could be found in the literature that utilises measurements of arbitrary rigid-body motion. Recorded time domain data are used to identify simultaneously all 10 inertia parameters using the general non-linear equations (3a) and (3b) [3, 15]. A special measurement robot is used that can provide arbitrary spatial motion to the test specimen (Fig. 6). Bryant angles, rotational velocities and accelerations as well as interface forces and torques are measured and serve as input to the identi\"cation algorithm. The method uses time domain data which must be low-pass \"ltered in order to avoid systematic errors due to in#uences of the elasticities of the test specimen. For a thorough description of the measurement robot and the identi\"cation algorithm refer to [3, 15]. A high risk of damage due to accelerated spatial motion of the test specimen exists" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000511_j.addma.2021.102277-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000511_j.addma.2021.102277-Figure2-1.png", + "caption": "Fig. 2. The experimental set-up employed for the emissivity and thermal conductivity estimations; (a) general overview of the test bench; (b) details of the sample support system; (c) picture of the sample and heater at high temperature during a test.", + "texts": [ + " Indeed, under steady-state conditions, these two properties are sufficient to define the temperature field within the ion source, since only radiative and conductive thermal fluxes are present, assuming that thermal convection is negligible due to the high vacuum environment required for the operation of ISOL high temperature devices. At Legnaro National Laboratories of National Institute for Nuclear Physics (INFN-LNL), two different methodologies were developed for the high temperature evaluation of \u03b5 and k [26,27], utilizing a dedicated experimental set-up (Fig. 2). Such test bench consists of a vacuum chamber, capable of reaching vacuum levels around 10-6 mbar, within which an Ohmic heater is placed. Such resistor, made of ultrapure graphite, is properly shaped, in order to provide a concentrated and uniform circular hot spot of approximately 20 mm diameter in its centre, whose temperature can be adjusted up to 2000 \u25e6C according to the assigned heating current. A disk-shaped sample with a diameter in the range of 30\u201340 mm can be placed above the hot spot" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002663_mssp.2000.1345-Figure5-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002663_mssp.2000.1345-Figure5-1.png", + "caption": "Figure 5. Principle of balancing machine.", + "texts": [ + " The only hardware demand is a suspension wire while no software is needed. Time requirements for testing and data processing are medium to high (if an adapter is required) while the accuracy of the results is low. The main problem is to numerically determine the coordinates of the centre of gravity (only geometric information [5]). The balancing method yields the centre of gravity location of the test specimen [5, 8, 9, 12}14]. Balancing machines are in principle horizontal beams supported by knife edges (Fig. 5). The balancing of the test specimen's weight is provided by travelling weights or load cells. Since the lever arms of the counter forces are known, the coordinates of the centre of gravity can be calculated if the mass of the test specimen is known. Presuming that the orientation of the body-\"xed frame is equal to the orientation of the inertial frame according to Fig. 5 the second row of equations (5b) yields equation (14) if no external torques act: 0\"!+ i mAP i ffP i !mg(!m AC ). (14) hgigj mAP 1 m cw g If the lever arm and the masses of the counter weight and the test specimen are known, equation (14) gives m AC \"mAP i m cw m . (15) In order to identify all coordinates of the centre of gravity three tests are necessary. The balancing method is safe and it is well approved in industry. The necessity for mounting the mechanical system can limit the applicability and an adapter may be required" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure24.2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure24.2-1.png", + "caption": "Fig. 24.2 Permanent magnets and movement", + "texts": [ + " 260 small Ne-Fe-B permanent magnets are attached to the rotor surface so that the North and the South poles are located alternately. Four armature winding units are positioned on the stator. Each armature winding unit has three windings. The pitch of the windings is 2/3 of the pitch of permanent magnets. Therefore, locally, the relation between the armature windings and the permanent magnets is almost the same as that of the conventional one DOF linear synchronous motor. Armatures A and A\u2019 drive the rotor in the same direction and Armatures B and B\u2019 drive the rotor in the direction perpendicular to the first one. Figure 24.2 shows the positions of permanent magnets on the rotor. The output shaft is at the vertical position in Fig.24.2 (a) and at the position rotating around Y axis in Fig.24.2 (b). Permanent magnets are attached on the rotor so that the North and the South poles are located alternately on the concentric circles. The centers of the concentric circles are the X axis and the Y axis. Even when the rotor rotates around Y axis as in Fig.24.2 (b), the relation between the permanent magnets and the armature windings are the same on the vertical direction as in Fig.24.2 (a). In a similar way, when the rotor rotates around X axis, the relationship between the permanent magnets and the armature windings are the same on the vertical direction as in Fig.24.2 (a). Therefore, the rotor can rotate around each axis simultaneously. 282 Tomoaki YANO Air-cored coils are used to avoid torque pulsation with the cogging torque. The rotor position is measured by the encoders A and B. The specifications are shown in Table 24.1. The motor took on a structure in which all electromagnetic forces directly drive the rotor. Therefore, the motor of this type is expected to be a high torque. Fig.24.3 shows the block diagram of the motor driving system. Basic drive concept is the same as that of the conventional one DOF linear synchronous motor" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003082_cdc.1994.411460-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003082_cdc.1994.411460-Figure2-1.png", + "caption": "Figure 2: Planar VTOL aircraft", + "texts": [ + " This inverse is stable and agrees with Hirschorn\u2019s for minimum phase systems, but is noncausal (rather than unstable) in the nonminimum phase case, which results in initial condition mismatch. 2376 We apply this approach to the simplifies VTOL aircraft example considered in [4]. Note that the feedback design relies heavily on the flatness of the system, and it is indeed a very strong structural property, but quite a lot of (idealized) physical systems seem to be flat - and VTOL aircraft is one such flat system. As in [4], we consider a very simplified PVTOL (Planar Vertical Take Off and Landing) aircraft (see figure 2). Let (i\u2019,X E ) be a fixed inertid frame, and ( i b , j\u2019b, Lb), with j\u2019b = j\u2019be a moving frame attached to the aircraft (body axes). The forces acting on the system are: The equations of motion is written in terms of the center of mass C as m!c = r T + P l + P z + m i ac = C t l x Pl +ct2 x P z , where Zc is the acceleration of C and 8c is the angular m s mentum about C. M I and Mz are the points at which the forces F1 and F2 are located. Expanding these equations gives where J is the moment of inertia about C, and 1 the distance from C to points MI and Mz" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000433_j.jmrt.2021.08.152-Figure11-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000433_j.jmrt.2021.08.152-Figure11-1.png", + "caption": "Fig. 11 e Fracture mechanisms of specimens S1 (a) and S2 (b).", + "texts": [ + " Based on this explanation, we can propose a mechanism to explain the secondary cracks observed in the present experiment. A crack tip will be blocked at a grain boundary or be blunted by the movement of dislocations. The plastic zone moves by dislocation slip near the crack tip, which releases the stress around the crack tip. However, in this case, the stress relaxationmight not be fast enough. Therefore, a significant tensile stress acts on notch-like cracks and, thus, a secondary crack can propagate at the striation, as shown in Fig. 8(c). A schematic diagram of the fracture mechanism is shown in Fig. 11, which is based on the actual fracture conditions of the two samples. The results show that the blue lath has an a lamellar structure, the grain size of sample S1 is significantly larger than that of sample S2, and the a bundle domain in sample S2 has finer a lath grains, as shown in Figs. 5 and 6. The black dots in the diagram represent gas porosities in the samples. There are more defects in sample S1 than in S2, as shown in Fig. 4, and there are local super-sized defects. The red line in the diagram represents the propagation path of the main crack in the sample" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002565_s0043-1648(03)00338-7-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002565_s0043-1648(03)00338-7-Figure2-1.png", + "caption": "Fig. 2. Generating rack and gear in two meshing positions.", + "texts": [ + "1016/S0043-1648(03)00338-7 Nomenclature a, aH centre distance of gear pair and Hertz semi-contact width d offset distance at point on involute curve dar, E co-ordinate transformation matrix from Sr to Sa and Young\u2019s modulus E\u2217 composite modulus, 1/E\u2217 = (1 \u2212 \u03bd2 1)/E1 + (1 \u2212 \u03bd2 2)/E2 h, h0, ha wear depth, accumulated wear and addendum of generating rack I, i, j instantaneous centre of rotation and unit vectors in rectangular co-ordinates kw wear coefficient m, mpos,max module of generating rack and number of meshing positions M ik, M ro co-ordinate transformation matrices from Sa k to Sa i and So to Sr n, n\u0302 number of teeth in gear model minus one and normal unit vector p, P pressure and contact load (force per unit length) compressing contacting flanks r, rw radii of generating pitch circle (r = \u03c0m/2) and working pitch circle ra, rb, r tip radius, base radius (rb = r cos\u03b1t) and position vector R, Rrel radii of curvature and relative radius of curvature of offset involute curve s, s\u2217 transverse and wear modified transverse gear tooth on generating pitch circle sw, S sliding distance and co-ordinate system (x, y) t\u0302 tangent unit vector T, Tw torque (per unit length) of gear and local temperature in contact region v, wpnt,max sliding velocity and number of wear points x, z addendum modification coefficient and number of teeth of gear Greek letters \u03b1t, \u03b1wt transverse pressure angle of generating rack and working transverse pressure angle \u03b8 rotation angle between So and Sr \u00b5, \u03bd friction coefficient and Poisson\u2019s ratio \u03c1, \u03c4 tip radius of generating rack angular pitch of gear (\u03c4 = 2\u03c0/z) \u03c6 rotation angle of gear \u03c61,min, \u03c61,max minimum and maximum rotation angle of gear \u03d5, \u03d50 angular displacements of gear during generating process (superscript 0, xa = 0) \u03c8, \u03d5i auxiliary angle and total angular displacement during generation of involute curve Subscripts\u2014free index i gear i, i = 1, 2 j tooth flank j, j = \u22121 (left), j = +1 (right) n tooth n, n = 1, ni Subscripts\u2014dependent index k gear k, k = 1, 2 \u2227 k = i l tooth l, l = n if j = +1, l = n+ 1 if j = \u22121 \u2227 i = 1, l = n\u2212 1 if j = \u22121 \u2227 i = 2 Superscripts a global co-ordinate system located at I o local tooth co-ordinate system (wear modified tooth) r global co-ordinate system located at gear centre v local tooth co-ordinate system (non-worn tooth) 0 xa = 0 1 and 2 lower and upper limit The wear will change the geometry of the involute gear flanks. Therefore, the parametric equations for a wear mod- ified involute gear will be derived. This must be done for both the right and left flank, since double flank action is considered. Litvin\u2019s [2] position vector approach will be used to determine the geometric and kinematic expressions. An involute gear may be defined by its meshing with a rack with straight-lined flanks. Fig. 2 shows such a rack and a gear in two positions during a cycle of contact in a trans- verse plane. In the left position, a point on the right flank is generated and in the right position a point on the left flank is generated. During the cycle of contact, the successive positions of the straight-lined flanks will envelop two involute curves. One co-ordinate system for every flank j on every tooth n of every gear i is used. Any point in co-ordinate system Sv inj can be located with the position vector rv inj which is defined by [3] rv inj(\u03d5inj)= [ xv inj(\u03d5inj) yv inj(\u03d5inj) ] = [ ri sin \u03d5inj\u2212(ri\u03d5inj\u2212 1 2 sij) cos\u03b1t cos(\u03d5inj\u2212j\u03b1t) ri cos\u03d5inj+(ri\u03d5inj\u2212 1 2 sij) cos\u03b1t sin(\u03d5inj\u2212j\u03b1t) ] (1) where sij = jm( 1 2\u03c0 + 2xi tan \u03b1t) (2) is the transverse gear tooth thickness on the pitch circle" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003126_j.bios.2005.08.004-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003126_j.bios.2005.08.004-Figure1-1.png", + "caption": "Fig. 1. Schematic diagram of the flow cell positioned with a bamboo inner shell membrane immobilized with GOx and an oxygen optode membrane: (1) plastic tube for sample in; (2) temperature probe; (3) fixing screws; (4) PTFE cover; (5) sample chamber; (6) plastic tube for sample out; (7) seal ring; (8) quartz glass coated with oxygen-sensitive optode membrane and bamboo inner shell membrane with immobilized GOx; (9) flow cell stand; (10) quartz glass; (11) oxygen-sensitive optode membrane; (12) bamboo inner shell membrane with immobilized GOx.", + "texts": [ + " Preparation of oxygen-sensitive optode embrane Silica gel (20 mg) adsorbed with [Ru(dpp)3][(4-Clph)4B]2 as evenly spread on 704 silicone rubber and adhered to the urface of a clean transparent quartz glass to form a siliconeased oxygen-sensitive film. The thickness of the oxygenensitive film was estimated to be approximately 10 m. The xygen-sensitive film was left in ambient conditions for at east 24 h to completely cure and kept at room temperature ntil further use. .2.3. Assembly of fluorescent glucose biosensor The bamboo inner shell membrane immobilized with GOx as landed on the surface of an oxygen-sensitive optode embrane. A flow cell as shown in Fig. 1 was positioned in spectrofluorometer for fluorescence measurements. About .5 mL standard or sample solution was injected into the flow ell with the use of a 2.0 mL syringe. All fluorescence measurements were done on a Hitachi F-4500 spectrofluorometer (Tokyo, Japan) with computer control and data recording. The excitation and emission slits were set at 5.0 nm, respectively. The emission intensity of the fluorescent material, [Ru(dpp)3][(4-Clph)4B]2, at 610 nm was collected at an excitation wavelength of 470 nm" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002775_41.681229-Figure5-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002775_41.681229-Figure5-1.png", + "caption": "Fig. 5. The direction of applied force for swinging up the pendulum. (a) Driving the cart from right to left. (b) Driving the cart from left to right.", + "texts": [ + " To utilize the proposed adaptive control law, the pendulum must be firstly swung up from the pendant position to the upward position. Let us define the angle of the pendulum, as shown in Fig. 4. Since the cart can only move within a limited length, we must try to swing the pendulum up by driving the cart on the rail back and forth. This is similar to a human playing on a swing. Based on physical intuition, the two algorithms to swing up the pendulum are summarized below, and the direction of the applied force on the cart is shown in Fig. 5. 1) Driving the cart from right to left is summarized as follows: and apply positive voltage to drive the cart to left; and or apply negative voltage on the cart until the cart is stopped; 2) Driving the cart from left to right is summarized as follows: and apply negative voltage to drive the cart to right; and or apply positive voltage on the cart until the cart is stopped; is the swing-up voltage and is the traveling length of the cart. When the pendulum is swung up to the upward position, the adaptive control law is switched to stabilize the inverted pendulum" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000068_tie.2021.3057002-Figure20-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000068_tie.2021.3057002-Figure20-1.png", + "caption": "Fig. 20. Temperature distribution of rotor with ventilation cooling structure under no-load operation condition (\u2103)", + "texts": [ + " According to the geometry of the proposed novel rotor hybrid ventilation cooling structure, a new prototype of 315kW, 6kV HVLSSR-PMSM rotor with ventilation cooling structure is manufactured, as shown in Fig. 18. The lead-exit wires of the temperature measuring sensors in the motor are shown in Fig. 19. For verifying that the proposed design approach could provide satisfactory results practically, the temperature of the prototype with rotor hybrid ventilation cooling system is investigated in case of no-load operation, and the detail temperature distribution is shown in Fig.20. The losses of the entire motor at this operation are stator iron loss, winding copper loss, mechanical loss, which are 5510W, 2228W, and 4862W respectively. The temperature rise of the motor with rotor hybrid ventilation cooling structure is tested. Due to the limitation of the test site conditions, only the no-load temperature rise of the motor is tested, and test results are shown in Table VI. Measuring point Original structure New structure \u25b3T Test1 74.5 59.37 -15.13 Test2 89.5 64.92 -24.58 Test3 79" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002839_978-3-662-03845-1-Figure1.14-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002839_978-3-662-03845-1-Figure1.14-1.png", + "caption": "Fig. 1.14. Droplet deposited on a fibre: (a) partial wetting; (b) total wetting", + "texts": [ + " Equipment: \u2022 Hairs; \u2022 carbon fibres and textile filaments (radius 1-20 )lm); \u2022 fishing line (0.5 mm) and weight. A droplet will not spread out along a fibre! This is true even for total wetting (5 > 0). Because ofthe cylindrical symmetry, the L/G interface is greater than the S/L interface, and a sleeve distribution is unstable. On a fiber, the only difference between the spreading of a wetting liquid and that of a non-wetting liquid is the existence of a microscopic film, invisible to the naked eye, in the former case (see Fig. 1.14). This film can be revealed by using a fluorescent liquid. Another method consists in depositing two droplets, one large and one small, of a non-volatile liquid (e.g., polydimethylsiloxane PDMS) very close to each other. If the droplets are connected by a microscopic film, the small one will slowly empty itself into the larger one (over a period of about one day). Measuring the decrease R( t) in the radius provides information about the 1.5 Wetting of Fibres 19 dimensions of the liquid sheath, of thickness about 200 A" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003019_j.jmatprotec.2003.12.009-Figure10-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003019_j.jmatprotec.2003.12.009-Figure10-1.png", + "caption": "Fig. 10. Laser manufactured W/Ni component.", + "texts": [ + " The manufactured sample demonstrated that the present laser rapid manufacturing system and process was stable enough to produce good practical components. Fig. 9 shows the actual direct manufacturing process of the W60Ni40 collimation component, with the processing parameters: laser power of 2000 W, beam diameter of 3 mm, scanning speed of 0.3 m/min and powder feed rate of 8 g/min. The entire manufacturing took about 60 h to build the 307 mm high collimation component with section pattern as shown in Fig. 1. No cracking and obvious porosity appeared in the as-manufactured component. The as-manufactured W60Ni40 collimation component is shown in Fig. 10. 1. Laser direct manufacturing based on laser cladding technology has been developed to directly manufacture a cylinder-shaped W/Ni alloy collimation component for a hard X-ray telescope. 2. The characteristics of laser cladding tungsten and tungsten nickel alloys have been investigated. A triangleshaped clad appeared when vertically overlap W and W90Ni10 alloy. The W60Ni40 and W45Ni55 alloys showed good forming capability for manufacturing. Many thanks for the fund supports from the Tsinghua University 985 Key Project and the Fundamental Research Fund of the Mechanical Engineering College" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003983_j.wear.2009.06.017-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003983_j.wear.2009.06.017-Figure3-1.png", + "caption": "Fig. 3. Fixed surface grid on the gear tooth surface.", + "texts": [ + " The same is true for Xp and Xfp. As the rotational axes remain the same, axes zg and zfg (and zp and zfp) also coincide, with the gear rotational axis pointing from the vertex of the pitch cone to the back face. The shaft offset E is defined as the distance between yfg and zfp (E /= 0 for hypoid gears and E = 0 for spiral bevel gears). In addition, in line with the contact model that will be introduced later, a local curvilinear surface coordinate system (T,S) is used to define grids of tooth surfaces as shown in Fig. 3. Curvilinear coordinate parameter T divides the surfaces equally along the face width direction (from toe to heel) varying in value from T = \u22121 to 1. Likewise S along the profile direction (from root to tip) is defined 1598 D. Park, A. Kahraman / Wear 267 (2009) 1595\u20131604 f ( p b i c c s g e r o c rom S = 0 to 48. The location of each grid point ij is denoted by Ti,Sj) where i \u2208 [0,I] and j \u2208 [0,J]. This results in (I + 1) \u00d7 (J + 1) grid oints at which pressure time histories and sliding distance must e computed on both pinion and gear surfaces" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002644_1.1398289-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002644_1.1398289-Figure4-1.png", + "caption": "Fig. 4 Position vector of groove radius center: \u201ea\u2026 x-z plane; and \u201eb\u2026 x-y plane.", + "texts": [ + "1cosH lvbS t1 p vb D1g j lJ G , (6) where vb , C jl , and g j l are the spinning frequency of the ball, the amplitude of ball waviness and the initial phase angle of ball waviness, respectively. The contact force of the ball bearing supporting a rotating system acts along the contact angle, and its angle can be defined by the positive or the negative angle, as shown in Fig. 1. The equations of motion of a rigid rotor can be expressed in terms of the mass center so that the position vectors of the inner and outer groove radius center of the j th ball, Ri j and Ro j , should be defined with respect to the mass center of a rotating system consistently, as shown in Fig. 4. They can be expressed as follows: RW i j5Ri cos c j \u0131W1Ri sin c jW1aikW (7) RW o j5Ro cos c j \u0131W1Ro sin c jW1aokW . (8) The azimuth angle of the j th ball in x-y plane c j , can be expressed with the rotating frequency of the cage. c j5vct1 2p Z ~ j21 ! (9) The radial and axial components of these position vectors of the inner and outer races are Ri , Ro , ai , and ao , respectively, and they can be expressed in terms of the pitch diameter Dm , the distance between inner and outer groove radius centers BD , the distance between the center of the ball and the mass center of rotor dB , and the contact angle a" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure23.4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure23.4-1.png", + "caption": "Fig. 23.4 Schematics of the mathematical model", + "texts": [ + " Namely, when the input frequency is varied with fixed amplitude of the input voltage, the amount of overshoot decreases as the input frequency approaches to the motor\u2019s natural frequency. Dynamic Characteristics of Ultrasonic Motors 271 The next step is to construct a mathematical model that can predict the measurement results shown in 1.3. It is noted that a detailed derivation of the mathematical 272 Akira SAITO and Takashi MAENO modeling, analysis procedure, as well as the parameter identification method can be found in Ref. [1]. The schematics of the model are shown in Fig.23.4. The model consists of three sub-models: oscillator model, stator-rotor interface model, and rotor model as illustrated in Fig.23.4, and they are separately discussed below. In the proposed model, the stator is modeled as a three degrees-of-freedom (DOF) oscillator consisting of a rigid disk, torsional springs and dampers, which is an extension to the model proposed in Ref. [11]. Namely as shown in Fig.23.4a, the bending modes excited by the deformation of the piezoelectric ceramics are modeled as the vibrations due to the moments about X and Y axes, which are generated by the piezoelectric material. This yields the vibration distribution along the perimeter of the upper surface of the rigid disk, which agrees well with that of the real stator. Now, the formulation on the modeling of the oscillator is divided into two parts: (i) electromechanical conversion at the piezoelectric ceramics, and (ii) the vibration of the stator excited by the moment", + "3) where I is the inertia tensor of the stator, s is the angular velocity of the stator, MP ME MC and MD are the moments due to the force generated by the piezoelectric ceramics, elastic restoring force of the stator, contact force at the contact interface, and the damping force generated by the dampers. In the proposed model, the frictional contact force developed at the stator-rotor interface is calculated using a finite number of three-dimensional springs and dampers that are attached to the equally-spaced nodes in the circumferential direction along the rim of the stator [18], and the Coulomb friction model. The schematic of the springs is shown in Fig.23.4b. The algorithm for calculating the frictional force is described as follows. If the frictional force at each node does not exceed the maximum static frictional force, the stator contacts with the rotor at the node without slipping. The maximum static frictional force f i max at the ith node is calculated as i max if s nf i n (23.4) where f i n is the force normal to the contact surface, and s is the static friction coefficient. When the frictional force reaches the maximum static frictional force, slipping occurs between the node and the spring; hence a dynamic friction force f i d is generated" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure14.6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure14.6-1.png", + "caption": "Fig. 14.6 Experimental apparatus for pumping performance", + "texts": [ + " The flow pattern in the case of the multi-pins and holes type of electrodes must be numerically and experimentally investigated, since the output power strongly depends on the flow pattern of the ECF jet. 158 Yutaka TANAKA and Shinichi YOKOTA The shape, arrangement and gap of the electrodes on the delivery pressure and flow rate of the pump due to the ECF jet are experimentally investigated. The pressure due to the ECF jet strongly depends on the number and shape of the needles and the gap distance of the electrodes. The experimental apparatus for measurement of pressure is illustrated in Fig.14.6. The needle type of the positive electrode is attached with a special fixture on a micrometer stage for feeding. The ring type of the negative electrode is installed in the inlet of a manometer tube. The gap distance between the positive and negative electrodes is adjusted by the micrometer. The output pressure and flow rate are measured by pressure and flow sensors according to the applied dc voltage. Design and Fabrication of Micro Pump for Functional Fluid Power Actuation System 159 The three types of positive electrode as shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002565_s0043-1648(03)00338-7-Figure6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002565_s0043-1648(03)00338-7-Figure6-1.png", + "caption": "Fig. 6. Overlapping tooth flanks in two meshing positions.", + "texts": [ + " The simplified method has been compared with other methods with good results and it is fast since no iterations are needed to calculate the wear. However, the method cannot predict the correct wear at the pitch point or at those positions where the gears change from one to two teeth pair in contact (or vice versa). Therefore, we will determine the sliding distance that one point slides against its mating flank during one infinitesimal change in the meshing position of the gear pair. The solid geometry in Fig. 6 shows the not deformed mating tooth flanks (which therefore overlap each other) at an arbitrary position during the mesh cycle. Sliding takes place between the gear flanks during meshing, but since lubricant is present, we can ignore the tangential elastic displacement of the contact points. Due to the contact pressure the flanks are displaced parallel to the ya in+ and ya kn+ axes. The dashed geometry shows the tooth flanks at a position where gear i and gear k have rotated, respectively d\u03c6i and d\u03c6k from the position represented by the solid geometry", + " In addition, we need a kinematic relation that relates d\u03b8inj with d\u03b8klj. In Section 3.4, we assumed that the pair of points that is in rigid contact will form a contact pair also after the elastic deformation of the gears. In reality, the local contact deformation gives rise to sliding between the contacting tooth flanks during the elastic deformation. However, since this deformation is very small, we can ignore it here as well and as a result the kinematic relation between the two overlapping gear flanks in Fig. 6 may be defined by ra inj = M ikr a klj = \u2212ra klj (29) Both the co-ordinates xa inj and xa klj in Eq. (29) will be equal to zero when the unit normal vector n\u0302 a inj (or n\u0302 a klj since the flanks will share a common normal) has the same direction as the ya inj axis. We denote those values on \u03d5inj and \u03d5klj when this happens by \u03d50 inj and \u03d50 klj. We get n\u0302 a inj(\u03d5 0 inj, \u03b8inj) = [ j cos(\u03d50 inj + \u03b8inj \u2212 j\u03b1t) \u2212j sin(\u03d50 inj + \u03b8inj \u2212 j\u03b1t) ] = j = [ 0 1 ] (30) A solution to these equations is \u03d50 inj(\u03b8inj) = \u2212\u03b8inj + j\u03b1t + \u03c0(1 + 1 2j) (31) Isolation of \u03b8inj in expression (31) and then substitution into Eq", + " (9), (29) and (32) and then determine the differentials( 1 + j dhklj/d\u03d50 klj rk cos\u03b1t ) d\u03d50 klj= \u2212 zi zk ( 1 + j dhinj/d\u03d50 inj ri cos\u03b1t ) d\u03d50 inj (33) If the differences between the maximum and minimum wear depths of the flanks are small, the terms h\u2032 klj/rk cos\u03b1t and h\u2032 inj/ri cos\u03b1t in Eq. (33) will be very small compared to 1 (see Section 6), thus we can assume that these terms are equal to zero. These assumptions and the differential of \u03d50 inj (and \u03d50 klj) in Eq. (31) give us d\u03b8klj = \u2212 zi zk d\u03b8inj (34) We now obtain by combining Eqs. (28), (29) and (34) dswinj = ( 1 + zi zk ) |ya inj d\u03b8inj| (35) Since lubricant is present between the two non-conforming tooth flanks in Fig. 6, the frictional forces are low compared with the normal forces. Furthermore, if the contact width is much smaller than the relative radius of curvature of the flanks, the strains are small and each solid can be considered as an elastic half space, and we can apply Hertz contact theory to determine the contact width and the contact pressure between the tooth flanks [19]. According to [20], the Hertzian semi-contact width aH and pressure pinj may be defined by aH(\u03b8inj) = \u221a 4PinjR rel inj \u03c0E\u2217 , pinj(\u03d5inj, \u03b8inj) = 2Pinj \u221a a2 H \u2212 xa2 inj \u03c0a2 H (36) where Rrel inj is the relative curvature and E\u2217 is the composite modulus", + " (37) we get Rinj(\u03d5inj)= |(ri\u03d5inj \u2212 1 2 s \u2217 inj) cos\u03b1t \u2212 jri sin \u03b1t| = ya0 inj + rwi sin \u03b1wt (38) We now obtain from Eqs. (29) and (38) Rklj = \u2212ya0 inj + rwk sin \u03b1wt (39) The relative curvature may now be defined by Rrel inj(\u03d5 0 inj) = Rinj(\u03d5 0 inj)Rklj(\u03d5 0 inj) Rinj(\u03d5 0 inj)+ Rklj(\u03d5 0 inj) (40) Combining Eqs. (24) and (35) and integrating the obtained differential equation gives us hinj(\u03d5inj)= h0,inj(\u03d5inj)+ kw i ( 1 + zi zk ) \u00d7 \u222b \u03b82 inj \u03b81 inj pinj(\u03d5inj, \u03b8inj)|ya inj(\u03d5inj, \u03b8inj)| d\u03b8inj, \u03b81 inj < \u03b8 2 inj (41) where h0,inj(\u03d5inj) is the accumulated wear. If gear i is rotating clockwise in Fig. 6, then the lower limit of integration, \u03b81 inj, is the angle of the gear when the point enters the contact zone and the upper limit of integration, \u03b82 inj, is the angle of the gear when the point leaves the contact zone. If the gear rotates in the opposite direction, then these conditions are reversed. To determine \u03b81 inj and \u03b82 inj, we first conclude from Eqs. (15) and (16) that xr inj = xo inj cos \u03b8inj + yo inj sin \u03b8inj = roinj sin(\u03b8inj + \u03c8inj) (42) where roinj(\u03d5inj)= |ro inj(\u03d5inj)| = \u221a ((ri\u03d5inj \u2212 1 2 s \u2217 inj) cos\u03b1t \u2212 jri sin \u03b1t)2 + rbi2, sin\u03c8inj = xo inj roinj (43) We obtain by rearranging Eq" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure2.7-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure2.7-1.png", + "caption": "Fig. 2.7 Experimental setup", + "texts": [ + "34 MHz. The slider material was Si. The contacting surface was dry etched to be fabricated a lot of projections for friction drive. The contact area was 4 by 4 mm2. Thin film material were used as friction material on Si slider. The materials were diamond like carbon. Thickness of the film was 0.1 \u03bcm. The slider used for the experiment had 5 \u03bcm diameter projections with intervals of 14 \u03bcm on their friction drive surface. The height of the projections was 0.5 \u03bcm. An experimental setup is shown in Fig.2.7. On the stator device, the silicon slider is placed with applying pre-load by a plate spring. The pre-load was designed to be 8.7 N. The motion of the slider is guided with a ball bearing linear slider placed beneath the stator SAW device. Surface Acoustic Wave Motor Modeling and Motion Control 15 For characterize the motor speed response, transient responses of the motor were measured by changing the driving voltage, namely, driving power. The speed of a SAW motor depends on the driving power. Due to the unsymmetrical construction of the electrodes arrangement, the propagating power without a slider was already imbalanced" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003003_tmag.2004.843349-Figure6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003003_tmag.2004.843349-Figure6-1.png", + "caption": "Fig. 6. Result of 3-D FEA flow analysis indicating air velocity distribution on the whole SRM model.", + "texts": [ + "448 m/s, which is equivalent to the whirl of air between speed 1200 and 2000 rpm. A similar observation in the air pocket at the rotor interpolar region shows that the iron surfaces s8 and s9 are dissipating heat at the air velocities 2.234 and 3.351 m/s. Velocities less than 2 m/s may be ignored as they are not near the iron surfaces and oriented at the midregion of the air pocket. Turbulence of air is inherently 3-D, and hence, air flow analysis in 3-D can only be helpful in predicting the turbulence of air inside SRM. Results of such a 3-D flow analysis are shown in Fig. 6. It has to be noted that in a 3-D flow analysis, results can also indicate varying pressures at various air pockets. This is obvious as the velocity of air is not constant. As the pressure of air is not of analysis interest, say for thermal analysis, the analyst can safely omit it. The option of animating the air turbulence when the rotor rotates is possible. Thermal modeling using thermal equivalent circuit of electric motors has been extensively done in the past for thermal analysis, which dates back to early 1920 [4]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000282_s11665-021-05905-y-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000282_s11665-021-05905-y-Figure1-1.png", + "caption": "Fig. 1 (a) Schematic diagram of the WAAM-CMT process, (b) CCW 3D model diagram, (c) schematic diagram of an AM part showing the positions of the tensile test samples and metallographic and hardness sample, (d) the size of tensile test samples in mm", + "texts": [ + " (Ref 12) showed that by feeding ER5356 welding wire and adding titanium powder, Al-Mg alloy thin-walled parts could be manufactured by welding wire + arc additive manufacturing (WAAM). The authors reported that the internal crystal morphology changed from columnar to equiaxed crystal, and the mechanical properties were improved. As a new type of wire that has emerged in recent years and been widely studied, CWW is generally composed of 7 fine wires twisted together, with one wire in the middle as the central wire and six wires twisted and wound around the central wire. Fig. 1(b) shows the 3D model of CWW. It has been demonstrated for various arc welding processes (including electrogas welding) and, when compared to a solid single-wire, has the advantages of high deposition efficiency, self-rotation of welding arc, and energy savings. Chen et al. (Ref 13, 14) found that the cable wire deposition rate was 40% higher than that of the monofilament under the same conditions, which improved the welding quality. Due to the agitation of the molten pool by the rotating arc, the superheated droplets are transferred directly to the side wall or the molten pool near the side wall, promoting the heating and melting of the base material", + " This paper reports a novel work in which CWW was utilized for WAAM, and the mechanical properties and microstructure of the printed workpiece were investigated. The 6061-T6 aluminum alloy plate with a size of 250 9 180 9 10 mm3 was used as a substrate. Before deposition, the working face of the substrate was polished with sandpaper and the surface was cleaned with acetone. AA5356 aluminum alloy CWW with a 1.6 mm diameter was employed as the filling material (elemental composition of the wire and forming substrate are given in Table 1). The experiments were performed on a WAAM-CMT system (Fig. 1a), which mainly consists of a six-axis Fanuc robot, robot control cabinet, Fronius CMT-Advance power source, wire feeding system, and shielding gas system. High purity (99.99%) argon gas was used as the shielding gas. The contact tube-to-work distance (CTWD) was kept at 18 mm. The process parameters are shown in Table 2. The thin wall has a total of 40 layers, and each layer is composed of two welding seams. During the printing process, a high-speed camera with a frame rate of 1000 frames per second was used to capture images to observe the state of the welding wire and weld pool. The tensile tests of the parts made of WAAM were carried out in two directions, parallel to the substrate (sample 1) and perpendicular to the substrate (sample 2), as shown in Fig. 1(a). The tensile test sample size is shown in Fig. 1(d). Samples for the microstructural analysis and microhardness measurement were taken from the transverse cross section removed from the center of the built column, as shown in Fig. 1(c). The phase analysis of the sample was carried out with a (Bruker D8 advance) x-ray diffractometer (XRD). The XRD sample was polished with sandpaper. The scanning speed was 4 /min, and the scanning range was 20 to 90 with Cu Ka radiation. Before metallographic observation, the sample needed to be polished and then etched with HF solutions for 10 s. The morphology, defects, and fracture of the samples were characterized by a CVOK 4XC-TV optical microscope (OM) and Phenom-XL Journal of Materials Engineering and Performance scanning electron microscope (SEM)", + " During the process of WAAM, a high-speed camera was used to observe the state of the molten pool and transfer of the molten metal droplets. As shown in Fig. 2, the typical process of CMT (Ref 17) can be seen: arc ignition, droplet formation, short circuit, and wire retraction. These four steps continuously loop. The cable welding wire is composed of 7 filaments. Compared with the previous single-stranded wire (Ref 18, 19), the printing efficiency is higher, and it is easier to melt and produce larger droplets (as shown in Fig. 1b). The wire moves toward the weld pool and sends the melting droplets and wire into the molten pool via short circuit transfer. The wire retracts to separate the melt droplets. The whole process is very stable without a lot of splashes. The shape of the molten pool is also relatively stable, which has a positive effect on the formation of components. It can be seen from Fig. 3 that the surface of the sample is relatively smooth without any visible defects. However, the upper heat dissipation speed is slow, and the boundary between layers is not clear" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000545_jestpe.2021.3055224-Figure31-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000545_jestpe.2021.3055224-Figure31-1.png", + "caption": "Fig. 31 2D FE-predicted electromagnetic performance of the designed and prototyped BDFRM with a multi-layer barrier rotor, (a) electromagnetic torque vs. allocation of specific electric loading and torque angle, (b) electromagnetic efficiency vs. allocation of specific electric loading and torque angle. The diamond denotes the operating point for motor sizing.", + "texts": [ + " Similar to sizing approaches of the conventional DCM, IM and SM, the magnetic saturation and flux leakage need to be considered by a few coefficients that will be determined by iterations in the design process. The specifications and main electromagnetic performance of the designed BDFRM based on the air-gap field modulation theory are tabulated in TABLE V. It can be seen that the torque and efficiency are related to the allocation of specific electric loadings and the torque angle, as shown in Fig. 31. It also shows that the maximum torque occurs close to the operating point with the specific electric loadings equally allocated between the two stator windings and a torque angle close to \u03c0/2, as predicted from the analytical equation (27). Authorized licensed use limited to: Carleton University. Downloaded on May 31,2021 at 22:24:43 UTC from IEEE Xplore. Restrictions apply. 2168-6777 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000562_j.mechmachtheory.2021.104380-Figure7-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000562_j.mechmachtheory.2021.104380-Figure7-1.png", + "caption": "Fig. 7. Prototype of the studied 6-DOF PCM with three flexible limbs.", + "texts": [ + " Based on the closed-form gradient (17) , the inverse problem of kinetostatics analysis of the studied PCMs can also be solved efficiently using the steepest-decent searching algorithm [53] . The update theme of the iterative searching process can be represented as x (k +1) in v = x (k ) in v \u2212 (\u2207 (k ) in v )\u22121 f (k ) in v (18) where the variables are defined in the same way as those in (15) . In this section, a prototype of the illustrated 6-DOF 3- PR F lex R parallel continuum manipulator is developed as shown in Fig. 7 , to verify the effectiveness of the proposed kinetostatics modeling and analysis method. Experiments on the reachable workspace and positioning accuracy of the developed prototype have been conducted to validate the correctness of the proposed approximation approach. From the results, it can be stated that the proposed method can predict the kinetostatics behavior of the parallel continuum manipulators precisely and be used for position control of such kind of flexible parallel manipulators. The developed prototype consists of three identical \u2018 PR F lex R\u2019 flexible limbs", + " Ordinary spring steel stripes are adopted for the limbs\u2019 slender flexible links to generate large deflections coupled at the moving platform. A aluminum alloy plate is utilized as the manipulator\u2019s moving platform, which is connected to the flexible limbs through passive revolute joints. Steel parts are used as the main components to connect the flexible links to the PR drives and the moving platform. The developed prototype is assembled in a symmetric way about its central axis. As exhibited in Fig. 7 , the position of proximal end and distal end of the flexible link in the j th limb are denoted as p bj and p dj . The three PR drives are evenly mounted on the base platform along the vertical direction. As shown in Fig. 7 , the radius of their distribution circle is 150 mm . And the rotational axes of the active R joints are in the corresponding radial directions. On the distal end, the passive revolute joints are equally distributed on the moving platform with radius of 50 mm . Likewise, their axes are also along the radial directions, pointing to the center of the moving platform. The slender flexible links in the three limbs, namely the spring steel stripes, are identical to each other, of the effective length 270 mm and the cross-section size 10 mm \u00d7 0 ", + " 8 mm , as indicated in the figure. In the proposed modeling, the number of discretized segments of flexible links is set to 54(the length of each segment 5 mm ). In addition, the elastic and shearing modulus of the spring steel are set to E = 196 . 5 GPa and G = 80 . 5 GPa , respectively. In the experimental apparatus, the motion tracking system \u2018OptiTrack\u2019 is used to measure the real-time pose of the manipulator\u2019s moving platform via three spherically mounted reflectors (SMRs), as illustrated in Fig. 7 . To identify the assembling errors of the PR drives, another set of SMRs are mounted on the output stage of each compound actuator, as complementary measurements of the actuator\u2019s active inputs. Thus, not only the end-effector pose g st , but also the corresponding position and orientation of the PR drives can be captured simultaneously in the validation experiments. In addition, the SoftBUS communication protocol is employed to connect the controller of the servo motors (Maxon RE40) and the software of the OptiTrack system, together" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003428_j.jbiomech.2005.12.011-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003428_j.jbiomech.2005.12.011-Figure2-1.png", + "caption": "Fig. 2. (a) To select PGs for skewness angle measurement, 13 13 grids were used. (b) PG skewness angle (y) is defined as the absolute angle between the orientation of the small PG and a direction normal to the fibril, no matter which direction the PG is skewed. (c) The protocol of PG selection is as follows: (i) PGs overlapping with grid dots were selected for measurement (angles 1, 2, and 3); (ii) if there were two PG orientations passing through the grid dot and it was difficult to judge which PG overlaps the most, the one with the smaller skewness angle was selected (angle 4); (iii) PGs with longitudinal orientation (marked by circle) were ignored. Arrow shows the orientation of collagen fibrils.", + "texts": [ + " Ultra-thin sections, 85 nm thick, were cut with a diamond knife and mounted on uncoated grids. Samples were then observed with TEM (Philips CM12). A commercial software package (Image Pro Express\u2014Media Cybernetics, Inc.) was used to quantify skewness angle. Three images were randomly selected for quantification of PG skewing angle for each specimen, giving a total of 15 images. Image subsections, roughly 3 mm 3 mm in size, were overlaid with a 13 13 grid. Only those PGs that corresponded to a grid point were selected for skewness angle measurement (Fig. 2a). Skewness angle (y) was defined relative as the angle between the PGs and a line normal to the fibril (Fig. 2b). When the PG is underformed and thus perpendicular to the fibril, the skewness angle is zero. In practice, we measured the angle between the main axis of the PG and the fibril, a or a0. Skewness angle can thus be calculated by subtracting 901 from a or a0, and then taking the absolute value (Fig. 2b). In practice, the direction of orientation of each object was set manually and angles were computed automatically. The protocol used was as follows: (i) PGs overlapping with grid dots were selected for measuring (angles 1, 2, and 3 in Fig. 2c). (ii) Occasionally, two PG J. Liao, I. Vesely / Journal of Biomechanics 40 (2007) 390\u2013398 393 orientations passed through the grid dot and it was difficult to judge which overlaps the most. We made an arbitrary decision to select the one with the smaller skewness angle for the sake of consistency (angle 4 in Fig. 2c). (iii) Since our main purpose is to track the response of interfibrillar PG bridges under external load, PGs with longitudinal alignment were ignored (circle in Fig. 2c). These PGs do not change their alignment angle with load and probably do not participate in the interaction between fibrils. After all the data were compiled, comparisons of measured PG angles between chordae fixed at different loads were done by one-way analysis of variance (ANOVA) using SigmaStat (SPSS Inc., Chicago, Illinois). In the load-free chordae, the dark-staining PGs appeared as an abundant network organized perpendicular to the collagen fibrils (Fig. 3a). The distribution of the PGs in cross-section was not as uniform as in longitudinal sections of chordae (Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000131_j.matcom.2020.12.030-Figure8-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000131_j.matcom.2020.12.030-Figure8-1.png", + "caption": "Fig. 8. Simulated path tracking results of the end-effector of the WMR synthesized by the proposed RZNN model (9) with dynamic DN y(t) = 0.025exp(-t). (a) Actual trajectory of the end-effector and desired path. (b) Position errors of the end-effector. (c) Motion trajectories of the WMR. (d) top view of the motion trajectories of the movable platform.", + "texts": [], + "surrounding_texts": [ + "In order to further verify the robustness and effectiveness of the proposed RZNN model (9) for solving IKP of WMR in noise-polluted environment, the original ZNN model activated by Sign-bi-power activation function is used to complete the same windmill-shaped trajectory tracking task under the same noise environment. The original ZNN model for solving IKP of WMR is shown below. B \u2022 \u0398 = \u2022 rmd (t) + \u03bb\u0393 ( \u2022 rmd (t) \u2212 \u2022 rm(t) ) + N (t) (17) It can be observed that the RZNN model (9) for solving IKP of WMR is similar to the original ZNN model (15). ere, if the ZNN model is activated by the previous reported activation functions in Table 1, we call it original ZNN odel; if the ZNN model is activated by the new presented power-versatile activation function (PVAF), we call it ZNN model in this paper. It is worthy to mention that the ZNN model activated by the Sign-bi-power activation unction in Table 1 is nearly the most effective computing tool for solving time-varying problems, which even nables the ZNN model converge in finite time [30]. The comparisons between the two counterparts are relatively ational and meaningful. The simulated results of the end-effector of the WMR tracking the same windmill-shaped trajectory synthesized y the original ZNN model (15) activated by the Sign-bi-power activation function in Table 1 with the same dynamic oises in Table 2 are presented in Figs. 10\u201317. As seen from Figs. 10(a), 12(a), 14(a) and 16(a), the actual trajectories f the end-effector seriously deviate from the desired windmill-shaped path. That is to say, the end-effector of the MR synthesized by the original ZNN model (15) activated by Sign-bi-power activation function fails to complete y the path tracking task under the interference of noises. It can be observed in Figs. 10(b), 12(b), 14(b) and 16(b) that the position errors e = (ex, ey, ez)T of the end-effector are all relatively large, and some of them even reach to 0.5 m, which further indicates the failure of the path tracking task. More detailed simulation results of the motion trajectories synthesized by the original ZNN model (15) activated by the Sign-bi-power activation function in Table 1 during the windmill-shaped path tracking task execution can be found in Figs. 10(c\u2013d), 12(c\u2013d), 14(c\u2013d) and 16(c\u2013d). For the purpose of comparison and observation, the simulated variables of the WMR synthesized by the original ZNN model (15) activated by Sign-bi-power activation function during the path tracking task execution are presented in Figs. 11, 13, 15 and 17. All the above simulation results reveal that the original ZNN model (15) does not possess robustness for solving IKP of WMR, and it is very vulnerable to noise, which indicates that it is not suitable for the practical applications with noises and disturbances. Based on the above simulation results and analysis, we can draw the conclusion that the proposed RZNN model (9) has excellent and inherent noise and disturbance canceling ability, which enables the proposed RZNN model (9) be more suitable for the practical applications of solving IKP of WMR with noises and disturbances." + ] + }, + { + "image_filename": "designv10_6_0003003_tmag.2004.843349-Figure15-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003003_tmag.2004.843349-Figure15-1.png", + "caption": "Fig. 15. Model of SRM with fins and terminal box.", + "texts": [ + " 14, which indicate that the steady-state temperature is attained at 356 K, whereas without considering the eddy-current loss, it was 350 K. 3) Thermal Analysis Considering Fins: The temperature rise of the electric machines is kept under permissible limits by providing fins. It is possible to increase the heat energy transfer between the outer surface of the machine and the ambient air by increasing the amount of the surface area in contact with the air. Fins are the corrugations provided throughout the outer surface of the frame. When fins are provided on the outer frame of the machine, as shown in Fig. 15, the surface area of heat dissipation gets increased, thus effecting the heat dissipation. It is of the kind called radial fin with rectangular profile. In order to increase the fin effectiveness, various possible combinations of fin dimensions are to be considered. Steadystate thermal analysis has to be carried out for each combination. The fin dimension which produces the least steady-state temperature rise is usually selected for the end product. Table I is the summary of steady-state thermal analysis performed on varying fin dimensions" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002463_bf00118823-Figure14-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002463_bf00118823-Figure14-1.png", + "caption": "Fig. 14. Sketch, following Berg [26], of the cross-section of a spirochete's helical cell body and of its closely fitting external sheath, showing the \"roller bearing\" action of the rotating flagella between the sheath's inner surface and the cell body's outer surface. These rotate in opposite directions with rotation speeds ws and WB respectively.", + "texts": [ + " Only after the establishment (around 1974) of the existence of rotary motors driving bacterial flagella [15] did it first become possible to find a convincing biomechanical resolution of the enigma [25,26]; indeed this can in retrospect be perceived as having been the only possible resolution obeying fundamental angular-momentum principles. Here, that successful resolution is summarised before I go on to consider its implications for the external flow field. The rotary motors cause each of the two flagella to turn in the same sense so that, at each cross-section (Fig. 14) within the above-mentioned narrow space between cell body and sheath, the flagella act as roller bearings that permit the sheath and the cell body to be in relative rotary motion. This is achieved by the sheath turning in one direction at rotation speed ws (the same all along the sheath) and the cell body turning in the opposite direction at rotation speed wB; where, if as is the internal radius of the sheath and aB the external radius of the cell body, then asws = aBWB (because both are equal to the circumferential velocity of the rotating flagella)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003521_j.conengprac.2007.04.008-Figure10-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003521_j.conengprac.2007.04.008-Figure10-1.png", + "caption": "Fig. 10. Top view of TRMS.", + "texts": [], + "surrounding_texts": [ + "In developing Lagrangian based model the TRMS configuration has been divided into three subsystems; the first one consists of the free\u2013free beam (tail and main beams), tail rotor, main rotor, tail shield and the main shield, the second one comprises the counterbalance beam and weight, and finally the third one is a pivoted beam." + ] + }, + { + "image_filename": "designv10_6_0000062_012121-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000062_012121-Figure3-1.png", + "caption": "Figure 3. The scheme of the unit with a universal working body in two projections a - view from above; b - view from the side; 1 and 2 - the first and third sections in the form of three frames;3 - front", + "texts": [ + " The design of the multifunctional tillage unit under consideration allows in one pass to carry out the soil slitting in the vertical plane to a depth twice the depth of cultivation, moldboard loosening of the soil with pruning of weeds, additional crushing and harrowing of the soil to a width equal to the width of the cultivator. Our Center has developed more than one design of tillage equipment, including those with automated regulation of the depth of tillage and combined devices [8,9,10,11]. Currently, the work is going on to improve the design of the multifunctional tillage unit (Figure 3), which consists of three sections in the form of a frame structure, the main one is located in the center and two folding ones are fixed to it on the sides. The side sections contain three frames. On the front frames of the side sections, four slotters and cultivator shares are installed. The middle frame consists of two tines on which the cultivator's legs are fixed. The rear frames contain one leg each. The paws are installed with the possibility of overlapping the front paws by 2 ... 4 cm. The rear frames of the side sections contain a needle grinder and a tooth harrow, the total width of which is equal to the width of three paws with overlapping" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002903_s0168-874x(01)00100-7-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002903_s0168-874x(01)00100-7-Figure2-1.png", + "caption": "Fig. 2. Formation schema of rack cutter surface G.", + "texts": [ + " The equation of the llets of the involute helical pinion are as follows: R(i) 1 = (O(i;P) rx \u2212 r(P)f sin (i;P)f + r1) cos 1 \u00b1 (O(i;P) rx \u2212 r(P)f sin (i;P)f ) cot (i;P)f sin P sin 1 (O(i;P) rx \u2212 r(P)f sin (i;P)f + r1) sin 1 \u2213 (O(i;P) rx \u2212 r(P)f sin (i;P)f ) cot (i;P)f sin P sin 1 \u2212(O(i;P) ry \u00b1 r(P)f cos (i;P)f ) cos P \u2212 ( O(i;P) ry \u00b1 O(i;P) rx cot (i;P)f \u2212 r1 1 sin P ) tan P sin P i = 2 and 4: (2) Similarly, the upper and lower signs refer to the left-side and right-side llets, respectively. Here, r(P)f denotes the radius of the llet, and (i;P)f and uP are parameters of the tool surface. Fig. 2(a) depicts the normal section of the rack cutter G applied to the generation of the modi ed helical gear, which comprises four major regions. Regions 1 and 3 generate the left-side and right-side working surfaces of the gear, while regions 2 and 4 generate the left-side and right-side llets, respectively. Regions 1 and 2 are symmetric with regions 3 and 4, respectively, with respect to the X (G) r -axis. For simplicity, only the design parameters of regions 1 and 2 are shown in Fig. 2(a). In practice, a curved-template guide can be employed on a conventional hobbing machine to produce a varied plunge of the hob cutter during gear generation. Fig. 2(b) illustrates the formation of the imaginary rack cutter surface G when a hob cutter moves with a varied plunge during the gear generation process. An auxiliary coordinate system S(G)a (X (G) a ; Y (G) a ; Z (G) a ) which translates along the line O(G) c O(G) a (i.e. axis Z (G) a ) is set up rst. Line O(G) c O(G) a forms an angle G with axis c of the coordinate system S(G)c (X (G) c ; Y (G) c ; Z (G) c ). The normal section of the circular-arc rack cutter is rigidly attached to coordinate system S(G)r (X (G) r ; Y (G) r ; Z (G) r ) with its origin O(G) r moving along a curve of radius R(G) \u2018 ", + " Therefore, coordinate system S(G)r shifts by a variable amount, EG, with respect to coordinate system S(G)c . Parameter G indicates the position of point O(G) r on the curved-template guide and EG is the corresponding shift of the hob. Parameter (G)max denotes the extreme value of (G) at which the parameter EG reaches its maximum value E(G) 2 . Parameters W and G represent the face width and the helix angle of the gear, respectively. The signi cant diIerences between the normal sections of P (Fig. 1(a)) and G (Fig. 2(a)) are the shapes of regions 1 and 3 which generate the working surfaces of tooth pro les. Regions 1 and 3 of the normal section of rack cutter G are circular arcs rather than straight lines, to produce tooth crowning in the pro le direction of the generated gear. The deviation between the circular-arc and the straight line results in a built-in parabolic TE on the generated tooth surface. A curved-template guide is employed on a conventional hobbing machine to produce a varied plunge of the hob cutter during the gear generation process", + " Based on the FEA results, the maximum principal stress is \u22121059:4 MPa, which is very close to the Hertzian contact stress, !H = \u22121024:34 MPa (calculated from Appendix A). Therefore, the proposed FEA method can be used to evaluate the contact stress. Recall that for the double-crowned gear generation, parameter RG indicates the radius of the rack cutter\u2019s normal section, while parameter R(G) \u2018 denotes the radius of the curved-template guide along which the hob cutter moves during the generation process, as shown in Fig. 2. Therefore, RG is related to the deviation of the generated tooth pro le from the standard involute curve. The deviation results in a pre-designed parabolic TE of this helical gear set. On the other hand, R(G) \u2018 aIects the contact areas and the degree of lengthwise crowning is inversely proportional to R(G) \u2018 . Consequently, increasing the design parameter R(G) \u2018 increases the contact area as well as a reduced contact stress. According to the gear tooth mathematical model and the FEA results, Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000208_j.matdes.2021.109725-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000208_j.matdes.2021.109725-Figure3-1.png", + "caption": "Fig. 3. Tensile test spe", + "texts": [ + " All EBSD scans performed were taken from the closest position available to the centre of the block section, remote from any simulated cooling holes present. Micro-hardness values were recorded on the as-built and post solution heat treated samples using a Vickers hardness indenter. A 1 kg load, HV (1), was used throughout. 25 measurements were taken from each material, across the full width of the sample, and data from the tests was analysed using Minitab statistical analysis software. Ten tensile tests were performed on round cylindrical specimens (as depicted in Fig. 3) of the post solution heat treated material, using the \u2018low\u2019 parameter set (energy density of 1.60 J/mm2). All testing was undertaken in accordance with ASTM E21-17 [17] at a temperature of 850 C. A decision was made to test only the low energy density parameter set since this batch of specimens would be expected to contain the highest levels of porosity, and therefore test results are likely to contain more scatter, specifically for properties such as ultimate tensile strength (rUTS) and percentage elongation" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure24.9-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure24.9-1.png", + "caption": "Fig. 24.9 Top view", + "texts": [ + " Twelve of them are attached at the center of the edges of the virtual octahedron inscribed in the stator. Seven of them are attached at the center of the faces of the virtual octahedron inscribed in the stator without the upper face. The upper face is open for the output shaft. The number of the turns of each armature coil is 153. The inner diameter and the outer diameter of the acrylic shell are 90mm and 110mm respectively. The developed motor is air-cored type without back yoke to avoid the cogging torque. The output torque of the developed motor is small but motor control is easy. Figure 24.9 is the upper view of the designed 6-8 spherical stepping motor when the output shaft is at the vertical position. The permanent magnets are positioned at every 90 degrees around the output shaft and North Poles and South Poles are positioned alternately. The pairs of coils (1,1\u2019), (2,2\u2019) and (3,3\u2019) are positioned at every 120 degrees around the output shaft. The relationship between the permanent magnets and the armature coils is similar to that of the conventional three Actuator with Multi Degrees of Freedom 287 phase planer stepping motor with two pairs of permanent magnets", + " Therefore, when I supply three phase sinusoidal currents to the armature coils (1,1\u2019), (2,2\u2019) and (3,3\u2019), the rotor will rotates around the output shaft. Fig. 24.10 Bottom view Fig. 24.11 Tilt view 288 Tomoaki YANO Figure 24.11 is the view of the designed 6-8 spherical stepping motor from the direction of the arrow. One of the iron cores is just under the armature coil 245. The position of the armature coil 245 is the center of the triangle formed from coil2, coil4 and coil5. The positions of the permanent magnets and the coils (2,6\u2019), (5,24\u2019) and (4,25\u2019) are same as Fig.24.9. Therefore, when I supply three phase sinusoidal currents to the armature coils (2,6\u2019), (5,24\u2019) and (4,25\u2019), the rotor will rotates around coil245. At the back view of Fig.24.11, the relationship between the permanent magnets and the armature coils is same as Fig.24.11. Therefore, when I supply three phase sinusoidal currents to the appropriate armature coils, the rotor will rotates around coil245. The rotor has six iron cores and the stator has seven armature coils at the center of the face of the octahedron inscribed in the stator" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003788_978-1-4020-5967-4-Figure8-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003788_978-1-4020-5967-4-Figure8-1.png", + "caption": "FIGURE 8. The wedge (Mechanics 2.15). Drachmann\u2019s drawing (The Mechanical Technology, p. 72) is from Ms L.", + "texts": [ + " If we imagine detaching the rightmost section of the weight Z from the sections G\u030cBT. , it will hold those sections in equilibrium. Thus a force equal to \u00bc the total weight of Z, applied at K, balances \u00be the total weight (G\u030cBT. ), and a slightly larger force will move it.36 In the case of the wedge and screw the similarity to the concentric circles is much less clear. Since Heron claims that the screw is simply a twisted wedge (2.17), I shall concentrate here on the analysis of the wedge in 2.15 (see Fig. 8).37 The argument is in two stages: (1) First Heron claims that any blow, even if it is slight, will move any wedge. The idea is to divide 35 Mechanics, 2.12 (Opera, vol. II, p. 126.1\u20135); Engl. trans. Drachmann, The Mechanical Technology, p. 70, modified. 36 In general, letting F represent the moving force, W the weight, and n the total number of segments of rope that bear the weight, we have F:W :: 1:n. 37 Note however that the analysis of the screw as a twisted wedge is supported by explicit reference to a practical procedure for making a screw, viz", + " Thus just as in the concentric circles, the effect of a small force can equal that of a large one; the difference is that in the circles the effectiveness of a force depends on its distance from the centre, while in the wedge it depends on the distance over which the force acts. Similarly, in the case of the screw Heron notes that a screw with tighter threads will be able to move a larger load by means of the same force, but it will 39 Mechanics, 2.15 (Opera, vol. II, p. 134.21\u201331); Engl. trans. Drachmann, The Mechanical Technology, p. 73, modified. 40 Alternatively, in Fig. 8, if the force BG\u030c is applied to the whole wedge MD, the load will be displaced by MD in a given time t. But if the force BH, equal to \u00bc BG\u030c, is applied to the sub-wedge RD, then the load will be moved by \u00bc MD in time t and by MD in 4t. THEORY AND PRACTICE IN HERON\u2019S MECHANICS 31 require a greater time to do so.41 The key idea in the analyses of both the wedge and the screw is thus that of compensation between forces and the times (and distances) over which they act: if we reduce the force, we must increase the time (see further below, pp" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure14.2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure14.2-1.png", + "caption": "Fig. 14.2 Schematic of cylindrical ECF pump", + "texts": [ + " Such excellence in performance makes it possible to suppress generation of noise and vibration. Thus it can safely be affirmed that the pump is adequate to be used for micro-driving. The Dibutyl decanedioate (DBD), which has long been put to practical use as standard ECF, is made use of in this study. DBD is the electro-conjugate fluid with the density of 936.34 kg/m3 (@20 degrees Celsius) and viscosity of 9.07 10-3 Pa s (@20 degrees Celsius). The cylindrical type of micro ECF pump has been deigned and fabricated. Figure 14.2 illustrates a proposed cylindrical ECF pump for micro fluid power actuation system. The positive needle electrode with a number of array pins is located on one side of a narrow tube. The negative electrode with ring geometry is assigned to outlet port of the tube. The chamber in the tube is filled with the ECF. When a dc voltage is applied between the positive and negative electrodes, the ECF jets 156 Yutaka TANAKA and Shinichi YOKOTA are locally generated from the tip of positive needle electrodes to the negative ring electrode by applied non-uniform electric field" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003286_bf01175968-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003286_bf01175968-Figure4-1.png", + "caption": "Fig. 4. a, b P l a n ~ r e x a m p l e s w i t h / ~ 1, c, d, e Spa t i a l e x a m p l e s w i t h ] ~ 3", + "texts": [ + " We are thus led to the following result: a) Number of contacts needed ~ 7 - - / ; b) The contact normals belong to the reciprocal 6 - - / system; c) They form an opposition. Specifically, for ] ~ 1, the six normals belong to a linear complex; for / ---- 2, the five normals belong to a linear congruence; for / ~ 3, the four normals belong to a regulus; for ] - - 4, the three normals are concurrent and coplanar; for / ~ 5, the two normals are in line. Figs. 4a, 4b give planar examples with / - - 1 while Figs. 4c, 4d, 4e give spatial examples with / ---- 3. In Fig. 4a the opposite end of P1 (for example) must fall within the are P2P~. Similarly in Fig. 4c the opposite end of P1 (for example) falls within the spherical triangle P2P3P4. Fig. 5 shows a cylindrical element with six contact normals suitably chosen to provide a revolute pair, ] ~ 1. 8 Acta Mech. 52/1--2 \" Let the initial number of degrees of freedom possessed by the body be b and the freedoms left after the contacts are applied be / . The initial mot ion of b degrees of f reedom can be described b y means of (6 - - b) l inearly independent screws qi (7\" ~ 1 to 6 - - b) of the reciprocal (6 - - b) system", + " Let the number of contacts in the i-th stage be q, the total number of contacts c, the totM number of stages s and the number of degrees of freedom finally remaining b e / . We then have from the previous section: ~ = b - - / ~ + 1; c, = / ~ - - / ~ + 1; . . . ; e, = / ~ _ ~ - - / + 1. Adding, we obtain the number of contacts needed: c = b - - / + ~ . C7) The conditions under which the reactions become determinate have been pointed out in the previous section. The following are examples of reduction of freedom in stages. (i) The flat element of Fig. 4 d or 4 e may bc further restrained by a contact scheme whose projection on a plane parallel to the flat is as in :Fig. 2a to obtain / ~- 0; total number of contacts ----- 8; if the additional four contacts are eoplanar (]~'ig. 2a) and therefore linearly dependent; the reactions become determinate and one contact each from the two sets of contacts is unloaded; (ii) The cylindric element of Fig. 5 may be first restrained by five contacts on the cylindrical surface to obtain ] ~ 2 and then two contacts, one each on the end planes, may be applied to obtain / -~ 1 and a revolute pair; total number of contacts ~ 7 as against 6 in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002486_978-3-662-03729-4_1-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002486_978-3-662-03729-4_1-Figure4-1.png", + "caption": "Fig. 4. The reference and the current configurations of a body and one of its lines", + "texts": [], + "surrounding_texts": [ + "A dual number a is defined as the sum of a prim al part a, and a dual part ao, namely, a = a+ Eao, (1) where E is the dual unity, which verifies E =/:. 0, E2 = 0, while a and ao are real numbers, the former being the primal part of a, the latter its dual part. Actually, dual numbers with complex parts can be equally defined (Cheng and Thompson 1996). For the purposes of this chapter, real numbers will suffice. If ao = 0, ais called areal number, or, correspondingly, a eomplex number; if a = 0, a is called a pure dual number; and if neither is zero a is called a proper dual number. Let b = b + bo be another dual nu mb er . Equality, addition, multiplication, and division are defined, respectively, as a=b a = b, ao = bo (2a) a+b = (a + b) + E(aO + bo) (2b) ab ab + E(abo + aob) (2c) a ~ _ (abo - aob) b =/:. 0. (2d) b b E b2 ' From eq.(2d) it is apparent that the division by a pure dual number is not defined. Hence, dual numbers do not form a field in the algebraic sense; they do form a ring (Simmons, 1963). All formal operations involving dual numbers are identical to those of ordinary algebra, while taking into account that E2 = E3 = ... = 0. Therefore, the series expansion ofthe analytie junetion f(x) of a dual argument x is given by f(x) = f(x + EXo) = f(x) + EXo d:~) . (3) As a direct consequence of eq.(3), we have the expression below for the exponential of a dual nu mb er x: (4) and hence, the dual exponential eannot be a pure dual number. The dual angle {j between two skew lines Cl and C2 , introduced by Study (1903), is defined as {j = () + ES, (5) where () and S are, respectively, the twist angle and the distance between the two lines. The dual trigonometrie functions of the dual angle (j are derived directly from eq.(3), namely, cosO = COSB-EssinB, sinO = sinB+EscosB, tanO = tanB+Essec2 B .(6) Moreover, all identities for ordinary trigonometry hold for dual angles. Like wise, the square root of a dual number can be readily found by a straightfor ward application of eq.(3), namely, r;: r:: Xo v x = v x + E 2y'x , (7) A dual vector a is defined as the sum of a primal vector part a, and a dual vector part aa, namely, a=a+Eao, (8) where both a and ao are Cartesian, 3-dimensional vectors. Henceforth, all vectors are assumed to be ofthis kind. Further, let a and b be two dual vectors and c be a dual scalar. The concepts of dual-vector equality, multiplication of a dual vector by a dual scalar, inner product and vector product of two dual vectors are defined below: a = b a=b and ao=bo ; (9a) ca ca+E(cOa+cao) ; (9b) a\u00b7b = a\u00b7 b + da\u00b7 bo + ao . b) ; (9c) axb = a x b + da x bo + ao x b) . (9d) In particular, when b = a, eq.(9c) leads to the Euclidean norm of the dual vector a, i.e., (ge) Furthermore, the six normalized Pl\u00fccker coordinates of a line C passing through a point P of position vector p and parallel to the unit vector e are given by the pair (e, p xe), where the product eo == p x e denotes the moment of the line. The foregoing coordinates can be represented by a dual unit vector e*, whose six real components in e and eo are the Pl\u00fccker coordinates of C, namely, e* = e + E eo, with Iiell = 1 and e\u00b7 eo = 0 . (10) The reader is invited to verify the results summarized below: Lemma 2.1. For e* == e + E eo and f* == f + do defined as two dual unit vectors representing lines C and M, respectively, we have: (i) 1f e* x f* is a pure dual vector, then C and M are parallel; (ii) if e* . f* is a pure dual number, then C and Mare perpendicular; (iii) C and Mare coincident if and only if e* x f* = 0; and (iv) C and M intersect at right angles if and only if e* . f* = O. Dual matrices can be defined likewise, i.e., if A and A o are two real n x n matrices, then the dual n x n matrix A is defined as A=:A+EAo . (11) We will work with 3 x 3 matrices in connection with dual vectors, but the above definition can be applied to any square matrices, which is the reason why n has been left arbitrary. Equality, multiplication by a dual scalar, and multiplication by a dual vector are defined as in the foregoing cases. More over, matrix multiplication is defined correspondingly, but then the order of multiplication must be respected. We thus have that, if A and Bare two n x n dual matrices, with their primal and dual parts self-understood, then AB = AB + E(ABo + AoB) . (12) Therefore, matrix A is real if A o = 0, where Odenotes the n x n zero matrix; if A = 0, then A is called a pure dual matrix. Moreover, as we shall see below, a square dual matrix admits an inverse if and only if its primal part is non singular . Now we can define the inverse of a dual matrix, if this is non singular. Indeed, it suffices to make B = A -1 in eq.(12) and the right-hand side of this equation equal to the n x n identity matrix, 1, thereby obtaining two matrix equations that allow us to find the primal and the dual parts of A -1, namely, AB = 1, ABo + AoB = \u00b0 , whence B = A -1, B o = -A -1 AoA -1 , which are defined because A is invertible by hypothesis, and hence, for any nonsingular dual matrix A, A -1 = A -1 _ E A -1 AoA -1 . (13) Note the striking similarity of the dual part of the foregoing expression with the time-derivative of the inverse of A(t), namely, :t[A -let)] = -A -l(t)A(t)A -let) . In order to find an expression for the determinant of an n x n dual matrix, we need to recall the general expression for the dual function defined in eq.(3). However, that expression has to be adapted to a dual-matrix argument, which leads to f(A) = f(A) + Etr [Ao (:i) T]IA=A . (14) In particular, when f(A) = det(A), we have, recalling the formula for the derivative of the determinant with respect to its matrix argument (Angeles 1982), for any n x n matrix X, d~ [det(X)] = det(X)X-T , where X-T denotes the transpose of the inverse of X or, equivalently, the transpose of X-I. Therefore, tr [Ao (:i) T]IA=A = det(A)tr(AoA -1) , and hence, det(.A) = det(A)[I + dr(AoA -1)]. (15) Now we can define the eigenvalue problem for the dual matrix .A defined above. Let A and e be a dual eigenvalue and a dual (unit) eigenvector of .A, respectively. Then, .Ae = Ae, lIell = 1 . (I6a) For the foregoing linear homogeneous equation to admit a nontrivial solution, we must have det(h - .A) = 0 , (I6b) which yields an nth-order dual polynomial in the dual number >.. Its n dual roots, real and complex, constitute the n dual eigenvalues of .A. Note that, associated with each dual eigenvalue Ai, a corresponding dual (unit) eigen vector er is defined, for i = 1, 2, ... , n. Moreover, if we recall eq.(4), we can write eA = eA + E AoeA . (17) U pon expansion, the foregoing expression can be cast in the form eA = (I + E Ao)eA :f; eA(1 + E A o) , (18) the inequality arising because, in general, A and Ao do not commute. They do so only in the case in which they share the same set of eigenvectors. A special case in which the two matrices share the same set of eigenvectors is when one matrix is an analytic function of the other. More formally, we have Lelllllla 2.2. 1/ F is an analytic matrix /unction 0/ matrix A, then the two matrices (i) share the same set 0/ eigenvectors, and (ii) commute under multiplication. Typical examples of analytic matrix functions are F = AN and F = eA, for an integer N. 3. Fundamentals of Rigid-Body Kinematics We review in this section some basic facts from rigid-body kinematics. For the sake of conciseness, some proofs are not given, but the pertinent references are cited whenever necessary. 3.1 Finite Displacements A rigid body is understood as a particular case of the continuum with the special feature that, under any given motion, any two points of the rigid body remain equidistant. A rigid body is available through a configuration or pose that will be denoted by B. Whenever a re/erence configuration is needed, this will be labelled BO. Moreover, the position vector of a point P of the body in configuration B will be denoted by p, that in BO being denoted correspondingly by pO. A rigid-body motion leaving a point 0 of the body fixed is called a pure rotation, and is represented by a proper orthogonal matrix Q, i.e., Q verifies the two properties below: QQT = 1, det(Q) = +1. (19) According to Euler's Theorem (Euler 1776), a pure rotation leaves a set of points of the body immutable, this set lying on a line C, which is termed the axis 0/ rotation. If we draw the perpendicular from an arbitrary point p of the body to C and denote its intersection with C by pI, the angle E . (43) However, since D and E are unrelated, they do not share the same set of eigenvectors, and hence, they do not commute under multiplication, the fore going expression thus not being furt her reducible to one single exponential. Nevertheless, if the origin is placed on the Mozzi-Chasles axis, as depicted in Fig. 3, then the dual rotation matrix becomes Cl = Q+Ed*EQ, (44) where d*E is, apparently, the cross-product matrix of vector d*e. Further more, the exponential form of the dual rotation matrix, eq.( 43), then simpli fies to Cl = e( +f d*)E or, if we let J = CP + E d*, then we can write Cl = eJE. 3.2 Velo city Analysis Upon differentiation with respect to time of both sides of eq.(27), we obtain p _ a = Q(pO _ aO) , and, if we solve for (pO - a O) from the equation mentioned above, we obtain (45) where QQT is defined as the angular-velocity matrix of the motion under study, and is represented as 0, namely, (46a) It can be readily proven that the foregoing matrix is skew-symmetric, Le., OT = -0 . (46b) Moreover, the axial vector of 0 is the angular-velocity vector w: w = vect(O) . We can now write eq.(45) in the form (46c) (47) whence, p - w x p = \u00e4. - w x a == VO = const . (48) Therefore, the difference p - w x p is the same for all points of a rigid body. The kinematic interpretation of this quantity is straightforward: If we rewrite vO in the form VO = P + w x (-p), then we can readily realize that, -p being the vector directed from point P of the rigid body to the origin 0, vO represents the velocity of the point of the body that coincides instantaneously with the origin. Furthermore, we express d, as given by eq.(33), in terms of the position vector of an arbitrary point P, p, thus obtaining (49) Upon differentiation of the two sides of the above expression with respect to time, we obtain d=p-Qpo , which can be readily expressed in terms of the current value of the position vector of P, by solving for pO from eq.(49), namely, d = p - O(p - d) or d - w x d = P - w x p , (50) and hence, the difference d - w x d is identical to the difference p - w x p, i.e., d -w x d = vo. (51) Furthermore, upon dot-multiplying the two sides of eq.(48) by w, we obtain an interesting result, namely, w\u00b7p=w\u00b7\u00e4., and hence, (52) Theorem 3.4. The velocities 0/ all points 0/ a rigid body have the same projection onto the angular-velocity vector 0/ the motion under study. Similar to the Mozzi-Chasles Theorem, we have now Theorem 3.5. Given a rigid body B under general motion, a set 0/ its points, on a line ,c, undergoes the identical minimum-magnitude velocity v* parallel to the angular velocity w. The Pl\u00fccker coordinates of line ,c, grouped in the 6-dimensional array A, are given as w f== Ilwll' (53) where v O was previously introdueed as the velo city of the point of B that coincides instantaneously with the origin. Line .c is termed the instant screw axis-ISA, for brevity. Thus, the instantaneous motion of B is defined by a serew ofaxis .c and piteh p', given by (54) where :P is the velocity of an arbitrary point P of B, the produet :P . w being eonstant by virtue of Theorem 3.4. A proof of the foregoing results is available in (Angeles 1997). 3.3 The Linear Invariants of the Dual Rotation Matrix We start by reealling the linear invariants of the real rotation matrix (Angeles 1997). These are defined as q == veet(Q) = (sin<,b)e, tr(Q) - 1 qo= =eos<,b. - 2 (55a) Note that the linear invariants of any 3 x 3 matrix ean be obtained from simple differenees of its off-diagonal entries and sums of its diagonal er\u00fcries. Onee the foregoing linear invariants are ealculated, the natural invariants ean be obtained uniquely as indicated below: First, note that the sign of e ean be ehanged without affecting q if the sign of <,b is ehanged aeeordingly, whieh means that the sign of -or that of e, for that matter-is undefined. In order to define this sign uniquely, we will adopt a positive sign for sin <,b, which means that <,b is assumed, heneeforth, to lie in the interval 0 ~ <,b ~ 7r. We ean thus obtain the inverse relations of eq.(55a) in the form e = 11:11' <,b = arctan (\"~\"), q # 0, (55b) the case q = 0 being handled separately. Indeed, q vanishes under two eases: (a) <,b = 0, in whieh ease the body undergoes a pure translation and the axis of rotation is obviously undefined; and (b) <,b = 7r, in which ease Q is symmetrie and takes the form For <,b = 7r: Q = -1 + 2eeT , (55e) whenee the natural invariants beeome apparent and ean be readily extraeted from Q. Similar to the linear invariants of the real rotation\u00b7 matrix, in the dual ease we have cl == veet(Q), A _ tr(Q) - 1 qo = 2 . (56) Expressions for the foregoing quantities in terms of the motion parameters are derived below; in the sequel, we also derive expressions for the dual natural invariants in terms of the same parameters. We start by expanding the vector linear invariant: veet(Q) = veet(Q + fDQ) = veet(Q) + fveet(DQ) . But, by virtue of eq.(20), veet(Q) = (sin4\u00bbe. (57a) (57b) Furthermore, the seeond term of the rightmost-hand side of eq.(57a) ean be readily ealculated if we reeall Theorem 3.2, with d == veet(D): 1 veet(DQ) = \"2[tr(Q)l - Q]d . (57e) Now, if we reeall expression (20), we obtain tr(Q)l- Q = (1 + eos4\u00bbl- sin4>E - (1- eos4\u00bbeeT . Upon substitution of the foregoing expression into eq.(57e), the desired ex pression for veet(DQ) is readily derived, namely, 1 . veet(DQ) = \"2[(1 + eos4\u00bbd - slll4>e x d - (1 - eos4\u00bb(e\u00b7 d)e] , (57d) and henee, 1 . cl = (sin 4\u00bbe+ f\"2[(eos 4\u00bb( e . d)e + (1 + eos 4\u00bbd + (slll4\u00bbd x e -(e\u00b7 d)e]. (57e) On the other hand, the position veetor p* of the Mozzi-Chasles axis, given by eq. (34), can be expressed as * 1 sin 4> 1 1 p = - ex d + -d - -(e\u00b7 d)e , 21 - cos4> 2 2 (58a) and hence, * 1 sin 4> 1 sin 4> 1 p xe = -2 1 4> d - -2 1 4> (e\u00b7 d)e + -2d Xe. - eos - eos (58b) Moreover, let us reeall the identity 1 + cos 4> _ sin 4> sin 4> - 1 - eos 4> ' (58e) which allows us to rewrite eq.(58b) in the form * 1 1 + eos 4> d 1 1 + cos 4> (d) 1 p x e = - - - e . e + -d x e 2 sin 4> 2 sin 4> 2' (58d) whenee, (sin 4\u00bbP* xe = ~[(1 + eos 4\u00bbd - (1 + eos 4\u00bb(e\u00b7 d)e + (sin 4\u00bbd x e] , and cl takes the form q = (sin4\u00bbe + E [(cos4\u00bb(e\u00b7 d)e + (sin4\u00bbp* xe] . (59) If we now recall eqs.(31) and (32), d . e == d* = P4>, while p* x e is the moment of the associated Mozzi-Chasles axis, eo, and hence, eq.(59) becomes q = (sin 4\u00bbe + E[( cos 4> )p4>e + (sin 4> )eo] . Thus, q can be furt her simplified to q=e*sinJ, J==4>(l+Ep) , (60) (61) where e* is the dual unit vector representing the Mozzi-Chasles axis, i.e., e*=e+Eeo\u00b7 Now, such as in the real case, we can calculate the dual natural invariants of the motion under study in terms of the foregoing dual linear invariants. We do this by mimicking eqs.(55b), namely, e* = II~II' J = arctan (\"!\") , Ilqll::f. 0, (62) where Ilqll is calculated from eq.(ge), which gives Ilq112, the square root of the latter then following from eq.(7), thus obtaining Ilqll = sinJ = sin4> + E(e\u00b7 d) cos4> , and hence, upon simplification, e* = e + EP* xe = e + Eeo , (63) (64) which is rightfully the dual unit vector of the Mozzi-Chasles axis. Further more, tr(Q) = tr(Q) + Etr(DQ) , where, from Theorem 3.3, tr(DQ) turns out to be tr(DQ) = -2[vect(Q)]\u00b7 d = -2sin4>(e\u00b7 d) , whence, tr(Q) = 1 + 2cos4> - E2(sin4\u00bbe\u00b7 d, and so, from the second of eqs.(56), (jo == cosJ = cos4> - E(sin4\u00bb(e\u00b7 d) , which, by virtue of eqs.(31), leads to (jo = cos4> - E(sin4\u00bbd*, J = 4>+Ed* = 4>(1 +Ep). (65a) (65b) (65c) (65d) In summary, the dual angle of the dual rotation under study comprises the angle of rotation of Q in its primal part and the axial component of the dis placement of all points of the moving body onto the Mozzi-Chasles axis. Upon comparison ofthe dual angle between two lines, as given in eq.(5), with the dual angle of rotation J, it is then apparent that the primal part of the latter plays the role of the angle between two lines, while the corresponding dual part plays the role of the distance s between those lines. It is noteworthy that a pure rotation has a dual angle of rotation that is real, while a pure translation has an angle of rotation that is a pure dual number. Example 1: Determination of the screw parameters of a rigid-body motion. We take here an example of (Angeles 1997): The cube of Fig. 5 is displaced from configuration A \u00b0 BO ... HO into configuration AB ... H. Find the Pl\u00fccker coordinates of the Mozzi-Chasles axis of the motion undergone by the cube. Solution: We start by constructing Q: Q == [i* j* k* J, where i*, j*, and k* are the dual unit vectors of lines AB, AD, and AE, respectively. These lines are, in turn, the images of lines AO BO, AO DO, and AO EO under the rigid-body motion at hand. The dual unit vectors of the latter are denoted by iO*, jO*, and kO*, respectively, and are parallel to the X, Y, and Z axes of the figure. We thus have i* = _ja +\u20aca x (_jO), j* = kO +\u20aca x kO, k* = -io +\u20aca x (-iO) , where a is the position vector of A, and is given by a = [2 1 -lf a. Hence, i* = _ja + w( -io - 2ko) ~* J kO + \u20ac a(io - 2jD) k* = Therefore, [ - \u20aca Q= -1 -\u20ac2a whence, +\u20aca - \u20ac2a 1 vect(Q) = ~ -1 + c:2a , [ 1 - \u20aca ] -1-\u20aca Thus, tr(Q) = - c:(2a) , A v'3 -a v'3 v'3 IIvect(Q)1I = 2\"\" + \u20ac v'3 = 2\"\" - \u20ac\"3 a . Therefore, the unit dual vector representing the Mozzi-Chasles axis of the motion at hand, Ei*, is given by Ei* = vect(Q)/llvect(Q)II, Le., Ei\" = _1 ~ [!ll-\u20ac~ .(~ [!I]-v'3 - ~ [-;1] v'3) . v'3/2 2 -1 3/4 2 -'-1 3 2 -1 2 After various stages of simplification, the foregoing expression reduces to \u2022\u2022 = ~ [ ~:] +, ~ [ !} Thus, the Mozzi-Chasles axis is parallel to the unit vector e, which is given by the primal part of e, while the dual part of the same dual unit vector represents the moment of the Mozzi-Chasles axis, from which the position vector p* of P\", the point of the Mozzi-Chasles axis closest to the origin, is readily found as p* = e x eo = i [3 2 I]T." + ] + }, + { + "image_filename": "designv10_6_0000202_j.mechmachtheory.2021.104330-Figure11-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000202_j.mechmachtheory.2021.104330-Figure11-1.png", + "caption": "Fig. 11. Three configurations of the deployable grasping parallel mechanism shown in (a)\u2013(c) illustrate the folded, fully deployed, and grasping configurations of the whole mechanism, respectively. (d)\u2013(f) present the corresponding physical prototype of such a deployable grasping parallel mechanism.", + "texts": [ + " This auxiliary sub-mechanism consists of three successive revolute joints whose rotation axes are along Y a -axis and a 2R spherical sub-chain. In Fig. 10 (b), a deployable grasping parallel mechanism can be assembled using the base and platform to connect the grasping submechanism and two auxiliary sub-mechanisms. After that, the folded configuration of the whole mechanism is obtained, as shown in Fig. 10 (c). Further, this paper also shows the fully deployed configuration and the grasping configuration of such a mechanism, as presented in Fig. 11 (b) and (c), respectively. Three configurations of this deployable grasping parallel mechanism are verified using the corresponding physical prototype, as provided in Fig. 11 (d) to (f). Besides, this deployable grasping parallel mechanism can grasp objects at any configuration of the deployment motion, which is demonstrated as presented in Movie S2. In this case, the standard base of constraint-screw system for the auxiliary sub-mechanism is S r a = { S r a1 = (1 , 0 , 0 , 0 , 0 , 0) T S r a2 = (0 , 1 , 0 , 0 , 0 , 0) T } , (50) which denotes a constraint force along X a - and Y a -axes, respectively. The standard base of motion-screw system for this mechanism can be written as follows: S a = \u23a7 \u23aa \u23aa \u23aa \u23aa \u23a8 \u23aa \u23aa \u23aa \u23aa \u23a9 S a1 = ( 1 , 0 , 0 , 0 , 0 , 0 ) T S a2 = ( 0 , 1 , 0 , 0 , 0 , 0 ) T S a3 = ( 0 , 0 , 1 , 0 , 0 , 0 ) T S a4 = ( 0 , 0 , 0 , 0 , 0 , 1 ) T \u23ab \u23aa \u23aa \u23aa \u23aa \u23ac \u23aa \u23aa \u23aa \u23aa \u23ad " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002551_9781420049763.ch3-Figure3.21-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002551_9781420049763.ch3-Figure3.21-1.png", + "caption": "FIGURE 3.21 Instantaneous voltage, current, and power.", + "texts": [ + " v t V t V V e i t I t I I e j j ( ) cos( ) ( ) cos( ) = + \u00ab = = + \u00ab = 2 2 * * * * * * * * w a w b a b p t v t i t V I t t V I V I t ( ) ( ) ( ) cos( ) cos( ) cos( ) cos( ) = = + + = -[ ] + + +[ ] 2 2 * * * * * * * * * * * * w a w b a b w a b \u00a9 2000 by CRC Press LLC D ow nl oa de d by [ U ni te d A ra b E m ir at es U ni ve rs ity ] a t 2 1: 48 3 0 O ct ob er 2 01 6 of time) in addition to a sinusoidal term. Furthermore, the frequency of the sinusoidal term is twice that of the voltage or current. Plots of v, i, and p are shown in Fig. 3.21 for specific values of a and b. The power is sometimes positive, sometimes negative. This means that power is sometimes delivered to the terminals and sometimes extracted from them. The energy which is transmitted into the network over some interval of time is found by integrating the power over this interval. If the area under the positive part of the power curve were the same as the area under the negative part, the net energy transmitted over one cycle would be zero. For the values of a and b used in the figure, however, the positive area is greater, so there is a net transmission of energy toward the network" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003317_s11044-008-9126-2-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003317_s11044-008-9126-2-Figure3-1.png", + "caption": "Fig. 3 Double pendulum", + "texts": [ + " This can be shown to always be the case; for example, if p = 0, then Case 1, Type 2 and Case 3, Type 4 lead to the same In, It ,vS n and vS t (= 0), hence to the same solution. h. A collision theory can be formulated without the bisection of the collision time, i.e., without the introduction of t\u0304 (39), as in Appendix C. This theory underlies that used by Kane and Levinson in [31]. It can be shown, with the aid of a table similar to Table 1 that it offers unique and coherent, but energy inconsistent solutions. Figure 3 shows a double pendulum S consisting of uniform rods A and B , each of length l and mass m. Let q1 and q2 be the orientation angles of the rods, and let ui = q\u0307i (i = 1,2). Suppose that at time t1 the endpoint B\u0304 of B strikes H , a flat surface, and that at t1 q1 = 20, q2 = 30 deg and u1 = \u22120.1, u2 = \u22120.2 rad/sec. It is required to evaluate the change in the kinetic energy of S following the collision, for m = 3 kg and l = 2 m. To this end, n and t are identified as n = \u2212n1 and t = \u2212n2, where n1 and n2 are the unit vectors shown in Fig. 3. Next, the velocity of B\u0304 at t1, which is the velocity of approach, and the equation of motion of S are generated and cast as follows vB\u0304 (t1) = vA = \u22120.2684n + 0.5343t, \u22121/3ml2 [ 4u\u03071 + 3/2 cos(q1 \u2212 q2)u\u03072 + 3/2 sin(q1 \u2212 q2)u 2 2 ] = 0, \u22121/3ml2 [ 3/2 cos(q1 \u2212 q2)u\u03071 + u\u03072 \u2212 3/2 sin(q1 \u2212 q2)u 2 1 ] = 0. Substitutions in (20), (24), and (34) yield mnn = 0.3365, mtt= 0.8134, mnt = \u22120.5071, = 0.0166, and \u03b1 = 1.9908. The top rows 1\u20134 of Table 2 show cases with different values of e and \u03bc corresponding to the four cases of [31], for which \u03bcmtt \u2212mnt > 0,\u03bcmtt +mnt < 0 and > 0; and if solved as in Appendix C (Kane and Levinson\u2019s solution), then inequalities (74) reduce to \u03b1 < (1 + e)rm and \u03b1 > \u2212(1 + e)rp " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003438_jra.1985.1087013-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003438_jra.1985.1087013-Figure3-1.png", + "caption": "Fig. 3. Link representation of the PUMA 560 arm.", + "texts": [ + ", rotating the base coordinates through elk, then through - ( 8 2 + 8,) i , and finally through 04k. The Joint 6 axis is perpendicular to and 2$01.00 0 1985 IEEE ELGAZZAR: EFFICIENT KINEMATIC TRANSFORMATIONS FOR THE PUMA 560 ROBOT 143 WAIST 320' I (JOINT 1) UPPER ARM SHOULDER 286' ELBOW 284O WRIST ROTATION 280 TRUNK - FLANQE 632 ' intersects the Joint 5 axis. It coincides with the centerline of the gripper mounting flange. The link representation of the robot arm at any arbitrary position is shown in Fig. 3. The position of the end effector is expressed in joint coordinates as 8 = (el, 02, 03, e,, 05, and in Cartesian coordinates as R = (r,., r,, r,, rp, re, r$) where the superscript T denotes the transpose. The vector r = (rx, ry , r,) is the position vector and rp , re , r$ are the rotations about the z-axis, the new - x axis, and the new z-axis that aligns the base coordinates with the tip coordinates. The rotation parameters were chosen to correspond with the arrangement of the joints at the wrist and hence simplify the solution", + " This is because \\cos rol = 1 is a singular point in the representation of rotations. If sin re = 0, the orientation of the wrist will depend on the sum of r, and r, and not on their individual values. In this study if sin ro = 0, ro is set to zero or depending on the sign of cos ro, and the angle r, is set to zero. Then r,, is found using the equations developed in [l] as follows: r,, = 81 + atan2 (2 sin (8, + B6)/[cos (8, + 8,) + cos ro] , cos (04 + 0 6 ) ) Position Vector: The position vector r is derived next. Referring to Fig. 3, and substituting 8; for (8, - S), the values of the projections of the vector n on the z-axis w, and on the Xy plane wb are expressed as w,=z2 COS 0 2 + 1 3 COS (e,+e;) (1) wb = l2 sin 8, + l3 sin (0, + 8;). (2) Since wb makes an angle 0, with the y-axis the vectors n, w2, and w1 can be written as n = - w b sin 8 , i + w b cos 0 , j + w,k wz=(n,+d2 cos 81)i+(n,+d2 sin 0 , ) j + w , k ELGAZZAR: EFFICIENT KINEMATIC TRANSFORMATIONS FOR THE PUMA 560 ROBOT 145 Arm Configuration Parameters: Given a set of joint angles, the arm configuration is determined by evaluating the parameters k l , kz, and k3" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000284_j.addma.2021.102123-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000284_j.addma.2021.102123-Figure1-1.png", + "caption": "Fig. 1. (a) Build directions and (b) geometry of laser powder bed fusion (LPBF) specimens.", + "texts": [ + " The laser melting and fusion was performed under an Ar atmosphere using a ytterbium-fiber laser with a power of 200 W, a beam diameter at the focal point of 100 \u00b5m and a scan speed of 4 m/s. The thickness of each powder layer was ~40 \u00b5m, the hatching space was set to 25 \u00b5m and a meandering scanning strategy was employed with the scanning direction rotated by 67\u25e6. In terms of the build direction, three different directions were used, depending on the orientation of the specimen\u2019s main axis. As shown in Fig. 1a, the specimens were built in the horizontal/parallel (X) and vertical/perpendicular (Z) directions as well as at an angle of 45\u25e6. The specimens included in this investigation, which were 3D printed with the final shape and geometry, comprised tensile bar specimens with a nominal diameter of 10 mm, standard Charpy-V notch specimens, circumferentially notched and fatigue pre-cracked tensile bar specimens (CNPTB; \u03d5 10 mm) for fracture-toughness measurements [33], 20 \u00d7 20 \u00d7 100 mm3 square blocks and square-shaped wear test specimens of 25 \u00d7 25 \u00d7 10 mm3 (Fig. 1b). After removal from the H13 tool-steel base plate, the specimens were heat treated in an IPSEN vacuum furnace VTTC324-R. Two heattreatment procedures were used. The first set of as-built specimens was directly age-hardened at 490 \u25e6C for 6 h, followed by slow cooling to 60 \u25e6C at a cooling rate of ~1 \u25e6C/min, as recommended by the maraging steel powder supplier EOS. The second set was first heated to 840 \u25e6C at a heating rate of 3 \u25e6C/min, solution treated at 840 \u25e6C for 1 h, followed by slow cooling to 490 \u25e6C (cooling rate of 1 \u25e6C/min) and age hardening at 490 \u25e6C for 6 h", + " The impact toughness at room temperature was measured with a Charpy impact test machine with a 300-J pendulum according to the ASTM E23 standard. For the fracture-toughness measurements, non-standard CNPTB specimens were used. In both cases (impact and fracture toughness) a V-notch was introduced by grinding after the heat treatment, with the position of the notch for the horizontal (X) and 45\u25e6-build directions being in the in-plane (X-1) or transverse direction (X-2), as shown in the inset of Fig. 1b. Furthermore, in the case of the fracturetoughness specimens, a fatigue pre-crack of about 0.5 mm was made in the notch root using rotating-bending loading. As explained in Ref. [33], the fracture toughness can be calculated (Eq. 1) by subjecting a CNPTB specimen to a tensile load until fracture, and measuring the load at fracture and the diameter of the brittle-fracture area. For each property, at least five parallel specimens were tested so as to obtain statistically relevant data and then average value and standard deviation were calculated" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002647_tcst.2002.806450-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002647_tcst.2002.806450-Figure3-1.png", + "caption": "Fig. 3. Thruster mounting geometry.", + "texts": [ + " Note that the quaternion satisfies the following normalization equation: (1) Let , the design problem is formulated as (2) in which The objective is to synthesize such that the closed-loop system is stabilized and its performance is enhanced. For the ROCSAT-3 spacecraft under consideration, the control torque is generated by modulating the thrusters. The relationship between the 4 1 thruster control input and the 3 1 control torque is established in the following. The four thrusters are mounted on the side face of the ROCSAT-3 in each corner of the square as shown schematically in Fig. 3. Each circle in the figure stands for the thruster. The mounting \u2013 plane is orthogonal to the body axis and at a distance along the axis from the center of mass. The side length of the thruster assembly is . Thus, the moment arms in the spacecraft body axes are, respectively (3) To achieve attitude controllability, the thruster directions are canted from the axis by to produce control moment along the -axis. The direction of force generated by each thruster in the body-fixed \u2013 plane is also different from the principle axes by 45 as shown in the arrow around each thruster in Fig. 3. As a result, control torques along different axes can be generated. For example, a combination of thrusters 2 and 4 produce torque, and so forth. The unit thruster force vectors are indeed (4) where and and stands for and , respectively. Let be, respectively, the thrust generated in each thruster. The resulting control torque on the spacecraft is in which and are the moment arm and thruster force direction vector of each thruster, respectively. Let , the control torque can then be expressed as (5) where the th column of is " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002839_978-3-662-03845-1-Figure1.22-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002839_978-3-662-03845-1-Figure1.22-1.png", + "caption": "Fig. 1.22. A fibre drawn from a bath of liquid at speed V: (a) V < Vm; (b) V> Vm", + "texts": [ + " In total wetting conditions (8E = 0), Vm = 0 and a film is invariably deposited. The threshold speed for depositing a film on a plane surface, a fibre, or inside a capillary can be deduced directly from the law of motion of the contact line in partial wetting conditions, as illustrated in Fig. 1.21: V = ~V*(82 - 82 ) . 6ln E minimum speed given by dV/d8 = 0, which implies 8E 1 *83 8m = V3 ' Vm = 9V3ln V E\u00b7 Experimentally, a value of about 12 is found for log lno When V < Vm , there exists a dynamical contact angle and a meniscus (see Fig. 1.22a). When V > Vm , a macroscopic film is drawn along by the plate, or left behind the droplet in the capillary tube (see Fig. 1.22b). l. 7 Forced Wetting 27 This threshold speed Vrn plays an important role in Langmuir-Blodgett de posits, in the study of molecular electronics or for the control of wettability. A monolayer of insoluble surface active agents floating on the surface of water is transferred to a plate drawn at speed V from the bath. We must have V < Vrn in order to avoid pulling a water film along with the surfactant. 1.7.3 Film Thickness on a Fibre (or in a Capillary Tube) The thickness e of a film drawn from a liquid bath was studied by Landau, Levich and Deryaguin in the 1940s. Figure 1.22b shows the dragged film of thickness e and the dynamical meniscus which joins up with the static menis cus. We can determine the length l of the join, by writing down the condition that the Laplace pressure at the join with the static meniscus should be zero: ~_ Ie =0 b+e [2 . This implies that l rv v;;b. Moreover, the Laplace pressure in the film is I/b, whereas the pressure in the static meniscus is zero. Consequently, a flow is set up in the dynamical meniscus, given by Poiseuille's law e2 I V ~ ---;J lb " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000145_j.jmapro.2021.04.022-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000145_j.jmapro.2021.04.022-Figure1-1.png", + "caption": "Fig. 1. SLM process schematic presentation.", + "texts": [ + " Moreover, this research work directs towards the considerations of wall thickness as design factor, like other parameters mentioned above, in the performance of functional or operational parts for SLM. In this study, a comprehensive range of thin-walled thickness were selected (that are 0.5 mm, 0.8 mm, 1 mm, 1.15 mm, 1.5 mm, 18 mm, 2 mm, 2.5 mm, 3 mm, 3.5 mm, 4 mm, and 5 mm) to provide a strong and healthier correlation of macro-mechanical behavior. SLM was selected as the AM process to manufacture thin-walled specimens. The method of fabricating a part by SLM is demonstrated in Fig. 1. Firstly, the 3D-CAD file is converted to sliced-layers form and then transferred to the machine. Secondly, the build plate is heated (temperature is material dependent). Thirdly, a layer of powder from the powder feeder with a pre-defined layer thickness is spread over the heated build plate by wiper blades. The uniformity of the deposited layer is critical to prevent it from the defects or porosities [21]. Fourthly, a laser beam focused onto the powder-bed is carried through an optical fiber and radiated onto the powder layer", + " The porosities are reduced with the increment in the wall thickness which can be observed in 3.50 mm wall thickness specimen (see Fig. 11c and d) and 5.0 mm thick specimen (see Fig. 11e and f). From the OM observations of the lateral surface of the thin-walled specimens, the quantity and size of porosities and voids are smaller for thick specimens (greater than 1.50 mm wall thickness). The AlSi10Mg thin-walled specimens were built with the best density and the relative density with varying wall thickness is shown in Fig. 1. The highest relative density of 99.86 % was achieved in the 0.50 mm test specimen. Then, the relative density was decreased gradually from 99.86 % to 93.60 % as the wall thickness increase from 0.50 mm to 1.50 mm. From the 1.50 mm to 1.80 mm wall thickness, there is a gradual increment in the relative density, which has also influenced the mechanical behavior of the test specimens (see section 3.5). The value of the relative density increased from 95.78 % to 97.58 % for the 2.50 mm\u20133.0 mm specimens, respectively, and then a gradual increment of 1 % in relative density is observed from 3" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000562_j.mechmachtheory.2021.104380-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000562_j.mechmachtheory.2021.104380-Figure2-1.png", + "caption": "Fig. 2. The principal axes decomposition of the discretized elastic segments [44] .", + "texts": [ + " To facilitate the understanding, a brief introduction to the adopted discretization-based approach for elastostatics modeling of slender flexible links is provided in this sections. It can be thought of as a special kind of finite element method, in which rigid-body linkages with elastic joints, rather than small-size elastic elements, are introduced to approximate the force-deflection behaviors of small segments discretized from the flexible links. Using the proposed method, a slender flexible link will be discretized into a large number of small elastic segments, as illustrated in Fig. 2 . For each segment, a spatial six-DOF linkage with rigid bodies and passive elastic joints is employed to characterize the structural flexibility approximately. Since those discretized segments are small, linear approximation assumptions are made to characterize their force-deflection behavior. In our method, the synthesis of the approximation linkages is realized by means of applying the principal axes decomposition [43] to the structural compliance matrices of the discretized segments. The concept of principal axes decomposition was initially proposed for the synthesis of Cartesian compliance using springy elements", + " For flexible links with uniform cross section, the 6-DOF elastic linkage approximate to the discretized segments can be specified as \u23a7 \u23aa \u23aa \u23a8 \u23aa \u23aa \u23a9 t 1 = [ e 1 0 ] c 1 = \u03b4 EI xx , \u23a7 \u23aa \u23aa \u23a8 \u23aa \u23aa \u23a9 t 2 = [ e 2 0 ] c 2 = \u03b4 EI yy , \u23a7 \u23aa \u23aa \u23a8 \u23aa \u23aa \u23a9 t 3 = [ e 3 0 ] c 3 = \u03b4 GI zz \u23a7 \u23aa \u23aa \u23a8 \u23aa \u23aa \u23a9 t 4 = [ 0 e 1 ] c 4 = \u03b43 3 EI yy , \u23a7 \u23aa \u23aa \u23a8 \u23aa \u23aa \u23a9 t 5 = [ 0 e 2 ] c 5 = \u03b43 3 EI xx , \u23a7 \u23aa \u23aa \u23a8 \u23aa \u23aa \u23a9 t 6 = [ 0 e 3 ] c 6 = \u03b4 EA (2) where e 1 , e 2 , and e 3 are the unit vectors associated with the principal axes of the segment\u2019s cross section, of area A . While I xx , I yy , and I zz correspond to the three principal area moments, respectively. \u03b4 denotes the length of segment, and E and G are the elastic and shearing modulus. It is worth noting that, in the principal axes decomposition (1) , the first three components, namely t i, 1 , t i, 2 , and t i, 3 , form a set of mutually orthogonal revolute joints intersected at the center of the segment, as shown in Fig. 2 . On the other hand, the last three, namely t i, 4 , t i, 5 , and t i, 6 , correspond to a set of mutually orthogonal prismatic ones. It should be noted that, the joint twists in (2) , are represented with respect to the principal coordinate of the segment, such that all these elastic joints pass through the origin of it. Further, to some extent, the motion of the elastic joints in the approximation linkage can be related to particular deformation of the segments\u2019 structural compliance. Thereinto, t i, 1 and t i, 2 correspond to the bending about the x -axis and y -axis, respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure3.5-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure3.5-1.png", + "caption": "Fig. 3.5. Direct branch", + "texts": [ + " The solution to all these dependences is included in the dynamic analysis al gorithm in the form of a special subroutine. Let us consider another example of a mechanism containing a closed chain. It is the mechanism shown in Fig. 3.2. For this scheme which contains a kinematic Daralleloqram there is no simple approximative '55 solution. The mechanism has to be considered as a closed chain. The kinematic scheme of such a mechanism is given in Fig. 3.4. Let us define the direct branch (solid line in Fig. 3.5). Such a simplified mechanism has n de~rees of freedom (d.o.f.) and we define n generalized coordi nates q, , ... ,qn' It is an open chain and we may use the method from Para. 2.3 to form the dynamic model. In fact we find the matrices wd , vd which determine the acceleration energy (2.3.35) and the left hand side of Appel's equations (see eq. (2.3.36)). The upper index \"dO in dicates that the direct branch is consider only. 156 Let us now add the segments 2' and 2\" which close the chain (Figs. 3" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002789_robot.1995.525717-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002789_robot.1995.525717-Figure1-1.png", + "caption": "Figure 1. SR400 robot.", + "texts": [ + " The number of moving links (denoted n) is equal to 8 and the number of joints (denoted Nj) is equal to 9. It contains a closed loop of parallelogram type. It is actuated with N=6 brushless motors. The description of the geometry of the robot is carried out using the modified Denavit and Hartenberg notation [l]. The coordinate frame j is fixed on link j, the z, axis is along the axis of joint j, the xj axis is along the common perpendicular of z, and one of the succeeding axis on the same link (see Fig. 1). In the case of closed loop robot, the geometric parameters are determined for an equivalent tree structure by opening each closed loop. Then two frames are added on the opened joints [ 11, thus the number of frames is equal to : Nf = n + 2B=10, where B is the number Of closed loops (B = Nj - n). The geometric parameters of the 10 frames of the SR400 Robot are given in [2]. Owing to the parallelogram loop, the following geometric constraint relations between the joint positions are verified : 83=~/2-82+87, 88=82-87, 8g=d2+83=n-82+ 87 (1) Since motors 5 and 6 are fixed on link 4, a mechanical coupling exists between the joints 5 and 6 such that : &j =ems - 0s (2) 0 m6 is the velocity of motor 6 referred to the joint side, 6 i is the velocity ofjoint j" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003815_j.mechmachtheory.2009.06.001-Figure19-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003815_j.mechmachtheory.2009.06.001-Figure19-1.png", + "caption": "Fig. 19. Defective generators with three identical pitches and one P pair.", + "texts": [ + " The four pitches must not be all equal. Pitches may be equal to zero but not all zeros. When four pitches are zeros, the chain generates the planar gliding motion, {Y(u, 0)} = {G(u)}. By the same token, one can demonstrate that if two screw pitches are equal, then two P pairs must not be perpendicular to u. For instance, two chains of Fig. 18 actually generate the 3-dof pseudo-planar motion rather than 4-dof X-motion. Furthermore, if three screw pitches are equal and one P pair is perpendicular to the parallel H axes, as shown in Fig. 19, these chains are trivial chains of a subgroup of pseudo-planar motion and never generate X-motion. One additional defective generator, a series of four prismatic pairs that generates {T} instead of {X(u)}, is displayed in Fig. 20 for completeness. Case B. A product of two factors is a 2D subgroup and one among the other two factors is included into this subgroup. For example, p1\u2013p2; A2 2 line\u00f0A1; u\u00deor\u00f0A1A2\u00de u \u00bc 0 ) fH\u00f0A1; u; p1\u00degfH\u00f0A2; u; p2\u00deg \u00bc fC\u00f0A1; u\u00deg; A3 2 line\u00f0A1; u\u00de ) fH\u00f0A3; u; p3\u00deg fC\u00f0A1; u\u00deg ) \u00bdfH\u00f0A1; u; p1\u00degfH\u00f0A2; u; p2\u00deg {H(A3, u, p3)}{H(A4, u, p4)} = {C(A1, u)}{H(A3, u, p3)}{H(A4, u, p4)} = {C(A1, u)}{H(A4, u, p4)} \u2013 {X(u)}" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000142_tmech.2021.3068259-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000142_tmech.2021.3068259-Figure1-1.png", + "caption": "Fig. 1. Mobile robot machining system for large-scale workpiece machining", + "texts": [ + " In Section III, the manner of constituting a cluster system is described, and the consensus performance and resistance index for different topologies are addressed. The criteria for selecting the cluster system are discussed in Section IV with the simulation results, while the experimental results of the cluster machining of large-scale workpieces are presented in section V. Finally, the conclusions are provided in Section VI. II. TOPOLOGICAL STRUCTURE OF CLUSTER SYSTEM The mobile robot machining system consists of a mobile platform with an industrial robot arm, as shown in Fig. 1. Four Mecanum wheels are set in the mobile platform to ensure omnidirectional mobility. The ABB-4600 robot arm has a workspace of 2.2 m and a load of 45 kg. An onboard laser is place in the front of the platform and can locate the position of the mobile platform through calibrated landmarks. The mobile property enables cooperation among mobile robots and constitutes a cluster machining system. The multi-mobile robot cluster system is featured as a group of robots that can share information and maintains consensus motion" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002493_02783640122067255-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002493_02783640122067255-Figure1-1.png", + "caption": "Fig. 1. The model is sketched with leg, neck, and back joints noted. There are a total of 10 degrees of freedom, 2 per leg as well as a back joint and a neck joint. All joints are rotary, except for prismatic knee and elbow joints. Three separate rigid shapes are used for the rump, body, and neck/head, and each leg is constructed with an upper rigid segment and a lower rigid segment. Mass is distributed throughout the model in a realistic manner using horse morphological data. At the distal end of each leg is a single ground contact point. The viscoelastic property of a natural running surface is modeled using springs and dampers aligned in vertical and horizontal directions. A compliant ground was required so that each model foot would not slip at first ground contact. The vertically aligned ground springs allowed each foot to penetrate the running surface, enabling the horizontal ground springs to hold the foot in place. Ground stiffness was adjusted so that the limbs only penetrated the ground by a small amount when running (\u223c0.3 cm). Damping was then adjusted to minimize oscillations between the ground and foot. For a detailed description of model structure, see Herr and McMahon (2000).", + "texts": [ + " To model galloping, four legs are required to show the footfall patterns of stance. Each leg must retract and protract in the sagittal plane about a shoulder or hip joint and change length about an elbow or knee joint. Furthermore, the model\u2019s neck and back should not be rigid. In slow-motion films of galloping horses, neck and back flexion can easily be observed with the eye. It is reasonable to ask whether these flexibilities are important to the overall mechanical behavior of a galloping horse. The horse model is described in Figure 1. In a previous investigation by Herr and McMahon (2000), a model of equivalent structure was developed to study the mechanics and energetics of quadrupedal trotting. Although the structural details of this model are equivalent to the galloping model presented here, the control strategies are nonetheless distinct. As is described in Section 2.2, the footfall patterns of galloping differ from those of trotting, requiring that the control strategies of a trotting model be distinct from those necessary for the stabilization of a galloping model", + " Cavagna, Heglund, and Taylor (1977) discovered that during ground contact in running, fluctuations in forward kinetic energy of the center of mass are in phase with changes in gravitational potential energy. They hypothesized that quadrupeds most likely store elastic strain energy in tendon, ligament, and perhaps even bone to reduce fluctuations in total mechanical energy during each running step. To represent these elastic structures in the galloping model, ideal linear springs were used to simulate limb, back, and neck behavior in stance. To model whole-limb compliance, springs were placed at knee and elbow prismatic joints (Fig. 1) so that each stance limb would go through a period of compression followed by a period of extension in a manner similar to a at UNIV TEXAS PAN AMERICAN on October 5, 2014ijr.sagepub.comDownloaded from vertebrate limb. Leg springs were also used in the galloping models of McMahon (1985) and Nanua (1992) and the trotting models of McMahon and Cheng (1990) and Herr and McMahon (2000). Of course, if all quadrupedal joints behaved as passive springs throughout stance, galloping could not be sustained, simply on the basis of energy conservation" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003384_20.278859-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003384_20.278859-Figure2-1.png", + "caption": "Fig. 2 - Typical 100-Line FiniteElement Flux Plot ( 8 = 607", + "texts": [ + " To solve this system of nonlinear equations a Newton-Raphson method can be applied[4]. This consists of evaluating R for CP=O, solving Eqn. 13, for a new CP calculating a new R using that 'P, solving Eqn. 13 and so on until the difference between 0 solutions reaches some specified small value. It should be noted that the R matrix used in Eqn. 13 is defined using p = AB/AH while The R values used to calculate the changes in CP required to move towards a solution of Eqn. 13 are defined using p = dB/dH. v. COMPARISON m FINITE-ELEMENT RESULTS Fig. 2 shows a typical finite-element flux plot for the machine that was analyzed. The flux plot was expanded to 100 lines to show pole-to-pole and pole-to-core leakage. Figs. 3 and 4 compare the equivalent circuit model predictions for flux at the stator pole bases in three phases with finite-element results for unsaturated and saturated single-phase excitation respectively. Fig. 5 shows flux in one phase of a two-phase excited machine - equal excitation at the same level of Figs. 3 and 4 - for the unsaturated and saturated cases and compares this with the single-phase excitation case" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000066_j.isatra.2021.01.016-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000066_j.isatra.2021.01.016-Figure3-1.png", + "caption": "Fig. 3. Last trailer of real and reference robots and the error signals.", + "texts": [ + " The tracking error array for the last railer is defined as \u03b5 = qnr \u2212 qn. As shown in Fig. 2, since the ast trailer is intended for the tracking control, it is aimed that the istance vector between the real and the reference robot which is escribed as \u03c1 = [ ex ey ]T \u2208 R2 and also the orientation angle = \u03c8 \u2212 \u03b8n to converge toward the origin i.e. limt\u2192\u221e\u03c1 = 02\u00d71, imt\u2192\u221e\u03c6 = 01\u00d71. This will maneuver the real vehicle to follow he reference vehicle. Therefore, the aim is that limt\u2192\u221e\u03c8 = \u03b8n. s can be seen from Fig. 3, \u03c8 represents the angle of the distance ector (\u03c1) with the horizon, which, can be described as \u03c8 = tan2 ( ey, ex ) . .1. Generation of reference trajectories The reference trajectories in the two-dimensional space are onsidered as \u03ber (t) = [ xr (t) yr (t) ]T . Using the same kineatic model (Eq. (8)) as q\u0307r (t) = S(qr) ur , for the reference obot, we have x\u0307r = unr cos \u03b8nr and y\u0307r = unr sin \u03b8nr . The first desired kinematic input can be easily obtained as unr (t) =\u221a x\u03072r + y\u03072r and the orientation angle of the last trailer as \u03b8nr (t) = tan2 {y\u0307r (t), x\u0307r (t)}" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure4.2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure4.2-1.png", + "caption": "Fig. 4.2. Arthropoid manipulator VE-2", + "texts": [ + " 25 ******** ACTUATOR IN JOINT 3 IS NOT CORRECT; TORQUE-SPEED TEST IS NEGATIVE; OPTIONS: - CHOOSE A NEW ACTUATOR 2 - CHANGE THE REDUCTION RATIO 3 - REDUCE THE WORKING OBJECT MASS 4 - REDUCE SOME OTHER MASSES User: 5 - INCREASE THE EXECUTION TIME 6 - OTHER POSSIBILITIES TYPE THE NUMBER OF THE OPTION CHOSEN: Computer: TYPE THE NEW ACTUATOR CHARACTERISTICS (STALL TORQUE[N]; NO LOAD SPEED[r.p.m]; POWER[W]) User: 12. 3000. 2000. 245 With this new actuator the tests are positive i.e. the actuator suits its application. This was only a fictitious example demonstrating the communication with the design game algorithm. Here is a detailed example which illustrates the procedure of manipulator design using the game algorithm. Example. We consider a problem of designing a manipulator VE-2 (Fig. 4.2.a) having six degrees of freedom. It is intended for spot-welding tasks and some assembly tasks. Its kinematical scheme is arthropoid and shown in Fig. 4.2.b. Some manipulator parameters are adopted and given in Fig. 4.2.b,c. The other parameters have to be determined. Let us first consider the ques tion of segments geometry. Segments 2 and 3 are in the form of rectan gular tubes made of light alloy A\u00a3Mg3. The cross sections (Fig. 4.3.) are defined by Hx2 ' Hy2 and Hx3 ' Hy3 ' so these parameters have to be determined. The actuators which drive the joints S2' S3 are placed in manipulator base. The torques are transported to the corresponding joints where there are Harmonic Drive reducers. The reducers in joints S2' S3 have the masses of about 7kg and the mechanical efficiencies n = 0", + " Thus, the parameters to be determined are: cross section dimensions of segments 2 and 3, and parameters of actuators S2 and S3' and finally, the reduction ratio. 247 The manipulator is tested on the assembly task shown in Fig. 4.4. The object should be moved along the trajectory AoA1A2A3. The velocity pro file on each straight-line part of the trajectory is triangular. The changes in orientation are also shown in Fig. 4.4. The execution time is T = T1 + T2 + T3 The manipulat~r starting position is given in Fig. 4.2.b. The constraint is that the position error due to elastic deformations be smaller than u = 0.002 m. p The design (i.e. determination of parameters) is carried out by using the design game procedure. The procedure started with the initial cross section dimensions: Hx2 = 0.25m, Hy2 = 0.13m, Hx3 = 0.16m, Hy3 = O.OSm. We first choose the 2kW D.C. motors as the actuators for the joints 52' 53. Catalog parameters (stall torque P~ and no-load rotation speed n~) m m m m . . were: P2M 10Nm, n 2M = 2500, P 3M = 10 Nm, n 3M = 2500", + " We shall explain this fact in more detail in the example, but let us say here that, for instance, the actuators chosen determine completely the segments which form the gripper (the last three segments if a six d.o.f. manipulator is considered). We may say that there usually exist one or two segments which should be optimized. If a cylindrical (Fig. 2.44) or spherical (Fig. 4.6) manipulator is in question, there is usually one main segment forming the manipulator arm and this is the one to be optimized. With anthropomorphic (Fig. 2.53) or arthropoid (Fig. 4.2) manipulators there are two main segments which form the manipulator arm and which should be optimized. We can make some further simplifications in order to reduce the number of parame ters to be optimized. The lengths of segments can be considered as known since they directly follow from the reachability conditions im posed. The forms of segment cross-section (not the cross-section di mensions but only its general form) can be different. Several forms of cross-section can be checked, but in one optimization procedure this is considered to be known", + " In fact the influence of the execution time is stronger for larger operation speeds and it is con siderable only in the domain of very fast motions. But, such speeds 256 257 are usually too high for practical application. Hence, we conclude that it is enough to perform the optimization with one value of execution time, the shortest one. That time corresponds to the largest operation speed which can be required from the device in its practical operation. Example 2. Let us again consider the arthropoid manipulator VE-2 (Fig. 4.2). It has been described in the example in 4.1. The problem is to choose the values of cross-section dimensions of segments 2 and 3 (Fig. 4.3). There are eight parameters defining these two cross-sections: hX2' Hx2 ' hY2' Hy2 ' h x3 ' Hx3 ' hy3' Hy3 \u00b7 In order to reduce the number of parame ters to be optimized we first introduce the constant ratios from Fig. 4.3. i.e. 0.9, 0.85, 0.9, 0.85 (4.3.1) But, there still remain four independent parameters. If we adopt 1 .5, 1.5 (4.3.2) then there are only two independent parameters: Hx2 and Hx3 ", + " 4.9). 259 This procedure can also be used for optimization when there are more than two independent parameters. One should take care of the fact that if the number of parameters increases the procedure may become very time-consuming. Hence, we suggest two or three independent parameters. We think that in almost all problems we are interested in, the number of independent parameters can be reduced to two or three. Let us see an example. Example. We consider again the arthropoid manipulator VE-2 (Fig. 4.2). It was described in the example in 4.1. The problem is to choose the values of cross-section dimensions of segments 2 and 3. (Fig. 4.3). There are eight parameters defining these two cross-sections. In the example 2 in 4.3.1. the number of independent parameters was reducedby introducing the constant ratios (4.3.1) and (4.3.2). In that way there remain two independent parameters Hx2 and Hx3 ' In 4.3.1. the problem was further reduced to one-parameter optimization. It was first doneby considering the two segments (2 and 3) to be equal (Hx2 = Hx3 )' After that, the same was done in the other way by introducing the constant ratio between the two segments (Hx2 = 1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000058_j.triboint.2020.106785-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000058_j.triboint.2020.106785-Figure1-1.png", + "caption": "Fig. 1. Load distribution on rolling elements of a cylindrical roller bearing and its measurement principle.", + "texts": [ + "106785 Received 31 August 2020; Received in revised form 6 November 2020; Accepted 19 November 2020 Tribology International 155 (2021) 106785 Not only the static load distribution over rolling elements in load zone, but also the real time dynamic load distributed on specific positions of load zone can be measured by the proposed method. The effect of the instrumented housing on the load distribution of bearing and stiffness of the whole structure was analyzed with finite element modeling. An experimental system was developed to investigate the load distribution behavior of a commercially available cylindrical roller bearing by using the proposed method. The load distribution among the rolling elements of a cylindrical roller bearing subjected to an external radial load and its measurement principle are illustrated in Fig. 1. The external radial load Fr is overlapped with the vertical axis of the bearing and goes towards bottom of the bearing. Contact deformation occurs between the rolling elements and raceways and an uneven but symmetric load distribution appears on the rolling elements [1]. To obtain this load distribution, the load transmitted through each roller must be measured. For this purpose, a new method based on the detection of strain response of the outer ring is proposed. In order to identify and locate the positions of the rolling elements, as shown in Fig. 1(a), the bottom rolling element is set to be 0, and the others are numbered as 1L, 1R and so on respectively. A roller bearing is usually installed in a housing fixture as shown in Fig. 1(a). In our method, a series of notches are introduced to the inner surface of the housing fixture as shown in Fig. 1(b), which provides enough space to the strain gauge and makes it possible to detect the strain signal of the outer ring. Strain gauges can be circumferentially placed on the surface of outer ring at these notched places. As illustrated in Fig. 1(c), with the existence of the notch, the corresponding part of outer ring can be considered as a beam structure. According to beam theory, whenever there is a roller rolling over the notch position, a strain response can be produced at the outer surface of outer ring. At the configuration shown in Fig. 1(b), the relationship between the measured strains and the load distribution can be related with a compliance matrix: [\u03b5\u03b1] = [k\u03b1\u2212 \u03b2][F\u03b2] (1) where \u03b1 and \u03b2 represent the roller numbers such as 0, 1L, 1R, 2L, 2R and so on. [\u03b5\u03b1] is the measured strain distribution, [F\u03b2] is the load distribution on the rolling elements, k\u03b1\u2212 \u03b2 represents the strain at the roller position \u03b1 due to a unit force applied at roller position \u03b2 when all other loads are zero. Once the strain distribution is measured and the compliance matrix is obtained, the load distribution in a bearing can be calculated as follows" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003983_j.wear.2009.06.017-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003983_j.wear.2009.06.017-Figure2-1.png", + "caption": "Fig. 2. Definition of the coordinate systems of a hypoid gear pair.", + "texts": [ + " The ear tooth surfaces with wear (Gp ij ) and (Gg ij ) are then fed into the ontact model for prediction of the updated contact pressures (Pp ij ) n g nd (P ij ) n for all rotational positions n \u2208 [0,N] and the same process is epeated until another geometry update is needed. Here, the supercript ( \u2208 [0,K]) is the index for geometry (pressure) updates, where is the maximum number of geometry updates corresponding to he maximum allowable wear depth. 2.2. Coordinate system and surface grids In order to perform a wear simulation, a family of spatial Cartesian coordinate frames is defined as shown in Fig. 2. Inertial coordinate frames Xp(xp,yp,zp) and Xg(xg,yg,zg) are attached to the pinion and the gear, and rotate with them, while two other coordinate frames Xfp(xfp,yfp,zfp) and Xfg(xfg,yfg,zfg) are established as fixed reference frames. Origins of Xg and Xfg coincide in Fig. 2. The same is true for Xp and Xfp. As the rotational axes remain the same, axes zg and zfg (and zp and zfp) also coincide, with the gear rotational axis pointing from the vertex of the pitch cone to the back face. The shaft offset E is defined as the distance between yfg and zfp (E /= 0 for hypoid gears and E = 0 for spiral bevel gears). In addition, in line with the contact model that will be introduced later, a local curvilinear surface coordinate system (T,S) is used to define grids of tooth surfaces as shown in Fig", + " Kahraman / Wear a b p t t ( a l p t r ( w R F o ( mounts and they are no longer in contact with each other, while oth are still within the contact zone. The distance between the oints ij and b at n = ns + 1 is equal to the amount of relative sliding hat takes place as gears rotated from n = ns to n = ns + 1. At this posiion, the coordinates of these two points are given as (Xp fg ) ij n=ns+1 and Xg fg ) b n=ns+1 . These position vectors can be obtained from (Xp fg ) ij n=ns nd (Xg fg ) b n=ns by applying certain coordinate rotations and trans- ations. According to Fig. 2, the position vector of point ij on the inion surface with respect to the fixed coordinate Xfp at the rotaional position n = ns is obtained from the given position vector with espect to the other fixed coordinate Xfg as Xp fp ) ij n=ns = Rf (Xp fg ) ij n=ns + Tf (3a) here f = [ \u22121 0 0 0 \u2212cos sin 0 sin cos ] , (3b) ig. 8. Wear depth profiles after various geometry updates cycle at an input torque f T = 300 Nm: (a) wear on the pinion surface (hp ij ) and (b) wear on the gear surface hg ij ) . 267 (2009) 1595\u20131604 Tf = {\u2212E 0 0 } ", + " Initial wear patterns of (a) the pinion surface and (b) the gear surface just be here vij f is the sliding velocity vector between two mating points j and b at an instant when gears are at rotational position n, and t is the time elapsed between positions n and n + 1. The sliding elocity vector is defined as vij f ) n = (vp fg ) ij n \u2212 (vg fg ) b n (7) here (vp fg ) ij n and (vg fg ) b n are the velocities of points ij and b on the inion and gear surfaces at position n, both defined with respect to he fixed gear reference frame Xfg as vp fg ) ij n = R\u22121 f [\u03c9p fp \u00d7 (Xp fp ) ij n ], (8a) vg fg ) b n = \u03c9g fg \u00d7 (Xg fg ) b n (8b) here p fp and g fg are angular velocities of the pinion and gear reltive to their respective fixed coordinate frames as shown in Fig. 2. ith these, the sliding velocity vector is defined as\u23a7 b g b p b p vpg f ) ij n \u23a8 \u23a9 (yg) \u03c9 \u2212 (yg) \u03c9 cos + (zg) \u03c9 sin \u2212(xg)b\u03c9g + (xg)b\u03c9p cos + E\u03c9p cos \u2212[(xg)b + E]\u03c9p sin (9) hile both methods of computing sliding distances result in very lose results, the first method was preferred in this study since it elates to the wear model directly. e first geometry update ( = 0) for various V, H, G and A values at T = 300 Nm. 2.5. Computation of the wear depth With (Pp,g ij ) n and (sp,g ij ) n\u2192n+1 in hand, the wear depth accumulated at each surface grid node ij between two rotational positions n to n + 1 at the th geometry update is given as (\u0131hp,g ij ) n\u2192n+1 = 1 2 k [ (Pp,g ij ) n + (Pp,g ij ) n+1 ] (sp,g ij ) n\u2192n+1 (10) During one complete wear cycle c, the surface grid node ij is loaded for a number of consecutive rotational positions (ns \u2264 n \u2264 ne)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003628_s11044-008-9121-7-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003628_s11044-008-9121-7-Figure1-1.png", + "caption": "Fig. 1 3-RPS parallel manipulator", + "texts": [ + " Perhaps the handling of several parameters or the lack of a systematic methodology of analysis increases the difficulty of the extension of these works to the full dynamics of MSHRMs built with an optional number of modules. In this work, the kinematics and dynamics of modular spatial hyper-redundant manipulators formed from Revolute+Prismatic+Spherical and RPS-type limbs are addressed via the theory of screws and the principle of virtual work. The base module of the MSHRM considered here is the well-known 3-RPS parallel manipulator, Fig. 1. This popular in-parallel manipulator was introduced by Hunt [26] and consists of a moving platform and a fixed platform connected to each other by means of three extendible limbs type RPS. The limbs are connected, respectively, at the moving platform and at the fixed platform by means of three distinct spherical joints and three distinct revolute joints. According to the classical Kutzbach\u2013Gr\u00fcbler criterion, this spatial mechanism has three degrees of freedom, two rotations, and one translation", + " The process is continued until the specific MSHRM has been reached. In particular, the last platform is called the output platform. 3 Kinematic model 3.1 Finite kinematics In this subsection, the forward position analysis (FPA) of the proposed hyper-redundant manipulator is carried out analytically using simple geometric procedures for a detailed explanation of the FPA of a 3-RPS parallel manipulator, which has a direct connection with this subsection; the reader is referred to [36, 40, 41]. Consider the 3-RPS parallel manipulator shown in Fig. 1. When the three prismatic joints are locked, the parallel manipulator becomes the 3-RS structure shown in Fig. 3. Under this consideration, the FPA of the parallel manipulator is established as follows. Given the limb lengths qi , i \u2208 {1,2,3}, compute the feasible locations of the moving platform, body 1, with respect to the fixed platform, body 0, through the computation of the coordinates of the centers of the spherical joints attached at the moving platform, points ai , i \u2208 {1,2,3}, expressed in the reference frame XYZ", + " Finally, assuming that a MSHRM is composed of n modules, then the transformation matrix of each moving platform, with respect to the fixed platform, body 0 is obtained applying recursively the procedure described in this subsection. Indeed, 0Tk = k\u22121\u220f j=0 j Tj+1, k \u2208 {1,2, . . . , n}. (8) 3.2 Infinitesimal kinematics of the modular spatial hyper-redundant manipulator In this subsection, the velocity and acceleration analyses of the MSHRM are carried out by means of the theory of screws. The kinematics of open serial chains using screw theory is the basis of this subsection; for a detailed explanation of it the reader is referred to [42\u201344]. Consider the 3-RPS parallel manipulator shown in Fig. 1. In order to satisfy the rank of the Jacobian matrix spanned by the infinitesimal screws of the limbs of the mechanism, the parallel manipulator is modeled as a 3-CPS manipulator (CPS = Cylindrical + Prismatic + Spherical), in which the translational displacements of the cylindrical joints are null. Figure 5 shows the infinitesimal screws of one limb of the 3-CPS parallel manipulator. With this consideration, the velocity state 0V1 O = [0\u03c91 0v1 O ]T and the reduced acceleration state 0A1 O = [0\u03c9\u03071 0a1 O \u2212 0\u03c91 \u00d7 0v1 O ]T of the moving platform, body 1, with respect to the fixed platform, body 0, can be obtained, respectively, in screw form through any of the i-th limbs, i \u2208 {1,2,3}, of the parallel manipulator as follows 0V1 O = [ 0\u03c91 0v1 O ] = 5\u2211 j=0 j\u03c9 i j+1 j $j+1 i (9) and 0A1 O = [ 0\u03c9\u03071 0a1 O \u2212 0\u03c91 \u00d7 0v1 O ] = 5\u2211 j=0 j \u03c9\u0307 i j+1 j $j+1 i + $Liei (10) where \u2022 0\u03c91 and 0\u03c9\u03071 are the angular velocity and acceleration of the moving platform, \u2022 0v1 O and 0a1 O are the velocity and acceleration of a point O fixed to the moving platform which is instantaneously coincident with a point of the fixed platform, \u2022 k\u03c9 i k+1 and k\u03c9\u0307 i k+1 are the joint velocity and acceleration rates of body k + 1 with respect to the adjacent body k, both in the same limb" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure2.29-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure2.29-1.png", + "caption": "Fig. 2.29. Definition of total orientation in terms of two directions", + "texts": [ + " Let us now discuss the problem of total orientation. When we consider the example in Fig. 2.20(b) we conclude that with the total orientation not only the direction (*) but also the direction (**) is important. So the total orientation may be considered in terms of two directions. Leter, we shall show that for the one direction given, the other is replaced by the rotation angle ~. Let us introduce the two directions: the main direction (b) and the auxiliary one (c). These directions are perpendicular to each other (Fig. 2.29). Let us first define these directions with respect to the gripper. For :t- ... such definition unit vectors hand 5 are used (Fig. 2.29). These vectors are expressed in the gripper b.-f. system. They are constant and represent the input values. In order do define the two directions (b), (c) with respect to the external system we use the three angles 6, ~, ~ (Fig. 2.29). The two directions on the gripper should coincide with the two directions in the external space. It should be pointed out that the gripper b.-f. system and the external system need not coincide. Hence, the generalized position vector is x = [x y z e ~ ~lT (2.4.62) g For positioning we use (2.4.13), (2.4.14) Le. 68 w Il'q + 0' Dimensions of matrices are: q (6x1), Il' (3x6), 0' (3 x 1). (2.4.63) Let A be the transition matrix of the gripper b.-f. system and A the g transition matrix of the orientation system" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure2.48-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure2.48-1.png", + "caption": "Fig. 2.48b. Scheme of manipulation task", + "texts": [ + " Examples In this paragraph we present several examples illustrating the opera tion of the algorithm for dynamic analysis. We demonstrate the use of adapting blocks, the calculation of various dynamic characteristics and some testings. The first example (2.8.1) deals with a 4 d.o.f. 106 manipulator. In (2.8.2) and (2.8.3) two 5 d.o.f. manipulators are con sidered. Finally, in (2.8.4) we present an example of a manipulator with 6 d.o.f. 2.8.'. Example' We consider a cylindrical manipulator UMS-2V - variant with 4 d.o.f. The external look and manipulator data are presented in Fig. 2.48a. This figure also shows the choice of generalized coordinates (internal coordinates) q\" q2' q3' q4 and the adopted b.-f. systems. The kinematic scheme of manipulator is shown in Fig. 2.48b. The minimal configuration consists of one rotational (q,) and two linear (q2' q3) degrees of fre ed?m. With this 4 d.o.f. variant, the gripper is connected to the min imal configuration by means of a rotational joint (q4). Manipulation task. The manipulator carries a 3kg mass working object. The moments of inertia of the working object are Ix4 = Iy4 = Iz4 = 0.0' kgm2 (with respect to the corresponding b.-f. system). The object is to be moved along the trajectory Ao A, A2 A3 (Fig. 2.48b). Every part of the trajectory (Ao+A\" A,+A2 , A2+A3 ) is a straight line. Object ro tation for the angle TI/2 has to be performed on the trajectory part Ao+A\" and the backward rotation (- \u00a5) on the part A,+A2 \u2022 The complete scheme of manipulation task is shown in Fig. 2.48b. We have to notice a few things. If a cylindrical manipulator has to reach the points Ao ' A\" A2 , A3 , it usually follows the trajectory rep resented by a dashed line in Fig. 2.49. This is done because of sim plier control synthesis. In this example we have chosen straight line motion betwen two points (full line in Fig. 2.49) in order to demon strate the algorithm possibilities. Triangular velocity profile is adopted. Adapting block 4-2 is suitable for this manipulation task because it T = [x y z q4 l Now, let us discuss the\u00b7 in-uses the position vector X g put values" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000400_tmech.2021.3068138-Figure14-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000400_tmech.2021.3068138-Figure14-1.png", + "caption": "Fig. 14: Means and standard deviations of the robot\u2019s tracking errors for six different subjects in the walking experiments based on the finite-time human-following control (FT), the PID based human-following control (PID), the free mode control (FMC), and the virtual spring control (VSC)", + "texts": [ + " Besides, the tracking error of the PID based human-following method cannot guarantee convergence in finite-time, which is the advantage of our proposed method. Considering the possibility that the previous humanfollowing control methods can achieve the proposed humanfollowing rule in the real world, we choose the PID control method, the free mode control method [12], and the virtual spring control method [14] for comparison. The means and standard deviations of human-following error are shown in Fig. 14. As shown in Fig. 13 and Fig. 14, the finite-time based human-following system can obtain excellent performance for meeting the proposed human-following rule with faster convergence, smaller error and less vibrations than the PID based human-following system. Although there might exist the most suitable parameters for the PID based human-following system to obtain good performance, it\u2019s time-consuming to find the perfect parameters in the real application. Further, the stability and the robustness of the PID based humanfollowing system cannot be ensured. According to Fig. 14, and the human-following performance, the finite-time humanfollowing control has the faster rate of convergence, less vibrations and smaller error than the other three control methods. Besides, the limitation of this study is that all the experiments are conducted with six healthy subjects. Comparing with the movements detected by the OptiTrack, the proposed intention estimation algorithm can successfully Authorized licensed use limited to: Dedan Kimathi University of Technology. Downloaded on May 24,2021 at 23:41:11 UTC from IEEE Xplore", + " The accurately estimated walking intention enables the robot to follow the target user correctly and keep the fixed relative posture with the user all the time, which is not only conducive to providing the timely assistance for the user at the appropriate position when necessary, but also conducive to measuring and recording the user\u2019s gait data correctly by the robot. The timely assistance can enhance the user\u2019s safety during the independent rehabilitation walking. The temporal and spatial parameters of the gait data can be analyzed to evaluate the user\u2019s walking condition and the recovery state. According to Fig. 14 and the human-following performance, the finite-time human-following control has the faster rate of convergence, less vibrations and the smaller error than the other three control methods. The proposed human-following rule and human-following system are approved by doctors. What\u2019s more, the human-following system is suggested to be used in a room and open whereas commodious outdoors. In summary, the proposed human-following rule can be applied in the similar accompany or indirect human-robot interaction scenarios as well, e" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003813_j.ijfatigue.2010.09.021-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003813_j.ijfatigue.2010.09.021-Figure1-1.png", + "caption": "Fig. 1. (a) The computational domain and grid mesh used in this study and (b) the definition of an Eulerian yz line with the consecutive material points passing through the computational domain.", + "texts": [ + " Assuming no slippage at the lubricant and solid surface interfaces and considering both the Poiseuille and Couette flows, the viscous shear stress acting on one of the surfaces (body 1) is written as q\u00f0x; y; t\u00de \u00bc 1 2 h\u00f0x; y; t\u00de @p\u00f0x; y; t\u00de @x g x us h\u00f0x; y; t\u00de \u00f06\u00de where g x \u00bc g= cosh\u00f0sm=s0\u00de is the effective viscosity for a Ree-Eyring fluid. Meanwhile, within the contact regions where the film thickness breaks down, the shear stress is defined as q\u00f0x; y; t\u00de \u00bc l p\u00f0x; y; t\u00de where l is the friction coefficient between the asperity contacts. A typical value of l = 0.1 under the boundary lubrication conditions [26\u201328] is used in this study. Fig. 1a shows the three-dimensional computational grid containing the contact zone. This Eulerian (fixed in space) 3D computational domain contains Nx Ny Nz grid elements, and its dimensions are dictated by the half Hertzian widths a and b in the x and y directions such that 1:875a 6 x 6 1:125a, 1:5b 6 y 6 1:5b and 0 6 z 6 a, where the z axis points down into the material, representing the depth. The grid increment Dz is designed to be variable to allow a finer grid in the regions near the surface to capture the local variations induced by the surface roughness, while the Dx and Dy increments in Fig. 1a are kept constant and sufficiently small to capture the surface roughness profiles in both directions. When a certain material point enters the computational domain of Fig. 1a as the contacting bodies roll, its stress components due to the instantaneous surface normal pressure and shear distributions must be predicted. By modeling the contact at any time instant t as an elastic half space subjected to both p(x, y, t) and q(x, y, t), the transient stress states below the contact surface can be determined by using the classical potential theory [25,29,30] as ~rijk;t \u00bc XNx m\u00bc1 XNy n\u00bc1 \u00f0~Sij;mn pmn;t \u00fe ~Tij;mn qmn;t\u00de \u00f07\u00de where ~rijk;t is the stress tensor at an arbitrary grid point ijk with coordinates (xi, yj, zk) (at the depth of zk under the surface grid node ij1) at time t", + " The closed-form formulations of ~Sij;mn and ~Tij;mn can be found in Ref. [30]. Eq. (7) also has the form of discrete convolution and can be evaluated the same way as that of the surface elastic deformation of Eq. (4) using the DFT convolution technique. Regardless of which multi-axial fatigue criterion is used [4,15,31\u201338], the mean and alternating values of the shear and normal stresses of each material point are required to assess its fatigue damage. At each time instant t, the stress components ~r\u00f0x; y; z; t\u00de within the Eulerian control volume (Fig. 1a) are recorded according to Eq. (7). Introducing a Lagrangian reference frame XYZ that is attached to the moving contacting body \u2018 (\u2018 = 1, 2) and stating the relationship between the two frames as x = X + u\u2018t, y = Y and z = Z, the time history of the stress tensor for the material point (X, Y, Z) is found as ~R\u00f0X;Y; Z; t\u00de \u00bc ~r\u00f0X \u00fe u\u2018t;Y; Z; t\u00de \u00f08\u00de Any residual stresses caused by the surface machining and heat treatment processes (measured along the z axis) can be superimposed onto the predicted elastic stress fields, which alters the mean values while leaving the alternating stress amplitudes unchanged", + " Once the macro crack plane is located, the orthogonal coordinate system x0\u2013y0\u2013z0 is defined such that the z0 direction corresponds to the normal vector of the macro crack plane and y0 points into the direction in which the shear stress amplitude on this crack plane is maximum. The characteristic plane is then arrived at through a rotation about the x0 axis by an angle a from the macro crack plane [4,15], forming a new frame of x0\u2014y00\u2014z00, where z00 is the normal vector of the characteristic plane and y00 is on the characteristic plane perpendicular to x0. sa1 and sa2 in Eq. (11) are the shear stress amplitudes in the x0 and y00 directions, respectively. Finally, the fatigue lives are determined by solving Eq. (11) numerically. As illustrated in Fig. 1b for the contacting body 1, the Lagrangian material points am (m = 1, 2, . . . , M) passing through the computational domain along an Eulerian line jk having y = yj and z = zk (i.e. at the same depth and the same axial coordinate) would have identical fatigue lives if the contacting surfaces were perfectly smooth such that p(x, y, t) = p(x, y) and q(x, y, t) = q(x, y). For the general case of rough surfaces, however, the variation of the fatigue lives of the population of the material points am traveling in the x direction is dictated by the statistical characteristics of the roughness profiles R1(x, y, t) and R2(x, y, t) of the mating surfaces (moving at unequal speeds of u1 and u2, respectively) as defined in Eq", + " When comparing the predictions with the experimental measurements, it is assumed that the crack propagation life to grow a pit to the size specified above is negligible compared to the crack nucleation life under the high cycle contact fatigue condition [18,19]. The baseline contact condition is defined as ur \u00bc 6:6 m=s, SR = 0.25, lubricant inlet temperature of 90 C and Rq = 0.6 lm with four loading levels of ph = 2.72, 2.41, 2.24 and 1.90 GPa. The simulations are repeated at an oil temperature of 60 C as well. The computational domain of Fig. 1a is discretized into over half a million mesh elements (Nx = 256, Ny = 128 and Nz = 20). The simulations cover around 8 and 10 mm long surface roughness segments for surface 1 and 2, respectively, which are sufficiently long to represent the surface irregularity characteristics. The grid resolution employed in the y direction is somewhat coarser, since both the contact surfaces are textured axially along the y direction resulting in limited variations along the y axis [14]. The fully reversed bending fatigue strength of the gear steel used (SAE 4620M) was provided by the project sponsor as Sb N \u00bc 2500N 0:0658 n microscope images of the cross sections of two pitted specimens", + " In order to show the transient nature of the contact fatigue analysis of lubricated rough surface contacts, the mixed EHL solutions at three different time instants are shown in Fig. 7 under the same contact conditions as in Fig. 6. Significant variations in p(x, 0, t) and h(x, 0, t) are observed with time t. Approximately, 21% of the Hertzian contact area is subject to asperity contacts in Fig. 7a while this ratio is about 10% and 4% for the other two time instants in Fig. 7b and c. This implies considerable variations of the resultant stress fields with t as well. Referring to Fig. 1b, the histograms of the fatigue lives of the populations of the material points traveling through the computational domain along the same yz lines are constructed. For the baseline condition with ph = 2.41 GPa for example, the histograms of the crack nucleation lives at different depth of \u00f0y; z\u00de \u00bc \u00f00;5\u00de; \u00f00;32\u00de; \u00f00;71\u00de; \u00f00129\u00de and (0, 213) lm are compared in Fig. 8. Here, the probability distributions of the fatigue lives at different z obey the lognormal distribution. As the depth increases, the crack nucleation life probability distribution moves to the right, indicating longer fatigue life" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000068_tie.2021.3057002-Figure18-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000068_tie.2021.3057002-Figure18-1.png", + "caption": "Fig. 18. New rotor mixed ventilation structure prototype.", + "texts": [ + " Temperature distribution of rotor with ventilation cooling structure under load operation condition (\u2103) Structural parts Rotor without ventilation cooling structure Rotor with ventilation cooling structure highest lowest highest lowest Stator core 155 108 154 111 Rotor core 179 152 145 106 Permanent magnet 179 153 145 114 Authorized licensed use limited to: Shenyang Aerospace University. Downloaded on June 14,2021 at 19:57:11 UTC from IEEE Xplore. Restrictions apply. 0278-0046 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. According to the geometry of the proposed novel rotor hybrid ventilation cooling structure, a new prototype of 315kW, 6kV HVLSSR-PMSM rotor with ventilation cooling structure is manufactured, as shown in Fig. 18. The lead-exit wires of the temperature measuring sensors in the motor are shown in Fig. 19. For verifying that the proposed design approach could provide satisfactory results practically, the temperature of the prototype with rotor hybrid ventilation cooling system is investigated in case of no-load operation, and the detail temperature distribution is shown in Fig.20. The losses of the entire motor at this operation are stator iron loss, winding copper loss, mechanical loss, which are 5510W, 2228W, and 4862W respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002459_s0963-8695(03)00011-2-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002459_s0963-8695(03)00011-2-Figure1-1.png", + "caption": "Fig. 1. Translational model dimensions of a spur gear tooth.", + "texts": [ + " Fault detection is achieved by the use of conventional time and frequency domain analyses, and fault indicating measures are applied to both the gear vibrations and their residual signals to reflect the progression of wear. The paper concludes with the application of the developed stiffness assessment technique to the test spur gears to quantify the damage to the spur gear teeth after each vibration measurements. The tooth stiffness of a spur gear in the direction of the predominant (tangential) component of the transmitted load W can be calculated by considering the translational model [9] shown in Fig. 1. The radial component, Wr; simply tends to compress the tooth and the rim and, therefore, makes very little contribution to the tooth deflection in the tangential direction [15]. In contrast, the tangential component, Wt; Nomenclature a half of the dynamic distance between two suspended teeth Ai cross-sectional area b tooth face width E modulus of elasticity in bending FMO ratio of the peak-to-peak vibration to the sum of the meshing tones FM1 ratio of the amplitude of the second tooth- meshing harmonic to its fundamental (in dB) FM4A fourth statistical moment of the residual signal FM4B ratio of the standard deviation of the residual signature to that of the original vibration G modulus of elasticity in shear hd tooth thickness at the root ht tooth thickness at the tip If ; Ig mass moment of inertia of the frame and gear Ii second moment of area ks equivalent stiffness of the pre-load screw fixing kt1 single tooth stiffness ktor torsional spring effect of the pre-load screw k1; k2 equivalent translational spring effects of the two points of suspension Lt tooth length mf ; mg mass of the frame and test gear Mi; Mi\u00fe1 bending moments acting on xi and xi\u00fe1 NA4 ratio of the FM4A to the square of the average variance of the residual signal Pp peak-to-peak value RMS root mean square value Si; Si\u00fe1 slopes at points xi and xi\u00fe1 u\u00f0x; t\u00de harmonic deflection function V shear force Wr; Wt radial and tangential components of gear load W X relative displacement yrim rim deformation ytotal total deflection at the tip in tangential direction yi; yi\u00fe1 deflections of points xi and xi\u00fe1 yi\u00fe1;i relative displacement of point xi\u00fe1 with respect to point xi Z number of teeth on a gear as shear coefficient di element thickness u relative rotation r mass density ft angle between tooth load and its tangential component v angular frequency attempts to bend and shear the tooth. If ytotal denotes the total deflection at the tip in the direction of tangential load, then the overall stiffness of the gear tooth kt1 can be expressed as follows: kt1 \u00bc Wt ytotal \u00f01\u00de To facilitate calculation of ytotal; the tooth can be divided into a finite number of elements as depicted in Fig. 1. If i is an element located between xi and xi\u00fe1 along the neutral axis of the tooth with thickness di; cross-sectional area Ai; and second moment of area Ii; then the deflection of point xi\u00fe1 can be expressed as follows yi\u00fe1 \u00bc yi \u00fe yi\u00fe1;i \u00f02\u00de where yi\u00fe1 and yi denote the total deflections of the points xi\u00fe1 and xi; respectively, and yi\u00fe1;i represents the relative displacement of point xi\u00fe1 with respect to point xi: The relative displacement in Eq. (2) contains both bending and shear deformations in the cross-section", + " Two models, translational and torsional, are used primarily to predict the static and dynamic properties of either a single tooth or of a complete gear system [9]. The torsional model is generally used when the factors affecting operational performance (i.e. torsional stiffness, gear tooth spacing and profile errors, etc.) are considered [9,12,13,17,18]. When the problem involves finding the vibration properties of a single tooth or determining the gear tooth stiffness, the translational modal shown in Fig. 1 can be used [9,14,15]. In general, all teeth on a gear have the same dimensions and the same mechanical properties. Their vibration characteristics such as amplitude, natural frequencies, and mode shapes will therefore, be very similar. When a fault, either localised or distributed, is incurred by a tooth, tooth stiffness reduces and the vibration characteristics of that tooth change. Tooth vibration characteristics thus contain information, which has potential for use in the severity assessment of gear tooth faults" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003391_0076-6879(88)37005-9-Figure9-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003391_0076-6879(88)37005-9-Figure9-1.png", + "caption": "FIG. 9. Enzyme competition electrode for measurement of NAD \u00f7 using a G O D - G D H membrane.", + "texts": [ + " Amplification makes use of a part of the GOD excess which is unused in the absence of NADH. The overall reaction represents the oxidation of NADH by oxygen, with glucose acting as the mediator between the two enzymes. The problem of measuring cofactor concentrations with electrochemical sensors may be solved if a cofactor-dependent enzyme is coupled with an oxidase, with both competing for the same substrate. The competition of GOD and GDH for glucose was used to develop a bienzyme electrode for determination of the oxidized cofactor, NAD \u00f7 (Fig. 9). The reaction between glucose and NAD \u00f7 is characterized by the equilibrium constant, K -- 3 \u00d7 10 7 M. ~3 The reaction proceeds in both directions depending on the concentrations of the partners. The above-described GOD-GDH 13 C. C. Liu and A. K. Chen, Process Biochem. Sept./Oct., p. 12 (1982). different glucose concentrations. Conditions are as in Fig. 1. membrane is used in combination with electrochemical measurement of oxygen consumption at -600 mV. Glucose, I mM in 0.1 M phosphate buffer, pH 7" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure3.30-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure3.30-1.png", + "caption": "Fig. 3.30a. Surface-type constraint and the reaction force", + "texts": [ + " The approach to this problem will differ from the one used in previous paragraphs (3.4.3 - 3.4.11). A noniterative approach was employed in these paragraphs. The model was formed allowing the calculation of both the accelerations and the reactions. The model was in the form of a system of linear equations with respect to accelerations and reactions. Here, we use a different approach proposed in [8]. Let us explain it. The influence of the surface-type constraint is taken into account through the reaction force F (Fig. 3.30). The dynamic model is formed which includes the reaction. If nominal dynamics has to be calculated, 210 the motion and the reaction are known and the model is solved for the drives P. In a simulation problem we start from an initial state which satisfies the constraint imposed. We calculate the reaction from the condition that after integration over a short time interval 6t the constraint has to be satisfied again. Let a moving surface (nonstationary constraint) be defined by fIx, y, z, t) o (3" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003788_978-1-4020-5967-4-Figure5-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003788_978-1-4020-5967-4-Figure5-1.png", + "caption": "FIGURE 5. Galileo, De motu, chap. 14.", + "texts": [ + " arrikat) applied at its end (B) is identified with the force applied to the circumference of the larger circle, the weight (t iql) to be lifted (G\u030c) with the weight on the arm of the smaller circle, and the fulcrum (D) with the centre of the two circles. Since the ends of the lever trace out arcs on concentric circles as the weight is lifted, the analysis of 2.7 can be applied directly: if the ratio of the length of the longer arm BD to that of the shorter arm DA is equal to the ratio of the weight G\u030c to the moving force applied at B, the lever is in equilibrium; if it is greater than the ratio of G\u030c to B, the force will lift the weight.33 The reduction of the wheel and axle to the concentric circles is just as direct (2.10; Fig. 5). The wheel corresponds to the larger circle and the axle to the smaller; the weight (t iql) is hung from the axle and the moving force (al-quwwat al-muh. arrikat ) applied at the circumference of the wheel.34 32 Dioptra, ch. 37 (Opera, vol. III, p. 310.26\u20137); see below, pp. 34\u201335. Pappus, Pappi Alexandrini collectionis quae supersunt, VIII, vol. III, p. 1066, makes the same point in the same language. 33 On the second use of the lever, discussed in Mechanics 2.9, see below, pp. 43\u201345. 34 Heron himself remarks in 2", + " When it comes to scales, Cardano explicitly reproaches Aristotle for not taking into account the position relative to the centre of the earth in his considerations of the speed of the movement of rotation; this means, as it did in Archimedes, that verticals are not parallel but meet at a point.31 He invokes neither Archimedes nor Jordanus de Nemore, who guided Tartaglia. With a diagram similar to Fig. 4a, Cardano describes as natural those movements that move toward the centre e, and as non-natural (praeter naturam) those that, from the side, move away, as if e now represented the centre of the world.32 The following diagram (Fig. 5b) would make one think of Heron of Alexandria33 if one did not know that his Mechanica was at the time unavailable in Europe.34 We cannot therefore say where Cardano may have drawn his inspiration and his criticisms. He also suggests that the Mechanica is not by Aristotle, because it seems to him so very obscure. Cardano reasons in a sharply different context from the one he criticizes, for he always situates himself in the whole of the earth, with its centre. Hence it is clear that the only natural movements for him are those directed toward this centre, and that circular motion is more or less violent only insofar as it is more or less removed from this direction", + "36 He followed the teaching of Francesco Maurolico in Messina, before the latter became interested in the Mechanica.37 Moletti engaged in the geometric and dynamic problemsraisedbyPseudo-Aristotlewithout reservationandwithoutcriticism. His demonstration of the fact that rectilinear motion can result from the combination of two circular movements is not so much a criticism as a parenthetical remark aimed at addressing Copernicus. Let us turn to his version of the fundamental demonstration, which indeed comes first. The natural movement of line BE should be along BF to bring it to FG (see Fig. 5a), but this does not take place:38 This posited, I say that point I would be moved more against its natural movement than point B would be. Because the natural movement of the line would be along the straight lines BF and EG, which cannot be because of the violence that point E produces by being in a fixed place; but point B would be moved by its natural [movement] along the arc BR and point I along the arc IN and such movement we shall call with Aristotle the natural movement of the line.39 35 On Moletti\u2019s treatment of the Mechanica in general, see Laird, The Unfinished Mechanics", + " 39 \u201cCi\u00f2 stante, dico che \u2018l ponto I si sar\u00e0 mosso pi\u00f9 contra il natural movimento suo, che non haver\u00e0 fatto il ponto B. Perch\u00e9 il movimento naturale della linea sarebbe per le rette BF et EG, il che non potendo essere per la violenza che \u2018l ponto E fa con l\u2019 essere in quel luogo fermo; per\u00f2 il ponto B si mover\u00e0 per il natural suo per la circonferenza BR et il ponto I per la circonferenza IN, et tal movimiento chiameremo con Aristotele movimento secondo la natura della linea\u201d (Moletti, Dialogue, ed. and trans. in Laird, The Unfinished Mechanics, pp. 93\u201395). FIGURE 5a. FIGURE 5b. It is easy to recognize Piccolomini\u2019s paraphrase in the \u201cviolence\u201d exerted by the centre of the circle. But it seems that Moletti hesitates concerning the natural motion, straight for the radii EB and EI, but curved along the circle for the points B and I; the natural movement of line BI is thus also that which leads it toward both RN and FO, depending on whether CIRCULAR AND RECTILINEAR MOTION IN THE MECHANICA 165 it is considered as part of the scheme or not. It seems therefore that the \u201cnatural\u201d no longer represents a category properly speaking, but becomes an adjective permitting the description of what is happening. Points B and I are nonetheless considered as diverted with respect to a movement that would otherwise have been rectilinear or natural, and the space FR is said to be traversed by a violent movement. The classical demonstration can now continue: point B is diverted with respect to a rectilinear movement by a space FR and point I by the space ON, greater than FR.40 Lastly, I should note that the particular position of Fig. 5a, in which all the natural movements are vertical \u2013 which was not the case for Piccolomini \u2013 at first has no impact on Moletti\u2019s reasoning. The reason for this situation becomes clear when Moletti proposes another demonstration of what he calls \u201cthe principle of mechanics\u201d, which is that movement is easier on large circles than on small ones. For in this alternative demonstration, weight and the vertical intervene. The largest circle is said to be closer to the natural movement of vertical fall than the smaller, which can be seen in Fig. 5b where the two circles are tangent to the same vertical line. In this Moletti is directly inspired by a passage from Niccol\u00f2 Tartaglia\u2019s Quesiti, who with a similar diagram says that the weight is greater on AE than on AC. We can also find this reasoning and a similar diagram, at almost the same moment, in the Mechanicorum liber of Guidobaldo dal Monte of 1577.41 It is thus clear that only the movement of vertical fall is natural for Moletti in his paraphrase of the Mechanica. Although the context in which he situates his circular motion is different from that of Cardano, the result is the same for our purposes: when gravity intervenes explicitly in the systems considered, no non-vertical rectilinear motion can be said to be natural", + "42 This argument is in fact used in the Mechanica, and then by certain commentators, but to explain the effectiveness of the sling in the twelfth question. We thus see to what degree the intuition of the link between force and movement is tied to the particular phenomenon considered. In his Mechanicorum liber, Guidobaldo refers to Archimedes\u2019 treatise On the Equilibrium of Planes and reasons only with weights and verticals directed toward the centre of the world. Scales are nonetheless represented by a circle and the comparison with circles of different curvature intervenes to show, as did Moletti and Tartaglia (see Fig. 5b), that the longer the beam of the scales, the closer the circle it describes is to vertical natural motion, and the freer and hence the \u201cheavier\u201d the weight when compared to a shorter beam.43 When Guidobaldo comes much later to the lever, he again uses the geometry of the circle, of two concentric circles, to prove that the displacements of the extremities are proportional to the distance from the centre.44 He is now able to state, as a deduction from this demonstration and from the Archimedean law of the lever,45 that the ratio of the force to the weight equals the inverse of the ratio of their displacements", + " autem curvum, unde si \u00e0 dicta rota particula aliqua sue circunferentiae disiungeretur, absque dubio per aliquod temporis spatium pars separata recto itinere feretur per aerem, ut exemplo \u00e0 fundis, quibus iaciuntur lapides, sumpto, cognocere possumus, in quibus, impetus motus impressus naturali quadam propensione rectum iter peragit, cum evibratus lapis, per lineam rectam contiguam giro, quem primo faciebat, in puncto, in quo dimissus fuit, rectum iter instituat, ut rationi consentaneum est\u201d (Benedetti, Diversarum speculationum, De mechanica, cap. 14, p. 159; Engl. trans. in Drake and Drabkin, Mechanics in Sixteenth-Century Italy, pp. 186\u2013187. Fig. 5 is taken from this work, p. 189). itself until destroyed by an outside resistance. This notion is not exceptional at this time in northern Italy.51 In his criticisms of the Physics, Benedetti directly attacked the Aristotelian category of natural motion for upward or downward motion, for they are not perpetual; he maintains the natural character of circular motion, which alone can perpetuate itself.52 One considers that the part separated from the whole will return to its natural place by the shortest path, which likely includes the starting point of the tangent, but Benedetti does not return to this, except to say that this is not the natural starting point", + "44 ii) The ratio of the forces required to raise a body vertically and on a given inclined plane is equal to the ratio between the respective gravities on these planes.45 If we know the gravity, we can answer the two initial questions. At the time of De motu, Galileo consistently assumes that the speeds follow the ratios of the gravities.46 Thus Galileo\u2019s purely geometric demonstration aims to determine the ratio between the gravities of a body on different inclined planes.47 To do so, the gravity of a body on an inclined plane is reduced to the gravity of a body suspended on a bent lever.48 Galileo imagines (Fig. 5) 43 The term most frequently used in this chapter of De motu to designate the measurement of motion is not velocitas, but rather celeritas, which we translate here as \u201cspeed\u201d; as we indicate below, if there is a problem, it concerns not the term used, but its meaning. 44 Galilei, Le opere, vol. I, p. 297: \u201cPrius hoc est considerandum, quod etiam supra animadvertimus: scilicet, quod manifestum est, grave deorsum ferri tanta vi, quanta esset necessaria ad illud sursum trahendum; hoc est, fertur deorsum tanta vi, quanta resistit ne ascendat\u201d" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002461_70.478428-Figure7-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002461_70.478428-Figure7-1.png", + "caption": "Fig. 7. A sketch of the fire truck system showing @e virtual extension that is added in front of the rear steering wheel. These vehicles are equipped with a long ladder on the trailer and are used by lire departments in large cities in the United States. The extra steering wheel at the rear of the trailer is used for improved", + "texts": [ + " The bottoms of the chains in the multiinput chained form are the (5 , y) coordinates of the rear axle and the hitch angle &, and the rest of the coordinates are found through mfferentiation according to (5) , To illustrate the procedure presented in this paper for converting multisteering trailer systems into chained form, the algorithms given in Section ID will be followed for two example systems. A. Fire Truck Although the fire truck example has been examined extensively in previous work, it can also be considered in terms of the algorithms described in this paper, and in fact, the formulation is somewhat different than in [4]. In that paper, the bottoms of the chains in the multiinput chained form were chosen to be the (5, y) position of the passive axle along with the angle of the trailer (see Fig. 7). Because of the relative simplicity of the three-axle system, that choice allowed kinematic equations to be put into multiinput chained form without using dynamic state feedback. The fire truck fits into the class of multisteering trailer systems, thus the kinematic equations can also be converted into multiinput chained form using a virtual extension (and a different choice of states at the bottoms of the chains). Although this extension is not necessary for this particular system, no systematic procedure is known for transforming a general multisteering trailer system into multiinput chained form without using the sort of virtual extension that is proposed in this paper. The kinematic equations for the fire truck can be obtained from (3) and will not be repeated here. The system has two steering trains, the first has length two and the second has length one. Since there is one passive axle in front of the second steering train, this train will be augmented by the addition of one virtual axle as described in Section III-C. The angle of this virtual axle is denoted 0;. A sketch of the extended system is shown in Fig. 7. The 22\u201d 6 y (the chains are written upside down here to show the order in which the coordinates are calculated: starting at the bottom). The resulting equations are in multichained form. 3. A Five-Axle System Consider a five-axle system with two steering wheels, depicted in Fig. 8. In effect, this system is a fire truck with two passive trailers. With these extra trailers, the (2, y) position of the first passive axle, along with the trailer angle $I, will no longer define the entire state of the system" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002577_87.553662-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002577_87.553662-Figure1-1.png", + "caption": "Fig. 1. The two-link robotic manipulator.", + "texts": [ + " Design Algorithm Step 1) Choose a desired attenuation level, Step 2) Choose the weighting matrix with and the weighting matrix such that for singular case for nonsingular case. Step 3) Calculate the parameter i.e., for singular case for nonsingular case. Step 4) Select the neural-network functions for in (12). Step 5) Obtain the corresponding adaptive neural networkbased control law The corresponding smooth projection update law can be obtained as in Remark 12. In this section, we test our proposed adaptive neural control design on the tracking control of a two-link robot by using a computer. Consider a two-link manipulator described in Fig. 1 with system parameters as link masses (kg), lengths (m), angular positions (rad), and applied torques (Nm). The parameters for the equation of motion (3) are [15] where and the shorthand notations are used. Suppose that the trajectory planning problem for a weightlifting operation is considered and the two-link manipulator suffers from the time-varying parametric uncertainties, unmodeled friction forces, and exogenous disturbances. The adaptive neural model reference tracking control with the desired performance (19) is employed to treat this robotic trajectory planning problem" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure33.13-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure33.13-1.png", + "caption": "Fig. 33.13 The schematic of prototype", + "texts": [ + "11 can rotate the rotor, however, both of rotational speed and torque were not stable, so the vibration mode of PZT beam, the propagation of vibration, and the loss of transmission at the contact, etc. must be carefully adjusted. Y. FURUKAWA, T. KAGA, K. MAKITA, T. WADA and A. NAKAJIMA Development of Ultrasonic Micro Motor with a Coil Type Stator 397 It will bring more miniaturized ultrasonic micro motor if the stator itself can possess both the functions of vibrator and driver. So, the stator itself was made of PZT as shown in Fig.33.13, where the coil type PZT stator generates and propagates an ultrasonic vibration once excited by alternative voltage. For this purpose, a tube PZT was ground to a coil with a specified pitch by a specially designed grinding machine. Figure 33.14 and Table 33.9 show the photograph and the specification of prototype respectively. This could rotate, although still unstable, when the alternative 398 voltage of 90Vp-p is applied. It is necessary to verify the vibration mode of PZT coil and how the vibration is converted to the rotational force" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000161_j.optlastec.2021.107337-Figure31-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000161_j.optlastec.2021.107337-Figure31-1.png", + "caption": "Fig. 31. Schematic illustration of the repeated pattern left by track overlapping and seen on sample cross-sections.", + "texts": [ + " Optics and Laser Technology 143 (2021) 107337 The travel speed was varied in the experiment for fabricating the samples shown in Fig. 10 and Fig. 11. Since the powder feed rate remained unchanged, hatch spacing h and offset of nozzle in z-direction between two adjacent layers had to be adapted. In order to minimize the trial-and-error of parameter adjustments, the following method was used: A DED sample is made by stacking partially overlapped tracks and a repeated pattern can be seen on the sample cross-sections perpendicular to the tracks, as shown in Fig. 31. The area of one element is assumed to be inversely proportional to the travel speed, and a reference area Aref can be calculated by: Aref = \u03b1\u22c5Wref \u22c5Href (1) where Wref and Href are the width and height of the element, and \u03b1 is a constant factor. Wref and Href are equal to the hatch spacing and offset of nozzle in z-direction respectively that have been experimentally optimized. Wref and Href ar eparameters that have been experimentally optimized. If the travel speed changes, the new area An is assumed to be given by \u03b1, Wn and Hn in the same way" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003543_intmag.2006.376221-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003543_intmag.2006.376221-Figure1-1.png", + "caption": "Fig. 1 High-speed PM BLDC motor", + "texts": [ + " Therefore, it is essential to develop practical techniques to reduce the rotor eddy current, e.g., decreasing the armature current time harmonics [1], segmenting the magnets [2], using special magnetization patterns [3] and multiphase windings [4]. This paper will study the influence of retaining sleeve and conductive shield on the rotor loss, such that appropriate sleeve and shield can be selected. In the paper, a 2-pole 3-phase high-speed PM BLDC motor with ratings of 3kW @ 150,000rpm is considered, as shown in Fig.1, the magnets being SmCo. In order to improve the mechanical strength, the rotor is usually protected with a non-magnetic sleeve, such as a carbon fiber sleeve which has very low electrical conductivity but poor thermal conductivity, or titanium alloy / stainless steel sleeve which has high electrical and thermal conductivity. The influence of different retaining sleeves on the rotor loss is analyzed with FEM, as given in the first rows in Tables I and II. It is seen that the eddy current loss in the conductive titanium sleeve is much higher than that in the carbon fiber sleeve" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002936_0020717011011226-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002936_0020717011011226-Figure1-1.png", + "caption": "Figure 1. The Furuta pendulum system. I0, inertia of the arm; L0 , total length of the arm; m1, mass of the pendulum; l1, distance to the centre of gravity of the pendulum; J1, inertia of the pendulum around its centre of gravity; \u00b30, rotational angle of the arm; \u00b31, rotational angle of the pendulum; and \u00bd , input torque applied on the arm.", + "texts": [], + "surrounding_texts": [ + "The inverted pendulum is a very popular experience used for educational purposes in modern control theory. The structure of the conventional inverted pendulum is the rail-cart type which consists of a cart running on a rail and a pendulum attached to the cart. The inverted pendulum of this type has the movement limitation of its cart as a restriction of the control system. On the other hand, the Furuta pendulum has a di erent structure. It has a direct-drive motor as its actuator source and its pendulum attached to the rotating shaft of the motor. This inverted pendulum on the rotating arm was \u00aerst developed by K. Furuta at the Tokyo Institute of Technology. The experiment is called the TITech pendulum (see Futura et al. 1992, Yamakita et al. 1995, Iwashiro et al. 1996). Since the angular acceleration of the pole cannot be controlled directly, the Furuta pendulum is an underactuated mechanical system. Therefore, the techniques developed for fully-actuated mechanical robot manipulators cannot be used to control the Furuta pendulum. Furuta et al. (1992) proposed a robust swing-up control using a subspace projected from the whole state space. Their controller uses a bang\u00b1bang pseudo-state feedback control method. Yamakita et al. (1995) considered di erent methods to swing up a double pendulum. One is based on an energy approach and another one is based on a robust control method. Iwashiro et al. (1996) considered a golf shot with a rotational (Furuta) pendulum using control methods based on an energy approach. Olfati-Saber (1999) proposed a semi-global stabilization for the rotational inverted (or Furuta) pendulum using \u00aexed point controllers as for the cart-pole system. Then he introduced new cascade normal forms for underactuated mechanical systems (Olfati-Saber 2000). The main bene\u00aet of this transformation was to reduce the overall system to control a lower order non-linear subsystem in the normal form. He illustrated his result with the example of the rotational pendulum. Contrary to the technique proposed here, the magnitude of the control input in his scheme increases as the initial state is further from the origin. The stabilization algorithm proposed here is an adaptation of the technique presented in the work of Lozano et al. (2000) which deals with the inverted pendulum. We will consider the passivity properties of the Furuta pendulum and use an energy based approach to establish the proposed control law. The control algorithm\u2019s convergence analysis is based on Lyapunov theory. In } 2, we present the model of the Furuta pendulum obtained using Euler\u00b1Lagrange equations. We also establish its passivity properties. The control law is developed in } 3 and the stability analysis of the closed-loop system are given in } 4. Simulations are presented in } 5 and conclusions are \u00aenally given in } 6." + ] + }, + { + "image_filename": "designv10_6_0002429_s0039-9140(96)02071-1-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002429_s0039-9140(96)02071-1-Figure1-1.png", + "caption": "Fig. 1. Configuration of fibre-optic biosensor and flow cell set-up: 1, bifurcated optical fibre bundle; 2, plastic syringe cylinder; 3, plastic body of syringe needle; 4, poly(methacrylate) cylinder; 5, 19G gauge syringe needles; 6, white PTFE cylinder as reflector; 7, glass bead mixture (containing immobilized acetylcholinesterase and thymol blue) packed in a microwell; 8, bare 32-fibre plastic optical fibre bundle; 9, nylon mesh support.", + "texts": [ + " Sensor construction and flow-cell configuration The sensitive enzyme reagent phase of the optical biosensor was prepared by homogeneously mixing 10 mg portions of each of the glass-immobilized acetylcholinesterase and thymol blue indicator preparations. When not in use, this reagent mixture was stored in a refrigerator under 0.1 M phosphate buffer solution (pH 7.0). To construct the optical sensor, an aliquot of the reagent phase was pipetted out and deposited in the microwell (100\u2013150 mm deep and 1.55 mm diameter) of a specially fabricated fibre-optic probe head (Fig. 1). The beads were blotted dry, then carefully packed until a thin and compact glass layer was produced. The glass materials were then retained in place using a fine nylon mesh, which in turn was supported by a plastic tube. The fibre-optic probe was inserted into a flow cell assembly, which was machined from a Perspex cylinder (1 cm diameter\u00d71 cm high). The flow cell device incorporated two 19G (20\u00d71 mm o.d.) stainlesssteel needles, positioned diametrically opposite each other, to serve as the solution inlet/outlet" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000499_j.surfcoat.2021.127492-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000499_j.surfcoat.2021.127492-Figure2-1.png", + "caption": "Fig. 2. Schematics of (a) mechanical polishing and (b) PVD coating.", + "texts": [ + ", contact force, rotating speed, and polishing time). The contact force of the parallel-type spindle head was adjusted in six steps (50\u2013300 gf) based on the stability of the machine, as listed in Table 4. It was observed that the stability of the machine and the polishing quality were low under low contact forces (50, 100, 150, 200 gf) compared to those under the high (300 gf) contact force because of the K.-T. Yang et al. Surface & Coatings Technology 422 (2021) 127492 vibration of the machine caused by the rough surface (Fig. 2a). Therefore, the contact force was optimized to 250 gf, and the rotating speed was set as 1500 rpm in the range of 1000\u20133200 rpm, based on the surface uniformity and stability. The polishing process employed in this study can be roughly divided into two parts, namely rough and high polishing. Most of the uneven surfaces formed by the melt pools were removed by rough polishing considering the peak\u2013valley lengths. If the spindle head could not fully cut the surface up to the valley points, pool-like defects were observed", + " PVD has been mainly used for the surface treatment of stainless steel exterior parts owing to its advantages. Therefore, PVD coating was performed for improving the surface quality and physical characteristics of the surfacetreated 17-4 PH blocks. PVD coating was performed by breaking down the target material (Ag) into atoms or molecules by first heating or colliding it with Ar+ ions. Subsequently the atoms or molecules were condensed and solidified on the surface of the product to form a thin film, as shown in Fig. 2b. A plasma was developed by injecting inert argon gas into a vacuum chamber and applying power to the target side. The Ar+ ions generated in the plasma were irradiated at the target, and the charge density difference caused the target to eject under the shock energy. The molecules of the target material and nitrogen gas were injected into a chamber. A compound (AgN) was finally deposited on the surface of the product. The PVD color of the surface rarely disappears over time, and PVD can achieve a uniform and higher appearance quality than an electrochemical process" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003947_j.nonrwa.2010.08.021-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003947_j.nonrwa.2010.08.021-Figure1-1.png", + "caption": "Fig. 1. Dynamic model of spur gear pair system.", + "texts": [ + " The remainder of this paper is organized as follows. Section 2 derives single degree-of-freedom dynamic models for the spur gear pair systemwith and without a nonlinear suspension effect, respectively. Section 3 describes the techniques used in this study to analyze the dynamic response of the spur gear pair system. Section 4 presents the numerical analysis results obtained for the behavior of the spur gear system under various operational conditions. Finally, Section 5 presents some brief conclusions. Fig. 1 presents a schematic illustration of the dynamic model considered in the present analysis. In this model, cg is the damping coefficient of the gear mesh, kg is the stiffness coefficient of the gear mesh, e is the static transmission error and varies as a function of time, I1 is the mass moment of inertia of Gear 1, I2 is the mass moment of inertia of Gear 2, R1 is the base circle radius of Gear 1, R2 is the base circle radius of Gear 2, \u03d51 is the angular displacement of Gear 1, \u03d52 is the angular displacement of Gear 2, T1 is the torque acting on Gear 1, and T2 is the torque acting on Gear 2", + ", X \u2032\u2032 + 2dX \u2032 + f (X) + \u03b6X3 = P(t), (9) where \u03b6 = k2b2 meff\u03c9 2 n . In analyzing the nonlinear dynamics of the spur gear pair system, the current analysis non-dimensionalizes the nonlinear dynamic equations given in Eqs. (7) and (9) using the dimensionless damping coefficient, d, and the dimensionless rotational speed ratio, s, i.e., X \u2032\u2032 + 2d s X \u2032 + f (X) s2 = P(t) s2 , (10) X \u2032\u2032 + 2d s X \u2032 + f (X) s2 + \u03b6 X3 s2 = P(t) s2 , (11) where d = cg 2 \u221a meffkg and s2 = \u03c92 \u03c92 n . In this study, the nonlinear dynamics of the spur gear pair system shown in Fig. 1 are analyzed using Poincar\u00e9 maps, bifurcation diagrams, the Lyapunov exponent and the fractal dimension. The basic principles of each analytical method are reviewed in the following sub-sections. The dynamic trajectories of the spur gear system provide a basic indication as to whether the system behavior is periodic or non-periodic. However, they are unable to identify the onset of chaoticmotion. Accordingly, some other form of analytical method is required. In the current study, the dynamics of the spur gear system are analyzed using Poincar\u00e9 maps derived from the Poincar\u00e9 section of the gear system" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure4.6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure4.6-1.png", + "caption": "Fig. 4.6. Spherical manipulator VE-4", + "texts": [ + " 252 It should also be said that we do not optimize the parameters of all segments. Some segments are completely determined by the constructive solutions adopted. We shall explain this fact in more detail in the example, but let us say here that, for instance, the actuators chosen determine completely the segments which form the gripper (the last three segments if a six d.o.f. manipulator is considered). We may say that there usually exist one or two segments which should be optimized. If a cylindrical (Fig. 2.44) or spherical (Fig. 4.6) manipulator is in question, there is usually one main segment forming the manipulator arm and this is the one to be optimized. With anthropomorphic (Fig. 2.53) or arthropoid (Fig. 4.2) manipulators there are two main segments which form the manipulator arm and which should be optimized. We can make some further simplifications in order to reduce the number of parame ters to be optimized. The lengths of segments can be considered as known since they directly follow from the reachability conditions im posed", + " Before giving the examples let us describe the optimization procedure. In the case of one parameter the procedure is quite simple. The param eter should be reduced as much as possible. The first possibility is to decrease the parameter successively until some constraint is vio lated. The last permissible value is the optimal one. In order to find 254 this optimal value in shorter time we may use some of one-dimensional -search techniques such as the binary search or the golden ratio search [10 1 \u2022 Example 1. Let us consider a spherical manipulator VE-4 (Fig. 4.6). The segments 1, 2, 4 and 5 are completely determined by the constructive solutions adopted. The third segment has the form of a cylindrical tube made of steel (p = 7,85.10 3 kg/m3 , E = 2,1.10 11 N/m2, a 5.108 N/m2, safety p coefficient \\! = 3). This tube can be pulled out of the second segment up to 0.8 m. This results in the segment being 1.2 meters long. Thus the cross-section dimensions of this segment remain to be chosen. The cylindrical tube cross-section is defined by the outside radius (R) and the inside radius (r), as shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002950_0885328206055998-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002950_0885328206055998-Figure1-1.png", + "caption": "Figure 1. Schematic of pin-on-disc wear setup used in the present study.", + "texts": [ + " Saturated calomel electrode (SCE) and graphite electrode were used as the reference and the counterelectrodes, respectively during electrochemical polarization. All values of potential in this article are reported with respect to SCE. Electrochemical experiments were carried out using the computer controlled VersaStat II, Potentiostat/Galvanostat (EG&G, Princeton Applied Research). Wear-corrosion tests were conducted on a pin-on-disc type wear machine with a provision for a cylindrical container that allowed wear testing in aqueous environment. The schematic of such a wear setup is illustrated in Figure 1. For conducting wear-corrosion test, 50mm long and 3mm diameter zirconia pin was used. The zirconia pin was chosen because it is frequently used as a ceramic cup that pairs with the metallic stem or ceramic head in total hip replacement (THR) surgery. The flat base (contact surface) of zirconia pin was prepared by abrading and polishing against a series of emery papers ranging from at NORTH CAROLINA STATE UNIV on May 11, 2014jba.sagepub.comDownloaded from 240 to 600 grit. The procedure for preparing the contact surface of zirconia pins was uniform for all pins used in the present wear study [13]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003153_02640419308730001-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003153_02640419308730001-Figure1-1.png", + "caption": "Figure 1 Pictorial representation of angles of sideslip (/?) and track (x) and the azimuth angle (jj/). Note the velocity vector is the projection of the velocity vector of the javelin's centre of mass onto the horizontal (xy) plane of the earth axis system.", + "texts": [ + " This angle is denned by Hopkin (1966) as the attitude angle between the x-axis (longitudinal axis) of the javelin (Fig. 2) and the horizontal xy-plane of the earth axis system. Values of 6 at the instant of right foot take off or drag in the delivery stride, 6(T4), and javelin release, 6(0), are also presented in Table 8. The azimuth angle, i]/ [attitude angle defined by Hopkin (1966) as the projection of the javelin's x-axis, or longitudinal axis, on to the horizontal xy-plane of the earth axis system and the horizontal x-axis of the earth axis system; see Fig. 1], would also help describe the 'carry' of the javelin but was omitted from this study since very little deviation from 0\u00b0 during carry was noted. Also relating to the 'carry' of the javelin, Witchey (1973) found that better throwers had a larger value of the distance between right hip and javelin mass centre (Dhj) at the start of the delivery stride (T3). This parameter, also presented in Table 8, has theoretical weight, since a large value of Dsj will increase the acceleration path of the javelin and will allow greater work to be done on the javelin prior to release", + "2 ms\"');in this study, air speed readings were not taken, and hence F(0) is taken as being equal to the magnitude of the velocity vector of the javelin's centre of mass relative to the ground, FK(0). a Angle of attack (Fig. 2): the angle between the javelin's x-axis (longitudinal axis) and the projection of V on to the xz-plane of the javelin's body axis system (\u00b10.5\u00b0; positive for clockwise rotations, when looking along the positive direction of the javelin's y-axis, from the javelin's x-axis to V). a = aK, the angle of attack relative to the air, since it is assumed that V(0) = FK(0) (Hopkin, 1966). P Angle of sideslip (Fig. 1): the angle between the xz-plane of the javelin's body axis system and V (\u00b10.5\u00b0; positive to the left). /? = /?K, since it is assumed that F(0)=FK(0) (Hopkin, 1966). % Angle of track (Fig. 1): the angle between the earth's horizontal x-axis and the projection of the tangent to the flight path (i.e. the direction of V) on to the earth's horizontal xy-plane (\u00b10.5\u00b0; positive to the left). y Angle of climb (flight path angle; y(0) is the release angle) (Fig. 2): the angle between the tangent to the flight path (i.e. the direction of V) and the horizontal xy-plane of the earth axis system (\u00b10.5\u00b0; positive for climbing). a Incidence magnitude:, the angle between the javelin's x-axis and V (\u00b10", + " has been dealt with extensively in aeronautics and missile aerodynamics (e.g. Hopkin, 1966). The problem is exaggerated in javelin and discus throwing because there is a large angular velocity component (> 1 Hz) about the one determinate axis. This makes it unhelpful to have the two indeterminate axes fixed within and rotating with the body. In cases such as this, it is usual and convenient to define indeterminate axes relative to another axis system. In this study, the javelin's y-axis was defined as perpendicular to the javelin's x-axis (Fig. 1) and lying in an earth axis system horizontal plane passing through the javelin centre of mass (positive to the left). The z-axis is then determined by the formation of a right-handed orthogonal system (Fig. 2). It should be noted that, although pitch rate is an important variable in javelin throwing, the values in Table 9 are prone to considerable uncertainty owing to javelin vibration (see Hubbard and Alaways, 1988). Pitch rate has been mentioned in some reports of twodimensional studies without mention of the fact that only in two-dimensional work is the pitch rate equal to the time rate of change of the inclination angle (9)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure6.1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure6.1-1.png", + "caption": "Fig. 6.1 Schematic layout of the XYZ microstage", + "texts": [ + " In order to achieve accurate X and Y linear motion of the stage, the XYstage should have higher symmetric structure to minimize the cross-axis coupling. In this microstage, the stage corners or sides should be supported by above enlarging mechanisms. \u2018Parallelogram mechanism\u2019 has a high symmetry in their structure for enlarging the displacement, but most of them are driven by asymmetrically arranged piezoactuators. A novel parallelogram mechanism for the stage with six degrees of freedom is designed, and the actuator is integrated into the parallelogram mechanism. This integration allows a high symmetric structure in the design. Fig.6.1 shows the schematic figure of the stage design and the parallelogram mechanism. Four arms with parallelogram mechanism support the center stage and the double-layered piezostack actuator is integrated in each center of the arm. The double-layered piezo-stack actuator, as the cross section is shown in the top of Fig.6.2(a), consists of two stacked piezoactuators, and the stacked piezoactuators can be individually driven by applying an appreciate voltage. The doublelayered piezo-stack actuators can elongate to drive the stage in XY-plane, and can bend to move into out-of-plane" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003287_tbme.2005.851530-Figure10-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003287_tbme.2005.851530-Figure10-1.png", + "caption": "Fig. 10. Coordinate systems used in the frontal plane for (a) the single support phase and (b) the double support phase. The origin is set to the position of the ZMP in the single support phase and to the center of the feet in the double support phase.", + "texts": [ + " The coefficients , can be calculated using these boundary conditions where is the position of the ZMP at the beginning of stage . Among the variables described above, the following parameters are used for the optimization: \u2022 the position of COM at OTO, HR, OIC; \u2022 the velocity at OTO. The position of the COM at MS is determined so as to compensate for the angular momentum generated during the single support phase. Therefore, the number of parameters for the AMPM in the sagittal plane is four. APPENDIX II APPLICATION OF THE AMPM FOR CALCULATION OF MOTION IN THE FRONTAL PLANE The coordinate systems used here are shown in Fig. 10. The distance between the feet when they are both on the ground is . The COM moves during the double support phase. After switching to the single support phase, it moves along until it stops and returns back the same path. The relationships between the ZMP, COM, and ground force during the single support phase are (13) where is the position of the COM along the horizontal axis, is a constant value that is correlated with ground force direction and position of the COM [Fig. 10(a)]. Using the terminal condition and at time , the motion of the COM can be finally written as (14) where is the velocity when the single support starts, and . Since the duration of the single support phase is determined by the motion in the sagittal plane, can be calculated by setting , in (14). As a result, can be calculated as The and -component of the ground force can be written as Since the trajectories of the ground force, COM, and ZMP are known, rotational moment around the sagittal axis can be calculated as The double support phase can be modeled as follows" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure2.21-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure2.21-1.png", + "caption": "Fig. 2.21. Spraying powder along the prescribed trajectory", + "texts": [ + " In case (a) it is only important that the axis (*) is vertical and so it is the case of partial orientation. In case (b) not only the direction (*) but also the direction (**) is impor tant. For the given direction (*) the direction (**) may be replaced by angle ~. Hence, the case (b) represents the total orientation. Fig. 2.20(c), (d) shows something analogous but for assembly tasks. 52 We now consider two examples which demonstrate that the orientation representation chosen (direction and angle) really follows from prac tical manipulation tasks. Fig. 2.21. presents a task of spraying pow der along a prescribed trajectory. The task reduces to the need to realize the motion of an object (container) along the trajectory (a) (i.e. positioning) and along the trajectory the container should rotate around the direction (b) according to the prescribed law W(t). So, the orientation representation in terms of one direction and the rotation angle directly coincide with the functional motion of manipulator. In this case the choice of the direction is different from that in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002489_s0165-0114(99)00072-x-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002489_s0165-0114(99)00072-x-Figure3-1.png", + "caption": "Fig. 3. Two-dimensional illustration of domain of sliding mode [2].", + "texts": [ + " Therefore, a bounded region of can be changed into \u00a1 6kmax = , which can be regarded as a domain of the fuzzy variable . Also, since a minimum value of is larger than the maximum value of chattering, chattering does not occur in the system trajectory. De!nition 1 (Decarlo [2]). A domain Q on the manifold s=0 is a sliding-mode domain if for each \u00bf0, there is a \u00bf0, such that any motion starting within a n-dimensional -vicinity of Q may leave the n-dimensional -vicinity of Q only through the n-dimensional -vicinity of the boundary of Q, see Fig. 3. Some work on the automatic tuning of the boundary layer in VSS has been reported. The distance to the sliding surface was used in [9] and k was determined by using s in [5]. In this paper, the boundary layer thickness of the VSS with fuzzy boundary layer is determined by the change of s. Instead of input T and output Q given in (14), the fuzzy rules make use of |s| as input and as output. The membership functions for |s|; are given in Fig. 4. Usually, the tracking performance in VSS is represented by =x\u0303 for the maximum value of the boundary thickness [13]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000210_tie.2021.3075886-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000210_tie.2021.3075886-Figure1-1.png", + "caption": "Fig. 1: Schematic of the CTRUAV with the body-fixed frame and inertial frame.", + "texts": [ + " Different TRUAVs were proposed in the above works, but none of them applied the coaxial tilt-rotor (CTR) scheme. Coaxial rotors scheme is a practical solution and has been applied in various aircrafts, such as Kamov series helicopter of Russia [23], Airbus A400M A400M transport plane of European Union [24], and single-axis coaxial rotor UAV [25], [26]. In this work, a coaxial tilt-rotor unmanned aerial vehicle (CTRUAV) has been designed and assembled. The CTRUAV has a novel structure and possesses two pairs of front coaxial tiltable rotors and one fixed-axis rear rotor, as shown in Fig. 1. Comparing with other single-rotor TRUAVs mentioned above, the proposed CTRUAV enjoys the following advantages: Firstly, the rotational directions of coaxial rotors are opposite. Hence, the Coriolis force, the reaction torques, and the torques caused by blade flapping on the coaxial rotors are counteracted, which means we can simplify the above features of the coaxial rotors and do not need to design extra control logic for these factors. Furthermore, CTRUAV possesses control redundancy. If a failure happens on the rotor of each coaxial-rotor module, the CTRUAV is still controllable theoretically, thus the safety redundancy is improved", + " The rear rotor module consists of a 20-Amp ESC, a 2206- type motor, and a 8040-type rotor. 4). The flight control hardware system includes a STM32-F405 microprogrammed control unit (MCU) with the max working frequency of 168MHz, an inertial measurement unit (IMU) which integrates an accelerometer, a gyroscope, and a control signal receiver. The IMU measures states of the CTRUAV and communicates with MCU by I2C bus on the frequency of 100Hz. The flight control hardware system outputs pulse width modification (PWM) signals to control the servos and motors. As shown in Fig. 1, the inertial frame I{Xi,Yi,Zi} follows the North-East-Down (NED) notation, and the bodyfixed frame B{Xb,Yb,Zb}, which coincides with the center of gravity (CoG) of the CTRUAV, follows the standard aircraft notation where the Zb points downwards, the Xb towards the longitudinal flight direction and the Yb towards the right direction. The key geometric dimensions of the CTRUAV prototype are depicted in Fig. 5, where lb is the distance from the rear rotor to the CoG of CTRUAV in direction Xb, l f and ls are the distance from the coaxial tilt-rotor modules to CoG in directions Xb and Yb, respectively", + " The tilt axis of the coaxial rotors coincides with XbYb plane of the bodyfixed frame B, which means the distance from the tilt axis to CoG in directions Zb is zero. The overall mechanisms of the CTRUAV\u2019s maneuvers are illustrated in Fig. 6, which are achieved by varying the thrusts and tilt angles of the rotors. III. DynamicModeling To design the control strategy for the CTRUAV prototype, its dynamic model is derived. We first define the generalized coordinates based on the two reference frames described in Fig. 1 as follows: q = [\u03be> \u03b7>]> \u2208 R6, where \u03be = [x y z]> \u2208 R3 Authorized licensed use limited to: University of Saskatchewan. Downloaded on July 07,2021 at 16:22:54 UTC from IEEE Xplore. Restrictions apply. 0278-0046 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. denotes the coordinates of the CoG of the CTRUAV in inertial frame I, and x, y, z are positions along Xi, Yi, Zi, respectively; \u03b7 = [\u03c6 \u03b8 \u03c8]> \u2208 R3 denotes the CTRUAV\u2019s attitude angle in Euler coordinate system, with the roll angle \u03c6, the pitch angle \u03b8, and the yaw angle \u03c8", + " In the control input u, Fxzb = [Fxb Fzb]> contains the rotors\u2019 thrust forces, where Fxb and Fzb are the component forces along direction Xb and Zb, respectively, and \u03c4\u03b7 = [\u03c4\u03b7 \u03c4\u03b8 \u03c4\u03c8]> is the torque generated by the imbalance of the thrust and the reaction torque of the rotors. The control input u is calculated as follows Fxb Fzb \u03c4\u03c6 \u03c4\u03b8 \u03c4\u03c8 = Fr s\u03b1r + Fls\u03b1l \u2212Fr c\u03b1r \u2212 Flc\u03b1l \u2212 Fb \u2212Fr c\u03b1rls + Flc\u03b1lls + \u03c4r s\u03b1r + \u03c4ls\u03b1l Fr c\u03b1rl f + Flc\u03b1ll f \u2212 Fblb \u2212Fr s\u03b1rls + Fls\u03b1lls + \u03c4b \u2212 \u03c4r c\u03b1r \u2212 \u03c4lc\u03b1l , (13) where the forces and torques can be simplified as Fr = ct f (\u03c92 1 + \u03c92 4), Fl = ct f (\u03c92 2 + \u03c92 3), Fb = ct\u03c9 2 5, \u03c4r = cq f (\u2212\u03c92 1 + \u03c92 4), \u03c4l = cq f (\u2212\u03c92 2 + \u03c92 3), \u03c4b = cq\u03c9 2 5, with the rotational speed \u03c9i of rotor i (i = 1 \u223c 5) illustrated in Fig. 1 , the thrust coefficients ct f , ct, and the torque coefficients cq f , cq. In order to counteract the reaction torque, the Coriolis force, and the torques caused by blade flapping, each pair of coaxial rotors are set to rotate at the same speed and opposite directions, which means \u03c91 = \u03c94 = \u03c9r, \u03c92 = \u03c93 = \u03c9l. Then, the control input allocation is given by Fxb Fzb \u03c4\u03c6 \u03c4\u03b8 \u03c4\u03c8 = 2ct f 0 2ct f 0 0 0 \u22122ct f 0 \u22122ct f \u2212ct 0 \u22122ct f ls 0 2ct f ls 0 0 2ct f l f 0 2ct f l f \u2212ctlb \u22122ct f ls 0 2ct f ls 0 cq s\u03b1r\u03c9 2 r c\u03b1r\u03c9 2 r s\u03b1l\u03c9 2 l c\u03b1l\u03c9 2 l \u03c92 5 , (14) Considering that the CTRUAV is underactuated, the transfer matrix G is not a square matrix and is given by G(q) = [ R 03\u00d73 03\u00d72 I3 ] , Authorized licensed use limited to: University of Saskatchewan" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002839_978-3-662-03845-1-Figure8.7-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002839_978-3-662-03845-1-Figure8.7-1.png", + "caption": "Fig. 8.7. Local volume fractions of monomer \u00a2(r) at distance r from an arbitrary monomer in a semidilute solution of very low concentration \u00a2. Solid curve, monomers from the chain going through the origin. Dashed curve, volume fraction of other chains. Scales are logarithmic, so that power laws appear as straight lines. Within a blob size ~ the total volume fraction is dominated by the chain passing through the origin. Beyond the distance ~ the total volume fraction is dominated by other chains", + "texts": [ + " There if two chains are joined, the two halves tend to be aligned, and the mean-squared end-to-end distance is significantly more than doubled, in accordance with self-avoiding walk behavior. Though our interpenetrating chains have the overall structure of a simple random walk, the original ~-chains that were joined to create the final chains have their original self-avoiding structure. Semidilute chains thus obey two different fractal laws. The amount of chain n(r) enclosed in a radius r grows as r5/3 if a \u00ab r \u00ab ~. But for ~ \u00ab r \u00ab R n(r) grows as r2. The ~-chains are often called blobs [8.2]. The density of monomers around a given monomer is shown in Fig. 8.7. The chains of a semidilute solution each come in contact 282 8. Polymer Solutions: A Geometric Introduction with arbitrarily many others. The various chains are strongly entangled with one another. The result resembles a network of random strands. From the joining construction above we can also understand the osmotic pressure in a semidilute solution. As noted above, the pressure is important because it counts the amount of free energy stored in the solution. Before the joining process, we have seen that this energy is about kT per chain" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003619_s0263574708004268-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003619_s0263574708004268-Figure3-1.png", + "caption": "Fig. 3. Three-link model of grounded planar biped.", + "texts": [ + " Note also that the joint velocity in the last equation conserves the coupling momentum at zero: Hf l \u03b8\u0307 = 0. A necessary condition for the existence of the Reaction Null-Space is that the number of joints n is larger than the DOF\u2019s of the foot. Note that this is not the case with the planar model introduced in the previous section. Indeed, the inertia coupling matrix Hf l is 3 \u00d7 2, and we have an underactuated system at hand. We can make use of the selective Reaction Null-Space, though, to control particular component(s) of the reaction. Consider the model shown in Fig. 3. This is the same threelink model as already described, but now attached to the ground. With this model, balance will be ensured by always keeping the total CoM on the vertical. In other words, we will ignore the imposed force component in the z direction and the moment component nf (cf. Fig. 2). Hence, the selective Reaction Null-Space will be applied to control the imposed force component in the x direction only. Denote by r the position of the CoM, with components: rx = m1lg1S1 + m2(l1S1 + lg2S12) m1 + m2 rz = m1lg1C1 + m2(l1C1 + lg2C12) m1 + m2 " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002603_joe.2002.805098-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002603_joe.2002.805098-Figure2-1.png", + "caption": "Fig. 2. Coordinate system.", + "texts": [ + " The measured signals generated from the AUV\u2019s motion are used to develop the two nonlinear observers for estimating the linear damping coefficients. The AUV block represents the real plant and includes a 6 DOF nonlinear model of the NPS AUV II [10]. The values of the linear damping coefficients resulting from this block are used as true values and then compared with the estimated ones. In nonlinear observers, 6 DOF AUV equations of motion and the augmented states for the linear damping coefficients are included. Thus, the observer model describes surge, sway, heave, roll, pitch, and yaw motions. The coordinate system is shown in Fig. 2. The 6 DOF equations of motion for the observer model are as follows: Surge: Sway: Heave: Roll: Pitch: Yaw: (1) where , , and are the velocity of surge, sway, and heave motion and , , and are angular velocity of roll, pitch, and yaw motion, respectively. , , , , , and represent the resultant forces and moments with respect to , , and axis, in this order, and their detailed expressions and nomenclatures are described in [10]. In order to estimate the linear damping coefficients, these coefficients have to be modeled as extra state variables" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002818_027836499501400202-Figure5-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002818_027836499501400202-Figure5-1.png", + "caption": "Fig. 5. Robot with a rotational five-bar closed loop.", + "texts": [ + " Eliminate 111X~, lI~TY~, lLIZ~ when j < rl. (They represent the translational links before rl, where wj = 0.) We note that X X~ , ... , ZZj have been eliminated by the application of rule 2. 7. Examples Let us consider a 5-DOF robot with a single closed-loop; three cases are considered: 1. The closed loop is five planar bars from which the active joint is a prismatic one (Fig. 4). 2. The closed loop is five planar bars with rotational joints only; the distance between joints 2 and 3 is equal to zero (Fig. 5). 3. The closed loop constitutes a parallelogram in which links 3 and 4 and links 2 and 5 are parallel (Fig. 5). To illustrate the efficiency of using the base parameters in the calculation of the dynamic model, the cost of the dynamic model of the third example will be given. 7.1. Example 1 The 5-DOF robot shown in Figure 4 has eight joints, seven moving links, and one closed loop. The geometric parameters of the robot are given in Table 2, assuming that joint 8 has been opened. Joints 1, 2, 5, 6, and 7 are active, while joints 3, 4, and 8 are passive. The final result is summarized in the following: The number of base inertial parameters of the robot is 38; these are given in Table 3", + " There are 18 independent at Bobst Library, New York University on February 11, 2015ijr.sagepub.comDownloaded from 122 Table 2. Geometric Parameters of Example 1 parameters and 20 that are the result of regrouping some parameters. There are 32 eliminated parameters: 1. The following 12 parameters have no effect on 2. The following 20 parameters have been regrouped: The regrouping relations (parameters on which the letter R is added in Table 3) are: 7.2. Example 2: Robot With Rotational Five-Bar Closed Loop The 5-DOF robot shown in Figure 5 has eight joints,, seven moving links, and one closed loop. Joints 1, 3, 4, 6, and 7 are motorized, while joints 2, 5, and 8 are not motorized. The geometric parameters of the robot are given in Table 4, assuming that joint 8 has been opened to construct the equivalent tree structure. at Bobst Library, New York University on February 11, 2015ijr.sagepub.comDownloaded from 123 Table 3. Minimum Inertial Parameters of Example 1 Table 4. Geometric Parameters of a Robot With a Rotational Five-Bar Closed Loop The final results are summarized in the following: The number of minimum inertial parameters of the robot is 40; these are given in Table 5" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003080_dasc.2000.886895-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003080_dasc.2000.886895-Figure1-1.png", + "caption": "Figure 1. M.I.T. Xcell-BO with avionics system", + "texts": [ + " To make aggressive maneuvering safer and decrease overarching dependence on skills of a pilot, it is necessary to design a feedback control system with adequate closed loop bandwidth. We are preparing a demonstration of fully autonomous flight featuring aggressive maneuvers, including split-S and longitudinal loop. This paper describes an avionics system we implemented to achieve high-bandwidth feedback control, robust to modeling errors and gusts. Vibration isolation with proper frequency characteristics is essential for high-g flight of a rotorcraft. We summarize our successful vibration mount design in the paper. Description of a test vehicle Our test vehicle, shown in Figure 1, is an alcohol-powered Xcell-60 hobby helicopter. It has a two-blade teetering rotor augmented with Bell-Hiller stabilizing bar. Rotor diameter is 5 ft. Gross takeoff weight (with 7 lbs of avionics added to the airframe) is 18 lbs. A well-trained RC pilot has performed high-speed 2 g turns, full longitudinal loops, and high-rate stall turns with the data acquisition payload. Rotor speed range is 1500-1700 RPM. An electronic governor maintains commanded rotor speed by adjusting throttle commands" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003823_ma071104y-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003823_ma071104y-Figure2-1.png", + "caption": "Figure 2. Stretching of LCE films with a homeotropic alignment.", + "texts": [ + " The tensile measurements of the film specimens were conducted with a UTM-500 equipped with a temperature-controllable box. The both edge areas (about 2 \u00d7 2 mm) of the specimens were mechanically clamped, so that the effective initial length in the stretching direction was about 10 mm. The considerably large ratio of the effective length to the width (ca. 5) is expected to provide sufficient freedom to lateral displacement by stretching except for the vicinity of the clamped region. The specimen was uniaxially stretched in the z-direction normal to the initial director in the x-direction (Figure 2). The slowest available cross-head speed of the tensile tester (0.5 mm/ min) was employed to adjust to the considerably slow strain rate in the IR dichroism measurement (as described later). The stretching process was recorded by a video camera. The dimensional variations in the y- and z-directions during elongation were evaluated by video analysis. Infrared Dichroism Measurements. The IR dichroism measurement of the LCE films under tension was conducted using a custom-built stretching device. The film specimen was clamped at both ends in the same manner as in the tensile measurement" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002681_j.mechmachtheory.2004.04.003-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002681_j.mechmachtheory.2004.04.003-Figure4-1.png", + "caption": "Fig. 4. The reference frames used at the input and output points of contact.", + "texts": [ + " What happens when slip occurs, namely when torque is transmitted, is only slightly different from the above written scenario since the slip is always very small and, hence, the axes of rotation of the roller relative to the discs would result only slightly tilted relatively to those depicted in the Figs. 2 and 3. Now consider the contact area between the roller and the discs. In this region the elastic deformations of the bodies have a large influence on the relative velocity motion, and this one can no more be classified as a rigid motion. The region of contact is an elliptical area centered at the point of contact. The ellipse principal axes, (see Fig. 4) lay on the y-axis (the major) and on the x-axis (rolling direction, the minor). In order to calculate the shear strain of the lubricant we need to find an explicit formulation of the relative velocity field in the contact region. Observe that, over the contact area the bodies cannot penetrate each other, thus the relative velocity, because of the elastic deformations, do not have any component normal to the area of contact. Hence, assuming a negligible tangential deformation of the elastic bodies, the velocity of the roller points relative to the input and output discs, respectively, can be written, in the region of contact, as: v21 \u00bc v21A \u00fe x21spin ^ \u00f0Pin A\u00de \u00f01\u00de v23 \u00bc v23B \u00fe x23spin ^ \u00f0Pout B\u00de \u00f02\u00de Pin and Pout are points of the roller, while the velocity vectors v21A and v23B stand for the relative velocity between roller and discs at the center points A and B of the contact areas. Since we are considering only steady-state behavior v21A and v23B do not have components along the y-axes, yin and yout (see Fig. 4), but only along the x-axes. The previous Eqs. (1) and (2) show that the relative motion between the roller and the discs in the contact region, can be split into a pure translation, given by the vectors v21A and v23B, and a pure spin motion about the z-axes. When studying the toroidal traction drives, it is useful to define the input and output slip coefficients, usually referred to as creep coefficients Crin and Crout: Crin \u00bc jx1jr1 jx2jr2 jx1jr1 ; Crout \u00bc jx2jr2 jx3jr3 jx2jr2 \u00f03\u00de A small amount of creep must be always present to allow the transmission of torque" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure2.43-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure2.43-1.png", + "caption": "Fig. 2.43. Froces and moments acting on the \"free\" end of a segment", + "texts": [ + "28) make possible the recursive calculation -+ -+ -+-+ of deviations u i and ~i starting with Uo = 0, ~o = O. But, the deformations ~~1, ~el of the segment \"in still remain to be found. 1 1 The segment \"i\" will be considered as a cantilever beam having the lower end S. fixed and the upper end Si+1 free. The action of the next segment 1 ->-> \"i+1\" is replaced by total joint force -FSi +1 and moment -MSi +1 . The -> -> sign \"-\" follows from the previous assumption that FSi+ 1 ' MSi +1 act on the next segment \"i+1\" (see 2.5.3). Thus, the following forces and mo-> ments (Fig. 2.43) act on the free end of segment \"in: joint force FSi +1 ' moment MS' l' gravity force ~~Pg(g = {O, 0, -9.81}), and nominal iner1+ 1 tial force -~~P~Si+1 (~Si+1 is the nominal acceleration of the point Si+1). 93 Now, the linear deviation ttI~ is: (2.5.29) and the angular deviation (2.5.30) ai' Si' Yi , 0i are matrix influence coefficients. These coefficients will now be discussed but, before that, we conclude that equations (2.5.27) and (2.5.28) combined with (2.5.29) and (2.5.30) allow recur--+ -+ --+--+ sive calculations of ~1'~l, \u2022\u2022\u2022 ,un-1'~n-1 and finally the deviations of gripper point A i.e. uA ' ~A' Influence coefficients. Let us consider a segment \"i\" and its b.-f. system 0ixiYizi (Fig. 2.43). Since the segment is considered as a can tilever beam, in the b.-f. system it holds (2.5.31) and (2.5.32) where a xi 0 0 0 Sxi 0 iii 0 a yi 0 i -Syi 0 0 0 0 a zi 0 0 0 (2.5.33) 0 -Yxi 0 0 xi 0 0 Yi Yyi 0 0 8. 0 0 yi 0 1. 0 0 0 0 0 0 zi a xi is the influence coefficient for the bending deflection (linear deviation) along the axis xi' under the action of the force at the 94 point S. l' Similarly, a . is defined in terms of the Yl\u00b7 axis. l+ yl a zi is the influence coefficient for extension along the zi axis, under the action of the force at Si+1' It can usually be neglected by taking a zi = O" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002589_1.1344902-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002589_1.1344902-Figure2-1.png", + "caption": "Fig. 2 The compliant, three-ball chain", + "texts": [ + " (6) The former solution is obtained by assuming that B2 and B3 are in contact when B1 strikes and they can be treated as a single mass (v2 15v3 1). The second solution, on the other hand, is obtained by assuming that B2 and B3 are not in contact when B1 strikes, which leads to the impulse condition t350. Having two equally possible solutions poses a serious difficulty in accepting this approach as a valid way of solving this problem. 2.2 Impulse Correlation Ratio. We now consider the compliant model that is presented in Fig. 2, which is the example considered in Brogliato @4#. For simplicity, we will choose m1 5m25m35v1 251 and v2 25v3 250. When all the balls are in contact, their displacements can be obtained as follows: q15 t 3 2 k~2g2g1!sin~Akg1t ! ~kg1!3/2~g12g2! 1 k~2g2g2!sin~Akg2t ! ~kg2!3/2~g12g2! (7) q25 t 3 1 k~g2g1!sin~Akg1t ! ~kg1!3/2~g12g2! 2 k~g2g2!sin~Akg2t ! ~kg2!3/2~g12g2! (8) q35 t 3 1 kg sin~Akg1t ! ~kg1!3/2~g12g2! 2 kg sin~Akg2t ! ~kg2!3/2~g12g2! (9) where g1511g1A12g1g2 and g2511g2A12g1g2. The left and right impulses acting on B2 can be written as follows: Dt25E 0 t k~q22q1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002942_physreve.67.051702-Figure5-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002942_physreve.67.051702-Figure5-1.png", + "caption": "FIG. 5. Proposed structure of the banana-smectic fibers. ~a! A banana-shaped molecule with the principal refractive indices. ~b! Proposed layer and director structure ~jelly-roll @21# configuration! of the B2 phase. Upper row: three-dimensional 3D view. Lower row: cross section. ~c! Proposed layer and director structure of the B7 fibers. Upper row: 3D view. Lower row: cross section. Note that the difference between the director structures in the B2 and B7 phases is that in the B2 the long axes of the average molecules are in the plane of the cross section, whereas in the B7 phase they are tilted away. @18#.", + "texts": [ + " This clearly shows that the single fibers are fluids along the fiber axis. Such a situation can be achieved by rolling the smectic layers into concentric cylinders ~so-called \u2018\u2018jelly roll\u2019\u2019 @21# structure!. Observations of the fibers with a l/4 wave plate inserted at 45\u00b0 with respect to the crossed polarizers indicate that the refractive index along the fiber is lower than normal to it. In addition, we find that the birefringence increases toward the outer part of the fiber. Considering the principal refractive indices illustrated in Fig. 5~a!, one can see in Fig. 5~b! that the effective birefringence is n22n3 at the core, which is smaller than the birefringence (n12n2) at the bark of the fiber. In the bundles, electric fields induce a flow along the fiber axis. The direction of the flow depends on the sign of the electric fields, but in different fibers it can be opposite. In the B2 bundles, the flow effects average out and the overall diameter remains unchanged. In the B7 fibers, the flow direction appears to be the same in all strands and a net flow is observed" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000407_j.msea.2021.141254-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000407_j.msea.2021.141254-Figure1-1.png", + "caption": "Fig. 1. Illustrations of (a) the island exposure strategy with 90\u25e6 rotation for SLM and (b) the as-built Ti6Al4V bars.", + "texts": [ + " The primary focus of the present study was to determine the effects of the embedded spherical pores of different sizes and locations, to mimic the accidently appeared sub-millimeter scale printing defects, on the tensile properties and failure behaviors of the SLM Ti6Al4V specimens. Whether those embedded pores could be detected and how they would deteriorate the tensile properties were also discussed. The specimens were fabricated by the Concept Laser M2 SLM equipment with gas-atomized Ti6Al4V powders (Al: 6.2, V: 3.95, Fe: 0.21, O: 0.10, C: 0.013, N: 0.02, H: 0.006, Ti: balance, wt%). The Ti6Al4V powder particles with powder size ranging from 20 \u03bcm to 60 \u03bcm were used. The island exposure strategy was utilized to reduce residual stress during printing, as shown in Fig. 1(a). The optimal processing parameters were employed in the present study and the values are shown in Table 1. The processing chamber was filled with argon during printing. The as-built specimens were annealed at 800 \u25e6C for 2 h followed by furnace cooling for stress relieving, then the cylinder bars were cut off by the wire-cut electric discharge machining (WEDM) from the basal plate, as shown in Fig. 1(b). The phase constituents were identified by an X-ray diffractometer (XRD) operated at 45 kV and 200 mA. The XRD profiles were recorded in 2\u03b8 range 10\u201390\u25e6 using the Cu-K\u03b1 radiation (\u03bb = 1.54 \u00c5) with step size of 0.02\u25e6 and a scan speed of 10\u25e6/min. The samples were ground with 800\u20133000 GRIT grinding papers, then polished with SiO2 polishing suspension followed by etching in Kroll reagent (HF: HNO3: H2O = 2:1:17) for the microstructure observation. The porosity of bulk materials and the morphology of embedded pores were analyzed by computed tomography (CT) using YXLON Y" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000563_j.triboint.2021.107106-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000563_j.triboint.2021.107106-Figure4-1.png", + "caption": "Fig. 4. Four Bearing Test Rig used for experimental fluid drag loss measurements.", + "texts": [ + " Ensuring a minimum of three cells across each clearance in the mesh provided an accurate consideration of the k-\u03c9 SST turbulence model, with maximum y+ values not exceeding three. A total of 2.8 \u00d7 106 and 8.0 \u00d7 106 tetrahedral elements were used in the DGBB and RNRB models, respectively. Images of the fluid domain and unstructured mesh are presented in Fig. 3. In order to corroborate the analytical results obtained from Ansys Fluent software, a Four Bearing Test Rig (FBTR) was designed and developed to measure frictional torque of four test bearings operating under various conditions. Fig. 4 provides a CAD model and photograph of the FBTR. The four test bearings are mounted inside a housing that allows radial load application through a spring loading system and load cell. Bearings are symmetrically spaced inside the housing such that no bending moments are generated from the radial load application. The two middle bearings sit in a floating ring which is connected to the spring loading system, capable of applying up to 2.5 kN, while the two outer bearings sit in rings fixed to the housing" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003117_70.246062-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003117_70.246062-Figure3-1.png", + "caption": "Fig. 3. System behavior for the simulation in the absence of joint limits and obstacles.", + "texts": [ + " To avoid this, we place an upper limit on the norm of the input. If uTu > 1.0, we proportionally reduce the input, by changing k l , such that uTu = 1.0. Changing k1 does not cause any inconsistency with the theory we developed in Section III. Fig. 1 shows the trajectory of the elbow coordinates of the manipulator for the simulation in the absence of joint limits and in the absence of obstacles. Fig. 2 shows the trajectory of the joint variables. The behavior of the system for this case is observed in Fig. 3 at eight different intermediate stages. The convergence time for the simulation was approximately 4.65 s. The actual time taken for the simulation was approximately 7.5 mins on a SUN 4/260 computer. B. End-Effector Trajectory Planning with Joint Limits Next, we imposed joint limits and carried out a simulation using the Lyapunov-like functions 211 of (16) and V ~ J of (19) in hierarchy, for the same initial and desired configuration given by (26) and (27). The joint limit for all the joints were set at 180" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003256_tia.2006.876081-Figure8-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003256_tia.2006.876081-Figure8-1.png", + "caption": "Fig. 8. Infrared sensor mounted at a hole through an end-bearing plate of the test motor.", + "texts": [ + " The test induction motor is driven by a three-phase-voltage source PWM inverter. A permanent magnet dc generator with a resistor bank was used as the load of the test motor. A single-chip digital signal processor (DSP) (TMS320F240) is used to control the induction-motor inverter and perform the proposed temperature-estimation method. In order to verify the proposed temperature-estimation method, an infrared K-type thermocouple (OS36SM-K-440F) was mounted at a hole through one of the bearing plates of the test motor, as shown in Fig. 8, to measure the stator and rotor winding temperature in real time. The temperature measurements were compared with the Ts and Tr estimates to find out the accuracy of the proposed temperature-estimation method. The constant Volts/Hz scheme was used to run the test motor at a full-rated load (rated speed, 3396 r/min, and rated torque) and 20% rated load (20% rated speed, 680 r/min, and rated torque) for 120 min. Low-amplitude 60- and 95-Hz signals, and 10- and 14-Hz signals, which yield good sensitivities of Is versus Rs and Rr at the rotor speed of 3396 and 680 r/min, respectively, are injected into the motor using the induction-drive inverter" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000131_j.matcom.2020.12.030-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000131_j.matcom.2020.12.030-Figure4-1.png", + "caption": "Fig. 4. Simulated path tracking results of the end-effector of the WMR synthesized by the proposed RZNN model (9) with dynamic NDN y(t) = 0.025t. (a) Actual trajectory of the end-effector and desired path. (b) Position errors of the end-effector. (c) Motion trajectories of he WMR. (d) Top view of the motion trajectories of the movable platform.", + "texts": [], + "surrounding_texts": [ + "In this part, the RZNN model for solving IKP of the WMR without interference will be analyzed. Theorem 1. Considering the proposed RZNN model (8) in ideal no noise environment, no matter whether the dynamic system is in any initial state, the RZNN model (8) converges to the exact solution of IKP of the WMR in fixed time tb: tb \u2264 1 \u03bbbk ( b a )1/p ( 1 + 1 pk \u2212 1 ) a w c fi 4 w C T \u2264 i P \u2212 w A Proof. According to the defined error function (5) and its convergence formula (6), the error function array E(t) of RZNN model (8) can be expressed as d E(t)/dt = \u2212\u03bb\u0393 (E(t)), and its correspondent subsystems can be obtained s: dei (t) dt = \u2212\u03bb\u03c4 (ei (t)) i \u2208 {1, 2, . . . n} (12) here ei (t) is the i th element of E(t). As the new power-versatile activation function (7) is used, vi(t) = |ei (t)| is adopted as the Lyapunov function andidate to prove the fixed-time convergence of the RZNN model (8). The time differentiation of vi(t) is dvi(t) dt = \u2022 ei (t)sgn (ei (t)) = \u2212\u03bb\u03c4 (ei (t)) sgn (ei (t)) = \u2212\u03bb (( a |ei (t)|p + b )k sgn(ei (t)) + cei (t) + d sgn(ei (t)) ) sgn (ei (t)) = \u2212\u03bb (( a |ei (t)|p + b )k + c |ei (t)| + d ) \u2264 \u2212\u03bb ( a |ei (t)|p + b )k = \u2212 ( \u03bb 1/k ( av p(t) + b ))k According to Lemma 1, the bounded time ti of the i th subsystem can be directly obtained as: ti \u2264 1 \u03bbbk ( b a )1/p ( 1 + 1 pk \u2212 1 ) Based on the above analysis, the upper bound convergence time of (8) can be obtained: tb = max(ti ) \u2264 1 \u03bbbk ( b a )1/p ( 1 + 1 pk \u2212 1 ) As the bounded time tb is independent of the initial state of the dynamic system, and the RZNN model (8) is xed-time stable in the condition of no noise. \u25a0 .2. RZNN model analysis with noise Interference and noises are inevitable in practical implementation of neural networks, and the RZNN model (9) ith various interference and noises will be discussed in this part. ase 1: Dynamic disappearing noise (DDN) When the N(t) in (9) is a DDN, Theorem 2 will ensure the stability of the RZNN model (9). heorem 2. If the proposed RZNN model (9) is attacked by a DDN N (t), and the i th element of N (t) satisfies |ni (t)| \u03b4|e j (t)| and \u03bbc \u2265 \u03b4 (\u03b4 \u2208 (0, +\u221e)), ei (t) stands for the i th element of E(t). No matter whether the dynamic system s in any initial state, the RZNN model (9) converges to the exact solution of IKP of the WMR in fixed time tb: tb \u2264 1 \u03bbbk ( b a )1/p ( 1 + 1 pk \u2212 1 ) roof. Similar as Theorem 1, the error function array E(t) of RZNN model (9) can be expressed as dE(t)/dt = \u03bb\u0393 (E(t)) + N (t), and its correspondent subsystems can also be obtained as: dei (t) dt = \u2212\u03bb\u03c4 (ei (t)) + ni (t) i \u2208 {1, 2, . . . n} (13) here ei (t) stands for the i th element of E(t), and ni (t) stands for i th element of N(t). Here, vi(t) = |ei (t)| is adopted to prove its fixed time convergence. The time differentiation of vi(t) is dvi(t) dt = \u2022 ei (t)sgn (ei (t)) = (\u2212\u03bb\u03c4 (ei (t)) + ni (t)) sgn (ei (t)) (14) s the new power-versatile activation function (7) is used, |ni (t)| \u2264 \u03b4|ei (t)| and \u03bbc \u2265 \u03b4, the following formula is obtained: t T | m P d w R o dvi(t) dt = \u2022 ei (t)sgn (ei (t)) = (\u2212\u03bb\u03c4 (ei (t)) + ni (t)) sgn(ei (t)) = ( \u2212\u03bb (( a |ei (t)|p + b )k sgn(ei (t)) + cei (t) + d sgn(ei (t)) ) + ni (t) ) sgn (ei (t)) = \u2212\u03bb ( a |ei (t)|p + b )k \u2212 \u03bbc \u23d0\u23d0ei j (t) \u23d0\u23d0 \u2212 \u03bbd + ni (t)sgn (ei (t)) \u2264 \u2212\u03bb ( a |ei (t)|p + b )k + (\u03b4 |ei (t)| \u2212 \u03bbc |ei (t)|) \u2264 \u2212\u03bb ( a |ei (t)|p + b )k = \u2212 ( \u03bb 1/k ( av p(t) + b ))k Based on Lemma 1, the bounded time ti of the i th subsystem can be directly obtained as: ti \u2264 1 \u03bbbk ( b a )1/p ( 1 + 1 pk \u2212 1 ) The upper bound convergence time of RZNN (7) is obtained as: tb = max(ti ) \u2264 1 \u03bbbk ( b a )1/p ( 1 + 1 pk \u2212 1 ) Based on the above analysis, we can conclude that the RZNN model (9) in the presence of DDN converges to he exact solution of IKP of the WMR in fixed time tb, and tb is also irrelevant to the initial state of the dynamic system. \u25a0 Case 2: Dynamic non-disappearing noise (DNDN) When the N(t) in (9) is a DNDN, Theorem 3 will ensure the stability of the proposed RZNN model (9). heorem 3. If the proposed RZNN model (9) is attacked by a DNDN N (t), and the i th element of N (t) satisfies ni (t)| \u2264 \u03b4 and \u03bbd \u2265 \u03b4 (\u03b4\u2208 (0, +\u221e)). No matter whether the dynamic system is in any initial state, the RZNN odel (9) converges to the exact solution of IKP of the WMR in fixed time tb: tb \u2264 1 \u03bbbk ( b a )1/p ( 1 + 1 pk \u2212 1 ) roof. Similar to the proof of Theorem 2, the error function array E(t) of RZNN model (9) can be expressed as E(t)/dt = \u2212\u03bb\u0393 (E(t)) + N (t), and its correspondent subsystems can also be obtained as: dei (t) dt = \u2212\u03bb\u03c4 (ei (t)) + ni (t) i \u2208 {1, 2, . . . n} (15) here ei (t) stands for the i th element of E(t), and ni (t) stands for i th element of N(t). We still choose vi(t) = |ei (t)| as the Lyapunov function candidate to prove the fixed-time convergence of the ZNN model (9). The time differentiation of vi(t) is dvi(t) dt = \u2022 ei (t)sgn (ei (t)) = (\u2212\u03bb\u03c4 (ei (t)) + ni (t)) sgn (ei (t)) (16) Since the power-versatile activation function (7) is adopted, |ni (t)| \u2264 \u03b4 and \u03bbd \u2265 \u03b4, the following formula is btained: dvi(t) dt = \u2022 ei (t)sgn (ei (t)) = (\u2212\u03bb\u03c4 (ei (t)) + ni (t)) sgn(ei (t)) = ( \u2212\u03bb (( a |ei (t)|p + b )k sgn(ei (t)) + cei (t) + d sgn(ei (t)) ) + ni (t) ) sgn (ei (t)) = \u2212\u03bb ( a |ei (t)|p + b )k \u2212 \u03bbc |ei (t)| \u2212 \u03bbd + ni (t)sgn (ei (t)) \u2264 \u2212\u03bb ( a |ei (t)|p + b )k + (\u03b4 \u2212 \u03bbd)( p )k ( 1/k ( p ))k \u2264 \u2212\u03bb a |ei (t)| + b = \u2212 \u03bb av (t) + b t t 5 t e c 5 e W Table 2 Different noises. NO. Noise item Expression 1 Constant noise (CN) n(t) = 0.025 2 Non-disappearing noise (NDN) n(t) = 0.025(t) 3 Periodic noise (PN) n(t) = 0.025*cos(t) 4 Disappearing noise (DN) n(t) = 0.025*exp(\u2212t) Based on Lemma 1, the bounded time ti of the i th subsystem can be directly obtained as: ti \u2264 1 \u03bbbk ( b a )1/p ( 1 + 1 pk \u2212 1 ) The upper bound convergence time of RZNN (9) attacked by a DNDN is obtained as: tb = max(ti ) \u2264 1 \u03bbbk ( b a )1/p ( 1 + 1 pk \u2212 1 ) Based on the above analysis, we can conclude that the RZNN model (9) attacked by a DNDN converges to he exact solution of IKP of the WMR in fixed time tb, and tb is also irrelevant to the initial state of the dynamic system. \u25a0 It is worthy to point out that Theorems 1\u20133 demonstrate that the proposed RZNN not only has the ability to converge to the exact solution of IKP of the WMR in fixed time tb, but also rejects interference and noises, and hese are two important improvements of the original ZNN model. . Simulations and comparisons In this section, simulation results of a WMR with its three-dimensional model presented in Fig. 1 are investigated o demonstrate the robustness and effectiveness of the proposed RZNN model (9) in dynamic noise-polluted nvironment for solving the IKP of the WMR. Part A is the simulation and analysis of the RZNN model. For omparison, part B is simulation and analysis of the original ZNN model. .1. Wheeled mobile robot (WMR) path tracking via RZNN model in noise-polluted environment In this section, the end-effector of the WMR is expected to track a windmill-shaped trajectory task. During the xecution of this task, i.e., t \u2208 [0, Td ], the X, Y and Z axes of the desired path rmd (t) for the end-effector of the MR are as follows:\u23a7\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a8\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23aa\u23a9 rmd X (t) = r sin ( 2 ( 2\u03c0 sin ( \u03c0 t 2Td ) \u00d7 sin ( \u03c0 t 2Td ) + \u03c0 6 )) \u00d7 cos ( 2\u03c0 sin ( \u03c0 t 2Td ) \u00d7 sin ( \u03c0 t 2Td ) + \u03c0 6 ) +0.321 \u2212 r cos (\u03c0 6 ) rmdY (t) = r sin ( 2 ( 2\u03c0 sin ( \u03c0 t 2Td ) \u00d7 sin ( \u03c0 t 2Td ) + \u03c0 6 )) \u00d7 sin ( 2\u03c0 sin ( \u03c0 t 2Td ) \u00d7 sin ( \u03c0 t 2Td ) + \u03c0 6 ) +0.079 \u2212 r sin (\u03c0 6 ) rmd Z (t) = 1.672 where the task duration is preset to be Td = 20 s, the coefficient r = 1.551 m and \u03b3 = 1, and the initial location of the movable platform is set to be (Xm(0), Ym(0), Zm(0)) = (0, 0, 0), and the initial value of the combined angle vector of the WMR is set to be \u0398(0) = [0, 0, \u03c0 /6, \u03c0 /3, \u03c0 /6, \u03c0 /3, \u03c0 /3, \u03c0 /3]T rad. In addition, the considered time-varying noises in this task are shown in Table 2, the Constant noise, Non-disappearing noise and Periodic noise in Table 2 are all dynamic non-disappearing noises, and the Disappearing noise is a classic dynamic disappearing noise. The parameters of the WMR are presented in Table 3. y W p r F F a l t Table 3 Parameters of WMR used in simulations. Parameters Description Value (m) d Distance from P0 to Pm 0.1 b Radius of the movable platform circle 0.32 r Radius of the driving wheels 0.1025 L1 Length of link 1 0.065 L2 Length of link 2 0.555 L3 Length of link 3 0.19 L4 Length of link 4 0.13 L5 Length of link 5 0.082 L6 Length of link 6 0.018 Fig. 2. Simulated path tracking results of the end-effector of the WMR synthesized by the proposed RZNN model (9) with dynamic CN (t) = 0.025. (a) Actual trajectory of the end-effector and desired path. (b) Position errors of the end-effector. (c) Motion trajectories of the MR. (d) Top view of the motion trajectories of the movable platform. The simulated results of the end-effector of a WMR tracking the windmill-shaped trajectory synthesized by the roposed RZNN model (9) with various dynamic noises are presented in Figs. 2\u20139. The corresponding simulation esults of the tracking task polluted by dynamic non-disappearing noises (DNDN) 1\u20133 in Table 2 are presented in igs. 2\u20137, and the tracking task polluted by the dynamic disappearing noise (DDN) 4 in Table 2 is presented in igs. 8\u20139. As seen from Figs. 2(a), 4(a), 6(a) and 8(a), no matter whether under the influence of any noise, the ctual trajectory of the end-effector (red dotted line) almost overlaps the desired windmill-shaped path (blue solid ine), which indicates that the end-effector of the WMR synthesized by the proposed RZNN model (9) completes T he path tracking task successfully. Figs. 2(b), 4(b), 6(b) and 8(b) show the position errors e = (ex, ey, ez) of the t e t t p nd-effector (deviations between the actual trajectory and the desired windmill-shaped path), and it can be observed hat the position errors are all close to zero, which further illustrates the successful completion of the path tracking ask. Figs. 2(c\u2013d), 4(c\u2013d), 6(c\u2013d) and 8(c\u2013d) present more detailed motion trajectories of the WMR and its movable latform during the path tracking task execution, stable and smooth WMR motion can be observed. H m R f e r b n o W Moreover, in order to further study the resolution of redundant manipulator and analyze the motion control capability of the proposed RZNN model (9), the simulated variables of the WMR synthesized by the proposed RZNN model (9) with various dynamic noises during the path tracking task execution are presented in Figs. 3, 5, 7 and 9. As demonstrated in Figs. 3(a), 5(a), 7(a) and 9(a), no matter whether under the influence of any noise, the joint angles of the WMR during the path tracking task execution are relatively steady and stable. Figs. 3(b), 5(b), 7(b) and 9(b) present the rotational angles of driving wheels during the path tracking task execution. It can be observed that the rotational angles of driving wheels change regularly as the drawn windmill-shaped trajectory, and they are almost stationary (no rotation of the wheels) at the start and end of the trajectory tracking task. In addition, the location coordinates (Xe, Ye, Ze)T of end-effector are presented in Figs. 3(c), 5(c), 7(c) and 9(c) during the path tracking task execution. As seen from Figs. 3(c), 5(c), 7(c) and 9(c), the location coordinate Ye of the end-effector has no change, and this is because the drawn windmill-shaped path is a two-dimensional trajectory. The above results illustrate the excellent robustness and effectiveness of the proposed RZNN model (9) for solving IKP of WMR with various noises and disturbances." + ] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure2.20-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure2.20-1.png", + "caption": "Fig. 2.20. The partial and the total orientation", + "texts": [ + " It can also be considered in the following way: some given body axis (or some arbi trary fixed direction on the body) coincides with ~ prescribed direc tion in the space and the rotation angle around this direction is also prescribed. The term total orientation is used also. Pant~al o~ientat~on of a body only means that the given body-fixed di rection concides with the prescribed direction in space (which can be changeable according to some law). The difference between the partial and the total orientation is shown in Fig. 2.20. In Fig. 2.20(a), (b) the task of transferring a container with liquid is shown. In case (a) it is only important that the axis (*) is vertical and so it is the case of partial orientation. In case (b) not only the direction (*) but also the direction (**) is impor tant. For the given direction (*) the direction (**) may be replaced by angle ~. Hence, the case (b) represents the total orientation. Fig. 2.20(c), (d) shows something analogous but for assembly tasks. 52 We now consider two examples which demonstrate that the orientation representation chosen (direction and angle) really follows from prac tical manipulation tasks. Fig. 2.21. presents a task of spraying pow der along a prescribed trajectory. The task reduces to the need to realize the motion of an object (container) along the trajectory (a) (i.e. positioning) and along the trajectory the container should rotate around the direction (b) according to the prescribed law W(t). So, the orientation representation in terms of one direction and the rotation angle directly coincide with the functional motion of manipulator. In this case the choice of the direction is different from that in Fig. 2.20(a), (b) because of different manipulation tasks. The next example represents screwing a bolt in (Fig. 2.22). Let us now analyze the need for a certain number of d.o.f.: To solve the positioning task, which is a part of every manipulation task, three d.o.f. are needed. 53 To solve the positioning task along with the task of partial orienta tion, five d.o.f. are necessary. To solve the positioning task along with the task of full orientation, six d.o.f. are necessary. Manipulators with four, five and six d", + "59) represents the system of 5 equations which should be solved for the 5 unknowns Q1' Q2' Q3' Q4' q5\u00b7 It is clear that the 5x5 matrix inverse now appears. The third block (6-3). A manipulator with 6 d.o.f. solves the positi oning task along with the task of total orientation. Positioning will be treated in external Cartesian coordinate system (x, y, z), so these coordinates will be included in the position vec tor Xg. Let us now discuss the problem of total orientation. When we consider the example in Fig. 2.20(b) we conclude that with the total orientation not only the direction (*) but also the direction (**) is important. So the total orientation may be considered in terms of two directions. Leter, we shall show that for the one direction given, the other is replaced by the rotation angle ~. Let us introduce the two directions: the main direction (b) and the auxiliary one (c). These directions are perpendicular to each other (Fig. 2.29). Let us first define these directions with respect to the gripper" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000493_j.vacuum.2021.110365-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000493_j.vacuum.2021.110365-Figure2-1.png", + "caption": "Fig. 2. Schematic illustrations of the (a) laser scanning and (b) laser remelting strategies. (Z-axis of the coordinate system is parallel to the building direction).", + "texts": [ + " Fabrication of all samples was carried out on an SLM DiMetal-100H machine (Guangzhou Laseradd Technology Co. Ltd., China), which had an ytterbium fiber laser with a wavelength of 1.06 \u03bcm and a maximum power of 240 W. The optimized processing parameters during selective laser melting of ZnO/AlSi10Mg mixed powers were set as follows: laser power 240 W, scanning speed 400 mm/s, hatch spacing 0.06 mm and layer thickness 0.03 mm. A laser scanning strategy with layer rotation of 90\u25e6 was used during selective laser melting process (Fig. 2a). For easy description, the selective laser melting process would be referred to as \u201cSLM\u201d in the rest of this paper. The laser remelting strategy was employed to remelt the solidified pre-layer after its corresponding powder layer had been selectively melted, meaning that any one of the slice layers had two passes of laser scan. The optimized processing parameters of laser remelting were set as follows: laser power 240 W, scanning speed 800 mm/s, hatch spacing 0.06 mm. The laser remelting path aligned with the direction of the previous SLM tracks (Fig. 2b). The laser remelting process in this study would be referred to as \u201cSLRM\u201d. To Y. Chen et al. Vacuum 191 (2021) 110365 limit oxygen contamination during SLM and SLRM processes, the building chamber was under an argon pressure of 200 Pa and the oxygen content was less than 0.1%. Cubic samples with a dimension of 8 mm \u00d7 8 mm \u00d7 8 mm were fabricated using SLM and SLRM. The relative density of the fabricated samples was evaluated on the polished surface by image analysis [30,31]. The YZ-planes from the fabricated samples were ground and mechanically polished up to 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003425_978-3-540-30301-5_34-Figure33.22-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003425_978-3-540-30301-5_34-Figure33.22-1.png", + "caption": "Fig. 33.22 BLEEX foot design (exploded view)", + "texts": [], + "surrounding_texts": [ + "In designing an exoskeleton, several factors had to be considered: Firstly, the exoskeleton needed to exist in the same workspace of the pilot without interfering with his motion. Secondly, it had to be decided whether the exoskeleton should be anthropomorphic (i. e., kinematically 0 0.2 HS TOStance Swing 0.4 0.6 0.8 1 Angle (deg) Time (s) 15 10 5 0 \u20135 \u201310 \u201315 \u201320 \u201325 Fig. 33.17 Three sets of adjusted CGA data of the ankle flexion/extension angle. The minimum angle (extension) is \u2248 \u221220\u25e6 and occurs just after toe-off. The maximum angle (flexion) is \u2248 +15\u25e6 and occurs in late stance phase matching), or non-anthropomorphic (i. e., kinematically matching the operator only at the connection points between human and machine). Berkeley ultimately selected the anthropomorphic architecture because of its transparency to the pilot. It is also concluded that an exoskeleton that kinematically matches the wearer\u2019s legs gains the most psychological acceptance by the user and is therefore safer to wear. Consequently, the exoskeleton was designed to have the same degrees of freedom as the pilot: three degrees at the ankle and the hip, and one degree at the knee. This architecture also allowed the appropriately scaled clinical human walking data to be employed for the design of the exoskeleton components, including the workspace, actuators, and the power source. A study of clinical gait analysis (CGA) data provides evidence that humans expend the most power through the sagittal plane joints of the ankle, knee, and hip while walking, squatting, climbing stairs, and most other common maneuvers. For this reason, the sagittal-plane joints of the first prototype exoskeleton are powered. However, to save energy, the nonsagittal degrees of freedom at the ankle and hip remain unpowered. This compels the pilot to provide the force to maneuver the exoskeleton abduction and rotation, where the required operational forces are smaller. To reduce the burden on the human operator further, the unactuated degrees of freedom are spring loaded to a neutral standing position. Human joint angles and torques for a typical walking cycle were obtained in the form of independently collected CGA data. CGA angle data is typically collected via human video motion capture. CGA torque data is calculated by estimating limb masses and inertias and applying dynamic equations to the motion data. Given the variations in individual gait and measuring methods, three independent sources of CGA data [33.42\u201344] were utilized for the analysis and design of BLEEX. This data was modified to yield estimates of exoskeleton actuation requirements. The modifications included: (1) scaling the joint torques to a 75 kg person (the projected weight of the exoskeleton and its payload not including its pilot); (2) scaling the data to represent the walking speed of one cycle per second (or about 1.3 m/s); and (3) adding the pelvic tilt angle (or lower back angle depending on data available) to the hip angle to yield a single hip angle between the torso and the thigh, as shown in Fig. 33.16. This accounts for the reduced degrees of freedom of the exoskeleton. The following sections describe the use of CGA data and its implication for the exoskeleton design. The sign conventions used are shown in Fig. 33.16. Part D 3 3 .8 Figure 33.17 shows the CGA ankle angle data for a 75 kg human walking on flat ground at approximately 1.3 m/s versus time. Although Fig. 33.17 shows a small range of motion while walking (approximately \u221220\u25e6 to +15\u25e6), greater ranges of motion are required for other movements. An average person can flex their ankles anywhere from \u221238\u25e6 to +35\u25e6. The exoskeleton ankle was chosen to have a maximum flexibility of \u00b145\u25e6 to compensate for the lack of several smaller degrees of freedom in the exoskeleton foot. Through all plots, TO stands for toe-off and HS stands for heel-strike. Figure 33.18 shows the adjusted CGA data of the ankle flexion/extension torque. The ankle torque is almost entirely negative, making unidirectional actuators an ideal actuation choice. This asymmetry also implies a preferred mounting orientation for asymmetric actuators (one sided hydraulic cylinders). Conversely, if symmetric bidirectional actuators are considered, spring loading would allow the use of low-torque-producing actuators. Although the ankle torque is large during stance, it is negligible during swing. This suggests a system that disengages the ankle actuators from the exoskeleton during swing to save power. The instantaneous ankle mechanical power (shown in Fig. 33.19) is calculated by multiplying the joint angular velocity (derived from Fig. 33.17) and the instantaneous joint torque (Fig. 33.18). The ankle absorbs energy during the first half of the stance phase and releases energy just before toe off. The average ankle power is positive, indicating that power production is required at the ankle. Similar analyses were carried out for the knee and the hip [33.45] and [33.46]. The required knee torque has both positive and negative components, indicating the need for a bidirectional actuator. The highest peak torque is extension in early stance (\u2248 60 Nm); hence asymmetric actuators should be biased to provide greater extension torque. The hip torque is relatively symmetric (\u221280 to +60 Nm); hence a bidirectional hip actuator is required. Negative extension torque is required in early stance as the hip supports the load on the stance leg. Hip torque is positive in late stance and early swing as the hip propels the leg forward during swing. In late swing, the torque goes negative as the hip decelerates the leg prior to heel strike. CGA data, which provided torque and speed information at each joint of a 75 kg person, was also used to size the exoskeleton power source. The information suggested that a typical person uses about 0.25 HP (185 W) to walk at an average speed of 3 mph. This figure, which represents the average product of speed and torque, is an expression of the purely mechanical power exhibited at the legs during walking. Since it is assumed that the exoskeleton is similar to a human in terms of geometry and weight, one of the key design objectives turned out to be designing a power unit and actuation system to deliver about 0.25 HP at the exoskeleton joints. Part D 3 3 .8 The BLEEX kinematics are close to human leg kinematics, so the BLEEX joint ranges of motion are determined by examining human joint ranges of motion. At the very least, the BLEEX joint range of motion should be equal to the human range of motion during walking (shown in column 1 in Table 33.1), which can be found by examining CGA data [33.42\u201344]. Safety dictates that the BLEEX range of motion should not be more than the operator\u2019s range of motion (shown in column 3 of Table 33.1). For each degree of freedom, the second column of Table 33.1 lists the BLEEX range of motion which is in general larger than the human range of motion during walking and less than the maximum range of human motion. The most maneuverable exoskeleton should ideally have ranges of motion slightly less than the human\u2019s maximum range of motion. However, BLEEX uses linear actuators, so some of the joint ranges of motion are reduced to prevent the actuators\u2019 axes of motion from passing through the joint center. If this had not been prevented, the joint could reach a configuration where the actuator would be unable to produce a torque about its joint. Additionally, all the joint ranges of motion were tested and revised during prototype testing. For example, mockup testing determined that the BLEEX ankle flexion/extension range of motion needs to be greater than the human ankle range of motion to accommodate the human foot\u2019s smaller degrees of freedom not modeled in the BLEEX foot. It is natural to design a 3-DOF exoskeleton hip joint such that all three axes of rotation pass through the human ball-and-socket hip joint. However, through the design of several mockups and experiments, we learned that these designs have limited ranges of motion and result in singularities at some human hip postures. Therefore the rotation joint was moved so it does not align with the human\u2019s hip joint. Initially the rotation joint was placed directly above each exoskeleton leg (labeled \u2018alternate rotation\u2019 in Fig. 33.20). This worked well for the lightweight plastic mockup, but created problems in the full-scale prototype because the high mass of the torso and payload created a large moment about the unactuated rotation joint. Therefore, the current hip rotation joint for both legs was chosen to be a single axis of rotation directly behind the person and under the torso (labeled \u2018current rotation\u2019 in Fig. 33.20). The current rotation joint is typically spring loaded towards its illustrated position using sheets of spring steel. Like the human\u2019s ankle, the BLEEX ankle has three DOFs. The flexion/extension axis coincides with the human ankle joint. For design simplification, the abduction/adduction and rotation axes on the BLEEX ankle do not pass through the human\u2019s leg and form a plane outside of the human\u2019s foot (Fig. 33.21). To take load Part D 3 3 .8 off of the human\u2019s ankle, the BLEEX ankle abduction/adduction joint is sprung towards vertical, but the rotation joint is completely free. Additionally, the front of the exoskeleton foot, under the operator\u2019s toes, is compliant to allow the exoskeleton foot to flex with the human\u2019s foot. Since the human and exoskeleton leg kinematics are not exactly the same (merely similar), the human and exoskeleton are only rigidly connected at the extremities (feet and torso). The BLEEX foot is a critical component due to its variety of functions. \u2022 It measures the location of the foot\u2019s center of pressure and therefore identifies the foot\u2019s configuration on the ground. This information is necessary for BLEEX control.\u2022 It measures the human\u2019s load distribution (how much of the human\u2019s weight is on each leg), which is also used in BLEEX control. \u2022 It transfers BLEEX\u2019s weight to the ground, so it must have structural integrity and exhibit long life in the presence of periodic environmental forces.\u2022 It is one of two places where the human and exoskeleton are rigidly connected, so it must be comfortable for the operator. As shown in Fig. 33.21, the main structure of the foot has a stiff heel to transfer the load to the ground and a flexible toe for comfort. The operator\u2019s boot rigidly attaches to the top of the exoskeleton foot via a quickrelease binding. Along the bottom of the foot, switches detect which parts of the foot are in contact with the ground. For ruggedness, these switches are molded into a custom rubber sole. Also illustrated in Fig. 33.21 is the load distribution sensor, a rubber pressure tube filled with hydraulic oil and sandwiched between the human\u2019s Universal joint Force sensor Knee connection Hip connection Length adjustment Accelerometer Knee and hip manifold Knee actuator Knee valve Hip valve Hip actuator Fig. 33.24 BLEEX thigh design Part D 3 3 .8 foot and the main exoskeleton foot structure. Only the weight of the human (not the exoskeleton) is transferred onto the pressure tube and measured by the sensor. This sensor is used by the control algorithm to detect how much weight the human places on their left leg versus their right leg. The main function of the BLEEX shank and thigh are for structural support and to connect the flexion/extension joints together (Figs. 33.23 and 33.24). Both the shank and thigh are designed to adjust to fit 90% of the population; they consist of two pieces that slide within each other and then lock at the desired length. To minimize the hydraulic routing, manifolds were designed to route the fluid between the valves, actuators, supply, and return lines. These manifolds mount directly to the cylinders to reduce the hydraulic distance between the valves and actuator, maximizing the actua- tor\u2019s performance. The actuator, manifold, and valve for the ankle mount to the shank, while the actuators, manifold, and valves for the knee and hip are on the thigh. One manifold, mounted on the knee actuator, routes the hydraulic fluid for the knee and hip actuators. Shown in Fig. 33.26, the BLEEX torso connects to the hip structure (shown in Fig. 33.20). The power supply [33.47\u201349], controlling computer, and payload mount to the rear side of the torso. An inclinometer mounted to the torso gives the absolute angle reference for the control algorithm. A custom harness (Fig. 33.27) mounts to the front of the torso to hold the exoskeleton to the operator. Besides the feet, the harness is the only other location where the user and exoskeleton are rigidly connected. Figure 33.26 also illustrates the actuator, valve, and manifold for the hip abduction/adduction joint." + ] + }, + { + "image_filename": "designv10_6_0000208_j.matdes.2021.109725-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000208_j.matdes.2021.109725-Figure1-1.png", + "caption": "Fig. 1. Sample geometry for vertically built LPBF samples.", + "texts": [ + " The parameters are subsequently described as, low, medium and high, representing the relative energy densities for the different parameters, as detailed in Table 3. The number of parameters was reduced further based on specific energy limits, as specified in Eq. (1), where energy density (ED is calculated by: ED \u00bc 1:5 < P \u00f0h:m\u00de < 3:5 \u00f01\u00de Where P represents power (W), h is hatch distance (mm) and m is line speed (mm/s). The sample geometry used in the study is based on the work carried out by Risse [12] as part of the EU funded MERLIN research programme and is illustrated in Fig. 1. Please note that the simulated cooling holes are for a related study. The heat treatments adopted in this research differ from the conventional heat treatments used for wrought Haynes 282. Previous studies [13,14] showed that supersolvus c\u2019 heat treatments are required to reform the as-built microstructure through grain recrystallisation in LPBF CM247LC. Similarly, solution heat treatments on LPBF Haynes 282 require higher temperatures to ensure that recrystallisation takes place. For example, typical solution heat treatment temperatures for wrought materials are 1150 C [15], whereas the solution heat treatment temperature used in some experiments is 1250 C" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000477_lra.2021.3068115-Figure9-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000477_lra.2021.3068115-Figure9-1.png", + "caption": "Fig. 9. Experimental setup of the variable stiffness test.", + "texts": [ + " The terminal of the force meter was attached to the forceps via a wire rope. In the test, the forcep was driven to rotate with the tension readings displayed on the force meters screen from 0 to 3.31 N. It means that the grasping force achieved by the forceps is larger than 3 N, which is satisfied with most regular operations such as knotting, suturing, and holding the surgical instruments [32]. The manipulator\u2019s stiffness in two conditions is tested and evaluated in this section. As shown in Fig. 9, the manipulator was fixed on the support. A force sensor (Resolution: 2.5 mN, Authorized licensed use limited to: University of Prince Edward Island. Downloaded on May 29,2021 at 19:13:45 UTC from IEEE Xplore. Restrictions apply. OMD-10-SE-10 N, Optoforce Ltd.) was mounted to the motion stage, with its top kept in touch with the side of the manipulator. As the manipulator\u2019s structure is asymmetric, both directions\u2019 stiffness was tested, vertical to the rotation axes for deployment. In each direction, two states, including low stiffness and high stiffness, were set" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003964_j.bios.2010.07.073-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003964_j.bios.2010.07.073-Figure2-1.png", + "caption": "Fig. 2. SEM micrograph of the front part of the shaft of the fabricated silicon m i e", + "texts": [ + " Additional electrodes can be integrated on the same microprobe at application-desired positions with minor widening of the shaft. 2.2. Fabrication of the silicon microprobes The microprobes are fabricated starting with a 300 m (1 0 0) O. Frey et al. / Biosensors and Bioele ( a p L p p t 3 a a L a i 1 f t d m r p s 2 w 2 a 5 o a c t l a PD by cyclic voltammetry. The optimised protocol consisted of 15 icroprobe and close up view of the KOH-recessed Pt microelectrode. The metal nterconnection track is laid across the inclined side wall appearing after the KOH tch. enlarged tip) and Fig. 2-A in Section 3 that essentially decreases the mount of space required in the lateral dimension (=lower-width robes). Subsequently, 200 nm of thermally grown dry oxide and 200 nm PCVD silicon nitride layers are successively deposited as bottom assivation. The metallisation (20 nm of Ta and 130 nm of Pt) is atterned by a lift-off process using a combination of thick phooresist AZ4562 (AZ Electronic Materials GmbH, Germany) and LOR B (MicroChem Corp., Newton, USA). A total resist thickness of bout 8 m is required to reliably cover the edges of the recesses nd produce well-defined metal structures (b)", + " Biosensors were calibrated immediately before nd after their implantation. Concentration scale bars in graphs of ection 3 refer always to the calibration measurement performed efore the tests. Following the conclusion of each experiment rats were sacificed with an overdose of sodium pentobarbitone (200 mg/ml) nd perfused with 4% paraformaldehyde via the transcardiac route. ctronics 26 (2010) 477\u2013484 Brains were removed, sectioned on a microtome and stained with Cresyl Violet. 3. Results and discussion 3.1. Microprobe arrays Fig. 2-A shows a SEM micrograph of the front part of a single silicon microprobe with the two KOH-recessed electrodes and the larger reference electrode. The DRIE process allowed wellreproduced shape of the probe with respect to the designed masks (<2 m accuracy). Very sharp tips facilitating the brain insertion were achieved. An assessment of the quality of the Pt microelectrodes by cyclic voltammetry in 1 M H2SO4 solution showed good surface characteristics and a roughness factor of <2 determined using the hydrogen desorption charge (210 C/cm2, Bard and Faulkner, 2001). The AgCl layer on the larger electrode has a homogeneous thickness and good coverage of the underlaying Pt. A packaged 4-shaft comb is shown in Fig. 2-B. 3.2. Functionalisation\u2014general remarks Electrochemical aided adsorption highly qualifies for the functionalisation of microelectrodes in a three-dimensional configuration because it allowed to deposit well-localised membranes with incorporated choline oxidase, l-glutamate oxidase or simply BSA on dedicated electrodes in a very controlled way. Connecting several electrodes resulted in equal depositions on all electrodes. The exact mechanism of the electrodeposition is assumed to be either electrophoretically driven (Strike et al" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000481_j.msea.2021.141185-Figure18-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000481_j.msea.2021.141185-Figure18-1.png", + "caption": "Fig. 18. Sketch of slip length relative to maximum shear stress orientation of (a) 45\u25e6 dominant lath orientation compared to (b) 0 and 90\u25e6 lath orientations.", + "texts": [ + "41 Lath angle [\u25e6] Mode ~0\u25e6 & 90\u25e6 ~45\u25e6 Table 4 Mean tensile properties. \u00b1 range indicates one standard deviation. Rp0.2 [MPA] Rm [MPa] Rm/ Rp0.2 Fracture [%] E [GPa] AF Vertical 1054 \u00b1 24.0 1214 \u00b1 9.54 1.15 9.18 \u00b1 0.767 116 \u00b1 2.47 AF Horizontal 1113 \u00b1 22.0 1290 \u00b1 9.06 1.16 6.28 \u00b1 0.605 116 \u00b1 6.05 BA Vertical 927 \u00b1 15.7 1140 \u00b1 12.3 1.23 6.60 \u00b1 0.561 108 \u00b1 2.53 BA Horizontal 997 \u00b1 19.3 1160 \u00b1 9.43 1.16 3.74 \u00b1 0.607 105 \u00b1 4.30 G.M. Ter Haar and T.H. Becker Materials Science & Engineering A 814 (2021) 141185 the load direction, as depicted on Fig. 18. Moridi et al. [50] further proposed that primary \u03b1\u2019 contain less dislocations due to auto-tempering during cyclic heating and therefore provide a \u201clong dislocation mean free path.\u201d Poor slip \u03b1\u2032-\u03b1\u2032 transmissibility both internal and across PBGs was found. This provides evidence that PBG boundaries inhibit deformation. It follows that due to a relatively higher density of PBG boundaries in the XY-plane (compared to the Z-axis), deformation will be inhibited to a larger degree when material is loaded parallel to the XY-plane (i" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000068_tie.2021.3057002-Figure12-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000068_tie.2021.3057002-Figure12-1.png", + "caption": "Fig. 12. New rotor hybrid ventilation cooling structure.", + "texts": [ + " However, a better rotor cooling system could reduce the working temperature which benefiting of higher reliability and robust, or lower the magnets thermal level in the view of cost. III.DESIGN OF NEW ROTOR VENTILATION COOLING STRUCTURE AND ANALYSIS OF COOLING EFFECT Through theoretical analysis, a hybrid ventilation cooling structure, which is combined of shallow air groove, axial ventilation groove, and radial ventilation hole, is proposed to be fabricated on the fan-shaped cylinder structure of a petal rotor. The processing schematic is shown in Fig. 12. In Fig. 12, the new rotor cooling structure layout ensures that the solid rotor has sufficient mechanical strength, and reserves space for other rotor components such as starting cage bars. Considering that the cooling air passing through the rotor axial ducts can be thrown into the stator radial ventilation ditches pushed by the centrifugal force from rotor rotating, the number and size of rotor radial ventilation holes are processed accordingly to the stator radial ventilation ditch one by one. In addition, the electromagnetic performances may be influenced by the change of rotor ventilation cooling structure, the no-load performance comparison between the original and new machine is shown in Table IV" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003349_j.snb.2006.02.035-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003349_j.snb.2006.02.035-Figure2-1.png", + "caption": "Fig. 2. The configuration of the screen-printed thick-film sensor.", + "texts": [ + " The sensor was then fired in a urnace, stepping to a peak temperature of 850 \u25e6C with 10 min well time at the peak. Subsequently, the insulation layer was rinted using a 280 mesh screen and cured in an oven at 110 \u25e6C or 10 min. Finally, the sensor was again fired in a furnace, steping to a peak temperature of 850 \u25e6C with 10 min dwell time t the peak. After fabrication, the area of the working electrode on which the enzyme cholesterol oxidase was immobilized) as approximately 0.15 cm2 (7.5 mm \u00d7 2 mm). Fig. 2 shows the onfiguration of the screen-printed thick-film sensor. t m f r .4. Immobilization of cholesterol oxidase on the gold orking electrode by self-assembly A self-assembled monolayer was first formed on the gold orking electrode of the thick-film sensor. A thiol solution was repared using MPA in the concentration of 10 mM, typically, L of the MPA solution was applied onto the gold working lectrode, and the sensor was left to dry at room temperature for h to allow the formation of the SAM. Then 8 L of a mixture f EDC and cholesterol oxidase from Streptomyces sp", + " Fabrication of the cholesterol biosensor by mmobilization of cholesterol oxidase on a gold working lectrode through self-assembly .2.1. Electrochemical characterization of the fabricated holesterol biosensor Based on the results of our experiments, gold was chosen as he working electrode material for the fabrication of a cholesterol iosensor due to its higher response current and better sensitivity e t c b n the CV curves and the response current of Pt working electrode was obtained ver platinum, and a three-electrode thick-film sensor as shown n Fig. 2 was screen-printed. A self-assembly approach as indiated in Section 1 was used to immobilize cholesterol oxidase ovalently on the Au working electrode of the thick-film sensor. The response to cholesterol of this biosensor was evaluated xperimentally, using a known cholesterol concentration. A drop 50 L) of 150 mg/dL cholesterol solution was placed onto the ensor surface and after 2 min of incubation time, cyclic voltametry was carried out. The same procedure was also used for the ackground solution consisting of only 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000232_j.ymssp.2021.108403-Figure8-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000232_j.ymssp.2021.108403-Figure8-1.png", + "caption": "Fig. 8. Decomposition of the meshing vibration signals.", + "texts": [ + " Therefore, the transfer path and the direction variation of gear action lines should be taken into account at the same time when developing the vibration signal model of planetary gear trains. Further, the resultant signals can be presented in the form of the vector superposition of the meshing vibration signals from all the sun-planet and ring-planet pairs. Naturally, one should present the difference between the directions of the action lines of the sun-planet and ring-planet pairs and the collecting direction of the transducer, thus determine the form of the vector superposition. As illustrated in Fig. 8, there occur angles between the action line directions of the sun-planet and ring-planet pairs and the collecting direction of the transducer, which change periodically as the carrier rotates. Accordingly, the transducer just perceives the vibration components projecting in the collecting direction. The projecting components of the meshing vibration signals for the sunplanet and ring-planet pairs can be represented as [35] av sn(t) = asn(t)cos(\u03b1s \u2212 \u03c8i) = asn(t)cos(\u03b1s \u2212 \u03c9ct \u2212 \u03c8n) (41) av rn(t) = arn(t)cos(\u03b1r + \u03c8i) = arn(t)cos(\u03b1r + \u03c9ct + \u03c8n) (42) where asn(t) and arn(t) (i = n, n = 1, 2, \u2026 , N) are the meshing vibration signals for the sun-planet and ring-planet pairs, respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003742_1.4000277-Figure11-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003742_1.4000277-Figure11-1.png", + "caption": "Fig. 11 Cross section of finite element model", + "texts": [ + " The uniform pressures qic and qir re given by qic = 1 aicL1 j=1 n Qij, qir = 1 airL1 j=1 n Qij 18 here L1 is the carriage length, ai is the major axis of the contact llipses of the ith ball and raceway grooves, and the suffixes c and refer to the carriage and rail, respectively. If there is no restraint to the carriage in the FE model under the niform pressures qic and qir, the FE analysis shows carriage itching, which occurs due to the inevitable calculation errors. To 11102-6 / Vol. 132, JANUARY 2010 om: http://tribology.asmedigitalcollection.asme.org/ on 01/27/2016 Terms prevent this, a certain area of the upper surface of the carriage was restrained to six degrees of freedom, as shown in Fig. 11. 4.5 Calculation Procedure of Vertical Stiffness Using Flexible Model. The vertical stiffness calculation flow chart, using the flexible model, is shown in Fig. 13. The detailed calculation procedure is as follows: Step 1. The groove radii rc and rr of the carriage and rail, the carriage length L1, the crowning drop of the carriage C xij , the reference ball diameter d0, the oversize 0 of balls, the nominal contact angle 0, the number n of the loaded balls in a raceway groove, the Young\u2019s modulus E, the density , and the Poisson\u2019s ratio are given" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003521_j.conengprac.2007.04.008-Figure8-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003521_j.conengprac.2007.04.008-Figure8-1.png", + "caption": "Fig. 8. Twin rotor MIMO system.", + "texts": [ + " It is noted that in order to simplify the figure the x- and y-axes have been drawn from O2. According to Figs. 8\u201310 the following equation can be obtained: rx\u00f0R1\u00de \u00bc R1 sin ah cos av \u00fe h cos ah; ry\u00f0R1\u00de \u00bc R1 cos ah cos av h sin ah; rz\u00f0R1\u00de \u00bc R1 sin av: 8>< >: (12) It should be noted that ah has no effect on the rz(R)\u2019s and for simplicity it can be assumed to be zero as shown in Fig. 9. Let \u00bdrx\u00f0R2\u00de; ry\u00f0R2\u00de; rz\u00f0R2\u00de denotes the coordinate of point P2 on the counterbalance beam parameterized in the distance R2 from O1 (that means P2O1 \u00bc R2). According to Fig. 8 the following equation can be obtained: rx\u00f0R2\u00de \u00bc R2 sin ah sin av \u00fe h cos ah; ry\u00f0R2\u00de \u00bc R2 cos ah sin av h sin ah; rz\u00f0R2\u00de \u00bc R2 cos av: 8>< >: (13) For more accuracy the point P3 can be considered with the coordinate \u00bdrx\u00f0R3\u00de; ry\u00f0R3\u00de; rz\u00f0R3\u00de on the pivoted beam where R3 is the distance between P3 and O: rx\u00f0R3\u00de \u00bc R3 cos ah; ry\u00f0R3\u00de \u00bc R3 sin ah; rz\u00f0R3\u00de \u00bc 0: 8>< >: (14) In this case the vertical angle is constant and so the velocities related to each part can be obtained by differentiating Eqs. (12)\u2013(14) with respect to time and the square magnitude of the velocity of Pi is given by v2\u00f0Ri\u00de \u00bc v2x\u00f0Ri\u00de \u00fe v2y\u00f0Ri\u00de \u00fe v2z\u00f0Ri\u00de; i \u00bc 1; 2; 3" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000232_j.ymssp.2021.108403-Figure6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000232_j.ymssp.2021.108403-Figure6-1.png", + "caption": "Fig. 6. A typical configuration of a planetary gear train with 4 equally spaced planets and a transducer mounted on the housing.", + "texts": [ + " The obtained curve of the mesh stiffness can be represented as ksn(t) = ksnm + \u2211L \u2113=1 [ k(\u2113)snacos(\u2113(\u03c9mt \u2212 2\u03c0\u03b3sn + \u03c6ek) ) + k(\u2113)snbsin(\u2113(\u03c9mt \u2212 2\u03c0\u03b3sn + \u03c6ek) ) ] (33) krn(t) = krnm + \u2211L \u2113=1 [ k(\u2113)rna cos ( \u2113 ( \u03c9mt \u2212 2\u03c0\u03b3\u0302 rn + \u03c6ek )) + k(\u2113)rnbsin ( \u2113 ( \u03c9mt \u2212 2\u03c0\u03b3\u0302 rn + \u03c6ek ))] (34) where ksnm and krnm denote the mean components of ksn(t) and krn(t); k(\u2113)sna, k (\u2113) snb and k(\u2113)rna,k(\u2113)rnb represent the harmonic coefficients of ksn(t) and krn(t); \u03c6ek denotes the phase difference between the transmission error and the mesh stiffness. In general, a planetary gear train is composed of one sun gear, one ring gear, one carrier and several planet gears. Fig. 6 shows a typical configuration of a planetary gear train with 4 equally spaced planet gears. As shown in Fig. 6, the ring gear is fixed to housing and the sun gear rotates about its own axis. The carrier that holds planet gears rotates about the center of the planetary gear train. With the carrier rotation, the planet gears rotate not only about their own axes that are fixed to the carrier but also about the center of the planetary gear train. The planet gears are located between the ring gear and the sun gear, and mesh simultaneously with both of them. Compared with fixed-shaft gear train, a planetary gear train claims more complicated structures and gear motions, which makes the vibration signals of a planetary gear train much more complicated than those of a fixed-shaft gear train", + " The internal excitation vector F(t) induced by the error displacement excitation can be expressed as F(t)= [ \u2211N n=1 f 1 spn, \u2211N n=1 f 1 rpn, 0, f 2 sp1 + f 2 rp1, \u2026 , f 2 spN + f 2 rpN ]T (37) f 1 spn = f b sn[\u2212 sin\u03c8sn, cos\u03c8sn, 1]T, f 1 rpn = f b rn[\u2212 sin\u03c8rn, cos\u03c8rn, 1]T, f 2 spn = f b sn[sin\u03c8sn, \u2212 cos\u03c8sn, 1]Tf 2 rpn = f b rn[sin\u03c8rn, \u2212 cos\u03c8rn, \u2212 1]Tn = 1 , 2, 3, \u2026 , N (38) f b in = \u2212 kin(t) \u23a7 \u23a8 \u23a9 ein \u2212 bin 0 ein + bin \u03b4in > bin \u2212 bin\u2a7d\u03b4in\u2a7dbin \u03b4in < \u2212 bin (i = s, r) (39) where esn and ern are the error displacement excitations of the nth sun-planet and the nth ring-planet pairs induced by manufacturing/ assembly errors and gear surface wear; \u03c8sn = \u03c8n \u2013 \u03b1s, \u03c8 rn = \u03c8n + \u03b1r (\u03b1s and \u03b1r denote the mesh angles of the sun-planet and the ringplanet pairs; \u03c8n = 2\u03c0(n\u20131)/N denotes the circumferential location angle of the nth planet gear around the sun gear; N denotes number of planet gears). The influence of the gear surface wear can be incorporated into the system\u2019s dynamic model through analytical formulations of wear-induced displacement excitation and mesh stiffness. By solving Eq. (35) with fourth-order Runge-Kutta integration method, one may gain the vibration source signals of the planetary gear train under healthy and worn conditions. As shown in Fig. 6, the transducer is vertically mounted on the top of the gearbox housing. The vibration signals acquired by the transducer mainly consist of the meshing vibration from all the sun-planet and ring-planet pairs. The transfer path of the meshing vibration from the meshing point to the fixed transducer consists two parts: from the meshing vibration source to the housing position corresponding to each planet gear location; from the corresponding housing position to the transducer installation position" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000262_j.mechmachtheory.2021.104299-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000262_j.mechmachtheory.2021.104299-Figure4-1.png", + "caption": "Fig. 4. The model of the i th nonlinear contact element.", + "texts": [ + " Both the left and right side of the wide-faced double-helical gear pair are discretized into a series of thin slices along gear width, and the engagement process of the left side of the sliced wide-faced gear pair is shown in Fig. 3 , where r p and r g are the radii of base circle of driving and driven gears, \u03c9 p and \u03c9 g are the rotation speeds of driving and driven gears, O p and O g are the rotation centers of driving and driven gears. N 1 N 2 is the theoretical meshing line, B 1 B 2 B 3 B 4 is the plane of action, \u03b2b is the helix angle of the base circle. The model of the i th nonlinear contact element is shown in Fig. 4 , where \u03c8 and \u03b1 are the installation angle and mesh angle, O Li p and O Li g are the rotation centers of the i th nonlinear contact element. k Li m is the mesh stiffness of the i th nonlinear contact element for the left gear pair, e Li m represents the clearance caused by tooth flank errors and system flexibility. The k L i m and k R i m for the i th nonlinear contact element of left and right gear pairs can be calculated using k L i m = M \u2211 i =1 k i , k R i m = N \u2211 i =1 k i (1) where M and N are the number of contact point for the i th nonlinear contact element of the left and right gear pairs respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000272_j.msea.2021.141306-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000272_j.msea.2021.141306-Figure2-1.png", + "caption": "Fig. 2. (a) Schematic diagram of laser scanning path, (b) The printed parts by LMD process and size of tensile specimen.", + "texts": [ + " Before LMD process, it was sanded with sandpaper, then ultrasonically cleaned in absolute ethanol and finally dried. The LMD process is performed on a five-axis additive and subtractive hybrid CNC machine tool (SVW80C-3D) equipped with a 2000 W fiber laser (YLS-2000). The protective gas and carrier gas are nitrogen. The optimal process parameters of LMD shown in Table 1 are determined on the basis of preliminary experiments. The thin-walled parts with a size of about 62*32*2.5 mm was formed using the bidirectional laser scanning path as shown in Fig. 2(a) during the LMD process, and the samples were taken in the front, top and side for the analysis of microstructure and phase composition. The sampling position and size of the tensile sample along the scanning direction (SD) and the building direction (BD) are shown in Fig. 2(a)(b). Moreover, the infrared thermometer (Endurance 1R) is used in the manufacturing of thin-walled samples by the LMD process, which is used to obtain temperature data at different heights (three points A, B, C as shown in Fig. 2 (a)) during the alloy solidification process. As a comparative experiment, the cast samples with a size of 60*20*20 mm were made of pure metals of Cr, Co, and Ni (purity\u226599.9 wt%) by vacuum suspension smelting. The samples on the front, top and side of the printed thin-walled parts was ground with 240-3000 mesh sandpaper and then polished with 2.5 \u03bcm diamond suspension, and 0.05 \u03bcm SiO2 colloidal oxide polishing suspension is used for ultimately polishing. The samples were etched by metallographic etching solution (100 ml alcohol, 100 ml HCl and 5g CuCl2) to observe the microstructure by laser digital scanning microscope (Olympus LEXT OLS4100)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000088_s11665-021-05781-6-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000088_s11665-021-05781-6-Figure3-1.png", + "caption": "Fig. 3. Schematic representation of microstructure at different locations", + "texts": [ + " The samples were placed in a scanning electron microscope (Make: EVO 18 and Model: ZEISS) to get the magnified microstructure and the chemical compositions plots through EDS analysis (Ref 23,24). Besides, the grain size and misorientation angle were determined from the EBSD analysis. Both longitudinal and transverse sections were checked for the microhardness values using the Vickers Hardness tester with 500 gf load and 10 s duration as per ASTM E384 -17. (Ref 25-27). The microstructures were taken from transverse and longitudinal directions in three different locations of the whole build structure in three different locations (A, B, and C), as displayed in Fig. 3 and 4. The transverse section optical micrograph reveals the different layers involved in the welding process, starting from the base metal up to the top layer. The variation in the microstructure along the layers is observed due to the change in the cooling rate. At base metal and the initial layer, the cooling rate is considerably high; this is because the first layer\u2019s cooling takes place through the base plate itself, either by heat dissipation or by heat flow to space around the base plate (Ref 10)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003862_13506501jet504-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003862_13506501jet504-Figure1-1.png", + "caption": "Fig. 1 Schematic of the PCS instruments UTF measurement system", + "texts": [ + "comDownloaded from The term hard EHL contacts is used for contacts where both solid bodies have a high modulus of elasticity. In linear elastic EHL problems the elastic properties of the solids can be expressed by one parameter instead of four, the reduced or equivalent modulus of elasticity Er = { 1 2 [( 1 \u2212 \u03bd2 1 E1 ) + ( 1 \u2212 \u03bd2 2 E2 )]}\u22121 (1) The measurements of the central film thickness were performed on a PCS Instruments EHL ultra thin film (UTF) measurement system, which is described in Johnston et al. [15] (see Fig. 1). The PCS ultra device uses a smooth steel ball on a flat optical disc, which implies that it has a circular contact geometry. The ball is a super finished Cr steel ball. The rig is applied in rolling motion mode, i.e. the optical glass disc drives the ball, which is supported by three small ball bearings. The two at the left are slightly higher in position than the right one, to eliminate contact spin under pure rolling. More disc and ball details are listed in Table 1. Two lubricants were tested: a reference oil, HVI60, and a base oil, which is a blend with unknown value for the pressure\u2013viscosity coefficient", + " He states that almost all but a few numerical and experimental results (at that time) can be expressed in a relationship between his groups L\u0303 (the speed group) and \u03b1\u03c3Hz (the load group) L\u0303 \u2248 0.95(\u03b1\u03c3Hz) 0.91 (24a) which can be transformed into L \u2248 0.000 14 M 3.4 (24b) Essentially, this is a fit of a cloud of results that have a rather high correlation. Most of the current measurements are located far outside this area, having \u03b1\u03c3Hz values of 10.4 (HVI60) and 13.2 < \u03b1\u03c3Hz < 18.5 (base oil A), while 1.53 < L\u0303 < 7.14 and 1.64 < L\u0303 < 10.8, respectively. From Greenwood\u2019s [26] results\u2021 the central film \u2021See Fig. 1 in Greenwood [26]. The Greenwood non-dimensional central film thickness is almost constant irrespective of the experi- mental or numerical conditions, for the 74 results collected from the literature. The average value is 1.49 with a standard deviation of 0.24. Note that Greenwood himself refrains from providing a curve fit of all the data collected. Proc. IMechE Vol. 223 Part J: J. Engineering Tribology JET504 at University of Manitoba Libraries on June 8, 2015pij.sagepub.comDownloaded from thickness reads H\u0303c \u2248 1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure30.1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure30.1-1.png", + "caption": "Fig. 30.1 Configuration of actuator, rolling (top) and oscillation type (bottom)", + "texts": [], + "surrounding_texts": [ + "352 Toshiro HIGUCHI and Toshiyuki UENO\nmagnetostrictive material of high Curie temperature. So far, we have investigated micro actuator photothermally driven by Laser pulse [1], however, found that it is not practical because of low energy conversion and difficulty of driving condition and positioning alignment (Laser) in micro scale [2]. Here, we propose thermal driven actuator based on self-excited oscillation using bending of bimetal, simple with a few components, and describes the experimental results to discuss the possibility for high temperature usage. Micro magnetostrictive (Fe-Ga alloy) actuator advantages of low voltage driving, high mechanical strength and wide temperature operation is also discussed.\nThermal actuator has two configurations, one is rolling and the other is oscillation type [3]. The rolling type is a ring of bimetal strip. (two metals layers with different thermal expansion coefficient bonded together), which the outer layer has larger coefficient. When it is placed and heated on a plate of high temperature (more than 50 C higher than the environment), it rotates and rolls to one direction. The oscillation type is a metal disk with a weight (the center of mass is located below the center) bound with a bimetal (the outer layer has larger coefficient). The disk rolls periodically right and left and does not continue the oscillation because of damping by friction and air, however it on the heated plate (> 50 C) does continue the oscillation as shown in Fig.30.2. That motion is self excited oscillation. The principle how the torque for the rotation is generated by the heated plate is explained as follows (see Fig.30.3). Normally, the thermal conduction resulting temperature distribution in bimetal becomes asymmetric due to imperfect shape and contact condition when the actuator is put on the plate. If the temperature of left side is higher than the right and the thermal deformation (bending inside) of the left is larger than the right, the summation of the deformation yields the torque which makes the ring to rotate to right direction. The torque is also generated continually during the rotation because the temperature just behind the contacting (back side to moving direction) is higher than that of the forward (the front side before the contact is cooled by heat dissipation). Figure 30.3 right shows the thermal imaging of the rolling bimetal (going to right). It was observed that the temperature of back side (after contact) to the moving direction is higher and we felt thrust force to right direction at the time.", + "354 Toshiro HIGUCHI and Toshiyuki UENO\nThermal impact drive actuator as shown in Fig.30.4 is constructed using the principle [4]. The actuator is the disk with weight and bimetal, placed on L shaped mover. When the actuator is heated on the plate of high temperature, the disk oscillating hit the bars of L shape in a cycle, which the impact force generates step displacement. Prototype consists of the disk of brass (40 mm diameter and 20 mm width) with bimetal of 0.15 mm thickness consists of 22Ni-4Cr-Fe and 36 Ni-Fe (bending ratio 14.5\u00d710-6/K), and mover of Aluminum. The gear of rack and pinion is used to prevent the slippage and constraint the movement of the disk. As shown in Fig.30.5, the step displacement of 10 m per impact from the oscillation of 15 mm amplitude was obtained when the plate temperature of 140 C . The continuous step movement was verified.\nThe thermal actuator based on the self excited-oscillation is considered endurable for high temperature usage (<1000 C) in electric furnace because of the following reasons." + ] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure16.2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure16.2-1.png", + "caption": "Fig. 16.2 Ciliary vibration drive", + "texts": [ + " Following research topics have been studied: Developments of ciliary vibration mechanism fit for a long flexible cable [4, 5] Numerical analyses of the driving mechanism of ciliary vibrations [5, 7] Modeling of a flexible cables and controlling cable's motion by distributed driving force [9] Development of the active scope camera system [4-7] Control method of a turn direction of the active scope camera [6, 8] Evaluation of the active scope camera for rescue activities [6] In this chapter, the mechanism of ciliary vibration drive and its optimal design are described. In addition, an application of the ciliary drive mechanism applied for the active scope camera system is introduced. The ciliary vibration drive generates driving on a cable by vibrating inclined thin sting or wire cilia. Ciliary bending and recovery movement during vibration makes cilia tips stick and slip rapidly and generates distributed driving force on the cable. Cilia covering the cable surface of the cable (Figure 16.2) vibrate and generate driving over the entire flexible cable regardless of location and contact angle. This design is applicable to flexible cables such as scope cameras. Actuation of Long Flexible Cables Using Ciliary Vibration Drive 179 This architecture has the following advantages and disadvantages: Distributed cilia do not interfere with cable flexibility. Component can be small. Shape of mechanisms can be arbitrarily modified. Driving is distributed over the cable. Driving is small. Contact conditions sometimes adversely affect driving" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003670_978-3-642-82195-0-Figure6.12-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003670_978-3-642-82195-0-Figure6.12-1.png", + "caption": "Fig. 6.12. Redundant manipulator motion - configuration space performance index", + "texts": [ + " If one is dealing with real-time application of the proposed algorithm, the information on the critical distance should be obtained from higher control level utilizing sensors. The proposed collision avoidance algo rithm itself is convenient for real-time implementation, since it gives an explicit solution for joint rates at each sampling period, and em ploys no iterative procedures. Its computational complexity is modest compared with other proposed algorithms [100, 103]. It can be applied to moving objects, as well as to stationary obstacles. The algorithm presented will be illustrated by an example of a robot with 5 revolute joints (Fig. 6.12). The first link rotates about a ver tical axis, while the remaining joints have horizontal axes. The mani pulation task to be performed is a straight line motion xe(t) of the manipulator tip x (t) = xO+A(t) (xF_XO), O" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000016_j.mechmachtheory.2020.104097-Figure13-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000016_j.mechmachtheory.2020.104097-Figure13-1.png", + "caption": "Fig. 13. Parameter design space of the walking transmission mechanism.", + "texts": [ + " For further investigating the influence of dimension combination on transmission performance, we are more curious about the proportional relation of the drive side rod q 1 with respect to the connecting rod q 2 , so here define \u03c3 = q 1 / q 2 = w 1 / w 2 , and let \u03c3 \u2208 (0, 1]. As a consequence, Eq. (22) can be expressed as ( 1 + \u03c3 ) w 2 + w 3 + w 4 = 4 (23) Hence, w 2 , w 3 , w 4 are three independent non-dimensional optimization parameters, and \u03c3 is a variable parameter. Con- straint inequations for constructing the physical model are derived as { 0 < w 3 , w 4 < 4 0 < w 2 < 4 / ( 1 + \u03c3 ) (24) Eqs. (23) and (24) indicate the parameter design space of the multi-mode transmission mechanism illustrated in Fig. 13 , which is the tetrahedron ABCD in frame O \u2212 w 2 w 3 w 4 . When \u03c3 is given as a constant value, the design space will become an isosceles triangle plane, for instance, the plane ABC corresponds with \u03c3 = 0 , and the plane BCD corresponds with \u03c3 = 1 . For any \u03c3 \u2208 (0, 1], the parameter design space is represented as plane BCE , where point E is a point in line segment AD and has the coordinate of 4 / ( 1 + \u03c3 ) in axis w 2 . The mapping function between the variables in frame O \u2212 w 2 w 3 w 4 and frame B \u2212 xyz can be given by \u23a1 \u23a2 \u23a3 w 2 w 3 w 4 1 \u23a4 \u23a5 \u23a6 = O B T \u23a1 \u23a2 \u23a3 x y 0 1 \u23a4 \u23a5 \u23a6 , or \u23a1 \u23a2 \u23a3 x y 0 1 \u23a4 \u23a5 \u23a6 = ( O B T )\u22121 \u23a1 \u23a2 \u23a3 w 2 w 3 w 4 1 \u23a4 \u23a5 \u23a6 (25) where O B T = [ 0 2 \u221a 4+2 ( 1+ \u03c3 ) 2 1+ \u03c3\u221a 2+ ( 1+ \u03c3 ) 2 0 \u2212 \u221a 2 2 \u22121 \u2212\u03c3\u221a 4+2 ( 1+ \u03c3 ) 2 1 \u221a 2+ ( 1+ \u03c3 ) 2 4 \u221a 2 2 \u22121 \u2212\u03c3\u221a 4+2 ( 1+ \u03c3 ) 2 1 \u221a 2+ ( 1+ \u03c3 ) 2 0 0 0 0 1 ] The ORI is the first-line index for the multi-mode transmission mechanism, and demanded to be as large as possible in both modes" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003659_tmag.2008.2001450-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003659_tmag.2008.2001450-Figure1-1.png", + "caption": "Fig. 1. General schematic diagram of a BLDC motor without slots.", + "texts": [ + " Section IV deals with the development of the analytical model for a stator with slots, and the results of comparison between the analytical model and FEM results is also presented in this section. In Section V, the model to determine back-EMF using the results obtained in Section IV is given. The model of cogging torque and the comparison between analytical results and FEM is given in Section VI. Finally, conclusions are drawn in Section VII. The general configuration of a permanent-magnet brushless DC motor (BLDC) considered in the present work is shown in Fig. 1. In the above figure, , , and represent the relative permeability of stator iron, permanent magnets, and rotor iron, respectively. The radii , , , and represent outer radius of the motor, inner radius of the stator, radius of the magnets, and radius of the rotor, respectively. In the present analysis, it is assumed that the region exterior to the motor is air. For the motor shown in Fig. 1, the magnetic field vector and magnetic field density vector are coupled by the following set of equations: in the exterior region (1a) in the stator region (1b) in the air-gap region (1c) in the magnet region (1d) in the rotor region (1e) 0018-9464/$25.00 \u00a9 2008 IEEE where is the magnetization vector of the permanent magnets. The amplitude of the magnetization vector , for a multipole motor with permanent magnets having a linear second quadrant demagnetization characteristics, is given by (2) The direction of depends on the orientation and magnetization of the permanent magnets", + " For the air-gap region, the Laplace equation is (5a) In the magnet region, the quasi-Poissonian equation is (5b) In the stator iron region, the Laplace equation is (5c) For the rotor iron region, the Laplace equation is (5d) Finally for the exterior region, the Laplace equation is (5e) where , , , , and represent the magnetic scalar potential in the air gap, magnet, stator, rotor, and the exterior (outer) region, respectively. From (2), we get (6) where (7) The boundary conditions for the motor shown in Fig. 1 are as follows: (i) at the interface between the stator and the exterior region (8a) (8b) where and are the tangential component of the magnetic field vector in the exterior region and the stator iron, respectively, whereas and are the radial component of the magnetic field density vector in the exterior region and the stator iron, respectively. (ii) at the interface between the stator and the air gap (8c) (8d) where is the tangential component of the magnetic field vector in the air-gap region whereas is the radial component of the magnetic field density vector in the air-gap region", + " (iii) at the interface between the air gap and the permanent magnet (8e) (8f) where is the tangential component of the magnetic field vector in the magnet region whereas is the radial component of the magnetic field density vector in the magnet region. (iv) at the interface between the magnet and the rotor iron (8g) (8h) where is the tangential component of the magnetic field vector in the rotor iron region whereas is the radial component of the magnetic field density vector in the rotor iron region. The dimensions , , , and are depicted in Fig. 1. The general solution of the system of (5) and (6) are (9) (10) (11) (12) (13) where , , , , , , , and are constants to be determined. These constants are determined by solving the boundary conditions given in (8) and using (2) and (1). Upon substituting back the constants and into (11) and using (4) and (1), the air radial and tangential components of the air-gap field distribution are obtained as follows: (14) (15) where when the field distribution in the air gap is given by (16) (17) where This model has been applied to three-phase slotless BLDC motor with radial, parallel, sinusoidal magnitude, and sinusoidal angle magnetization", + " Since all coils in the stator can be described in terms of a sequence of equivalent single-tooth coils [12], hence the flux linked by each coil is the sum of fluxes linked by each individual tooth coils. Fig. 11 shows a coil and its single-tooth equivalent. The flux linked by the coil in Fig. 11 is given by (47) where angular tooth offset; flux linked by first tooth. The flux linked by a tooth is given by (48) In the above equation, by substituting the radial component of the air-gap field at the stator inner surface (20) becomes (49) where is the air-gap field at the stator surface, is the inner radius of the stator (Fig. 1), and is the length of the motor. In the above equation, the integrand is independent of the axial direction. Hence, the above equation can be simplified as (50) The back-EMF of a single-tooth equivalent coil is given by (51) where is the number of turns in the coil. The back-EMF of a general coil is the sum of back-EMFs of its single-tooth equivalent coils. For the coil shown in Fig. 11, the back-EMF is given by (52) Having developed the necessary set of equations, this model is tested and results for the air-gap field are compared with FEM" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure30.7-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure30.7-1.png", + "caption": "Fig. 30.7 Vibrator using a Galfenol rod of 1mm diameter. Fixture and housing are welded to the rod", + "texts": [ + " A pre-stress mechanism is not necessary in view of the high tensile strength of Galfenol ( > 400 MPa). 3. Low drive voltage due to low impedance of the coil. The actuators can be driven by voltages of a few volts with a small power supply. 4. Wide temperature operation range. Low temperature operation in liquid nitrogen has been demonstrated, and high temperature operation is limited by Curie temperature. The magnetostrictive vibrator consists of a pin of iron-gallium alloy (Fe81.6Ga18.4, Galfenol), a drive coil, and housing as shown in Fig.30.7. The overall dimensions are 2 mm diameter and 6 mm long (fixed on a brass fixture in the picture of Fig.30.7 right). The coil is made of 0.04 mm diameter polyimide wire with 270 turns to give a resistance of 17 . The end caps attached to the pin and housing for the flux path are made of Permalloy. A magnetic field is applied by a closed magnetic circuit along the axial direction of the Galfenol pin resulting in axial Development of New Actuators for Special Environment 357 displacement. The Galfenol pins, 1 mm diameter by 5 mm long, were fabricated from a 6.35 mm diameter by 50 mm long rod prepared by the Free Stand Zone Melting technique" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002784_j.conengprac.2004.01.004-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002784_j.conengprac.2004.01.004-Figure1-1.png", + "caption": "Fig. 1. Scheme of dynamic identification of thrusters. (Left) horizontal thrusters. (Right) vertical thrusters.", + "texts": [ + " Recently, we proposed to carry out the identification using the one step integral of the dynamics equation (Tiano, Carreras, Ridao, & Zirilli, 2002; Carreras, Tiano, El-Fakdi, Zirilli, & Ridao, 2003b). In this case, LS is used to estimate the model parameters which minimize the one step prediction error of the velocity vector (in the following we will call this method \u2018\u2018the integral\u2019\u2019 method). In this paper, we compare the results obtained with both methods, through exhaustive experimentation with URIS UUV (see Fig. 1). A brief review of the UUV mathematical models generally used in the literature is presented in Section 2 of this paper. In Section 3 the two identification methods, the direct and the integral, used in this paper are presented. In Section 4 a description of the experimental identification process is reported. Section 5 refers to the experimental setup used. The results obtained with both methods are shown in Section 6. Finally, some concluding remarks are done in Section 7. As described in the literature (Fossen, 1994), the nonlinear hydrodynamic equation of motion of an underwater vehicle with six degree of freedom (DOF), in the body fixed frame, can be conveniently expressed as Bt\u00fe G\u00f0Z\u00de D\u00f0Bu\u00deBu\u00fe tp \u00bc \u00f0BMRB \u00fe MA\u00de B \u2019u\u00fe \u00f0BCRB\u00f0Bu\u00de \u00fe CA\u00f0Bu\u00de\u00de Bu; \u00f01\u00de where B \u2019v is the accelerations vector; Bv the velocity vector; Z \u00bc \u00f0f y c\u00deT the roll, pitch and yaw angles; Bt the forces and moments exerted by thrusters; G\u00f0Z\u00de the gravity and buoyacy forces; D\u00f0Bn\u00de the linear and quadratic damping matrixes; tP the not modelled perturbations; BMRB the inertia matrix; BMA the added mass matrix; BCRB the rigid body coriolis and centripetal matrix; and BCA the hydrodynamic coriolis and centripetal matrix", + " The unique variables measured were the propeller angular speed and the robot position. The general force/torque (Bt) acting on the robot was computed using the thrusters\u2019 static affine model and the robot velocity was computed through numerical differentiation. The identification process was organized as follows: Phase 1: Thruster identification. Four experiments were run: two for the vertical thrusters (one in each sense) and two for the horizontal thrusters. The parameter to be estimated was CTi: A mechanical structure, like the one seen in Fig. 1, was used. The vehicle is driven in different steady-state conditions. When the robot\u2019s velocity is stabilized, the force exerted is calculated using a dynamometer. By means of several measures, parameter CTi is estimated. URIS has four identical thrusters so the static affine thruster model described in Eq. (3) was identified. Phase 2: Uncoupled experiments. The experiments excite the vehicle in one DOF; the input signals used were STEPs and PRBSs signals. Fig. 2 shows the experiments for each DOF" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000284_j.addma.2021.102123-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000284_j.addma.2021.102123-Figure2-1.png", + "caption": "Fig. 2. (a)Tribological test set-up and (b) testing directions for vertical (Z) printing direction.", + "texts": [ + " For each property, at least five parallel specimens were tested so as to obtain statistically relevant data and then average value and standard deviation were calculated. B. Podgornik et al. Additive Manufacturing 46 (2021) 102123 KIc = P D3/2 ( \u2212 1.27+ 1.72 D d ) (1) where P is the load at fracture, D is the non-notched diameter (10 mm) and d is the diameter of the brittle-fractured area. Finally, dry-sliding wear tests aimed at determining the abrasive and adhesive wear resistance as a function of the heat treatment and build direction were performed under reciprocating sliding motion using a ball-on-flat contact configuration (Fig. 2a). To eliminate any influence of the surface roughness, all the specimens were mirror polished to an average surface roughness of 0.05 \u00b5m. For the abrasive wear, an Al2O3 ball (~1750 HV) with a diameter of 32 mm was used as an oscillating counter-body, thus concentrating all the wear to the 3D-printed maraging steel specimen. The wear tests were performed at room temperature, a relative humidity of about 50%, an average sliding speed of 0.12 m/s, a load of 74 N, corresponding to a nominal contact pressure of 1", + " The adhesive wear was evaluated under the same contact conditions, but using a hardened 100Cr6 steel ball (58 HRc) as the counter-body and a normal load of 100 N (corresponding to the same initial contact pressure of 1.0 GPa), thus promoting adhesive wear mechanisms and material transfer. In terms of sliding direction, for the horizontal (X) build direction the tests were performed on top of the individual layer. However, for the vertical (Z) build direction, the sliding tests were performed along (Z-X) and across (Z-Y) individual layers, as shown in Fig. 2b. At least three parallel specimens/tests were performed for each case, with specimens being ultrasonically cleaned in ethanol and dried in air prior to the dry-sliding wear test. During testing, the coefficient of friction was recorded continuously and the average steady-state value was calculated. After the test the wear scars were analyzed and the wear volume measured using a 3D optical measurement system Alicona InfiniteFocus G4. Using Eq. (2) the wear rate k was calculated, taking into account the wear volume V, the load FN and the sliding distance s", + "9\u22c510\u2212 5 mm3/Nm is shown by the aged specimens built in the horizontal direction (X), i.e., in-plane tests performed in the individual layer with more homogeneous microstructure and smaller number of interfacial defects. By changing the printing direction and performing wear tests in the vertical plain, the wear rates increased by more than 30% to about 3.9\u22c510\u2212 5 mm3/Nm. In this case, also the orientation of the layers plays a role, as shown in Fig. 13. For the tests performed across the layers (Z-Y, Fig. 2b) the wear rate was 3.7\u22c510\u2212 5 mm3/Nm and for the parallel testing direction (Z-X, Fig. 2b), even higher values of about 4.1\u22c510\u2212 5 mm3/Nm were recorded, also showing the most distinctively abraded wear track (Fig. 14b). Similar behavior can also be observed for the inclined printing direction (45\u25e6), with testing along the layers B. Podgornik et al. Additive Manufacturing 46 (2021) 102123 resulting in about 15% higher wear rates. However, as the distance between the individual layers is apparently increased, the wear rates for the inclined build direction are, for the specimens tested in the X any Y directions, in the range of 3" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003305_j.jsv.2005.03.011-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003305_j.jsv.2005.03.011-Figure1-1.png", + "caption": "Fig. 1. The slider-crank mechanism. (a) The physical model of a slider-crank mechanism, (b) the experiment equipment of a slider-crank mechanism.", + "texts": [ + " This study successfully demonstrates that the dynamic formulation can give a wonderful interpretation of a slider-crank mechanism by comparing it with the dynamic responses of the experimental results. Furthermore, a new identified method using the RGA is proposed, and it is confirmed that the method can perfectly search the parameters of a slider-crank mechanism through the numerical simulations and experiments. A slider-crank mechanism is a single-looped mechanism with a very simple construction shown in Fig. 1(a); the experimental equipment of a slider-crank mechanism is shown in Fig. 1(b). It consists of three parts: a rigid disk, which is driven by a servomotor, a connecting rod and a slider. Fig. 1(a) shows the physical model of a slider-crank mechanism, where the mass center and the radius of the rigid disk are denoted as point \u2018\u2018O\u2019\u2019 and length \u2018\u2018r\u2019\u2019, respectively. The length of the connected rod AB is denoted by \u2018\u2018l\u2019\u2019. The angle y is between OA and the X-axis, while the angle f is between the rod AB and the X-axis. In the OXY plane, the geometric positions of gravity centers of the rigid disk, connected rod and slider, respectively, are as follows: x1cg \u00bc 0; y1cg \u00bc 0, (1) x2cg \u00bc r cos y\u00fe 1 2 l cosf; y2cg \u00bc 1 2 l sinf, (2) x3cg \u00bc r cos y\u00fe l cosf; y3cg \u00bc 0", + " Decomposing Q into p and q, the system equations become Mpp \u20acp\u00feMpq \u20acq\u00feUT pk \u00bc Qp Np, (28a) Mqp \u20acp\u00feMqq \u20acq\u00feUT qk \u00bc Qq Nq, (28b) Up \u20acp\u00feUq \u20acq \u00bc c. (28c) By using Eqs. (28a) and (28c) and eliminating k and \u20acp we obtain k \u00bc \u00f0UT p \u00de 1 \u00bdQp Np Mpp \u20acp Mpq \u20acq , (29) \u20acp \u00bc U 1p \u00bdc Uq \u20acq . (30) Eqs. (28b), (29) and (30) can be combined in the matrix form as M\u0302\u00f0q\u00de\u20acq\u00fe N\u0302\u00f0q; _q\u00de \u00bc F\u0302, (31) where M\u0302 \u00bcMqq MqpU 1p Uq UT q \u00f0U T p \u00de 1 \u00bdMpq MppU 1p Uq , (32) N\u0302 \u00bc \u00bdNq UT q \u00f0U T p \u00de 1Np \u00fe \u00bdMqpU 1p UT q \u00f0U T p \u00de 1MppU 1p c, (33) F\u0302 \u00bc Qq UT q \u00f0U T p \u00de 1Qp. (34) For a slider-crank mechanism shown in Fig. 1(a), we have p \u00bc \u00bdf ; q \u00bc \u00bdy , Uq \u00bc \u00bdr cos y ; Up \u00bc \u00bd l cosf , Mpp \u00bc \u00bdA ; Mpq \u00bc \u00bdE ; Mqp \u00bc \u00bdE ; Mqq \u00bc \u00bdB , Np \u00bc \u00bdKW ; Nq \u00bc \u00bdPW , Qp \u00bc \u00bd\u00f0FB \u00fe FE\u00del sinf ; Qq \u00bc \u00bd\u00f0FB \u00fe FE\u00der sin y t , where A, B, E, KW and PW can be seen in Appendix A. Eq. (31) is a set of differential equations with only one independent generalized coordinate vector q \u00bc \u00bdy . It is seen that the entries of M\u0302, N\u0302 and F\u0302 of Eq. (31) have two independent variables y and f. By using Eq. (4) and its time derivative, we could derive the equation with only one independent variable y as follows: M\u0302\u00f0y\u00de\u20acy\u00fe N\u0302\u00f0y; _y\u00de \u00bc F\u0302 \u00f0y\u00de, (35) where M\u0302 \u00bc \u00f02m3 \u00fem2\u00de \u00fe m3 c r cos y h i r3 c cos y sin2 y \u00fe \u00f0m2 \u00fem3\u00der 2 sin2 y \u00fe 1 3 m2 l c 2 \u00f0r cos y\u00de2 \u00fe 1 2 m1r 2 \u00fe Jm, N\u0302 \u00bc m2r 2 sin y cos y 1 l2 3c2 \u00fe r c cos y\u00fe \u00f0lr\u00de2 3c4 cos2 y\u00fe r3 2c3 cos y sin2 y m2 r3 2c sin3 y\u00fem3r 2 sin y cos y 1 r2 c2 sin2 y\u00fe r2 c2 cos2 y\u00fe 2r c cos y \u00fe r4 cos2 y sin2 y c4 \u00fe r3 c3 sin2 y cos y m3 r3 c sin3 y _y 2 \u00fe Bm _y\u00fe 1 2 m2gr cos y, F\u0302 \u00bc Ktiq \u00f0FB \u00fe FE\u00der sin y 1\u00fe r c cos y , c \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi l2 r2 sin2 y p " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002499_0022-0728(94)03673-q-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002499_0022-0728(94)03673-q-Figure1-1.png", + "caption": "Fig. 1. The MPTW used in the experiments.", + "texts": [ + "58 g cm -3 is the density of the wet Nafion \u00ae membrane V Izl is the volume of Nation \u00ae solution used to modify the electrode, S cm 2 is the modified area and 10 is a conversion factor. The electrolyte solutions were prepared from A R grade reagents and distilled water. A-o(+)-g lucose (AR, Guangzhou Chemical Reagent Factory), L(+)ascorbic acid (AR, Northeast Pharmaceutical Factory), L-cysteine (AR, Chemical Reagent Factory of the Second Caoyang Middle School, Shanghai) and uric acid (Sigma) were used as received. The MPTW used in this work is shown in Fig. 1. We have described the MPTW technique and its application in electrochemistry elsewhere [26-28]. The wave C D E F G H in Fig. 1 was used to obtain an active Pt surface and the wave IJK was used to record the voltammograms after activation. 3. Results and discuss ion Fig. 2 shows the cyclic vol tammogram (CV) of 12 mM glucose oxidation on a Pt electrode without activation pret reatment in 0.1 M N a O H ( C - F in Fig. 1). Three oxidation peaks (A, B and C) appeared in the positive-going scan, and a cathodic peak D and an anodic peak ~ appeared in the negative-going scan. The present observations were consistent with literature data [7] where the observations were carried out at a high glucose concentration of 0.1 M. The appearance of the anodic peak P~ in the negative-going scan in the same potential range as that of A in the positive-going scan shows that peaks A and X do not represent a simple redox process of an adsorbed species" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002948_s0022-460x(03)00002-6-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002948_s0022-460x(03)00002-6-Figure1-1.png", + "caption": "Fig. 1. Unperturbed resonant level curves.", + "texts": [ + "x x \u00fe x3 \u00bc e\u00f0g cos ot d \u2019x\u00de; \u00f06\u00de Eq. (6) can be written as a set of state equation: \u2019x \u00bc y; \u2019y \u00bc x x3 \u00fe e\u00f0g cos ot dy\u00de; \u00f07\u00de where the force amplitude g; frequency o; and the damping d are variable parameters and e is a small scaling parameter. Solving Eq. (7) for e \u00bc 0; we obtain a center at \u00f0x; y\u00de \u00bc \u00f071; 0\u00de and a hyperbolic saddle at \u00f00; 0\u00de: The level set of Eq. (7) can be written as H\u00f0x; y\u00de \u00bc y2 2 x2 2 \u00fe x4 4 \u00bc 0; \u00f08\u00de which includes two homoclinic orbits, G0 \u00fe;G 0 and a point p0 \u00bc \u00f00; 0\u00de as shown in Fig. 1. The unperturbed homoclinic orbits are given by q0\u00fe\u00f0t t0\u00de \u00bc ffiffiffi 2 p sech\u00f0t t0\u00de; ffiffiffi 2 p sech t t0\u00f0 \u00detanh t t0\u00f0 \u00de h i ; q0 \u00bc q0\u00fe: \u00f09\u00de Within each of the loops G0 7; there is a family of periodic orbits with one-parameter k, which may be written as qk \u00fe\u00f0t t0\u00de \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 k2 r dn t t0ffiffiffiffiffiffiffiffiffiffiffiffiffi 2 k2 p ; k ! ; ffiffiffi 2 p k2 2 k2 sn t t0ffiffiffiffiffiffiffiffiffiffiffiffiffi 2 k2 p ; k ! cn t t0ffiffiffiffiffiffiffiffiffiffiffiffiffi 2 k2 p ; k " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure31.4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure31.4-1.png", + "caption": "Fig. 31.4 Prototype motor for driving test in vacuum", + "texts": [ + " Considering such characteristics that can hardly be found in other alternative actuators, introducing this motor into special environments would bring considerable benefits. The motor is typically operated in dielectric liquid to realize high field strength, which in turn leads to larger thrust force. According to Paschen\u2019s law, the breakdown voltage of air becomes larger as the pressure decreases. Therefore, in considerably high vacuum, the motor is expected to have a large force generation capability due to the increased breakdown voltage, even without dielectric liquid. The motor was tested in vacuum using a prototype shown in Fig.31.4 [7]. Since lubrication is one of the major problems in vacuum, the motor is equipped with a 368 Akio YAMAMOTO linear guide to avoid the direct friction between the slider and stator. At a chamber pressure of 10-3Pa, the prototype was driven in an open loop by applying a three phase ac voltage with amplitude of 1.5 kV0-p and a frequency of 1 Hz. The resultant motion is shown in Fig.31.5. The driving signal was switched every 3 seconds to alter the driving direction. No stepping-out was observed for the operation" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003599_jo00152a029-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003599_jo00152a029-Figure1-1.png", + "caption": "Figure 1. Cyclic voltammogram of 1.0 mM a-methyldopamine ( lb) in 1 M HCIOl at a scan rate of 0.050 V/s. The scan was initiated at +0.3 V.", + "texts": [ + " 18, 279; 1979, 18, 287. Jr., Recent Dev. Mass. Spectrom. Biochem. Med. 1979, 2, 317. 2899. 39, 1980. Chem. 1978,21, 548. Am. Chem. SOC. 1967,89, 447. extensive kinetic-mechanistic investigation of the anodic oxidation of these physiologically important catecholamines. Cyclic voltammetry of 1.0 mM a-methyldopamine (lb) in 1 M perchloric acid (pH 0.60) a t 25 OC indicated that the system lb - 2b is irreversible a t the carbon paste electrode. A typical voltammogram at a scan rate of 0.050 V/s is shown in Figure 1. The anodic peak (A) for the process lb -, 2b occurred at E,, = 0.679 V (SCE) and the cathodic peak (A') for the reverse process 2b - lb at E,, = 0.518 V, yielding a peak separation of 161 mV. Calculation of the theoretical anodic peak current (ipa),12J3 assuming an irreversible charge transfer involving two electrons and that the transfer coefficient (a) = 0.5 and using a diffusion coefficient derived from chronoamperometry (D = 0.53 X lov5 cm2/s), gave a value of i, = 118.2 pA. This value correlated well with the experimentally determined quantity of 117" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003659_tmag.2008.2001450-Figure11-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003659_tmag.2008.2001450-Figure11-1.png", + "caption": "Fig. 11 (a) Coil with a span of 4 slot pitches. (b) Single-slot equivalent.", + "texts": [ + " This difference can be attributed to the fact that at tooth edges flux concentration occurs and the relative permeance function is unable to take into account this flux concentration effect. The voltage induced in the in the stator windings by varying magnetic field in the air gap is known as back-EMF. Since all coils in the stator can be described in terms of a sequence of equivalent single-tooth coils [12], hence the flux linked by each coil is the sum of fluxes linked by each individual tooth coils. Fig. 11 shows a coil and its single-tooth equivalent. The flux linked by the coil in Fig. 11 is given by (47) where angular tooth offset; flux linked by first tooth. The flux linked by a tooth is given by (48) In the above equation, by substituting the radial component of the air-gap field at the stator inner surface (20) becomes (49) where is the air-gap field at the stator surface, is the inner radius of the stator (Fig. 1), and is the length of the motor. In the above equation, the integrand is independent of the axial direction. Hence, the above equation can be simplified as (50) The back-EMF of a single-tooth equivalent coil is given by (51) where is the number of turns in the coil. The back-EMF of a general coil is the sum of back-EMFs of its single-tooth equivalent coils. For the coil shown in Fig. 11, the back-EMF is given by (52) Having developed the necessary set of equations, this model is tested and results for the air-gap field are compared with FEM. The air-gap field density is not compared with the experimental result due to difficulty in measurement of the air-gap field. However, since the back-EMF is evaluated from the air-gap field distribution, comparison of experimental values of back-EMF and those obtained by the analytical methods implicitly establish the validity of the analytical methods" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003077_20.102936-Figure14-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003077_20.102936-Figure14-1.png", + "caption": "Fig. 14. (a) Limiting isoplethals from radial considerations f o r b = 5 x lo -* m (solid lines), $, = 7 mV, x = 6 x and other parameters as Fig. 2 for various fields. Dashed lines show the shift of the 1 T isoplethal as b increases. The heavy dashed line shows the large particle limit of buildup. (b) Curves showing the limit of the region of azimuthal stability for E , = 4 T, q = IO-' N . s . m-', p = lo3 kg . and for various flow velocities. Other parameters as Fig. 14(a).", + "texts": [ + " Neglect of the short range term gives From (50) the locus of zero radial velocity for n = n, can be derived for various fields (various U,,) by calculating rUL(radial) at a series of 8 values. In cases where saturation buildup is governed entirely by the radial condition (see below), these locii constitute the limiting isoplethals. Examples of such locii for particles of radius 5 X lo-' m (n, = lo2' particles per m3>, no = 10\" particles per m3, M = 1.7 T, lc/o = 7 mV, a = 25 x lop6 m, x = 6 X (so that the DD effect can be justifiably neglected), and for fields in the range 1-8 T, are shown in Fig. 14(a). Clearly (50) is also the particular solution, at n = n,, of (48) when applied to static colloids. There the second term on the right-hand-side of (48) goes to zero because vOa = 0. Here it goes to zero at the solid interface where a, /a = r,. Thus (50) is the equivalent of (28) with n = nsr the only difference being that here it is expressed in terms of velocity coefficients urn, and vda as opposed to W and kT*. Therefore in cases where the radial condition defines the solid builduplimit in flowing colloids, the buildup shape and volume is as in the static colloid case. However, it is to be expected that the buildup would take much longer in the static case where the migration of particles through the static continuous phase must be relied upon for buildup formation. In the flowing colloid case the particles are \"presented\" to the capture center at a rate governed essentially by vO. Fig. 14(a) also shows (dashed curves) the radially determined saturation buildup profiles for particles of b = 2 x 5 x and m at B = 1 T. These curves thus belong to the family of the innermost solid curve and serve to demonstrate that, as b increases, the radial limits of solid buildup approach those traditional in larger particle HGMF (heavy dashed line) and given by (16). This demonstrates that fine particle theory merges with normal particle (b > 1 pm) theory at the high b limit of the ultrafine range. It is important to remember at this stage that the curves of Fig. 14(a) do not necessarily correspond to the buildup in a flowing colloid. They merely define a region within FLETCHER: FINE PARTICLE HIGH GRADIENT MAGNETIC ENTRAPMENT 361 1 When considering the buildup interface then a, /a = r, for small particles and since the boundary of the region in which the azimuthal condition is satisfied is approximately cylindrical, especially at the lower 8 values, then dn/de = 0 ((47) and thus (52) describe the variation of n with 8 at constant r). Thus (52) simplifies considerably to give a limiting curve, the locus of zero azimuthal velocity, within which azimuthal stability exists", + " (56) This azimuthal condition is much less severe than that given by (53), implying that capture is now possible if U0 _ _ - (52) 9 3612 IEEE TRANSACTIONS ON MAGNETICS, VOL. 21, NO. 4, JULY 1991 which means that van Kleef 's experimental flow velocities were well within that which results in no collection of particles ( 2 cm.s-'). From (56) a critical angle for azimuthal stability 8, can be defined as 90' bvii2 e, = arc cos (c (57) Beyond this angle, azimuthal considerations prevent any particle being stable at the surface of the wire. Plots showing the limits of azimuthal stability according to (56) are shown in Fig. 14(b) for Bo = 4 T and for various flow velocities. The particle and colloid parameters are the same as have been used for Fig. 14(a). The 4 T plot of Fig. 14(a) thus shows the corresponding area of radial stability. The consequences of solid buildup are clear. For a particle to arrive and remain at a section of solid interface, r -2 Fields in T 1...1 T a.. . . .10 270' 2...4 T b. . . . .5xlOI; Fig. 15. Saturation buildup profiles at various fields and flows. Solid lines show boundanes determined by radial considerations, dashed lines determined by azimuthal considerations. Other parameters as Fig. 14. 3...8 T C.....2X10 that section must fall within a region in which both the radial and azimuthal conditions are satisfied. The final saturation buildup profile thus follows the limiting curve (radial or azimuthal), which is closest to the collection center at any value of 8. Typical profiles for various Ho and vo (other parameters as in Fig. 14) are shown in Fig. 15, where solid lines represent boundaries defined by the radial condition and dashed lines those defined by the azimuthal condition. The radial condition is never satisfied when 181 > 45\", and so front face buildup is excluded in that zone. When 181 < 45\" the saturation buildup profile is determined by either (1) the radial condition exclusively (when raL(radial) < raL(azimuthal) at all 8) resulting in a full buildup lobe, (ii) a combination of the radial (at high 8) and the azimuthal (at low 8) conditions when a truncated lobe is produced, or (iii) by the azimuthal condition exclusively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003763_s12239-010-0006-4-Figure8-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003763_s12239-010-0006-4-Figure8-1.png", + "caption": "Figure 8. Beams with cross-section 49.", + "texts": [ + " From Table 1, sections 16, 18, 20 and 49 give the largest values for TSWSP, whereas sections 13, 34 and 50 give largest values for WTSP. The two cross-sections with bigger values of WTSP and TSWSP are selected to be optimized, that is, cross-sections 13, 50, 20 and 49. Section 13 corresponds to a beam located at the left hand side on the back of the bus struc- WTSP= WSP TSSP ------------ TSWSP= TSSP WSP ------------ ture; section 20 is the cross-section of the beam located at the top of the back door in the longitudinal direction. Sections 49 and 50 correspond to the beams shown in Figure 8 and 9, respectively. It can be seen that the beams that have cross-section number 49 belong to the chassis, which must support most of the load transmitted by the wheels. Beams that have section number 50 belong to the front wheel supports. Having selected the cross-section more sensitive to changes in torsional stiffness and to weight, the proposed optimization method was carried out in these beams. 6.2. Results of the Optimization Process Optimization was first carried out by applying the fitness function ff1 defined by equation (4) over the cross-sections given by the sensitivity analysis, cross-section 13, 20, 49 and 50" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure3.37-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure3.37-1.png", + "caption": "Fig. 3.37. Two cases of collision", + "texts": [ + " Cylindrical and rectangular assembli tasks Cylindrical problem. Let us consider a manipulation task in which a cylindrical working object has to be inserted into a cylindrical hole When the nominal dynamics is calculated we prescribe the motion in such a way that no impact happens during the insertion. 225 Let us now discuss the perturbed motion. In the first time interval T1 the peg is moved towards the hole. It is a motion without any constra ints. At the begining of the insertion an impact happens (Fig. 3.37a,b). The impact is of the type discussed in Para. 3.5.3. The constraint is discussed in 3.4.12. In order to find the point of collision (point A in Figs. 3.30 and 3.37) we have to solve the equations (3.4.177) and (3.4.178) defining the cylindrical hole and the cylindrical peg. While the peg is moving towards the hole there is no real solution to this equation system. The impact happens when this system has one real so lution only. Thus, in each iteration the system has to be solved nume rically" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure9.11-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure9.11-1.png", + "caption": "Fig. 9.11 Piezoelectric micropump using fluid inertia effect in pipe", + "texts": [ + " Utilizing the fluid inertia effect in the outlet pipe, the micropump flows out in both pumping and suction periods and obtains output flow larger than the displacement. The fabricated micropump with 2.3 cm3 in volume can generate fluid power up to 0.22 W in water pumping. Also, for higher output fluid power, a full-wave rectifying micropump that has two sets of pump chamber, inlet check valve and outlet pipe was proposed and the validity was confirmed experimentally. Furthermore, for pumping higher viscosity fluid like homogeneous ERF, the micropump using a multi-reed valve was proposed and fabricated as shown in Fig.9.11. As a result of silicone oil pumping, 1.6 times higher output fluid power density was realized than the pump with a conventional reed type check valve. The objective, research outline and some research results of our research to realize new microactuators using functional fluids were briefly introduced. We are convinced of the validity of the new microactuators using functional fluids. Acknowledgments A part of the research was supported by Grant-in-Aid for Scientific Research in Priority Areas No" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002839_978-3-662-03845-1-Figure7.30-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002839_978-3-662-03845-1-Figure7.30-1.png", + "caption": "Fig. 7.30. Example of a calender", + "texts": [ + "8 Processing Thermoplastic Polymers 255 In sheet or film production, the die is just a slit of perfectly controlled width. It may be several metres long. For films like those made with poly( ethylene glycol terephthalate), the material is still very hot when it is quenched by reception onto a rotating cylinder. It cools extremely rapidly. In the case of plate materials, the main problem is to produce perfectly controlled thickness. This is done by passing the still hot material through a calender, consisting of two cooled rotating rollers (see Fig. 7.30). The shape is fixed by lowering the temperature below glass transition. Poly(methyl methacrylate) window panes used in the construction industry are made by this process. Tubes and pipes are prepared by extrusion. However, in order to output a perfectly constant diameter and thickness from the die, the still hot plastic material must pass through a shaping device (see Fig. 7.31). By applying pres sure within the tube, the polymer is forced onto a calibration die, then cooled in a bath, usually of cold water" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002461_70.478428-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002461_70.478428-Figure3-1.png", + "caption": "Fig. 3. Showing the velocity relationships between two bodies when the rear body is a steerable car.", + "texts": [ + " The linear velocity of body i - 1 can be broken into its two perpendicular components: one is in the direction of the linear velocity of body i, and the other is along the direction of the angular velocity of body i. The two linear velocities are related by the cosine of the angle between them, (1) U; = cos (O;-l - 0;) and the projection of the angular velocity is by the sine of the difference angle, L; 4; = sin (0;- - 0; (2) which gives the kinematic equations for the angles of the passive trailers, 8;. The equations are only slightly more complicated when the rear body is a steerable car instead of a passive trailer (refer to Fig. 3). Projecting onto the line connecting the two bodies, the relationship between the two linear velocities is u;;1 cos (8;;l - $ 3 ) = v i 3 cos ( - $ 3 ) , that is, both velocities are multiplied by the cosine of the angle between the velocity vector and the connecting bar. Now, because the velocity of the rear body, vi:', is no longer perpendicular to the angular velocity vector LA? & , this linear velocity will also contribute to the angular velocity & . Adding up the contributions of the two linear velocities, the relationship ~ ; ~ + , i 3 = sin - q~)v;:~ - sin - $ 3 ) ~ ; ~ for j E { 1, " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000326_j.mechmachtheory.2021.104264-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000326_j.mechmachtheory.2021.104264-Figure1-1.png", + "caption": "Fig. 1. Planetary gear modal testing setup top view schematic diagram showing (A) a load cell arm that fixes the input shaft to the bedplate through a load cell and (C) a compliant coupling that isolates the gearbox from (D) the torque actuator.", + "texts": [ + " Measured elastic-body vibration is verified by a finite element/contact mechanics model, and ring gear nodal diameter components observed in experiments match analytical model predictions. The elastic-body modes have large tooth mesh deflection and experience significant dynamic mesh loads in operation. The experimental planetary gear has practical dimensions similar to a long-used production helicopter gear whose ring gear is relatively thick compared to many modern ones and has relatively stiff supports. The frequencies of vibration modes considered in this paper are within the operating mesh frequency range of helicopter gears and other practical systems. Fig. 1 depicts the experimental test stand. The custom fixtures, test articles, and setup are discussed in detail in [53] . A spur planetary gear similar to a production helicopter one is stationary during testing. The ring gear mates to the fixtures with a slip fit and is secured by 16 bolts. A static torque is applied to the carrier while the sun and ring gears are rotationally constrained by the fixtures, thus loading all the tooth meshes. An MB Dynamics Modal 50 shaker excites the system near one planet-ring mesh. A network of uniaxial accelerometers measures the dynamic behavior of the system. Four accelerometers are mounted tangentially to the sun gear, carrier, and planet gears near meshing interfaces. The ring gear has 16 equally spaced accelerometers oriented radially. Fig. 1 shows that a load cell at the end of a radial arm (A) mounted to the bedplate fixes sun gear shaft rotation and measures the applied preload torque. A compliant coupling (C) connects the system to the torque actuator (D), which acts as a rigid boundary. Fig. 2 shows photographs of the experimental system from overhead with the modal shaker stinger attached directly to a planet gear with a force sensor to measure the input excitation and a driving point accelerometer. The shaker stinger is attached along the line of action of the planet-ring gear mesh" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003670_978-3-642-82195-0-Figure5.2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003670_978-3-642-82195-0-Figure5.2-1.png", + "caption": "Fig. 5.2. The plane manipulator", + "texts": [ + " Owing to the nonlinearity of the equa tions involved, a numerical approach is necessary for the solution of this problem. In [59] an example of the optimal joint trajectories and the corresponding optimal control signals is given. Bearing in mind the fact that the control is nominal, i.e. it does not take any unexpected disturbances which may act on the system into account, the optimal motion synthesis is too complex. The time-optimal motion synthesis for the three degree-of-freedom mani pulator shown in Fig. 5.2, has been considered in [60]. The joint axes are parallel which results in the plane manipulator motion. The first two links have the same length L, and negligible masses (m1 =m 2=0). The length of the third link equals zero, the mass m3 and the moment of inertia of the third link are specified. The Cartesian coordinates x, y and the angle ~3 (Fig. 5.2), specifying the gripper orientation, are considered to be external coordinates. The assumptions introduced, concerning the manipulator structure, make the derivation of the dynamic equations of motion, which relate between 189 the driving torques P. and the external coordinates possible. The time~ * -optimal control problem is to determine such admissible control Pi(t), i=1 ,2,3 which transfers the system from the initial position xO, yO to the final position x 1 , y1 along a straight line trajectory" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002754_s0731-7085(98)00129-0-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002754_s0731-7085(98)00129-0-Figure2-1.png", + "caption": "Fig. 2. Static gas cell for amperometric sensing. The inlet port can be used to inject gases directly or to introduce a liquid sample for head-space analysis.", + "texts": [ + " Vanadia-based sensors have been used for the study of gaseous analytes. Because it is highly colored, it is not compatible with optical interrogation. We developed an amperometric sensor for ammonia which employed a three-electrode array that was coated with a thin film of vanadia as the active element [28]. Ammonia is not normally electroactive; however, by modifying the indicator electrode with a film of a ruthenium oxide catalyst prior to coating the array with vanadia, the oxidation of ammonia was promoted. Using a static gas sample (Fig. 2), a calibration curve that was linear over the range 2\u201327 mmol ml\u22121 (gas) was obtained. We also developed a carbon monoxide sensor using silica that was formulated to retain water in the pores as the solid electrolyte [6]. The detection limit was 5 ppm (volume). However, the most important factors were that the sensitivity remained constant for at least 40 days after an initial drop over the first 2\u20134 days and the sensitivity was independent of humidity over the range 9\u201376%. This is in contrast with the humidity dependence of the sensitivity of comparable sensors but with organic polymers as the electrolyte", + " This swelling alters the size and shape of these channels, thereby changing the proton diffusion, which is the charge-carrier mechanism, through the polymer. We have reported on the use of Nafion as both an SPE and solid phase extractor for the determination of several neutral organic compounds in the gas phase [43]. An interdigitated microelectrode (IME) was coated with a ruthenium oxide catalyst. A Nafion overlayer was then cast over the modified IME. The electrode assembly was placed in a closed cell to control the humidity. In a typical test, a linear response to 200\u20131000 ml of methanol vapor in a 15 ml cell like that in Fig. 2 was obtained. A detector for NO in physiological media was reported by Malinski and Taha [46]. Nafion was used to discriminate against anionic interferents such as NO2 \u2212. Electrodes were covered with a polymeric film consisting of monomeric tetrakis(3-methoxy-4-hydroxyphenyl)porphyrin with nickel as the central metal and a Nafion overlayer. The porphyrin was the electrocatalyst for the detection of NO. Detection limits of 20 nM for differential pulse voltammetry and 10 nM for amperometry were obtained" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000150_s11771-021-4687-9-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000150_s11771-021-4687-9-Figure1-1.png", + "caption": "Figure 1 Dimetal-100 SLM equipment: (a) Schematic diagram; (b, c) Three-dimensional model", + "texts": [ + " 18Ni300 has important applications in the molds because of its ultra-high strength and good toughness. CoCr has important applications in the field of dentistry due to its good biocompatibility. FGM made from these materials will make full use of their advantages and be used more widely in the fields such as automotive, marine and construction machinery. The experiment was carried out on Dimetal-100 SLM equipment (South China University of Technology, China) with the schematic diagram of the equipment shown in Figure 1. The equipment is mainly composed of a 500W fiber laser (YLR-500WC, IPG), optical transmission regulation system, gas circulation system, building chamber, powder feeding device, cooling system, and the main control software. The laser is guided by a high-precision optical path transmission system, and it is basically the same throughout the working plane. The maximum fabricating dimensions of the equipment are 100 mm \u00d7 100 mm \u00d7 100 mm, the scanning speed is 10\u22127000 mm/s, the focused spot diameter is 70 \u03bcm, and the precision can reach \u00b10" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003244_s11071-005-1398-y-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003244_s11071-005-1398-y-Figure1-1.png", + "caption": "Figure 1. One stage gear system. Note, the relative displacement is x = r1\u03c81 \u2212 r2\u03c82.", + "texts": [ + " [16] and Kuang and Lin [17] examined the effect of tooth wear. The vibration response of gear systems to stochastic forces has been analysed [4, 14, 15, 18]. In practice it is important to minimise the effect of noise and keep the machine as close as possible to a stable response. In this paper we classify meshing faults and examine the effect of broken teeth and meshing stiffness fluctuations on the vibration response. The possibility of amplitude jumps in systems with meshing defects is demonstrated. Consider the single gear-pair system shown in Figure 1. In non-dimensional form, the equation of motion can be written [4, 9, 12] as d2 d\u03c4 2 x + 2\u03b6 \u03c9 d d\u03c4 x + k(\u03c4 )g(x, \u03b7) \u03c92 = B(\u03c4 ) = r1 M1(\u03c4 ) I1 + r2 M2(\u03c4 ) I2 , (1) where \u03c4 = \u03c9t, (2) 2\u03b6 = cz [ r2 1 I1 + r2 2 I2 ] , \u03c9, \u03b6 , k(\u03c4 ), g(x, \u03b7), \u03b7 and B(\u03c4 ) [4] and the other symbols are defined in Table 1 and shown in Figure 1. Often the excitation torque is assumed to be sinusoidal, and in this case B(\u03c4 ) will take to form, B(\u03c4 ) = B0 + B1cos(\u03c4 + ) \u03c92 . (3) In the analysis that follows, the stiffness functions k(\u03c4 ) and g(x, \u03b7) need special attention. g(x, \u03b7) has a piecewise character due to the backlash \u03b7, and is shown in Figure 2. k(\u03c4 ) is the meshing stiffness arising from the interaction of a single-pair or multiple teeth in contact. For an ideal gear system we have followed references [4, 12] and assumed that this meshing stiffness changes periodically" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003815_j.mechmachtheory.2009.06.001-Figure16-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003815_j.mechmachtheory.2009.06.001-Figure16-1.png", + "caption": "Fig. 16. Class IV of X-motion generators with one hinged parallelogram \u2013 III.", + "texts": [], + "surrounding_texts": [ + "The famous Delta robot [20] implements successfully hinged parallelograms in three limb chains that are generators of three X-motions. Various potential applications of X-motion generators with parallelograms are going to be elucidated in further works. In fact, circular translation and rectilinear translation are not the same motion. The opposite bars of a 1-dof hinged parallelogram can move while remaining parallel. Hence, the coupling between two opposite bars generates relative 1-dof circular translation that is a 1D manifold contained in the 2D subgroup of planar translation; the plane is the one of the parallelogram. Consequently, for a small motion, a hinged parallelogram is equivalent to a prismatic pair. Replacing all P pairs by hinged parallelograms, we obtain all possible X-motion generators including hinged parallelograms; these generators are shown in Figs. 6\u20138. Flattened parallelograms are singular and must be avoided. When only one P pair for each of the generators shown in Fig. 4 is replaced by one hinged parallelogram, Figs. 9 and 10 are readily obtained. Here, we must notice that the four generators, (III9) PRRPa, (III11) PHHPa, (III12) HPPaH and (III14) RPPaR in Fig. 10 are cancelled out because they have architectures that are equivalent by kinematic inversions to chains shown in Fig. 9. PaPaRHIII1( ) ( III2 PaPaRR) PaPaHH)III3( Figs. 11\u201313 are generators of X-motion obtained by the replacement of the two P pairs in chains of Fig. 5 by two hinged parallelograms. Likewise, Figs. 14\u201316 are X-motion generators derived by replacing only one P pair in each generator of Fig. 5 with one hinged parallelogram. That way, we obtain a total of eighty-two chains having at least one parallelogram, noticing that the kinematic inversion of each of these foregoing chains is also an adequate chain for generating X-motion. 4. Defective X-motion generators A defective chain for generating X-motion arises from the permanent singularity of the chain. Then the chain does never generate the desired X-motion. Such a phenomenon is not properly a singularity. As a matter of fact, singular means specific of special poses of the chain. However, such an abuse of language has some practical interest because the same geometric condition may yield transitory or permanent failure in the generation of X-motion. Clearly, open chains obtained from the trivial or exceptional 4-bar 1-dof closed chains with 1-dof Reuleaux pairs by splitting in two parts for any one link are defective X-motion generators. Using group dependency, we can derive all possible cases of defective chains for the generation of Schoenflies motion. In general, the singularity happens iff the following set equation fH\u00f0N1;u; p1\u00degfH\u00f0N2;u; p2\u00degfH\u00f0N3;u; p3\u00degfH\u00f0N4;u;p4\u00deg \u00bc fEg \u00f010\u00de does not imply the set equations fH\u00f0N1;u; p1\u00deg \u00bc fH\u00f0N2;u; p2\u00deg \u00bc fH\u00f0N3;u; p3\u00deg \u00bc fH\u00f0N4;u; p4\u00deg \u00bc fEg: \u00f011\u00de which are solved iff the helical motion angles are equal to zero. Here, the subset of displacements represents variations of position from the home posture. The absence of displacement necessarily belongs to the set of feasible displacements. Set Eq. (10) is the mathematical model of a mechanism obtained from the open chain pictured in Fig. 1 by welding the distal bodies i and j on a fixed frame. Such a closed-loop mechanism generally cannot move and, then, the open chain of Fig. 1 effectively generates X-motion. If a link in the closed mechanism can move, then the generator of X bond is defective or permanently singular. Two kinds of singularities may happen; the undesired motion either has only infinitesimal amplitude or can have finite amplitude. The detection of undesired infinitesimal motion is done through the study of a possible linear dependency of the four twists. This topic will be studied in another work. On the other hand, group theory is a fruitful tool for PPPR)b(PPPH)a( Pl Pl Fig. 22. Defective generators with three coplanar P pairs. the characterization of finite motion. Beyond the trivial and exceptional cases that are explained through the group dependency of displacement subsets, only four paradoxical cases were definitely established by Delassus [19]. Myard\u2019s work [24] is also devoted to the study of paradoxical closed chains with five or six revolute pairs, which are beyond the subject of our paper. In spite that special exceptional chains have been misled to be paradoxical ones in [25], the paradoxical mobility still cannot be explained only by the group dependency, which does not require the use of the Euclidean metrics. The paradoxical chains of Delassus can yield passive motion with finite amplitude. This kind of singularity will be confirmed in further work. Neglecting the paradoxical mobility, which is transitory in an open chain, a link of the previous mechanism can move permanently iff two open sub-chains generate two dependent kinematic bonds, the intersection of which is not {E}. In order to avoid the defective generators, the following cases must be considered: Case A. In set Eq. (10), a product of three factors is equal to a 3D subgroup of {X(u)} and the fourth 1D factor is included in this subgroup. Referring to Fig. 17, if the four pitches are equal, then \u00bdfH\u00f0A1; u; p\u00degfH\u00f0A2; u; p\u00degfbiH\u00f0A3; u; p\u00deg \u00bc fY\u00f0u; p\u00deg and fH\u00f0A4;u; p\u00deg fY\u00f0u; p\u00deg implies [{H(A1, u, p)}{H(A2, u, p)} {H(A3, u, p)}] {H(A4, u, p)} = {Y(u, p)}{H(A4, u, p)} = {Y(u, p)} \u2013 {X(u)}. Hence, this chain fails in generating Schoenflies motion for any pose and, in other words, it is a defective chain for the generation of X-motion. The four pitches must not be all equal. Pitches may be equal to zero but not all zeros. When four pitches are zeros, the chain generates the planar gliding motion, {Y(u, 0)} = {G(u)}. By the same token, one can demonstrate that if two screw pitches are equal, then two P pairs must not be perpendicular to u. For instance, two chains of Fig. 18 actually generate the 3-dof pseudo-planar motion rather than 4-dof X-motion. Furthermore, if three screw pitches are equal and one P pair is perpendicular to the parallel H axes, as shown in Fig. 19, these chains are trivial chains of a subgroup of pseudo-planar motion and never generate X-motion. One additional defective generator, a series of four prismatic pairs that generates {T} instead of {X(u)}, is displayed in Fig. 20 for completeness. Case B. A product of two factors is a 2D subgroup and one among the other two factors is included into this subgroup. For example, p1\u2013p2; A2 2 line\u00f0A1; u\u00deor\u00f0A1A2\u00de u \u00bc 0 ) fH\u00f0A1; u; p1\u00degfH\u00f0A2; u; p2\u00deg \u00bc fC\u00f0A1; u\u00deg; A3 2 line\u00f0A1; u\u00de ) fH\u00f0A3; u; p3\u00deg fC\u00f0A1; u\u00deg ) \u00bdfH\u00f0A1; u; p1\u00degfH\u00f0A2; u; p2\u00deg {H(A3, u, p3)}{H(A4, u, p4)} = {C(A1, u)}{H(A3, u, p3)}{H(A4, u, p4)} = {C(A1, u)}{H(A4, u, p4)} \u2013 {X(u)}. Hence, three axes must not be coaxial. Fig. 21a shows such a defective chain with three coaxial H pairs. The subgroup {C(A1, u)} can also be generated by PH or HP arrays (PR or RP when the pitch of H is zero) if the P is parallel to the H axis (R axis). Fig. 21b\u2013f shows other defective X-motion generators being in this situation, in which the replacement of any screw H by revolute R yields a defective X-generator chain, too. In Fig. 22, the cases with three prismatic pairs that are parallel to a plane are defective generators of X-motion and must also be avoided. Case C. A product of two factors is a 2D subgroup and the product of the other two factors is another subgroup, which is dependent with respect to the first subgroup. In other words, the intersection of the two 2D subgroups is a 1D subgroup. From the list of products of dependent subgroups [5], we obtain only two possible situations, namely, C1. [{H(A1, u, p1)}{H(A2, u, p2)}][{H(A3, u, p3)}{H(A4, u, p4)}] = {C(A1, u)}{C(A3, u)} if A2 e line (A1, u) and A4 e line (A3, u). We have {C(A1, u)} \\ {C(A3, u)} = {T(u)}. Hence, if two axes are collinear, then, the other two axes must not be collinear. For instance, the open chain of Fig. 23a is a defective chain for the generation of X-motion. The subgroups {C(Ai, u)} with either (i= 1 or 3) or (i= 1 and 3),can also be generated by PH or HP arrays (PR or RP when the pitch is zero) if the P is parallel to the H axis (R axis). These defective generators are shown in Fig. 23b\u2013f. It is noteworthy that a defective X generator happens when a revolute pair arbitrarily replaces any screw in these generators. C2. [{H(A1, u, p1)}{H(A2, u, p2)}][{H(A3, u, p3)}{H(A4, u, p4)}] can be equated to {C(A1, u)}{T(Pl)} with {C(A1, u)}\\{T(Pl)} = {T(u)}; in this case, the plane Pl of vectors s3, s4 is parallel to u. Consequently, if two screws are coaxial, then the plane of two P pairs must not be parallel to the screw axis. The chain in Fig. 24a shows this kind of defective generator. It is a defective chain with a passive exceptional mobility. Once more, the subgroup {C(A1, u)} can also be generated by PH or HP arrays (PR or RP when the pitch is zero) when the P is parallel to the H axis (R axis), as shown in Figs. 24b and c. Here, special cases of Fig. 22 are discarded for simplicity. Case D. If two adjacent pairs generate the same 1D subgroup, then, obviously, the open serial chain generates a 3D manifold included in the 4D subgroup {X(u)}. The required four DOFs of a generator of X-motion are not achieved. Hence, two adjacent H or R pairs must not be coaxial with the same pitch and two adjacent P pairs must not be parallel. Moreover, in a PPP subchain two non-adjacent P pairs that are parallel remain parallel, what must be avoided, such as Fig. 26g. Chains belonging to this case are shown in Figs. 25 and 26, in which R pairs can replace H pairs. To sum up, the defective X-motion generators are briefly tabulated in Table 3. These open chains have passive internal 1- dof mobility: the connectivity is 3 instead of 4. Moreover, their inversions are also defective chains for generating X-motion." + ] + }, + { + "image_filename": "designv10_6_0002461_70.478428-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002461_70.478428-Figure2-1.png", + "caption": "Fig. 2. the rear body is a passive trader.", + "texts": [ + " This procedure defines all the derivatives of the angles of the passive axles as well as the derivatives of the hitch angles. All that remains are the derivatives of the steering angles, which are defined to be the inputs. Starting at the rear of the train, let the linear velocity of the last body be denoted wTm. Then the derivatives of x and y are the projections of this velocity onto the horizontal and vertical directions, y = sin erm vn\", x = cos on\", Vn\",. Let vi represent the linear velocity of the axle with angle 0:. Consider first the case of a passive trailer; refer to Fig. 2 for clarification. Although this figure has been drawn for two TILBURY et aL: MULTISTEERING TRAILER SYSTEM 809 passive trailers, these calculations are still valid when the front body (z - 1) is steerable. The linear velocity of body i - 1 can be broken into its two perpendicular components: one is in the direction of the linear velocity of body i, and the other is along the direction of the angular velocity of body i. The two linear velocities are related by the cosine of the angle between them, (1) U; = cos (O;-l - 0;) and the projection of the angular velocity is by the sine of the difference angle, L; 4; = sin (0;- - 0; (2) which gives the kinematic equations for the angles of the passive trailers, 8;" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003001_robot.2001.933204-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003001_robot.2001.933204-Figure2-1.png", + "caption": "Figure 2: (a) 4 bar linkage (b) Cut at joint ( c ) Cut at link", + "texts": [ + " Remark 4 The above analysis of direct Lagrangian method considers only holonomic constraints. For nonholonomic constraints, such as the case of a hand grasping an object under rolling constraints as in Figure 1 (d), only the LagrangeD'Alembert formulation will yield the correct equations, see e.g. [2] p.277 for details(the rolling constraints has been incorporated into the grasping constraint). 9 Example Here for illustration purpose, we considered a simple example of 4 bar linkage. This is the simplest possible kind of parallel manipulator which is shown in Figure 2 (a). If we choose joint C as the end effector, joint A as the actuator, then by cutting joint C, we can have a tree system as shown in figure 2 (b). However if we want to account for the torque such as friction in joint C, we may cut the link BC instead of the joint C, as shown in figure 2 (c). If we attach a frame at the middle of 13 and let its coordinates be (z, y, 4) . Then the structure equations are : z = 11 cos(a1) + (142) cos(al+ a2) (28) g = 11 sin(a1) + ( 1 z / 2 ) sin(al+ a2) 13 sin(b1) + (I2/2) sin(bl + bz) (p = a l + a n = b l + b z - . r r = l4 + 13 cos(bi) + (12/2) cos(bi + bz) = After differentiating we have : where (29) Configuration singularity occur when the matrix [-Jal - J a Z J b l J b Z ] drop rank. For more details, you may see 1111 and [12]. From p.165 of [2], the dynamics of a two-link planar robot such as link a has the following form : D a ( % a , " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002565_s0043-1648(03)00338-7-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002565_s0043-1648(03)00338-7-Figure1-1.png", + "caption": "Fig. 1. Conceptual model of backlash control with conical involute gears.", + "texts": [ + " However, in some machines, such as industrial robots and other precision machines, one aims for as little backlash as possible, since such backlash normally reduces precision and makes the control of the machine very difficult. Very precise gears and mountings reduce or eliminate the backlash, but high-precision gearing is an expensive means of limiting backlash. Therefore, special design, fabrication, and assembly methods have been developed to permit the use of imperfect gears and associated parts without the drawback of significant backlash. One gear that is increasing in popularity and may respond to such demands is the so-called conical involute gear (see Fig. 1) [1]. This gear is an involute gear, which has tapered tooth thickness, tapered root and tapered outside diameter. \u2217 Corresponding author. Tel.: +46-8-790-74-47; fax: +46-8-20-22-87. E-mail address: jesper@md.kth.se (J. Brauer). Each transverse tooth profile represents (approximately) a spur gear with different degrees of addendum modification and tip radius. The backlash can be eliminated by moving one of the gears in the axial direction. Another way, which also is used in industry, to control backlash consists of meshing spur gears tightly by adjusting the centre distance of the gear pair" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure3.24-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure3.24-1.png", + "caption": "Fig. 3.24. Gripper subject to a linear joint constraint", + "texts": [ + "119) NOw, all the elements of dynamic model (3.4.32) are determined and the model can be solved. Friction is treated in a way similar to the discussion in the previous paragraph, but here, there is no longitudinal motion and, accordingly, no longitudinal friction components. 196 3.4.9. Linear joint constraint We consider a manipulator having the gripper connected to the ground, or to an object which moves according to a given law, by means of a .... joint permitting one translation only. Let h be the unit vector of translation axis (Fig. 3.24). Let us first discuss the prescribed motion of the object to which the gripper is connected (non stationary constraint). Let us define this motion in the same way as it was done in Para. 3.4.7. Thus, the linear motion is defined by * * xA = f1 (t) , YA f2 (t) , (3.4.120) and angular motion by * * e = \u00a34 (t), q> = \u00a35 (t), (3.4.121) If we connect the gripper to the moving object (Fig. 3.24), then h (on .... * .... the gripper) has to coincide with h (on the object) and s has to co.... * .... incide with s (since relative rotation around h is not possible). Thus e * e , * q> , * 1jJ (3.4.122) Introducing orientation coordinate systems for the gripper and for the object (as was done in Para. 3.4.7), we find that the relative trans- lation can be defined by u * x sA -*o A s (see Fig. 3. 1 9) . -*- A A 197 (3.4.123) If a six d.o.f. manipulator (n=6) is considered, u is a free parameter" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003715_tps.2010.2076355-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003715_tps.2010.2076355-Figure2-1.png", + "caption": "Fig. 2. Diagram of the force on the PM of the VMRPMSM. (a) Analytic object. (b) The PM moves upward. (c) The PM moves downward.", + "texts": [ + " We assume the following: 1) The mass of the main PM is distributed homogeneously; 2) the smoothness of the PM is uniform over its surface, and the coefficient of the dynamic friction is equal to the coefficient of static friction; and 3) the effect of the gravitational force is negligible. For the machine discussed in Section VI, the gravitational force is 0.174 N for one PM, but the centrifugal and the electromagnetic forces are 11.37 and 11.55 N, respectively. The ratio of the gravitational force to the electromagnetic force is 1.52%, so we can neglect the effect of the gravitational force. The force on the PM is shown in Fig. 2. Fe is the electromagnetic force; Fen and Fet are the normal and tangential components of the electromagnetic force in the x-axis. Fc is the centrifugal force, Fu is the frictional force, and \u03b8 is the angle between the electromagnetic force and the centerline of the PM slot. We define the variable s as the distance between the main PM and the secondary PM. The relationship between the centrifugal force and speed is a quadratic function. The premise that FW may be achieved in the VMRPMSM is based on the assumption that the two opposing forces on the PMs, the electromagnetic force and the centrifugal force, can be balanced" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure2.54-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure2.54-1.png", + "caption": "Fig. 2.54. Scheme of manipulation task", + "texts": [ + " Example 2 Let us consider the arthropoid manipulator having 5 degrees of freedom. It has been designed for manipulation with heavy loads. The minimal configuration consists of three rotational d.o.f. (q1' q2' q3) and the gripper is connected to the minimal configuration by means of two ro tational joints (q4' q5). The external look, manipulator data, the cho ice of generalized (internal) coordinates, and the adopted b.-f. sys tems are shown in Fig. 2.53. 111 Manipulation task. The manipulator has to move a 250 kg mass object along the trajectory Ao A1 A2 A3 (Fig. 2.54). Every part of the trajec tory (Ao+A\" A1+A2 , A2+A3 ) is a straight line. The velocity profile on each part is triangular. The complete scheme of manipulation task, i.e. the initial position, the trajectory of object motion and the changes in object orientation, is shown in Fig. 2.54. It can be concluded that in this task the partial orientation only is necessary. Thus, this ma nipulation task consists of positioning along with partial orientation, so five d.o.f. are enough. It is evident from the manipulation task scheme (Fig. 2.54) that the direction (b) is the most important. In order to define the direction :1: (b) with respect to the gripper we use the unit vector h = {a, 1, O} (expressed in the gripper b.-f. system 06x6Y6z6). The two angles 8, ~ define the direction (b) with respect to the external system Oxyz. We T use the adapting block 5-2, so the position vector is X =[x y z 8 ~l . g The nubmer of points to be reached is m = 3. The initial position is defined by q(to ) = [0 -n/6 -4n/6 -n/6 OlT. Now, the input list defining the manipulation task is: m 3 Indicator of adapting block 2 Indicators for profiles 222 Initial position q(to ) 0 -n/6 -4n/6 -n/6 0 Xg1 = [x Y z 8 ~]A1 1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000545_jestpe.2021.3055224-Figure24-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000545_jestpe.2021.3055224-Figure24-1.png", + "caption": "Fig. 24 Prototypes, (a) rotor of the BDFRM and SynRM, (b) rotor of the BDFIM, (c) stator of the BDFIM and BDFRM with a 8-pole SW1 and 4-pole SW2, (d) stator of the SynRM with a 6-pole winding.", + "texts": [ + "5-kW PMSM was used as a prime mover during the generating operation of machines under test and as a load machine during the motoring operation. Phase currents and line-to-line voltages were measured by current transducers LEM CASR15-NP and voltage transducers LEM LV25-p, respectively. The steady-state torque can be directly measured by the torque transducer HBM T20WN installed between the PMSM and the machine under test for higher accuracy or estimated from the measured currents of the PMSM. Photos of the BDFIM, BDFRM and SynRM prototypes under test, which share the same standard YZR-112 frame, are shown in Fig. 24. They can be replaced by other machine topologies used in this paper, such as the FRPM machine, etc. B. Inductances By applying modulation operators to winding functions of machine windings, the inductance can be expressed as: 21 sat 0 stk 0 ,ij r g e i jL k r g l W M W d (14) where ksat is the saturation coefficient, Wi(\u03d5) and Wj(\u03d5) are winding functions of i-th and j-th windings, respectively. Starting from (14), the closed-form equation for main self-inductance of phase-A winding in a 6-pole SynRM prototype with a multi-layer barrier rotor can be written as: 22 0 stk _ 1_ _ SynRM sat , , , , 0 4 2 cos 2 g ph s w sA ms r e d q d q p p p p p p p p r r l N k L k g p C C C C p (15) where , d p pC and , q p pC are magnetic field conversion factors between the source MMF and the air-gap MMF drop after modulation in d-axis and q-axis positions, respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002649_9.754811-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002649_9.754811-Figure1-1.png", + "caption": "Fig. 1. Definition of the variable %:", + "texts": [ + " Less conservative controllers may be obtained by incorporating the growth properties of the function in the design of the functions In this subsection, we will present and analyze the new adaptive controller. As we have already mentioned, we will use a controller which switches between the CEFL and ADF controllers depending whether belongs or does not belong to In order to avoid any possibility of sliding motions [15], we will use a hysteresis switching [13], [19] described as follows: Let us define the function as2 follows: if if and if and if where The definition of the variable can be easily understood by looking at Fig. 1. More precisely, in Fig. 1 we have plotted a possible trajectory of the term in the case where 2% (t) = lim !t %( ); where < t: then and moreover remains one until enters the set After enters the set switches to zero and remains zero until exits the set After exits the set the variable switches to one and remains equal to one, although enters the set (since does not enter ). The variable controls the switching policy of the proposed controller. In particular, if then the controller is an ADF controller, while when the controller is a CEFL controller" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002514_robot.2001.933055-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002514_robot.2001.933055-Figure2-1.png", + "caption": "Figure 2: Definition of the frames", + "texts": [ + "000 2001 IEEE 2859 L = [ 11 12 1, 14 15 16 ]T (1 -a) platform with respect to the base is denoted by: Typically each variable is given as: I I oJf,r 1. = q . + q \" . ' T m = [ O F ] 0 0 0 where qi is the prismatic position is a fixed offset value. 2.1 The geometric parameters (1-b) reading and 4 0 ~ ~ i This matrix is a function of the 24 parameters and the 6 leg lengths of the robot. The location of the base frame Fo with respect to the world reference frame F.l of the environment is given by a transformation matrix Z. In addition, the matrix E denotes the location of the end-effector frame FE in frame F, of the platform (cf. Figure 2). The location of the endeffector frame relative to the world reference frame is: -IT, =Z.'T,.E (3) Thus, the coordinates of point A, relative to frame F.l are given by: {-'r..)=-'T0 . { ' ~ r } = ~ . { ':I} (4) We define the frame Fo fixed with respect to the base and the frame F, fixed with respect to the movable platform. They are defined as follow [7]: The coordinates of point Bi relative to frame FE are: As the matrices Z and E can be defined arbitrarily by the are necessary to define each of them" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003162_50008-0-Figure7.43-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003162_50008-0-Figure7.43-1.png", + "caption": "FIGURE 7.43", + "texts": [ + "42) is the locus of the contact and it can be seen that the distance 'S' between the gear teeth contact and the pitch line is continuously changing with the contact position during the meshing cycle of the gears. It is thus possible to model any specific contact position on the tooth surface of an involute gear by two rotating circular discs of radii (RAsin~F + S) and (RBsin ~F - S) as shown in Figure 7.42. This idea is applied in a testing apparatus generally known as a ' twin disc' or ' two disc' machine shown schematically in Figure 7.43. Since the gear tooth contact is closely simulated by the two rotating discs, these machines are widely used to model gear lubrication and wear and in selecting lubricants or materials for gears. It is much cheaper and more convenient experimentally to use metal discs instead of actual gears for friction and wear testing. The wear testing virtually ensures the destruction of the test specimens and it is far easier to inspect and analyse a worn disc surface than the recessed surface of a gear wheel" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000356_j.cirpj.2021.07.004-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000356_j.cirpj.2021.07.004-Figure1-1.png", + "caption": "Fig. 1. Schematic representation of the top view of the laboratory L-PBF system with the illumination side (left), the process chamber (middle) and the imaging side (right). Illustration redrawn from Ref. [26].", + "texts": [ + " aterials and methods Experiments were conducted using spherical gas atomized TiAl-4V powder of particle size distribution between 15 mm and 5 mm. High-quality technical Argon 5.0 and Helium 4.6 (less han 10 ppm and 40 ppm impurities, respectively), and a mixture f argon and helium, were employed to establish the process tmosphere. Table 1 lists some relevant properties of these gases or the study. Laboratory L-PBF system with shadowgraphy setup The setup for the shadowgraphy experiments is presented in Fig. 1 and was as follows. The L-PBF process was illuminated from one side with collimated light, and on the opposite side, a highspeed camera focused on the process plane, captured the shadows of objects obstructing the light. It is therefore a valuable asset for observing the dynamic generation of metal vapour and particles during the L-PBF process [26]. One of the main advantages of this technology is the possibility of using high acquisition frequency (greater than 10 kHz) despite the use of relatively weak LED lighting" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003121_1.5058617-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003121_1.5058617-Figure1-1.png", + "caption": "Figure 1 . Examples of cladding methods: a) 1 -D translation; b) 1 - D rotation; c) 2-D translation with straight vertical buildup; d) 2-D translation with curved vertical buildup", + "texts": [ + " The heat removal during solidification would be into the thermal mass of previous clads; this m ust have caused a systematic orientation of the dendrites that setup a uniform prefered slip system orientation. Powder Uti l i zation : Percent utilization of the powder was calculated from the known powder feed rate (g/min) , the duration of the laser time, and the weight gain for each pass. The 1 -D plate was run with unchanged beam diameter, power, and powder feed rate. Of the 1 1 .0 g/min coming from the feed tube, the weight increased just below 1 0 g/min for a 90% ICALEO (1993)/561 utilization. Figure 1 0 shows that data point as well as the utilization for several different beam diameters for the concentric nozzle used in cladding the 2-D cylinder. The beam diameters ranged from 1 .25 to 2.05 mm, while the laser power was increased from 3100 to 3450 watts to supply adequate power density to melt the substrate. It would be fair speculation that the slope of the off-axis nozzle would sustain a higher utilization at the smaller beam diameters because of its ability to concentrate the powder into a smaller cross-section" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003047_1.1767819-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003047_1.1767819-Figure4-1.png", + "caption": "Fig. 4 3-RRS wrist", + "texts": [ + " QED The 3-RRS Wrist The number of degrees of freedom ~dof number! of the 3-RRS mechanism ~Fig. 1! can be computed with the Gru\u0308bler equation: F56~n21 !2( j ~62fj! (11) where F is the dof number of the mechanism, n is the number of links and fj is the dof number of the j-th kinematic pair. The 3-RRS mechanism ~Fig. 1! is composed of eight links ~n58!, three spherical pairs (fj53) and six revolute pairs (fj51). Substituting these data into Eq. ~11! gives F53. Therefore the 3-RRS mechanism has three dof, i.e., is not overconstrained. Figure 4 shows a 3-RRS mechanism encountering the following mounting and manufacturing conditions: i. the revolute pair axes converge towards a single point; ~mounting and manufacturing condition! ii. the centers of the spherical pairs are not aligned; ~manufacturing condition! SEPTEMBER 2004, Vol. 126 \u00d5 851 16 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F 852 \u00d5 Vol. 126, SEPTEMBER 2004 rom: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/28/20 iii. the point the revolute pair axes converge towards does not lie on the plane located by the three spherical pair centers; ~manufacturing condition! Henceforth a 3-RRS mechanism encountering these geometric conditions will be called 3-RRS wrist. In the following paragraphs of this section it will be shown that the 3-RRS wrist is a spherical parallel manipulator when the three revolute pairs adjacent to the base are actuated. With reference to Fig. 4, the points Ai, i51,2,3, are the spherical pair centers and the point C is the point the revolute pair axes converge towards. The point C is fixed in the base. Moreover, Sb is a reference system fixed in the base and Sp is a reference system fixed in the platform. Figure 5 shows the i-th leg, i51,2,3, of the 3-RRS wrist. According to Fig. 5, w1i and u1i are respectively the axis unit vector and the joint coordinate of the revolute pair adjacent to the base and w2i and u2i are respectively the axis unit vector and the joint coordinate of the revolute pair not adjacent to the base" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003457_20080706-5-kr-1001.00138-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003457_20080706-5-kr-1001.00138-Figure2-1.png", + "caption": "Fig. 2. Roll motion and altitude.", + "texts": [ + " The controller design which stabilizes the dynamics of the UAV is presented in section 3. Section 4 reports the experimental setup and depicts the experimental results. Finally some concluding remarks and perspectives are given in section 5. Before providing the dynamical equations of the TPhoenix UAV, it results interesting to illustrate the way as the UAV drives the attitude based on rotors tilting. Roll motion and Altitude: The roll motion of the vehicle is regulated by the difference in the angular velocity of rotors (see Fig. 2). The altitude is controlled by increasing or decreasing the thrust of the rotors. 978-3-902661-00-5/08/$20.00 \u00a9 2008 IFAC 803 10.3182/20080706-5-KR-1001.3881 Pitch motion: The advantage of this configuration is the addition of an extra mass, besides the ones of the rotors, which is placed down enough to provide a weightbased torque, obtaining then, a pendular damped effect (naturally stable), see Fig. 3. To counteract this pendular motion, the rotors tilt parallel (at the same time) in opposite sense of the pitch motion maintaining the upwards position, emulating a mobile pivot, and moreover behaving as damping factor" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003162_50008-0-Figure7.11-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003162_50008-0-Figure7.11-1.png", + "caption": "FIGURE 7.11", + "texts": [ + "0 -aIm] I Maximum Shear Stress \"Uma x -\" 0.304 Pmax -- 0.304 x 55.4 I = 16.8 [MPa] I Depth at which Maximum Shear Stress Occurs z = 0.786b = 0.786 x (5.75 \u2022 10 -6) I - 4.5 \u2022 10 -6 [m] I ELASTOHYDRODYNAMIC LUBRICATION 303 9 Contact between Two Crossed Cylinders with Equal Diameters The contact area be tween two cylinders with equal diameters crossed at 90 ~ is bounded by a circle. This configuration is frequently used in wear experiments since the contact parameters can easily be determined. The contacting cylinders are shown in Figure 7.11 and the contact parameters can be calculated according to the formulae summar ized in Table 7.1. Geomet ry of the contact be tween two cylinders of equal diameters wi th axes perpendicular . Since R A - R B then in this ~configuration Rax radius according to (7.2) is given by: = o% Ray = RA, Rbx = R B and Rby = ~. The reduced 1 1 1 1 1 1 1 2 O O O O R--=Rx + Ry + R--BB + RA + R A (7.10) which is the same as for a sphere on a plane surface. If the cylinders are crossed at an angle other than 0 ~ or 90 ~ i" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002837_physrevlett.84.1631-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002837_physrevlett.84.1631-Figure3-1.png", + "caption": "FIG. 3. Geometry for the relation u1 1 a 2 u2 p. Rectangles are unit cells of the concatenated helices, with radii R6, pitches p6, and tangents t6.", + "texts": [ + " Let the tangents to the right and left helices make angles u6 with the two (asymptotic) helical axes z6. Continuity of the tangents at the junction of the two axes requires that the axes be rotated about the junction by a \u201cblock\u201d angle a p 2 u1 2 u2 (Figs. 2 and 3) a tan21 t1 k1 2 tan21 t2 k2 , (12) where k6 and t6 are the curvature and torsion of the two helices. This simple law, first due to Hotani [20], was intuited through observations of the conformations of reconstituted bacterial flagella. It follows from the geometrical construction in Fig. 3. (Note that u2 is negative for left-handed helices.) When j fi 0, it can be shown that the block angle deviates from (12) through a correction of order ktj2. Hotani\u2019s measurements [20] allow us to estimate [8] an upper bound of j & 80 nm. Consider now solutions propagating between the two minima V6 of an asymmetric potential [21]. There are two regimes of interest: inertial and viscous. If, in the former, we deal with potentials V with V1 2V2, then a front solution exists propagating along helices of torsion V6 (with no external mechanical stress) traveling at a speed c p jDV ja 2I, where DV is the potential difference (Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000068_tie.2021.3057002-Figure19-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000068_tie.2021.3057002-Figure19-1.png", + "caption": "Fig. 19. Temperature measuring element lead-out line of a new type of rotor mixed ventilation structure prototype.", + "texts": [ + " 0278-0046 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. According to the geometry of the proposed novel rotor hybrid ventilation cooling structure, a new prototype of 315kW, 6kV HVLSSR-PMSM rotor with ventilation cooling structure is manufactured, as shown in Fig. 18. The lead-exit wires of the temperature measuring sensors in the motor are shown in Fig. 19. For verifying that the proposed design approach could provide satisfactory results practically, the temperature of the prototype with rotor hybrid ventilation cooling system is investigated in case of no-load operation, and the detail temperature distribution is shown in Fig.20. The losses of the entire motor at this operation are stator iron loss, winding copper loss, mechanical loss, which are 5510W, 2228W, and 4862W respectively. The temperature rise of the motor with rotor hybrid ventilation cooling structure is tested" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003420_elan.200804253-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003420_elan.200804253-Figure1-1.png", + "caption": "Fig. 1. Design and fabrication of the thick-film microflow electrochemical biosensor detector. Screen-printed 3-electrode system (A) with carbon working and counter electrodes (a), Ag/AgCl reference electrodes (b), and copper traces (c); Graphic of the partially rolled sensor (B) with insulator (d), screen-printed inks (e) and copper contact traces (c) for the external connections; Photo of actual rolled, silicone-coated electrode (C) with electrical leads (f).", + "texts": [ + " This communication describes the design, fabrication, optimization and in-vitro testing of a minimally invasive electrochemical biosensor for monitoring health markers in tears, based on a miniaturized, flexible, thick-film amperometric enzyme electrode. The use of the tear fluid for noninvasive and minimally invasive monitoring has received considerable recent attention [4, 5]. Tear fluid is an advantageous fluid for biodetection as it flows continuously, and is a relatively clean body fluid compared to the relatively static interstitial fluid used in subcutaneous monitoring. Recent activity has led to flexible electrochemical sensors for tear [6] or cardiac [7] monitoring fabricated by lithographic (thin-film) techniques. As illustrated in Figure 1, our new sensing device consists of enzyme-containing thick-film carbon electrodes, printed on a flexible polyimide substrate and rolled into a 0.7 mm diameter flow cell. Such laterally rolled geometry and dimension make it suitable for insertion into the lacrimal canaliculus (through which the tear fluid passes), in a manner similar to the widely used insertion of punctum Electroanalysis 20, 2008, No. 14, 1610 \u2013 1614 G 2008 WILEY-VCH Verlag GmbH&Co. KGaA, Weinheim plugs that reduce the irritation of dry eyes with relatively few complications [8]", + " Of particular importance was accommodating the three printed electrodes within the shortest possible flow cell (down to 1 mm in length and 0.7 mm diameter), compatible with such insertion. The insertion application called for a soft, flexible sensor constructed using biocompatible materials. Additionally, considerations were made when choosing fabrication techniques amenable for future large-scale production. Accordingly, our design utilized screen printed 100 mm wide band electrodes on a flexible, copper-clad polyimide substrate (Fig. 1). The polyimide substrate, similar to Kapton, is ideal for miniaturization purposes as it will withstand mechanical stress while it is rolled tightly into miniature tubing [7]. The selected materials are conducive to delicate biocompatible insertion, and the fabrication using screen printing and copper lithography is very attractive for any future large-scale production. First, copper leads were fabricated on the polyimide substrate in a common setting, using a bench top etching technique. The copper pads were made to form contact to the screen-printed band electrodes on one end and solder to insulated wires for electrical connection on the other (Fig. 1A,c and B,c). This step was accomplished in a brief (1 h) process by applying a thin coat of photoresist onto the copper-clad polyimide. The photoresist could then be UV treated, developed, and etched to remove excess copper in a process similar to printed circuit board fabrication. Next, as shown in Figure 1A, 100 mmwide band carbon working and counter electrodes (a) and a silver/silver chloride reference electrode (b) were printed onto the substrate, overlapping the etched copper pads (c) to make electrical contact. An insulator layer was then applied over most of the electrode area (Fig. 1B,d). Particular care had to be taken to properly align the junctions where the copper and ink overlap (Fig. 1B,e) to insure proper sensor function. The sensor was then rolled laterally to form a tubular flow cell configuration (with an inner diameter, ID of 580 mm). Such rolling was accomplished using a custom fabricated jig, featuring two concentric needles with medial slits which could be rotated on a step-motor to roll the sensor between them. The three electrodes were thus inlayed on the innerwall of the flow cell (Fig. 1B), perpendicular to the flow direction. A cyanoacrylate adhesive was applied to the back of the rolled sensor to hold its tubular shape. Electrical connectionswere folded outside the flow channel to insulate them, yielding an extremely small flow sensor (0.7 mm i.d.; Fig. 1C), suitable for lacrimal insertion in a biocompatible casing. Finally, electrical leads were included (for in-vitro testing) and the sensor was packaged in a small diameter polyethylene tubing for subsequent experimentation. Additional factors taken into consideration for fabrication included optimizing the enzyme:ink ratios, curing temperature and the electrode geometry. A full description of the microfabrication process is given below in theExperimental Section. The flexible microflow detector was evaluated first for on-line monitoring of the catecholamine neurotransmitters norepinephrine and dopamine", + " The flow-cell biosensorwas connected to a syringe pump (KDS100, KD Scientific, Holliston, MA) as the fluid source with a 6-way injection valve (Rhoedyne Model 7010, Rhoedyne LLC, Rohnert Park, CA) and a 200 mL sample loop. The flow-cell sensor was placed immediately after the outlet of the injection valve to minimize sample dispersion. The microsensor was fabricated using a semi-automatic screen-printer (MPM SPM-AV, Speedline Technologies, Inc., Franklin, MA) to print conductive inks onto the flexible substrates to form the basic electrode layout of Figure 1. A double-sided copper-clad flexible polyimide laminate (Pyralux, E. I. du Pont Co. Wilmington, DE, AP8515R, 25 mm thick, 18 mm Cu each side) served as the substrate for the screen-printing (Fig. 1A). The copper was etched using simple photolithography techniques to create copper junction pads (to which external wires could be soldered to provide electrical contacts outside the rolled electrode; Fig. 1C,f). Briefly, ca. 1 mL positive photoresist (MEGAPOSITSPR220 7.0 positive photoresist, Rohmand Haas Electrochemical Materials, Marlborough, MA) was applied to a 10.16 cm 3.38 cm section of the substrate by spin-coating (3000 RPM, 60 s) onto the Cu-clad substrate which was fixed with a temporary adhesive to an alumina substrate. Following a 3 min soft bake at 100 8C, the substrate was exposed to a monochromatic UV light for 90 s with the positive copper trace transparency mask in place. The exposed photoresist was developed using 418 Developer (sodiumhydroxide, 0", + ", Canada) for 90 s. The copper was then etched off using ammoniumpersulfate (410 etching, 1.1 M inwater, MG Chemicals, Ltd.) in a bubbling etching tank at ca. 45 8C with air bubbling. Once the excess copper was removed, leaving the necessary copper traces, the substrate was rinsed with water and then acetone (to remove undeveloped photoresist), coated with tin using an electroless tinning solution (MG Chemicals, Toronto, Ontario, CA), and was ready for screen printing. Images of the copper contacts are shown in Figure 1A and B. As shown in Figure 1A, once the copper traces were complete (c), the reference electrode (b)was screen-printed using a silver/silver chloride ink (b) (E2412, Ercon, Inc., Wareham, MA) and a custom-made stainless steel mask (DEK USA, San Jose, CA), and subsequently cured at 100 8C for 1 h. Then, the working and counter electrodes were printed using a graphite ink (a) (E3449, Ercon, Inc., Wareham, MA) loaded and mixed with GOx enzyme (X-S from Aspergillus niger, lyophilized powder, 151000 U gm 1 solid, Sigma, St. Louis, MO)", + " The ink mixture was prepared such that the activity of the enzymewas 10000 Ugm 1 of the composite ink. The carbon electrodes were cured at 40 8C for 6 h to remove the solvent and ensure minimal effect upon the enzyme stability. A final layer of insulator was applied and cured for 6 h at 40 8C to complete the process. The enzymemicrosensors were stored at 4 8C until use. A graphite ink without GOx, used for measurements of neurotransmitters biomarkers, was cured at 100 8C for 6 h. The miniature flow-cell sensor was prepared by first soldering three electrical wires (Fig. 1C,f) to the copper junctions. The electrodes were cut out individually andwere rolled into a cylindrical shape (using a custom-made jig) such that the three electrodes were oriented perpendicular to the flow direction (Fig. 1B). The rolled sensor was glued to hold its rolled configuration (using a cyanoacrylate adhesive) and the flow-through tubular sensor was then inserted, using tweezers and under a stereomicroscope, into a polyethylene tube (0.7 mm ID micromedical tubing, Scientific Commodities, Inc., Lake Havasu City, AZ). The wires and copper traces were folded over the outside of the tubing and then coated in an insulating layer.A larger Tygon tubing (1.59 mmID)was placed over the outlet such that the wires were still exposed, while mechanically securing the microsensor during bench top experimentation" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003457_20080706-5-kr-1001.00138-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003457_20080706-5-kr-1001.00138-Figure4-1.png", + "caption": "Fig. 4. Yaw motion.", + "texts": [ + "3881 Pitch motion: The advantage of this configuration is the addition of an extra mass, besides the ones of the rotors, which is placed down enough to provide a weightbased torque, obtaining then, a pendular damped effect (naturally stable), see Fig. 3. To counteract this pendular motion, the rotors tilt parallel (at the same time) in opposite sense of the pitch motion maintaining the upwards position, emulating a mobile pivot, and moreover behaving as damping factor. Yaw motion: The yaw motion is driven via the rotors\u2019 differential tilting generating the required torque to provoke a rotation (see Fig. 4). Let I={iIx , jIy , kI z } denote the right handed inertial frame, B={iBx , jBy , kB z } denotes frame attached to the body\u2019s aircraft whose origin is located at its center of gravity (see Fig. 5). Two auxiliary frames are obtained from the tilting motion. The first tilting, to drive the yaw motion, produces the frames Y1= { iY1 x , jY1 y , kY1 z } and Y2= { iY2 x , jY2 y , kY2 z } . Afterwards, the frame P= { iPx , jPy , kP z } appears at regulating the pitch motion. Let the vector q = (\u03be, \u03b7)T denotes the generalized coordinates where \u03be = (x, y, z)T \u2208 \u211c3 denotes the translation coordinates relative to the inertial frame, and \u03b7 = (\u03c8, \u03b8, \u03c6)T \u2208 \u211c3 describes the vehicle orientation expressed in the classical yaw, pitch and roll angles (Euler angles)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002554_s0956-5663(02)00094-5-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002554_s0956-5663(02)00094-5-Figure1-1.png", + "caption": "Fig. 1. Schematic representation of phenol detection using tyrosinase electrode (a) and H2O2 /HRP-SPCEs (b).", + "texts": [ + " In order to develop enzymatic phenol sensors, various sensor systems have been introduced based on a number of approaches; oxygen consumption during the enzymatic reaction (Campanella et al., 1993), substrate recycling system (Makower et al., 1996) and redox mediators (Gru\u0308ndig et al., 1992). In the presence of tyrosinase, phenol is oxidized to oquinone via catechol by oxygen (Toussaint and Lerch, 1987; Casella et al., 1996). Classically, the enzymatic product, o-quinone, is reduced at low potential (Kulys and Schmid, 1990) and the schematic diagram is shown in Fig. 1a. As can be seen, the dashed line represents the fact that the electrochemical reduction of quinones is incomplete. This is because quinones are highly unstable * Corresponding author. Fax: /44-191-222-6227 E-mail address: calum.mcneil@ncl.ac.uk (C.J. McNeil). 0956-5663/02/$ - see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 5 6 - 5 6 6 3 ( 0 2 ) 0 0 0 9 4 - 5 in water and they easily polymerize to polyaromatic compounds (Horowitz et al., 1970). In spite of this problem, sensors based on this approach have been reported using graphite electrodes and graphite-epoxy based composite electrodes (Ortega et al", + " The present system demonstrates the lack of an absolute requirement for the extraneous addition of H2O2 in a combined tyrosinase/HRP approach to phenol sensing. Unlike previous systems based on HRP (Lindgren et al., 1997) and tyrosinase/HRP (Cosnier and Popescu, 1996), this essential species was electro-generated on the surface of the printed carbon enzyme electrodes employed in this study from dissolved oxygen. Thus, in an important and novel aspect, incorporation of HRP into the carbon ink facilitated catalysis of H2O2 reduction with concomitant rapid oxidation of catechol to o -quinone. A schematic diagram of the overall reaction is shown in Fig. 1b. In line with the previous work of Cosnier (Cosnier and Popescu, 1996), it is suggested that the additional HRP /H2O2 system can improve the electrode sensitivity for phenols compared with using tyrosinase alone as the phenol-sensing element. However, the present system is designed as a single-use, disposable technology and is significantly simpler to prepare and operate. Poly(carbamoylsulfonate) (PCS) hydrogel prepolymers were supplied by SensLab GmbH (Leipzig, Germany) and poly(vinyl alcohol) bearing styrylpyridinium groups (PVA-SbQ) matrix (SPP-H-13) was from Toyo Gosei Kogyo Co" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002542_j.mechmachtheory.2004.07.013-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002542_j.mechmachtheory.2004.07.013-Figure2-1.png", + "caption": "Fig. 2. The patient positioning system.", + "texts": [ + " The manipulator is used as a high accuracy robotic patient positioning system (PPS) in a proton therapy research facility constructed at the Massachusetts General Hospital (MGH), the Northeast Proton Therapy Center (NPTC) [2,19]. The robotic PPS places a patient in a high energy proton beam delivered from a proton nozzle carried by a rotating gantry structure (see Fig. 1). The PPS is a six degree of freedom manipulator that covers a large workspace of more than 4m in radius while carrying patients weighing as much as 300 lbs (see Fig. 2). Patients are immobilized on a \u2018\u2018couch\u2019\u2019 attached to the PPS end-effector. The PPS, combined with the rotating gantry that carries the proton beam, enables the beam to enter the patient from any direction, while avoiding the gantry structure. Hence flexibility offered by robotic technology is needed. The required absolute positioning accuracy of the PPS is \u00b10.5mm. This accuracy is critical as larger errors may be dangerous to the patient [20]. The required accuracy is roughly 10 4 of the nominal dimension of system workspace, which is a greater relative accuracy than most industrial manipulators", + " If redundant parameters are introduced after the error model expansion (which can be verified from the condition number of the pseudoinverse of the Identification Jacobian), then classical numerical methods can be applied to eliminate them. An advantage of the polynomial approximation is the modeling of non-linear elasticity, through terms with order higher than three, as well as considering a general formulation for geometric errors that are allowed to vary in their own frames such as in the case of rail curvature. In the next section, the geometric and elastic compensation method is applied to the patient positioning system. The PPS is a six degree of freedom robot manipulator (see Fig. 2) built by General Atomics [2]. The first three joints are prismatic, with maximum travel of 225cm, 56cm and 147cm for the lateral (X), vertical (Y) and longitudinal (Z) axes, respectively. The last three joints are revolute joints. The first joint rotates parallel to the vertical (Y) axis and can rotate \u00b190 . The last two joints are used for small corrections around an axis of rotation parallel to the Z (roll) and X (pitch) axes, and have a maximum rotation angle of \u00b13 . The manipulator end-effector is a couch, supporting the patient in a supine position, accommodating patients up to 188cm in height and 300lbs in weight in normal operation. The intersection point of the proton beam with the gantry axis of rotation is called the system isocenter. The treatment volume is defined by a treatment area on the couch of 50cm \u00b7 50cm and a height of 40cm (see Fig. 2). This area covers all possible locations of treatment points (i.e. tumor locations at a patient). The objective is that the PPS makes any point in this volume be coincident with the isocenter at any orientation. The joint parameters of the PPS are the displacements d1, d2, d3 of the three prismatic joints and the rotations h, a, b of the three rotational joints. A 6-axis force/torque sensor is placed between the couch and the last joint. By measuring the forces and moment at this point, it is possible to calculate the patient weight and the coordinates of the patient center of gravity", + " From the system kinematic model with no errors, the ideal coordinates of NTP were calculated and subtracted from the experimentally measured values to yield the vector DX(q,w). Four hundred and fifty measurements were used to evaluate the basic uncompensated accuracy of the PPS and the accuracy of the compensation method described above. Two different payloads were used: one with no weight and another with a 154 lb weight at the center of the treatment area. The PPS configurations used were grouped into two sets: Set (a) Treatment volume. The eight vertices of the treatment volume (see Fig. 2) are reached with the NTP with angle h taking values from 90 to 90 with a step of 30 , for a total of 112 configurations. Set (b) Independent motion of each axis. Each axis is moved independently while all other axes are held at the home (zero) values. The step of motion for d1 is 50mm, for d2 20mm, for d3 25mm and for h 5 , resulting in 338 configurations. The PPS uncompensated accuracy combining the two sets is shown in Fig. 7. The data points represent the positioning errors of NTP. It is clearly seen that in spite of the high quality of the PPS physical system, its uncompensated accuracy is on the order of 10mm" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure33.10-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure33.10-1.png", + "caption": "Fig. 33.10 Prototype of ultrasonic micro motor with foil type stator", + "texts": [ + "9 (b), the vibration draws an elliptical motion at any point of surface, however, it saturates and decays with thinner foil such as less than 50 m taking the amplitude of vibration into account. The rotor rotates in the same direction of propagation of the progressive wave because the frictional force which is induced by expansion of stator by the ultrasonic wave becomes larger than the frictional force which is induced by the elliptical locus of ultrasonic wave. 394 A prototype of ultrasonic micro motor with 2.7 mm outer diameter and 9.1 mm length has been developed as shown in Fig.33.10. It consists of a rotor, a stator (foil made coil), a case and a stopper, each size of which is shown in Table 33.4. The arm has 1.0 m length. The rotor is so placed around the stator as to fit smoothely between them adjusting the outer diameter of stator with the inner diameter of rotor. The rotor is covered with a cylindrical case and supported axially and radially by fitting one end of the case with the stopper. The foil and case are made of stainless steel and TI polymer respectively in order to give enough heat and wear resistance" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003156_robot.1986.1087680-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003156_robot.1986.1087680-Figure3-1.png", + "caption": "Figure 3. The TH8 Robot", + "texts": [], + "surrounding_texts": [ + "V I . APPLICATION AND CONCRETE EXAMPLE\nThe algori thm presented previously has been programmed i n o r d e r t o o b t a i n a u t o m a t i c a l l y t h e dynamic model of robots composed of open chahn r ig id bodies . For a genera l robot of n r o t a t i o n a l j o i n t s the maximum on-line computation complexity of the model is given by( 105n-92) mul t ip l i ca t ions and (94n-86) addi t ions ( o r s u b s t r a c t i o n s ) , i .e f o r n=6 w e have 538 multiplications and 478 addi t ions . For a r e a l r o b o t , t h e number of operat ions w i l l be reduced considerably, for example for the Stanford manipulator (SM) ,Fig. 1, wi th no iner t ia l parameters equal zero , the number of operat ions i s e q u a l t o 301 mul t ip l i ca t ions and 295 addi t ions . A s tudy of the poss ib le regrouping and el iminat ion of i n e r t i a l parameters as g i v e n i n s e c t i o n 3 w i l l reduce more t h e number of operat ions, f o r t h e SM the number of operations w i l l become 247 mul t ip l i ca t ions and 230 a d d i t i o n s . I n a d d i t i o n i f some elements o f t he ine r t i a l pa rame te r s are supposed equa l t o zero because of the geometry of t h e l i n k s , t h e number of the operat ions w i l l be reduced. A s an example i f w e s imp l i fy the S M parameters such t h a t MXi (i=l,. . .,5)=MZ2 = My3 = MY5=0 and '2 (i=l, . .5) is diagonal (this s i m p l i f i c a t i o n chresponds t o the d a t a g i v e n i n [18]),while 6 J 6 , 6 E 6 , become 187 mul t ip l i ca t ions and 152 addi t ions . - n7, 1 7 a re gene ra l , t he number of opera t ions w i l l\nTable 1\nV I I . CONCLUSION\nTh i s pape r p re sen t s an e f f i c i en t method fo r so iv ing the inverse dynamic problem of robots. The method g ives a model which makes it p o s s i b l e f o r c o n t r o l purpose i n r e a l time. The number of operat ions of our model are t h e least of a l l t h e methods presented till now, t a b l e (1) . A Fortran program has been developed t o g i v e a u t o m a t i c a l l y t h e model of any robot cons i s t ing o f open c h a i n r i g i d l i n k s . The method is based on a NEWTON-EULER fo rmula t ion l i nea r i n t h e iner t ia l parameters and on an i terat ive symbolic technique. Thus the obtained model takes the advantages of the r a p i d i t y o f numerical i t e r a t ive me thods , and those of symbolical methods i n t a k i n g i n t o acc o u n t t h e p a r t i c u l a r i t y of each robot.\nAn approach t o condensate the l i n k s i n e r t i a l p a r a - meters i n o r d e r t o o b t a i n t h e i r minimum number i s presented. The conaensation process is carried out by the use o f t he ine r t i a ma t r ix and the g rav i ty force vector of an expanded LAGRANGE model. The condensat ion of the parameters ha5 been used in reducing the ope ra t ion counts of the NEWTON-EULER model.\nI\nGeneral robot Stanford manipulatoi METHOD\nn D.0 . f s i m p l i f i e d genera l n=6\nMu1 t.\n595 595 595 lOln - 11 AddiSub.\n800 800 800 137n - 22 Luh 181\nI.., Megahed [ 101 1667 12n 5 3 +lln2+2$ n-78 Mult.\nAddjSub. g n 3 + 8n +T n-73 1330\nMu1 t .\n646 646 Mult.\n194 302 475 94n - 09 Add/ Sub.\n229 314 538 105n - 92\nAdddS ub . 394 394\nMu1 t .\n2 647 ? ?\nKhalil [14]\nKane [ I 1 1 no t g iven ?\n.,., ,.,. Renaud [ 12 1 AddjSub. not given ? ? ?\nHorak 1201 Add./sub. Mult.\nno t g iven ? 36 1 256 ?\nwithout\n94n - 86 Add/Sub. regroup. given the\n2 26 301 538 105n - 92 Mult.\n152 230 478 94n - 86 AddiSub. r e g r o q I...rll 187 247 530 10Sn - 92 Mult. methodwith\n2 10 295 478\n..., I, - s i m p l i f i e d means t h a t J . (i=l,...,S) is diagonal, rnS.(i=l,..,,S) has only one non-zero component, while 626, 6 e 6 , n7, 2 7 are general .\ni i =1 .,., ,.,. i n t h i s m e t h o d t h g f o r c e s a n d moments exe r t ed by l i nk n upon e x t e r n a l o b j e c t are not taken into account .\ne.,.,. the corresponding models can be found in [ Z l ] . ... 4.1 ? t h e numbersof operat ions of these cases a r e n o t a v a i l a b l e f o r us .", + "REFERENCES\n[ l ] A.K. Bejczy, Robot Arm Dynamics and Control: NASA Technical Memorandum 33-669, Jet Propuls ion Labora tory , Cal i forn ia Ins t i tu te of Technology, Pasadena, CA ; 1974. [ 21 R. Paul , \"Advanced I n d u s t r i a l Robot Control Systems': School of Electrical Engineering, Purdue Univers i ty , TR-EE-78-25, West Lafaye t te , I.N.,1978. [3] M.K. Ra iber t , B.K.P. Horn,'Manipulator control using the conf igura t ion space method!' The I n d u s t r i a l Robot, vol. 5, no 2 , 1978, pp. 69-73. [4] W. K h a l i l , A. Liegeois , A. Fournier , Commande Dynamique de Robots'! RAIRO Automatique, Systems Analysis and Control, vol. 13, no 2, 1979, pp. 189- 201. [5 ] C.S.G. Lee, M . J . Chung, An adap t ive con t ro l s t ra t igy for mechanical manipulators ' : IEEE Transact ion on Automatic control , vol . AC-29, no 9, September 1984, pp. 837-840. 161 V.D. Tourass i s , C.P. Neuman,'Robust Nonlinear Feedback Control for Robotic Manipulators'! IEE Proceedings, vol. 132, Pt . D, no 4 , j u ly 1985,\n[ 7 ] J.J. Uicker,\"On t h e Dynamic Analys is of spa t ia l l inkages us ing 4x4 matr ices? Ph. D. Thesis , Northwestern University, 1965. [8] J . Y . S . Luh, M.W. Walker, R. Paul, On-line Computational scheme for mechanical manipulators:) ASME Transact ion, J. of Dynamic Systems, Measurements and Control, vol. 102, no 2, 1980, pp.69-76. [g] J . M . Hollerbach,\"A recursive formulation of manipulators dynamics and a comparative study of dynamics formulation complexity: IEEE, Transact ion on Systems, man and cybernetics, vol. 10, no 11,\n[ 101 S. Megahed,('Contribution d l a model isat ion geomdtrique e t dynamique des robots rnanipulateurs d st ructure de chaine cindmatique s imple ou complexe, Applicat ions Z l eu r connnande:' Doct. d ' E t a t Thesis, Toulouse, 1984, France.\n(I I\n6\nt\npp. 134-143.\nU\n1980, pp. 730-736.\n[ 1 1 ] T.R. K a n e , D. Levinson, The use of Kane's Dynamica1 Equat ions in Robotics:' The i n t e r n a t i o n a l j o u r - nal of Robotics Research, vol. 2, no 3, 1983,pp.3-21. [ I 2 1 M. Renaud,\"A near Minimum I t e r a t i v e A n a l y t i c a l procedure for obtaining a robot-manipulator Dynamic rnodel'!IUTAM/IFT.MM Symposium on Dynamics of Multibody Systems, Udine, 1985. [13] T. Kanade, P. Khosla and N. Tanaka, Real-Time Control of CMU Direct-Drive Arm I1 Using Customized inverse dynamics:) Proceeding of 23rd CDC L a s Vegas, 1984. [14] W. Khal i l , J.F. Kleinfinger: Une model isat ion performante pour l a commande dynamique de robots:' RAIRO P P I I , France, v01.6, 1985. [15] J. Denavit, R.S. Hartenberg,(lA kinematic notat i on fo r l ower -pa i r mechanism based on matrices:' Journa l of appl ied mechanism, vo1.22,1955,pp.215-221. [16] W. K h a l i l , M. Gaut ier ,\"On the Derivat ion of the Dynamic Models of Robots': Proceeding of ICAR,Tokyo, Japan, 1985, pp- 243-250. [ 1 7 ] W. K h l i l , M. Gaut ier , J .F. Kleinf inger , Automatic Generation of I d e n t i f i c a t i o n Models of Robots, I I Journal of Robotics and Automation IASTED, vol. 1, no 1, 1985. [ 1 81 R. Paul, Robots manipulators :\"mathematics, programming and control': MIT Press , 1981. [ 191 E.P. Fer re i ra , \"Cont r ibu t ion d 1 ' I d e n t i f i c a t i o n de parametres e t d l a Commande Dynamique Adaptative de Robots Manipulateurs, Doct.Ing.Thesis,Toulouse, 1984, France. tr [20] D.T. Horak, A fast computational scheme f o r dynamic control of manipulators: American Control Conference, 1984, pp. 625-630. [21] J.F. Kleinfinger,\"Mod6lisation dynamique de robots .3 chaine cinematique ouverte, arborescente ou fermee en vue de leur commande'i Doctorat Thesis , Nantes , May 1986, France..\nII\nLt\n(1\n53 I" + ] + }, + { + "image_filename": "designv10_6_0000209_j.jmst.2021.03.008-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000209_j.jmst.2021.03.008-Figure1-1.png", + "caption": "Fig. 1. Schematic diagram of the DED process.", + "texts": [ + " The interfacial morphology, microstructure, and element istribution between steel and copper alloy are revealed in deail. The mechanism of crack formation is discussed. Furthermore, he strength of both the vertically and horizontally combined coper/steel bimetal is investigated. This paper advances the undertanding of the interfacial characteristics of heterogeneous mateials and provides guidance and reference for the fabrication of ulti-material components by DED. C The DED machine used is illustrated in Fig. 1 . The system ainly consists of a 6 kW continuous-wave IPG YLR-60 0 0 fiber aser (\u03bb = 1 . 06 \u03bcm ) , a 6-axis robot (KUKA), a powder feeder HUST-III), and a self-made laser head. The movement of the laser ead along the X-Y plane and the raise of Z direction is controlled ia a 6-axis robot. The argon shielding gas is used to protect the eposition from oxidation. Details about the DED system have also een described previously [30] . Self-developed martensite stainless steel (07Cr15Ni5) powder as used as the starting material" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure16.10-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure16.10-1.png", + "caption": "Fig. 16.10 Turning in open space by twisting the root", + "texts": [ + " Therefore, the strategy in narrow gaps, where the moving head guides the direction to follow walls, cannot be applied. The active scope camera turns by itself when the top part is gradually curved, because slant driving force is applied. Because stiffness of the cable in the twisting (roll) direction is high, the top part makes roll motion when the root is twisted manually. Then it changes the direction of the gradual curve of the top part, and turns. Therefore, control of the twisting angle enables the scope camera change the direction in open space as shown in Figure 16.10. The turning capability in open space without the side wall was evaluated by the minimum turning radius. The minimum turning radius was about 1 m when the ground was a flat linoleum-covered floor. Hence, the active scope camera can change the direction of motion even if there is no side wall to follow. 186 Masashi KONYO and Satoshi TADOKORO The height of bump that the active scope camera could get over was measured. The bump was made of a wood block, and the running surface was a linoleumcovered floor" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000500_j.matlet.2021.130508-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000500_j.matlet.2021.130508-Figure2-1.png", + "caption": "Fig. 2. Fiber optic biosensor based on GO-coated LPFG (a) LPFG surface with hydroxylation treatment (b) GO deposition (c) EDC/NHS-treated (d) GOD-immobilized LPFG [15].", + "texts": [], + "surrounding_texts": [ + "Diabetes is considered as the third most frequently encountered incurable chronic disease affecting the lives of millions of the peoples all over the World and the number is raising day by day. It is generally caused by the increase in sugar level in human body fluids i.e. blood, tear, urine, serum etc., which ultimately leads to heart, kidney, eye problems etc. This can only be avoided by proper treatments and routine diagnosis. Conventional diagnosis of glucose is time consuming and costly, therefore it is the quest of the time to develop a low cost, rapid and reliable glucose sensor with high selectivity and sensitivity [1\u20135]. Discovery of graphene as nanomaterial has spectacularly accelerated the direction of research. Due to its honey comb like structure with extra high surface area, it has vast range of applications in all sectors. Fabrication of graphene or its functionalised form (graphene doped with metal/metal oxide NPs/conducting polymer like chitosan) over the electrode enhances the electrochemical properties of the electrode and hence makes the detection process faster. Researchers throughout the globe have prepared an enormous number of enzymatic or noneznymatic nanocomposites and used it for the fabrication of electrode of choice for monitoring of glucose. Nanofabrication is cost-effective, less toxic and provides fast response with LOD. In addition to that it also increases the biocompatibility, hydrophility, reproducibility and reusability of the biosensor [6\u201310]. This short review addresses the achievements made by both enzymatic and non-enzymatic graphene nanocomposites to prepare various nanobiosensors including electrochemical, optical and fluorogenic for the detection of glucose level in human body fluids (Figs. 1\u20137) [14]." + ] + }, + { + "image_filename": "designv10_6_0000279_j.cja.2021.05.010-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000279_j.cja.2021.05.010-Figure1-1.png", + "caption": "Fig. 1 Model of vertical take-off and landing fixed-wing UAV.", + "texts": [ + " Simulation and comparison are conducted to demonstrate the effectiveness of the designed controller and the algorithm. The conclusion is drawn in Section 6. The vertical take-off and landing fixed-wing UAV is modeled as a six-degree-of-freedom dynamics. 30 It is supposed that the hybrid UAV is a rigid body with mass m and the products of inertia Ixy = Iyz = 0. [x, y, h, u, h, w] is in the inertial frame Og-xgygzg fixed to the ground. [u, v, w, p, q, r] is described in the body frame Ob-xbybzb attached to the center of mass. The platform and the frames are shown in Fig. 1. The transition primarily takes place in the longitudinal motion, and the corresponding dynamics is shown in detail as follows: _u \u00bc vr wq gsinh\u00fe Fx m _w \u00bc uq vp\u00fe gcoshcosu\u00fe Fz m _q \u00bc Iz Ix Iy pr Ixz Iy p2 r2\u00f0 \u00de \u00fe M Iy 8>< >: \u00f01\u00de where Fx and Fz are the forces along the xb and zb axes, respectively; M is the pitch moment, including torques created by both rotors and wings. The angular kinematic equation of the motion is optimization approach to active disturbance rejection control parameters tuning oi" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002697_1.2801147-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002697_1.2801147-Figure1-1.png", + "caption": "Fig. 1 Spatial six-degree-of-freedom parallel manipulator", + "texts": [ + " Indeed, because of the parallel mechanical architec ture, exact parallel algorithms can be derived which do not require any iterative procedure. It is shown that this formulation leads directly to practical implementations with one processor for each of the subchains connecting the platform to the base of the manipulator. Examples of application of this novel ap proach to planar and spatial parallel manipulators are then pre sented. 2 Inverse Kinematic Problem A spatial six-degree-of-freedom parallel manipulator is repre sented schematically in Fig. 1. It consists of a base Aj ... Ae and a platform Bi . . . Bf, which are connected via 6 legs or kinematic chains. Each of the legs is attached to the base through a Hooke or Cardan joint and to the platform by a spherical joint. Moreover, each of the legs comprises an actuated prismatic joint which controls the length of the leg. All the other joints are unactuated. Globally, the mechanism has six degrees of freedom which allows the positioning and orientation of the platform arbitrarily with respect to the base", + " Furthermore, the position of the joints on the base\u2014points A, \u2014 are denoted by vectors a,, / = 1, . . . , 6 and the position of the joints on the platform\u2014points iS,\u2014by vectors b, , / = 1, . . . , 6. Vectors a, are constant when expressed in frame 'R while vectors b, are constant when expressed in frame 'B'. Finally, let vector r = [r,, r,, r j ^ denote the position of point O' with respect to point O expressed in frame \"R and let Q be the matrix representing the rotation from frame \"R to frame 'R'. From Fig. 1, one can write: [b,]\u00ab = [r]\u00ab + Q[b,.]\u00ab., i = l, (1) Contributed by the Dynamic Systems and Control Division for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received by the DSCD July 7, 1994; revised manuscript received January 5, 1995. Associate Technical Editor: B. Siciliano. where the index outside the square brackets indicates the refer ence frame in which a vector is expressed. Subtracting vector B; from Eq. (1) , one obtains [b,. - a,L = [r]\u00ab + Q[b,]\u00ab", + " It is re called that this does not include some kinematic computations that would be necessary to obtain the acceleration of the mass center of each of the links. These computations, which are required in both the serial and the parallel implementation, can also be easily parallelized. This would increase the gain in computation time provided by the parallel algorithm. 4.2 Spatial Six-Degree-of-Freedom Parallel Manipula tor. The computational complexity of the algorithm will now be discussed for the general case of a spatial six-degree-offreedom parallel manipulator such as the one described in Sec tions 2 and 3 and represented in Fig. 1. 4.2.1 Inverse Kinematics. The inverse kinematics is paral lelized using the procedure presented in Section 2.1. The com putation of the joint variables is performed according to Eq. (4). This requires 12 multiplications, 14 additions and one square root per processor. Then, the evaluation of each row of the Jacobian matrix requires 18 multiplications and 9 additions, considering that some of the quantities needed have already been computed in the inverse kinematics procedure. Finally, the computation of one row of the derivative of the Jacobian matrix requires 48 multiplications and 24 additions" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003319_1.2194037-Figure11-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003319_1.2194037-Figure11-1.png", + "caption": "Fig. 11 Schematic of the experimental setup for double-pass single layer LADMD process", + "texts": [ + " Consequently, the local solidification time tf, which is the ratio of the difference between liquidus and solidus temperatures to the local solidification velocity, also changes with a similar trend. For the mild steel and tool steel materials, average solidus and liquidus temperatures used were 1703 and 1733 K, respectively. 5.1 Experimental Setup. The simulation program for doublepass four-layer laser aided DMD was verified with the experimen- tal results for temperature, residual stress, and microstructure. For rom: http://heattransfer.asmedigitalcollection.asme.org/ on 01/28/2016 Te temperature measurements, as shown in Fig. 11, three thermocouples were spark-welded at points a, b, and c. The metal deposition started at a distance of 0.008317 m from the front edge as seen in the figure through a total length of 0.03556 m. The substrate plate dimensions and the locations of points a, b, and c on it are shown in the figure. The material for the substrate was mild steel while the deposited metal was H13 tool steel. CO2 type cw Gaussian laser beam with a traverse speed of 12.7 mm/s was chosen. The nominal laser power used was approximately 680 W, while the beam diameter and the stand-off distance were 1 and 8 mm, respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000326_j.mechmachtheory.2021.104264-Figure16-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000326_j.mechmachtheory.2021.104264-Figure16-1.png", + "caption": "Fig. 16. Planetary gear (a) vibration shape and (b) ring gear elastic-body nodal diameter components of the first cluster 3 mode, 3198 Hz (number 17), from FE/CM simulation.", + "texts": [ + " The FRF shows a dominant peak in the 3500 Hz mode (number 18). According to [54] , this is a rotational mode and [37] analytically predicts the three nodal diameter component for this mode type. It is likely that the 3500 Hz mode is captured accurately but is affecting the results for the 3410 Hz mode that has lower vibration amplitude. The FRF from the FE/CM model in Fig. 10 shows better spacing between modes 17 and 18 in cluster 3. As a result, the vibration shape for mode 17 is distinct from mode 18 in computer simulation results. Fig. 16 shows the vibration shape in this first cluster 3 mode and the relative amplitude of its nodal diameter components. This is a translational mode from [54] , and [37] analytically predicts the four nodal diameter component for this mode, agreeing with the FE/CM results in Fig. 16 . We see that experiments and the FE/CM model show moderate elastic-body ring gear deformation in all three gear mode clusters that were previously thought to be exclusively discrete-body modes containing no elastic continuum deformation. Natural frequencies and vibration amplitudes agree well between the experiments and FE/CM model. The deformed ring gear shapes differ in some cases, likely due to inter-modal interference or because FE/CM model approximations do not capture some details of the experimental setup" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003815_j.mechmachtheory.2009.06.001-Figure5-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003815_j.mechmachtheory.2009.06.001-Figure5-1.png", + "caption": "Fig. 5. Class IV of X-motion generators.", + "texts": [ + " When only one P pair for each of the generators shown in Fig. 4 is replaced by one hinged parallelogram, Figs. 9 and 10 are readily obtained. Here, we must notice that the four generators, (III9) PRRPa, (III11) PHHPa, (III12) HPPaH and (III14) RPPaR in Fig. 10 are cancelled out because they have architectures that are equivalent by kinematic inversions to chains shown in Fig. 9. PaPaRHIII1( ) ( III2 PaPaRR) PaPaHH)III3( Figs. 11\u201313 are generators of X-motion obtained by the replacement of the two P pairs in chains of Fig. 5 by two hinged parallelograms. Likewise, Figs. 14\u201316 are X-motion generators derived by replacing only one P pair in each generator of Fig. 5 with one hinged parallelogram. That way, we obtain a total of eighty-two chains having at least one parallelogram, noticing that the kinematic inversion of each of these foregoing chains is also an adequate chain for generating X-motion. 4. Defective X-motion generators A defective chain for generating X-motion arises from the permanent singularity of the chain. Then the chain does never generate the desired X-motion. Such a phenomenon is not properly a singularity. As a matter of fact, singular means specific of special poses of the chain" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000550_s00170-021-06818-9-Figure17-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000550_s00170-021-06818-9-Figure17-1.png", + "caption": "Fig. 17 Schematics of hatch spacings showing theoretical conditions of a 0.02mm overlap, b 0 mm overlap, c 0.02mm offset, and d 0.04mm offset", + "texts": [ + "1 mm created a clear overlap between neighboring scan tracks. It is noteworthy that although neighboring tracks might just be touchingwith 0.1 mm hatch spacing, the changes in the geometry and behavior of the melt pool due to increased energy input can, however, cause an overlap of adjacent tracks. The overlap is most pronounced when the width of the melt pool is larger for high-energy input, which leads to more molten metal powder [36]. In this case, hatch spacing of 0.08 mm and 0.10 mm fall into the same category as shown in Fig. 17a and b. Overlapping tracks create denser parts, as all the powders get irradiated creating a better fusion build and as such, there is less chance of creating unmelted areas between tracks. This is the main reason samples with low hatch spacing do not require extreme laser power to create a fully consolidated part. For the G1C2\u2013G2B1 combination, the hatch spacing of 0.08 mm as well as 0.10 mm created overlapping tracks for a better fusion of powder particles andmore dense parts; this is the reason why samples with better overlap have lower porosities and generally higher densities", + " This is because the pores or cracks are filled with unmelted powders that do not entirely form part of the structure but are registered in determining the mass of the part [37]. The buoyancy of porous parts can also affect the final density calculation, which requires that the sample pores be covered so that the bubbles emitted from them do not affect the weight in water. According to the ASTM standard B962-17, this step can be skipped if no observable bubbles are present when the sample is immersed in water. High hatch spacings, as seen in Fig. 17c and d, warrant the use of high laser power or slower scanning speeds (more dwell time) to give sufficient energy to melt the powders as well as to create a larger melt pool for a more consolidated part that will register low porosities. However, concentrating too much laser energy in a localized area leads to vaporization of metal powder particles as well as the introduction of gas-filled pores, which will ultimately lead to a lower-density part. For samples with a higher hatch spacing, either the laser power needs to be increased considerably or a reduction of scanning speed (more dwell time) is required to deliver enough energy to the powder to achieve a similar level of porosity", + " Also, sample G1C2 showed the presence of a keyhole crack with a high aspect ratio that cut through grain boundaries (Fig. 15a); however, increasing the hatching space introduced LOF cracks that were connected (Fig. 15b). Increasing the laser power eliminated the LOF cracks seen in the sample, but at the same time, were microcracks formed on the grain boundary as well as within the grains themselves (Fig. 16). Crack formations were attributed to either lowVED or high VED values. On one hand, cracks formed as a result of low VED ranges are formed when LOF pores align usually within hatch spacings (Fig. 17). On the other hand, parts with high VED values had cracks that are usually formed as a result of residual stress due to the vast thermal gradient that the printing process introduced into parts during printing. These types of cracks were formed along the grain or melt pool boundaries because these were high-energy regions. These reasons contributed to higher hardness values observed in samples within the 44.44 and 111.11 J/mm3, while samples on the extreme ends of that spectrum showed lower hardness values" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure2.11-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure2.11-1.png", + "caption": "Fig. 2.11. Linear virtual displacement", + "texts": [ + "48) 40 where the expression in square brackets represents the vector box pro duct. Now the total work of gravity forces, according to (2.3.44), (2.3.48), is equal to and the total work of active forces, according to (2.3.43), (2.3.49), is oA (2.3.50) Now, by definition, the generalized force is Q~rot) 1 M ~ [+ + +(i)] Pi + k:imk g, e i , r k (2.3.51 ) where ;~i) is given by (2.3.46). Let us now consider a linear joint S., and let us allow the linear coJ ordinate qj to have a virtual displacement oqj' keeping all other coordinates constant (Fig. 2.11). Over that displacement the work will be done by the driving force pF and the gravity forces of segments J j, j + 1, ... ,no For driving force (2.3.52) 41 Note that with the linear virtual displacement the whole part of chain (from Sj to the free end) is moved linearly by O;j ~jOqj (Fig. 2.11). Thus, the work of gravity is ->- ->- n e . g ( I mk )\u00b7 0 q . J k=j J By (2.3.52) and (2.3.53) the total work is By definition the generalized force is Q ~transl) J F -+ -+ n P. + e.g I mk J J k=j (2.3.53) (2.3.54 ) (2.3.55 ) By considering expressions (2.3.51) and (2.3.55), it may be noted that the expressions for generalized forces may be written in the form Q P + y (2.3.56 ) where P is the drives vector given by (2.3.4c) and Y is a vector given as Y s.=O l s.=1 l and that Y is calculated independently of P" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003676_tro.2006.886276-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003676_tro.2006.886276-Figure1-1.png", + "caption": "Fig. 1. Three-joint robot leg on the right side with reference frames and the corresponding Denavit\u2013Hartenberg link parameters.", + "texts": [ + " The legs in protraction are assumed to have predetermined tip-point trajectories with respect to the robot body [5]. The legs in retraction are assumed to be supporting the body without any slippage on their tip points. Therefore, they also follow a predetermined trajectory with respect to the robot body. Those legs on the ground are assumed to have hard-point contact with friction, which indicates that the interaction between the tip of the leg and the ground is limited to three components of force, one normal and two tangential to the surface [12]. A. Kinematics of a Single Three-Joint Leg In Fig. 1, a graphical representation of a three-joint robot leg on the right side of the robot body is given, with the attached reference frames, corresponding joint variables, and the corresponding Denavit\u2013Hartenberg link parameters [9]. In this figure, the body (b) and the zeroth reference frames are attached to the robot body. The value of the angle between the third axes of the body and zeroth frames is 45 . The ground frame (g) is attached to the ground as the inertial frame. The resulting transformation matrices between the frames are given in (1) and (2), shown at the bottom of the next page" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure3.33-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure3.33-1.png", + "caption": "Fig. 3.33. Grinding task", + "texts": [ + "37) is prescribed and we can solve the nominal dynamics. This calculation of nominal dynamics also includes the time interval T1 in which the pencil is moving towards the surface. We prescribe this motion so as to avoid impact. When the perturbed motion is considered, the pencil comes to the sur face and the terminal state of T1 does not satisfy the surface con straint. The impact appears and we solve it by using the theory from Para. 3.5.1 (eq. 3.5.10 or 3.5.12). Thus obtaining the initial condi- 223 Grinding task. Fig. 3.33a,b shows the task of fine grinding. A moving surface results in relative velocity and friction force F f . In the case (a) a plane surface is considered. It rotates as shown in the figure. But, in practice this is not an ideal plane and the rota tion axis is not exactly perpendicular to the plane. Thus, the motion of the surface is not a simple rotation (Fig. 3.34). The reaction and, accordingly, the friction are not constant and produce vibrations of the working object (and the gripper). 224 In the case shown in Fig. 3.33b the cylindrical surface is considered. Rotation is not ideal since it is not an ideal cylinder (Fig. 3.35a) and the rotation axis is not in the exact center of the circle. For this reason the reaction is not constant and vibrations of the working object appear. All these effects can be included in the calcu lation. But, there are some effects which can not be taken into account. These are high frequency vibrations due to grains of grinding wheel. Thus, this calculation of grinding dynamics is approximative" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002692_02783649922066394-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002692_02783649922066394-Figure3-1.png", + "caption": "Fig. 3. Projection of configuration space C onto the space of leg-lengths L, with C folding back on itself. The branch locus is the projection of the fold set. The figure depicts the family of configuration spaces foliating the space 8, and \u22020 \u2202\u03b8 as an oriented volume (here a vector) pointing upward on an upward-facing region of C.", + "texts": [ + " As pointed out by Hunt and McAree (1998), the conclusion that special configurations coincide with coalesced assemblies also follows from Schoenflies\u2019s work (1886, ch. 3, sect. 3), where the perspective is that of screw geometry. We leave it to the reader to reconcile one view with the other. Consider the projection of C onto the space of leg-lengths L, \u03c0 : L \u00d7 \u03b8 7\u2192 L, noting that pre-images of this map for given leg lengths are the solutions to the forward kinematics. Here we want to view the projection geometrically, as in Figure 3. The resulting bifurcation set corresponds to critical leg-rod lengths where the number of ways of assembling the platform changes or branches, either increasing or decreasing by two (or some multiple of two) as pairs of solutions go from being complex to real and vice versa, consistent with eq. (14). We call the locus of critical leg lengths the branch locus. Leg lengths on the branch locus have some or all of their assembles coalesced, and these coalesced assemblies are, by the arguments of Section 4, necessarily special configurations. The structure of C is locally linear at regular configurations, consistent with eq. (7). At first-order special configurations, it is locally quadratic, consistent with eq. (14), folding back on itself. For both devices these fold sets have codimension 1 in C, as does the depiction of the fold of Figure 3. It is standard to interpret a matrix determinant as the oriented volume defined by the rows of the matrix, with the sign giving orientation; see for instance the work of Strang (1988, sect. 4.1). The row space of \u22020 \u2202\u03b8 is complementary to C, and gives the rate at which the platform triangle distorts as the angles \u03b8 are altered. On an upward-facing region, e.g., atP \u2032, the volume defined by the rows of \u22020 \u2202\u03b8 is directed upward, the de- terminant being positive. On a downward-facing region, e.g., at P \u2032\u2032, \u22020 \u2202\u03b8 is oriented downward, the determinant there being negative", + " Should three assemblies coalesce, the linkage relies on thirdorder constraints and the propensity to wobble, now cubic, is much greater. If double coalescence is intolerable because the linkage structure is too poorly conditioned to be useful, triple coalescence is more so. This argues that triply coalesced assemblies are pernicious and best avoided, or better still, \u201cdesigned out\u201d by judicious dimensioning. Figure 4 provides a more fundamental interpretation of triple coalescence and suggests why it gives a sufficient prerequisite for never-special motions. Here the fold of Figure 3 has been folded. When C (the configuration space) is projected into leg space, the branch locus cusps at the point P . Points inside the cusp, e.g., A\u2032, have three local pre-images (assemblies) inC; points outside it have one; and atP the three assemblies coalesce. This \u201cfolding of the fold set\u201d is known as a cusp-type singularity (Poston and Stewart 1978; Bruce and Giblin 1992), and eq. (24) amounts to a crude form of the versal unfolding of this singularity. By diffeomorphism, eq. (24) could be brought into model form (for instance, see Bruce and Giblin\u2019s work (1992)), although we do not pursue this here" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure25.2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure25.2-1.png", + "caption": "Fig. 25.2 Experimental apparatus", + "texts": [ + " The material of the transducer is piezoelectric single crystal and very brittle. In the contact with the silicon slider under the friction drive, the material was easy to wear out. Moreover, the silicon projections enhance the wear. As a result, lifetime of the motor was reduced. To solve this problem, the S-DLC films were expected to avoid the wear in the friction surface. Segment-Structured Diamond-Like Carbon Films Application 293 For the following experiments, new experimental apparatus was fabricated. Figure 25.2 is a photograph of the apparatus. In this apparatus, the LiNbO3 transducer was guided by a linear guide. The slider was fixed on a preload mechanism. The moving part of the motor is called \u201cmoving table\u201d. For standardization the name in our research, the slider is called \u201cslider\u201d, though it was fixed. The preload mechanism consisted of the half of a steel ball, a ring and a plate spring, as illustrated in the figure. The couple of the ball and the ring kept the slider parallel to the transducer surface" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002407_1.1344898-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002407_1.1344898-Figure3-1.png", + "caption": "Fig. 3 Arrangement of the laser scanner for geometry profile measurement", + "texts": [ + " The green laser wavelength is selected to optimize the stripe contrast to the red-near infrared radiation of the hot material surface. The laser stripe is shed across the deposited bead, and trails at d517 mm distance behind the torch, from which it is separated by a tungsten-incandescent cloth partition in contact with the moving part surface, to minimize light interference from the arc. The deflections of this laser line as it intercepts the deposited material reflect the geometric profile Z(y) of the latter ~Fig. 3!, and are monitored by an optical CCD camera with a narrow band-pass filter at the laser wavelength. The optical image is digitized by a computer-interfaced frame grabber at 30 frames/s, with 8-bit gray-scale resolution. Using laser triangulation techniques, the image processing software retrieves the solid surface geometry with a spatial resolution of 0.08 mm in the transverse ~width! and 0.13 mm in the vertical ~height! direction. A precision-machined aluminum bar with reference step gradations is used for accurate calibration of the optical scanning system" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003375_j.ab.2005.01.050-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003375_j.ab.2005.01.050-Figure1-1.png", + "caption": "Fig. 1. Setup of the imaging system. (A) Fast gateable CCD camera; (B) optical emission filter (KV 550); (C) light-guiding adapter consisting of 96 optical fibers (diameter 3 mm); (D) 96-well microtiterplate (black with transparent bottom); (E) optical excitation filter (BG 12); (F) pulsable LED array with 96 UV light-emitting diodes (kmax = 405 nm).", + "texts": [ + " Fluorescence measurements and time-resolved (gated) intensity detection were performed on a GENios+ microtiter plate reader (Tecan, Gro\u0308dig, Salzburg, Austria; www.tecan.com). The excitation filter was set to 405 nm and the emission filter to 612 nm. All experiments were performed at a programmed temperature of 30.0 \u00b1 0.1 C. Either black Fluotrac200 microtiterplates or black plates with a flat transparent bottom (Greiner bio-one, Frickenhausen, Germany; www.greiner-lab.com) were used. The device used in this study has been previously reported [35,36] and was used with minor modifications. As shown schematically in Fig. 1, it is composed of a fast gateable CCD camera (SensiMod; from PCO, Kelheim, Germany; www.pco.de), a pulsable LED array with 96 UV light-emitting diodes (kmax 405 nm, Roithner Laser Technik, Vienna, Austria; www.roithner-laser.com), a pulse generator (Scientific Instruments DG 535, Sunnyvale, CA, USA; www.srsys.com; not shown in Fig. 1), an optical emission filter (KV 550; Schott, Mainz, Germany; www.schott.com), and an optical excitation filter (BG 12; Schott), with a light-guiding adapter consisting of 96 optical fibers (diameter 3 mm) for matching the focus of the CCD camera. A computer was used for control and visualization of the experiments that were programmed in Interactive Data Language (IDL; from Research Systems, Boulder, CO, USA; www.rsinc.com). The manipulation and calculation of the images, such as the rotation and cropping of the images, the subtraction of the dark image (blank, without illumination) from the fluorescent image, and the integration of the single images and their ratioing, were done by a self-developed program based on Matlab (6", + " Rapid lifetime determination imaging (RLD), in contrast, is based on the acquisition of two windows after excitation [40,41], the ratio of intensities of the two windows enabling a straightforward determination of decay time. Moreover, RLD\u2014in being a gated method also\u2014can efficiently suppress background ns fluorescence. The resulting intensity-based and lifetime-based GOx images are displayed in Fig. 4. They indicate that the fluorescent probe EuTc is applicable to all four schemes. The intensity-based images (FII, see Fig. 4A; TRI, see Fig. 4B) are affected by flash-to-flash variations in intensity and by variations in the brightness from LED to LED in the battery of light sources (Fig. 1). This results in high well-to-well standard deviations. The high inhomogeneities in the single wells result from scattering effects. The lifetime-based images (PDR and RLD, see Figs. 4C and 4D), in contrast, reveal good homogeneity due to their independence of intensity variations of the excitation light, the quantity of the fluorophore present in the wells, and that of scattered light. Cutoff optical filters and a common ns pulse generator are adequate for the optimal time-resolved imaging of GOx" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000326_j.mechmachtheory.2021.104264-Figure7-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000326_j.mechmachtheory.2021.104264-Figure7-1.png", + "caption": "Fig. 7. Finite element/contact mechanics model of the three-planet system with 16 finite element node probes equally-spaced around the excited planet gear and ring gear.", + "texts": [ + " The model predicts discrete-body vibrations of all gear components for direct comparison to the experiments for these degrees of freedom. The software outputs the deflection of any specified node. We use this tool to obtain the elastic deformation of 16 nodes on the ring gear coinciding with the experimental accelerometer locations in Fig. 6 . Eventually the elastic-body motion of the excited planet also drew interest, so 16 nodes (with #1 pointed toward the sun gear in the \u2212x p direction and numbered counterclockwise) are also probed around this gear body, as illustrated in Fig. 7 . The FE/CM model uses boundary conditions that simulate experimental conditions. Numerical values are contained in [53] . The rotational stiffnesses of the sun gear and carrier shafts (obtained analytically and by finite element analysis) are applied to the rotational degrees of freedom of those components, although our prior work [53] shows that these parameters do not affect the frequency range of current interest. The model applies experimentally measured translational stiffnesses of carrier and sun gear bearings", + " The stiffness resisting elastic-body deformation of the ring gear in the fixtures was captured by increasing the elastic modulus of the outermost row of ring gear elements by one order of magnitude, identified iteratively to bring FE/CM results into agreement with experiments. Ring gear splines are also used in the model to simulate the stiffness provided by the 16 bolts in the fixtures. Using similar correlation between FE/CM model results and experiments, the stiffness resisting elastic-body deformation of the planet gears in the bearings was captured by increasing the elastic modulus of the innermost row of planet gear elements by about two orders of magnitude. Fig. 7 illustrates these FE/CM model features. It is also necessary to account for additional mass and inertia of gear bodies not represented in the finite element mesh. The facewidth of each gear component is thinner than its main body. The FE/CM model uses the facewidth to define the axial thickness of elements, so the additional mass of the thicker gear bodies must be represented separately. Starting from our original work in [53] , we have used the width of the gear teeth in the FE/CM model plus an additional lumped mass/inertia attached to each gear component that accounts for the material in thicker areas of the gear bodies and the added mass/inertia of the planet gear adapter flanges in Fig", + " 11 b shows minimal elastic-body ring gear vibration in cluster 2 from experimental measurements. The one nodal diameter component is dominant, and this component represents discrete-body translational motion where the ring gear moves as a rigid body. The FE/CM model, however, shows interesting elastic-body motion in this cluster. Fig. 14 shows the vibration shapes for cluster 2 modes from computer simulation. The magnitude A and phase \u03c6 of the translational components of 16 ring gear nodes and 16 planet gear nodes highlighted in Fig. 7 are calculated from the impulse response to animate the elastic motion of these components by plotting A sin ( \u03c9t + \u03c6) for each of finite element node. The deflected ring gear shape has four lobes in the 26 6 6 Hz mode and three lobes in the 2808 Hz mode. Fig. 14 c confirms that the ring gear vibration in these modes is principally in the four and three nodal diameter components, respectively. It is unclear why the experiments show minimal elastic-body vibration in cluster 2, but the FE/CM model has interesting deformation", + " Experimental measurements to support this are not possible, but a finite element natural frequency analysis of an unconstrained planet gear extracted from the full planetary gear model shows that it has a two nodal diameter elastic continuum mode in this frequency range. The full FE/CM model reveals this to be a prominant feature of the 5860 Hz mode. The planar elastic-body deflections at 16 mesh nodes equally-spaced around the planet gear are obtained using finite element probes, as noted in Fig. 7 , just like on the ring gear in prior experiments and simulations. Fig. 25 shows the FE/CM discrete-body (rotational and translational) and elastic-body acceleration frequency response functions of the excited planet gear from a combined torque/force impulse to the experimentally excited planet gear. The combination of a force and torque input simulates the effect of the shaker mounted along the ring-planet line of action in experiments and excites modes with rotational and translational motion" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000474_s00170-020-06432-1-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000474_s00170-020-06432-1-Figure3-1.png", + "caption": "Fig. 3 a Monitoring device with integrated pyrometer. b Monitoring devicewith integrated pyrometer and CCD camera. 1, fiber laser; 2, beam expander; 3, laser beam/thermal signal separating mirror; 4, scanner head; 5, F-theta lens; 6, powder bed; 7, mirror; 8, pyrometer lens; 9, fiber tip; 10, optical fiber; 11, pyrometer; 12, CCD camera (reproduced from [22, 24], Copyright (2010,2012), with permission from Elsevier and Japan Laser Processing Society)", + "texts": [ + " The thermal radiation intensity of the surface of the laser action area is recorded by a CCD camera or pyrometer at one or two spectral intervals and is related to the thermal radiation intensity of the blackbody simulator located in the same surface area. The system integrates two types of sensors: two-dimensional sensor digital CCD camera and single-point sensor pyrometer based on the photodiode. In situ temperature monitoring provides the possibility to optimize the forming process of high-porosity powder [21]. To continuously monitor the surface temperature (the temperature of the laser impact zone), Pavlov et al. used optical fiber to connect the dual-range pyrometer (11, Fig. 3a) recording the surface thermal radiation with the Phenix PM-100 optical unit (10, Fig. 3a). The results showed that the pyrometer signal generated in the laser impact zone is sensitive to the changes of the main operating parameters (powder layer thickness, hatch spacing, scanning speed, etc.), and the device can be used for in situ monitoring of molding quality. The influence of molding parameters on the structure and porosity can be judged by the different signals generated by the pyrometer [22]. To ensure that the intensity of LED scattering radiation exceeds all other emissivities except the laser impact area, an LED ring illumination system is used to illuminate the forming area [23]. Doublenskaia et al. added a CCD camera (560 \u00d7 760 pixels) to the device as shown in Fig. 3b. The CCD camera (12, Fig. 3b) measures the thermal radiation from the heat-affected zone (HAZ). Because the coefficient of thermal conductivity of the powder bed is 20 times lower than that of bulk material, the average temperature increases with the increase of powder layer thickness. From a certain critical value, the pyrometer signal and brightness temperature reach the maximum value and stable value due to the disappearance of the contact between the melted powder layer and the substrate. Therefore, all laser energy is absorbed by the powder and there is no heat loss in the substrate (as shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003655_0005-1098(84)90015-3-Figure12-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003655_0005-1098(84)90015-3-Figure12-1.png", + "caption": "FIG. 12. k* Root locus for numerical example of Section 8.", + "texts": [ + " Such a sampling rate is fairly slow in that it represents five times the speed of the modeled pole; however, sampling of the unmodeled dynamics occurs at barely once per cycle. The equivalent discrete-time system is now given by y(t) = (0.629)(1 + 0.0399q-1)(1 + O.O048q-1)q -1 (1 -0.67q-1)[(1 -0 .0017q- i ) 2 + (0.0018q- x) 2 ] [u(t)]. (38) We note there is no longer a non-minimum phase zero, as was the case in (28) where the plant was sampled faster. Indeed, the poles and zeroes of the unmodeled dynamics are very close to each other so that their effects almost cancel. This effect will always occur with slow sampling. Figure 12 shows the k* root locus of the nominal controlled plant of (14) when the open loop plant is described by (38). From Fig. 12, we notice that all the nominal control system poles can be placed close to the origin and that the nominal closed-loop controller of Fig. 1 can be made to match the model fairly closely. The yd* root locus of Fig. 13 then shows that the unmodeled dynamics hardly come into play allowing the full ?d* = 2 of (23) gain with retention of stability. The parameters were started at zero. The system adjusts quickly to follow the model as if no unmodeled dynamics were present. Thus, the third design guideline has been demonstra ted: Sample the s y s t em s lowly enough to remove the efJects o f unmode led dynamics " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002484_1.2834121-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002484_1.2834121-Figure1-1.png", + "caption": "Fig. 1 Waviness of the bearing and one wave of the inner ring", + "texts": [ + " The point of interest is the amplitude of the wavy surface with respect to central point at a certain angle from the reference axis. Waviness exists on all surfaces. To simplify the problem, first the inner ring waviness and then the outer ring and ball waviness will be considered. 2.1 Inner Race Waviness. If it is assumed that the inner race surface has a circumferential sinusoidal wavy feature, the radial clearance consists of a constant part and a variable part. The amplitude at the angle 9' (see Fig. 1) is directly related to the wavelength. This can be clearly seen if one wave is flattened out (see Fig. 1). Since it is assumed the wave is sinusoidal the amplitude can be expressed as fol lows; Tp sin 2n^ (7) where F^ is the amplitude of the wave. If there is a constant interference or clearance applied, Eq. (7) will take the form of: (8) In the case of angular contact ball bearings, F^ is replaced by the deflection due to the preload. Equation (8) consists of a constant part and a variable part. From Fig. 1: L = re' (9) since the wavelength is the length of the inner race circumfer ence divided by the number of waves on the circumference. k = Inr N (10) Substituting Eq. (9) and Eq. (10) into Eq. (8): F, = Fo + F^sin (Nd') (11) Since the inner race is moving at the speed of the shaft and the ball center at the speed of cage, for the inner race waviness, 6' should be replaced with an angle 0, for the ith ball (see Fig. 2). = \u2022& + (a;,. - u),,)t + yi (12) If a point a on the circumference of the outer race and a point b at the ball center are assumed at the initial time and initial position at an angle 'd apart from a reference axis, as seen in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000145_j.jmapro.2021.04.022-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000145_j.jmapro.2021.04.022-Figure2-1.png", + "caption": "Fig. 2. a) The rectangular thin-walled and cubic bulk samples, b) Building orientation in the vertical z-axis direction, and c) Checkerboard scanning strategy with 67\u25e6.", + "texts": [ + " Usually, the thick-walled samples in the range of 6\u2212 10 mm have been manufactured to obtain tensile specimens for testing, but in the present study, the wall thickness is changing for each test specimen such as 0.50\u20135.0 mm. For each combination of parameters, two rectangular samples for tensile testing with a dimension of 56 mm \u00d7 10.5 mm x Wt were formed, where Wt is the wall thickness of specimens. Two bulk samples with a dimension of 8 \u00d7 6 \u00d7 10 mm were also manufactured for investigating the effect of process parameters on the densification and hardness which are shown in the top right side of Fig. 2a. A total of 24 numbers (02 sets) rectangular thin-walled specimens were produced to make tensile specimens (see Fig. 2a). The building direction of the test specimen is in the vertical direction along the Z-axis which is shown in Fig. 2b. A checkerboard scanning strategy was chosen to minimize residual stresses during the fabrication of test specimens [32]. For one specific powder layer, the checkerboard is scanning linearly, and the linear scanning direction rotates with 67\u25e6 for the next powder layers, as shown in Fig. 2c. The samples were cut from the substrate by wire cutting machine. The tensile test specimens were produced according to E8/E8M subscale as shown in Fig. 3 [33]. Y. Zhang et al. Journal of Manufacturing Processes 66 (2021) 269\u2013280 The gas-atomized AlSi10Mg powder characteristics were examined and its chemical composition is presented in Table 2. Analysis of the asreceived gas-atomized AlSi10Mg alloy powder revealed that more than 78 % of the evaluated particles have the size in the range of 10\u201363 \u03bcm, as shown in Fig", + " The small particles contribute to the high energy absorption of the laser beam because of the increased specific surface area of material [34]. The spherical morphology of powder provides good flowability and consistent layer distribution. Bigger bunches of length larger than 60 \u03bcm were also detected. Prior to the SLM process, the powder was dried in a vacuum furnace at 70 \u25e6C for 4 h and then sieved in an inert atmosphere to isolate particles between 15 \u03bcm\u201358 \u03bcm. Two sets of thin-walled specimens were manufactured to ensure uniformity and reproducibility of the SLM process which is shown in Fig. 2a. The wall thickness of fabricated thin-walled test specimens was measured at different locations, and the variations in wall thickness from the model designed value to actual fabricated value are shown in Fig. 6 with an error bar. It was observed that the deviations in the wall thickness are less for 0.5, 0.8, and 5.0 mm thickness specimens. The maximum deviation of 5.5 % is found for 1.0 mm thin-walled specimen and the minimum variance of 0.25 % in the 0.80 mm wall thickness. The deviations in the wall thickness are created due to high thermal stresses and material shrinkage during the deposition process" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000019_j.ymssp.2020.107373-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000019_j.ymssp.2020.107373-Figure2-1.png", + "caption": "Fig. 2. The structure of the star gearing transmission of a GTF aero engine.", + "texts": [ + " Fig. 1 shows the structural diagram of the star gear-rotor-bearing transmission system of a GTF gearbox, which is composed of a star gearing system, input shaft (the rotor between the low-pressure compressor and sun gear), output shaft (the rotor that connects the ring gear and fan), and bearings that support the input and output rotors. The gravity of the entire gearbox and the torque generated by the gear meshing is carried through the planet carrier supported by the elastic base of the cabin. Fig. 2 shows the gear transmission structure of a GTF aero engine where the fan-driven gearbox has a five-way shunting gear transmission structure, which includes the sun gear, star gear, ring gear, and planet carrier. The sun gear is a floating part that is splined with the input shaft, and meshes with five star gears that have uniform distribution of the circumferences. The star gears are designed with gear-bearing integration. The star gears are internally supported by bearings, and meshed with the ring gear, which is a semi-floating component that is the output of the gear train, and is connected to the output shaft by bolts" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000562_j.mechmachtheory.2021.104380-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000562_j.mechmachtheory.2021.104380-Figure4-1.png", + "caption": "Fig. 4. The parallel continuum manipulators with three active PR drives.", + "texts": [ + " On the basis of the discretization-based approach in Section 2.1 , this section presents the kinetostatics modeling of the studied parallel continuum manipulator. Comparing to the existing kinetostatics modeling methods of flexible limbs, the advantage of the proposed one is that, both the active and the passive joints in the limbs can be uniformly integrated in the model as same as the elastic ones. Therefore, robot kinematics and statics approaches can be utilized to establish the whole kinetostatics models in a convenient way. As exhibited in Fig. 4 , the studied parallel continuum manipulator is actuated by three PR drives. It is noted that the PR joint is a compact 2-DOF compound joint, which can generate linear motion along a specific line, and meanwhile, angular motion about a perpendicular axis. The rotations of timing pulley A and B in the same and opposite directions correspond to the pure rotation R and linear motion P of timing pulley C, respectively. Thus, the limbs can be denoted as the \u2019 P R F lex R\u2019 structure (here \u2018F lex \u2019 denotes a flexible link)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure18.12-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure18.12-1.png", + "caption": "Fig. 18.12 (a) Coordinate system of the X-rotated Y-cut LiNbO3 plate. (b) The elastic compliance correlates with the second rotation angle", + "texts": [ + "11. Resonant modes with oblique vibration are obtained by combining a longitudinal mode and a flexural mode. These modes are then referred to as coupling modes. An X-rotated Y-plate of LiNbO3 can strongly excite in-plane bulk vibrations by the piezoelectric transverse effect at the X-rotation angles, , ranging from 120\u00ba to 160\u00ba, and the longitudinal and flexural modes appear independently in the rectangular vibrator. On the other hand, by applying the second rotation in the y'-axis, as shown in Fig.18.12(a), the longitudinal and flexural modes are combined to convert two coupling modes, which are called the upper and lower modes, that correspond to the resonant frequency. This occurs because the second rotation changes the elastic compliances, especially sE 35, into non-zero values, as shown in Fig.18.12(b). Since the propagation wave in the length direction is bent by a function of the anisotropic sE 35, the components of the longitudinal and flexural waves are converted alternately each other and are coupled. Consequently, coupling modes can be realized in vibrators having a symmetrical outer shape, and these vibrators can be driven by a uniform single-phase electric field in the thickness direction. The vibrator dimensions and crystal rotation angles were determined by FEM. For example, vibrator was designed so that the displacement ratio uH/uV approached 1 in both the upper and lower modes" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002683_s0141-6359(00)00066-0-Figure11-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002683_s0141-6359(00)00066-0-Figure11-1.png", + "caption": "Fig. 11. The pneumatically actuated pin extends underneath the vee block to support the LRU.", + "texts": [ + " A more significant motivation for the wide vee is the frictional constraint against rotation, which is an order of magnitude stiffer than the LRU frame. The potential static twist in the frame due to friction is much less than the requirement for initial alignment. Physically, the upper vee consists of two pin-slot constraints that passively engage as the LRU lifts into place. As Fig. 10 shows, each constraint consists of a tapered pin attached to the structure and a slotted receiver at the top of the LRU. Conversely, the lower mount is active and formed by two vee blocks on the LRU that can travel past retracted pins on the structure. As Fig. 11 shows, the pins extend to receive the vee blocks and support the weight of the LRU, which ranges from 300 to 600 kgf depending on LRU type. Each pin mechanism is actuated by a pneumatic cylinder and for safety reasons is incapable of retracting under the weight of the lightest LRU. Due to the angle of the pin, the load is primarily compressive across its 32 mm diameter. A parameterized model of the NIF LRU was developed using the methods described in this paper. The positions of the constraints were set largely by geometric considerations, but the angles of the constraints were controlled by four variable parameters to be optimized: 1) the pin angle of the lower mount, 2) the outside vee angle of the lower mount, 3) the inside vee angle of the lower mount, and 4) the slot angle of the upper mount" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003815_j.mechmachtheory.2009.06.001-Figure24-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003815_j.mechmachtheory.2009.06.001-Figure24-1.png", + "caption": "Fig. 24. Defective generators with a passive exceptional mobility.", + "texts": [ + " These defective generators are shown in Fig. 23b\u2013f. It is noteworthy that a defective X generator happens when a revolute pair arbitrarily replaces any screw in these generators. C2. [{H(A1, u, p1)}{H(A2, u, p2)}][{H(A3, u, p3)}{H(A4, u, p4)}] can be equated to {C(A1, u)}{T(Pl)} with {C(A1, u)}\\{T(Pl)} = {T(u)}; in this case, the plane Pl of vectors s3, s4 is parallel to u. Consequently, if two screws are coaxial, then the plane of two P pairs must not be parallel to the screw axis. The chain in Fig. 24a shows this kind of defective generator. It is a defective chain with a passive exceptional mobility. Once more, the subgroup {C(A1, u)} can also be generated by PH or HP arrays (PR or RP when the pitch is zero) when the P is parallel to the H axis (R axis), as shown in Figs. 24b and c. Here, special cases of Fig. 22 are discarded for simplicity. Case D. If two adjacent pairs generate the same 1D subgroup, then, obviously, the open serial chain generates a 3D manifold included in the 4D subgroup {X(u)}" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002876_j.matdes.2004.12.015-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002876_j.matdes.2004.12.015-Figure1-1.png", + "caption": "Fig. 1. Schematic of the developed power absorption test rig: 1, motor; 2, generator; 3, test gear; 4, standard gear; 5, torque sensor; 6, accelerometer; 7, microphone; 8, temperature sensor; 9, speed sensor; 10, counter; 11, coupling; 12, bearing block; 13, base plate.", + "texts": [ + "25 mm are chosen for the present investigation. Test gears were made using an injection molding machine at a molding pressure of 125 MPa and melt temperature of 513 K. The dimensions of the test gears are shown in Table 1. Test gears were mated against the hobbed stainless steel (SS 316) gears. Mechanical properties of the test gear material are shown in Table 2 [18]. A polymer absorption type gear test rig is used for the performance evaluation of molded test gears. A schematic diagram of the developed test rig is shown in Fig. 1. In this test rig, the test gear is driven using a direct current (DC) motor and can be run at any speed up to 1500 rpm. Test gear drives the identical standard stainless steel gear, which is connected to DC generator. The required test torque is introduced by loading the rheostat connected to the generator. Torque transmitted, number of cycles run, vibration level, sound level, and gear tooth surface temperature were measured and stored in a personal computer based data acquisition system. Detail methodology and results of test gear condition monitoring are discussed elsewhere [19]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003788_978-1-4020-5967-4-Figure11-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003788_978-1-4020-5967-4-Figure11-1.png", + "caption": "FIGURE 11. Combination of four powers to move a weight of 1000 talents with a force of 5 talents (Mechanics 2.29). Drawing of a figure in Ms L (Drachmann, The Mechanical Technology, p. 90).", + "texts": [ + "21: These things having been done, if we imagine the chest AB placed on high, and we tie the weight to the axle EZ, and the pulling force to the wheel X , neither side will go downwards, even if the axles are turning easily and THEORY AND PRACTICE IN HERON\u2019S MECHANICS 35 the engagement of the wheels is fitted nicely, but the force will balance ( , o o \u0301 ) the weight as in a balance ( , \u00b4 o\u0302 o\u0301 ). But if we add a little more weight to one of them, the side where the weight is added will sink ( \u0301 ) and go downwards, so that, if just the weight of one mina is added to the force of five talents, it will overpower ( \u0301 ) the weight and pull it.45 As a final tour de force Heron describes how all the powers except for the wedge can be combined to achieve the same mechanical advantage of 200:1 (2.29; Fig. 11). The discussion of the powers in combination prompts Heron to remark on a further important aspect of their operation, the phenomenon of delay 45 Heron, Dioptra, 37 (Opera, vol. III, pp. 310.20\u2013312.2); Engl. trans. Drachmann, The Mechanical Technology, p. 26, slightly modified. Throughout the passage \u201cforce\u201d translates \u0301 and \u201cweight\u201d \u0301 o . Pappus, Pappi Alexandrini collectionis quae supersunt, VIII, vol. III, p. 1066.19\u201331, expresses the same idea in the same language. See also Heron, Mechanics, 1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003794_j.mechmachtheory.2009.01.008-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003794_j.mechmachtheory.2009.01.008-Figure1-1.png", + "caption": "Fig. 1. The general 6\u20136 Stewart mechanism 17.", + "texts": [ + " Later, they improved the dialytic elimination algorithm [10], with which the size of the Sylvester\u2019s matrix leading to a 40th-degree univariate equation has been reduced to 15 15. This paper presents a new algorithm for the forward displacement analysis of the general 6\u20136 Stewart platform, which directly leads to a 40th-degree univariate equation from a constructed 13 13 Sylvester\u2019s matrix without factoring out or deriving the greatest common divisor, by borrowing some ideas from [6,10] and using the Gr\u00f6bner bases [11]. Two numerical examples are provided to confirm these theoretical results. The kinematic model of the general 6\u20136 Stewart mechanism is shown in Fig. 1. The six leg lengths provided by the prismatic joints in each leg are the six inputs to control the location and orientation of the moving platform. For both moving and fixed platform, the spherical joints Bi and Ai (i = 1,2, . . . ,6) are not restricted to lie in a plane. Locate a fixed frame XYZ with its origin at A1 and attach a moving frame X0Y0Z0 to the upper platform with its origin at B1. Let ai denote the vector from the origin of the fixed frame to the grounded spheric pair Ai, bi denote the vector expressed in moving frame from the origin of the moving frame to the spheric pair Bi, P (px,py,pz) denote the vector from A1 to B1 expressed in the fixed frame, li denote the ith leg length" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003141_j.automatica.2006.08.007-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003141_j.automatica.2006.08.007-Figure1-1.png", + "caption": "Fig. 1. The vertical take-off and landing aircraft (VTOL) model.", + "texts": [ + " Additionally, it is shown that the bound of the inverse-input error decays exponentially with the increase of the preview time, and that the decay rate is related to the unstable poles of the linearized internal dynamics. Moreover, the quantification of the required preview time is illustrated by applying the results to the VTOL aircraft model. In this section, we illustrate the preview-based stableinversion technique to achieve precision trajectory tracking, by using a simplified nonlinear model of VTOL aircraft shown in Fig. 1 (Al-Hiddabi & McClamroch, 2002b; Hauser et al., 1992; Martin et al., 1996). We start by describing the VTOL aircraft dynamics and the inversion-based control scheme. We consider the following simplified VTOL aircraft model (see, e.g., Al-Hiddabi & McClamroch, 2002b; Hauser et al., 1992; Martin et al., 1996),[ x\u0308 z\u0308 ] = [\u2212 sin \u03b5 cos cos \u03b5 sin ] [ u1 u2 ] + [ 0 g ] M [ u1 u2 ] + [ 0 g ] , (1) \u0308 = u2, (2) y = [ y1 y2 ] = [ x z ] , (3) where x and z are the horizontal and vertical positions of the aircraft mass center, respectively, is the roll angle and g = 1 is the normalized gravitational acceleration" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002839_978-3-662-03845-1-Figure9.8-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002839_978-3-662-03845-1-Figure9.8-1.png", + "caption": "Fig. 9.8. (a) Distribution of the director around a singularity line or disclination, perpendicular to the plane of the figure. (b) Different types of singularity", + "texts": [ + " These are indeed the fine, mobile threads we observed in such great numbers under the microscope, and which gave their name to the phase. F.e. Frank called these structural de fects disclinations, to describe the discontinuity in director inclination or tilt. The distribution of the director around the singularity is easily determined by its optical properties in polarised light. The main singularities were first characterised by G. Friedel and F. Grandjean in 1910. In order to do this, consider a disclination line viewed from the end and mark the tangents to the director field in the plane perpendicular to the line (see Fig. 9.8a). The schematic corresponds to what is easily observed in thin layers, without special treatment of the substrate, when molecules are confined to the plane of the layer. The resulting texture is called a Schlieren texture. The strength or rank of the line 5 is defined as the total rotation f2 of the director along a closed path around the line, divided by 27r (i.e., f2 = 27r5). It is attributed a sign + or - depending on whether the director rotation occurs 9.2 Nematic Liquid Crystals 299 in the same direction as the path is traversed or in the opposite direction. Figure 9.8b shows director configurations around lines 8 = =f1/2 and 8 = =f1, in the case where n is parallel to the singularity line. These lines are called dihedral or wedge disclinations. When n is perpendicular to the singularity line, they are called twist or screw disclinations. A general line may be mixed, but it has the same rank along its whole length. It is amusing to note that the distortion around a suitably oriented pair of lines + 1/2 and -1/2 disappears completely at some distance from the singularities. The director distribution around a wedge disclination can be calculated from the free deformation energy. To simplify, assume that Kl = K2 = K3 = K, so that the deformation energy becomes 1 2 Fd = \"2 K(\\le) . The equilibrium condition obtained by minimising the total energy is just \\l2e = 0 . Solutions have the form e(r) = m\u00a2(r), in good agreement with optical observations. With the notation of Fig. 9.8, we have l\\lel = 8/r, where r is the distance from the line. The distortion energy per unit length of line, also called the line tension, can be written in polar coordinates l R 1 (8)2 Td = rc \"2 K --:;: 27rr dr 300 9. Liquid Crystals (9.9) R is of the order ofthe sample dimensions and rc is the radius ofthe disclination core, i.e., the distance of molecular order over which Hooke-type elasticity is no longer valid. We must add the disclination core energy to (9.9). This is difficult to calculate exactly, but it does not exceed the energy of the disordered nematic [rv kB(T - Tc)], where Tc is the nematic to isotropic transition temperature" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003425_978-3-540-30301-5_34-Figure33.23-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003425_978-3-540-30301-5_34-Figure33.23-1.png", + "caption": "Fig. 33.23 BLEEX shank design", + "texts": [], + "surrounding_texts": [ + "In designing an exoskeleton, several factors had to be considered: Firstly, the exoskeleton needed to exist in the same workspace of the pilot without interfering with his motion. Secondly, it had to be decided whether the exoskeleton should be anthropomorphic (i. e., kinematically 0 0.2 HS TOStance Swing 0.4 0.6 0.8 1 Angle (deg) Time (s) 15 10 5 0 \u20135 \u201310 \u201315 \u201320 \u201325 Fig. 33.17 Three sets of adjusted CGA data of the ankle flexion/extension angle. The minimum angle (extension) is \u2248 \u221220\u25e6 and occurs just after toe-off. The maximum angle (flexion) is \u2248 +15\u25e6 and occurs in late stance phase matching), or non-anthropomorphic (i. e., kinematically matching the operator only at the connection points between human and machine). Berkeley ultimately selected the anthropomorphic architecture because of its transparency to the pilot. It is also concluded that an exoskeleton that kinematically matches the wearer\u2019s legs gains the most psychological acceptance by the user and is therefore safer to wear. Consequently, the exoskeleton was designed to have the same degrees of freedom as the pilot: three degrees at the ankle and the hip, and one degree at the knee. This architecture also allowed the appropriately scaled clinical human walking data to be employed for the design of the exoskeleton components, including the workspace, actuators, and the power source. A study of clinical gait analysis (CGA) data provides evidence that humans expend the most power through the sagittal plane joints of the ankle, knee, and hip while walking, squatting, climbing stairs, and most other common maneuvers. For this reason, the sagittal-plane joints of the first prototype exoskeleton are powered. However, to save energy, the nonsagittal degrees of freedom at the ankle and hip remain unpowered. This compels the pilot to provide the force to maneuver the exoskeleton abduction and rotation, where the required operational forces are smaller. To reduce the burden on the human operator further, the unactuated degrees of freedom are spring loaded to a neutral standing position. Human joint angles and torques for a typical walking cycle were obtained in the form of independently collected CGA data. CGA angle data is typically collected via human video motion capture. CGA torque data is calculated by estimating limb masses and inertias and applying dynamic equations to the motion data. Given the variations in individual gait and measuring methods, three independent sources of CGA data [33.42\u201344] were utilized for the analysis and design of BLEEX. This data was modified to yield estimates of exoskeleton actuation requirements. The modifications included: (1) scaling the joint torques to a 75 kg person (the projected weight of the exoskeleton and its payload not including its pilot); (2) scaling the data to represent the walking speed of one cycle per second (or about 1.3 m/s); and (3) adding the pelvic tilt angle (or lower back angle depending on data available) to the hip angle to yield a single hip angle between the torso and the thigh, as shown in Fig. 33.16. This accounts for the reduced degrees of freedom of the exoskeleton. The following sections describe the use of CGA data and its implication for the exoskeleton design. The sign conventions used are shown in Fig. 33.16. Part D 3 3 .8 Figure 33.17 shows the CGA ankle angle data for a 75 kg human walking on flat ground at approximately 1.3 m/s versus time. Although Fig. 33.17 shows a small range of motion while walking (approximately \u221220\u25e6 to +15\u25e6), greater ranges of motion are required for other movements. An average person can flex their ankles anywhere from \u221238\u25e6 to +35\u25e6. The exoskeleton ankle was chosen to have a maximum flexibility of \u00b145\u25e6 to compensate for the lack of several smaller degrees of freedom in the exoskeleton foot. Through all plots, TO stands for toe-off and HS stands for heel-strike. Figure 33.18 shows the adjusted CGA data of the ankle flexion/extension torque. The ankle torque is almost entirely negative, making unidirectional actuators an ideal actuation choice. This asymmetry also implies a preferred mounting orientation for asymmetric actuators (one sided hydraulic cylinders). Conversely, if symmetric bidirectional actuators are considered, spring loading would allow the use of low-torque-producing actuators. Although the ankle torque is large during stance, it is negligible during swing. This suggests a system that disengages the ankle actuators from the exoskeleton during swing to save power. The instantaneous ankle mechanical power (shown in Fig. 33.19) is calculated by multiplying the joint angular velocity (derived from Fig. 33.17) and the instantaneous joint torque (Fig. 33.18). The ankle absorbs energy during the first half of the stance phase and releases energy just before toe off. The average ankle power is positive, indicating that power production is required at the ankle. Similar analyses were carried out for the knee and the hip [33.45] and [33.46]. The required knee torque has both positive and negative components, indicating the need for a bidirectional actuator. The highest peak torque is extension in early stance (\u2248 60 Nm); hence asymmetric actuators should be biased to provide greater extension torque. The hip torque is relatively symmetric (\u221280 to +60 Nm); hence a bidirectional hip actuator is required. Negative extension torque is required in early stance as the hip supports the load on the stance leg. Hip torque is positive in late stance and early swing as the hip propels the leg forward during swing. In late swing, the torque goes negative as the hip decelerates the leg prior to heel strike. CGA data, which provided torque and speed information at each joint of a 75 kg person, was also used to size the exoskeleton power source. The information suggested that a typical person uses about 0.25 HP (185 W) to walk at an average speed of 3 mph. This figure, which represents the average product of speed and torque, is an expression of the purely mechanical power exhibited at the legs during walking. Since it is assumed that the exoskeleton is similar to a human in terms of geometry and weight, one of the key design objectives turned out to be designing a power unit and actuation system to deliver about 0.25 HP at the exoskeleton joints. Part D 3 3 .8 The BLEEX kinematics are close to human leg kinematics, so the BLEEX joint ranges of motion are determined by examining human joint ranges of motion. At the very least, the BLEEX joint range of motion should be equal to the human range of motion during walking (shown in column 1 in Table 33.1), which can be found by examining CGA data [33.42\u201344]. Safety dictates that the BLEEX range of motion should not be more than the operator\u2019s range of motion (shown in column 3 of Table 33.1). For each degree of freedom, the second column of Table 33.1 lists the BLEEX range of motion which is in general larger than the human range of motion during walking and less than the maximum range of human motion. The most maneuverable exoskeleton should ideally have ranges of motion slightly less than the human\u2019s maximum range of motion. However, BLEEX uses linear actuators, so some of the joint ranges of motion are reduced to prevent the actuators\u2019 axes of motion from passing through the joint center. If this had not been prevented, the joint could reach a configuration where the actuator would be unable to produce a torque about its joint. Additionally, all the joint ranges of motion were tested and revised during prototype testing. For example, mockup testing determined that the BLEEX ankle flexion/extension range of motion needs to be greater than the human ankle range of motion to accommodate the human foot\u2019s smaller degrees of freedom not modeled in the BLEEX foot. It is natural to design a 3-DOF exoskeleton hip joint such that all three axes of rotation pass through the human ball-and-socket hip joint. However, through the design of several mockups and experiments, we learned that these designs have limited ranges of motion and result in singularities at some human hip postures. Therefore the rotation joint was moved so it does not align with the human\u2019s hip joint. Initially the rotation joint was placed directly above each exoskeleton leg (labeled \u2018alternate rotation\u2019 in Fig. 33.20). This worked well for the lightweight plastic mockup, but created problems in the full-scale prototype because the high mass of the torso and payload created a large moment about the unactuated rotation joint. Therefore, the current hip rotation joint for both legs was chosen to be a single axis of rotation directly behind the person and under the torso (labeled \u2018current rotation\u2019 in Fig. 33.20). The current rotation joint is typically spring loaded towards its illustrated position using sheets of spring steel. Like the human\u2019s ankle, the BLEEX ankle has three DOFs. The flexion/extension axis coincides with the human ankle joint. For design simplification, the abduction/adduction and rotation axes on the BLEEX ankle do not pass through the human\u2019s leg and form a plane outside of the human\u2019s foot (Fig. 33.21). To take load Part D 3 3 .8 off of the human\u2019s ankle, the BLEEX ankle abduction/adduction joint is sprung towards vertical, but the rotation joint is completely free. Additionally, the front of the exoskeleton foot, under the operator\u2019s toes, is compliant to allow the exoskeleton foot to flex with the human\u2019s foot. Since the human and exoskeleton leg kinematics are not exactly the same (merely similar), the human and exoskeleton are only rigidly connected at the extremities (feet and torso). The BLEEX foot is a critical component due to its variety of functions. \u2022 It measures the location of the foot\u2019s center of pressure and therefore identifies the foot\u2019s configuration on the ground. This information is necessary for BLEEX control.\u2022 It measures the human\u2019s load distribution (how much of the human\u2019s weight is on each leg), which is also used in BLEEX control. \u2022 It transfers BLEEX\u2019s weight to the ground, so it must have structural integrity and exhibit long life in the presence of periodic environmental forces.\u2022 It is one of two places where the human and exoskeleton are rigidly connected, so it must be comfortable for the operator. As shown in Fig. 33.21, the main structure of the foot has a stiff heel to transfer the load to the ground and a flexible toe for comfort. The operator\u2019s boot rigidly attaches to the top of the exoskeleton foot via a quickrelease binding. Along the bottom of the foot, switches detect which parts of the foot are in contact with the ground. For ruggedness, these switches are molded into a custom rubber sole. Also illustrated in Fig. 33.21 is the load distribution sensor, a rubber pressure tube filled with hydraulic oil and sandwiched between the human\u2019s Universal joint Force sensor Knee connection Hip connection Length adjustment Accelerometer Knee and hip manifold Knee actuator Knee valve Hip valve Hip actuator Fig. 33.24 BLEEX thigh design Part D 3 3 .8 foot and the main exoskeleton foot structure. Only the weight of the human (not the exoskeleton) is transferred onto the pressure tube and measured by the sensor. This sensor is used by the control algorithm to detect how much weight the human places on their left leg versus their right leg. The main function of the BLEEX shank and thigh are for structural support and to connect the flexion/extension joints together (Figs. 33.23 and 33.24). Both the shank and thigh are designed to adjust to fit 90% of the population; they consist of two pieces that slide within each other and then lock at the desired length. To minimize the hydraulic routing, manifolds were designed to route the fluid between the valves, actuators, supply, and return lines. These manifolds mount directly to the cylinders to reduce the hydraulic distance between the valves and actuator, maximizing the actua- tor\u2019s performance. The actuator, manifold, and valve for the ankle mount to the shank, while the actuators, manifold, and valves for the knee and hip are on the thigh. One manifold, mounted on the knee actuator, routes the hydraulic fluid for the knee and hip actuators. Shown in Fig. 33.26, the BLEEX torso connects to the hip structure (shown in Fig. 33.20). The power supply [33.47\u201349], controlling computer, and payload mount to the rear side of the torso. An inclinometer mounted to the torso gives the absolute angle reference for the control algorithm. A custom harness (Fig. 33.27) mounts to the front of the torso to hold the exoskeleton to the operator. Besides the feet, the harness is the only other location where the user and exoskeleton are rigidly connected. Figure 33.26 also illustrates the actuator, valve, and manifold for the hip abduction/adduction joint." + ] + }, + { + "image_filename": "designv10_6_0003241_j.jmatprotec.2005.05.014-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003241_j.jmatprotec.2005.05.014-Figure1-1.png", + "caption": "Fig. 1. Schematic of laser deposition process.", + "texts": [ + " Keywords: Titanium; Laser deposition; LENSTM; Ti\u20136Al\u20134V The process of using a laser to consolidate a metal powder is essentially a derivative of a rapid prototyping technique that has been used for several decades to produce threedimensional shapes in polymeric materials for mock-ups of parts during design. The attraction of the process is that it transforms a powder directly to a solid without the necessity of dies, with the concomitant long lead times and expense that this can imply. In both processes a series of layers of material are built up, with a laser used to melt powder that is fed into the region where the beam and substrate meet, see Fig. 1. In order to produce components of appreciable size the beam, or more often the component base, is generally moved back and forth under automatic control across a surface in order to produce a layer. Having deposited a layer of material, either the component base is moved down or the beam is re-focused in preparation for the deposition of the succeeding layer. The movement to control the deposition is derived from the output \u2217 Corresponding author. Tel.: +44 1252 393808; fax: +44 1252 393947. E-mail address: awisbey@qinetiq" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002463_bf00118823-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002463_bf00118823-Figure3-1.png", + "caption": "Fig. 3. Illustrating axial motions of fluid (x-components of 47r#u/h), computed for a 2 = / 3 ~ = 0.5 in the plane x = 0 intersected by the helix at the point y = b, z = 0. Because a change by -4-7r in the polar angle \u00a2 has the same effect on the velocity field (19) as a sign change for X = R/b, the solid line (computed for \u00a2 = 0 and real X) gives values on the y-axis with X = y/b while the broken line (\u00a2 = rr/2) gives values on the z-axis with X = z/b. Axial velocities which are negative (that is, in the direction of swimming) are precisely balanced by \"backflow\" in the positive z-direction, as indicated by Eq. (28).", + "texts": [ + " Helical distributions of stokeslets 43 It may be noted that, for large [X[, the function B1 tends exponentially to zero like a multiple of the Bessel function K0(ISl), whereas B2 becomes algebraically small like a multiple of X -2. This latter function appears just in the z-component of (21), which it causes to fall off like X - 1 in the expected vortex-type far field. These distinctions become even clearer in Figs. 3 and 4, depicting fluid velocity components in the x-direction (along the axis of the helix) as well as in planes at right angles to it. In Fig. 3 the solid line shows the x-component of expression (21) for 47r#u/h, which, once again, falls off exponentially for large IXl \u2022 It may also be noted that its limiting value as X ~ 1 does not precisely depend on a replacement of expressions (22) by (23), because of the need to incorporate the extra term (24); thus, the solid line represents - a 3 X B 1 for general X but for A striking feature of Fig. 3 is that the solid line exhibits for X > 0 the expected negative axial velocities, associated with swimming movements in directions opposite to that of wave propagation; but that, in stark contrast, there is flow in the positive x-direction (backflow) for X < 0. As already mentioned this corresponds to motions of fluid where ff = yr. Also, a computation of the x-component of 47r#u/h for \u00a2 = 7r/2 and ~b = -1r /2 (easy because the integral (19) in these cases offers no convergence problems) again yields positive values - given by the broken line in Fig. 3. Moreover, no exhaustive computing is needed to see that, for general values of X, negative and positive values of the axial velocity are in exact balance - in the sense that their ~b-average is zero. In fact, the integral with respect to ~b of the x-component of (19) from ~b = -Tr to Helical distributions of stokeslets 45 \u00a2 = rr vanishes; simply because f ~ X sin(0 - \u00a2)d\u00a2 r [0~202 + f12(X2 - 2X cos(O - \u00a2) + 1)] 3/2 = - - ~ [a202 + #2(X2 - 2Xcos(0 - \u00a2) + 1)]l/2 _~ (28) is zero (the integrated term takes the same value at both limits)", + " Such a vortical interpretation is further reinforced by a study of curve (b), which plots the y-component of 4rr#u/h where \u00a2 = 7r/2 (values for positive X) and where \u00a2 = -7r /2 (values for negative X). Once again, the broken lines indicate values given by Eq. (30); which, this time, have already begun to coincide with curve (b) for ISl > 2.5. Yet curve (c), in another striking contrast, plots the z-component of 47r#u/h for \u00a2 = +7r/2; which are values of \u00a2 for which the z-component of the vortical far field (30) is zero. This is why curve (c) depicts much more localised motions which (just as in Fig. 3) fall off exponentially for large IXl. A geometrically much clearer feel for the distribution of velocity components in the plane x = 0 (at right angles to the axis of the helix) is obtained when the data of Fig. 4 are replotted as in Fig. 5. This shows the velocity vector at points y = 0.4bN, z = 0 (where N takes integer values from - 2 0 to +20; thus, the actual position y = b, z = 0 of the helix itself is Helical distributions of stokeslets 47 omitted) as derived from curve (a), and also the velocity vector at points y = 0, z -- 0.4bN (for the same range of N) as derived from curves (b) and (c). Each vector represents the velocity resolved onto the plane x = 0 (for x-components see Fig. 3) with its length giving the magnitude of that resultant (on the scale indicated in Fig. 4) and the arrow giving its direction. This pattern of velocity vectors in Fig. 5 shows the salient features of the flow field in the y, z plane very clearly. Near the helix itself (y = b, z = 0) which, per unit length, exerts in the negative z-direction a force (0, 0, - h ) , strong velocity components in the negative z-direction are induced (even on the z-axis itself). At rather greater distances, on the other hand, these become overshadowed by the collective effect of the average torque per unit length generated all along the helix. Against the background of this physical interpretation of y- and z-components of the flow field in the plane x = 0 it is worth reconsidering the earlier results on x-components (Fig. 3) with the aim of asking at the conclusion of Section 2 if they can be given any analogous interpretation. Any such enquiry must, of course, begin by acknowledging its greater difficulty, resulting from the fact that x-components of flow in the plane x = 0 cannot be influenced by the action of a stokeslet which actually lies in that plane. Thus any attempt at a physical interpretation of those x-components of flow must relate them to the effect of stokeslets in nearby planes with either positive or negative s", + " The computations have been carried out for the value a 2 = 0.1 suggested by the above discussion - a value in sharp contrast to the case (27) used in Section 2 for the analysis of flow fields around flagella of eukaryotic microorganisms. As before, the three-dimensional flow field is computed on the plane x = 0; the flow field on any other plane x = constant being obtained from this by a simple rotary displacement. Fluid velocity components in the x-direction (parallel to the axis of the helix) are shown in Fig. 16. Here, just as in Fig. 3, the solid line gives the x-component of 47r#u/h on that axis z = 0 which passes through the location (0, b, 0) of the helix itself; this is the sum of contributions (for \u00a2 = 0, 7r) from the x-components of (21) and (64). The broken line, again as in Fig. 3, shows how the same quantity varies on the perpendicular axis y = 0; here, it is derived from the x-components of (19) and (63) for \u00a2 = +7r/2. Both distributions become negligible (as mentioned above)when I XI = R/b > 2. Actually, the distribution of axial velocity (unlike that of azimuthal velocity studied below) is in both cases found to be dominated by the self-rotation contributions (64) and (63); just as the swimming velocity U0 was found earlier to be dominated for a 2 = 0.1 by the self-rotation contribution (68)", + " 16 is that both curves display a large positive flow in the cylindrical region y2 + z 2 < b 2 interior to the helix (the region between the two vertical broken lines); it corresponds in the electromagnetic problem, of course, to the strong axial magnetic flux induced inside a coil of wire along which a current passes. This powerful interior flow through the coils of a swimming spirochete (at an average velocity exceeding that of the organism itself) may be a specially important conclusion of this paper. (Evidently, it is in sharp contrast with the absence of any mean axial flow for the case illustrated in Fig. 3.) But before commenting further on this conclusion I outline computational results for velocity components in a plane perpendicular to the axis of the helix. The solid lines (a), (b) and (c) in Fig. 17 (where, actually, the vertical scale is expanded twofold compared with that in Fig. 16) have meanings exactly as specified in Fig. 4. However, in sharp contrast to Fig. 4, these distributions again exhibit rapidly decaying far fields, essentially negligible for IX] > 2. For example, curve (a) plots the z-component of 47r#u/h on the axis z = 0, while curve (b) plots its y-component on the axis y = 0; both, then, are distributions of azimuthal components of velocity", + " 16 and 17, the steep rate of decline as x increases is associated with the axial wavenumber k/a which has just been identified. Indeed, for this axial wavenumber, solutions of the Stokes equations without vortical far fields have asymptotic behaviours which include (alongside algebraic factors) an exponential factor e (-k/~)R = e (-~/~)x (because R = bX and fl = bk). (72) For a 2 --- 0.1 this is e -3X whereas for a 2 = 0.5 it is e-X; a contrast which explains both the still greater localisation for curve (c) shown in Fig. 17 as against Fig. 4, and that found in the curves of Fig. 16 by comparison with those of Fig. 3. Nonetheless the most important feature of Fig. 16 (and one which also is in complete contrast to Fig. 3) is the large positive flux through the coils of a swimming spirochete. This strong interior jet-like flow (at an average velocity exceeding that of the organism itself) is potentially advantageous for the life-style of these bacteria. Thus, as a spirochete moves forwards, it is continuously exposed around the outside of the helix to new fluid approaching from in front, while at the same time a jet of fluid coming from behind passes through the interior of the helix. Both features should combine to bring a rather rapid flow of nutrients (as well as of chemical signals) towards the spirochete's close proximity and so help to maintain its energetic swimming movements", + " To a survey of these features previously described [ 1 ], the present paper adds an analysis of the flow field of that helical distribution of stokeslets which models zero-thrust swimming. In any plane perpendicular to the axis of the helix, motions parallel to that axis are found to have zero means; indeed, their azimuthal average is zero at each distance from the axis. In particular, fluid motion at speed U0 near the organism's surface is reciprocated by neighbouring equal and opposite motions of fluid (Fig. 3), a conclusion interpreted in Fig. 6 from the geometrical nature of stokeslet fields. Yet motions in the plane itself are far less localised, being dominated (Fig. 5) by the vortical far field associated with the axial torque acting on the fluid. Nevertheless, where this torque is counteracted by an equal and opposite torque due to cell-body rotation, with its Helical distributions of stokeslets 75 far field described by the rotlet singularity (curl of a stokeslet), the flow field of the organism as a whole falls off much more rapidly (Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure3.34-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure3.34-1.png", + "caption": "Fig. 3.34. Vibrations", + "texts": [ + " The impact appears and we solve it by using the theory from Para. 3.5.1 (eq. 3.5.10 or 3.5.12). Thus obtaining the initial condi- 223 Grinding task. Fig. 3.33a,b shows the task of fine grinding. A moving surface results in relative velocity and friction force F f . In the case (a) a plane surface is considered. It rotates as shown in the figure. But, in practice this is not an ideal plane and the rota tion axis is not exactly perpendicular to the plane. Thus, the motion of the surface is not a simple rotation (Fig. 3.34). The reaction and, accordingly, the friction are not constant and produce vibrations of the working object (and the gripper). 224 In the case shown in Fig. 3.33b the cylindrical surface is considered. Rotation is not ideal since it is not an ideal cylinder (Fig. 3.35a) and the rotation axis is not in the exact center of the circle. For this reason the reaction is not constant and vibrations of the working object appear. All these effects can be included in the calcu lation. But, there are some effects which can not be taken into account" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003317_s11044-008-9126-2-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003317_s11044-008-9126-2-Figure2-1.png", + "caption": "Fig. 2 Impulse plane", + "texts": [ + " Replacing In and It in (33) and (23) with I\u0303n and I\u0303t , respectively, and setting vS t = 0 in (23), one obtains equations of lines in the I\u0303t \u2212 I\u0303n plane, namely, forward sliding line LFS \u21d2 I\u0303t = (33) \u2212\u03bcI\u0303n, (55) sticking line LST \u21d2 I\u0303t = (23) \u2212( I\u0303nmnt + vA t ) /mtt, (56) reverse sliding line LRS \u21d2 (33),(55),(56) I\u0303t = \u03bcI\u0303n \u2212 2\u03bcvA t /(\u03bcmtt \u2212 mnt), (57) with I\u0303n regarded as an independent variable. Note that the reverse sliding line crosses point G, the intersection point of lines LFS and LST; and that, by (55) and (56), I\u0303n(G) = vA t /(\u03bcmtt \u2212 mnt). (58) Lines LFS,LST and LRS, drawn in Fig. 2, and, in particular, their respective slopes \u2212\u03bc,\u2212mnt/mtt and \u03bc, can be used to look at values of I\u0303n and I\u0303t as the collision proceeds, and to describe events occurring during collisions. With vA t > (9b),(21b) 0, all I\u0303t \u2212 I\u0303n relations start at the origin and vary in accordance with LFS, until forward sliding is completed either before point G is reached\u2014then the collision ends with forward sliding characterized by \u2212mnt/mtt > \u2212\u03bc (if I\u0303n(G) > 0) or by \u2212mnt/mtt < \u2212\u03bc (if I\u0303n(G) < 0); or at point G", + " In that event, either sticking\u2014governed by LST , or reverse sliding\u2014governed by LRS, follow depending on whether |mnt|/mtt < \u03bc (then the inertial forces are not large enough to overcome friction and produce reverse sliding) or \u2212mnt/mtt > \u03bc, respectively. The conditions for sticking, reverse sliding, and forward sliding can thus be written, respectively, as |mnt|/mtt < \u03bc \u21d2 \u03bcmtt \u2212 mnt > 0, \u03bcmtt + mnt > 0, (59) \u2212mnt/mtt > \u03bc \u21d2 \u03bcmtt + mnt < 0 (mnt < 0), (60) \u2212mnt/mtt > \u2212\u03bc \u21d2 \u03bcmtt \u2212 mnt > 0, \u2212mnt/mtt < \u2212\u03bc \u21d2 \u03bcmtt \u2212 mnt < 0 (mnt > 0). } (61) Now, if sticking follows forward sliding (Type 1), then In > I\u0303n(G) > 0 (Fig. 2). Substitutions from (47a) and (58) lead in view of inequality (59a) to [\u03b1 \u2212 (1 + e)rm]/( rm) < 0. (62) If reverse sliding follows forward sliding (Type 2), then again In > I\u0303n(G) > 0. Substitutions from (49a) and (58) yield \u03b1/(mnn + \u03bcmnt) < (1 + e)rm/(mnn + \u03bcmnt) (since mnt < (60) 0, and hence rm > (36a) 0) indicating that mnn + \u03bcmnt > 0 \u21d2 \u03b1 < (1 + e)rm, mnn + \u03bcmnt < 0 \u21d2 \u03b1 > (1 + e)rm. } (63) Lastly, if a collision terminates with forward sliding (Type 3), then either I\u0303n(G) > In > 0 or I\u0303n(G) < 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure2.69-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure2.69-1.png", + "caption": "Fig. 2.69. Scheme of manipulation task", + "texts": [ + "2 s is not posible and with the trapezoidal profile even T(Ao~A1} = 1 s is posible. One can conclude that with this manipulator and this manipulation task the trapezoidal profile is more convenient, because the actuator capabilities are used in a more efficient way (Fig. 2.67). 2.8.4. Example 4 In this example we present the manipulator GORO-80 having six rotatio nal degrees of freedom. Fig. 2.68a, shows the external look,Fig. 2.68b. shows the kinematical scheme, and in Fig. 2.68c. there is a table with the manipulator data. The manipulation task is shown in Fig. 2.69. The initial position of manipulator (Ao in Fig. 2.69) is given in 2.68b. Working object has to be inserted into a hole as shown in Fig. 2.69. First, the object is moved from Ao into a position A1 . Keeping in mind the form of the object and the hole, it is clear that the total orientation is necessary. It is shown in Fig. 2.69 via two directions (b) and (c) i.e. via two vec~ ~ tors hand s. Now insertion is performed. The working object is moved from A1 to A2 along the direction (b) without any change in orientati on. Each straight line motion is performed with the triangular velocity 119 m Ir < I P [ Nm J > 0. 4 pm M r \\ \u2022 -1 . --- / .... ..r Ao ~ 0. 2 0. 1 \u2022\u2022 .\u2022 \u2022 : ..:- =:: :: I .... .. , ~ 1 0 . ~ ... :; .- -~ .. , . ~ .. , I I 1 . 2. pm m ax \\ m - n ~ (c o n st ra in t) T = 3 .2 5 I 3. F ig . 2 .6 3 . D ia g ra m s pm - nm (t o rq u e " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002407_1.1344898-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002407_1.1344898-Figure1-1.png", + "caption": "Fig. 1 Thermal material transfer in layered manufacturing", + "texts": [ + " These include fused deposition modeling, ballistic particle manufacturing @2#, microcasting @3#, thermal spraying @4#, scan welding @5#, as well as arc, plasma and laser machining @6#. In such solid freeform fabrication ~SFF! methods, a CAD model of the solid part geometry dictates the progressive mass transfer from a localized source in onedimensional material beads adjacent to each other. The abutting beads form successive two-dimensional layers, properly contoured to the respective model sections, and stacked so as to generate the desired three-dimensional product morphology ~Fig. 1!. This thermal material deposition determines the geometric accuracy of the part and its dimensional tolerances. Thus, dynamic modeling and sensory control of the process phenomena are of primary importance to thermal manufacturing techniques. Combined thermo-mechanical analysis of their coupled heat and mass transfer mechanisms in the literature has been addressed in the context of classical processes, such as thermal welding and cutting, in mainly two directions. On the one hand, numerical simulations have been based on finite-difference, finite-element and boundary value methods @7#", + " are stored in standard composite video format for subsequent off-line analysis by special thermal image processing software, and they are also processed simultaneously in real time by the frame grabber installed on the control computer during closedloop operation. Figure 4 shows such an infrared thermal field at nominal GMAW process conditions. In additive thermal manufacturing processes, such as GMAW, the material is supplied under the localized, traveling source, and deposited on the solid substrate ~Fig. 1!. The material is fed in molten droplets ~thermal spray, ballistic particle manufacturing! or in solid form such as wire ~fused deposition modeling, microcasting, GMAW!, powder ~surface hardfacing! etc, and melts together with a portion of the substrate under the thermal torch action. After a transient, the generated three-dimensional molten puddle reaches a steady-state size and morphology, following the source in its motion on the substrate. As the puddle moves, molten material at its rear interface solidifies to generate the bead along its motion" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003689_j.jmatprotec.2008.04.046-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003689_j.jmatprotec.2008.04.046-Figure1-1.png", + "caption": "Fig. 1 \u2013 Schematic of the belt polishing setup (a) and the appearance of roughing (b), i.e. Cubitron 907E, and finishing (c), i.e. Trizact 307EA, abrasive media.", + "texts": [ + " high tool stepovers, cutter diamters); smoother surfaces (Rt = 5 m) replicate areas of the omponents with reduced stiffness that can only bear reduced oading (material removal rates) or those that have limited tool ccessibility, i.e. tight radii, that require smaller diameters of ball nose) milling cutters. Related to finishing operations of the two types of preilled surfaces of the TSCA-E components, two polishing ethods have been taken into consideration: (a) Belt polishing using an air powered tool (Dynafile) oriented at = 30\u25e6 tilt angle (Fig. 1a), backward (up grinding) feed direction, employing 3M coated aluminium oxide belts (13 mm width) with the following grades: (i) randomly distributed grains, Cubitron 907E (for roughing), Fig. 1b; (ii) grains replicated into pyramids, Trizact 307EA (for finishing), Fig. 1c. b) Bob polishing using machine tool spindle oriented at = 20\u25e6 tilt angle (Fig. 2a), backward feed direction, employing off-the shelf and customised 10 mm tool diameter made of the following abrasive 3M materials/grades: SiC Scotch-Brite 2 Fine, Fig. 2b; polycrystalline diamond (PCD 74\u2014mesh 250), Fig. 2c. Belt polishing was performed in both dry and chilled air onditions (\u221230 \u25e6C below room temperature at 6 bar) supplied y a Vortex tube (Exair 3825 spot cooler) close to the cutting one (3 mm ahead the contact wheel of the belt polisher)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure26.1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure26.1-1.png", + "caption": "Fig. 26.1 Schematic picture of the structure of an EAP actuator with the three layer structure", + "texts": [ + " The concentration of carbon nanotube is chosen high enough so that the carbon nanotubes are partially contacted with one another within the electrode layer. In this way, it is ensured that the electrical potential at the surface of the electrode layer and that in the middle are the same at equilibrium. One separator layer was sandwiched by two electrode layers and they were heat pressed to form an actuator as a whole. Metal electrodes were attached to the electrode layers at the both sides (see Fig.26.1). When voltage is applied between the metal electrodes, the ions in all the three layers redistribute in response to the electric field induced by the voltage. At the molecular level, the ions accumulate near the surface of the carbon nanotube molecules in the electrode layers. Electrical double layers form at the surface of all the carbon nanotube molecules that are electrically connected with the metal electrode. Note that the surface area that is available for the electrical double layers to form is much larger than the surface area of the electrode layer that is exposed to the air, because of the entangled network of carbon nanotubes inside the electrode layer" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000495_j.wear.2021.203963-Figure13-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000495_j.wear.2021.203963-Figure13-1.png", + "caption": "Fig. 13. Running test bench.", + "texts": [ + " 12 shows the preload test bench, which is comprised of a linear motor, two aerostatic slideways, an aerostatic moving platform, and a Futek LSB302S pull pressure sensor. Due to the carriage of the tested LRG is connected with the work table through the pull pressure sensor, the carriage can therefore move reciprocally along the rail and the aerostatic slideway when the worktable is driven by the linear motor. The preload can then be obtained through the drag force measured by the pull pressure sensor, which was measured in triplicate in both the forward and backward travels. Fig. 13 shows the running test bench, which is comprised of an AC servo motor (\u2460), a gantry, a pin gear (\u2461), a rack (\u2462), two liner rolling guides (\u2468), and a loading mechanism. The loading mechanism is comprised of a servo motor (\u2463), 2 gears (\u2464), a trapezoidal guide screw (\u2465), and two pressure sensors (\u2466). The carriage of the tested LRG (\u2469) is connected with the nut of the trapezoidal guide screw through a Fiche technique FN3000-A2 pressure sensor, once the gears are driven by the servo motor, the load will be applied on the nut of the trapezoidal guide screw, the pressure sensor, and the carriage of the tested LRG in sequence" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003314_ip-d.1990.0003-Figure6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003314_ip-d.1990.0003-Figure6-1.png", + "caption": "Fig. 6 Two-link manipulator", + "texts": [], + "surrounding_texts": [ + "for the ACAC algorithm. Using this formula, we can predict the value of u[(K + 1)T] using the values of the present state variables. In other words, if u[(K + 1)T] is\n1\n0.4 0.8 1.2 1.6 2 -1.21\nx l , rad\nequal to zero or changing its sign when compared with u(KT), then we can conclude that the RP will hit or cross the sliding mode U = 0 in the next step. It then tells us\n36\nthat we have to change the control to the CAC algorithm.\nNow let us consider two examples that will illustrate the power of CAC and ACAC algorithms. i\nExample 1 : Consider the following nondimensionalised unstable second-order linear system: r1 x2 = 0 . 3 ~ ~ x 2 + 0.5~\u2019 + U A h,x , + h 2 x z + U\nWe specify the system convergence rate c = 0.4. The sampling time of computer control if 0.01 s. And the initial condition is (x,(O), ~ \u2019 ( 0 ) ) = (2, 0). First, if we choose a, = 4.3, a2 = 4.5 and a = 10, then these parameters still satisfy the existence condition of the sliding mode. However, they do not satisfy the requirement of our CAC algorithm. The chattering phenomenon under this VSS control is shown in Fig. 2.\nNext, we apply our CAC algorithm to this system, i.e. U = - a , x , - a z x 2 - $xl. The level of chattering, A, is required to be no more than 0.5, then the control gains can be calculated. We obtain a , = cZ + h , = (0.4)\u2019 + 0.3 = 0.46, and I $ I = a = A = 0.5. The chattering alleviated result is shown in Fig. 3. The result indicates that the chattering phenomenon can be suppressed.\nExample 2 : Consider a nondimensionalised linear system that takes the form of eqns. 10, we will drive it towards the origin from the initial value (0, 2), by first using the CAC and then the ACAC algorithm, respectively.\nSet c = 1 and A = 0.3. The parameters are given by Step I: CAC:\na , = 2c + h, = 2 x 0.4 + 0.5 = 1.3\na: = 1 a i = 2 a\u2019 = 0.3\n(i) Reaching-phase control:\na: = (1 + A)\u2019 = (1 + 0.5)\u2019 = 2.25\nStep 2: ACAC:\nwhere A = 0 . 5 ~ = 0.5\na i = 2c + 2h = 2 x 1 + 2 x 0.5 = 3\na\u2019 = (A)\u2019 + = (0.5)\u2019 + 3.75 = 4\nwhere 1 = 12.5A = 3.75\nI E E PROCEEDINGS, Vol. 137, P f . D, No. I, J A N U A R Y 1990", + "(ii) CAC: the same as step 1\nThe sampling time is 0.05 s. The phase portraits and the time waveforms of x , ( t ) are given in Figs. 4 and 5. The solid lines and dashed lines denote the simulation results of ACAC and CAC, respectively. We see from these Figures that the ACAC algorithm shortens the hitting time considerably.\nThe mass of both links, rn, and m , , is represented by point masses at the end of the links. The links are of length d, and d , , respectively. The manipulator hangs straight down in the gravity field of acceleration g. The generalised co-ordinates are chosen to be 0, and 0 2 . The harmonic drives used to transmit torques are modelled as spring elements with coefficients k , and k, .\nDynamical equations of this manipulator are as follows.\nTI = [ (m, + mz)(dl)\u2019 + mz(d,)\u2019 + 2m, d , d , cos 0,]8, + [m2(d2)\u2019 + m2 d , d , cos 0,]4, - 2m, d , d , sin (0,)8,8, - m2 d , d , sin (0,)(8,)\u2019\n+ (m, + mz)g d , sin (0,) + m2 g d , sin (0, + 0,) + k , 0 , + AJ,\nT, = [m,(d,)\u2018 + m2 d , d , cos (0,)]4, (30)\n+ m2(d2)28, - 2m, d , d , sin (0,)8,8, - m2 d , d , sin (02)(81)2 + m,g d, sin (0, + 0,)\n+ kz 0, + AJz (31) where T, and T, are torques applied at joints 1 and 2, respectively. AJ, and AJ, denote the unmodelled higher order terms. The derivation procedures for eqns. 30 and 31 are similar to that in Reference 16. The dynamical equations above are too complex to handle for VSS control purposes. However, we can apply a global nonlinear transformation [3] to transform the nonlinear\nIEE PROCEEDINGS, Vol. 137, Pt. D, No . I , J A N U A R Y 1990\nmodel above into the model as system eqns. 1 and use ACAC to control this system. Let us define the state vectors as follows:\n[x,, x2 , x3, x4iT [e,, 8,, + ez, 8, + 8,iT x XI e [x,, X31T\nx, 0 [x, , x4y (32)\nAnd define the following constants rl, r , , r 3 , r4 and r5 by\n1 - r 3 sin (xl) - (x, + k,)x, + k , x , - Af, + Af2 r, sin (x, - xI)(x4)\u2019 - r , sin (x, - X , ) ( X ~ ) ~ - r 5 sin (x,) + k,(x, - x,) - AJ,\n(34)\n-\n4 W(X1)[k3, i4]T - F(xj\nIt is easy to show that W is nonsingular. Thus, the inverse of W, W - \u2019 , exists. The vector F includes the nonlinear coupling between both links and part of the linear, nonlinear and uncertain terms in the original dynamical equations. Let\n(35)\nFrom eqns. 34 and 35, we transform the dynamical equations of this two-link manipulator into the similar form of system eqns. 1 :\nV = [TI - T,, TZIT 44 [U,, u2IT\nI x, = x, 8, = W-\u2019(x , )F(x) + W-\u2019(x , )V\nThe ACAC technique described in Section 2 is then applied to system eqns. 36. The reference system is chosen to be\n8, = x, xz = U A A,(u, , \u201c,)XI + A,(u,, U 2 ) X , } (37)\n+ Y(U1, CJ2)Xl\nwhere\nAccording to eqns. 36 and 37, we have\nF(kT) = WX,(kT) - V((k - 1)T)\n37", + "and\nV(kT) = WU(kT) - F(kT)\nFinally, the torques applied to links 1 and 2 are\n[TI, T2IT = CO1 + 0 2 , 021\u2019\nExample 3 : The experiments discussed in References 5 and 9 are repeated here for comparison. Hence, the system parameters used in eqns. 36 will be the same as in References 5 and 9. They are as follows: m, = 0.5 kg, m, = 6.25 kg, d , = 1.0 m, d, = 0.8 m, k , = 0.0 kgm/s and k, = 0.0 kgm/s. The initial conditions are given by xl(0) = -2.784 rad, x,(O) = - 1.204 rad and il(0) = i3(0) = 0.0 rad/s. Moreover, the sampling time and the slopes of the sliding lines are also the same as in References 5 and 9, T = 2 ms, c, = 0.5 and cq = 0.4. Applying ACAC to this system, set A, = 0.75 and- A, = 0.4. We chooze = Ai = 0.75 and a, = 4.1A2 = 1.64, then, according to reaching-phase control law and the CAC algorithm, the parameters in eqns. 37 can be determined as follows: (For simplification, we define aij 4 [at, ah] to stand for the values of the a$ in the reaching-phase control and ah in CAC 1 < i, j < 2.) = 3c, = 1.5, Z q = 1 . 5 ~ ~ = 0.6,\n[ - 1 , -0.161 = [r-4, 00.251\n[-2, O I -0.81 A 2 = [C4b-11\n3 : reaching-phase control 0.75: CAC\nand\n2 : reaching-phase control 0.4: CAC 1 $ 2 1 = {\nThe simulation results of our ACAC shown in Figs. 7, 8 and 9.\nReference 9 exhibits the same trajectories using regulated derivative control. It still has slight chattering in the velocity trajectory. From Figs. 8 and 9, we can see that\n0.5r\nalgorithm are I\n-1 2 -0.8 -0.4 0\nx j , rad\nFig. 9 Phase trajectory of i J t ) ~ x,(t)\nThe phase plane trajectories for the position control experiment using decentralised state feedback algorithm in Reference 5, have some serious chattering problems.\n38\nour ACAC algorithm has almost no chattering at all. Moreover, the maximum torques for joints 1 and 2 are 144.929 Nm and 42.9545 Nm. They are only about onethird of the torques used in References 5 and 9. Finally, it is clear from Fig. 7 that our clear-cut benefit is not obtained at the expense of the time required to reach the steady state.\n6 Conclusion\nIn the design of VSS control, the problems of \u2018chattering\u2019 on he sliding mode and the slow \u2018hitting time\u2019 during the reaching phase are serious. This leads to restriction of the applications of VSS control. In this paper, we have proposed a new ACAC algorithm that can solve these two problems simultaneously. This algorithm has been applied to uncertain linear and nonlinear systems. The resulting trajectories of a two-link manipulator have indicated the success of this algorithm. Most importantly, the good performance of this algorithm is not obtained at the expense of the time required to reach the steady state. Moreover, the maximum torques for robotic applications are also reduced to approximately one-third of previous\nI E E PROCEEDINGS, Vol. 137, P t . D, No. I , J A N U A R Y I990" + ] + }, + { + "image_filename": "designv10_6_0000335_j.msea.2021.141134-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000335_j.msea.2021.141134-Figure1-1.png", + "caption": "Fig. 1. Design of the tensile test specimen. (A: gage length for the measurement of the strain, B gage length for measurement of the force).", + "texts": [ + " The alloy powder used in this study was virgin and obtained from SLM Solutions, GmbH (L\u00fcbeck, Germany). The nominal composition of the powder is given in Table 1. The composition of the AlSi10Mg samples after the build process was estimated by utilizing x-ray fluorescence spectroscopy (XRF) and is shown in Table 2. One set of AlSi10Mg samples have been T5 heat treated (stress relieve, 300 \u25e6C for 2 h and cooled in air) and the other set have been T6 heat treated (520 \u25e6C for 6 h and water quenching and afterwards 160 \u25e6C for 6 h and air cooling). The used tensile test specimen design is shown Fig. 1. The compressive tests were conducted on cylindrical specimens with a diameter and a height of 6 mm. All samples were machined from the SLM-produced rods such that the orientation of the symmetry axis was parallel to the building direction. Quasi-static (\u03b5\u0307=0.001 s\u2212 1) tensile and compression tests were carried out on a mechanical universal testing machine produced by Zwick/Roell (Germany). A calibrated load cell with a maximum load of 100 kN was used for force measurement. Tensile and compression tests under quasi-dynamic load conditions (\u03b5\u0307=1 s\u2212 1) were performed on a servo-hydraulic universal testing machine with a calibrated load cell of 20 kN", + " The kinetic energy of the flywheel was high enough to ensure near constant speed during the measurement time. The dynamic compression tests (\u03b5\u0307=100 s\u2212 1) were performed at a drop weight tower using a mass 600 kg and a drop height of 18 mm. For the high strain rate compressive tests (\u03b5\u0307\u22651000 s\u2212 1) a Split Hopkinson apparatus with bar diameters of 20 mm was used. For the tensile tests and \u03b5\u0307\u2264100 s\u2212 1 the force was calculated by using data from two strain gauges glued on the specimen next to the gage length (see area B in Fig. 1) in combination with the known Young\u2019s modulus. At a test velocity of ~12 m/s, the force was measured with strain gauges at the sample holder utilizing the elastic wave according to the Hopkinson principle by measuring the elastic tension wave in a long rod. Assuming the validity of the theory of the propagation of elastic waves in thin rods, the stress-time signal can be determined from the measured strain-time signal of the rod. The strain for experiments with strain rates \u03b5\u0307\u22641 s\u2212 1 was measured by the DIC-system (digital image correlation) ARAMIS (GOM)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003438_jra.1985.1087013-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003438_jra.1985.1087013-Figure1-1.png", + "caption": "Fig. 1 . PUMA 560 robot arm. Degrees of joint rotation and member identification.", + "texts": [ + " 0882-4967/85/0900-014 forearm link. These differences affect the solution of the first three joints. Special attention is given to the arm configurations and the singularities. Configuration parameters are defined and used to find the correct solution when solving for the inverse kinematics. Also presented is a method to obtain the arm configuration parameters from a known set of joint angles. 11. DEFINITIONS A . Robot Joint Variables and Cartesian Vector The PUMA 560 robot has six revolute joints arranged as shown in Fig. 1. The Joint 1 axis coincides with the centerline of the trunk link l I . The joint angle is measured in the counterclockwise direction from the positive y-axis. The Joint 2 axis is perpendicular to and intersects the Joint 1 axis and coincides with the centerline of the shoulder. The shoulder is an offset of length dl between the trunk and the upper arm, This offset is parallel to the x-y plane and is in the negative x-axis direction when is equal to zero. Link 12, the upper arm, rotates around the Joint 2 axis an angle 02", + " The vector r = (rx, ry , r,) is the position vector and rp , re , r$ are the rotations about the z-axis, the new - x axis, and the new z-axis that aligns the base coordinates with the tip coordinates. The rotation parameters were chosen to correspond with the arrangement of the joints at the wrist and hence simplify the solution. B. Arm Configuration The robot arm has similarities with the human arm geometry. Robot manipulators are defined accordingly as having a shoulder, an elbow, and a wrist (see Fig. 1). The robot arm may be righty or lefty, that is, the first three joints of the robot resemble a human's right or left arm, respectively. The elbow can have two configurations; elbow up, where the elbow's position is above the line joining the shoulder to the wrist; and elbow down, where the elbow's position is below that line. Also, the wrist can assume two solutions: the no-flip wrist for which the Joint 5 angle is positive and the flip wrist for which the Joint 5 angle is negative. The arm configuration- parameters kl , kz, and k3 are defined as follows: + 1, lefty - 1, righty kz= [ + 1, elbow up - 1, elbow down k3= [ + 1 , no-flip - 1, flip" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000342_j.ijthermalsci.2021.107011-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000342_j.ijthermalsci.2021.107011-Figure4-1.png", + "caption": "Fig. 4. Conduction between two elastic spheres in contact.", + "texts": [ + "146 (3) Idepth(z) = Isurface e\u2212 \u03b1z (4) where Re is the reflective coefficient on the surface, r is the radial distance from the center of the laser beam, P is the power of the laser beam, RL is the radius of the laser beam, \u03b1 is the extinction coefficient, z the depth location and w the correction coefficient in the Beer-Lambert law. Unlike heat transfer in homogenous media, thermal conduction in granular media like powder beds is defined as transfer of energy by diffusion between objects in physical contact, Watson et al. [26]. The traditional continuum conduction model is not suitable for the laser melting process. A discrete model is needed to describe the thermal behavior of the powder bed. Heat flow by conduction between two particles i and j in a granular system is illustrated in Fig. 4. It consists of two components: conduction through the contact area Qc and conduction through air Qe. Total heat conduction between two particles is then given by: M. Boutaous et al. International Journal of Thermal Sciences 167 (2021) 107011 Qi,j =Qc;i,j + Qe;i,j Qc could be estimated based on the Fourier equation: Qc;i,j = \u2212 kcAc dTi,j dx (5) where kc = 2kikj ki+kj is the harmonic mean of the conductivity of the particles [J/(K\u22c5s\u22c5m)] and Ac = \u03c0a2 is the contact area between particles [m2]. Because the size of the particles i and j is very small, usually less than 100\u03bcm, the thickness of the contact region d is assumed to be the same as the thickness of the thermal conduction distance, so the thermal gradient between two particles could be approximated by: dT dx \u2248 \u0394Ti,j d (6) Then (5) can be modified as: Qc;i,j = \u2212 kcAc d \u0394Ti,j = \u2212 Hc\u0394Ti,j, Hc = kcAc d = \u03c0kca2 d (7) where \u0394Ti,j = Ti \u2212 Tj [K] and Hc is the heat transfer coefficient [J/(K\u22c5 s)]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000019_j.ymssp.2020.107373-Figure6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000019_j.ymssp.2020.107373-Figure6-1.png", + "caption": "Fig. 6. The model of the spur gear meshing.", + "texts": [ + " The contact deformation is expressed as dcj \u00bc 1:275F0:9 j E0:9 12eB 0:8 \u00f012\u00de where E12e \u00bc 2E1eE2e= E1e \u00fe E2e\u00f0 \u00de Finally, the total deformation in the point of gear contact is d12j \u00bc dbj \u00fe dfj 1 \u00fe dcj \u00fe dbj \u00fe dfj 2 \u00f013\u00de where 1 represent the driving spline, and 2 represents the driven spline. Therefore, the meshing stiffness at meshing point j is Kj \u00bc Fj d12j \u00f014\u00de Assume there are n pairs of teeth of a spline that is in contact, the contact stiffness can be expressed as The basic parameters of the star gear transmission system are shown in Table 1. The calculated time-varying meshing stiffness of the spur gear for external meshing and internal meshing pairs are shown in Fig. 5. The meshing process of spur gear pair is illustrated in Fig. 6(a), in which the gear meshing along the gear teeth is divided into approach process, and recess process, in which the direction of friction force experience change, therefore, the equivalent force acting on the gear teeth is varied during the two process, in which Fa; f a indicate the axial force component, Fb; f b indicate the bending force component. The model of the spur gear meshing is illustrated in Fig. 6(b) where the velocities of the driving and driven gear at the meshing point can be written as vM1 \u00bc x1 O1M vM2 \u00bc x2 O2M \u00f016\u00de where v i is the velocity at the meshing point, andxi is the angular velocity at the meshing point. Therefore, the sliding speed vs on the meshing point M can be described as v s \u00bc vM1sina1 vM2sina2 \u00f017\u00de where, a1 is pressure angle. Since O1M sina1 \u00bc N1M and O2M sina2 \u00bc N2M , Eq. (17) can be expressed as Vs \u00bc x1 N1M x2 N2M \u00f018\u00de The meshing point M moves along the direction of the meshing line at absolute velocity x1rb1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002648_978-94-015-9064-8_13-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002648_978-94-015-9064-8_13-Figure1-1.png", + "caption": "Figure 1. Parallel Manipulator", + "texts": [ + " ~s {Adf and {BiH, respectively. Points Ai and Bi are, respectively, 127 J. LenarCic and M. L. Husty (eds.), Advances in Robot Kinematics: Analysis and Control, 127-136. \u00a9 1998 Kluwer Academic Publishers. referred to as the ankle- and hip attachment points of leg i. These systems are known as Stewarl Gough platform manipulators, when the leg architecture is restricted to an actuated prismatic joint con nected to the EE through a passive spherical joint and to the base via a universal joint, such as the odd numbered legs of Fig. 1. At the dis placement level, the direct kinemat ics problem pertains to the determi nation of the actual pose-i.e., the position and orientation-of the EE relative to the base from a set of joint-position readouts. Using the position of the six prismatic joints as input data, Raghavan (1993) reported numerical experiments showing up to forty real and imaginary possible solutions for this problem. The underlying fortieth-degree polynomial can be obtained with a procedure proposed by Husty (1996)", + " In order to cope with this uncertainty, Tancredi, Teillaud and Merlet (1995-a; 1995-b) derived geometric conditions allowing for the uniqueness of the solution under joint sensor layouts using four extra sensors. Here, we use a wide variety of joint sensor layouts together with a more general leg architecture, i.e., three joints in series, either revolute or prismatic, with links of general geometry and ending with a spherical joint at the hip-attachment point, such as the even numbered legs shown in Fig. 1. Such a study has already been conducted by Notash and Podhorodeski (1994; 1995), but only for the subclass of three-branch parallel manipulators, i.e., manipulators with only three legs. Although joint-sensor redundancy was clearly present in all the works on the addition of sensors, none of them attempted to reduce the amplification of the errors by minimizing the inconsistencies arising from geometrical and sensor inaccuracies as well as elastic deformations of links and looseness in mechanical joints. In this paper, we cope with these errors by means of joint-sensor redundancy together with least-square solutions. In order to describe the motion of the EE relative to the base, let us attach frame A to body A and frame B to body B, such as shown in Fig. 1 The pose of the EE relative to the base, namely 1t\", is thus defined as a twelve dimensional array, namely, (1) where p is the position vector of the origin of B in A, and r the nine dimensional array constructed from the three rows of the 3 x 3 proper orthogonal matrix R representing the orientation of B in A such that: (2) with B, = [~~ ~i ~~], R ~ [ ~J), r = [ :n ' (3) for an arbitrary vector bi. Each leg of a parallel manipulator defines a kinematic loop passing through the origins of frames A and B, and through the two leg attachment-points" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000290_j.msea.2021.141721-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000290_j.msea.2021.141721-Figure1-1.png", + "caption": "Fig. 1. Thirteen steps of manufacturing an industrial AM part via LPBF method.", + "texts": [ + " Metal additive manufacturing (AM) is an extensively used, rapidly emerging technology that has the potential of revolutionizing traditional manufacturing methods. Currently, laser powder bed fusion (LPBF) is one of the most popular AM procedures used for fabricating hightemperature materials like Ni-based superalloys [1\u20134]. Creating complex geometries with high precision, and lowering material wastage are known as the main irrefragable capabilities of this layer-wise method compared to the subtractive ones [5,6]. Fundamentally, there are 12 steps to go through to fabricate an AM part from pre-alloyed powder via LPBF, as schematically represented in Fig. 1. It should be noted that a post-treatment may be considered as step 13 to further enhance the properties of the LPBF components intended for use in industries. Among all Ni-based superalloys, IN718 has been appropriately manufactured via LPBF process regarding its excellent weldability [7]. On the other hand, the presence of porosities and lack of fusions (LOF) along with mechanical anisotropy are recognized as the major issues that have already decelerated the industrialization of AM IN718 products [6,8]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003742_1.4000277-Figure8-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003742_1.4000277-Figure8-1.png", + "caption": "Fig. 8 Ball-raceway contact in flexible model \u201eFv>0\u2026", + "texts": [ + " 7, 0 is the nominal contact angle, Oci and Ori are the raceway groove curvature centers of the carriage and rail, respectively, and the suffix i refers to the raceway groove number i. The raceway groove radii of the carriage and rail are rc and rr, respectively. The distance s0 between Oci and Ori is s0 = rc + rr \u2212 d0 2 where d0 is the reference ball diameter ball diameter with zerooversize . The oversize of balls is defined as 0 = d \u2212 d0 3 where d is the actual ball diameter. Substituting Eq. 3 into Eq. 2 , the following equation is obtained s0 = rc + rr \u2212 d + 0 = m0 + 0 4 In Eq. 4 m0 = rc + rr \u2212 d 5 Next, the ball-raceway contact in the flexible model is shown in Fig. 8. Under a preload 0 0 and a vertical load FV, the jth ball in the ith raceway groove in a linear bearing is compressed by ball load Qij, as shown in Fig. 8, in which cij is the Hertzian deformation between the jth ball in the ith raceway groove and the carriage, and rij is the Hertzian deformation between jth ball in the ith raceway groove and rail. Under a preload 0 0 and a vertical load, the carriage and rail are subjected to the reaction forces of Qij. Due to these reaction forces, the ith groove of the carriage will expand ci in the direction of ci, while the ith groove of the rail will shrink ri in the direction of ri. In the flexible model, due to the deformations ci and ri and the vertical displacement v, the raceway groove curvature centers of the carriage and rail are O ci and O ri, respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003648_elan.200603814-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003648_elan.200603814-Figure1-1.png", + "caption": "Fig. 1. Schematic structure of the multilayer membrane.", + "texts": [ + " Glass slides were negatively charged using the same method above, and immersed in 1% PDDA\u00fe 0.5 MNaCl aqueous solution to introduce positive charges on them, then modified in the same way as that of cysteamine modified gold electrodes. GOD is negatively charged in pH 7.0 PBS considering its isoelectric point (pI) of 4.2, which makes it suitable to Electroanalysis 19, 2007, No. 9, 986 \u2013 992 www.electroanalysis.wiley-vch.de E 2007 WILEY-VCH Verlag GmbH&Co. KGaA, Weinheim construct multilayer films via electrostatic assembly. As shown in Figure 1, initially, a layer of cysteamine was selfassembled onto the gold electrode surface via a covalent bond between SH and Au, then similarly, the exposed NH2 of cysteamine connected citrate stabilized GNP. The positively charged PDDA layer acted as a joining to connect firstly the negatively charged MWNTs to the negatively chargedGNP layer and thennegatively chargedGODto the MWNTs layer. Thus a stable GNP/MWNTs/GOD multilayer membrane could be obtained on the cysteamine modified electrode. Figure 2 shows the top AFM morphologies of a series of gold slides after modification of GNP, GNP/MWNTs or GNP/MWNTs/GOD multilayer films" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003818_physrevlett.100.078101-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003818_physrevlett.100.078101-Figure2-1.png", + "caption": "FIG. 2. Lumped parameter model consisting of two rigid links connected by a torsional spring (open circle). The top link is clamped. All drag is concentrated at the two filled circles.", + "texts": [ + " Front and side images of the steady-state threedimensional shape of the rotating rod at each torque were captured using a single camera and a single mirror. The imaging system was carefully calibrated to account for perspective, achieving an accuracy of 2 mm. At low torque, the rotation speed is relatively slow, and the rod bends slightly [Fig. 1(a)]. Above a critical torque, the rod adopts a helical shape and rotates much faster 0031-9007=08=100(7)=078101(4) 078101-1 \u00a9 2008 The American Physical Society [Fig. 1(b)]. To illustrate the physics, we first present a simple analysis of this shape transition using the lumped parameter model shown in Fig. 2. The rod is modeled by two rigid links of unit length connected by a torsional spring. The linkOP is fixed at angle between the rotation axis z\u0302 and the base of the rod in our experiment. Since the Reynolds number is small, we take Re 0. Thus, we may work in the rod\u2019s rotating rest frame without introducing fictitious forces. The flow in this frame at point r is!z\u0302 r. The torsional spring represents the bending resistance and is only sensitive to changes in the angle between the vectorsOP and PQ. Assuming 1 andK is sufficiently large, the moment about P on PQ from the spring is Mb K OP PQ K y; 2 x; 0 , where K is the torsional spring constant, and x; y; 2 rQ is the position of the point Q to leading order in . To find the steady-state position of Q, equate the moment on PQ due to the torsional spring to the moment on PQ due to the flow. Assuming all drag on PQ is concentrated at Q (Fig. 2), the viscous moment about P is Mv ! x; y; 0 , where is a resistance coefficient. Solving moment balance for x and y yields x 2 = 1 !=K 2 and y x !=K. As ! increases from zero, the link PQ deflects and y increases, which causes Q to experience a viscous force in the negative x direction. These forces push Q toward the rotation axis, and tend to cause the rod in our experiment to wrap around the z axis. As ! increases further, Q moves closer to the rotation axis, and y begins to decrease. There is also some drag on the linkOP, concentrated a distance d from O" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003045_1.2137795-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003045_1.2137795-Figure3-1.png", + "caption": "Fig. 3. Domains of optimal two-phase (a) and three-phase (b) motions.", + "texts": [ + ">= = x1* c( ) c 2 -- c 1\u2013( ) 1\u2013 1 3c\u2013 9c2 2c 7\u2013+( )1/2 +[ ] 1/2 ,= \u03a6 x( ) 2c x2 1 c\u2013( )+[ ]x c x2+( ) 1\u2013 .= x1* x1* 2 3 -- 1/2 4 3 -- 2 3 -- 1/2 x1 x2 1, u1 u2 u0 La \u00b5 ------ 1/2 ,= = = = = \u03c41 \u03c42 \u03c40 \u00b5L a ------ 1/2 ,= = = T 2\u03c40, V 0.5 \u00b5La( )1/2.= = DOKLADY PHYSICS Vol. 50 No. 11 2005 This case is presented in Fig. 2c. In the presence of constraint (5), the two-phase motion under consideration can be realized only when (13) The optimal motion is determined by the relations (14) Here, notation given by Eqs. (11) and (12) is used. Four cases (14) are associated with domains 1\u20134 in Fig. 3a. The boundaries of these domains are the straight lines c = 1, X = 1, and X = c and the curves X = c1/2 and X = marked by letters K and N, respec- tively. Regime a is realized in domain 2, while, in the other domains, regime b is realized. The passage to the original dimensional parameters in Eq. (14) can be carried out according to formulas (10). 3. An analysis of the three-phase motion (7) leads to two possible regimes for the motion of body M; they are denoted by a and b and are presented in Figs", + " 11 2005 In the case of the isotropic dry friction a+ = a\u2013 = a, in accordance with formulas (15)\u2013(17), we have In the presence of constraint (8), the three-phase regime of motion is realizable under the condition (18) The optimal motion is determined by the relations for max(1, c) < Y \u2264 Y*, (19) for Y > max(1, Y*), where the following notation is introduced: (20) The first case in (19) corresponds to the presence of a nonzero rest interval at the end of the period: here, t2 < T (see Fig. 4b). In the second case of (19), the rest interval at the end of the period is absent, as is demonstrated in Fig. 4c, and t2 = T. Figure 3b shows the c,Y-plane. The domains that correspond to the two cases (19) are marked by numbers 1 and 2, respectively. The figure depicts the lines c = 1, Y = 1, and Y = c, as well as the curve Y = Y*(c). In the case of the isotropic dry friction a+ = a\u2013 = a, Eqs. (19) and (20) take the form (21) w1 w3 a \u00b5 -- , w2 \u221e, \u03c41 \u03c43 2\u00b5L a --------- 1/2 ,= = = = = \u03c42 0,= \u2206v 2 2\u00b5La( )1/2, V \u00b5La 2 --------- 1/2 .= = Y max 1 c,( ).> y1 = 1, y2 = Y , y3 = 1, F = 2 Y c\u2013( ) c 1+( )Y1/2 Y 1+( )1/2 ------------------------------------------------ y1 1, y2 Y , y3 c2 Y 1+( ) Y c c 2+( )\u2013 ---------------------------- ,= = = F Y Y 1+ ------------ 1/2 = Y* c( ) c 1 c 2 2c c2+ +( )1/2 + +[ ]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002463_bf00118823-Figure8-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002463_bf00118823-Figure8-1.png", + "caption": "Fig. 8. Illustrating the active sliding movements required for a flagellum to execute helical undulations; these involve displacements of each tubule (relative to the next) described by the function G(z), with sliding velocities described by G' (Z), as in Eqs. (44) and (45).", + "texts": [ + " This shift (in the direction s increasing) is given by the second term on the right-hand side, which may be written A F ( k s - ~ot - ~b) with F ( Z ) = sin-l(f lsinZ). (43) The necessary pattern of shifts is revolving around the axoneme at angular velocity w = kc(see (6) above), with different phases ~ for each tubule. The shift relative to an adjacent tubule is A G ( k s - wt - \u00a2) with G ( Z ) = F ( Z ) - F ( Z - 2r/9) , (44) of which the time-derivative gives the sliding velocity as - w A C ' ( k s - w t - \u00a2 ) . (45) Fig. 8 shows the periodic functions G ( Z ) and G ' ( Z ) for the case a 2 = \u00bd on which I focus in Sections 2 and 3. The simple revolving pattern of sliding (45) is repeated for each value of s with a phase lag which increases in the direction of propagation. Helical undulation, then, makes no specially complex demands on the organisation of patterns of relative sliding of adjacent tubules in an axoneme. Accordingly, in the remainder of this section, I can concentrate primarily on its advantages and disadvantages in relation to propulsive efficiency" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003185_physrevlett.73.2841-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003185_physrevlett.73.2841-Figure1-1.png", + "caption": "FIG. 1. Geometry of the experiment. The white slabs represent hydrophobic barriers excluding the monolayer from the surface except in the narrow channel between them. Capillary depression keeps the water from rising into the channel; the contact angle is about 105 .", + "texts": [ + " Measurements of surface viscosity [2\u20145], surface shear relaxation [6\u20148], and flow in monolayers [9] also have a long history, but our understanding of these dynamic phenomena is incomplete. To what extent is the flow of a monolayer coupled to that of the water subphase? How do the flow properties depend on the structure of the film and the presence of domains or islands of coexisting phases? In order to answer these questions, we have examined a classical fluid dynamics problem, surface-pressure-driven flow through a channel (see Fig. 1). Our experiments differ from previous studies because, for the first time, the monolayer flow profile has been directly visualized and measured. Monolayers of tetradecanoic (TDA) or pentadecanoic (PDA) acid (Sigma or Nu-Chek Prep )9% pure) with a small amount (typically 0.01 mole fraction) of NBDhexadecylamine (Molecular Probes) were deposited from chloroform (Fisher spectranalyzed) solution on the surface of pure water (Millipore Milli-Q) contained in a custombuilt Teflon trough. The water temperature was controlled to ~0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure25.1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure25.1-1.png", + "caption": "Fig. 25.1 Schematic view of a SAW linear motor", + "texts": [ + " In this paper, we discussed application of DLC film as the wear-resistant film for the transducer and employed segment-structured DLC (S-DLC) films. In this chapter, installation of the S-DLC films to the friction surface of the SAW linear motor. At first, a silicon piece with the S-DLC films is described to confirm feasibility of the films as friction material for the SAW motor. Second, the stator transducer with S-DLC films on its surface is investigated. Finally, a new method to install the films on the LiNbO3 substrate is introduced. Figure 25.1 shows a schematic view of the SAW linear motor. The motor consists of a stator transducer and a slider. The transducer is a LiNbO3 128\u00b0 Y-cut X-prop substrate. When alternating current is applied to an interdigital transducer (IDT) on the substrate, Rayleigh wave, which is a kind of SAW, is generated and propagated to the direction indicated by the black arrow in the figure in the case of IDT (a) to apply the current. In progressive Rayleigh wave, micro-scopically, the surface of the substrate moves along an elliptical locus" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure2.8-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure2.8-1.png", + "caption": "Fig. 2.8. Determination of the transition matrix", + "texts": [ + "6) We now show the calculation of relative matrix Ai - 1 ,i' Let us consider a joint Si and suppose that it is rotational. The pro cess of calculation of a transition matrix is divided into two phases: the phase of \"assembling\" a joint and the phase of \"rotation\". The fol lowing vectors should be computed: .... a. _J. .... * .... -e. x (r\u00b7 1 \u00b7 x e.) _J. J.-,J._J. \\.... * .... e.x(r. 1 .xe.) \\ _J. 1-,J._J. (a) * a. J. (2.3.7) (b) ;- -+- -+ -+ -+ The vectors ~i and ai are perpendicular to :i and ei respectively. a i is the unit vector of the axis \"a\" and (2.3.7b) holds for qi=O (Fig. 2.8) \u2022 Introducing h. .... _J. b. } are obtained ~.x!., the three linearly independent vectors {~., !., _J. _J. ~ * *J. _J. (on the (i-l)-th segment). Introducing b. = e.xa., we -J. also obtain the three linearly independent vectors {~., J. J. 7: J. J. ~i' b i } (on the i-th segment). o Let Ai - 1 ,i be the transition matrix corresponding to qi O. Then (2.3.7b) holds and so: .... e. _J. .... a. -J. Now matrix notation will responding to the vector all other vectors in the o \":t A. 1 . a. , J. - , J" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003024_s0022-460x(03)00358-4-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003024_s0022-460x(03)00358-4-Figure2-1.png", + "caption": "Fig. 2. Contact between involute and rounded-out corner.", + "texts": [ + " From this position the gears are turned the angles Gp and Gg with an assumed load which, due to bearing deformations, will change the centre distance from a0 to a at the same time as the line between the gear centres is turned an angle t: Here a \u00bc ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0dp;x \u00fe dg;x\u00de 2 \u00fe \u00f0a0 \u00fe dp;y \u00fe dg;y\u00de 2 q ; \u00f01\u00de sin t \u00bc dp;x \u00fe dg;x a : \u00f02\u00de The gear deformation d is shown in Fig. 1 as an overlap between two undeformed gear teeth. Using the characteristics of the involute profile gives hp;f \u00bc gp \u00f0tan a0 \u00fe Gp \u00fe a\u00fe t a0\u00de; \u00f03\u00de hg;f \u00bc gg \u00f0tan a0 Gg \u00fe a\u00fe t a0\u00de; \u00f04\u00de where cos a \u00bc gp \u00fe gg a : \u00f05\u00de The deformation will be d \u00bc hp;f \u00fe hg;f \u00f0gp \u00fe gg\u00de tan a: \u00f06\u00de Instead of contact between the involute flanks of the two contacting gear teeth, the contact can take place between the involute flank on one of the gear tooth and the rounded-out corner on a tooth of the other gear. Fig. 2 shows a contact between the involute flank of the gear and the rounded-out corner of the pinion. When the gears are unloaded, the centre point of the tip rounding relative to a line between the gear centres is given by the angle g: With cos gp \u00bc gp Rp;tip r ; \u00f07\u00de this angle becomes g \u00bc tan gp \u00fe r gp tan a0 \u00fe a0 gp: \u00f08\u00de When loaded, the pinion and the gear turn the angles Gp and Gg; respectively. The position of the centre point of the tip rounding is in this position described by the angles kp and kg; for which kp \u00bc Gp g; \u00f09\u00de tan \u00f0kg t\u00de \u00bc \u00f0Rp;tip r\u00desin \u00f0kp \u00fe t\u00de a \u00f0Rp;tip r\u00decos \u00f0kp \u00fe t\u00de : \u00f010\u00de The position of the centre point of the tip rounding of the pinion can also be described by the angle gg; see Fig. 2. This angle can now be determined from cos gg \u00bc ggffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi \u00f0Rp;tip r\u00de2 sin2 \u00f0kp \u00fe t\u00de \u00fe \u00f0a \u00f0Rp;tip r\u00de cos \u00f0kp \u00fe t\u00de\u00de2 q : \u00f011\u00de The contact normal has the slope a \u00bc kg \u00fe gg t; \u00f012\u00de and the lever arms for the normal force in the contact point are hg;n \u00bc gg; \u00f013\u00de hp;n \u00bc a cos a hg;n: \u00f014\u00de The overlap d; which corresponds to the deformation in the contact point, is d \u00bc gg \u00f0gg \u00fe kg \u00fe tan a0 a0 Gg tan gg\u00de \u00fe r; \u00f015\u00de and the lever arms for the friction forces in the contact point are hg;f \u00bc gg tan gg r \u00fe d; \u00f016\u00de hp;f \u00bc hp;n tan \u00f0a\u00fe kp \u00fe t\u00de \u00fe r: \u00f017\u00de The last possibility of contact is between the involute flank of the pinion and the tip rounding of the gear" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002532_j.talanta.2003.11.008-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002532_j.talanta.2003.11.008-Figure2-1.png", + "caption": "Fig. 2. (a) General view and (b) schematic representation of conductometric biosensors.", + "texts": [ + " Two pairs of Pt (150 nm thick) interdigitated electrodes were constructed using the lift-off process on the Pyrex glass substrate (10 mm\u00d730 mm). A 50 nm thick intermediate Ti layer was used to improve the adhesion of Pt to the substrate. The central part of the sensor chip was closed by epoxy resin to define the electrode\u2019s working area. Both the digit width and interdigital distance were 10 m, and their length was about 1 mm. As a result, the \u201csensitive\u201d area of each electrode was about 1 mm2 (Fig. 2). The enzymatic membrane was prepared on the transducer surface by the cross-linking of enzyme with bovine albumin in saturated glutaraldehyde vapour [25]. A mixture containing 3.5% (w/w) enzyme, 5% bovine albumin, 10% glycerol in 20 mM phosphate buffer (pH 6.0) was deposited on the sensitive area of the sensor using a drop method, while another mixture of 10% (w/w) bovine albumin and 10% (w/w) glycerol in 20 mM buffer (pH 6.0) was deposited on the other electrode. The latter electrode was considered to be the reference sensor" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003508_tac.2008.2009615-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003508_tac.2008.2009615-Figure2-1.png", + "caption": "Fig. 2. Example of a Nyquist plot of the open-loop system with two relay controller.", + "texts": [ + " This suggests the technique of finding the parameters of the limit cycle\u2014via the solution of the harmonic balance equation [2] (5) where is the generic amplitude of the oscillation at the input to the nonlinearity, and is the complex frequency response characteristic (Nyquist plot) of the plant. Using the notation of the algorithm (2) and replacing the generic amplitude with the amplitude of the oscillation of the input to the first relay this equation can be rewritten as follows: (6) where the function at the right-hand side is given by Equation (5) is equivalent to the condition of the complex frequency response characteristic of the open-loop system intersecting the real axis in the point . The graphical illustration of the technique of solving (5) is given in Fig. 2. The function is a straight line the slope of which depends on ratio. The point of intersection of this function and of the Nyquist plot provides the solution of the periodic problem. Here, we summarize the steps to tune and : a) Identify the quadrant in the Nyquist plot where the desired frequency is located, which falls into one of the following categories (sets): b) The frequency of the oscillations depends only on the ratio, and it is possible to obtain the desired frequency by tuning the ratio (7) Since the amplitude of the oscillations is given by (8) then the and values can be computed as follows: if elsewhere (9) (10) Remark 1: It is possible to obtain the formulas for computing the exact values of and using the Locus of Perturbed Relay Systems (LPRS) method (see details in [1])" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003651_i2007-10170-y-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003651_i2007-10170-y-Figure4-1.png", + "caption": "Fig. 4. The scheme of photoactuation experiment, with the sample length controlled by a M icrometer and the exerted force recorded by Dynamometer.", + "texts": [ + " The efficiency of a UV-polarizer was so low that we could not use this sample/source for the measurement of the effects of polarization angle. The absorbed intensity of DO from LED source was \u223c 4mW/cm2 without a polarizer; from HG source \u223c 10mW/cm2 without a polarizer. The defocused beam from the ArL source provided \u223c 13mW/cm2 with the polarizer; this was the experimental system used in the polarization study. We remark as an aside that a very high local intensity of light is required to produce a significant photoactuation. In all experiments we kept the samples (10 \u00d7 5 \u00d7 0.3mm) at room temperature fixed in the dynamometer frame, Figure 4, measuring force with an accuracy of \u00b14 \u00b7 10\u22125 N and then converting it to engineering stress. This isostrain configuration has an advantage in that it avoids the need for the polymer chains to move and thus face complications due to entanglements and other viscoelastic phenomena. The experimental sequence was as follows: The mechanical history of the sample was eliminated by annealing at \u223c 100 \u25e6C, to start all experiments from the same conditions. The sample was clamped in the dynamometer and a small pre-strain (\u223c 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003628_s11044-008-9121-7-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003628_s11044-008-9121-7-Figure4-1.png", + "caption": "Fig. 4 Euclidean displacement of a rigid plate", + "texts": [ + " (5) Furthermore, since the coordinates of the points ai , i \u2208 {1,2,3} are easily expressed in the reference frame xyz, the corresponding 4 \u00d7 4 transformation matrix between the reference frames XYZ and xyz, 0T1, results in 0T1 = [ 0R1 0\u03c11 01\u00d73 1 ] , (6) where 0R1 is the rotation matrix. The computation of the rotation matrix 0R1 with the resulting coordinates, expressed in the reference frame XYZ, of the three points a1, a2, and a3 can be simplified by choosing appropriate locations for the reference frames XYZ and xyz. Consider a rigid plate A1A2A3; see Fig. 4 with a reference frame XYZ attached to it, and consider that after a Euclidean displacement, the pose of the plate changes according to the coordinates of the points a1, a2, and a3, expressed in the reference frame XYZ. Furthermore, by assuming that the Y axis of the reference frame XYZ is perpendicular to the plane A1A2A3, while the y axis of the reference frame xyz is perpendicular to the plane a1a2a3. The rotation matrix 0R1 between these reference frames results in 0R1 = [u\u0302x u\u0302y u\u0302z], (7) where \u2022 u\u0302x = ((\u03c1 \u2212 a2) + \u03bb(a3 \u2212 a2))/\u2016((\u03c1 \u2212 a2) + \u03bb(a3 \u2212 a2))\u2016 is a unit vector along the x axis, \u2022 \u03bb = d/\u2016a3 \u2212 a2\u2016, 1It is straightforward to show that once the feasible values for Z1 are calculated, the remaining components of the coordinates of the points ai are easily obtained from (1)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000094_tnnls.2021.3082994-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000094_tnnls.2021.3082994-Figure2-1.png", + "caption": "Fig. 2. Framework of single-link robot.", + "texts": [ + " Hence, the Zeno phenomenon will not appear. Remark 3: Obviously, there are nested hyperbolic tangent functions in the controller. The purpose of using the nested hyperbolic tangent functions is to apply Lemma 1 to eliminate the extra terms. In fact, the implementation of the developed controller is not complicated. Theoretically speaking, the convergence speed of the proposed control algorithm can be controlled faster as we increase the values of the design parameters ci . We consider the following single-link robot (see Fig. 2) to illustrate the efficiency of the developed two kinds of control schemes [35], [36]: Mq\u0308 + 1 2 mgl sin(q) = u, y = q (56) where q is the angle between the link and horizontal ground, M = 0.5 is the moment of inertia at the connection, u is the input torque, g = 9.8 is the acceleration due to gravity, and m = 1 and l = 1 are the mass and the length of the link, respectively. The system (56) can be rewritten as \u23a7\u23a8\u23a8 \u23a8\u23a9 x\u03071 = x2, x\u03072 = u \u2212 1 2 mgl sin(x1) /M y = x1 (57) where we can roughly get from the simulation results that the states are constrained in |x1| < 1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure3.11-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure3.11-1.png", + "caption": "Fig. 3.11. Hanipulator with additional force and moment acting on gripper", + "texts": [ + " We lo cate the problems appearing when a stationary constraint is substituted by a nonstationary one. Friction effects apper to be of main importan ce. Finally, we elaborate several cases of constraints, those which are interesting for practice (Para. 3.4.3. - 3.4.12). 165 3.4.1. Theory extension Let us consider a manipulator as an open chain of n segments, as con -> sidered in Para. 3.2. Let us apply an additional external force FA -> acting on gripper at point A and an additional external moment MA (Fig. 3.11 ) . Now, the dynamic model of such a mechanism will slightly differ from -> -> (2.3.2) since FA' MA must be included in the generalized forces. One obtains Wq (3.4.1) -> -> where FA' HA, are 3x1 matrices corresponding to FA' MA\u00b7 OF and OM are obtained from virtual displacement method. The additional component -> -> (QiFH) of generalized force Qi due to FA' MA is { ( -> ->i)-> = eixrA FA -> -> eiFA, If we introduce OF (n x 3) r :u with { -> dFi s.=O 1. s. =1 1. -> ->i eixrA, -> e i , (3.4.2) s.=O 1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002845_s100510050424-Figure17-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002845_s100510050424-Figure17-1.png", + "caption": "Fig. 17. Schematic diagram of the numerical model: (a) initial conditions: all masses i are in their initial position x0i without deformation; (b) interaction between the ith and the i + 1th bead: xi+1 \u2212 xi > 0 corresponds to an interpenetration between the two beads (or a compression of the nonlinear spring) whereas xi+1 \u2212 xi < 0 means that the beads are no more in contact (or the two springs are separated from each other); (c) directions of the interactions between the ith and the i+ 1th bead and between the i\u2212 1th and the ith bead.", + "texts": [ + " Consequently, the column can be treated as a chain of N mass points of mass m, each one interacting with its nearest neighbors through the Hertz\u2019s law, i.e., Fi = { k(xi+1 \u2212 xi)3/2 if xi+1 \u2212 xi > 0 0 otherwise \u2200 1 \u2264 i \u2264 N \u2212 1 , (9) where Fi is the interaction force between the ith and the i + 1th mass, xi the displacement of the ith masspoint from its initial position x0i without deformation, and k is a constant given in equation (12). With the convention on the positive direction of displacements xi (see Fig. 17), the ith mass interacts with the i + 1th, through the Hertz\u2019s law, if xi+1 \u2212 xi > 0 (see Fig. 17b) whereas they separate from each other if xi+1 \u2212 xi < 0. At t = 0 (see Fig. 17a), all the nonlinear springs are uncompressed, and an identical velocity vimp is imposed to each bead. The initial conditions of the problem are thus { xi(t = 0) = 0 x\u0307i(t = 0) = vimp \u2200 1 \u2264 i \u2264 N . (10) The sensor is represented by a nonlinear spring of constant K linked to an infinite mass. The parameter K of this spring is different from k, proper to all the other springs, in order to be close to the experimental conditions, since the Hertz\u2019s law coefficient for a sphere\u2013plane contact is different from the one for a sphere\u2013sphere contact", + " Thus, from equations (3) and (12), 5 This impact time is the smallest time scale appearing in the system, since equations (11) are defined in the quasi\u2013static limit where acoustic wave propagation within a bead is neglected. k = 6.9716\u00d7 109 N/m3/2 and K = 9.858\u00d7 109 N/m3/2. For most simulations, the choice for the impact velocity of the column, vimp = 0.3 m/s, will correspond to a height of fall of 4.6 mm. Figure 18 shows the temporal evolution of displacements xi(t), compared to their initial position, of each bead i during the collision of a column of N = 7 beads with a wall. With the conventions in Figure 17, a compression of the ith bead corresponds to a positive displacement xi. The seventh bead (i.e., the one at the top of the column) embeds itself linearly during the loading cycle (x7 increases), then performs its unloading cycle (x7 decreases), before separating from the sixth bead (x7 \u2212 x6 < 0) and going away upwards indefinitely with a constant velocity since the gravity is neglected. The bead at the bottom of the column (bead 1) embeds itself, then oscillates around a constant displacement, during all the collision, before doing its unloading cycle and leaving the wall (x1 < 0)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002681_j.mechmachtheory.2004.04.003-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002681_j.mechmachtheory.2004.04.003-Figure2-1.png", + "caption": "Fig. 2. The half toroidal CVT: spin motion and rolling motion of the roller depicted for no-slip conditions; (a) speed ratio equal to 1; (b) no spin condition (speed ratio differs from the unit value).", + "texts": [ + " The quantity e is the distance of the toroidal cavity from the disc axes, it is related to the aspect ratio k \u00bc e=r0 of the toroidal traction drive. Moreover in a half-toroidal CVT, the half cone-angle h of the roller is about 50\u201370 , whereas in a full-toroidal CVT the cone angle is 90 . All the remaining geometrical parameters are reported in Table 1. In this subsection the kinematics of the toroidal traction drives is analyzed during the steady state operation of the variator. Consider the roller and the discs as rigid bodies and assume no-slip at points A and B (see Fig. 2). Under these conditions, the motion of the roller relative to the input disc is a spherical rigid motion, of which the instantaneous axis of rotation can be easily determined as the straight-line through the points of null relative velocity A and X (the point X is the intersection of the roller absolute axis of rotation and the input-disc absolute axis of rotation). Similar arguments hold when studying the relative velocity field between the roller and the outputdisc, in this case the instantaneous axis of rotation of the relative motion is the straight-line BX. Let x1, x2 and x3 be, respectively, the absolute angular velocities of the input disc, of the roller and that of the output disc. The angular velocity of the roller relative to the input disc is, therefore, x21 \u00bc x2 x1, whereas that one relative to the output disc is x23 \u00bc x2 x3. Figs. 2 and 3 show these two relative velocities of rotation x21 and x23 both for the half-toroidal and fulltoroidal CVTs. It is clearly shown that, since the point of intersection H (see Fig. 2) of the two tangents to the toroidal cavity at points A and B does not always coincides with the point X, both the relative angular velocities x21 and x23 have non-zero spin vector components x21spin and x23spin, respectively. Moreover, the ratio \u00f0x21spin\u00dein=jx21j \u00bc \u00f0x23spin\u00deout=jx23j \u00bc sin a, assumes its maximum value for srID \u00bc r3=r1 \u00bc 1, since the distance between the points H and X is maximum for this value of the ideal speed ratio. Furthermore, Fig. 2 shows that, for the half-toroidal CVT, two points exist at which H and X coincide and the spin motion vanishes. Different considerations have to be done for the full-toroidal traction drive. This time, Fig. 3 shows that the point H goes to infinity, thus the spin motion never vanishes, and, because of the bigger angle a, it is always bigger than in the case of the half-toroidal CVT. Once again, the worst situation occurs for srID \u00bc 1, when (see Fig. 3) the modulus of the spin vector components x21spin and x23spin equals the modulus of absolute angular velocity of the output and input discs, respectively", + " As already discussed before, it is shown that, for the ideal case of no-slip, the worst condition as regards the magnitude of the spin occurs for c \u00bc 0, that is to say for srID \u00bc 1. In fact, replacing both Crin and Crout by zero, Eqs. (7) and (8) become: \u00f0r21\u00deno-slip \u00bc cos c \u00f01\u00fe k\u00de cos h sin h \u00bc \u00f0r23\u00deno-slip \u00f09\u00de Equation (9) shows that the two spin ratios r21 and r23 assume their maximum value when cos c \u00bc 1, i.e. c \u00bc 0. Observe that if cos h < \u00f01\u00fe k\u00de 1 two different values of the tilting angle c also exist at which the spin ratios vanish, as pointed out in Section 2.2 (see also Fig. 2). For full toroidal CVT replacing h by p=2 in Eq. (9) we obtain \u00f0r21FT\u00deno-slip \u00bc \u00f0r23FT\u00deno-slip \u00bc cos c which is always bigger than the spin ratios of an half-toroidal CVT. Fig. 5 shows, for no-slip conditions, the spin-ratios as a function of the ideal speed ratio srID. The CVT geometrical characteristics are reported in Table 1, where the radii of curvature r22 have been chosen in order to obtain the same maximum shear stress in both CVTs (see also Section 4.1). As before predicted the spin ratio of the full-toroidal CVT is about five times higher than that of the half-toroidal one" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002427_1.1321268-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002427_1.1321268-Figure1-1.png", + "caption": "Fig. 1 Free body diagram for longitudinal motion of an automobile", + "texts": [ + " In addition, the parameter estimates a\u0302 i are also guaranteed to converge to the correct values. Readers are referred to Yip and Hedrick @8# for proofs of Theorems 3 and 4. In this section an application of MSS will be presented, a combined brake/throttle controller for precision automated vehicle following Hedrick @13#. The control system was designed for use on an automatically controlled vehicle @14#. 4.1 Vehicle Dynamics. A free-body diagram, showing the major forces acting on the vehicle is shown in Fig. 1. It is assumed that no slip occurs at the wheels or across the vehicle\u2019s torque converter @14,15#. Thus, the engine speed, ve , and the vehicle speed, v , are related by v5Rghve (38) Performing a force and torque balance on the chassis, front and rear axles, we can obtain five equations: two at the front wheel, two at the back wheel, and one on the chassis. Since the brake and engine torque is the two control inputs, it is desirable to solve the equations for the acceleration of the vehicle in terms of these two inputs" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003024_s0022-460x(03)00358-4-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003024_s0022-460x(03)00358-4-Figure4-1.png", + "caption": "Fig. 4. Gear contact.", + "texts": [ + " The gears are mounted on linear elastic bearings with the stiffnesses cp and cg while the external inertias are mounted on stiff bearings. The transmission is driven by the torque Mdrive and is braked by the torque Mbrake: Loading the parts will, of course, give rise to elastic deformations. Also resisting forces due to the deformation velocity will however occur. This damping is assumed to be viscous, which implies that the torque on the gears can be expressed as Mp \u00bc c1 \u00f0G1 Gp\u00de \u00fe d1 \u00f0 \u2019G1 \u2019Gp\u00de; \u00f018\u00de Mg \u00bc c2 \u00f0Gg G2\u00de \u00fe d2 \u00f0 \u2019Gg \u2019G2\u00de: \u00f019\u00de An arbitrary contact between the gears is shown in Fig. 4, where the deformations of the bearings are dp;x; dp;y; dg;x; and dg;y: The forces in the contact depend on the elastic deformation, the friction between the gear teeth, and the damping due to the deformation velocity. The direction of the friction force and the damping force are dependent of the velocity. The relative velocities between the gear teeth in the normal direction, and in a direction perpendicular to that, are Dvn \u00bc \u2019Gphp;n \u00fe \u2019dp;x cos \u00f0a\u00fe t\u00de \u2019dp;y sin \u00f0a\u00fe t\u00de \u2019Gghg;n \u00fe \u2019dg;x cos \u00f0a\u00fe t\u00de \u2019dg;y sin \u00f0a\u00fe t\u00de; \u00f020\u00de Dvf \u00bc \u2019Gghg;f \u2019dg;x sin \u00f0a\u00fe t\u00de \u2019dg;y cos \u00f0a\u00fe t\u00de \u2019Gphp;f \u2019dp;x sin \u00f0a\u00fe t\u00de \u2019dp;y cos \u00f0a\u00fe t\u00de: \u00f021\u00de The equations of motion can now be formulated as J1 " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002798_j.jphotobiol.2004.04.001-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002798_j.jphotobiol.2004.04.001-Figure4-1.png", + "caption": "Fig. 4. Plots of CDRF and LC versus\u00f0\u00bdRF 0 \u00bdRF \u00de for photodegradation of riboflavin at 1.50 M phosphate concentration. (s) LC and (d) CDRF.", + "texts": [ + " The values of kobs (Table 5) at various phosphate concentrations represent the overall rate of riboflavin degradation and include the contribution of photoprocesses, in addition to normal photolysis and photoaddition reactions, occurring under the present experimental conditions. The rate constants for the two major reactions, i.e., photoaddition and photolysis were determined from the plots of [CDRF] and [LC] versus \u00f0\u00bdRF 0 \u00bdRF \u00de at various phosphate concentrations. A typical plot at 1.50 M phosphate concentration is shown in Fig. 4. The values of k1 (formation of CDRF) and k2 (formation of LC) were determined from the respective slopes [k1=\u00f0k1 \u00fe k2\u00de] and [k2=\u00f0k1 \u00fe k2\u00de] assuming that (k1 \u00fe k2) is equal to the value of kobs for the photodegradation of RF at a particular phosphate concentration. These values indicate that some other photoprocesses, e.g., formation of CMF and any other minor product, may also be involved. In order to evaluate the effect of phosphate ions on the rate of photodegradation of riboflavin, the values of kobs were plotted against total phosphate concentration (Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002724_s00170-003-1830-8-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002724_s00170-003-1830-8-Figure2-1.png", + "caption": "Fig. 2. Dynamic model of the transmission", + "texts": [ + " Thus, gear mesh stiffness is periodic with the period Te and can be approximated by [9]: k(t) = { kmax if nTe \u2264 t \u2264 (n + \u03b5\u22121)Te kmin if (n + \u03b5\u22121)Te \u2264 t \u2264 (n +1)Te (3) where n is an integer representing the nth gear mesh period. Fourier development of k(t) yields: k (t) = km + \u2206k \u03c0 \u221e\u2211 i=1 1 i [ sin 2i\u03c0(\u03b5\u22121) cos 2i\u03c0t Te +(1\u2212 cos 2i\u03c0(\u03b5\u22121) sin 2i\u03c0t Te ] (4) with: km = kmax (\u03b5\u22121)+ (2\u2212 \u03b5)kmin (5) \u2206k = kmax \u2212 kmin (6) and with km and \u2206k being positive. We will take kmax = 6107 N/m, kmin = 3107 N/m and \u03b5 = 1.66. Figure 3a represents the time variation of stiffness gear mesh k(t). 3.2 Dynamical model of the transmission A one-stage gearing train can be modelled by the two degrees of freedom system shown in Fig. 2, whose motion is described by the angular rotations \u03b81(t) and \u03b82(t), respectively, for the pinion (1) and the wheel (2) [9, 10, 14]. The pinion has a basis radius r1, inertia moment J1 and is subjected to the torque T1. The wheel has a basis radius r2, inertia moment J2 and is subjected to the torque T2. During gear mesh, the teeth oppose the bending stiffness k(t) represented by Fig. 3a and a damping torque (with the proportional viscous coefficient c(t)), which are both time dependent, depending on whether one or two pairs of teeth are engaged (Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002442_j.bios.2003.08.019-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002442_j.bios.2003.08.019-Figure1-1.png", + "caption": "Fig. 1. Cross-section of sensor device.", + "texts": [ + " The supernatant was passed through a small column of Sephadex G200 (approximately 100 l), which was sieved in the dry state through a 25 micron mesh sized filter (sieve no. 500, VWR Scientific, Westchester, PA, USA) prior to use. The column was washed with 100 l of PBS to remove unbound ConA and incubated in a freezer at \u221220 \u25e6C for 1 h. Then, it was freeze-dried (Ultra-Dry Benchtop RVT, Freezedry Specialties Inc., Osseo, MN, USA) and stored in the refrigerator until used. The fluorescence sensor featured a square geometry with a width of 0.7 cm and thickness of approximately 0.1 cm. A cross-section of the sensor is shown in Fig. 1. Both Sephadex beads dyed with alkali blue 6B and Alexa647 ConA were freeze-dried together, and then immobilized under dry conditions onto a polymer support layer using proprietary technology. The upper layer of the package consisted of a semipermeable regenerated cellulose membrane. Both layers were glued together along the outer edges of the sensor container with a cyanoacrylate adhesive, preventing leakage of Alexa647\u2013ConA out of the package. The dry sensor packages were wetted and degassed by perfusion in helium-purged buffer solution" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000274_j.mechatronics.2021.102554-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000274_j.mechatronics.2021.102554-Figure1-1.png", + "caption": "Fig. 1. The diagram of FAE mechanism.", + "texts": [ + " Furthermore, the stability conditions that bandwidth needs to meet are given from the perspective of transfer function. This paper is organized as following. Section 2 presents the design scheme and mathematical modeling of the flexible ankle exoskeleton. The control strategy of exoskeleton are elaborated in Section 3. In Section 4, we analyze and evaluate the designed controller by experiments. Finally, main conclusions are summarized in Section 5. A mechanism composition of FAE is proposed, including driving system, transmission system, and end-effector, which is shown in Fig. 1. The driving system consists of electrical motor, gear reducer, groove wheel, etc. To improve the control accuracy of FAE, Panasonic servo electrical motor with rated power of 1.5KW and rated torque of 4.77Nm and the precision planetary reducer are employed. The diameter of the groove wheel is designed to be 60 mm. The driving system and the endeffector are connected by the transmission system, which uses flexible structure composed of Bowden cable and spring. The Bowden cable sheath is made of speed change pipe of mountain bike, and the inner cable is made of 16 braided PE rope, which has strong toughness" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure3.16-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure3.16-1.png", + "caption": "Fig. 3.16. Gripper with spherical joint constraint", + "texts": [], + "surrounding_texts": [ + "This paragraph develops the theory dealing with manipulators having constraints imposed on gripper motion. Each constraint restricts to a certain extent the possibility for gripper motion. In this way the num ber of d.o.f. of the gripper is reduced. In order to avoid a purely theoretical discussion, we consider only these types of constraints which appear in practical problems. But, there are no obstacles to ex panding the theory to cover any type of constraints. We are mainly interested in manipulators having five or six d.o.f. since they are needed for the solution of manipulation tasks considered. Thus, nE{S, 6} holds. Further, we assume that there is no singularity with the manipulators and the tasks considered. First, we give an extension of the theory explained in Ch. 2. Then, an example of a stationary constraint is considered (Para. 3.4.2). We lo cate the problems appearing when a stationary constraint is substituted by a nonstationary one. Friction effects apper to be of main importan ce. Finally, we elaborate several cases of constraints, those which are interesting for practice (Para. 3.4.3. - 3.4.12). 165 3.4.1. Theory extension Let us consider a manipulator as an open chain of n segments, as con -> sidered in Para. 3.2. Let us apply an additional external force FA -> acting on gripper at point A and an additional external moment MA (Fig. 3.11 ) . Now, the dynamic model of such a mechanism will slightly differ from -> -> (2.3.2) since FA' MA must be included in the generalized forces. One obtains Wq (3.4.1) -> -> where FA' HA, are 3x1 matrices corresponding to FA' MA\u00b7 OF and OM are obtained from virtual displacement method. The additional component -> -> (QiFH) of generalized force Qi due to FA' MA is { ( -> ->i)-> = eixrA FA -> -> eiFA, If we introduce OF (n x 3) r :u with { -> dFi s.=O 1. s. =1 1. -> ->i eixrA, -> e i , (3.4.2) s.=O 1. (3.4.3) s.=1 1. 166 n-1( ) ->- ->-L r' -r + k=i kk k,k+1 and ->- dMi then we obtain the form (3.4.1). -> r' nn ->- + p riO o , (3.4.4) s.=O ~ (3.4.5) s. =1 ~ This extension was necessary since the constraints produce reaction force and reaction moment acting on gripper. These reactions will be determined so that the constraints are satisfied. 3.4.2. Surface-type constraint Let us consider an n-d.o.f. manipulator and impose the constraint that the point A of the gripper cannot move freely but is forced to be on a given surface (Fig. 3.12). The immobile surface is defined by h(x, y, z) o (3.4.6) An iterative approach to this problem is given in [8]. Here, we derive another, noniterative one. 167 If we introduce reaction force -> -> FA R no (3.4.7) where -> IFAI, -> Ilh(xA, YA' zA) R n 0 IVhl (3.4.8) and Ilh f out MA, i.e.: (3.4.10) The constraint (3.4.6) can be written in the form of velocities. By differentation: o (3.4.11 ) The next derivation produces the acceleration form o (3.4.12) where - -flSvAro (3.4.51) ->- where fl is friction coefficient and vAro is the unit vector ->- ->- ->- I v - v v Aro - Ar/l Ar (3.4.52) ->- and vAr is the relative velocity of gripper point A with respect to the surface. This relative velocity can be expressed by the difference -> vAr (3.4.53) ->- ->- where vA is the velocity of point A and Vs is the velocity of the cor\u2022 ->- responding surface point. Slnce vA can be obtained from (3.4.38) and ->- {afx af af} Vs = ~,~, atZ , one obtains Of Of x x aU 1 aU 2 Of Of vAr ..J.. -.::l aU 1 aU 2 (3.4.54) Of Of Z Z aU 1 aU 2 178 The friction force produces an additional component of generalized forces and thus the model (3.4.34) becomes where G' P + U - WJ- 1 (A -A) + D(G+G')S r r T I ]T - v 10 L \\.I Aro I ( 1 x 3 ) Finally the dynamic model (3.4.35) becomes and it can be solved for n unknowns (X r , S). (3.4.55 ) (3.4.56 ) (3.4.57) Jamming. The discussion presented holds when the joint A slides over the surface. If a manipulator starts from a resting position, it may happen that the driving torques applied can not move the point A over the surface because of friction. Something very similar happens if at one time instant the relative velocity becomes zero and we want to continue the relative motion. The case when the driving torques applied cannot produce the relative motion because of friction is called jam ming. In that case there is no sliding of point A over the surface. The friction force is less than \\.IS and is sonsidered as an unknown force. Let us find this force. If we introduce the unknown friction force Fi then the model (3.4.34) becomes where G is defined by (3.4.50). The friction has two independent com ponents along two tangential unit vectors. Thus or in matrix form Now the model obtains the form WJ- 1J X r r 179 Since in the case of jamming it is u1 = 0, u2 = 0 the model obtained can be solved for n unknowns: e, ~, ~, S, Ff1 , Ff2 if n=6 or e, ~, S, F f1 , Ff2 if n=5. The friction force has the absolute value IF'I = YF,2 + F,2 f f1 f2 This absolute value is tested against maximal possible value ~S. If I+F f' I h 1+ I ~ ~S then t ere is jamming of point A and the value of F f is correct. If we obtain IFfl > ~S, this value is not correct since slid ing will start. In this case there is no jamming. Let it be noted that we are talking about jamming of point A only. u 1 and u 2 are stopped but the gripper still has n r -2 d.o.f. (6, ~, ~ for n=6 or ~, ~ for n=5). Point A behaves as if it were fixed on a surface (see Para. 3.4.6) or some kind of rolling can appear (see. Para. 3.4.12). 3.4.5. Gripper moving along a line We consider a manipulator with a gripper subject to a line-type con straint. It means that the gripper cannot move freely but its point A is forced to move along a given line. The discussion of this problem will be similar to the discussion of surface-type constraint (Para. 3.4.4), and therefore it will not be as detailed. Let\"us define the relative position of the gripper point A with respect to the line by means of a parameter u (Fig. 3.15). The parameter equations of a moving line (nonstationary constraint) can be written in the form x fx(u, t) y (3.4.58) z = fz(u, t) 180 NOw, n n - 2 and the reduced position vec tor is r [u 6 T lP] , for n=5 X (3.4.59) r \\)!]T, [u 6 lP for n=6 i.e. u 2 6, u 3 lP, u 4 \\)!. z -2 u ~-----------y~------------; Cl.z 3f z au li 181 (3.4.61) The equations (3.4.61) can be written in the matrix form 3f xA x au Cl. x 3f YA -..-:t.. [lil + Cl. (3.4.62) Clu Y Clf zA z au Cl. z This acceleration form of the constraint requires that (3.4.58) and (3.4.60) be satisfied by the initial state. Now, the Jacobian form (3.4.25) can be obtained. The reduced Jacobian and the reduced adjoint matrix are: J = r Clf x au Clf ---..X Clu I I I I I I I I : O(3 x (n-3)) I I I 3f I Z I Clu : ----------1---------------- I O(n-3)x1: I((n-3)x(n-3)) ->- A r Cl. X Cl. y (3.4.63) Cl. Z o((n-3)x1) The reaction force FA is perpendicular to the line and, accordingly, ..,. to the tangent T as well. The tangent is Clf Clf 3f Z } ..,. {ClUx , ---..X T dU , dU (3.4.64 ) with the unit vector ..,. TIITI T 0 (3.4.65) Now, we have the conditions: ..,. ..,. ..,. 0 MA 0, ToFA (3.4.66 ) 182 which can be written in the form (3.4.30) where E (3.4.67) Now, all the elements of dynamic model (3.4.32) are determined and the model can be solved. If the concept of independent reaction component is to be appied then -+ -+ we define two unit vectors No and Bo perpendicular to each other and each of them perpendicular to the line. These vectors are -+ -+ B xT o 0 -+ -+ B (3.4.68) (3.4.69 ) and the force FA can be expressed in terms of two independent scalar components SN' SB: (3.4.70) The reduced reaction vector is R = r S SB] T (3 4 71) Ar IN\u00b7\u00b7 The matrix G which transforms the reaction components (eg. (3.4.33)) is G ~ No (3x1) : Bo (3x1) 1 ----------t----------- O(3x1) : O(3x1) (6x2) (3.4.72) Now, all the elements of the dynamic model (3.4.35) are determined and the model can be solved. Friction effects. Let us introduce the friction force -+ -llSVAro (3.4.73 ) where 183 S IFAI .jS~ + S2 B (3.4.74) and ... = ~Ar/I~Arl (3.4.75) vAro at af atr ... [x -.X. z \u2022 v Ar = au -- u au au The friction force produces an additional component of generalized forces and thus the model (3.4.34) becomes: or WJ- 1J X r r where Dp is as defined in (3.4.3). (3.4.76) The equation (3.4.76) defines the dynamic model in the presence of friction. However, the system is not linear with respect to SN' SB. If the nominal dynamics has to be calculated, this nonlinearity is not important since SA' SB are given and the system is solved for P. But, in a simulation problem the system has to be solved for Xr , SA' SB and the nonlinearity makes the problem rather complicated. 3.4.6. Spherical joint constraint We consider a manipulator having the gripper connected to the ground, or to an object which moves according to a given law, by means of a spherical joint (Pig. 3.16). The constraint can be expressed by the requirement that the point A moves according to f (t) y (3.4.77) 184 (nonstationary constraint). The velocity and the acceleration forms of this constraint are and f (t) y f (t) y (3.4.78) (3.4.79) Now, nr =n-3 and there are only three free parameters forming the reduced position vector { [8 [ 8 T IP 1 , for n=5 (3.4.80) for n=6 The Jacobian form (3.4.25) can be obtained if the reduced Jacobian and the reduced adjoint matrix are defined as l O(3x (n-3\u00bb 1 I ( (n-3) x (n-3\u00bb A r fx(t) fy(t) f (t) z (3.4.81 ) The reaction force FA has three independent components and the reaction 185 -+ moment equals zero (MA=O). The form (3.4.30) can be used if E (3.4.82) NOw, all the elements of dynamic model (3.4.32) are determined and the model can be solved. If we wish to use the form (3.4.33) then G (3.4.83) and the dynamic model (3.4.35) can be used. 3.4.7. Two d.o.f. joint constraint We consider a manipulator having the gripper connected to the ground (or to an object which moves according to a given law) by means of a two d.o.f. joint. Let the joint permit a relative translation along the -+ -+ unit vector h and a relative rotation around h (Fig. 3.17). Let it be stressed that when we talk about the gripper we understand the whole segment Un\" of the chain. Let us first discuss the prescribed motion of the object to which the 186 gripper is connected (nonstationary constraint). Let us define the lin * ear motion of the object (i.e., of its point A shown in Figs. 3.17 and 3.18) by * * * xA = f 1 (t) , YA = f 2 (t) , zA = f3 (t) (3.4.84 ) and the angular motion of the object by * * * e f4 (t) , 4J = f 5 (t) , ljJ = f6 (t) (3.4.85) * * * (see Fig. 3.18). The angles e , 4J , ljJ are defined for the moving object but in a way analogous to the definition of gripper angles e, 4J, ljJ in Para. 2.4. 187 * * * * Let us define an orientation coordinate system 0sxsYszs corresponding to the moving object, in a way analogous to the definition of gripper * orientation system (0 x y z in Para. 2.4). The origin 0 coincides * * s s s~s * ~* * s~* ~* ~* with A . Axis x is along h*, z is along s , and Ys along ~ = s xh \u2022 s s If we connect the gripper to the moving object, as shown in Fig. 3.17, ~ ~* then h (on the gripper) has to coincide with h (on the object) and * accordingly Xs coincides with xs. This means that e * e , * We note that the relative translation occurs along x . s* with respect to axis xs. coordinate of gripper point A * and Zs coordinates of point A --*- o A s --* A A equal zero it holds that (3.4.86) Let u 1 be the * Since the Ys (3.4.87) (see Fig. 3.19). Thus u 1 defines the relative translation. +* +* + Relative rotation is performed around.h (note h =h) and is defined by (3.4.88) If a six d.o.f. manipulator (n=6) is considered, u 2 is a free parameter * since ~ can be changed as we wish (~ is given by (3.4.85\u00bb. But, with a five d.o.f. manipulator (n=5) the angle ~ is not free but it follows from xA' YA' zA' e, ~, and hence, u 2 is not a free parameter. Let us now define the reduced position vector determining the position relative to the joint constraint. Since nr = n-4 it follows that 188 for n=5 (3.4.89) for n=6 The position of gripper point A can be expressed in the form (3.4.90) ---rand A A can be expressed in the object orientation system as ---rA A = {u1 , 0, O} (3.4.91) Thus, we obtain the matrix relation (3.4.92) * where A is the transition matrix s * of the object orientation system. As is obtained in a may analogous to that for gripper orientation system * * * (Para. 2.4). The difference is in that angles a , ~ ,~ appear . * .. * instead of a, ~, ~. analogy. The derivatives As' As can also be obtained by The first and the second derivative of (3.4.92) give and From (2.4.21) if follows that .* + F~*~ and * + G (3.4.93) (3.4.94) (3.4.95) * * * * where Fa*' F~*, F~* and G are defined by (2.4.21) but with a , ~ , ~ instead of a, ~, ~. Keeping in mind the structure of matrices Aa*' A~*, Aw* (see eq. 189 (2.4.16)) it is clear that the acceleration wA given by (3.4.94) will * \u2022 * .. * not depend on ~ or its derivatives ~ , ~ . The relation (3.4.94) can be transformed in to .. * f4J*l4J ~----------~v------------------------~) * a w (3.4.96) where f8*1' f4J*l' * a s1 are the first columns of the matrices F8*' F4J*' As' respectively. * . wA lS, determined by (3.4.84), i.e., (3.4.97) * * and 8 ,4J and their derivatives are given by (3.4.85), i.e., . * 8 . * 4J .. * 8 .. f 4 (t) , .. * 4J Keeping in mind (3.4.86) and (3.4.96) we may write the Jacobian form (3.4.25) where the reduced Jacobian and the reduced acjoint matrix are I I I O(3 x (n-5)) ------------~----------------I I I I O(l x (n-5)) ------------~----------------I I I I O(l x (n-5)) ------------~----------------I o I I \u00abn-5)x1): \u00abn-5)x(n-5)) f6 \u00abn-5)x1) (3.4.98) + The joint constraint imposed produces a reaction force FA and the re~ -+ -+* -+ +* action +*+ moment HA. The following conditions hold: FA1-h and MA1-h. Hence, -+*+ h FA o and h MA o or, in the matrix form: 0, o (3.4.99) These conditions can be written in the form (3.4.30) where l hT I l\"\" I 0(1 <3) I E = I (3.4.100) --------r-------I hT 0(1 <3) : 190 Now, all the elements of dynamic model (3.4.32) are determined and the model can be solved. If the concept of independent reaction components is to be applied, we ~ -+ -+- -+ introduce four independent reaction components. Since FA~h, MA~h and, -+ * -+ -+* accordingly, FA~xs, MA~xs' we express these reactions in terms of in-+-* +* +*-+* dependent components along the unit vectors s and ~ = s xh : (3.4.101) The reduced reaction vector is The matrix G which transforms the reaction components (eq. (3.4.33) is G l -:~~~~~-l-~~~~~~-l-~~~~~~-~-~~~~~~- j (3.4.103) I I * I * O(3x1) : O(3x1) : s(3x1) : ~(3X1) (6x4) Now, all the elements of the dynamic model (3.4.35) are determined and the model can be solved. Friction effects. We remember that the relative motion of the gripper ~ with respect to the joint connection is defined by u 1 = A A and u = * 2 = 1jJ - 1jJ \u2022 ... Let us find the friction force. We substitute the reaction moment MA -+ -+ -+-+ by two forces FM1 , FM2 , and the reaction force FA by two forces FF1' ... FF2 (Fig. 3.20). The lengths ~1 and ~2 are shown in Fig. 3.21a,b and they are defined as * if U1+LL (Fig. 3.21a). Now: 191 ->- R,2 ->- ->- R,1 ->- FF1 R,1+R,2 FA' FF2 R,1+R,2 FA (3.4.104) and ->- ->- ->- ->- ->- hXMA ->- hXMA FM1 R,1+R,2 , FM2 - R,1 +R,2 (3.4.105) The total forces are ->- ->- ->- ->- ->- ->- F1 FF1 + FM1 , F2 FF2 + FM2 (3.4.106) These forces determine the position of gripper points A; and A; which are in connection with the cylindrical constraint (Figs. 3.21, 3.22). ->- ->- The friction forces Ff1 and Ff2 act in these points. The absolute values of these friction forces (Pf1 and Pf2 ) are ~lp1 I 192 and ~IF21. The forces act in the directions opposite to the relative velocities of points Ai, Ai. Each velocity has two components: longi tudinal (along h) and tangential (along T). Thus, the relative veloci ties of Ai and Ai with respect to cylindrical constraint are (3.4.107) -+ -+ where R is the radius of the cylinder, and T1 , T2 are tangential unit -+ -+ vectors in points Ai, Ai (Fig. 3.22). The vectors T1, T2 can be found as NOw, the friction forces are (3.4.108 ) -+ -+ where v 1ro and v 2ro are unit vectors: ... ..,. ... v 2ro = v2r/lv2rl -+ Each friction force has a longitudinal (F~) and a tangential component ... (F t ) : 193 -u ->- ->- ->-->- -)1iF2icosa ->- -)1i F 2 i 1 ->- FQ,2 (Fn-h)h h h 0-2 2-2 u 1 +R u 2 ->- ->- ->- ->- -)1iF1 isina ->- R~2 ->- F t1 (Ff1 -T1 )T1 T1 -)1i F1 i T1 );2 2-2 u 1 +R u 2 - ->- ->- ->- ->- -)1iF2isina ->- ->- RU 2 ->- Ft2 (F n -T 2 )T 2 T2 -)1i F 2 i T2 0-2 2-2 U1+R u 2 These forces can be arranged in a different way to find the total lon gitudinal friction force: -> and the total friction moment (scalar value) around h: ->- ->- (3.4.109) (3.4.110) The friction forces Ff1 , Ff2 produce additional components of generalized forces and thus the model (3.4.34) becomes (3.4.111) where DF is defined by (3.4.3). The equation (3.4.111) defines the dynamic model in the presence of friction. However, the system is not linear with respect to the inde pendent reaction components RAr = [8 1 8 2 8 3 8 4 ]T since the friction forces depend nonlinearly on these components. If the nominal dynamics has to be calculated, this nonlinearity causes no additional problems since these independent components (i.e., the reactions FA' MA) are given and the system is solved for P. But, in a simulation problem the system (3.4.111) has to be solved for Xr , 8 1 , 8 2 , 8 3 , 8 4 and the pres ence of nonlinearity makes the problem rather complicated. This discussion on friction holds in the case when there is sliding in points A1 and A;. But, if friction is strong enough then jamming can appear and the discussion does not apply. Let us be more precise. If friction is strong enough then there will be no sliding in points A1 and A;. In such case rolling or jamming will appear. Also, there can be a rolling with sliding. These problems are rather complex and they 194 will not be considered here. 3.4.8. Rotational joint constraint We consider a manipulator having the gripper connected to the ground, or to an object which moves according to a given lew, by means of a ->- joint permitting one rotation only. Let h be the unit vector of rotation axis (Fig. 3.23). Let us first discuss the prescribed motion of the object to which the gripper is connected. Let this motion be defined by (3.4.113) * * e = f4 (t) , (jJ = fS (t) , (3.4.114) * as was done in the previous Para. 3.4.7. Note that A = A here, and, * * * accordingly, xA = xA ' YA = YA' zA = zA. Thus we use A only. The joint * * connection also produces: e = e and (jJ = (jJ \u2022 The parameter * u 1); - 1); (3.4.11S) defines the relative position of the gripper with respect to the moving object. If a six d.o.f. manipulator is considered, u is a free parame ter and nr n - S = 1. With a five d.o.f. manipulator the angle 1); is 195 not free but it follows from xA' YA' zA' 6, ~ and, accordingly, u is not free. In that case: nr = n - 5 = O. Since there are no free param eters with five d.o.f. manipulators, this problem is interesting for six d.o.f. manipulators only. Let us define the reduced position vector: = {not existing, for n Xr [u], for n 5 6 (3.4.116) The Jacobian form (3.4.25) can be obtained if the reduced Jacobian and the reduced adjoint matrix are defined as l O(5X(n-5\u00bb 1 I \u00abn-5) x (n-5\u00bb (3.4.117) For n=5 this form directly reduces to (2.4.13), (2.4.14) since there are no independent parameters. ->- ->- ->- The joint constraint produces a reaction moment MA satisfying MA~h, i. e. , o (3.4.118) ->- ->- and a reaction force FA which need not be perpendicular to h. Thus, the condition imposed on reactions can be expressed by (3.4.30) where E (3.4.119) NOw, all the elements of dynamic model (3.4.32) are determined and the model can be solved. Friction is treated in a way similar to the discussion in the previous paragraph, but here, there is no longitudinal motion and, accordingly, no longitudinal friction components. 196 3.4.9. Linear joint constraint We consider a manipulator having the gripper connected to the ground, or to an object which moves according to a given law, by means of a .... joint permitting one translation only. Let h be the unit vector of translation axis (Fig. 3.24). Let us first discuss the prescribed motion of the object to which the gripper is connected (non stationary constraint). Let us define this motion in the same way as it was done in Para. 3.4.7. Thus, the linear motion is defined by * * xA = f1 (t) , YA f2 (t) , (3.4.120) and angular motion by * * e = \u00a34 (t), q> = \u00a35 (t), (3.4.121) If we connect the gripper to the moving object (Fig. 3.24), then h (on .... * .... the gripper) has to coincide with h (on the object) and s has to co.... * .... incide with s (since relative rotation around h is not possible). Thus e * e , * q> , * 1jJ (3.4.122) Introducing orientation coordinate systems for the gripper and for the object (as was done in Para. 3.4.7), we find that the relative trans- lation can be defined by u * x sA -*o A s (see Fig. 3. 1 9) . -*- A A 197 (3.4.123) If a six d.o.f. manipulator (n=6) is considered, u is a free parameter. But, with a five d.o.f. manipulator (n=S) this parameter is not free since such a manipulator cannot solve the position along with the total orientation. Hence, for five d.o.f. manipulators this problem makes almost no sense. Since nr = n - S we introduce the reduced position vector as { not existing, for n=S [u] , for n=6 (3.4.124) Repeating the transformations (3.4.90) to (3.4.98) (from Para. 3.4.7), we obtain the acceleration * wA = a s1 u + CJ. w (3.4.12S) By differentiation, (3.4.121) gives .* f4 (t), .* .* f6 (t) e (jJ f S (t) , 1jJ (3.4.126) e* f4 (t) , * fs (t) , * f 6 (t) (fJ i{i (3.4.127) The Jacobian form (3.4.2S) can be obtained if the reduced Jacobian and the reduced adjoint matrix are defined as r * j a s1 (3 x 1) ----------- ; o (3.1 ) (3.4.128) -+ -r -+ . The joint constraint produces a reaction force FA satisfying FA~h, l.e., o (3.4.129) and a reaction moment MA which need not be perpendicular to h. Thus, the condition imposed on reactions can be expressed by (3.4.30) where 198 E [ hT \u00b0 ] (1<3) (l x 6) (3.4.130) Now, all the elements of dynamic model (3.4.32) are determined and the model can be solved. If the concept of independent reaction components has to be applied, -+ -+ we introduce five independent reaction components. Since FA~h and, ac-+ * cordingly, FA~xs we express it in terms of independent components along --+ -+-++ the unit vectors s and ~ = sxh: (3.4.131a) The reaction moment has three independent components: (3.4.131b) The reduced reaction vector is RAr = [S 1 S 2 S 3 S 4 S 5] ( 3 . 4 . 1 32) The matrix G which transforms the reaction components (eq. (3.4.33)) is G r ---~----~----~----~--~~:~~~-+--~~:~~~-~--~~~~~~ j (3.4.133) I I I I 0(3 x 1) : 0(3 x1): h : s : ~ (6x5) Now all the elements of the dynamic model (3.4.35) are determined and the model can be solved. 3.4.10. Constraint permitting no relative motion We consider a manipulator having the gripper connected to the ground (or to an object which moves according to a given law) in such a way that no relative motion is possible (Fig. 3.25). In this case the constraint can be expressed in the form. f 1 (t) , (3.4.136a) 199 e = f4 (t) , (3.4.136b) This problem makes sense for six d.o.f. manipulators only. However, even in that case there are no free parameters since nr = n-6=6-6=0. The second derivative of (3.4.136a,b) gives If we wish to write this relation in the form (3.4.25), it is clear that the reduced position vector and the reduced Jacobian do not exist. The reduced adjoint matrix is (3.4.137) The reaction force and reaction moment have three independent components each. It means that there are no conditions for reactions. If we con sider the projections on external Cartesian system as independent com ponents, then the relation (3.4.30) is unnecessary, i.e., it does not exist. Now, in a simulation problem, we do not use (3.4.32). We use (3.4.26) to solve q and then (3.4.28) to solve reaction RA. 200 3.4.11. Bilateral manipulation We consider two manipulators connected to each other by means of their grippers. In previous paragraphs (3.4.2 - 3.4.10) we considered closed chains obtained by connecting the last segment (gripper) of an open chain to the ground or to an object which moves according to a given law. Here we consider a closed chain formed of two open chains by con necting their last segments (grippers) to each other. The connection between the two grippers can be of any type considered in Para. 3.4.4- 3.4.10. All the theory from these paragraphs can easily be extended by considering another gripper instead of a moving object. From all different types of connections we choose the three cases which are most interesting for practice. Two d.o.f. joint connection. We consider two manipulators having the grippers connected to each other by means of a joint permitting one ~ relative translation (along the unit vector h) and one relative rotation (around h) (Fig. 3.26) Let the position vectors of the two manipulators (1) and (2) be 201 (3.4.138) If one of the manipulators (or both) has five d.o.f., the corresponding angle ~ does not appear in the position vector. We restrict our con sideration to manipulators having five or six d.o.f. For simplicity we assume n 1 = n 2 = n. Let us apply the theory derived in Para. 3.4.7 but here the gripper of manipulator (2) plays the role of moving object. The motion of this gripper (2) is defined by xA2 (t), YA2 (t) , ZA2 (t) , (3.4.139) i.e., Xg2 (t). Now the kinematics and the dynamics of manipulator (2) are described by (3.4.140) (3.4.141) The sign \"-\" of the term D2RA is due to action and reaction (RA is acting on manipulator (1) and -RA on manipulator (2)). Let us define the relative translation of the grippers by u = 1 (3.4.142) It is the relation (3.4.87) but with Al instead of A and A2 instead of * A . The relative rotation is defined by u = 2 (3.4.143) It is the relation (3.4.88) but with ~1 instead of ~ and ~2 instead of * ~ . The relation (3.4.94) becomes here .. ( 2) [ 0 0 1 T + 2A (2) [~ 0 01 T + ( 2) [.. 0 01 T wA2 + As u 1 s 1 As u 1 (3.4.144) 202 and (3.4.95) becomes (3.4.145) substituting (3.4.145) into (3.4.144) one obtains 2A' s( 2) [u' 1 0 01 T f ( 2) 8 f ( 2) .. ( 2) \u2022\u2022 wA2 + + 81 2 + 411 412 + a s1 u 1 (3.4.146) \\ Sw where f~~), f~~), a~~) are the first columns of the matrices F~2) , F~2), A~2), respectively. When the connection between the two grippers is made, then 8 1 = 8 2 , 411 412 (3.4.147) and accordingly 81 82 , iii 1 iii 2 (3.4.148) Now, the vector X g1 can be expressed as wA1 (3 x 1) I I f(2) I f(2) \u00b0 (3x3) : -81 (3 x 1): 411 (3 x 1) I (3 x (n-5)) ----------~----------~----------;--------------I I I 81 (1x1) I I \u00b0 I \u00b0 0(1x3) I I(1x1) I (1x1) I (1 x (n-5)) I I I ----------~----------~----------;--------------I I I iii 1 (1x1) I I I 0(1x3) : 0(1x1) : I(1x1) : 0(1x(n-5)) ----------~----------r----------+--------------I I I ~1((n-5)x1) \u00b0 1 0 1 0 II (n x 1) ((n-5)x3): ((n-5)x1): ((n-5)x1): ((n-5)x(n-5)) Xg1 (n x 1 ) + ~2((n-5)x1) Xg2 (nx1) ~------------------------y~------------------------~ J 1 ,2 (nxn) a (2) : \u00b0 s1 (3 x 1) I (3 x (n-5)) I ----------T-------------I 0(1x1) : 0(1 x (n-5)) I ----------T-------------I 0(1x1) : 0(1 x (n-5)) I ----------T-------------I \u00b0 ( (n-5) x 1 ) : I ( (n- 5) x (n-5) ) ~--------~y~----------~) J' r (n x (n-4) ) f u1 (1 x 1 ) 1 ----------- u2 ((n-5)x 1 ) + X r1 ((n-4) x1) 203 O(1 x 1) + ------------ (3.4.149) O\u00abn-5)x1) A' r (nx 1) or in the form J X + JIX + A' 1,2 g2 r r1 r (3.4.150) Let us note that, if the position of manipulator (2) is given by posi tion vector Xg2 of dimension (n 2x1), the position of manipulator (1) can be given in terms of the reduced position vector for n=5 (3.4.151) for n=6 of dimension (n1-4)x1. In this way we have n 2+n 1-4 free and independent parameters defining the position of the whole closed system. These are Xg2 and Xr1 . Kinematics and dynamics of the manipulator (1) are described by (3.4.152) (3.4.153) substituting (3.4.150) into (3.4.152) one obtains (3.4.154) and substituting q form (3.4.154) into (3.4.153): 204 Reaction vector RA contains two components: force FA and moment MA. -+ -+ -+-+ Since FA~h and MA~h it follows that (3.4.156) This can be written in the form o (3.4.157) where E (3.4.158) Combining the relations (3.4.140) and (3.4.141) one obtains (3.4.159) NOw, (3.4.155), (3.4.159) and (3.4.157) can be written together in the form 1 I 1 I W J- J' W1J-1 J 1 2: -D 1 1 1 r I ' I X P1 -1 (A~ -A1 ) r1 U1-\\~1J1 ---------~----------r----- ---------------: -1: o I W2J 2 I +D2 I I X P 2 -1 g2 + U2-W 2J 2 A2 ---------~----------r----- --------------- I I o : 0 : E RA 0 0 (3.4.160) In the case of nominal dynamics calculation, the accelerations xr1 ' Xg2 and reaciton RA are given. The system (3.4.160) is solved for P1 , P 2 \u2022 In the case of simulation problem, the drives P1 , P 2 areknown (3.4.160) represents a system of n 1+n 2+2 equations which should be solved for (n 1-4)+n 2-6 = n 1+n 2+2 unknowns (X r1 , Xg2 , RA). The concept of independent reaction components can also be applied. The reaction vector is (3.4.161) 205 where RAr is the reduced reaction vector (3.4.162) -+ containing four independent components along the unit vectors sand -+ -+-+ \u00a3 = sxh. Matrix G is G (3.4.163) (6 x 4) NOw, (3.4.155) and (3.4.159) become and (3.4.165) These two equations can be written together giving: l -1, 1 U1-W1J 1 (Ar-Ar ) + ---------~;------ U2-W2J 2 A2 (3.4.166 ) This system is simpler than (3.4.160) since it represents a set of n 1 +n 2 equations which should be solved for n 1-4+n 2+4 = n 1+n 2 unknowns (X r1 , Xg2 , RAr )\u00b7 The friction effects are taken into account in the same way as was done in Para. 3.4.7. Linear joint connection. We consider two manipulators having the grip pers connected to each other by a joint permitting one relative trans -+ lation only (Fig. 3.27). Let h be the unit vector of this translation. 206 I I I I I I I s~ II~I/ I I I I I I I I 4S1 1)~17 207 (3.4.170) Analogously to what was done for two d.o.f. joint, we can obtain or 81 \\I> 1 ~1 + I (2) I (2) I I(3'3) :fe1 :fIP1: 0 -------~-----~-----~---I I I I I I 0(1x3) : : 0 : 0 _______ J _____ ~ _____ ~ __ _ I I I I I I 0(1x3): 0: : 0 -------~-----~-----~---I I I 0(1x3)! 0 ! 0 ! v J 1,2 Sw 0 0 0 ~ A' r J 1 2X 2 + J'X + A' , g r r1 r wA2 (2) a s1 ------ 62 0 + ------ [til + \\1>2 0 ------ ~2 0 ) '-v----' J' r (3.4.171a) (3.4.171b) The joint connection produces a reaction force FA perpendicular to h and MA which need not be perpendicular to h. Thus o (3.4.172a) and this condition can be written in the form (3.4.172b) where E (3.4.173) 208 Now, all the elements of dynamic model (3.4.160) are determined and the model can be solved. The dimension of the model in n 1+n 2+1. The concept of independent reaction components can also be applied. Connection permitting no relative motion. We consider two manipulators having the grippers connected to each other by means of a connection permitting no relative motion (Fig. 3.28). 209 (3.4.176) It is a modification of the model (3.4.160) exist and J 1 ,2 equals identity matrix. 3.4.12. Extension of surface-type constraint since here X does not r In Para. 3.4.4 we considered the problem of surface-type constraint imposed on a gripper. By this constraint one given point of the gripper was required to be always on a given surface. Here, the constraint is slightly less severe. We introduce the request that the gripper has a contact with the surface by means of any of its points. It means that there does not exist one point which is always on the surface but dif ferent points make this contact at different time instants (Fig. 3.29). The approach to this problem will differ from the one used in previous paragraphs (3.4.3 - 3.4.11). A noniterative approach was employed in these paragraphs. The model was formed allowing the calculation of both the accelerations and the reactions. The model was in the form of a system of linear equations with respect to accelerations and reactions. Here, we use a different approach proposed in [8]. Let us explain it. The influence of the surface-type constraint is taken into account through the reaction force F (Fig. 3.30). The dynamic model is formed which includes the reaction. If nominal dynamics has to be calculated, 210 the motion and the reaction are known and the model is solved for the drives P. In a simulation problem we start from an initial state which satisfies the constraint imposed. We calculate the reaction from the condition that after integration over a short time interval 6t the constraint has to be satisfied again. Let a moving surface (nonstationary constraint) be defined by fIx, y, z, t) o (3.4.177) The problem with this surface representation will arise because of the friction effects and relative velocity with respect to the surface (see. Para. 3.4.2). This problem should be solved in each actual situ ation separately. Let the gripper (or the object carried by the gripper) be defined in the corresponding body-fixed (b.-f.) system by o (3.4.178) where xn ' Yn' zn are cordinates in b.-f. system. The constraint requires the gripper to have a contact with the surface by means of one point, i.e., the set of equations (3.4.177), (3.4.178) to have one real solution only. The solution has to be found numerical ly. Let the manipulator dynamics be described by the matrix model (see. Para. 3.4. 1 ) : or 211 (3.4.179) ->- where the unit vector no perpendicular to the surface is given by \\ ->-F\\ ->-(3.4.8), (3.4.9) and R = (scalar value), and v ro is the unit vector of relative velocity. Since the calculation of nominal dynamics is quite clear, let us ex plain the solution of simulation problem. We consider a time instant t with the state (q(t), q(t\u00bb which satis fies the constraint. The generalized accelerations are (3.4.180) If we consider the accelerations as constant over the short time in terval ~t, the new state (after integration) is q (t+~t) (3.4.181) q(t+~t) = q(t)~t + q(t) (3.4.182) Substituting (3.4.180) into (3.4.181) one obtains q (t+~t) 2 ~t w- 1 (P+U) + q(t)~t + q(t) + l ) Y a (3.4.183a) ~------~v~-------Jj If we use the notation q, q for q(t), q(t) and t new , qnew, qnew for t+~t, q(t+~t), q(t+~t), (3.4.183a) becomes qnew = a(q, q) + S(q, q)R (3.4.183b) 212 Now, let us note that the transformation of b.-f. coordinates (xn ' Yn' zn) into external coordinates (x, y, z) is: (x, y, z) (3.4.184) where Cn is the gripper center of gravity (c.o.g.), i.e., the origin of the b.-f. system and (x, y, z)C are the external coordinates of the n point C \u2022 , n An (q) is the gripper transition matrix which depends on joint coordinates q. There exists a simple procedure for the calculation of n-1 ( L (~~.+~ .. 1) + -;: , see Ch. 2). Let us use the notation (x, y, z)C n i=1 ~~ ~,~+ nn (x, y, z)C n n (q) (3.4.185) for this procedure. Thus, if (3.4.184) is applied for time instant t new , then (x, y, z) new (3.4.186) For the same time instant the constraint is fIx, y, z, t)new = 0 (3.4.187) and the gripper is defined by ( z )new lP x n ' Yn' n o (3.4.188) We cOhsider the system of equations (3.4.183b), (3.4.186), (3.4.187), (3.4.188). Let us explain this. It is required that the equations (3.4.187) and (3.4.188) have one real solution for (x, y, z)new only. To solve these equations numerically we use some appropriate method and the coordinate transformation (3.4.186). Since this transformation depends on qnew and accordingly on R (eq. (3.4.183)), the solution will also depend on R. Our intention is to find such a value of Rwhich, when used in (3.4.183) and (3.4.186), ensures that the equations (3.4.187) and (3.4.188) have one real solution only. This is an one -dimensional-search procedure. For instance, we may use a binary search method or a golden ratio search [10]. These methods are very efficient. However, the problem appears with the numerical solution of the system (3.4.187), (3.4.188). It is a rather complex task for any numerical method. 213" + ] + }, + { + "image_filename": "designv10_6_0003047_1.1767819-Figure5-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003047_1.1767819-Figure5-1.png", + "caption": "Fig. 5 i-th leg of the 3-RRS wrist", + "texts": [ + " Henceforth a 3-RRS mechanism encountering these geometric conditions will be called 3-RRS wrist. In the following paragraphs of this section it will be shown that the 3-RRS wrist is a spherical parallel manipulator when the three revolute pairs adjacent to the base are actuated. With reference to Fig. 4, the points Ai, i51,2,3, are the spherical pair centers and the point C is the point the revolute pair axes converge towards. The point C is fixed in the base. Moreover, Sb is a reference system fixed in the base and Sp is a reference system fixed in the platform. Figure 5 shows the i-th leg, i51,2,3, of the 3-RRS wrist. According to Fig. 5, w1i and u1i are respectively the axis unit vector and the joint coordinate of the revolute pair adjacent to the base and w2i and u2i are respectively the axis unit vector and the joint coordinate of the revolute pair not adjacent to the base. The point Bi is the foot of the perpendicular through Ai to the axis of the revolute pair not adjacent to the base. The point Di is the foot of the perpendicular through Bi to the axis of the revolute pair adjacent to the base. The geometric parameters ai, bi, di and hi are the lengths of the segments AiC, BiC, BiDi and AiBi respectively. Moreover, the link adjacent to the base is named 1i and the link adjacent to the platform is named 2i . Since the points Ai, Bi and C are fixed in the link 2i ~see Fig. 5! the lengths ai, bi and hi are constant. Therefore when the revolute pairs adjacent to the base are actuated and the platform moves the three points Ai, i51,2,3, fixed in the platform, are constrained to move on concentric spheres whose center is C and whose radii are respectively ai, i51,2,3. This condition and the manufacturing conditions ~ii! and ~iii! lead to the conclusion that the 3-RRS wrist\u2019s platform always satisfies the hypotheses of statement ~1!. Hence, the 3-RRS wrist\u2019s platform can exclusively accomplish spherical motions with center C, i.e., the 3-RRS wrist is a spherical parallel manipulator. Transactions of the ASME 16 Terms of Use: http://www.asme.org/about-asme/terms-of-use Downloaded F The position analysis consists in the solution of two problems: the direct position analysis ~DPA! and the inverse position analysis ~IPA!. The direct position analysis of the 3-RRS wrist is the determination of the platform orientations compatible with given values of the actuated joint coordinates u1i , i51,2,3, ~Fig. 5!. The inverse position analysis of the 3-RRS wrist is the determination of the actuated joint coordinate values compatible with a given platform orientation. In the implementation of these two problems the base point C can be also considered fixed in the platform since the platform accomplishes spherical motions with center C. Direct Position Analysis. Since the actuated joint coordinates have to assume given values, the revolute pairs adjacent to the base can be considered locked. If the actuated revolute pairs are locked, the 3-RRS wrist becomes the 3-RS structure shown in Fig", + " Therefore the DPA reduces to find the possible assembly configurations of the 3-RS structure. The closure equations of the 3-RS structure can be written as follows @Rbp p~Ai2C!1b~C2Bi!# 25hi 2 i51,2,3 (12) where Rbp is the rotation matrix that transforms the vector components measured in Sp into the vector components measured in Sb and the left-hand superscript p or b added to a vector indicates the reference system, Sp or Sb respectively, the vector is measured in. Expanding Eqs. ~12! yields the following relationships ~see Fig. 5! ai 21bi 212 b~C2Bi!\u2022@Rbp p~Ai2C!#5hi 2 i51,2,3 (13) Equations ~13! are linear in the entries of the Rbp matrix. Therefore, if the Rbp rotation matrix entries are expressed by using the three Rodrigues parameters @16#, Eqs. ~13! will become a three quadratic equation system in three unknowns: the values of the three Rodrigues parameters. In the literature, two procedures @17,18# have been presented for solving a three quadratic equation system in three unknowns. Both these procedures show that the Sylvester eliminant of such a system is an univariate eight degree polynomial with real coefficients", + " The N matrix definition ~23.1! leads to the following expression for det~N! det~N!5n1\u2022~n23n3! (24) where ni5~Ai2C!3w2i i51,2,3 (25) Therefore, the rotation singularities occur whenever the 3-RRS wrist configuration satisfies the following singularity condition n1\u2022~n23n3!50 (26) Condition ~26! is verified when the three vectors ni , i51,2,3, are all parallel to a single plane. Since the three vector ni , i51,2,3, are respectively perpendicular to the three planes of the triangles AiBiC, i51,2,3, ~see Fig. 5!, condition ~26! is verified when the intersection of these three planes is a straight line through C ~Fig. 7!. In fact, when this happens, the ni vectors are all parallel to every single plane perpendicular to that intersection line. The H matrix is singular when its determinant vanishes. Since the H matrix is diagonal, its determinant is the product of its three diagonal entries and vanishes when at least one of them vanishes. The inspection of definition ~23.2! reveals that the i-th diagonal entry vanishes when the i-th leg is fully extended or folded, i.e., when the points Ai, Bi and Di ~Fig. 5! lie on the same plane. Hence, the leg singularities occur when the 3-RRS wrist configuration has at least one leg fully extended or folded. In this paper a new three-equal-legged spherical parallel manipulator, named the 3-RRS wrist, has been presented. The 3-RRS wrist is not overconstrained and exhibits a simple architecture employing just three passive revolute pairs, three passive spherical pairs and three actuated revolute pairs adjacent to the frame. Moreover the kinematic analysis of the 3-RRS wrist has been addressed and fully solved" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000068_tie.2021.3057002-Figure9-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000068_tie.2021.3057002-Figure9-1.png", + "caption": "Fig. 9. Temperature distribution of each component in the motor", + "texts": [ + " The axial velocity of fluid in the air-gap is decreasing first and then rising in the stator core length region (0-550 mm). This is due to the parts of fluid in the air-gap flowing to the stator yoke back through the No. 1, No. 2 and No. 3 radial ducts, which reduces the cooling air in the air-gap, and then some of fluid in stator yoke flows back to air-gap through the No. 4, No. 5 and No. 6 radial ducts to the air-gap which increases the coolant in the air-gap. Based on physics calculation results, Fig. 9 shows the axial temperature distribution of the motor. In Fig. 9, along the axial direction (fan end to shaft extension end), the temperature of the components in the high-pressure solid rotor self-starting permanent magnet synchronous motor gradually increases, and the temperature difference between the components is large in the axial direction, and the lowest temperature is 105\u2103, which appears at the end of the windings of the fan end. Because there is no ventilation cooling structure on the solid rotor body and the air thermal conductivity in the air-gap is poor, the solid rotor body represents the hot spot, which has a temperature of 179\u2103" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003670_978-3-642-82195-0-Figure1.9-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003670_978-3-642-82195-0-Figure1.9-1.png", + "caption": "Fig. 1.9. Joint coordinate of a sliding kinematic pair", + "texts": [ + " In that case the projection of this vector onto the plane 1 ->- perpendicular to joint axis e i is not defined, so that the above definition of joint angle can not be applied. Then, it is necessary to in ->- troduce an auxilliary vector which is not colinear with e i , whose pro->- jection will determine joint angle qi. For example, if r ii is colinear with ei one can adopt vector qi1 or qi2 (Fig. 1.8) instead of ~ii' so that its projection determines the zero value of qi. The jOint coordinate for a sliding joint is defined in the following way. The center Zi of joint i lies on joint axis and is defined by the ini tial point of vector ~. 1 . (Fig. 1.9). One should select a point 1- ,1 Zi belonging to link Ci on the joint axis, which cojncides with Z. for 1 qi=O. For qi*O, the distance between these points equals is the vector between point Zi at link Ci _ 1 and the mass link Ci . Therefore, it depends on qi + r .. 11 +0 I .. 11 where ~~i is the distance between Zi and 0i for qi=O. ->- qi\u00b7 Vector r ii center of (1.3.1) Beside the local coordinate frames attached to the links, a reference, 12 fixed coordinate system Oxyz is to be assigned. With respect to this system external coordinates describing manipulation tasks, are defined" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003286_bf01175968-Figure6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003286_bf01175968-Figure6-1.png", + "caption": "Fig. 6. An example from plane motion with b ~ 2, a With indeterminate reactions with / = 0, b With determinate reactions", + "texts": [ + " (16) i=7- -b Since there are (b - - / 3- 1) unknowns Qi in the (b - - / ) Eqs. (16), the Qi are expressible in the form of Eq. (12), while the Q1 are already determined by (15), The contact reactions Q~ are now determinable as in section 3 and one of the (b - - / + 1) contacts is unloaded. (The argument of section 3 is valid here because 'the as are lineary dependent enabling equilibrium among the 2A~a~ and the ,~Ai are again positive.) An example from plane motion with b = 2, / ---- 0 is shown in Fig. 6a with indeterminate reactions and in Fig. 6b with determinate reactions. In Fig. 6b, P1, P2, Ps are linearly dependent normals. The resultant of their reactions acts along BC while the reaction from link AoA acts along AB. One of the contacts 1, 2, 3 will be unloaded. 8* I f we proceed to suppress some degrees of freedom by means of point contacts as described in the foregoing sections and then repeat the process for a further reduction in freedom, the total number of point contacts needed will be more than tha t of the single step solution considered previously. Let the number of freedoms present to s tar t with be b (degree of motion) and let the number of freedoms left after the first stage of restraint be ]1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002726_0045-7906(94)90021-3-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002726_0045-7906(94)90021-3-Figure4-1.png", + "caption": "Fig. 4. Configurations (a) and (b) have the maximum kinematic dexterity and fault tolerance, respectively, for the manipulator described in Fig. 1. Configurations (c) and (d) have the maximum dynamic dexterity and fault tolerance, respectively, for this same manipulator. Configurations (e) and (f) have the maximum dynamic dexterity and fault tolerance, respectively, for the manipulator described in Fig. 3. Although, the configurations of optimal dynamic fault tolerance are markedly different from the optimal kinematic fault tolerant configuration, locally optimal dynamic fault tolerant configurations exist near the optimal kinematic fault tolerant configuration.", + "texts": [ + " Clearly, the zeros of the dynamic dexterity measure must match those of the kinematic measure since they are both due to a rank deficiency in J. The effect of M-~ in the definition Dexterity optimization of kinematically redundant manipulators 279 of dm is basically limited to skewing and stretching the contours around these fixed minima. It is interesting to note, however, that the maxima for both measures are also relatively close to each other. The manipulator configurations for these maxima are illustrated in Fig. 4(a) and (c). The kinematic and dynamic fault tolerance measures for this manipulator are shown in Fig. 2. By comparing Fig. 1 with Fig. 2, the most striking feature is that the point minimum at the reach singularity has been expanded to include several lines of minima that partition the joint space. Physically, these minima represent all of the singularities of the resulting two-link manipulators that can occur after an arbitrary joint failure so that it is easy to geometrically describe the conditions that these minima represent", + " The existence of so many minima that partition the joint space has a profound effect on the resulting dynamic fault tolerance. Since the zeros of these two measures must match, there is a far less pronounced skewing effect due to M - l when calculating dfm. Thus for all practical purposes the manipulator is restricted to a small region of the joint space if it is to maintain some level of fault tolerance. It is interesting to note, however, that the globally optimal dynamic fault tolerant configuration is not within the same partition of joint space as the globally optimal kinematic fault tolerant measures [see Fig. 4(b) and (d)]. However, this is a minor point since the local maxima in each region are comparable. It is also interesting to note that despite the radical difference between the countours of km and kfrn, both of their optimal configurations occur at the same point, which is isotropic [6,7] [see Fig. 4(a) and (b)]. This is fortunate since one would not like to sacrifice the current normal performance of the manipulator in anticipation of a future joint failure. Finally, Fig. 3 illustrates the effect of changing the mass distribution on the dynamic dexterity and fault tolerance measures. Since the link lengths are the same as in the previous case, the kinematic measures are identical to those in Figs 1 and 2. The contours of dm are now quite different from the previous case, however, the optimal configuration has not substantially changed [see Fig. 4(c) and (e)]. Moving more of the mass towards the base of the manipulator tends to reduce the effect of the dynamics and therefore makes dm take on more of the characteristics of km. The same is true for the dynamic fault tolerance measure although the lines of singularities are still by far the most defining feature. 280 CHRISTOPHER L. LEwis and Ah'wnoh'Y A. MACtr~BWSgd V. C A L C U L A T I O N OF AN I N V E R S E In the previous section, globally optimal fault tolerant configurations were identified" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003018_0956-5663(96)87657-3-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003018_0956-5663(96)87657-3-Figure1-1.png", + "caption": "Fig. 1. Schematic representation of a disposable cuvette incorporating a sensor layer. It may be used for either absorbance, reflectance or fluorescence measurements.", + "texts": [ + " Before measurements, membranes were conditioned for 30 min by exposing them, alternatively, to ammonia solutions and vapors of acetic acid until the relative signal change on cycling from ammonia to acetic acid at 605 nm remained constant. Disposable 1 x 1 \u00d7 3.5 cm cuvettes (from Brand, Germany; prod. no. 7.590.05), made from polystyrene, were used throughout. The sensing membranes described above were cut into 1 x 3 cm pieces and glued onto one of the walls of the cuvettes with a two-sided glueing tape. A schematic of the cuvette with integrated sensor layer is shown in Fig. 1. This type of cuvette may be used for absorption (Fig. l(a)), reflection, or fluorescence (Fig. l(b)) measurements. Working protocols for measurement of enzyme inhibition Before inhibition can be measured, it is essential to know the full activity of the enzyme. In order to do so, 2.9 ml of 0.1 N maleate buffer (solution A) and 0.2 ml of buffered urease solution (solution B) were placed in the cuvette and thermostatted to 25\u00b0C. The enzymatic reaction was started by addition of 0.4 ml of a 1 M urea solution (solution C)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003521_j.conengprac.2007.04.008-Figure9-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003521_j.conengprac.2007.04.008-Figure9-1.png", + "caption": "Fig. 9. Front view of TRMS with ah \u00bc 0.", + "texts": [ + " Assume \u00bdrx\u00f0R1\u00de; ry\u00f0R1\u00de; rz\u00f0R1\u00de denotes the coordinate of point P1 on the free\u2013free beam parameterized in the distance R1 from O1 (that means P1O1 \u00bc R1). And also assume OO1 \u00bc h in which O is the original of the coordinates. It is noted that in order to simplify the figure the x- and y-axes have been drawn from O2. According to Figs. 8\u201310 the following equation can be obtained: rx\u00f0R1\u00de \u00bc R1 sin ah cos av \u00fe h cos ah; ry\u00f0R1\u00de \u00bc R1 cos ah cos av h sin ah; rz\u00f0R1\u00de \u00bc R1 sin av: 8>< >: (12) It should be noted that ah has no effect on the rz(R)\u2019s and for simplicity it can be assumed to be zero as shown in Fig. 9. Let \u00bdrx\u00f0R2\u00de; ry\u00f0R2\u00de; rz\u00f0R2\u00de denotes the coordinate of point P2 on the counterbalance beam parameterized in the distance R2 from O1 (that means P2O1 \u00bc R2). According to Fig. 8 the following equation can be obtained: rx\u00f0R2\u00de \u00bc R2 sin ah sin av \u00fe h cos ah; ry\u00f0R2\u00de \u00bc R2 cos ah sin av h sin ah; rz\u00f0R2\u00de \u00bc R2 cos av: 8>< >: (13) For more accuracy the point P3 can be considered with the coordinate \u00bdrx\u00f0R3\u00de; ry\u00f0R3\u00de; rz\u00f0R3\u00de on the pivoted beam where R3 is the distance between P3 and O: rx\u00f0R3\u00de \u00bc R3 cos ah; ry\u00f0R3\u00de \u00bc R3 sin ah; rz\u00f0R3\u00de \u00bc 0: 8>< >: (14) In this case the vertical angle is constant and so the velocities related to each part can be obtained by differentiating Eqs" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure3.29-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure3.29-1.png", + "caption": "Fig. 3.29. Gripper connected to the surface by means of any of gripper points", + "texts": [ + " Extension of surface-type constraint since here X does not r In Para. 3.4.4 we considered the problem of surface-type constraint imposed on a gripper. By this constraint one given point of the gripper was required to be always on a given surface. Here, the constraint is slightly less severe. We introduce the request that the gripper has a contact with the surface by means of any of its points. It means that there does not exist one point which is always on the surface but dif ferent points make this contact at different time instants (Fig. 3.29). The approach to this problem will differ from the one used in previous paragraphs (3.4.3 - 3.4.11). A noniterative approach was employed in these paragraphs. The model was formed allowing the calculation of both the accelerations and the reactions. The model was in the form of a system of linear equations with respect to accelerations and reactions. Here, we use a different approach proposed in [8]. Let us explain it. The influence of the surface-type constraint is taken into account through the reaction force F (Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002481_00207540050176111-Figure16-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002481_00207540050176111-Figure16-1.png", + "caption": "Figure 16. Operating cost of Nd : YAG laser (Havrilla 1997b) .", + "texts": [], + "surrounding_texts": [ + "Rapid metal forming systems using high power lasers have been surveyed and the important parameters associated with the clad qualities discussed. The laser metal forming process when applied to rapid prototyping is similar to the laser cladding process, so many of the same principles apply. Using known data about both laser cladding and current rapid prototyping methods, experimental hardware, system software, and process parameters were determined for the rapid metal forming method. Based on knowledge of the laser cladding process and commercial polymer rapid prototyping systems, limitations of the rapid metal forming process are also summarized." + ] + }, + { + "image_filename": "designv10_6_0003003_tmag.2004.843349-Figure20-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003003_tmag.2004.843349-Figure20-1.png", + "caption": "Fig. 20. 3-D modal analysis results at mode frequencies (a) 3089, (b) 1910, (c) 161, and (d) 900 Hz.", + "texts": [ + " The 3-D modal analysis reveals certain modes which are producing vibration (and the associated acoustic noise) in SRM due to rotor and housing structures. The mode frequency of 231.154 Hz (3467 rpm), shown in Fig. 19(a), is observed to produce twist of rotor. Modal frequency of 160 Hz [Fig. 19(b)] causes shaft bend with a severity at the shaft-rotor edge. Frequency of 364.5 Hz causes rotor structure and rear shaft vibration [Fig. 19(c)] and at 231.15 Hz [Fig. 19(d)], the rotor deforms at an angle. At modal frequencies of 3089 Hz [Fig. 20(a)], 1910 Hz [Fig. 20(b)], and 161 Hz [Fig. 20(c)], the housing also gets involved in contributing vibration. The rotor rocks up and down causing it to strike against the stator, transmitting the vibration till housing and foundation. The shaft bends. The drive may not be able to handle any load at these speeds. At 900 Hz [Fig. 20(d)], the housing with foundation undergoes vibration. A harmonic frequency analysis has been performed to identify whether the vibration of rotor and housing is within safe range. The aim is to obtain the SRM structure response at several frequencies with respect to displacement. Peak responses are identified and plotted as a graph. Stresses are reviewed at these frequencies. The weight of the rotor (w) is 3.75 kg. The balancing quantity ( ) and the damping ratio ( ) were assumed to be 2.5 and 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003866_j.nonrwa.2009.03.027-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003866_j.nonrwa.2009.03.027-Figure2-1.png", + "caption": "Fig. 2. Model of force diagram for pinion and gear.", + "texts": [ + " The remainder of this paper is organized as follows: Section 2 derives dynamicmodels for the gear-bearing systemwith a nonlinear suspension effect, strongly nonlinear gearmesh force and strongly nonlinear oil-film force; Section 3 describes the techniques used in this study to analyze the dynamic response of the gear-bearing system; Section 4 presents the numerical analysis results obtained for the behavior of the gear-bearing system under various operational conditions; and Section 5 presents some brief conclusions. Adynamicmodel to stimulate the gear-bearing systemunder the assumptions of nonlinear suspension effect and strongly nonlinear fluid-film force effect is established in Fig. 1. Fig. 2 presents a schematic illustration of the dynamic model considered between gear and pinion. Og and Op are the centers of gravity of the gear and pinion, respectively; O1 and O2 are the geometric centers of the bearing 1 and bearing 2, respectively; Oj1 and Oj2 are the geometric centers of the journal 1 and journal 2, respectively;m1 is the mass of the bearing housing for bearing 1 andm2 is the mass of the bearing housing for bearing 2; mp is the mass of the pinion and mg is the mass of the gear; Kp1 and Kp2 are the stiffness coefficients of the shafts; K11, K12, K21 and K22 are the stiffness coefficients of the springs supporting the two bearing housings for bearing 1 and bearing 2; C1 and C2 are the damping coefficients of the supported structure for bearing 1 and bearing 2, respectively; K is the stiffness coefficient of the gear mesh, C is the damping coefficient of the gear mesh, and e is the static transmission error and varies as a function of time" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000210_tie.2021.3075886-Figure5-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000210_tie.2021.3075886-Figure5-1.png", + "caption": "Fig. 5: The geometric distances of the CTRUAV prototype.", + "texts": [ + " The flight control hardware system outputs pulse width modification (PWM) signals to control the servos and motors. As shown in Fig. 1, the inertial frame I{Xi,Yi,Zi} follows the North-East-Down (NED) notation, and the bodyfixed frame B{Xb,Yb,Zb}, which coincides with the center of gravity (CoG) of the CTRUAV, follows the standard aircraft notation where the Zb points downwards, the Xb towards the longitudinal flight direction and the Yb towards the right direction. The key geometric dimensions of the CTRUAV prototype are depicted in Fig. 5, where lb is the distance from the rear rotor to the CoG of CTRUAV in direction Xb, l f and ls are the distance from the coaxial tilt-rotor modules to CoG in directions Xb and Yb, respectively. The tilt axis of the coaxial rotors coincides with XbYb plane of the bodyfixed frame B, which means the distance from the tilt axis to CoG in directions Zb is zero. The overall mechanisms of the CTRUAV\u2019s maneuvers are illustrated in Fig. 6, which are achieved by varying the thrusts and tilt angles of the rotors" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000202_j.mechmachtheory.2021.104330-Figure13-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000202_j.mechmachtheory.2021.104330-Figure13-1.png", + "caption": "Fig. 13. Three configurations of the deployable grasping parallel mechanism presented in (a)\u2013(c) show the folded, fully deployed, and grasping configurations of the whole mechanism, respectively. (d)\u2013(f) provided the corresponding physical prototype of such a deployable grasping parallel mechanism.", + "texts": [ + " The translational direction of the prismatic joint is along Z a -axis and three revolute joints form a 3R spherical sub-chain. Then, the auxiliary sub-mechanism is assembled with grasping sub-mechanism using the base and the platform to construct a deployable grasping parallel mechanism as illustrated in Fig. 12 (b). The folded configuration of such a mechanism can be seen in Fig. 12 (c). In addition, the fully deployed configuration and grasping configuration of the whole mechanism are shown in Fig. 13 (b) and (c), respectively. These configurations are also verified with the use of the physical prototype, as shown in Fig. 13 (d)\u2013(f). Movie S3 not only supplements Fig. 13 , but also presents several animations to show that this type of parallel mechanisms is capable of grasping objects at other deployed configurations of this mechanism. The standard base of the constraint-screw system for such an auxiliary sub-mechanism is S r a = { S r a1 = (1 , 0 , 0 , 0 , 0 , 0) T S r a2 = (0 , 0 , 0 , 0 , 1 , 0) T } , (55) which provides a constraint force along X a -axis and a constraint couple around Y a -axis. Then, the standard base of motionscrew system for this auxiliary sub-mechanism is S a = \u23a7 \u23aa \u23aa \u23aa \u23aa \u23a8 \u23aa \u23aa \u23aa \u23aa \u23a9 S a1 = (1 , 0 , 0 , 0 , 0 , 0) T S a2 = (0 , 0 , 1 , 0 , 0 , 0) T S a3 = (0 , 0 , 0 , 0 , 1 , 0) T S a4 = (0 , 0 , 0 , 0 , 0 , 1) T \u23ab \u23aa \u23aa \u23aa \u23aa \u23ac \u23aa \u23aa \u23aa \u23aa \u23ad , (56) where the second component in all the screws is equal to 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003704_ma7025644-Figure9-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003704_ma7025644-Figure9-1.png", + "caption": "Figure 9. Setup for the shear experiments and geometrical relation between the applied angle \u03b4 and the shear strain \u03b3.", + "texts": [ + " The analysis of the intensity distribution of the small-angle reflections reveals a correlation length of the smectic structure of about \u00ea ) 39 ( 2 nm (16 ( 2 layers), which remains unchanged during the deformation process of the elastomer. Shear Stress-Strain Experiments. Experiments on SmC side-chain elastomers with conical layer distribution structure already demonstrated that a shear field transforms a conical layer distribution structure into a monodomain possessing a uniform layer and director orientation.8,9 The basic question is whether the SmC main-chain elastomers exhibit a similar behavior. For the experiments, a self-constructed setup was used as shown in Figure 9, which allows the application of a shear force parallel and perpendicular to the director of the films. This setup can be used in a common stress-strain machine. A change in length, \u2206l ) l sin \u03b4, causes a shear angle \u03b3 of the sample by tan \u03b3 ) l sin \u03b4/(l cos \u03b4 - 2d). Note that under these experimental conditions no stress normal to the shear direction occurs. The shear stress \u03c4 was calculated for every shear angle \u03b3. Furthermore, the shear modulus G was determined for each shear deformation. To minimize friction of the joints, miniaturized ball bearings are employed" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003788_978-1-4020-5967-4-Figure9-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003788_978-1-4020-5967-4-Figure9-1.png", + "caption": "FIGURE 9. Combination of toothed wheels to move a force of 1000 talents with a force of 5 talents (Mechanics 2.21). Drachmann\u2019s rendering of the figure (The Mechanical Technology, p. 82) in Ms L is on the left; the figure from Heronis Alexandrini opera, vol. II, p. 148, is on the right. Neither is exactly faithful to the text, which states that the wheel\u2013axle ratios B:A, D:G\u030c, and Z:H are 5:1, 5:1, and 8:1, respectively.", + "texts": [ + " The wedge and the screw, on the other hand, become more powerful with a decrease in size: the angle of the wedge must be made more acute, and the screw threads more tightly wound. Chapters 21\u201326 of Book 2 discuss the combination of individual wheel and axles, levers, and compound pulleys, each of which is of manageable dimensions, to achieve a large mechanical advantage. As an example we may consider the use of a combination of wheel and axles to move a load of 1000 talents with a force of 5 talents (2.21; Fig. 9). Given the results established in the reduction, this would require a wheel with a radius 200 times that of its axle. But Heron shows that the same mechanical advantage can be achieved by a combination of three wheel and axles with ratios of 5:1, 5:1, and 8:1, respectively. He first describes the construction of a device in which the force exactly balances the weight to be moved, then states that the same force can be made to set the weight in motion by increasing one of the wheel-axle ratios slightly", + " Yet a reference to time would be puzzling if Heron had meant to state or imply R\u2032\u2032, since that relationship presupposes that the times of motion are equal for the moving force and the weight (see the next note). And in fact the discussion of the combination of wheel and axles that follows in 2.22 is precisely similar to the discussion of the compound pulley in ch. 24: the comparison is between the times taken by different moving forces applied at the circumference of different wheels to move the weight a given distance (alternatively, it is between the distances they travel in the different times they take to move the weight, assuming they move at the same speed). For example, in Fig. 9 a force of 40 talents applied at the circumference of wheel D must cover 5 times the distance as a force of 200 talents applied at the circumference of wheel B in order to raise the weight by the same distance (the wheel D must turn five times for the wheel B to turn once, and the two wheels have the same circumference). Heron concludes by stating the usual relationship between moving forces: \u201cthe ratio of the moving force (al-quwwat al-muh.arrikat) to the moving force (al-quwwat al-muh. arrikat) is inverse \u201d (Opera, vol" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure32.12-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure32.12-1.png", + "caption": "Fig. 32.12 Close-up of fabricated attitude control actuator", + "texts": [], + "surrounding_texts": [ + "1. Swan DW, Lewis TJ (1960) Influence of Electrode Surface Conditions on Electrical Strength of Liquified Gasses. J Electrochem Soc, 107(3):180-185 2. Mathes KN (1967) Dielectric Properties of Cryogenic Liquids. IEEE Trans Electr Insul, El2(1):24-32 3. Yamamoto A, Nakajima T, Kudoh K, Higuchi T (2006) Direct Electrostatic Transportation of Frozen Droplets in Liquid Nitrogen for Single Cryopreserved Cell Processing. Proc IEEE MEMS 2006:382-385 4. Egawa S and Higuchi T (1990) Multi-Layered Electrostatic Film Actuator, Proc IEEE MEMS 1990:166-171 5. Niino T, Higuchi T, Egawa S (1995) Dual Excitation Multiphase Electrostatic Drive. Proc IEEE IAS 1995:1318-1325 6. Yamamoto A, Niino T, Higuchi T (2006) Modeling and Identification of an Electrostatic Motor. Precis Eng, 30(1):104-113 7. Yamamoto A, Yasui H, Nishijima T, Higuchi T (2003) Electrostatic Linear Servo Motor with Built-in Position Sensor for Vacuum Environment. Proc IEEE ISIE 2003, 2:928-933 8. Nishijima T, Yamamoto A, Yasui H, Higuchi T (2006) A Built-in Displacement Sensor for an Electrostatic Film Motor. Meas Sci Technol, 17(10):2676-2682 9. Gassert R, Yamamoto A, Chapuis D, Dovat L, Bleuler J, Burdet E (2006) Actuation methods for applications in MR environments. Concepts Magn Reson, 29B(4):191-209 10. Moser R, Gassert R, Burdet E, Sache L, Woodtli HR, Erni R, Maeder W, Bleuler H (2003) An MR compatible robot technology. Proc IEEE ICRA 2003:670-675 11. Flueckiger M, Bullo M, Chapuis D, Gassert R, Perriard Y (2005) fMRI compatible haptic interface actuated with traveling wave ultrasonic motor. Proc IEEE IAS 2005:58-63 12. Yamamoto A, Ichiyanagi K, Higuchi T, Imamizu H, Gassert R, Ingold M, Sache L, Blueler H (2005) Evaluation of MR-compatibility of Electrostatic Linear Motor. Proc IEEE ICRA 2005:3669-3674 13. Yamamoto A, Rajendra M, Hirano Y, Kataoka H, Yokota H, Himeno R, Higuchi T (2007) Motion Generation in MRI Using an Electrostatic Linear Motor for Visualizing Internal Deformation of Soft Objects by Tagged Cine-MRI. Proc IEEE ISIE 2007:2741-2746 14. Mayoran R, Yamamoto A, Kataoka H, Oda T, Yokota H, Hirano Y, Himeno R, Higuchi T (2007) Application of an Electrostatic Film Motor in MRI-related Biomechanical Measurement. Proc JSME 2007 annual congress, 5:257-258 15. Rajendra M, Yamamoto A, Oda T, Kataoka H, Yokota H, Himeno R, Higuchi T (2008) Motion Generation in MR Environment Using Electrostatic Film Motor for Motion Triggered cine-MRI. IEEE/ASME Trans Mechatron, 13(3):278-285 16. Hara M, Matthey G, Yamamoto A, Chapuis D, Gassert R, Bleuler H, Higuchi T (2009) Development of a 2-DOF Electrostatic Haptic Joystick toward MRI/fMRI related Studies. Proc IEEE ICRA 2009:1479-1484 17. Yokokohji Y, Hollis R, Kanade T (1996) What you can see is what you can feel \u2013 development of a visual/haptic interface to virtual environment, Proc IEEE VRAIS 1996:46-53 Chapter 32 Micro Actuator System for Narrow Spaces Takefumi KANDA1 Abstract This chapter describes micro actuator systems for narrow spaces under specific environments. In the fields of scientific or medical instruments, there is a great demand for micro sensors and actuators. We have fabricated some micro sensors and actuators which can be used under such specific environment. Two types of micro actuator systems for narrow spaces have been fabricated and evaluated. Those are for precise tool control unit and attitude control unit. In the precise tool control unit, a micro servo motor using the micro ultrasonic motor and the magnetic encoder have been designed and fabricated. In the attitude control, flexible displacement sensor made of piezoelectric polymer and shape memory alloy actuator driven by optical source. 32.1 Introduction Many micro systems for narrow spaces have been studied for negotiating small pipes for inspections or human bodies for endoscopes [1]. For example, examinations and surgeries using endoscopes require a precision actuator system to control the configuration of the tools (cameras, manipulators and other instruments) and to drive them. In other cases, instruments for measurement may require specific environments, such as a strong magnetic field. Under these conditions, precise control of the instruments is also demanded. The goal of this work is to develop a micro actuator system for narrow spaces under such specific environments. This system requires micro sensors and actuators. In this work, micro sensors and actuators for precise tool control and attitude control are integrated in an actuator system for narrow spaces. A micro ultrasonic motor, micro magnetic encoder, flexible displacement sensor, and shape memory alloy actuator were developed for the system. 1 Takefumi KANDA Graduate School of Natural Science and Technology, Okayama University Under Specific Environment 376 Takefumi KANDA 32.2 Structure The micro actuator system for narrow spaces mainly consists of two parts: the precise tool control unit and the attitude control unit. For the precise tool control unit, a micro servo motor was developed. A micro ultrasonic motor and micro magnetic encoder are used to achieve precise control of tools. The ultrasonic motor is driven by vibration without magnetic devices. Therefore, using a magnetic sensor for the sensing is possible. The motor, including the magnetic encoder, has a diameter of 2.5 or 3.0 mm. For the attitude control unit, an actuator is used to control the attitude of a stick- or cylindrical-shaped body. In addition, the attitude of the body is detected by a sensor that has a flexible structure. To achieve these features, we used a shape memory alloy actuator driven by an optical source and a flexible displacement sensor using piezoelectric polymer. The optical waveguide in the actuator and the flexible displacement sensor were deposited using a paste injection system. 32.2.1 Micro Ultrasonic Motor and Sensor The micro servo motor consists of a micro ultrasonic motor and a micro encoder. Each device uses a piezoelectric vibrator and a micro magnetic resistive sensor. 32.2.1.1 Micro Ultrasonic Motor Configuration The micro ultrasonic motor is shown in Fig.32.1. This motor is the cylindrical type micro ultrasonic motor and uses a cylindrical piezoelectric vibrator [2\u20134]. The motor consists of a rotor, bearing, piezoelectric vibrator, and glass case. The rotor is joined to the output shaft and is made of stainless used steel. The bearing is made of poly (tetrafluoroethylene) (PTFE). The vibrator and the bearing are supported by a glass case. The glass case has a diameter of 1.8 mm and a height of 5.8 mm. To generate traveling waves, four divided electrodes are located on the outer surface of the piezoelectric vibrator. On the inside of the vibrator, an electrode is also deposited. These electrodes are made of non-electro-plating nickel. The four electrodes on the outer surface and the electrode on the inner surface of the cylindertype piezoelectric vibrator are used to oscillate the vibrator. The rotation direction is switched by changing the phase difference of the applied voltage sources between the outer electrodes [5]. Micro Actuator System for Narrow Spaces Under Specific Environment 377 32.2.1.2 Evaluation of Micro Ultrasonic Motor Performance To obtain large output torque, the relationship between the revolving velocity of the rotor, pre-load values, and applied voltage was measured experimentally. The surface velocity of the rotor shaft, which was joined with the rotor, was measured. A laser surface velocity meter was used to measure the surface velocity, and the revolution speed was estimated. The relationship is displayed in Fig.32.2. When the pre-load and the applied voltage were 1.5 mN and 29 Vp-p, respectively, the revolving velocity was 10,000 rpm. However, as shown in Fig. 32.2, the revolving velocity reached its peak when the applied voltage values were 20 and 29 Vp-p. In addition, the maximum revolving velocity was 1.1 \u00d7 104 rpm. To evaluate the output torque of the motor, the starting performance of the motor was measured experimentally. The revolving velocity was measured with the laser surface velocity meter. From the experimental results, the revolving speed and starting torque were evaluated using the calculated inertia and measured values for the relationship between the revolving velocity and time when the pre-load values were 1.0 or 2.0 mN. The relationship between the estimated starting torque and the applied voltage is shown in Fig.32.3. The driving frequency was set at 314 kHz. The maximum starting torque was estimated to be 5.5 Nm when the driving voltage and the preload were 40 Vp-p and 1.0 mN, respectively. As can be seen, the starting torque values peaked when the applied voltage values were over 30 Vp-p. 378 Takefumi KANDA 32.2.1.3 Micro Encoder and Servo Motor The micro encoder for detecting the rotating condition, which is generated by the micro ultrasonic motor, was created by using a micro magnetic resistive sensor. A schematic of the micro encoder is shown in Fig.32.4. The shaft driven by the micro motor is connected with the magnetic drum, which has a magnetic slit pattern. The magnetic resistive sensor detects the magnetic pattern on the drum. The minimum magnetic pattern pitch is 40 m from the resolution of the sensor. Therefore, when the magnetic drum has a diameter of 2.3 mm, the angular resolution is estimated to be 2\u00b0. In our evaluation, there were 10 magnetic patterns and the pattern pitch was 0.43 mm. The output 2-phase signal values from the magnetic resistive sensor are plotted in Fig.32.5. The detected signal was converted to a pulse wave using a pick-up circuit. As shown in Fig.32.5, the sensor detected the magnetic pattern on the drum. Micro Actuator System for Narrow Spaces Under Specific Environment 379 380 Takefumi KANDA 32.3 Attitude Control Unit 32.3.1 Structure and Evaluation Results For the attitude of a stick- or cylindrical-shaped body, the unit consists of a shape memory alloy (SMA) actuator and piezoelectric polymer sensor. The basic structure is shown in Fig.32.6. To achieve a bending motion, the SMA actuator is driven optically. An optical waveguide is connected to that actuator. The sensor and optical waveguide are made of polymer paste material and patterned by a paste injection system. 32.3.1.1 Flexible Displacement Sensor Displacement sensors that have flexible structures have been receiving increasing attention. This is mainly because the need for control of soft actuators is increasing. Many types of sensors having a flexible structure for soft actuators have been reported [1, 6\u20139]. In this work, the actuator generates large displacement, as discussed in the next section. Hence, the system needs a sensor that has a flexible structure for attitude control of the actuator. A paste type piezoelectric polymer, poly (vinylidene fluoride-trifluoroethylene) copolymer (P(VDF/TrFE)), was used to achieve a flexible displacement sensor. This polymer is different from many other types of piezoelectric polymers, which need an extension process to obtain a piezoelectric effect. This polymer can be formed by casting or spin coating. A schematic of the paste injection process is shown in Fig. 32.7. In this work, the paste injector nozzle was controlled by a 3\u00b0-of-freedom positioning machine. The patterned piezoelectric polymer and conductive paste film was deposited by the paste injection system [10]. A close-up of the patterned sensor is shown in Fig.32.8. The sensor detects the bending of the plate. The sensor is 20 mm in length, 5mm in width, and 30 m in piezoelectric-film thickness. The sensing performance of the fabricated sensor was evaluated by measuring the output voltage of the sensor. A bending deformation was given by a pneumatic actuator, and tip displacement was measured by a laser displacement sensor. The pick-up voltage was amplified by a charge amplifier circuit. The step response of the fabricated sensor is plotted in Fig.32.9. The sensor detected the motion of the plate but the stability needs to be improved. Micro Actuator System for Narrow Spaces Under Specific Environment 381 382 Takefumi KANDA 32.3.1.2 SMA Actuator Driven by Optical Source To control the attitude of a stick-type or cylindrical-shaped body, an SMA actuator was used to generate displacement. The SMA can be driven by heating. Electric residence heating by an electric current is mainly used. However, the electric residence heating requires wiring for the current supply and this wiring also becomes heated. In this work, heating of the SMA was achieved by an infrared radiation source. By use of an optical waveguide, the optical source can drive the SMA actuator without any electrical wiring. A schematic of the actuator is shown in Fig.32.10. An SMA sheet was attached to a Cu substrate. An optical fiber was connected to the optical waveguide element, which was made of polymer films. The fabricated actuator is shown in Figs. 32.11 and 32.12. The length of the driving section is 45 mm. The thickness of the optical waveguide is 0.77 mm. The waveguide element consists of underclad, core, and overclad layers. Each layer is made of polymer optic material. The fabricated sensor was driven by the infrared radiation source in an experiment. The measured detected force is plotted in Fig.32.13. The wavelength of the optical source was 830 nm. When the tip displacement was 4.2 mm, the generated force was 35mN. In this experimental result, the attenuation through the optical waveguide was large. Micro Actuator System for Narrow Spaces Under Specific Environment 383 384 Takefumi KANDA 32.4 Conclusion Two components for achieving micro actuator systems for narrow spaces have been fabricated and evaluated. For a precise tool control unit, a micro servo motor using a micro ultrasonic motor and magnetic encoder has been designed and fabricated. For attitude control, a flexible displacement sensor and SMA actuator driven by an optical source were evaluated. The performance of some micro actuator systems consisting of these components have been under testing in some experimental conditions. Acknowledgments This research was supported by the Ministry of Education, Culture, Sports, Science, and Technology through a Grant-in-Aid for Scientific Research on Priority Areas, No. 438, \u201cNext Generation Actuators Leading Breakthroughs\u201d. References 1. Wakimoto S, Suzumori K, Kanda T (2005) Development of Intelligent McKibben Actuator. International Conference on Intelligent Robots and System 2005 (IROS 2005): 2271-2276 2. Kanda T., Makino A, Ono T, Suzumori K, Morita T, Kurosawa M K (2006) A Micro Ultrasonic Motor using a Micro-machined Cylindrical bulk PZT transducer. Sensors and Actuators A 127: 131-138 3. Kanda T, Makino A, Oomori Y, Suzumori K (2006) A Cylindrical Micro-Ultrasonic Motor Using Micromachined Bulk Piezoelectric Vibrator with Glass Case. Jpn. J. Appl. Phys. 45: 4764-4769 4. Kanda T, Oomori Y, Kobayashi A, Suzumori K (2006) Cylindrical Piezoelectric Vibrators For Micro Ultrasonic Motors. 10th International Conference on New Actuators: 592-595 5. Morita T, Kurosawa M, Higuchi T (1999) Cylindrical Shaped Ultrasonic Motor Utilizing Bulk Lead Zirconate Titanate (PZT). Jpn. J. Appl. Phys. 38: 3327-3350 6. Shinohara T, Dohota S, Matsushita H (2004) Development of a soft actuator with a built-in flexible displacement sensor. 9th International Conference on New Actuators: 383-386 7. Just E, Bingger P, Woias P (2004) Piezo-polymer-composite actuators a new chance for applications. 9th International Conference on New Actuators (ACTUATOR 2004), Bremen Germany :521-524,. 8. van der Smagt P, Groen F, Schulten K (1996) Analysis and control of a Rubbertuator arm. Biological Cybernetics: 75, 433-440 9. Leivo E, Wilenius T, Kinos T, Vuoristo P, Mantyla T (2004) Properties of thermally sprayed fluoropolymer PVDF, ECTFE, PFA and FEP coatings. Progress in Organic Coatings 49: 69- 73 10. Yamamoto Y, Kure K, Iwai T, Kanda T, Suzumori K (2007) Flexible Displacement Sensor using Piezoelectric polymer for Intelligent FMA. International Conference on Intelligent Robots and System 2007 (IROS 2007): 765-770 Micro Actuator System for Narrow Spaces Under Specific Environment 385 Chapter 33 Development of Ultrasonic Micro Motor with a Coil Type Stator" + ] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure9.5-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure9.5-1.png", + "caption": "Fig. 9.5 ECF micro artificial muscle cell", + "texts": [ + "4 shows an inner structure of prototype with very thin structure. The prototype with the best configuration could detect the angular rate with input voltage of 640 V. If the angular rate is changed with 1 Hz, the prototype could follow it by increasing the input voltage to 1 kV. The ECF jet can possibly control the pressure of soft actuators. Namely, we can develop many kinds of micro soft actuators integrated with fluid power source. One application is an ECF micro artificial muscle cell shown in Fig.9.5. This artificial muscle mainly consists of an ECF tank membrane, a fiber-reinforced rubber tube and an ECF jet generator. The tank membrane and the fiber-reinforced tube are arranged to be a bicylindrical structure. Then the actuator could be a cell, easy to be integrated. When the ECF jet is generated, the inner pressure of the fiber-reinforced tube increases, resulting in making the artificial muscle cell contract. The fabricated cell with 13.5 mm \u00d7 14 mm generates contraction of 1.2 mm. The ECF micro artificial muscle cell developed here is suitable for integrating in combinations in series and parallel as shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure3.35-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure3.35-1.png", + "caption": "Fig. 3.35. Vibrations", + "texts": [ + " In the case (a) a plane surface is considered. It rotates as shown in the figure. But, in practice this is not an ideal plane and the rota tion axis is not exactly perpendicular to the plane. Thus, the motion of the surface is not a simple rotation (Fig. 3.34). The reaction and, accordingly, the friction are not constant and produce vibrations of the working object (and the gripper). 224 In the case shown in Fig. 3.33b the cylindrical surface is considered. Rotation is not ideal since it is not an ideal cylinder (Fig. 3.35a) and the rotation axis is not in the exact center of the circle. For this reason the reaction is not constant and vibrations of the working object appear. All these effects can be included in the calcu lation. But, there are some effects which can not be taken into account. These are high frequency vibrations due to grains of grinding wheel. Thus, this calculation of grinding dynamics is approximative. If a po lishing task is considered then the discussion performed can also be applied but the problem of high frequency vibrations is not important" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003491_6.2006-6557-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003491_6.2006-6557-Figure3-1.png", + "caption": "Figure 3. Region of Attraction for the Unstable Mode and Operating Region for \u03b2(x+)", + "texts": [ + " The solution of the anti-windup problem for exponentially unstable systems proposed by Teel employs a controller of the form \u03be\u0307 = A\u03be +B[sat(yc + v1) \u2212 yc] v1 = [\u03b2 \u2212 1]yc + \u03b1(x+ \u2212 \u03b2[x+ \u2212 \u03be+], \u03b2\u03ba(\u03be)) v2 = \u2212C\u03be \u2212D[sat(yc + v1) \u2212 yc] (5) where \u03b2(x+) is a function of x+(t) that takes values between zero and one, and \u03ba(\u03be) is a feedback that provides L2 stability of the error system governing the mismatch between the constrained and unconstrained closed loop systems. The proof is given in,16 and will obviously be omitted here; however, to understand the controller behavior, it is necessary to introduce some additional notation. Let X+ be defined as the region of the state space in which x+(t), the state corresponding to the unstable mode, can be driven back to the origin, and let the set X+ be conservatively chosen to be contained in X+ (see Figure 3). The anti-windup controller given by equation (5) is divided into two separate controllers that span three different operating regions defined by the function \u03b2(x+) as shown in Figure 3. The function \u03b2(x+) is a design parameter, whose choice affects the performance of the anti-windup controller. When x+ \u2208 X+ then \u03b2(x+) = 1. When x+ leaves X+, then \u03b2(x+) linearly tapers off until it reaches zero. In general the function \u03b2(x+) can be chosen to be a piecewise linear function interpolated and extrapolated from chosen data points. These data points are related to the regions X+ and X+. In the first operating region (x+(t) \u2208 X+, \u03b2(x+) = 1), the anti-windup controller takes a form similar to the one given by equation (2) written as \u03be\u0307 = A\u03be +B[sat(yc + v1) \u2212 yc] v1 = \u03b1(\u03be+, \u03ba(\u03be)) v2 = \u2212C\u03be \u2212D[sat(yc + v1) \u2212 yc]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002964_tsmca.2005.855777-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002964_tsmca.2005.855777-Figure2-1.png", + "caption": "Fig. 2. Link model of the golf swing.", + "texts": [ + " The solution of the forward problem requires substitution of the measured data into a set of nonlinear equations. Thus, employment of the gyro sensors essentially eliminates the difficulties of methods involving translation measurements. Details are provided on how to measure rotation (i.e., angle, angular velocity, and acceleration) and calculate the translation in 3-D space from the measured angles. The method is applied to the measurement of the golf-swing motion, as well as to the quantitative evaluation of golf skill. Fig. 1 shows the playback of a series of golf forms from address to finish. Fig. 2 shows a golfer\u2019s link model with 12 rods. 1083-4427/$20.00 \u00a9 2006 IEEE Hereafter, we describe the golf-driver swing form using Figs. 1 and 2. During (a) address up to (b) back swing in Fig. 1, the wrist 11) begins to move and arms 10) and 12), shoulder 8), and waist 6) twist around the Y -axis sequentially. During (c) top of swing up to (d) down swing in Fig. 1, the twisted waist 6), shoulder 8), and arms 10) and 12) are released sequentially. The distance between the knees is kept constant during the address", + " The left upper arm 10) and left wrist 11) maintain a straight line until impact with the ball. At the instance of (e) impact, the waist 6) and the shoulder lines 8) must be parallel to the ball direction. After the ball is off, the swing proceeds to (f) follow through and (g) finish. Here, we consider the golf-driver swing form, and determine how to measure the rotation and translation of each part of the body in the form, with the following assumptions. A1) The golf-driver motion can be described by the kinematical 12-links model shown in Fig. 2. A2) In the driver swing, the golfer\u2019s right arm can be described by one rigid rod as shown in Fig. 2. In the detailed kinematical model, the backbone and neck cannot be represented by two rods or one rod. But in the driver-swing motion, the backbone and the neck rotate as one rigid body. Thus, the model in Fig. 2 for the golf-driver swing motion, as cited in assumption A1), is not far from the actual situation. Further into the golf-driver motion by a righthanded golfer, the left arm leads the motion and plays the key role, whereas the right arm just follows the leading motion. Therefore, the model can be simplified by expressing the right arm by one rod in assumption A2). Using the assumptions above, we address the following problems to develop a measurement method and system for the golf-driver swing form: P1) build the kinematical model and analyze the model for motion; P2) develop the motion-measurement method under the model; P3) develop the measurement system; P4) verify the measurement system; P5) illustrate how the system can be applied", + " The vector p(t) of the coordinate and the rotational matrix R(\u03b8x(t), \u03b8y(t), \u03b8z(t)) is defined as p(t)= x(t) y(t) z(t) (1) R(\u03b8x(t), \u03b8y(t), \u03b8z(t))= cos \u03b8z(t) \u2212 sin \u03b8z(t) 0 sin \u03b8z(t) cos \u03b8z(t) 0 0 0 1 \u00b7 cos \u03b8y(t) 0 sin \u03b8y(t) 0 1 0 \u2212 sin \u03b8y(t) 0 cos \u03b8y(t) \u00b7 1 0 0 0 cos \u03b8x(t) \u2212 sin \u03b8x(t) 0 sin \u03b8x(t) cos \u03b8x(t) . (2) The vector p(t) is the coordinate at the top of the rod after it rotates through the angles \u03b8x(t), \u03b8y(t), and \u03b8z(t) from an initial position. The relation between the initial and final positions can be given by (3) using the Euler transformation as [21] p(t) = R (\u03b8x(t), \u03b8y(t), \u03b8z(t)) \u00b7 p(0). (3) From Assumption A1), the driver-swing form of a golfer is provided by the 12-rod link model as shown in Fig. 2. To locate the position of each rod on the absolute coordinate system, we must consider the relations between the rods for all rods simultaneously. Consider rods i and j connected to each other, with rod i nearer to the origin than rod j. Define the following variables and constants. Then, using these variables and constant, we can consider the motions of rods i and j. The motion is described basically as shown in Fig. 3 and given by the Euler transformation. The translation of the top of rod j is provided by a summation of the translations of the head of rod i", + " Potentiometers may be difficult to attach to the human body. The use of gyro sensors solves these difficulties. Integration of the angular velocities measured by gyro sensors from the initial angles during the address yields the angles of each part or rod as follows: [ \u03b8\u0301xn (t), \u03b8\u0301yn (t), \u03b8\u0301zn (t) ] = \u222b [ \u03c9\u0301xn (t), \u03c9\u0301yn (t), \u03c9\u0301zn (t) ] dt. (7) The substitution of the angles above into (4) yields their angles. Thus, to measure driver-swing form, we placed gyro sensors on each part of the golfer or rod as shown in Fig. 2. Table I shows the variety of placement sites under the link model in Fig. 2. In Table I, the numerals with ) represent the rod number in Fig. 2. For example, 1) + 2) in the model (M21) shows the situation in which the gyro sensors are placed on the left leg and left thigh. The designation 1,2) in model M22) shows placement of the gyro sensor on a single rod composed of the two rigid rods of the left leg 1) and left thigh 2). Models M22) and M32) are fairly simple. Model M22) combines rods 1) and 2) into one rod, and model M32) combines rods 1), 2), 3), and 4) into one rod unto which one gyro sensor is placed. These are simplifications and approximations of the model in Fig. 2. From the variety of models in Table I, the parts near the origin, such as the ankle, require fewer gyro sensors compared to those parts farther from the origin, such as the left wrist, which require more gyro sensors. Table I shows the variety of simple models that reduce the number of gyro sensors by creating one rod from several rods. We select one of these models depending on the measurement purposes. Therefore, to estimate motion or form in 3-D space, the best model for the purpose is selected from Table I, the gyro sensors are placed on the corresponding rod or body part, the angular velocity of each part is measured, and the Euler transformation is applied using (6)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002639_0168-874x(93)90075-2-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002639_0168-874x(93)90075-2-Figure4-1.png", + "caption": "Fig. 4. Hidden line plot of the finite element mesh of the tire.", + "texts": [ + " (iii) correct representation of the orientation of the carcasse, cap ply and of the belt plies by means of rebar elements; (iv) consideration of different types of rubber in different parts of the tire on the basis of the Mooney material law; (v) consideration of\"micro-buckling\" by reducing the elastic modulus to 5% of its original value in case of compressive stresses in the cords; and (vi) simulation of frictionless contact between the tire and a rigid plane. Figure 3 illustrates the different constituents of an automobile tire. The figure shows one half of a cross-section of an automobile tire with smooth tread including the different cord layers. Figure 4 shows a hidden line plot of the mesh. A cross-section of the tire is contained in Fig. 5. Because of symmetry, only one half of the tire is considered in the FE model. We remark that the assumption of reflective symmetry with respect to the equatorial plane is a simplification, because the displacement distribution in the contact zone is actually characterized by central symmetry [5 ]. However, this seems to play only a minor role as far as the structural stiffness and the pressure distribution are concerned" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003391_0076-6879(88)37005-9-Figure7-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003391_0076-6879(88)37005-9-Figure7-1.png", + "caption": "FIG. 7. Substrate amplification principle demonstrated by a GOD-GDH electrode for measurement of glucose.", + "texts": [ + " Operational conditions have to be adjusted in such a way that the dehydrogenase catalyzes the regeneration of the oxidase substrate. The substrate is continuously shuttled between the two enzymes. As a consequence, the electrochemically active product is formed in much higher amount than that of substrate diffusing into the membrane. Therefore the current exceeds that of a diffusion-controlled process. Substrate amplification is exemplified by the GOD-glucose dehydrogenase (GDH, EC 1.1.1.47) system. The gluconolactone formed in the GOD-catalyzed reaction is reconverted to glucose in the GDH-catalyzed reaction with NADH (Fig. 7). Twenty units GOD and 10 U GDH/cm 2 of the gelatin layer are coimmobilized. The glucose measurements are performed in 0.1 M phosphate buffer, pH 7.0, containing variable amounts of NADH (Fig. 8). The electrode is polarized to -600 mV. The glucose sample is added after attaining a constant baseline. An amplification factor of 8 is obtained in the solution containing 10 mM cofactor. The limit of detection is 0.8 /~M glucose. Amplification makes use of a part of the GOD excess which is unused in the absence of NADH" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000545_jestpe.2021.3055224-Figure32-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000545_jestpe.2021.3055224-Figure32-1.png", + "caption": "Fig. 32 Conventional FSPM machine with 12 stator slots and 10 rotor salient poles, and its three key elements, (a) whole machine, (b) source MMF, (c) modulator, (d) filter. PMs are magnetized in circumferential directions.", + "texts": [ + " This resultant MMF distribution produces the air gap flux density distribution that is of the same waveform; 3) Step 3: The fractional-slot concentrated windings wound on stator teeth extract effective air gap flux density harmonics and induce flux linkage and EMF; 4) Step 4: When supplied with AC currents, the stator windings create another source MMF, which then interact with the one created by PMs to produce torque. With the assistance of the standard formulation of operating principles, the performance of the FSPM machine depends on the cascade of three elementary parts, namely, the PM array (source MMF), stator teeth and rotor salient poles (modulator), and stator windings (filter), as shown in Fig. 32. According to the developed theory, changes in forms or relative positions of the three elements will not affect the operation of the machine, but there might be differences in terms of torque capability, efficiency, power factor, etc. By implementing the changes in one or some of the elementary parts, new machine topologies can be derived, which have been proposed and studied by the authors\u2019 extended research group lately. 1) Variant 1: If the PM array (source MMF) is moved from the middle of stator teeth to the middle of stator yoke and the PM width is reduced to match the yoke thickness, one can have the DSPM machine, whose PM arrangement and/or number of phases can be changed further to derive two new machines, namely, the DSPM machine with \u041f-shaped stator iron core segments as detailed in [56] and the stator PM-based variable reluctance resolver in [57]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000134_j.mtla.2021.101017-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000134_j.mtla.2021.101017-Figure2-1.png", + "caption": "Fig. 2. Image of the Plastometer, with the key components labeled.", + "texts": [ + " The cross-section was then accurately measured sing a micrometer prior to testing. Strain was measured using a video xtensometer, with an iMetrum system. Speckle patterns were applied n the surfaces to facilitate tracking. The focus was on the separation f speckles at both ends of the gage length - ie the (nominal) strain was eing measured in the same way as with a clip gage. All samples were ested until fracture. .4. PIP The equipment used in this work was the Indentation Plastometer hown in Fig. 2 . Four steps are involved in obtaining a tensile stresstrain curve from an indentation test. These are: (a) pushing a hard inenter into the sample with a known force, (b) measuring the (radiallyymmetric) profile of the indent, (c) iterative FEM simulation of the t ( o 2 h t r a t m w a ( e 2 t o i t o 2 i s s c [ \ud835\udf0e w i t w o f ( p o b c c b e g s S fi w v 2 s i l a e 3 3 F c F g a g c i est until the best fit set of plasticity parameter values is obtained and d) using the resultant (true) stress-strain relationship in FEM simulation f the tensile test" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002663_mssp.2000.1345-Figure9-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002663_mssp.2000.1345-Figure9-1.png", + "caption": "Figure 9. Principle of gravitational pendulum method.", + "texts": [ + " The time requirements for testing and data processing are high (especially if adapter is required) since only two coordinates of the centre of gravity and two products of inertia can be identi\"ed simultaneously. According to [8], a medium accuracy of $10% can be attained. The procedure has been approved in industrial applications. 4.2.2.1. Gravitational pendulum method. The moment of inertia about a speci\"ed pendulum axis can be identi\"ed using the gravitational pendulum method [5, 12]. Here the test specimen must be supported by knife edges or suspended by wires (Fig. 9). It then acts as a physical pendulum while the restoring torque is generated by the gravitation. In case that the mass and centre of gravity location of the test specimen are known, the moment of inertia about the pendulum axis can be calculated from the measured oscillation frequency (absolute method). If only the mass is known, the moment of inertia about the pendulum axis can be calculated using the measured oscillation frequencies of two tests with di!erent wire lengths (relative method). The mechanical system is mounted such that pendulum axis and y-axis of the inertial frame coincide. The g-axis of the body \"xed frame is chosen co-linear to the y-axis of the inertial frame (Fig. 9). The second row of equations (8b) yields equation (20) if no external torques act: H AggbGA#mgf AC b A \"0. (20) This is the equation of motion of a single-degree-of-freedom (sdof ) oscillator. If the mass and the centre of gravity location are known, the moment of inertia can directly be calculated using the measured oscillation frequency f 0 : H Agg\" mgf AC (2n f 0 )2 . (21) At least six tests (possibly less if principal inertial axes are known) with di!erent speci\"ed pendulum axes are needed in order to identify the complete inertia tensor [3, 5, 12]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003742_1.4000277-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003742_1.4000277-Figure2-1.png", + "caption": "Fig. 2 Vertical stiffness measuring apparatus", + "texts": [ + " Each test linear bearing consists of a rail, a carriage, a retainer, and balls. Each test linear bearing had four rows and the ball groupings were retained in phase by a retainer. All of the test linear bearings were preloaded with oversized balls. The preloads of the test bearings were light and medium. The specifications of the test linear bearings are shown in Table 1. 2.2 Vertical Stiffness Measurements. For the vertical stiffness measurements of the test linear bearings, the test rig and measurement apparatus shown in Fig. 2 were used. A vertical load FV was applied to the carriage of the test linear bearings through a block, load cell NMB: C2M1-500 K, Kanagawa, Japan using a universal testing machine Shimadzu Corporation: DSS-25T, Kyoto, Japan , while the rail was fixed to the bed with bolts. The vertical load FV varied from 12.6 N to 2000 N. The lowest value of FV, which is 12.6 N, was the initial load FV0, which was sum of the weights of the carriage and the block. The vertical displacement measuring points are shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003596_02640410601096822-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003596_02640410601096822-Figure1-1.png", + "caption": "Figure 1. Graphical representation defining hip and shoulder alignment. The shaded area represents shoulder alignment in the transverse plane.", + "texts": [ + " As both methods of motion analysis identify joint centres, the variation in methods used should not affect the comparisons of relationships observed with the within-bowler and between-bowlers conditions. The kinematic parameters selected for analysis (Table II) had previously been reported in the cricket performance literature (scientific and/or coaching), or hypothesized by the authors to affect ball release speed. Resultant vectors were used to report displacement, velocity, and joint angle data unless otherwise stated. Hip and shoulder alignments were reported in a two-dimensional transverse plane as described in Figure 1. Additional parameters were analysed in the within-bowler component due to the retrospective collection of the between-bowlers data. Stride length was taken as the distance between the joint centre of the right ankle at back foot contact and the left ankle at front foot contact. Ball release height was the vertical distance from the ground to the central core of the cricket ball. Centre of mass velocity was used to describe run-up velocity. The change in centre of mass velocity over the delivery stride was defined as the difference between the centre of mass velocity at release and the maximum centre of mass velocity over the delivery stride" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003926_1077546307080026-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003926_1077546307080026-Figure1-1.png", + "caption": "Figure 1. Schematic layout of the gearbox test rig.", + "texts": [], + "surrounding_texts": [ + "Using Parseval\u2019s theorem the total energy of a signal x t can be expressed as\nE\nx t 2 dt 1\nCh\nCW Tx b a 2 dadb\na2 (4)\nwhere E is the total signal energy and Ch is a constant called the admissibility condition which is determined from the squared magnitude of the Fourier transform ( H f 2) of the wavelet function.\nCh\nH f 2 d f\nf (5)\nMathematically, the wavelet transform offers flexibility in the selection of the analysing wavelet. The Morlet wavelet is used in this study because it is closely related to Fourier analysis and therefore easily understood in the context. Additionally, it gives good dilation and translation selectivity and is well adapted to the problem of locating abrupt changes in a signal. Moreover, the Morlet wavelet function is approximately progressive if its centre frequency is larger than 0.875 Hz. The progressivity condition means that the wavelet transform does not produce any interference in the time domain between the past and future (Staszewski, 1994). The Morlet wavelet is defined in the time and frequency domains as\nh t exp j2 f0t exp t2 2\n(6)\nH f 2 exp 2 2 f f0 2\n(7)\nwhere f0 is the wavelet centre (or oscillation) frequency and t . The Morlet wavelet itself is not admissible, but appropriate selection of the wavelet centre frequency (e.g., f0 0.875 Hz) makes the Morlet wavelet admissible in practice (Chui,1992 Meyer,1993).\nThe term CW Tx b a 2 in equation (4) can be considered to be the energy density (or scalogram) over the b-a plane. When such an energy density function is described, its mean frequency, which represents the energy centre of gravity at a certain time t, can be expressed as\nf t M1 t M0 t (8)\nwhere Mn t denotes the frequency moments at time t and n is the order of the frequency moment. The nth order frequency moment of a scalogram at time t can be expressed as\nMn t FN\n0\nf n CW Tx b a 2 d f (9)\nat UNIVERSITE LAVAL on May 10, 2015jvc.sagepub.comDownloaded from", + "A two-stage industrial gearbox, shown in Figures 1 and 2, was used for the tests. All the helical gears were made of steel and were ground and induction case-hardened. The other specifications of the gears are given in Table 1. The drive pinion at the first stage had 29 teeth meshing with a 40-tooth wheel. The pinion gear at the second stage, driven directly by 40-tooth wheel, had 13 teeth meshing with 33-tooth wheel. A 2.2 kW three-phase induction motor with a variable speed controller was used to drive the gearbox, and the power from the motor to the main shaft of the gearbox was transmitted by a pair of V-belt drive units. The gearbox was loaded by a DC motor the output of which was used to feed an adjustable resistor bank the 2.2 kW load capacity of the DC was much lower than that of the gearbox used, which is nearly 8.1 kW. For this reason, the face width of the pinion test gear was reduced from 12 mm to 4 mm so that it could be tested at reasonably high load. The vibration signal generated by the gearbox was detected by accelerometers located perpendicular to each other on the input shaft bearing housing, as shown in Figure 2. The position of the input shaft of\nat UNIVERSITE LAVAL on May 10, 2015jvc.sagepub.comDownloaded from", + "the gearbox was indicated by an inductive sensor producing one pulse for each rotation of the test pinion gear.\nSpecified gear load can be exceeded as a result of shock or cyclic load variation and, consequently, some teeth on a gear may be subjected to a higher load than the capacity of gear. In such cases, a pitting fault may occur in time on the tooth surfaces on which a higher load is experienced. Simulated surface pits were introduced on some of the pinion gear teeth using an electro-erosion machine, as shown in Figure 3, and were intended to replicate a pitting failure, initiating on a single tooth and then developing over the neighbouring tooth surfaces.\nFirst, a circular pit (whose diameter and depth are approximately 0.7 mm and 0.1 mm respectively) was seeded onto a single tooth surface as shown in Figure 4(b). This gear tooth, called the centre tooth, was positioned such that it came into mesh at approximately 300 pinion rotation. After that, in order to represent the progression of the fault, the number of defective teeth was increased to five and additional pits were introduced as shown in Figure 4(c) (5 pits total on the centre tooth, 3 pits on the adjacent two teeth, and 1 pit on each of the other two teeth). In the third stage, the severity of fault was increased by once more doubling the number of pits on these teeth. For the final stage of fault development, the number of pits was doubled again, and the surface of the centre tooth was completely covered by severe pitting marks as shown in Figure 4(e).\nat UNIVERSITE LAVAL on May 10, 2015jvc.sagepub.comDownloaded from" + ] + }, + { + "image_filename": "designv10_6_0002555_s0304-8853(03)00324-x-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002555_s0304-8853(03)00324-x-Figure1-1.png", + "caption": "Fig. 1. Geometry of the permanent magnet motor.", + "texts": [ + " Tel.: +86-531-8395869; fax: +86- 531-2955999. E-mail addresses: wangxh67@yahoo.com (X. Wang), yangyu bo@163.com (Y. Yang), fuday123@163.com (D. Fu). 0304-8853/03/$ - see front matter r 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0304-8853(03)00324-X FEM. Finally, the effects of some factors on cogging torque are discussed on the basis of the above, and several conclusions are drawn. The geometry of the surface-mounted permanent magnet motor discussed in this paper is as shown in Fig. 1. For convenience of study, following assumptions are made: * The permeability of iron is infinite. * The permanent magnets are supposed to be radially magnetized. * The slots are simplified to be rectangular. * The distribution of magnetic field in airgap is one-dimensional. * Position y \u00bc 0 is set to the midline of one of the permanent magnets. * All permanent magnets have the same dimen- sions and performances. * The permeability of permanent magnet is the same as that of air. As has been known, cogging torque Tcog is the variation of energy in motors when rotor rotates" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003815_j.mechmachtheory.2009.06.001-Figure21-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003815_j.mechmachtheory.2009.06.001-Figure21-1.png", + "caption": "Fig. 21. Defective generators with three coaxial H pairs.", + "texts": [ + " One additional defective generator, a series of four prismatic pairs that generates {T} instead of {X(u)}, is displayed in Fig. 20 for completeness. Case B. A product of two factors is a 2D subgroup and one among the other two factors is included into this subgroup. For example, p1\u2013p2; A2 2 line\u00f0A1; u\u00deor\u00f0A1A2\u00de u \u00bc 0 ) fH\u00f0A1; u; p1\u00degfH\u00f0A2; u; p2\u00deg \u00bc fC\u00f0A1; u\u00deg; A3 2 line\u00f0A1; u\u00de ) fH\u00f0A3; u; p3\u00deg fC\u00f0A1; u\u00deg ) \u00bdfH\u00f0A1; u; p1\u00degfH\u00f0A2; u; p2\u00deg {H(A3, u, p3)}{H(A4, u, p4)} = {C(A1, u)}{H(A3, u, p3)}{H(A4, u, p4)} = {C(A1, u)}{H(A4, u, p4)} \u2013 {X(u)}. Hence, three axes must not be coaxial. Fig. 21a shows such a defective chain with three coaxial H pairs. The subgroup {C(A1, u)} can also be generated by PH or HP arrays (PR or RP when the pitch of H is zero) if the P is parallel to the H axis (R axis). Fig. 21b\u2013f shows other defective X-motion generators being in this situation, in which the replacement of any screw H by revolute R yields a defective X-generator chain, too. In Fig. 22, the cases with three prismatic pairs that are parallel to a plane are defective generators of X-motion and must also be avoided. Case C. A product of two factors is a 2D subgroup and the product of the other two factors is another subgroup, which is dependent with respect to the first subgroup. In other words, the intersection of the two 2D subgroups is a 1D subgroup" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure18.17-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure18.17-1.png", + "caption": "Fig. 18.17 Operation principle of the disk-type gyro-sensor", + "texts": [ + " 214 Manabu AOYAGI, Takehiro TAKANO, Hideki TAMURA and Yoshiro TOMIKAWA The load characteristics of the modified electrode-type motor are shown in Fig.18.16, and the maximum efficiency is approximately 4 to 6%. The difference in the characteristics by the rotation direction and several problems must be improved by the structural modifications. However, it is found that a potentiality of the single crystal ultrasonic motor which consumes low power exists. We also investigated a new motor, the operation principle of which depends on a vibratory gyro. Figure 18.17 shows the disk-type vibratory gyro, and its basic principle is shown by the equivalent circuit in Fig.18.18. By inputting the moments M1 and M2 and considering the phase difference between them, the moment M3 is generated and rotates the rotor. This motor is referred to herein as the gyromoment motor (GMM). [9, 10] A number of GMMs are shown in Figs. 18.19 and 18.20. The CW and CCW rotation of the rotor can be determined easily by setting the phase difference between the moments M1 and M2. The driving method of the electromagnetic-type GMM is shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000553_j.jmapro.2021.03.059-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000553_j.jmapro.2021.03.059-Figure1-1.png", + "caption": "Fig. 1. Experimental setups.", + "texts": [ + " In addition, some measures to reduce or eliminate bulges were proposed to reduce the surface roughness of laser polishing. A continuous-wave fiber laser (Model: YLR-1000) at 1070\u2212 1080 nm wavelength, with a maximum power of 1000 W, from IPG Photonics Corporations, was used for laser polishing. And the intensity of the laser beam is the Gaussian distribution. The X-Y-Z three-dimensional working platform can move the samples in the vertical and horizontal directions to complete the laser polishing process, as shown in Fig. 1. Surface topography of samples before and after laser polishing was examined by a 3D measurement laser microscope (Model: OLS4100), surface roughness (Ra) was calculated based on the surface topography of samples. And chemical composition analysis of the samples is obtained by Gemini 300 scanning electron microscope (SEM). The 304 stainless steel was used as the experimental material, in the form of rectangular blocks, with 20 mm \u00d7 20 mm \u00d7 20 mm of dimension. And there are a lot of strip-shaped surface textures on the unpolished surface of the sample, leading to an initial surface roughness Ra of 1" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003972_1.2823085-Figure5-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003972_1.2823085-Figure5-1.png", + "caption": "Fig. 5 Schematic view of the melt pool, the powder jet, and the laser beam", + "texts": [ + ", combining two separate nonlinear terms uch as L2 2 /dp 2 to one individual term such as L2 /dp n . The parametric gray-box model is then presented by h\u0307 + h = 3 2 m\u0307 w0 db dp 1 + h t db tan cos n k v t 3 here h\u0307 is the derivative of the clad height m/s , m\u0307 is the powder ow rate kg/s , is the powder density kg /m3 , h0 and w0 are he steady state values of the clad height and width m , respecively see Fig. 4 , dp is the powder jet diameter m , is the ngle between the nozzle and the laser beam, db is the laser beam iameter see Fig. 5 , and , n, and k are unknown parameters that re identified through experimental analyses. Using the experiental results and the recursive least squares method, the model arameters are identified offline. The experimental tests are se- ournal of Manufacturing Science and Engineering om: http://manufacturingscience.asmedigitalcollection.asme.org/ on 01/29 lected with different processing parameters; therefore, a domain is obtained for each of the model parameters, which can be expressed as kmin k kmax min max nmin n nmax 4 Figure 6 shows the experimental results of the process transient response resulting from a random step in the scanning speed" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003820_j.jnucmat.2007.01.078-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003820_j.jnucmat.2007.01.078-Figure2-1.png", + "caption": "Fig. 2. Two different models with internal cooling channels fabricated by SLM technology.", + "texts": [ + " The SLM technology was applied for fabrication of several model objects that can be used in cooling systems of ITER. The \u2018models\u2019 have a particular geometry: (a) thin walls (to intensify heat exchange) and (b) internal cooling channels. An example of a thin-walled model is presented in Fig. 1 the box of 20 \u00b7 20 \u00b7 5 mm with inner compartment walls of the minimal possible thickness (140 lm in the present case). Long term stability of SLM process was controlled by fabrication of large-size thin-walled objects during 36 h. Two different models with internal cooling channels are presented in Fig. 2. The average bulk porosity is about 1%. Another example corresponds to ITER problematic where He will be used as a coolant. The goal is to augment the heat transfer coefficient in fingershaped divertor elements. The inner surface of a thimble should have a particular geometry. The results of fabrication of a model with similar geometry are presented in Fig. 3. Note that a single step manufacturing method was applied. Combination of steel\u2013Cu elements in the cooling systems is a conventional approach" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000202_j.mechmachtheory.2021.104330-Figure10-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000202_j.mechmachtheory.2021.104330-Figure10-1.png", + "caption": "Fig. 10. An example of the deployable grasping parallel mechanism. (a) The auxiliary sub-mechanism consists of five revolute joints that are denoted by y R y R y R u1 R u2 R. (b) Assembly of the deployable grasping parallel mechanism using the base, the platform, the grasping sub-mechanism, and two auxiliary sub-mechanisms. (c) The folded configuration of the whole mechanism.", + "texts": [ + " Thus, the structural characteristics of the auxiliary sub-mechanism in this case can be obtained as follows: 1) there must be two or three successive revolute joints, i.e., ( i R j R) N , ( i R j R k R) N , u1 R u2 R, or u1 R u2 R u3 R, 2) the revolute joint(s), except those in the successive revolute joints, must be y R, and 3) the prismatic joint(s) must be w P or w1 P w2 P. According to these structural characteristics, the enumeration of such auxiliary sub-mechanisms is listed in Table 2 . One example of the auxiliary sub-mechanism is illustrated in Fig. 10 (a), denoted by y R y R y R u1 R u2 R. This auxiliary sub-mechanism consists of three successive revolute joints whose rotation axes are along Y a -axis and a 2R spherical sub-chain. In Fig. 10 (b), a deployable grasping parallel mechanism can be assembled using the base and platform to connect the grasping submechanism and two auxiliary sub-mechanisms. After that, the folded configuration of the whole mechanism is obtained, as shown in Fig. 10 (c). Further, this paper also shows the fully deployed configuration and the grasping configuration of such a mechanism, as presented in Fig. 11 (b) and (c), respectively. Three configurations of this deployable grasping parallel mechanism are verified using the corresponding physical prototype, as provided in Fig. 11 (d) to (f). Besides, this deployable grasping parallel mechanism can grasp objects at any configuration of the deployment motion, which is demonstrated as presented in Movie S2. In this case, the standard base of constraint-screw system for the auxiliary sub-mechanism is S r a = { S r a1 = (1 , 0 , 0 , 0 , 0 , 0) T S r a2 = (0 , 1 , 0 , 0 , 0 , 0) T } , (50) which denotes a constraint force along X a - and Y a -axes, respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003623_robot.2009.5152390-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003623_robot.2009.5152390-Figure2-1.png", + "caption": "Fig. 2. X-4 Component Offsets.", + "texts": [ + " The intermediate step is to mount the vehicle on a gimbal for parameterisation and testing. This does not provide data on translational dynamic phenomena, but provides a first-cut for proving the function of flight regulators and performing characterisation experiments. The X-4 Flyer consists of a chassis, rotors, motors, power cells and avionics. Each subsystem is listed in the weightbudget, Table I, and described below. Component distances are measured with respect to the rotor plane, (masses \u00b10.005 kg, distances \u00b10.005 m) (see Fig. 2). The X-4 has an aluminium centre frame with carbon fibrefoam sandwich arms. Motors and batteries are mounted as far from the central axis as possible to slow the pitch and roll dynamics. The arms angle down slightly to provide more clearance between the bottom of the arms and flapping rotor tips. The rotor mounts are teetering hubs, a freely pivoting joint between the drive shafts and rotor blades. Avionics and sensors are mounted in a vibration-isolated pod housed inside the centre frame and each motor is mounted on rubber-isolated brackets" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002839_978-3-662-03845-1-Figure1.11-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002839_978-3-662-03845-1-Figure1.11-1.png", + "caption": "Fig. 1.11. Meniscus: (a) for a fibre; (b) for a plane surface, dipped into a liquid", + "texts": [ + " If eE is greater than 7r /2, the liquid will not penetrate, and it is re ferred to as non-wetting. Such is the case for the fluorinated cloths known as Gortex, which let air through, but not water; or for rocks when treated with polydimethylsiloxane (, = 21 mN /m) in the building industry. If eE is less than 7r /2, the liquid will penetrate, and it is referred to as wetting. 14 1. Droplets: Capillarity and Wetting When water is poured into a glass, the liquid rises a short way up the glass and forms a meniscus on a millimetric scale. Figure 1.11 shows two cases in which a meniscus forms when (a) a very fine fibre, of radius R \u00ab f);-l; (b) a solid plane, are dipped into a liquid. In the case of the fine fibre (Fig. 1. 11a), gravity can be neglected and the surface generated has zero curvature. Its profile z(x) can be determined from the statement that the tension is conserved: 21fz(xhcose = 21fbry, where e is defined as the angle of the slope (tan e = dz / dx). The profile deduced from this differential equation is a catenary curve x z (x) = b cosh b . In the case of the plane surface (Fig. 1.11), we equate the hydrostatic and capillary pressures at A. This leads to 1/ R = - pgz. The curvature is given by 1 de de R = ds = dz cos e , where ds is the curvilinear distance along the curve. The equation of the profile is found by integrating once to give 1 _f);2 Z 2 = 1 - sine. 2 This equation for e = eE gives the height h of the meniscus. For total wetting, eE = 0 and h( eE = 0) = V2f);-1. Once again, it can be checked that ISO - ISL carries the weight of the liquid lifted per unit length of the contact line" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000135_j.optlastec.2021.106917-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000135_j.optlastec.2021.106917-Figure2-1.png", + "caption": "Fig. 2. The established three-dimensional finite element model and the selection of monitoring sites.", + "texts": [ + " While the laser scanning over, high energy concentration made the molten pool front part obtain a short melting time and inherited the spot\u2019s circular contour. Meanwhile, the solidification time required at the end of the pool was longer, and the process happened gradually from both sides to the center. Hence the pool shaped large and round at the head, while long and thin at the tail. At the same time, owing to the increase of X. Shi et al. Optics and Laser Technology 138 (2021) 106917 temperature, three-dimensional size, temperature gradient and the melt velocity all increased. As shown in Fig. 2, according to the parameters of power P = 1200 W, scanning speed v = 16.67 mm/s and powder feeding rate u = 20 g/ min, monitoring points were set at different positions along the cross and longitudinal directions of the molten pool cross-section perpendicular to the scanning path. From the top to the bottom, monitoring points A to D were in order, which represented the top, center, interface between the molten channel and the substrate and bottom of the molten pool, respectively. Points B, E and F were distributed from the center of the pool to the edge along the horizontal direction" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003729_9780470612231.ch6-Figure6.8-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003729_9780470612231.ch6-Figure6.8-1.png", + "caption": "Figure 6.8. Schematic of a typical potentiometric cell assembly incorporating an ISE and reference electrode as the galvanic half cells and a high impedence voltmeter for measurement of the cell EMF", + "texts": [ + " Thus, by knowing the exact potential difference needed to compensate the EMF, such that no current flows, the determination of the EMF is possible. A potentiometric cell uses two electrodes, an indicator (working electrode) which is an ISE in this case, and a reference. The function of the reference is to maintain a constant potential in order to allow measurement of the potential at the indicator electrode. A typical cell, consisting of two electrodes (e.g. an ISE and reference electrode), a high impedance voltmeter and the sample solution, is shown in Figure 6.8. The ISE in this case is the indicator/working electrode and its purpose is to allow potentiometric determination of the activity of certain ions in the presence of other ions. The ISE thus constitutes one half of the Galvanic cell, consisting of an ion-selective membrane, an internal filling or contact solution (or solid contact in the case of solid state ISEs, e.g. a hydrogel) and an internal reference electrode. The external reference electrode gives the other half of the Galvanic cell. The external reference is typically an electrode such as Ag/AgCl, Cl- or Hg/HgCl, Cl- (calomel)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003786_tmech.2009.2032687-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003786_tmech.2009.2032687-Figure1-1.png", + "caption": "Fig. 1. Kinematic and static parameters of a spatial multilink chain.", + "texts": [ + " Homogeneous transforms, denoted Ti , are used to relate the reference frames attached to any two bodies in the system Ti = [ Ai \u21c0 di 0 1 ] (1) where Ai is a 3-by-3 rotation matrix, \u21c0 di is a 3-by-1 displacement vector, and 0 represents a 1-by-3 vector of zeros. The 3-by-1 vector \u21c0 ci is used to locate the CoM of an individual body in the local reference frame attached to body i, or relative to Ti . Finally, the mass of body i is given by mi , where the total mass of the system is M = \u2211 mi . A brief review of the main steps in the development of the statically equivalent serial chain of the example chain depicted in Fig. 1 is now presented. The CoM of any multilink chain \u21c0 CM , with a serial or a branched chain structure, can be expressed as the end-effector of an SESC. Fig. 2 illustrates this point for the branched chain depicted in Fig. 1. The process begins with the definition of the CoM of a collection of bodies, or the weighted sum of each body\u2019s COM location { \u21c0 CM 1 } = m1T1 { \u21c0 c1 1 } M + m2T1T2 { \u21c0 c2 1 } M + m3T1T3 { \u21c0 c3 1 } M + m4T1T3T4 { \u21c0 c4 1 } M . (2) Expanding \u21c0 CM = \u21c0 d1 + A1 \u21c0 r2 + A1A2 \u21c0 r3 + A1A3 \u21c0 r4 + A1A3A4 \u21c0 r5 (3) where \u21c0 r2 = m1 \u21c0 c1 + m2 \u21c0 d2 + (m3 + m4 ) \u21c0 d3 M , \u21c0 r3 = m2 \u21c0 c2 M \u21c0 r4 = m3 c3 + m4d4 M , \u21c0 r5 = m4c4 M . (4) Observe that with a complete knowledge of the kinematic and static parameters of the system, the \u21c0 ri vectors in (4) are known" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000202_j.mechmachtheory.2021.104330-Figure6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000202_j.mechmachtheory.2021.104330-Figure6-1.png", + "caption": "Fig. 6. The sub-chain consists of the grasping sub-mechanism, the base, and the platform.", + "texts": [ + " Namely, the new mechanism is the equivalent mechanism of a plane-symmetric Bricrad linkage due to their kinematical equivalence. Since the planesymmetric Bricard linkage has high deploy/fold ratio, the designed mechanism in Fig. 5 (f) is selected as the grasping submechanism. In the following work, we will design a base, a platform, and two auxiliary sub-mechanisms that are symmetric about the plane \u03c05 . Thus, we can construct a plane-symmetric parallel mechanism using proposed type synthesis method. The base and the platform of the whole mechanism are introduced, as shown in Fig. 6 . The revolute joints R 1 and R 2 are used to assemble the based and block 3 of the grasping sub-mechanism, and the revolute joints R 3 and R 4 are designed to hinged connect the platform and block 6 in the grasping sub-mechanism. After that, the sub-chain is constructed, consisting of the grasping sub-mechanism, the base, and the platform. Here, a local coordinate frame { O g - X g Y g Z g } is introduced, which is set as follows: X g -axis is located at the axis direction of revolute joint R 1 , Z g -axis is located at the plane determined by axes of revolute joint R 1 and R 3 , and it is perpendicular to X g -axis, the right-hand rule determines Y g -axis. The position vectors of revolute joints R 1 and R 3 are (0,0,0) T and ( x 3 , 0, z 3 ) T , respectively. Comparing Figs. 4 and 6 shows that X g -, Y g -, and Z g -axes are parallel to X 0 -, Y 0 -, and Z 0 -axes. The mobility of block 6 relative to block 3 is the motion-screw of grasping sub-mechanism as presented in Eq. (33) . Thus, the motion-screw system ( ( ( of the sub-chain (shown in Fig. 6 ) is S g = \u23a7 \u23aa \u23a8 \u23aa \u23a9 S g1 = ( 1 , 0 , 0 , 0 , 0 , 0 ) T S g2 = ( 1 , 0 , 0 , 0 , a, b ) T S g3 = ( 1 , 0 , 0 , 0 , z 3 , 0 ) T \u23ab \u23aa \u23ac \u23aa \u23ad , (34) where the last three terms in S g1 and S g3 are the cross products of the position vectors of R 1 and R 3 with respect to their corresponding screw axis vectors. According to the reciprocal screw theory, the sub-chain constraint-screw system can be obtained as follows: S r g = \u23a7 \u23aa \u23aa \u23a8 \u23aa \u23aa \u23a9 S r g1 = ( 1 , 0 , 0 , 0 , 0 , 0 ) T S r g2 = ( 0 , 0 , 0 , 0 , 1 , 0 ) T S r g3 = ( 0 , 0 , 0 , 0 , 0 , 1 ) T \u23ab \u23aa \u23aa \u23ac \u23aa \u23aa \u23ad , (35) which indicates that there is one constraint force along X g -axis and two constraint forces around Y g - and Z g -axes. i.e., they are restricted that the translational mobility along X g -axis and the rotational mobility parallel to the plane determined by Y g - and Z g -axes. Thus, the platform has three DOFs: translational mobility parallel to the plane determined by Y g - and Z g -axes, and rotational mobility around X g -axis. To let the whole mechanism have deployment and grasping mobility, the platform illustrated in Fig. 6 should have and only have the translational mobility along Z g -axis and rotational mobility around X g -axis. According to Eq. (35) and Fig. 6 , the platform has extra translation mobility along Y g -axis, which should be restricted using the auxiliary sub-mechanism. Hence, the auxiliary sub-mechanism should satisfy the following conditions: 1) it restricts the translational mobility along Y g -axis, 2) it does not restrict the translational mobility along Z g -axis, and 3) it does not restrict the rotational mobility around X g -axis. Here, one grasping plane and two auxiliary planes are introduced to construct the auxiliary sub-mechanism more conveniently" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000095_j.oceaneng.2021.109071-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000095_j.oceaneng.2021.109071-Figure1-1.png", + "caption": "Fig. 1. Illustrating UUV formation with {B} and {E} frames.", + "texts": [ + " Due to the expensive cost and simplifying mechanism, velocity measuring instruments may not be equipped on UUV body, and velocity information is unavailable for designing output feedback control. Such that, Lemma 3 can be employed to design a nonlinear finitetime velocity observer for estimating unmeasurable velocities. Consider a leader-follower formation system consisting of N underactuated UUVs with index set N = {1,2,\u22ef,N}. To accurately illustrate the motion of each UUV, earth-fixed frame {E} and body-fixed frame{B} are formulated in Fig. 1. The kinematic and dynamic model of the i-th UUV is provided as (Do and Pan, 2009; Fossen, 2011) { \u03b7\u0307i = J(\u03c8i)\u03bdi Mi\u03bd\u0307i + Ci ( \u03bdi ) \u03bdi + Di ( \u03bdi ) \u03bdi = \u03b4i(\u03c4) + wi (5) where \u03b7i = [xi, yi,\u03c8 i] T \u2208 \u211d3 is a vector of position (xi, yi) and yaw angle \u03c8 i \u2208 [0, 2\u03c0) in earth-fixed frame, respectively; \u03bdi = [ui, vi, ri] T \u2208 \u211d3is a velocity vector in surge ui, sway vi, and yaw riin body-fixed frame; wi = H. Liang et al. Ocean Engineering 233 (2021) 109071 [wui,wvi,wri] T denotes the external unknown disturbances; J(\u03c8 i) \u2208 \u211d3\u00d73is the rotation matrix, and \u041ci \u2208 \u211d3\u00d73, Ci \u2208 \u211d3\u00d73 andDi \u2208 \u211d3\u00d73 are the nondiagonal inertia matrix, Coriolis matrix and damping matrix, respectively, all of which are given by J(\u03c8i)= \u23a1 \u23a3 cos(\u03c8i) \u2212 sin(\u03c8i) 0 sin(\u03c8i) cos(\u03c8i) 0 0 0 1 \u23a4 \u23a6 (6a) \u041ci = \u23a1 \u23a3 m11i 0 0 0 m22i m23i 0 m23i m33i \u23a4 \u23a6 (6b) Ci = \u23a1 \u23a3 0 0 \u2212 m22ivi \u2212 m23iri 0 0 m11iui m22ivi + m23ri \u2212 m11iui 0 \u23a4 \u23a6 (6c) Di = \u23a1 \u23a3 d11(ui) 0 0 0 d22(vi, ri) d23(vi, ri) 0 d32(vi, ri) d33(vi, ri) \u23a4 \u23a6 (6d) where m11i = mi \u2212 Xu\u0307i,m22i = mi \u2212 Yv\u0307i,m23i = mixgi \u2212 Yr\u0307i,m33i = Izi \u2212 Nr\u0307i,d11(ui) = \u2212 (Xui + X|ui|ui|ui|),d22(vi,ri) = \u2212 (Yvi + Y|vi|vi|vi| + + Y|ri|vi|ri|), d23(vi, ri) = \u2212 (Yri + Y|vi|ri|ri| + + Y|ri|ri|ri|), d32(vi, ri) = \u2212 (Nvi + N|vi|vi|vi| + + N|ri|vi|ri|), d33(vi, ri) = \u2212 (Nri + N|vi|ri|vi| + + N|ri|ri|ri|)", + " (Ge and Wang, 2002) For\u2016W\u2016 \u2264 W*andW\u0303 = W \u2322 \u2212 W*, an error can be formulated by W\u0303 T \u0398(Z)=W \u2322 T \u0398(Z) \u2212 W*T\u0398(Z) (19) and then following inequalities can hold \u2212 \u03c7W\u0303 T W \u2322 T \u2264 \u03c7 2 (\u20d2 \u20d2 \u20d2 \u20d2 \u20d2 \u20d2W* \u20d2 \u20d2 \u20d2 \u20d2 \u20d2 \u20d2 2 \u2212 \u20d2 \u20d2 \u20d2 \u20d2 \u20d2 \u20d2W\u0303 \u20d2 \u20d2 \u20d2 \u20d2 \u20d2 \u20d2 2) (20a) ||\u0398i(Z)|| \u2264 ci (20b) where\u03c7andciare positive constants. The objective of this paper is to design an adaptive output-feedback formation controller for N underactuated UUVs such that each vehicle can track a desired leader with the prescribed performance, while the tracking errors are confirmed to the predefined performance bounds in the presence of model uncertainties and external disturbances. Let\u03b7l = [xl, yl,\u03c8 l] Tand\u03b7ir = [xir, yir,\u03c8 ir] Tbe the desired leader and reference trajectory of the i-th follower, respectively, as illustrated in Fig. 1. The predefined desired distancedif and angle\u03d5if are introduced to illustrate the relative position between\u03b7land\u03b7ir, which is formulated as follows \u23a7 \u23a8 \u23a9 xir = xl + dif cos ( \u03c8l + \u03d5if ) yir = yl + dif sin ( \u03c8l + \u03d5if ) \u03c8ir = \u03c8l (21) wherexl = xl + \u03belcos(\u03c8 l),yl = yl + \u03belsin(\u03c8 l). Define the transformed positions and yaw error \u23a7 \u23a8 \u23a9 xei = xi \u2212 xir yei = yi \u2212 yir \u03c8ei = \u03c8i \u2212 \u03c8ai (22) where\u03c8aiis an approach angle to track desired leader for the i-th UUV formulated as (Park, 2015) \u03c8ai = atan ( yei / xei ) tanh ( H2 / a0 ) +\u03c8l ( ( 1 \u2212 tanh ( H2 / a0 )) (23) wherea0is a positive constant, andH = \u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305\u0305 x2 ei + y2 ei \u221a " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003162_50008-0-Figure7.7-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003162_50008-0-Figure7.7-1.png", + "caption": "FIGURE 7.7 Geometry of two bodies with one convex and one concave surface in contact.", + "texts": [ + " The exact va lue of the el l ipt ici ty pa ramete r is defined as the ratio of the semiaxis of the contact ellipse in the t ransverse direction to the semiaxis in the direction of motion, i.e., k = a/b. The differences be tween the ell ipticity p a r a m e t e r 'k ' ca lcula ted f rom the approximate formula, Table 7.4, and the ellipticity parameter calculated from the exact formula, k = a/b, are very small [7]. The other parameters are as defined already. E X A M P L E Find the contact parameters for a steel ball in contact wi th a groove on the inside of a steel ring (as shown in Figure 7.7). The normal force is W = 50 [N], radius of the ball is Rax = Ray = R A = 15 \u2022 10 .3 [m], the radius of the groove is Rbx = 30 \u2022 10 .3 [m] and the radius of the ring is Rby= 60 x 10 .3 [m]. The Young's modulus for both ball and ring is E = 2.1 x 1011 [Pa] and the Poisson's ratio is ~ = 0.3. 9 Reduced Radius of Curva ture Since the radii of the ball and the grooved ring are Rax- 15 x 10 -3 [m], Ray= 15 x 10 -3 [m] and Rbx = -30 x 10 -3 [m] (concave surface), Rby-- -60 x 10 -3 [m] (concave surface), respectively, the reduced radii of curvature in the 'x' and 'y ' directions are: 1 1 1 1 1 - 33 " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002895_1.2826682-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002895_1.2826682-Figure2-1.png", + "caption": "Fig. 2 Kinematic and veiocity relationstiips between the pitch curve of a noncircular gear and the pitch circie of a shaper cutter", + "texts": [ + " How- R< rh cos (i,\u201e - tp) + rh\u00a3,\u201e sin {\u00a3,\u201e - ip) - rf sin (\u0302 ,\u201e ^r,, sin (C\u2122 - Ip) \u00b1 nU cos (f\u201e - ip) T rf cos (\u0302 ,\u201e iP) + rj: sin (9 + C\u201e - tp) - ip) \u00b1 rf cos {6 + \u00a3,,\u201e - Ip) (13) 94 / Vol. 120, MARCH 1998 Transactions of the ASME Downloaded From: http://mechanicaldesign.asmedigitalcollection.asme.org/ on 01/29/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use ever, in the derivation of noncircular gears, the instantaneous contact point between the cutting tool and the gear blank must be found first (Chang and Tsay, 1995). Realizing the generation mechanism and geometric relationship are necessary when the contact line method is adopted. As shown in Fig. 2, the pitch curve contact point is not always located on the Xf-axis; cutting interference may occur between the noncircular gear and the shaper cutter if the back-off motion of the cutter spindle is moving along the X/-axis during the return stroke. To avoid cutting interference, a special device must be employed (Katori et al., 1983). Therefore, the back-off motion of the cutter spin dle during the return stroke must always be given in the direc tion normal to the pitch curve of the noncircular gear at each contact point between the two pitch curves", + " However, for manu facture of noncircular gears, it may be theoretically considered that the pitch circle of the shaper cutter performs a pure rolling motion on the noncircular gear pitch curve. The pitch curve of the noncircular gear is seen as fixed, i.e., LJZ = 0. Derivation of the contact line can be further simplified using this concept. In this section, a complete mathematical model for noncircular gears including working surfaces, fillets, and bottom lands is developed by applying the inverse mechanism method. The inverse mechanism relationship is shown in Fig. 2, and the complete tooth profile of a noncircular gear can be obtained by considering the following equations (Litvin, 1989; Litvin and Tsay, 1985): R^\" = [MjJRW, {i=l ~ 6) and where X W F W - ) , \u00ab (18) (19) \u2014sin ((j) + y) cos ( -I- y) r^ cos 6 of the corresponding shaper cutter surfaces, and [Mzc] is the homogeneous coordinate transformation matrix transforming from coordinate system Sc to S2. X *'> and Y J'' are coordinates of the instantaneous center of rotation / represented in coordi nate system Sc', xi'^ and y['^ are the surface coordinates of the shaper cutter; and n'-J^^ and ny'c are the direction cosines of the shaper cutter unit normal n['^ represented along the X^ and Y^ axes", + " The absolute velocities of the shaper cutter and gear blank may be decomposed into two components: transfer velocity V\u201e. and relative velocity V,.. At the point of contact, the absolute velocities of the shaper cutter and gear blank are the same and can be related by V2 where and \u00a32 Vl +iu'~ 1)(1 - e f ) iVl +iu' ~ 1)(1 - e?), (29) (30) (31) coordinate system 5," + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003670_978-3-642-82195-0-Figure6.8-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003670_978-3-642-82195-0-Figure6.8-1.png", + "caption": "Fig. 6.8. Manipulator work space", + "texts": [ + " Let us consider a serial link manipulator with n degrees of freedom. The joint coordinate vector q = [q1 \u2022\u2022\u2022 qn]T belongs to the configura tion space Q = {q: qimin dmax ' the solution for the joint rates may be obtained in the usual manner, most frequently as the minimum norm solution, or by applying any of the procedures presented in Sections 6.2 and 6.3. However, when the distance between the critical point Xc on the arm and the obstacle lies between two given values (6.5.1) the presence of the obstacle should be taken into account, possibly by modifying the performance criteria so that motion is collission-free" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure3.36-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure3.36-1.png", + "caption": "Fig. 3.36. Cylindrical peg-in-hole task", + "texts": [], + "surrounding_texts": [ + "This paragraph discusses some problems which appear with practical ma nipulation tasks and which require the theory developed in the previous paragraphs. 3.6.1. Tasks with surface-type constraints Task of writing and drawing. Let us consider a manipulation task in which a manipulator has to write or draw on a given surface (Fig. 3.31). It a 5 d.o.f. manipulator has to write a letter or a sign on a given surface, we have to prescribe the independent parameters u 1 (t) and u 2 (t) in such a way as to obtain the desired letter. We also prescribe the angles 8(t) and ~(t) so as to obtain the desired orientation of the pencil (Fig. 3.32). In this way the complete reduced position vector Xr(t) (3.4.37) is prescribed and we can solve the nominal dynamics. This calculation of nominal dynamics also includes the time interval T1 in which the pencil is moving towards the surface. We prescribe this motion so as to avoid impact. When the perturbed motion is considered, the pencil comes to the sur face and the terminal state of T1 does not satisfy the surface con straint. The impact appears and we solve it by using the theory from Para. 3.5.1 (eq. 3.5.10 or 3.5.12). Thus obtaining the initial condi- 223 Grinding task. Fig. 3.33a,b shows the task of fine grinding. A moving surface results in relative velocity and friction force F f . In the case (a) a plane surface is considered. It rotates as shown in the figure. But, in practice this is not an ideal plane and the rota tion axis is not exactly perpendicular to the plane. Thus, the motion of the surface is not a simple rotation (Fig. 3.34). The reaction and, accordingly, the friction are not constant and produce vibrations of the working object (and the gripper). 224 In the case shown in Fig. 3.33b the cylindrical surface is considered. Rotation is not ideal since it is not an ideal cylinder (Fig. 3.35a) and the rotation axis is not in the exact center of the circle. For this reason the reaction is not constant and vibrations of the working object appear. All these effects can be included in the calcu lation. But, there are some effects which can not be taken into account. These are high frequency vibrations due to grains of grinding wheel. Thus, this calculation of grinding dynamics is approximative. If a po lishing task is considered then the discussion performed can also be applied but the problem of high frequency vibrations is not important. 3.6.2. Cylindrical and rectangular assembli tasks Cylindrical problem. Let us consider a manipulation task in which a cylindrical working object has to be inserted into a cylindrical hole When the nominal dynamics is calculated we prescribe the motion in such a way that no impact happens during the insertion. 225 Let us now discuss the perturbed motion. In the first time interval T1 the peg is moved towards the hole. It is a motion without any constra ints. At the begining of the insertion an impact happens (Fig. 3.37a,b). The impact is of the type discussed in Para. 3.5.3. The constraint is discussed in 3.4.12. In order to find the point of collision (point A in Figs. 3.30 and 3.37) we have to solve the equations (3.4.177) and (3.4.178) defining the cylindrical hole and the cylindrical peg. While the peg is moving towards the hole there is no real solution to this equation system. The impact happens when this system has one real so lution only. Thus, in each iteration the system has to be solved nume rically. In the next time interval (T 2 ) the motion of the peg is constrained. It is a surface-type constraint, the one discussed in Para. 3.4.12. Then the second impact happens (point A2 in Fig. 3.38a or A1 in Fig. 3. 38b) . After this second impact the motion of the manipulator is subject to two-d.o.f. joint constraint (Para. 3.4.7). However, if there are large perturbances, the motion after the second impact cannot be considered in this way but it is subject to two constraints of surface type (Fig. 226 3.39a).cylindrical joint constraint (two d.o.f) can'be used when the axis of the peg (*) is close enough to the hole axis (**) (see Fig. 3. 39b) \u2022 The problem of friction and jamming was considered in Para. 3.4.7 and 3.5. Rectangular problem. A rectangular assembly task is shown in Fig. 3.40. Such a manipulation task requires six d.o.f. manipulators since the total orientation of working object is needed. 3.6.3. Constraint permitting no relative motion We consider the final phase of an assembly task (Fig. 3.41a). In the phase of insertion we face the rectangular assembly problem. But, in this final phase the working object is fixed and no relative motion is possible. 227 Another example is shown in Fig. 3.41b. When the first two screws are screwed-in the object becomes fixed and no relative motion is possible. The theory covering these problems is explained in Para. 3.4.10. 3.6.4. Practical problems of bilateral manipulation Assembly tasks. Two most interesting tasks with bilateral manipulation are cylindrical and rectangular assembly tasks (Fig. 3.42). The whole discussion on cylindrical assembly task given in Para. 3.6.2 can be applied to bilateral manipulation. Case of no relative motion. The connection of the two grippers can be such that no relative motion is permitted. It happens in a task when one \"arm\" hands over the working object to the other. Then, there exists a time interval when both arms are in connection with the object (Fig. 3.43). Something very similar can happen if two manipulators are used together to move a very heavy load. 228 3.7. Examples Example 1 We consider an arthropoid six d.o.f. manipulator shown in Fig. 3.44. Its data are given in the table in Fig. 3.46. The manipulator has to draw a circle on a moving plane (Figs. 3.44, 3.45). Radius of the cir cle is R = 0.4m. At the initial time istant the manipulator is in the resting position and at the same time instant the plane begins to move up with the constant acceleration a = 0.6 m/s2 (Fig. 3.44). During drawing the pencil has to be perpendicular to the plane and produce the force S = 30N upon the plane. The friction coefficient is W=O.3. The drawing task has to be performed in T=2s with the triangular ve locity profile along the circle trajectory. If we follow the theory explained in Para. 3.4.4, the plane constraint is expressed in the form Ao Fig. 3.45. Circle to be drawn x y = f y 1 .2 1 2 z = fz = u 2 + 2 at + 0.4 229 In this example we first illustrate the calculation of\" nominal dynamics. 230 Hence, we prescribe the relative motion u 1 (t), u 2 (t) in such a way as to obtain the circle trajectory and the desired velocity profile. Thus u 1 R siny, u 2 R cosy where {'\"TIlT:, tT/2 The manipulator is driven by CEM-PARVEX D.C. motors: model M17 for the first three joints, and model F9M2 HA for gripper joints. Reduction ratio is N = 100 for all joints except for 52 where it is N = 150. The results of nominal dynamics calculation are presented in Figs. 3.47, 3.48, 3.49. Fig. 3.47 shows the relative motion of point A (i.e. the time histories of parameters u 1 and u 2). Fig. 3.48 shows the corre spondending time histories of the internal coordinates (q). Finally, Fig. 3.49 shows the nominal input control voltages. NOw, we present the results of simulation. 231 232 Let the manipulator start from a perturbed initial position. We first apply the nominal control voltage with no feedback. The sampling period is 1 Oms and the integration step is 1 ms. Figs. 3.50, 3.51, 3.52 pres ent the results of such simulation. Fig. 3.50 shows the perturbation in initial position and the deviations of internal coordinates from their nominal values. Such perturbed motion produces the error in drawing the circle (Fig. 3.51). Finally, Fig. 3.52 shows the nominal value of surface reaction (i.e. the force produced upon the surface) and its real value obtained by simulation. NOw, we make a new simulation applying the nominal control and the lo cal control (position feedback and velocity feedback). The results are presented in Figs. 3.53, 3.54. Fig. 3.53 shows the deviations form nominal motion. We see that stability is obtained. Tracking the circle trajectory is presented in Fig. 3.54. Let it be stressed that an effi cient control of force S requires a force feedback but it is not the topic of this book. 233 234 235 Example 2 We consider again the manipulator from Example 1 (data given in Fig. 3.46). This time the manipulator carries a 5 kg mass working object. The object is cylindrical and should be inserted into a cylindrical hole (Fig. 3.55). The hole is moving with a constant acceleration a = 2 m/s2, thus a nonstationary constraint is considered. It is assumed that there is no friction. The manipulation task consists in moving the ob ject into the hole for 0.3 m in the time interval T = 0.4 s, keeping all the time the initial orientation of the object. The manipulator starts from the resting position shown in Fig. 3.55. Let the relative coordinate u 1 (insertion coordinate) change with triangular velocity profile. Another relative coordinate (u2 ) is kept constant. We consider the motion without impact i.e. we consider the motion when the insertion has already begun. The theory explained in Para. 3.4.7. is used. 238" + ] + }, + { + "image_filename": "designv10_6_0003334_s11538-008-9296-3-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003334_s11538-008-9296-3-Figure1-1.png", + "caption": "Fig. 1 Schematic of an axoneme cross-section, depicting 9 microtubule doublets and the central pair of two microtubules. Also depicted are the dynein motors, the nexin links, and the radial spokes.", + "texts": [ + " Ciliary defects lead to a surprisingly wide range of clinical problems from polycystic kidney disease (PKD) to syndromes associated with obesity, hypertension, diabetes rhinitis, sinusitis, bronchiectasis, and retinitis pigmentosa (Afzelius, 1976, 2004, Eley et al., 2005; Pan et al., 2005; Davenport and Yoder, 2005; Fliegauf and Omran, 2006). For a recent review of cilia in human development and disease, see Vogel (2005). A cilium consists of a basal body and an axonemal core covered by a plasma membrane. The axoneme in a motile \u201c9 + 2\u201d cilium has two central microtubule singlets surrounded by nine microtubule doublets. A schematic of a cross-section depicting this \u201c9 + 2\u201d axonemal structure is shown in Fig. 1. The nine outer doublets are connected by radial spokes to a sheath surrounding the central pair. Other protein structures such as nexin serve as structural links supporting the axoneme. Thousands of dynein molecular motors are distributed along the length and circumference of the axoneme, each attached permanently at one end to an outer doublet, and able to attach and detach dynamically to the neighboring doublet. The beating of the cilium is achieved by ATP-driven dynein activation cycles that cause neighboring microtubule doublets to slide relative to each other (Witman, 1990; Murase, 1992)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002548_tsmcb.2003.810443-Figure12-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002548_tsmcb.2003.810443-Figure12-1.png", + "caption": "Fig. 12. Membership functions for AFSMC with five rules.", + "texts": [ + " Then, the control action for SMC becomes With the same adaptive laws in (24), and in AFSMC are adjusted to be 3.9945 and 0.0096, respectively. The performance comparison for state between SMC and AFSMC is shown in Fig. 10, and the control actions of SMC and AFSMC are shown in Fig. 11. From Figs. 10 and 11, AFSMC is seen to have better performance than SMC. To indicate the effect of the number of fuzzy rules on the performance of the AFSMC, an example is implemented. In this example, the input and output spaces of the fuzzy switching controllers are partitioned as in Fig. 12. Thus, five rules are constructed for each switching controller. With the adaptive laws (27) the parameters are adjusted to the following values: For simplicity, only the performance comparison of the state between the AFSMC with three and five rules is shown in Fig. 13. From Fig. 13, it can be seen that the performance of AFSMC with more rules is not necessarily better. Moreover, the forms of the membership values are more complicated for the AFSMC with more than three rules. Thus, to showing the guaranty of the sliding mode of the AFSMC with more than three rules is not as easy as in Section IV" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000262_j.mechmachtheory.2021.104299-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000262_j.mechmachtheory.2021.104299-Figure1-1.png", + "caption": "Fig. 1. Schematic diagram of a wide-faced double-helical gear transmission device.", + "texts": [ + " The rest of this paper are organized as follows: Section 2 gives the establishment process of a multi-point contact model for wide-faced double-helical gears considering system flexibility. The mesh misalignment caused by system flexibility and compensated tooth surface modification can be determined using this model. Section 3 proposes a multiobjective optimization mathematical model of tooth surface modification aiming to reduce the system vibration and improve the load distribution. Section 4 shows some numerical results and discussion. Section 5 summarizes some conclusions. Fig. 1 shows a wide-faced double-helical gear system which consists of two stepped shafts, a wide-faced double-helical gear pair, four bearings and a housing with complex structure. The power is input from the left side of shaft 1 where the driving gear locates, and output from the right side of shaft 2 where the driven gear locates. The basic parameters of the gear pair are given in Table 1 , and the structural parameters of shaft 1 and shaft 2 are given in Table 2 and Table 3 , respectively. The bearing stiffness parameters are given in Table 4 ", + " In our previous published work [14] , a universal three-dimensional quasi-static multi-point contact model for widefaced spur/helical gear pairs in consideration of shaft deflections has been developed, and the calculation method of mesh misalignment caused by shaft deflections has been proposed. The model has been verified via a comparison with the threedimensional contact finite element method. Hence, through extending the model, it can be applied in the calculation of mesh misalignment caused by system flexibility for wide-faced double-helical gear pairs. For the wide-faced double-helical gear system which is shown in Fig. 1 , the two stepped shafts can be discretized into a series of shaft elements with different outer and inner diameters, as shown in Fig. 2 , where B g represents the width of the left and right gear pair for the double-helical gear pair, B b represents the width of the four bearings which locate at different pedestals. The Timoshenko beam element with 2 nodes and 12 degrees of freedom is employed to establish the model of each shaft element. Both the left and right gear pair are modeled using a series of nonlinear contact elements with different stiffness values and various clearance values" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000033_tec.2020.2965180-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000033_tec.2020.2965180-Figure3-1.png", + "caption": "Fig. 3. Magnetic flux lines (a) without excitation and (b) with excitation.", + "texts": [ + " To recap, both the inner and outer PMs enhance the air-gap flux density, the outer PMs increase the flux density of the 0885-8969 (c) 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. stator pole, and the outer and inner PMs regulate the saturation level in the stator yoke and poles, respectively. The flux lines of the proposed PM-SRM are carried under excitation and nonexcitation conditions using finite element software, as shown in Fig. 3, which demonstrates the predicted flux flow patterns. To analyze the working principle of the PM-SRM, its MCM is derived and depicted in Fig. 4 assuming that phase A is energized. In the simplified MCM, Rsp, Rsy , Rry, Rg , and Rpm are the reluctances of the stator pole, stator yoke, rotor yoke, air-gap, and PM, respectively; Fc and Fpm are the magneto motive force (MMF) provided by the excited coil and PM; \u03d5pm1, \u03d5pm2, \u03d5sp, \u03d5sy , and \u03d5g are the magnetic flux of the outer and inner PMs, stator pole, stator yoke, and air-gap, respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003961_978-1-4419-7267-5-Figure16.1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003961_978-1-4419-7267-5-Figure16.1-1.png", + "caption": "Fig. 16.1 Decomposition of an under-actuated manipulator into component active and passive arms", + "texts": [ + " Observe that Na+Np = N, the total degrees of freedom in the system. We use the Ia and Ip sets of hinge indices to decompose the manipulator into a pair of manipulator subsystems: the active arm Aa, and the passive arm Ap. Aa is the Na degree of freedom manipulator resulting from freezing all the passive hinges (i.e., all hinges whose index is in Ip), while Ap is the Np degree of freedom manipulator resulting from freezing all the active hinges (i.e., all hinges whose index is in the set Ia). This decomposition is illustrated in Fig. 16.1. 316 16 Under-Actuated Systems Let \u03b8\u0307a \u2208 RNa , Ta \u2208 RNa and H\u2217 a \u2208 R6n\u00d7Na denote the vector of generalized velocities, the vector of generalized forces and the joint map matrix for arm Aa. Similarly, let \u03b8\u0307p \u2208RNp , Tp \u2208RNp and H\u2217 p \u2208 R6n\u00d7Np denote the corresponding quantities for arm Ap. The two vectors \u03b8\u0307a \u2208RNa and \u03b8\u0307p \u2208RNp , also represent a decomposition of the vector of generalized velocities \u03b8\u0307 in a manner consistent with the Ia and Ip sets, respectively. Similarly Ta and Tp are decompositions of T, and H\u2217 a and H\u2217 p are decompositions of H\u2217" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002692_02783649922066394-Figure9-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002692_02783649922066394-Figure9-1.png", + "caption": "Fig. 9. Paired configurations of Figure 2, with congruent platform and base triangles. The platform triangle is shaded. These two configurations are identical by superposition, but are distinguished by values \u03b8i , i = 1, 2, 3 once the platform and base are identified.", + "texts": [ + " If we fix a coordinate system in the base, the position and orientation of the platform triangle in this system uniquely defines the leg lengths and their directions. Now, suppose a new coordinate system is defined so that in this new system, the position of the platform triangle is same as that of the base triangle in the original system. Swapping platform and base triangles ordinarily gives a second, different, assembly, the two assemblies being identified by superposition. All regular assemblies are paired; this pairing is depicted in Figure 9. Since every regular assembly is one of a pair, every regular configuration in the neighborhood of a special configuration is paired. The implied conclusion that special configurations must themselves be paired holds with two exceptions, these being when \u03b1 = 0 and \u03b1 = \u03c0 , with \u03b1 as defined in Figure 2. Excepting these, all other special configurations are paired, the pairs again being identified by superposition. The corresponding components of the branch locus partitions leg space into regions differing by four assemblies" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003295_rob.4620060605-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003295_rob.4620060605-Figure3-1.png", + "caption": "Figure 3. Four-link robot in horizontal plane.", + "texts": [ + " This control scheme will now be applied to a direct-drive four-link Colbaugh, Seraji, and Glass: Obstacle Avoidance 73 1 planar robot in a series of computer simulations. The results presented here are samples selected from a comprehensive computer simulation study that is carried out to test the performance of the proposed controller. These examples are chosen for presentation because they illustrate the flexibility and versatility of the configuration control approach to obstacle avoidance. Consider the four-link robot in a horizontal plane shown in Figure 3. The robot parameters are link lengths I t = l2 = I3 = 1, = 1.0 meter, link masses m l = m2 = rn3 = m, = 10.0 kg, and joint viscous friction coefficients c, = c2 = c3 = c4 = 40.0 Nt . m/rad . s-'; the link inertias are modeled by thin uniform rods. The robot dynamic equation that relates joint torques T E R4 and joint angles 8 E R' is given in Ref. 20. T = z-i(e)e+ v(e, e) + ce (25) where the mass matrix H = [h,] E R4X4, Coriolis and centrifugal torque vector V = [ p i ] E R', and viscous friction coefficient matrix C = diag(ci) E R-IX4 have the following representations (here c2 = cos d2", + "67 + 10c4 h34 = h43 = 3.33 + 5 ~ 4 h44 = 3 -33 v4 = 5@34 + 5&34 + 5f&34 + 5&s4 + 5&34 + 5&4 c1= c2 = c3 = c4 = 40.0 + 1081&4 + lobl&zS34 + 10616& + lo&&, Note that the gravity vector is orthogonal to the plane of motion of the robot, so that no gravity torques appear in (25). It must be emphasized that the dynamic model (25)-(26) is used only to simulate the robot behavior and is not used in the control law formulation. The forward kinematics X = f ( O ) and end-effector Jacobian matrix J , for the robot shown in Figure 3 are Colbaugh, Seraji, and Glass: Obstacle Avoidance 733 The configuration control scheme that is applied to the four-link robot is given in (9)-(14), and is implemented using the control structure shown in Figure 1 . The terms E, and Ec are defined in (21), (22), where the active critical point locations and all necessary obstacle avoidance parameters are given by the recursive algorithm (17)-(20). The matrix J, is computed row by row using (24). Note that for the four-link robot with two end-effector coordinates to be controlled, we have r = 2 so that J, can possess at most two rows and therefore at most two critical points can be active simultaneously" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003764_s00170-010-2659-6-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003764_s00170-010-2659-6-Figure2-1.png", + "caption": "Fig. 2 Schematic of the laser powder deposition process", + "texts": [ + " Figure 1 shows the image taken during the deposition process. A high-speed camera is assisted by a green laser to capture the image of the molten pool. The glare of the molten pool is eliminated with the aid of proper optical filters. More information about the imaging technique can be found in Ref. [28]. As can be seen in Fig. 1, the laser beam melts partially the substrate and the powder particles (particles cannot be seen in this image) to form the deposition bead. The schematic of this process is shown in Fig. 2. The molten pool is divided into two sections: the leading half in which the substrate is melted and the trailing half in which the particles are melted and the clad is formed. This idea is used in defining the finite element model in Fig. 3. As shown in this figure, four regions can be distinguished: the white elements representing the substrate, the light gray elements representing the already activated elements of the clad, the dark gray elements representing the activated elements in the current time step that contain the molten feeding material, and the dotted region representing the leading half with the laser heat flux boundary condition" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003286_bf01175968-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003286_bf01175968-Figure2-1.png", + "caption": "Fig. 2. a Th6 beneral case of four contacts in plane space, b The simplest possible example of form closure by poinst contacts", + "texts": [ + " Contacts 2 and 3 are in a vee groove; Mong the z-axis; contacts 1 and 7 are parallel to the y-axis; contacts I f the normals are so chosen that some of them (six or less) are linearly dependent, the number of contacts needed will be more than tha t given by the foregoing analysis (see sections 5, 6). If the body shape is however such tha t linear dependence between six or less number of normals is unavoidable, the degree of freedom cannot be reduced to nil by any number of contacts. The cylinder and the sphere represent examples of body shape not permitt ing ] to be reduced below 1 and 3 respectively-. Fig. 2 a shows the general case of four contacts needed in plane space. The earlier discussion about screwing moments is here replaced by turning moments about points of intersection of contact normals. The applied force W replaces the wrench S. :Fig. 2b shows the simplest possible example of form closure by point contacts. In order to remove the indeterminacy of the reactions, we take the model nearer to physical reality: we assume supports deformable along the contact normals (or infinitesimal clearances), while continuing to regard the body as rigid. Let these deformations (and the corresponding infinitesimal rigid body movement components along the normals) be 61n, 62n, ..., 67n. The relationship between these components can be determined by setting to zero the work done by the equilibrating forces ~i = ~Ai : 7 Pi6i", + " We then have from the previous section: ~ = b - - / ~ + 1; c, = / ~ - - / ~ + 1; . . . ; e, = / ~ _ ~ - - / + 1. Adding, we obtain the number of contacts needed: c = b - - / + ~ . C7) The conditions under which the reactions become determinate have been pointed out in the previous section. The following are examples of reduction of freedom in stages. (i) The flat element of Fig. 4 d or 4 e may bc further restrained by a contact scheme whose projection on a plane parallel to the flat is as in :Fig. 2a to obtain / ~- 0; total number of contacts ----- 8; if the additional four contacts are eoplanar (]~'ig. 2a) and therefore linearly dependent; the reactions become determinate and one contact each from the two sets of contacts is unloaded; (ii) The cylindric element of Fig. 5 may be first restrained by five contacts on the cylindrical surface to obtain ] ~ 2 and then two contacts, one each on the end planes, may be applied to obtain / -~ 1 and a revolute pair; total number of contacts ~ 7 as against 6 in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000299_s11071-021-06364-9-Figure5-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000299_s11071-021-06364-9-Figure5-1.png", + "caption": "Fig. 5 Schematic diagram of the cutting process of the shearer", + "texts": [ + " (6), the PMSM current and mechanical motion equation can be expressed as: diq dt \u00bc R Lq iq \u00fe Kpq \u00fe R Kiq Kpx \u00fe R Kix x m xm Baxm iq Lq Jmh 00 m \u00bc 3 2 pniqwf Tp 8 > < > : \u00f010\u00de 2.3 Load characteristic model of cutting drum The torque of cutting drum is complicated, and different load torque will engender great influence on the system. Therefore, the cutting load characteristics must be fully considered when establishing the electromechanical coupling dynamics model. The main cause of the gear system vibration is the load torque in the cutting process, which is related to the haulage speed of the shearer, the cutting impedance of the coal seam and other factors. In Fig. 5, n is the cutting drum speed, Vq is the shearer traction speed, h is the instantaneous cutting thickness, bp is the width of the pick working part, lp is the pick intercept, and u is the cutting groove crack angle. At present, the modeling method proposed by the Former Soviet scholars [32, 33] has been widely used in the research of cutting load. On the basis of the resistance of the reference pick in coal cutting, the resistance is modified by considering the actual pick geometry and cutting conditions" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003619_s0263574708004268-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003619_s0263574708004268-Figure4-1.png", + "caption": "Fig. 4. Models for the (a) ankle and (b) hip strategies.", + "texts": [ + " (20) We implemented the ankle and hip strategies to control postural balance of a small humanoid robot HOAP-2,22 subjected to an impact force while standing upright. As already explained, the strategies differ in how they control joint and CoM motions: the ankle strategy displaces the CoM (within the BoS) by ankle joint movement, while the hip strategy minimizes CoM displacement from the vertical by movements in both ankle and hip joints. Thus, we will need two different models to realize the strategies. It will be shown, thereby, that it is possible to rely on just simple planar dynamical models. Figure 4 shows the models for the ankle and hip strategies. Both models include a spring-damper to ensure compliance with the impact force, either by ankle motion (Fig. 4(a)), or by hip/ankle motion (Fig. 4(b)). The impact force is evaluated via the acceleration sensor, embedded in the chest of HOAP-2. The data is then used to decide which one of the two strategies is to be invoked. For this purpose, we determined experimentally a threshold for the impact acceleration. Impacts, with acceleration values below/above the threshold, invoke the ankle/hip strategy, respectively. It should be apparent that the ankle strategy is modeled after an inverted pendulum. The equation of motion is: I \u03b8\u03081 \u2212 mglg sin \u03b81 = \u2212C\u03b8\u03071 \u2212 K\u03b81, (21) where I \u2261 I \u2032 + ml2 g , I \u2032 is the moment of inertia, and the other parameters are obvious form the model (see Fig. 4 (a)). This equation is simplified by ignoring the gravity term, which is justified by the high gear ratios and the internal highgain feedback controller of HOAP-2. Hence, we obtain the reference ankle joint acceleration from the above equation as: \u03b8\u0308 ref 1 = \u2212(C\u03b8\u03071 + K\u03b81)/I. (22) Further on, the moment balance equation during impact can be written as I \u03b8\u03081 = malg, (23) where a is the measured acceleration. Assuming a small impact time interval \u0394t , and using the relation \u03b8\u03081 = \u0394\u03b8\u03071/\u0394t , we obtain the ankle joint angular speed step change as \u0394\u03b8\u03071 = malg\u0394t/I", + " Though the step change in angular speed seems to be just a bit larger than in the previous experiment, from the ZMP graph it is apparent that the ZMP stays for relatively longer time, first at the \u201ctoe\u201d boundary, than at the \u201cheel\u201d boundary. This indicates posture instability and we can conclude that the robot was not able to maintain balance under the ankle strategy. We can also conclude that the impact acceleration threshold for invoking the hip strategy should be less than the critical impact acceleration used in this experiment. The kinematic and dynamic parameters for the hip strategy model (cf. Fig. 4(b)) are shown in Table I. Here also, Table I. Link parameters for the hip strategy model. Parameter m I l lg Unit [kg] [kgm2] [mm] [mm] Link 1 1.450 0.0057789 200 82.05 Link 2 4.961 0.03214829 10.251 http://journals.cambridge.org Downloaded: 18 Jul 2014 IP address: 134.153.184.170 time-variable spring-damper coefficients had to be used. The initial and final values for the 5th order polynomials for the coefficients were determined experimentally as Kinit = 0.1 Nm/rad, Kf inal = 0.7 Nm/rad, and Cinit = 0" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003317_s11044-008-9126-2-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003317_s11044-008-9126-2-Figure1-1.png", + "caption": "Fig. 1 3D collision", + "texts": [ + " , p; t1 \u2264 t \u2264 t2) (6) or in view of (5a), Fr + F \u2217 r + R \u00b7 vR r = 0 (r = 1, . . . , p). (7) During the collision, P is assumed to maintain contact with P \u2032, i.e., to coincide with P \u2032; and a plane S\u0303 exists which passes through P (\u2261 P \u2032) and is tangent to B and B \u2032 at P if both are locally smooth, or to B \u2032 if only B \u2032 is locally smooth. Name B and B \u2032 such that n, a unit vector perpendicular to S\u0303, makes vA \u00b7 n a nonpositive quantity. Aline t, a unit vector lying in S\u0303, with the projection of vA on S\u0303, making vA \u00b7 t a non-negative quantity (see Fig. 1). Finally, let s be a unit vector defined as s =\u0302n \u00d7 t. Then vR = vR \u00b7 nn + vR \u00b7 tt + vR \u00b7 ss. (8) For planar collisions vR = vR \u00b7 nn + vR \u00b7 tt, vA = vA \u00b7 nn + vA \u00b7 tt vS = vS \u00b7 nn + vS \u00b7 tt, (vA \u00b7 n \u2264 0, vA \u00b7 t \u2265 0), \u23ab \u23aa\u23aa\u23ac \u23aa\u23aa\u23ad (9) i.e., both vA and vS lie in the n\u2013t plane. Note that t can be defined t =\u0302n \u00d7 (vA \u00d7 n)/|n \u00d7 (vA \u00d7 n)|. (10) Equation (9a) makes it possible to replace (7) with Fr + F \u2217 r + R \u00b7 nvR r \u00b7 n + R \u00b7 tvR r \u00b7 t = 0 (r = 1, . . . , p; t1 \u2264 t \u2264 t2). (11) If it is assumed that t2 \u2212 t1 is \u201csmall\u201d compared to time constants associated with the motion of S, and that consequently, q1, " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003595_s00216-008-2049-1-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003595_s00216-008-2049-1-Figure3-1.png", + "caption": "Fig. 3 Obtained RMSEs in catechol concentration prediction for different transfer function combinations and neuron numbers in the hidden layer with input neuron number of 12 and Levenberg\u2013 Marquardt backpropagation (trainlm) as optimization algorithm. Numbers 1\u20135 represent the transfer function combinations Tansig\u2013 Purelin, Logsig\u2013Satlins, Satlins\u2013Purelin, Logsig\u2013Purelin, and Tansig\u2013 Satlins, respectively", + "texts": [ + " Variability will occur due to random initial values in the networks with exactly the same program [26] ; hence, each ANN program was run more than seven times to get the average RMSEs for the external test set to result in a true measure of performance. At first, the hidden neuron numbers and combinations of tan-sigmoidal (Tansig), log-sigmoidal (Logsig), pure-lineal (Purelin), and sat-lineal (Satlins) transfer functions were evaluated. The calculated RMSEs were plotted against different hidden neuron numbers and combinations of transfer functions in hidden and output layers synchronously. The lowest RMSE value was obtained with 15 hidden neurons and Satlins\u2013Purelin as transfer function as shown in Fig. 3. The effects of different optimization algorithms on the model performance were then evaluated as shown in Fig. 4. The ANN models with trainbfg, trainbr, traingd, and traincgb as optimization algorithms, respectively, could not meet the performance goal when the minimum gradient was reached in the training process. The ANN models by traingdm and traingdx got lower RMSE values sometimes, but were not steady with the increasing of training time. So trainlm was selected as the optimal algorithm to obtain the lowest RMSE value, steady result, and short training time" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003562_09544062jmes700-Figure6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003562_09544062jmes700-Figure6-1.png", + "caption": "Fig. 6 (a) Shear force test set-up, and (b) example QTC shear force test with 9.2 N normal and 3.2 N shear loads applied to the sensor", + "texts": [ + " Shear forces are often present in dynamic gripping actions, so it is important to ascertain how these sensors behave under this loading condition. The shear loads chosen for this test were based on peak shear forces of around 500 N, which occur between the hands and the grip during golf shots [21, 22], and then scaled based on the area over which they are applied. A three-legged circular load carrier (cylindrical legs, 6 mm diameter, 120\u25e6 spacing with 2 mm-thick rubber layer on each leg) was used to apply normal loads of 9.2 and 15.75 N to each sensor, as shown in Fig. 6(a). Data were collected from each sensor for 5 s and, after the data collection had begun, a shear load of 1.6 or 3.2 N was applied to each sensor via the load carrier (example sensor output for a QTC shear test is shown in Fig. 6(b). To determine the change in output due to shear over each 5 s test, the overall change in sensor output was first calculated by subtracting the mean sensor output from the last 0.5 s of data from the mean for the first 0.5 s. The change in output due to drift was then estimated and this was subtracted from the overall change in sensor output to give the contribution due to the application of a shear force. The shear sensitivity was then determined according to equation (6) by dividing the contribution to the sensor output due to shear by the applied shear force" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002831_3477.558842-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002831_3477.558842-Figure4-1.png", + "caption": "Fig. 4. Configuration of the wrist singularity for PUMA manipulator.", + "texts": [ + " Therefore, when the interior singularity occurs, J11 viewed in coordinate 3 becomes 3 J11 = 3 R0 0 J11 = 0 0 0 : (24) From (24), the linear singular direction of the forearm interior singularity is clearly in parallel with y3 axis. If both boundary and interior singularities are encountered, then 3 = 92:6864 and 2 = 90 . In this case, J11 viewed in coordinate 2 becomes 2 J11 = 2 R0 0 J22 = 0 0 0 0:149 0:865 0:434 0 0 0 (25) Therefore, the linear singular directions of the forearm boundary and interior singularities are in parallel with x2 and z2 axes. Wrist Singularity: The wrist singularity can be identified by checking the determinant of the matrix 0J22 in (17) as det 0 J22 = w S5 = 0: (26) Referring to Fig. 4, it can be seen that the wrist singularity happens when the z3 and z5 axes are collinear. In this configuration, the angular velocity about the x5 axis (i.e., 5 x) is unachievable. Thus, 5 J22 will have the structure 5 J22 = 0 0 0 0 1 0 1 0 1 : (27) Consequently, the singular direction of the wrist singularity is about the x5 direction. After analyzing all of the unescapable singularities of nonredundant manipulators, considerations and resolution methods for the inverse kinematics singularity problem will be presented in the next section" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002839_978-3-662-03845-1-Figure9.4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002839_978-3-662-03845-1-Figure9.4-1.png", + "caption": "Fig. 9.4. The three fundamental deformations of a nematic. (a) Splay, (b) twist, (c) bend", + "texts": [ + " Consequently, a weak external perturbation is capable of modifying the orientation, which is generally no longer constant throughout the sample, and must be modelled by a variable director n(r). The local direction may be imposed by anchoring the molecules onto solid surfaces, by the effects of flow, or by an electromagnetic field. In order to understand these effects, we must inquire into the energy associated with slow and continuous deformations. The latter are described in terms of three fundamental deformations, illustrated in Fig. 9.4: splay, twist and bend. ,oDx \\Jol. a x Consider first a small deviation on = n - no of the director n from the reference direction no, resulting from a displacement or = (ox, Oy, oz) . We have on\u00b7 no = O. Choosing the z direction to be along no, this means that to first order, on ;:::j (onx, ony, 0) , 294 9. Liquid Crystals since for small deformations, onz ~ (on; + on~)/2. Then by Taylor expansion, anx anx anx onx = ax Ox + ay Oy + az Oz , any any any ony = ax Ox + ay Oy + az Oz . These can be rewritten in matrix form: ( onx) = ~ (anx/ax + any/ay ony 2 0 1 ( 0 +\"2 any/ax - anx/ay + ~ (anx/ax - any/ay 2 any/ax + anx/ay s: (anx/az) + U z any/az . (9.1) (9.2) The first, second and fourth terms correspond to the three fundamental defor mations mentioned earlier. \u2022 The first term describes splay. It is isotropic in the (x, y) plane and has the symmetry of a vector in the z direction (see the arrow on top of the dome in Fig. 9.4a). \u2022 The second term has helical symmetry. This is clear if we consider the case nx = 0 and ny = const. x x (see Fig. 9.4b). \u2022 The fourth term has the symmetry of a vector lying in the (x, y) plane. In Fig. 9.4c, nx = const. x z and the vector lies in the x direction (see the arrow next to the arc in Fig. 9.4c). The third term describes a more complex deformation called saddle-splay. In deed, it is given by a symmetric real matrix with zero trace. It can therefore be diagonalised in some orthonormal frame with axes xo, Yo, relative to which it takes the form: The energy required to effect any deformation must be a quadratic function of the displacements. This is just the equivalent of Hooke's law as it is usually stated for solids. Since the energy must be invariant under any rotation of the reference frame, it can only be a function of scalar quantities, in this case the square of each of the terms taken separately" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002903_s0168-874x(01)00100-7-Figure9-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002903_s0168-874x(01)00100-7-Figure9-1.png", + "caption": "Fig. 9. De nition for orientation and dimension of a contact ellipse.", + "texts": [ + "4) where is the Poisson\u2019s ratio and E denotes the Young\u2019s modulus. A and B are determined by A= 1 4[' (1) \u2212 '(2) \u2212 (g21 \u2212 2g1g2 cos 2! + g22) 1=2]; (A.5) B= 1 4[' (1) \u2212 '(2) + (g21 \u2212 2g1g2 cos 2! + g22) 1=2]; (A.6) where '(1) = '(1)I + '(1)II ; (A.7) '(2) = '(2)I + '(2)II ; (A.8) g1 = '(1)I \u2212 '(1)II ; (A.9) and g2 = '(2)I \u2212 '(2)II : (A.10) Here, '(1)I and '(1)II represent the rst and second principal curvatures of the pinion surface 1, while '(2)I and '(2)II represent the rst and second principal curvatures of the gear surface 2, respectively. As Fig. 9 shows, angle ! is measured counterclockwise from i(2)I to i(1)I and can be evaluated by ! = tan\u22121 ( i(1)I \u00b7 i(2)II i(1)I \u00b7 i(2)I ) ; (A.11) where i(1)I and i(1)II denote the unit vectors of the rst and second principal directions for the pinion, while i(2)I and i(2)II represent the unit vectors of the rst and second principal directions for the gear, respectively. Furthermore, the principal directions and the principal curvatures of the pinion and the gear tooth surfaces, and the orientation of the contact ellipses can be determined according to the diIerential geometry and Litvin\u2019s approach [16,2]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003003_tmag.2004.843349-Figure16-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003003_tmag.2004.843349-Figure16-1.png", + "caption": "Fig. 16 (a) Steady-state temperature distribution in SRM with fins (a) at full load and (b) at twice the full load.", + "texts": [], + "surrounding_texts": [ + "The SRM model under consideration and the meshes formed during FEA are shown in Fig. 18. The length of the stator stack is 90 mm. The end shield has thickness of 10 mm. The shaft has a diameter of 25 mm. The main values set during simulation are: The Young\u2019s modulus N/m ; specific mass of winding kg/m ; total mass density kg/m ; Poisson\u2019s ratio . In the SRM, it is found that resonance occurs if the phase frequency or add harmonics coincides with the stator natural frequency, resulting in a peaking of the stator frequency. The phase frequency is given by [25] (C1) where is the speed in radians/s and is the number of rotor poles. Vibration is maximum if any of the frequencies (C2) are coincident with the natural frequency of the machine given by [25] (C3) where is the stator iron thickness in meters, is the mass density of the material in kilograms/cubic meter, and is the mean radius of the stator shell in meters given by where is the outer diameter of the stator. The governing Laplace equation that is solved iteratively to find the modal frequencies is (C4) where is the modal vector, and is the frequency of vibration. The solution is the th mode shape and is the corresponding natural frequency. The 3-D modal analysis reveals certain modes which are producing vibration (and the associated acoustic noise) in SRM due to rotor and housing structures. The mode frequency of 231.154 Hz (3467 rpm), shown in Fig. 19(a), is observed to produce twist of rotor. Modal frequency of 160 Hz [Fig. 19(b)] causes shaft bend with a severity at the shaft-rotor edge. Frequency of 364.5 Hz causes rotor structure and rear shaft vibration [Fig. 19(c)] and at 231.15 Hz [Fig. 19(d)], the rotor deforms at an angle. At modal frequencies of 3089 Hz [Fig. 20(a)], 1910 Hz [Fig. 20(b)], and 161 Hz [Fig. 20(c)], the housing also gets involved in contributing vibration. The rotor rocks up and down causing it to strike against the stator, transmitting the vibration till housing and foundation. The shaft bends. The drive may not be able to handle any load at these speeds. At 900 Hz [Fig. 20(d)], the housing with foundation undergoes vibration." + ] + }, + { + "image_filename": "designv10_6_0002681_j.mechmachtheory.2004.04.003-Figure6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002681_j.mechmachtheory.2004.04.003-Figure6-1.png", + "caption": "Fig. 6 shows the free body diagram of the input and output discs, and that one of the roller. The support bearing is modelled as a revolute movable joint, that prevents the translatory motion of the roller along the direction of its axis of rotation. The force balance of the roller gives:", + "texts": [ + " The CVT geometrical characteristics are reported in Table 1, where the radii of curvature r22 have been chosen in order to obtain the same maximum shear stress in both CVTs (see also Section 4.1). As before predicted the spin ratio of the full-toroidal CVT is about five times higher than that of the half-toroidal one. The presence of spin motion affects the full-toroidal traction drive more than the half-toroidal variator. But, on the other hand, the latter is affected by the support bearing losses, since the normal forces FN acting on the roller, at the points of contact, do not balance out (see Fig. 6). Therefore, a resulting axial force FR has to be supported by an axial bearing (one for each roller), that, because of its internal losses, causes a reduction of the CVT mechanical efficiency. On the other hand, the full-toroidal variator is not affected by this problem, since h \u00bc p=2, and the normal forces balance out. But, on the other hand, the full-toroidal CVT is much more affected by spin losses, thus it is necessary to carry out a comparison in order to single out which typology of CVT offers the higher mechanical efficiency" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003808_j.jsv.2007.05.053-Figure5-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003808_j.jsv.2007.05.053-Figure5-1.png", + "caption": "Fig. 5. Acceleration relationships of planetary gear set lumped inertias.", + "texts": [ + " 4 and considering the motion about gear centerlines we have J fs \u20acyfs \u00bc T fs 3rfsF sp; 3Jsp \u20acysp \u00bc 3rspF lp 3rspF sp, (2a,b) 3J lp \u20acylp \u00bc 3rlp\u00f0F lp F rs F r\u00de; Jrs \u20acyrs \u00bc T rs 3rrsF rs, (2c,d) Jcr \u20acycr \u00bc Tcr \u00fe 3\u00f0F rs Fr\u00de\u00f0rrs \u00fe rlp\u00de \u00fe 3F sp\u00f0rfs \u00fe rsp\u00de 3F lp\u00f0rsp \u00fe rlp\u00de, Jr \u20acyr \u00bc Tr \u00fe 3rrFr, \u00f02e; f\u00de where J and r are each gears inertia and radius and F is the mesh force, given by the tooth bending stiffness and relative displacement. Nomenclature for mesh forces and external torques applied to each gear is indicated in Fig. 4. Acceleration relationships are derived for the gear set via Fig. 5: \u00f0aB\u00det \u00bc \u00f0aC\u00det \u00fe \u00f0aB=C\u00det; \u20acyfsrfs \u00bc \u20acycr\u00f0rfs \u00fe rsp\u00de \u20acysprsp, (3a,b) \u00f0aE\u00det \u00bc \u00f0aF \u00det \u00fe \u00f0aE=F \u00det; \u20acyrsrrs \u00bc \u20acycr\u00f0rlp \u00fe rrs\u00de \u20acylprlp, (4a,b) \u00f0aG\u00det \u00bc \u00f0aF \u00det \u00fe \u00f0aG=F \u00det; \u20acyrrr \u00bc \u20acycr\u00f0rlp \u00fe rrs\u00de \u00fe \u20acylprlp, (5a,b) \u00f0aF \u00det sin e \u00bc \u00f0aD=F \u00det \u00f0aD=C\u00det sin c ; \u20acycr\u00f0rlp \u00fe rrs\u00de sin e \u00bc \u20acylprlp \u00f0 \u20acysprsp\u00de sin c (6a,b) which reduces to \u20acycr\u00f0rlp \u00fe rsp\u00de \u00bc \u20acylprlp \u00fe \u20acysprsp, (6c) where (a)t denotes the tangential acceleration of a point on a body with absolute point of reference taken as point A in Fig. 5 or a relative point of reference taken such as point G relative to point F. The acceleration relationships can be used to determine mesh displacement, hence mesh forces, via Fi \u00bc kiDxi (and by ignoring gear mesh damping), where k designates the mesh stiffness: F sp \u00bc ksp yfsrfs \u00fe ysprsp ycr\u00f0rfs \u00fe rsp\u00de ; F lp \u00bc klp ylprlp ysprsp \u00fe ycr\u00f0rlp \u00fe rsp\u00de , (7a,b) F rs \u00bc krs ylprlp \u00fe yrsrrs ycr\u00f0rlp \u00fe rrs\u00de ; Fr \u00bc kr ylprlp \u00fe ycr\u00f0rlp \u00fe rrs\u00de yrrr . (7c,d) A R TIC LE IN PR ES S The equations of motion are now formulated with the internal forces replaced by k and Dx and may be assembled to the undamped system I\u20ach\u00fe Kh\u00f0t\u00de \u00bc T\u00f0t\u00de, yielding the matrix elements: I \u00bc diag\u00bdJfs 3Jsp 3J lp Jrs Jcr Jr , (8a) K \u00bc 3r2fsksp 3rfsrspksp 0 0 3rfs\u00f0rfs \u00fe rsp\u00deksp 0 3rfsrspksp 3r2sp\u00f0ksp \u00fe klp\u00de 3rsprlpklp 0 3rsp \u00f0rfs \u00fe rsp\u00deksp \u00fe \u00f0rsp \u00fe rlp\u00deklp 0 0 3rsprlpklp 3\u00f0r2lpklp \u00fe r2lpkrs \u00fe r2lpkr\u00de 3rlprrskrs 3rlp \u00f0rsp \u00fe rlp\u00deklp \u00f0rlp \u00fe rrs\u00dekrs \u00fe \u00f0rlp \u00fe rrs\u00dekr 3rlprrkr 0 0 3rlprrskrs 3r2rskrs 3rrs\u00f0rlp \u00fe rrs\u00dekrs 0 3rfs\u00f0rfs \u00fe rsp\u00deksp 3rsp \u00f0rfs \u00fe rsp\u00deksp \u00fe\u00f0rsp \u00fe rlp\u00deklp \" # 3rlp \u00f0rsp \u00fe rlp\u00deklp \u00f0rlp \u00fe rrs\u00dekrs \u00fe\u00f0rlp \u00fe rrs\u00dekr \" # 3rrs\u00f0rlp \u00fe rrs\u00dekrs 3 \u00f0rfs \u00fe rsp\u00de 2ksp \u00fe \u00f0rsp \u00fe rlp\u00de 2klp \u00fe\u00f0rlp \u00fe rrs\u00de 2krs \u00fe \u00f0rlp \u00fe rrs\u00de 2kr \" # 3rr\u00f0rlp \u00fe rrs\u00dekr 0 0 3rlprrkr 0 3rr\u00f0rlp \u00fe rrs\u00dekr 3r2rskr 2 66666666666664 3 77777777777775 (8b) T\u00f0t\u00de \u00bc \u00bdT fs 0 0 T rs Tcr Tr T" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure1.7-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure1.7-1.png", + "caption": "Fig. 1.7. Structure of a decoupled manipulation robot", + "texts": [ + ") equals the number of independent parameters enabling all the desired positions to be at tained by the terminal device. 1.1.9. Compatibility When d.o.f. = d.o.f.t., which is a necessary, but not sufficient con dition so that a manipulation robot can perform some given task, the notion of compatibility expresses the possibility to find the configu ration of the manipulation robot which enables it to attain the desired state of the terminal device. 1.1.10. Decoupling the orientation from the position of the terminal device Consider the manipulation robot, the structure of which is presented in Fig. 1.7. 10 It possesses six connections of class 5 and enables the following gen eral states: - the first three connections are arbitrary, - the last three connections are rotational with axes intersecting at point 0 and mutually perpendicular, - position of point 0 depends only on the position of bodies B1 , B2 and B3 , - position of bodies B4 , B5 and B6 determines the orientation of the terminal device (last segment - gripper in Chapter 2) with respect to point O. This decoupling is intended to reduce the problem of determining the six parameters of the manipulation robot configuration to two indepen dent problems, each having three parameters only" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure31.3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure31.3-1.png", + "caption": "Fig. 31.3 Schematic illustration of a high-power electrostatic motor", + "texts": [ + " [5] generated thrust force of several newtons, or more, with characteristic length of several centimeters. These achievements proved that electrostatic actuators can be utilized to drive ordinary mechatronic devices. We have been trying to apply such high-power motors to special environments. The motor we have mainly focused on has been a film-based linear motor called Dual Excitation Multiphase Electrostatic Drive [5]. The motor has a characteristic length of several centimeters and generates thrust force of several tens of newtons. The basic structure of the motor is shown in Fig.31.3. In its simplest configuration, the motor consists of a pair of thin plastic films. Each film contains threephase parallel and skewed [6] electrodes that are aligned at regular intervals (typically 200 m). The motor is driven by high-voltage three-phase signals such as 1 to 2 kV0-p to generate practical thrust force. Since such high voltages cause electric discharges of the air, the motor is normally immersed in dielectric liquid, such as FlourinertTM (3M) or silicone oil. The motor operation is synchronous; the displacement or speed of the slider can be controlled in an open loop control" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002398_1.1379371-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002398_1.1379371-Figure1-1.png", + "caption": "Fig. 1 The free body diagram of an engaging spur gear pair", + "texts": [ + " Owing to the complex nature of wear processes, no reliable and simple quantitative law is presently available. In this work, a mathematical model including the considerations of gear dynamics and rough elastohydrodynamic lubrication is utilized to calculate the dynamic loads. An attempt will be made to analyze the effect of tooth wear upon the dynamic load histogram and its corresponding frequency spectrum variation, providing the possibility to monitor the tooth wear process and its effect for a spur gear pair. An engaged spur gear pair is shown in Fig. 1, in which T1 and T2 denote the input and output torque respectively. The radii of the base circles of the engaged gear pair are Rb1 and Rb2 , respec- Contributed by the Technical Committee on Vibration and Sound for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received Mar. 1999; revised Mar. 2001. Associate Editor: C. Pierre. rom: http://vibrationacoustics.asmedigitalcollection.asme.org/ on 05/24/2 tively. The dynamic contact loads at the contact points A and B are PA and PB " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002487_s0167-6911(99)00032-8-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002487_s0167-6911(99)00032-8-Figure1-1.png", + "caption": "Fig. 1. Variable length pendulum plant with l( ) = l0 + l1cos( ); l1=l0 = 0:5; g=l0 = 10 and ml20 = 1.", + "texts": [ + " The decreases in and or increases in the adaptive gain and NN node number l result in a better tracking performance. 3. It should be pointed out that HONNs used in this paper may be replaced by any other linear approximator such as radial basis function networks [5,20], spline functions [16] or fuzzy systems [23], while the stability and performance properties of the adaptive system are still valid. To verify the e ectiveness of the proposed approach, the developed adaptive controller is applied to a pendulum plant with a variable length l( ) [26] as shown in Fig. 1. The plant dynamics can be expressed in the form of system (1) with (x)= 0:5sin x1(1 + 0:5cos x1)x22 \u2212 10sin x1(1 + cos x1) 0:25(2 + cos x1)2 ; (x) = 1 0:25(2 + cos x1)2 ; d(t) = d1(t)cos x1; where x=[x1; x2]T=[ ; \u0307]T, u=T and d1(t)=cos (3t). The initial states [x1(0); x2(0)]T = [0; 0]T, and the reference signal yd=( =6)sin(t). The operation range of the system is chosen as = { (x1; x2) \u2223\u2223\u2223| x1 |6 2 ; |x2 |64 } : It can be checked that Assumptions 1 and 2 are satised and 4 96 (x)61; \u2200x \u2208 . The adaptive controller (14)\u2013(15) used in this example is described as: (x) = 1; = 10:0; the input vector is z = [x1; x2; es; es= ; s]T; a two-order neural network is selected with the elements si(z) in (10) choosing as s(z1); s(z2); s(z3); s(z4); s(z5), and the possible combinations of them (i" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure3.3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure3.3-1.png", + "caption": "Fig. 3.3. Two mechanisms containing closed chains", + "texts": [ + " For the solution of constrained minimization problem the conjugate gradient projection method is pro posed. A detailed explaination including numerical examples is given. The problem of interconnected multibody system with friction is discus sed in [7]. Newton-Euler's equations are used. The method is rather analytical. Several simple examples are solved. 154 General discussion and definitions. We consider a special mechanism of manipulation robot which contains a closed chain. Two examples are shown in Fig. 3.3a,b. In general, the first (a) has a spherical kine matic scheme, and the second (b) an arthropoid scheme. But, these schemes are more complex since they contain closed chains. Let us note that a closed chain appears because of a hydraulic cylinder (marked by (*) in Fig. 3.3) which is connected to two segments. We also note that the cylinder which drives a joint Si is connected to segments \"i-1\" and \"in. We shall not regard these schemes as robots with closed chains since there exists a satisfactory approximative approach which allows us to consider these schemes as open chains. The inertial forces of the cylinder are added to the corresponding segment (to segment 1 in case * (a), and segment 2 in case (b\u00bb. The linear coordinates qi are introduced instead of q .. The nonlinear dependences between q" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000132_j.mechmachtheory.2020.104229-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000132_j.mechmachtheory.2020.104229-Figure1-1.png", + "caption": "Fig. 1. Load distribution model of the planetary gear set, (a) Planet mesh phasing [49] , (b) Rigid approach vector calculation for compatibility conditions [43] , (c) Planet gear and carrier interface for equations of motion [43] .", + "texts": [ + " Given the limitations in the current literature, the primary objective of this paper is to develop a computationally efficient 3D dynamic load distribution model for planetary gear sets (based on the quasi-static formulation of Hu et al. [43] ), which can bridge the gap between the full-scale FE and discrete dynamic models. While the secondary objective is to utilize the developed model and study the effect of gear mesh phasing, tooth modifications, manufacturing errors, and contact ratio on the dynamic characteristics of planetary gear sets. A simple \u2018N\u2019 planet epicyclic gear set constitutes of \u20182N\u2019 simultaneous gear meshes (\u2018N\u2019 sun-planet (S-P) and \u2018N\u2019 ringplanet (R-P) meshes) as shown in Fig. 1 (a). Considering all the \u20182N\u2019 mesh contacts and \u20186(N + 3)\u2019 degrees of freedom of gear components, a multibody dynamic elastic contact model can be formulated. A numerical integration scheme, in conjunction with an iterative elastic contact algorithm [44 , 45] , is employed to solve for the dynamic load distribution at gear meshes and state space of the system. Major assumptions in the proposed model are as follows: \u2022 Contact line prediction ignores small variations caused by the rigid body motion of the gears", + " In a planetary gear set, all S-P and R-P meshes engage at a common mesh frequency but are subjected to unique phasing conditions, controlled by the number of planet branches, planet spacing angles, and gear tooth geometry [4 , 26 , 43 , 46\u201348] . Three phase shifts are unique to simple planetary gear sets; (i) sun-planet mesh phasing ( \u03b3spi ), (ii) ring-planet mesh phasing ( \u03b3rpi ), and (iii) sun and ring mesh phasing ( \u03b3sr ). Without any loss of generality, time varying theoretical contact lines are determined for the S-P1 mesh considering it as the reference mesh ( \u03b3sp1 = 0 ), later the contacts for the rest of the meshes are determined by appropriately phase shifting the reference as shown in Fig. 1 (a). The predicted contact lines are discretized into sufficiently small segments with the load intensity represented by a concentrated contact force acting at the center of the segment ( j \u2208 [1 , n mesh ] ), and kinematic relations are developed at each of these points [43] . As described in Eq. (1 ), the final separation vector ( Y j ) along the contact normal is computed by considering, the initial separation vector ( \u03b5 j ), elastic approach vector ( \u03b4 j ) and rigid approach vector ( U j ), to establish whether the contact is closed (Final gap: Y j = 0 , Contact force: F j \u2265 0 ) or open (Final gap: Y j \u2265 0 , Contact force: F j = 0 ); Y j = \u03b5 j + \u03b4 j \u2212 U j (1) Effective micro geometry modification (i", + " [ 1 C i, j + 2 C i, j ]{ F i } = { \u03b4 j } , i, j \u2208 [ 1 , n mesh ] (2) The rigid body vibratory motion of the member \u2018 q \u2019 ( q ) is transformed using the geometric matrix q G j ( Eq. (3 )) to com- pute the rigid approach vector q U j at point j along its contact normal [43] , q U j = [ q n j T { q r j \u00d7 q n j }T ] \u23a7 \u23aa \u23aa \u23aa \u23aa \u23a8 \u23aa \u23aa \u23aa \u23aa \u23a9 u qx u qy u qz \u03b8qx \u03b8qy \u03b8qz \u23ab \u23aa \u23aa \u23aa \u23aa \u23ac \u23aa \u23aa \u23aa \u23aa \u23ad = q G j q (3) Where, q n j is the normal vector at the contact point, and q r j is the radial vector from the center of body \u2018q\u2019 to the contact point, as shown in Fig. 1 (b). Once the rigid body vibratory motions are transformed along the normal at contact point j, the effective rigid approach vector is computed by considering the contributions of both the gear and pinion ( U j = 1 G j 1 + 2 G j 2 ). Finally, assembling these kinematic relations for all contact points in S-P and R-P meshes to obtain the overall compatibility conditions of the planetary gear set as follows; { Y sp Y rp } \u2212 [ C sp 0 0 C rp ]{ F sp F rp } + [ s G sp 0 p G sp 0 0 r G rp p G rp 0 ]\u23a7 \u23aa \u23a8 \u23aa \u23a9 s r p c \u23ab \u23aa \u23ac \u23aa \u23ad = { \u03b5 sp \u03b5 rp } Y \u2212 CF + G = \u03b5 { Y j > 0 , F j = 0 Y j = 0 , F j \u2265 0 , j \u2208 [ 1 , n mesh ] (4) As mentioned earlier, all bodies in the system are considered to be rigid, and equations of motion for the vibratory com- ponent of each member \u2018q\u2019 ( q ; q \u2208 s, r, p, c) are developed by considering; external loads ( T (ext) q ), gravitational loads ( T (gra v ) q ), fictitious loads ( T ( f ict) q ), gear mesh loads ( T (g) q ), support loads ( T (b) q ), and damping loads ( T (d) q ), acting on the members, M q \u0308 q = T (ext) q + T (gra v ) q + T ( f ict) q \u2212 T (g) q \u2212 T (b) q \u2212 T (d) q , q \u2208 [ s, r, p, c ] (5) The mass matrix of each rigid body is assumed to be a diagonal matrix consisting of lumped mass and moment of inertia terms, which are uncoupled ( M q = diag[ m q m q m q I qxx I qyy I qzz ] )", + " Considering all the members and assembling the global mass matrix ( M ), M \u0308 = \u23a1 \u23a2 \u23a3 M s 0 0 0 0 M r 0 0 0 0 M p 0 0 0 0 M c \u23a4 \u23a5 \u23a6 \u23a7 \u23aa \u23a8 \u23aa \u23a9 \u0308s \u0308r \u0308p \u0308c \u23ab \u23aa \u23ac \u23aa \u23ad (6) bearing members, and the global external load vector ( T (ext) ) is assembled as, T (ext) = { T (ext) s T (ext) r 0 T (ext) c }T (7) The gravitational force acting on each member in the planetary system is modeled as, T (gra v ) q = M q g , where g is the gravitational acceleration vector that has a standard magnitude of 9.8 m / s 2 (on earth\u2019s surface) while its direction depends upon the orientation on the gearset. A non-zero transverse component (along x or y direction according to Fig. 1 (c)) of gravitational force results in a skewed planet load sharing. The degree of skew observed is proportional to the mass of the gearset, while its qualitative nature depends on the kinematic configuration of the gearset. When the carrier is fixed, the skew in planet load sharing is time-invariant (constant), whereas when the carrier is rotating, the load sharing has a sinusoidal behavior with a period of one carrier rotation. Considering the gravitational loads on all the members of the planetary system, the global gravitational load vector is assembled as described in Eq", + " Also, the potential of this time-varying planet load sharing to excite any of the natural modes of the system are minimal for the gearset designs and operating conditions considered in this paper. But it should be noted that gravity could have a major role to play when it comes to the dynamic response of large scale planetary gears, like the ones used in wind turbines. T (gra v ) = { T (gra v ) s T (gra v ) r T (gra v ) p T (gra v ) c }T (8) When the carrier is either an input/output member of the planetary gear system (rotating carrier), the local planet coordinates ( Fig. 1 (c)) have an orbiting motion about the gearset center and are no longer inertial frames of reference. In order to compensate for the acceleration of planet coordinates, a fictitious centrifugal force acting radially outward upon the planets, T ( f ict) p = \u2212M p ( \u03c9 c \u00d7 ( \u03c9 c \u00d7 c r p ) ) , needs to be introduced in the equation of motion, where \u03c9 c is the angular velocity vector of the carrier and c r p is the radial vector from the center of the gearset to the planet pinhole center ( Fig. 1 (c)). Since the centrifugal force acts only on the planet gears, the global fictitious load vector is assembled as, T ( f ict) = { 0 0 T ( f ict) p 0 }T (9) Since the geometric transformation matrix ( q G j ) defined in Eq. (3 ) is orthogonal, its transpose ( [ q G j ] T ) can be used to transform the gear mesh forces ( q F j ), which are along the contact normal ( q n j ), back into the local coordinates of the member \u2018q\u2019 ( Fig. 1 (b)) as described in Eq. (10 ), T ( g ) q = [ q G j ]T q F j (10) For the sun/ring gear, contact points in all S-P/R-P mesh branches are considered ( Eq. (11 )), while for the planet gears, all contact points in the S-P & R-P meshes in the particular planet branch are considered ( Eq. (12 )) to compute the resultant mesh force. Since the carrier is a support structure, no gear mesh forces directly act on it ( Eq. (13 )). T q (g) = N \u2211 i =1 nqp ( i ) \u2211 j=1 q T j ( g ) ; q \u2208 s, r (11) T p(i ) ( g ) = nsp ( i ) \u2211 j=1 p(i ) T j ( g ) + nrp ( i ) \u2211 j=1 p(i ) T j ( g ) (12) These relations for each member are assembled to obtain the global gear mesh force vector ( T (g) ), T (g) = \u23a7 \u23aa \u23aa \u23a8 \u23aa \u23aa \u23a9 T (g) s T (g) r T (g) p T (g) c \u23ab \u23aa \u23aa \u23ac \u23aa \u23aa \u23ad = \u23a1 \u23a2 \u23a3 p G T s 0 0 p G T r s G T p r G T p 0 0 \u23a4 \u23a5 \u23a6 { F sp F rp } = G T F (13) As mentioned earlier, the bearing supports of each member \u2018q\u2019 are modeled as 6 \u00d7 6 discrete spring stiffness ( K bq ). For the central members (sun, ring, carrier) the bearing force relationship is straightforward with bearing stiffness matrices being diagonal ( T (b) q = K bq q , q \u2208 [ s, r, c] ), whereas the carrier and planet interface shown in Fig. 1 (c) is slightly more involved as described by Hu et al. [43] , resulting in coupling terms in the global stiffness matrix ( Eq. (14 )). T (b) = \u23a7 \u23aa \u23aa \u23a8 \u23aa \u23aa \u23a9 T (b) s T (b) r T (b) p T (b) c \u23ab \u23aa \u23aa \u23ac \u23aa \u23aa \u23ad = \u23a1 \u23a2 \u23a3 K bs 0 0 0 0 K br 0 0 0 0 K bp K bp/c 0 0 K bc/p K bc \u23a4 \u23a5 \u23a6 \u23a7 \u23aa \u23a8 \u23aa \u23a9 s r p c \u23ab \u23aa \u23ac \u23aa \u23ad = K b (14) Viscous damping is considered in the system, which is modeled using Rayleigh\u2019s model. The Rayleigh damping coefficients ( \u03b1 = 321 . 39 , \u03b2 = 7 . 13 E \u2212 07 ) are chosen such that variation of damping ratio ( \u03be = 0 " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003983_j.wear.2009.06.017-Figure9-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003983_j.wear.2009.06.017-Figure9-1.png", + "caption": "Fig. 9. Definition of hypoid gear pair position errors V, H, G and A.", + "texts": [ + " Yet, the wear depths on he gear teeth are not 3.42 times smaller that those on the pinion eeth; they are only about half of pinion wear depths. Apart from elical or spiral bevel gears where wear ratio is directly related to he kinematic ratio, this can be attributable to additional sliding xperienced by the gear mainly due to the pinion and gear blank eometry according to the shaft offset. The contact pattern and load distribution of a hypoid gear pair is ery sensitive to the position errors of pinion and gear with respect o each other. Fig. 9 defines four basic position errors that are conidered in this study. They are the position error V of the pinion long vertical (offset) direction, axial (horizontal) position error H f the pinion, the position error G along the gear axis direction and haft angle error A. Fig. 10 shows predicted initial wear patterns f the example gear pair under various combinations of V, H, G and A rrors to demonstrate the movement of the contact pattern and the esultant differences in wear behavior of hypoid gear pairs under he pinion torque value of T = 300 Nm" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure30.3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure30.3-1.png", + "caption": "Fig. 30.3 Principle of generating torque (left) and thermal imaging of rolling bimetal. (right). The asymmetric temperature distribution seems to generate torque for one directional rotation", + "texts": [ + " The oscillation type is a metal disk with a weight (the center of mass is located below the center) bound with a bimetal (the outer layer has larger coefficient). The disk rolls periodically right and left and does not continue the oscillation because of damping by friction and air, however it on the heated plate (> 50 C) does continue the oscillation as shown in Fig.30.2. That motion is self excited oscillation. The principle how the torque for the rotation is generated by the heated plate is explained as follows (see Fig.30.3). Normally, the thermal conduction resulting temperature distribution in bimetal becomes asymmetric due to imperfect shape and contact condition when the actuator is put on the plate. If the temperature of left side is higher than the right and the thermal deformation (bending inside) of the left is larger than the right, the summation of the deformation yields the torque which makes the ring to rotate to right direction. The torque is also generated continually during the rotation because the temperature just behind the contacting (back side to moving direction) is higher than that of the forward (the front side before the contact is cooled by heat dissipation). Figure 30.3 right shows the thermal imaging of the rolling bimetal (going to right). It was observed that the temperature of back side (after contact) to the moving direction is higher and we felt thrust force to right direction at the time. 354 Toshiro HIGUCHI and Toshiyuki UENO Thermal impact drive actuator as shown in Fig.30.4 is constructed using the principle [4]. The actuator is the disk with weight and bimetal, placed on L shaped mover. When the actuator is heated on the plate of high temperature, the disk oscillating hit the bars of L shape in a cycle, which the impact force generates step displacement" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000474_s00170-020-06432-1-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000474_s00170-020-06432-1-Figure2-1.png", + "caption": "Fig. 2 a Optical scheme of the system for temperature monitoring of the SLSmachine: 1, working area; 2, focusing objective; 3, laser telescope; 4, photodiodes; 5, digital video camera; 6, MCP; 7, prism with dichroic coatings. b Monitoring system for the melting process: 1, fiber laser output; 2, telescope; 3, 4, gradient dichroic beam splitters; 5, scanner head; 6, 9, 18, dichroic beam splitters; 7, 10, 14, 15, 19, lenses; 12, 13, 17, filters; 8, 16, CCD camera; 11, LED; 20, pyrometer fiber (reproduced from [21], Copyright (2010), with permission from Elsevier)", + "texts": [ + " It can be concluded that closed-loop control can ensure the stability of the forming process by monitoring relevant information and combining relevant data processing methods to develop optimization algorithms based on machine learning. The preliminary research combines the optical measuring device based on temperature distribution in the sintering area by the camera with the online optical temperature monitoring system based on the highest surface temperature of irradiation point by the high-speed dual-wavelength pyrometer, as shown in Fig. 2. The thermal radiation intensity of the surface of the laser action area is recorded by a CCD camera or pyrometer at one or two spectral intervals and is related to the thermal radiation intensity of the blackbody simulator located in the same surface area. The system integrates two types of sensors: two-dimensional sensor digital CCD camera and single-point sensor pyrometer based on the photodiode. In situ temperature monitoring provides the possibility to optimize the forming process of high-porosity powder [21]" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure3.5-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure3.5-1.png", + "caption": "Fig. 3.5 Experimental setup", + "texts": [ + " The deformation of the piezoelectric actuator can be controlled by supplying the charge. The corresponding current pulse with the error is provided. This method is a kind of the charge control methods because the charge amount is represented by the product of the pulse duration by the current value. Consequently, the displacement with little hysteresis in any range of the applied voltage is promised. The displacement can be predicted by counting the given pulses without the displacement feedback. Fig.3.5 illustrates an experimental setup. The driving circuit consists of three sets of the current sources and sinks: coarse-, medium- and fine-step ones. A set of the current source and sink were built on a board and three sets were connected in parallel. The measured minimum pulse duration of the current sources and sinks was 16 s. The displacement of a piezoelectric actuator with a capacitance of 1.4 F is magnified by a flexure hinge mechanism. It deforms 70 m at an applied voltage of 100 V with a hysteresis of 14%" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure2.41-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure2.41-1.png", + "caption": "Fig. 2.41. Linear and angular elastic deviation", + "texts": [ + " The basic idea of this approach to elastic manipulator is to consider it as an open chain of bodies, some of them being rigid and some of them being elastic canes, and to consider weights, inertial forces of nominal motion, and nominal joint forces and moments as known exter nal values calculated by means of dynamic analysis algorithm. Special indicators kei' i=1, \u2022\u2022\u2022 ,n are used to define the segments which are considered as elastic. k . el { 1, 0, for elastic segment \"i\" for rigid segment \"i\" (2.5.23) 90 ->- ->- Let us introduce the values u i ' ~i' i=1, \u2022.\u2022 ,n defining the elastic de->- viations from the nominal motion of rigid structure. u. is the linear ->- l deviation of joint Si+1' and change i.e. rotation vector) corresponding to the point A ~i is the angular deviation (orientation as shown in Fig. 2.41. Let the deviations ->- ->- (Fig. 2.16) be uA and ~A. Let us now make two assumptions. First, we assume that small deforma tions are considered and that these oscillations do not influence the nominal motion. In this way the internal coordinates keep their nominal time histories. Second, we make an approximation assuming that each 91 R, / up segment mass mi is divided into two parts ~i = mi 2 and ~i being concentrated on the lower side of cane (point Si) and R, =umi/2, ~i ~.p on the 1 upper side (point Si+1)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003628_s11044-008-9121-7-Figure7-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003628_s11044-008-9121-7-Figure7-1.png", + "caption": "Fig. 7 Home position of the MSHRM", + "texts": [ + " Ignoring spurious solutions, there is only one real solution available for the forward position analysis of the first module: a1 = (.3536130188,\u2212.4999992483, .3536130188) a2 = (.1292239221,\u2212.4999992482,\u2212.4828375377) a3 = (\u2212.4811619757,\u2212.4999992475, .1287759479) \u23ab \u23aa\u23aa\u23ac \u23aa\u23aa\u23ad Naturally, according to the periodical functions assigned to the generalized coordinates, this solution is the same taking properly the local reference frames attached to the corresponding moving platforms, for the remaining modules and, therefore, this solution is chosen as the home position of the SHRM, Fig. 7. Finally, the most relevant numerical results generated for the forward kinematics of the output platform are summarized in Fig. 8, whereas the resulting driving forces to control each one of the moving platforms of the MSHRM are provided in Fig. 9. In this work, the kinematic and dynamic analyses, including the computation of the driving forces of a modular spatial hyper-redundant manipulator formed from identical mechanical modules are approached using an harmonious combination of the theory of screws and the principle of virtual work" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003003_tmag.2004.843349-Figure22-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003003_tmag.2004.843349-Figure22-1.png", + "caption": "Fig. 22. Result of static stress analysis at full load.", + "texts": [ + " This force is spread over all the finite-element nodes at the shaft end. It is observed that there are 12 nodes. Thus, the equivalent force applied to each of the 12 nodes in direction is 5.1. Further, the sum of the weight of pulley and belt loading mechanism, belt\u2019s prestress and the housing with stator, which amounts to 7.85 kg, is divided to all the 12 nodes in a similar way and applied at the direction, as they act downwards. At this full-load model, a \u201cstress analysis\u201d is run whose output is shown in Fig. 22. Winding weight is considered as net mass along with the weight of the stator. The material considered has a maximum tensile stress of 45 kg/mm . The stress in the SRM on full load is simulated to be 21 kg/mm . It can readily be observed that the factor of safety is for the full-load case. Thus, the SRM can be operated at full load without any mechanical threat. This analysis can be extended for any load by a suitable application of boundary conditions. This paper, made up of three parts, discussed respectively, flow analysis, flow-analysis-based thermal analysis, and vibration analysis, all by 3-D FEA procedure (using FEA package ANSYS v" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002461_70.478428-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002461_70.478428-Figure1-1.png", + "caption": "Fig. 1. A multitrailer system with n (passive) trailers and m stemable axles.", + "texts": [ + " For the two input case, it was pointed out by Martin [ l l ] and Murray [131 that, modulo somewhat different regularity conditions, chained form systems are equivalent to flat systems for the type of drift-free systems that arise in nonholonomic motion planning. The results of the current paper indicate that this is not true for systems with more than two inputs without allowing for the possibility of dynamic state feedback. As such this work provides a valuable counterpoint to the results of Gardner and Shadwick [7] and Bushnell et al. [3]. U. THE SYSTEM MODEL Consider a multisteering trailer system, i.e., a system of n (passive) trailers and m (steerable) cars linked together by rigid bars, sketched in Fig. 1. Each body (trailer or car) is modeled as having only one axle, since, as has been 1042-296W95$04.00 0 1995 IEEE 808 IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION, VOL. 11, NO. 6, DECEMBER 1995 shown in [19], a two-axle car is equivalent (under coordinate transformation and state feedback) to a one-axle car towing one trailer. A. Conjiguration Space The steering axles are numbered from front to back, starting with 1 and going up to m, and the passive axles are numbered similarly from 1 to n. There are a total of n + m axles in the system", + " These states become the bottoms of the chains of integrators in the chained form, as mentioned above, and the rest of the coordinate transformation is found through differentiation (5). It is then verified that the transformation found in this manner is a local diffeomorphism and a valid change of coordinates. There is currently no generalization to the Goursat normal form for multiinput systems which gives necessary and sufficient conditions for converting systems into multiinput chained form using dynamic state feedback. For the multisteering system of Fig. 1, the (x, y) position of the last trailer along with all the hitch angles {$I, . . . , #m-l} between steering trains will determine the entire state of the system. To see this, consider the last steering train: using the technique described above for the n-trailer single-steering case, all the angles of the trailers up to and including that of the last (or mth) steerable axle can be found. However, the hitch angle @\u201d\u2019 ahead of this axle will not be determined by anything behind it. This is the reason that its evolution as a function of time is needed to specify the entire state of the system" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure2.37-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure2.37-1.png", + "caption": "Fig. 2.37. Reactions and drives in joints", + "texts": [ + "5.12b) and they are shawIl in Fig~ 1.36. ... F _ and enc:! are the forc(J and the moment the manipulator produces if in contact with some object on the gTound. (:fig. ~36a). If the last segment of the manipulator is free (not in contact with the groundl f niellt if written in b~-f. systems~ + Fend o? = 0 (Fig. 2.36b). Let us now consider a rotat.ional joir!t S1. In that jOint, tilcre is the driving torque 1 (with the directi.on along ), react moment (perpendi.cular ~i)' and the reaction force (Fig. 2.37a \" If the joJnt linear, tllen there is a driving force (along ;. t.he rf..:act ion 51 is force FHi {perpendicular + ~ to. \u20aci) f and the reaction lTlOTllent\" acting on the i-th segment (Fig. 2. 7bi. fI'hu2, tl~e tot.al forCE': in joint Si is: ->- , 1 r F + R:L s p, i. l (2\" 5\" 13) and t.he tot,al moment The reaction force can now be computed as 85 86 -+ s.P. l l and the reaction moment -+ -+ -+ where Pi' FSi ' MSi are already computed. (2.5.15) (2.5.16) When the total joint forces and moments are calculated, it is possible to compute stresses in manipulator segments" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002790_robot.1990.125962-Figure8-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002790_robot.1990.125962-Figure8-1.png", + "caption": "Figure 8. A Two Link Manipulator at the End Points of a Path in Cartesian Space", + "texts": [ + " In these examples, the two link manipulator shown in Figure 6 with the parameters given in Table 1 is used. Icl = 0.5 m 11 = 1.0 m mi = 1 kg I1 = 0.08 Kg-m2 Ti = 1 N-m Ic2 = 0.5 m 12 = 1.0 m m2 = 1 kg I2 = 0.08 Kg-m2 T2 = 1 N-m The zero inertia lines in joint space of the two link manipulator are shown in Figure 7. These lines are drawn for various angles, integrating Equation (14) for i=1,2. Also shown in Figure 7 is a path tangent to one of the zl lines. The point of tangency, marked by a square, is a critical point. The same path and the manipulator are shown in Cartesian space coordinates in Figure 8. Figure 9 shows the velocity limit curve and the time optimal trajectory obtained with the modified algorithm. The slopes of the maximum acceleration and deceleration along the limit curve are marked as short lines at several points. At most points, except the critical point, there is only one line, indicating that the maximum acceleration equals the maximum deceleration. The maximum acceleration at the critical point exceeds the limit curve which makes it a singular point. The optimal actuator torques for this trajectory are shown in Fig 10", + " Using the old algorithm and allowing the trajectory to cross the limit curve for some distance may cause chattering of the trajectory around the limit curve and multiple switches in the actuator torques. It is possible to find a path from point A to point B without critical points simply by avoiding tangency between the path and the zero inertia lines. For the case shown in Figure 7, the straight line path is free of critical points. Such a path is less sensitive to velocity errors and is more desirable where accurate motion is essential. A c t u a t o r 2 I ' A c t u a t o r 1 Figure 10. Optimal Actuator Torques for the Path in Figure 8. 5.2 A Singular Critical Arc This example demonstrates the existence of critical arcs and the ability of the modified algorithm to obtain successfully time optimal trajectories with smooth torque profiles. Critical arcs occur if the path follows one of the zero inertia lines for some distance. For the two link manipulator, one zero inertia line converges to a straight line in the joint space as can be seen in Figure 7. For the parameters given, this occurs at 02 = 131.3O where and the second row of the inertia matrix is constant: M2 = [O, mzlcZ2+Iz ] The zero inertia line perpendicular to M2 is [ 1, 0 ] which is a horizontal vector in the joint space" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003815_j.mechmachtheory.2009.06.001-Figure15-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003815_j.mechmachtheory.2009.06.001-Figure15-1.png", + "caption": "Fig. 15. Class IV of X-motion generators with one hinged parallelogram \u2013 II.", + "texts": [], + "surrounding_texts": [ + "The famous Delta robot [20] implements successfully hinged parallelograms in three limb chains that are generators of three X-motions. Various potential applications of X-motion generators with parallelograms are going to be elucidated in further works. In fact, circular translation and rectilinear translation are not the same motion. The opposite bars of a 1-dof hinged parallelogram can move while remaining parallel. Hence, the coupling between two opposite bars generates relative 1-dof circular translation that is a 1D manifold contained in the 2D subgroup of planar translation; the plane is the one of the parallelogram. Consequently, for a small motion, a hinged parallelogram is equivalent to a prismatic pair. Replacing all P pairs by hinged parallelograms, we obtain all possible X-motion generators including hinged parallelograms; these generators are shown in Figs. 6\u20138. Flattened parallelograms are singular and must be avoided. When only one P pair for each of the generators shown in Fig. 4 is replaced by one hinged parallelogram, Figs. 9 and 10 are readily obtained. Here, we must notice that the four generators, (III9) PRRPa, (III11) PHHPa, (III12) HPPaH and (III14) RPPaR in Fig. 10 are cancelled out because they have architectures that are equivalent by kinematic inversions to chains shown in Fig. 9. PaPaRHIII1( ) ( III2 PaPaRR) PaPaHH)III3( Figs. 11\u201313 are generators of X-motion obtained by the replacement of the two P pairs in chains of Fig. 5 by two hinged parallelograms. Likewise, Figs. 14\u201316 are X-motion generators derived by replacing only one P pair in each generator of Fig. 5 with one hinged parallelogram. That way, we obtain a total of eighty-two chains having at least one parallelogram, noticing that the kinematic inversion of each of these foregoing chains is also an adequate chain for generating X-motion. 4. Defective X-motion generators A defective chain for generating X-motion arises from the permanent singularity of the chain. Then the chain does never generate the desired X-motion. Such a phenomenon is not properly a singularity. As a matter of fact, singular means specific of special poses of the chain. However, such an abuse of language has some practical interest because the same geometric condition may yield transitory or permanent failure in the generation of X-motion. Clearly, open chains obtained from the trivial or exceptional 4-bar 1-dof closed chains with 1-dof Reuleaux pairs by splitting in two parts for any one link are defective X-motion generators. Using group dependency, we can derive all possible cases of defective chains for the generation of Schoenflies motion. In general, the singularity happens iff the following set equation fH\u00f0N1;u; p1\u00degfH\u00f0N2;u; p2\u00degfH\u00f0N3;u; p3\u00degfH\u00f0N4;u;p4\u00deg \u00bc fEg \u00f010\u00de does not imply the set equations fH\u00f0N1;u; p1\u00deg \u00bc fH\u00f0N2;u; p2\u00deg \u00bc fH\u00f0N3;u; p3\u00deg \u00bc fH\u00f0N4;u; p4\u00deg \u00bc fEg: \u00f011\u00de which are solved iff the helical motion angles are equal to zero. Here, the subset of displacements represents variations of position from the home posture. The absence of displacement necessarily belongs to the set of feasible displacements. Set Eq. (10) is the mathematical model of a mechanism obtained from the open chain pictured in Fig. 1 by welding the distal bodies i and j on a fixed frame. Such a closed-loop mechanism generally cannot move and, then, the open chain of Fig. 1 effectively generates X-motion. If a link in the closed mechanism can move, then the generator of X bond is defective or permanently singular. Two kinds of singularities may happen; the undesired motion either has only infinitesimal amplitude or can have finite amplitude. The detection of undesired infinitesimal motion is done through the study of a possible linear dependency of the four twists. This topic will be studied in another work. On the other hand, group theory is a fruitful tool for PPPR)b(PPPH)a( Pl Pl Fig. 22. Defective generators with three coplanar P pairs. the characterization of finite motion. Beyond the trivial and exceptional cases that are explained through the group dependency of displacement subsets, only four paradoxical cases were definitely established by Delassus [19]. Myard\u2019s work [24] is also devoted to the study of paradoxical closed chains with five or six revolute pairs, which are beyond the subject of our paper. In spite that special exceptional chains have been misled to be paradoxical ones in [25], the paradoxical mobility still cannot be explained only by the group dependency, which does not require the use of the Euclidean metrics. The paradoxical chains of Delassus can yield passive motion with finite amplitude. This kind of singularity will be confirmed in further work. Neglecting the paradoxical mobility, which is transitory in an open chain, a link of the previous mechanism can move permanently iff two open sub-chains generate two dependent kinematic bonds, the intersection of which is not {E}. In order to avoid the defective generators, the following cases must be considered: Case A. In set Eq. (10), a product of three factors is equal to a 3D subgroup of {X(u)} and the fourth 1D factor is included in this subgroup. Referring to Fig. 17, if the four pitches are equal, then \u00bdfH\u00f0A1; u; p\u00degfH\u00f0A2; u; p\u00degfbiH\u00f0A3; u; p\u00deg \u00bc fY\u00f0u; p\u00deg and fH\u00f0A4;u; p\u00deg fY\u00f0u; p\u00deg implies [{H(A1, u, p)}{H(A2, u, p)} {H(A3, u, p)}] {H(A4, u, p)} = {Y(u, p)}{H(A4, u, p)} = {Y(u, p)} \u2013 {X(u)}. Hence, this chain fails in generating Schoenflies motion for any pose and, in other words, it is a defective chain for the generation of X-motion. The four pitches must not be all equal. Pitches may be equal to zero but not all zeros. When four pitches are zeros, the chain generates the planar gliding motion, {Y(u, 0)} = {G(u)}. By the same token, one can demonstrate that if two screw pitches are equal, then two P pairs must not be perpendicular to u. For instance, two chains of Fig. 18 actually generate the 3-dof pseudo-planar motion rather than 4-dof X-motion. Furthermore, if three screw pitches are equal and one P pair is perpendicular to the parallel H axes, as shown in Fig. 19, these chains are trivial chains of a subgroup of pseudo-planar motion and never generate X-motion. One additional defective generator, a series of four prismatic pairs that generates {T} instead of {X(u)}, is displayed in Fig. 20 for completeness. Case B. A product of two factors is a 2D subgroup and one among the other two factors is included into this subgroup. For example, p1\u2013p2; A2 2 line\u00f0A1; u\u00deor\u00f0A1A2\u00de u \u00bc 0 ) fH\u00f0A1; u; p1\u00degfH\u00f0A2; u; p2\u00deg \u00bc fC\u00f0A1; u\u00deg; A3 2 line\u00f0A1; u\u00de ) fH\u00f0A3; u; p3\u00deg fC\u00f0A1; u\u00deg ) \u00bdfH\u00f0A1; u; p1\u00degfH\u00f0A2; u; p2\u00deg {H(A3, u, p3)}{H(A4, u, p4)} = {C(A1, u)}{H(A3, u, p3)}{H(A4, u, p4)} = {C(A1, u)}{H(A4, u, p4)} \u2013 {X(u)}. Hence, three axes must not be coaxial. Fig. 21a shows such a defective chain with three coaxial H pairs. The subgroup {C(A1, u)} can also be generated by PH or HP arrays (PR or RP when the pitch of H is zero) if the P is parallel to the H axis (R axis). Fig. 21b\u2013f shows other defective X-motion generators being in this situation, in which the replacement of any screw H by revolute R yields a defective X-generator chain, too. In Fig. 22, the cases with three prismatic pairs that are parallel to a plane are defective generators of X-motion and must also be avoided. Case C. A product of two factors is a 2D subgroup and the product of the other two factors is another subgroup, which is dependent with respect to the first subgroup. In other words, the intersection of the two 2D subgroups is a 1D subgroup. From the list of products of dependent subgroups [5], we obtain only two possible situations, namely, C1. [{H(A1, u, p1)}{H(A2, u, p2)}][{H(A3, u, p3)}{H(A4, u, p4)}] = {C(A1, u)}{C(A3, u)} if A2 e line (A1, u) and A4 e line (A3, u). We have {C(A1, u)} \\ {C(A3, u)} = {T(u)}. Hence, if two axes are collinear, then, the other two axes must not be collinear. For instance, the open chain of Fig. 23a is a defective chain for the generation of X-motion. The subgroups {C(Ai, u)} with either (i= 1 or 3) or (i= 1 and 3),can also be generated by PH or HP arrays (PR or RP when the pitch is zero) if the P is parallel to the H axis (R axis). These defective generators are shown in Fig. 23b\u2013f. It is noteworthy that a defective X generator happens when a revolute pair arbitrarily replaces any screw in these generators. C2. [{H(A1, u, p1)}{H(A2, u, p2)}][{H(A3, u, p3)}{H(A4, u, p4)}] can be equated to {C(A1, u)}{T(Pl)} with {C(A1, u)}\\{T(Pl)} = {T(u)}; in this case, the plane Pl of vectors s3, s4 is parallel to u. Consequently, if two screws are coaxial, then the plane of two P pairs must not be parallel to the screw axis. The chain in Fig. 24a shows this kind of defective generator. It is a defective chain with a passive exceptional mobility. Once more, the subgroup {C(A1, u)} can also be generated by PH or HP arrays (PR or RP when the pitch is zero) when the P is parallel to the H axis (R axis), as shown in Figs. 24b and c. Here, special cases of Fig. 22 are discarded for simplicity. Case D. If two adjacent pairs generate the same 1D subgroup, then, obviously, the open serial chain generates a 3D manifold included in the 4D subgroup {X(u)}. The required four DOFs of a generator of X-motion are not achieved. Hence, two adjacent H or R pairs must not be coaxial with the same pitch and two adjacent P pairs must not be parallel. Moreover, in a PPP subchain two non-adjacent P pairs that are parallel remain parallel, what must be avoided, such as Fig. 26g. Chains belonging to this case are shown in Figs. 25 and 26, in which R pairs can replace H pairs. To sum up, the defective X-motion generators are briefly tabulated in Table 3. These open chains have passive internal 1- dof mobility: the connectivity is 3 instead of 4. Moreover, their inversions are also defective chains for generating X-motion." + ] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure23.1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure23.1-1.png", + "caption": "Fig. 23.1 Structure of the USM and working principle of the USM", + "texts": [ + " 1 Akira SAITO Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48109-2125, USA 2 Takashi MAENO Graduate School of System Design and Management, Keio University, Hiyoshi, Kohokuku, Yokohama 223-8526, Japan 268 Akira SAITO and Takashi MAENO eling the dynamics of the USM for steady and unsteady state operating conditions. The major challenges for such modeling are the nonlinearities due to the contact interface at the rotor-stator interface [3][4], and due to the softening type nonlinearity of the stator vibration [5]. In this work, a bar-type USM (developed by Canon Inc. [6]) is used as a representative of the traveling wave type ultrasonic motors. The structure of the bartype USM, along with the schematic of the operation principle is shown in Fig.23.1. The bar-type USM is comprised of stator and rotor. A donut-shaped piezoelectric ceramic is embedded and bonded in the stator, and the rotor is in contact with the stator being pressed by a spring along the axial direction. By applying two-phase alternating voltage whose frequencies are close to the natural frequencies of the modes, the first two bending modes of vibration are excited. The planes of vibration for the modes are perpendicular to each other, and the phase difference of these vibration modes is adjusted to be 90 deg. Therefore, the stator shows a wobbling motion as shown in Fig.23.1c, and the trajectory of a point on the upper surface of the stator shows an elliptical orbit. Therefore the rotor is forced to rotate by the friction force generated between the rotor and the stator. The contact point changes in time; hence it is a traveling-wave type USM. In this chapter, the dynamics involved in these processes, including the electromechanical conversion at the piezoelectric ceramics, stator\u2019s dynamics, and the rotor\u2019s dynamics through the frictional interface are investigated" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003162_50008-0-Figure7.42-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003162_50008-0-Figure7.42-1.png", + "caption": "FIGURE 7.42", + "texts": [ + " As is the case with rolling bearings, it is essential to maintain an adequate EHL film thickness to prevent wear and pitting of the gear teeth. The same fundamental equations for EHL film thickness described for a simple Hertzian contact also apply for gears. However , before applying the formulae for contact parameters and min imum film thickness it is necessary to define reduced radius of curvature, contact load and surface velocity for a specific gear. The contact geometry is illustrated in Figure 7.42. Contact geometry of meshing involute gear teeth. The surface contact velocity is expressed as: U ~ U A Jr- U B COARASin~}/+ COBRBSin~ 2 2 where: R A, R B are the pitch circle radii of the driver and follower, respectively [m]; is the pressure angle (acute angle between contact normal and the common tangent to the pitch circles); COA, COB are the angular velocities of the driver and follower, respectively [rad/s]. Since: RA _ COB RB COA Then the contact surface velocity is: ELASTOHYDRODYNAMIC LUBRICATION 3 5 7 U = 0 ) A R A S i n V = ( 0 B R B S i n ~ (7.53) Assuming that the total load is carried by one tooth only then, from Figure 7.42, the contact load in terms of the torque exerted is given by: W = T B _ TB hB - RBCOS~ (7.54) where\" W hB TB is the total load on the tooth [N]; is the distance from the centre of the follower to interception of the locus of the contact with its base circle, i.e., h B = RBCOS ~ [m]; is the torque exerted on the follower [Nm]. The torque exerted on the driver and the follower expressed in terms of the transmitted power is calculated from: H H T A - - 9.55 m O) A N A H H T B = = 9.55 O) B N B where: NA, NB are the rotational speeds of the driver and follower, respectively [rps]; H is the transmitted power [kW]. Substituting into (7.54) yields the contact load. The min imum and central EHL film thicknesses can then be calculated from formulae (7.26) and (7.27). The line from 'C 1' to 'C 2' (Figure 7.42) is the locus of the contact and it can be seen that the distance 'S' between the gear teeth contact and the pitch line is continuously changing with the contact position during the meshing cycle of the gears. It is thus possible to model any specific contact position on the tooth surface of an involute gear by two rotating circular discs of radii (RAsin~F + S) and (RBsin ~F - S) as shown in Figure 7.42. This idea is applied in a testing apparatus generally known as a ' twin disc' or ' two disc' machine shown schematically in Figure 7.43. Since the gear tooth contact is closely simulated by the two rotating discs, these machines are widely used to model gear lubrication and wear and in selecting lubricants or materials for gears. It is much cheaper and more convenient experimentally to use metal discs instead of actual gears for friction and wear testing. The wear testing virtually ensures the destruction of the test specimens and it is far easier to inspect and analyse a worn disc surface than the recessed surface of a gear wheel" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000135_j.optlastec.2021.106917-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000135_j.optlastec.2021.106917-Figure3-1.png", + "caption": "Fig. 3. Simulated temperature distribution at different time: (a) 0.05 s, (b) 0.1 s, (c) 0.2 s, and (d) 0.3 s.", + "texts": [ + "19) where K0 is a constant characterizing the morphology of porous media, B is a constant close to zero to avoid the appearance of zero on the denominator. Due to the difference of the thermo-physical property between the substrate and added powder, material properties within the track would be applied to 316L through spatial coordinate judgment function. Accordingly, A2 would be applied to the remaining domain. The material properties of the substrate and added powder are present in Table. 1. The parameter used in the calculation are showed in Table 2. Fig. 3 presents the computed transient temperature field of the LIAM process at different time nodes (0.05 s, 0.1 s, 0.2 s, 0.3 s). With the increase of iteration time, the overall temperature distribution gradually increased, and the size of the molten pool in space expanded. Later, this growth entered into a steady-state. Owing to the following characteristics of laser: high energy density, high energy concentration, and Gaussian distribution in space, the temperature of the spot center increased rapidly where the matrix material began to melt and formed a molten pool, extending from the spot center to both sides" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002775_41.681229-Figure6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002775_41.681229-Figure6-1.png", + "caption": "Fig. 6. Experimental setup.", + "texts": [ + " When the pendulum is swung up to the upward position, the adaptive control law is switched to stabilize the inverted pendulum. Since the power of the dc motor and the length of the rail are limited, the switching conditions, i.e., velocity and angle of the pendulum, are not too large. If the current states of the pendulum satisfy the predetermined switching conditions, then the control stage is changed to the adaptive control law; otherwise, it remains in the swing-up stage. In this section, we illustrate the effectiveness of the proposed control scheme by an experiment. The experimental setup is shown in Fig. 6, and its actual fabricated system parameters are presented in Table I. The system consists of a cart moving along a limited-length rail, a pendulum hinged on the cart, so as to rotate in a vertical plane, and a cart-driving device that contains a dc motor, a servo amplifier, and a pulley-belt transmission system. Two photo encoders are used to detect the angle of the pendulum and the position of the cart. In order to obtain the velocities of the pendulum and the cart, numerical differentiation is used" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003208_978-3-642-79069-0-Figure3.6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003208_978-3-642-79069-0-Figure3.6-1.png", + "caption": "Fig. 3.6. Disc-electrophore sis apparatus. 1: cover, 2: gel tube holding device and upper electrode vessel, 3,3': cooling water inlet and out let, 4,4': rubber gasket, 5: glass tube with rod gel, 6: lower electrode compart ment, 7.7': electrode plug", + "texts": [ + "003 % of a tracking dye (Bromophenol blue or Bromophenol red) are applied directly on top of the concentration gel. The total polymer concentration of the large pore gel is 3.125 (g (100 ml)- '; acrylamide : BIS = 4: 1), while the total polymer concentration of the separation gel is 7.7 wt/vol. % and the ratio of acrylamide to BIS is 30: 1. The length of the large pore gel is approximately 5 -10 % of the length of the separation gel. Both types of gel are usually polymerized in glass tubes of an internal diameter of 6 mm and a length of 100 mm (Fig. 3.6). In the large pore gel, proteins are concentrated into a very narrow zone between faster migrating buffer ions (\"leading ions\") and slower migrating buffer ions (\"trailing ions\"). At the beginning of electro phoresis the leading ions (Cl-) are in the total gel column while the trailing ions (glycine) are exclusively in the electrode buffer. Under the influence of the electric field at alkaline conditions both types of ions start to migrate to the anode. However, the leading ions migrate faster than the proteins and the trailing ions thus leaving a zone of reduced conductivity behind", + " Methods to prepare gel slabs are described in Sect. 3.5.3.1. Round gels are preferably prepared in glass tubes of a length of 70 to 150 mm with an inner diameter of 5 to 6 mm. Micromethods use capillaries of a volume of 2, 5 or 10 fll and a length of 32.5,41.5 or 54.5 mm [28]. The glass tubes used in disc-electrophoresis should be made from the same length of tubing, should have plain and smooth ends and their outer diameter must be of a size that will fit tightly into the rubber gaskets of the upper elec trode vessel (Fig. 3.6). Before use the tubes are cleaned by treating them with 10 wt/vol.% dichromate sulphuric acid and by rinsing them with distilled water. When completely dried one end is capped with a plastic cap surrounding the tube and the capped tubes are mounted in a rack. Before pouring the gels the various stock solu tions needed (cf. Table 3.4) are warmed to room temperature while the electrode buffer is cooled down to a temperature of 4 - 8 \u00b0e. The stock solutions described in Table 3.4 can be kept at low temperatures for several weeks while the ammonium per sulphate solution has to be freshly prepared" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002663_mssp.2000.1345-Figure11-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002663_mssp.2000.1345-Figure11-1.png", + "caption": "Figure 11. Principle of bi\"lar pendulum method.", + "texts": [ + " An extension to this conventional method can be found in [17]. Here two moments of inertia and one product of inertia can be identi\"ed simultaneously using a special bi\"lar testing rig. Thus, the complete inertia tensor may be identi\"ed from only two di!erent tests. The moment of inertia about the rotation axis can be calculated using equation (24). The sti!ness of the rotational spring is hereby calculated from the geometry of the suspension. Based on [12] the rotational sti!ness of a multi-\"lar suspension according to Fig. 11 is k T \"mg ab h (25) where a, b, h is the geometry of the suspension according to Fig. 11. If the mass of the test specimen is known, the moment of inertia with respect to the centre of gravity can then be calculated using the measured oscillation frequency: H cff\" mgab/h (2n f 0 )2 . (26) At least six tests (possibly less if principal inertial axes are known) with di!erent speci\"ed pendulum axes are needed in order to identify the complete inertia tensor [3, 5, 12]. The multi-\"lar pendulum method is safe if the suspension is secure and the conventional method has been approved in industrial application" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002831_3477.558842-Figure8-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002831_3477.558842-Figure8-1.png", + "caption": "Fig. 8. Simulated motion trajectory of the SICQP method for Example 1.", + "texts": [ + " 7 with motion in x direction of base coordinate, xB , only. The initial settings are chosen as (0) = [152:09 38:06 77:60 0:15 39:67 0:10 ]T deg and _ (0) = [0 0 0 0 0 0 ]T rad/s: The orientation of the end-effector is planned to be fixed through the whole trajectory. It is noted that it takes 10 s to finish the whole motion and the desired trajectory passes through the forearm interior singular point at t = 8 s. In this example, k0 = 10; \"i = 0:06, and \"w = 0:28. For illustration, the simulated motion trajectory (of the SICQP method) is shown in Fig. 8. The simulation results are shown in Figs. 9 and 10. The restricted region lies within the vertical lines at t = 7:32 and 9.2 s. The root-sum-square values of the joint rates, k _ k, is shown in Fig. 9(a). Notably, when k _ k is considered, the PI method is the worst because discontinuity occurs at t = 8 s. As for the SRI and SICQP methods there are no discontinuities. However, the results of the SICQP method are much closer to the desired values (generated by the PI method other than the point at t = 8 s)" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002551_9781420049763.ch3-Figure3.22-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002551_9781420049763.ch3-Figure3.22-1.png", + "caption": "FIGURE 3.22 In-phase and quadrature components of V and I.", + "texts": [ + " The complex quantity S of which P is the real part is, therefore, called the complex power. Its magnitude is the product of the rms values of voltage and current: *S* = *V* *I*. It is called the apparent power and its unit is the volt-ampere (VA). To be consistent, then we should call Q the imaginary power. This is not usually done, however; instead, Q is called the reactive power and its unit is a VAR (voltampere reactive). An interpretation useful for clarifying and understanding the preceding relationships and for the calculation of power is a graphical approach. Figure 3.22(a) is a phasor diagram of V and I in a particular case. The phasor voltage can be resolved into two components, one parallel to the phasor current (or in phase with I) and another perpendicular to the current (or in quadrature with it). This is illustrated in Fig. 3.22(b). Hence, the average power P is the magnitude of phasor I multiplied by the in-phase component of V; the reactive power Q is the magnitude of I multiplied by the quadrature component of V. Alternatively, one can imagine resolving phasor I into two components, one in phase with V and one in quadrature with it, as illustrated in Fig. 3.22(c). Then P is the product of the magnitude of V with the in-phase component of I, and Q is the product of the magnitude of V with the quadrature component of I. Real power is produced only by the in-phase components of V and I. The quadrature components contribute only to the reactive power. The in-phase or quadrature components of V and I do not depend on the specific values of the angles of each, but on their phase difference. One can imagine the two phasors in the preceding diagram to be rigidly held together and rotated around the origin by any angle" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002756_0278364904047393-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002756_0278364904047393-Figure4-1.png", + "caption": "Fig. 4. System of two and three forces exerted on the front foot, equivalent to the ground contact forces. The dotted-line vector NB6 is applied only after the foot is flat on the ground, then \u03c6t6 = 0.", + "texts": [ + " We use the term sthenic constraints (sthenic is from Greek sthenos meaning \u201cforce\u201d), for restrictions formulated on active and passive interacting forces that are at work and at stake in the kinematic chain. First, technological limitations of actuators need to keep actuating torques within limits such that t \u2208 [t i , tf ] , \u03c4min i \u03c4i(t) (\u2261 ui(t)) \u03c4max i , i = 2, ..., 7. (28) Secondly, contact forces between the biped and the ground must satisfy unilaterality of contact together with non-sliding conditions. Figure 4 shows a way of representing such forces according to whether the foot exerts a single point contact or lies flat on the ground. At front foot level, the equivalence between these forces and the Lagrange multipliers appearing in eq. (7), and correlated to closure constraints (3)\u2013(5), is as follows (\u03bb1, \u03bb2, \u03bb3) = (TAB6 , NA6 +NB6 , NB6 ) (29) where NB6 = 0 for t \u2208 [t t , t t + \u03b5] . Contact constraints to be fulfilled at front foot level are t \u2208 [t t , t t + \u03b5] , NA6 > 0 , \u2223\u2223 TAB6 \u2223\u2223 < fNA6 (30) t \u2208 [t t + \u03b5, tf ] , NA6 > 0 , NB6 > 0,\u2223\u2223 TAB6 \u2223\u2223 < f (NA6 +NB6 )" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003729_9780470612231.ch6-Figure6.2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003729_9780470612231.ch6-Figure6.2-1.png", + "caption": "Figure 6.2. Chemical sensor or biosensor", + "texts": [ + " stored in memory, displayed visually on a monitor, or made accessible to the real world via a digital communications port. As demonstrated by Table 6.1, there are many important markets for chemical and biological sensors, ranging from the continuous monitoring of chemical processes in industry to carbon monoxide sensing in homes. A chemical sensor may be defined as \u201ca device, consisting of a transducer and a chemically sensitive film/membrane, that generates a signal related to the concentration of a particular species in a given sample\u201d. Schematically, it can be represented as shown in Figure 6.2. A biological sensor (a biosensor) may be defined as \u201ca device, consisting of a transducer and a film/membrane that contains a biological material e.g. an enzyme or an antibody, that generates a signal related to the concentration of a particular species in a given sample\u201d (see Figure 6.2). The signal from the sensor passes to an input buffer (e.g. an operational amplifier) which provides high input impedance and protection for the circuit. From there, the signal is digitized by the ADC and passes from the \u201canalog world\u201d into the \u201cdigital world\u201d. In digital form it can be processed, stored, displayed and made electronically available to other locations through digital communications networks. In a chemical sensor, a chemically selective process occurring in or on a chemically sensitive film or membrane is coupled to signal generation at the transducer" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002514_robot.2001.933055-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002514_robot.2001.933055-Figure3-1.png", + "caption": "Figure 3: Two different robots with the same orientation of one leg for a given configuration q", + "texts": [ + " When only one set of configurations is used with one Ujoint (respectively one S-joint) locked, a 7'h geometric parameter of the base (respectively of the platform) cannot be identified. If we analyze the numerical relations between this non identifiable parameter and the identifiable ones, we observe a dependence between the offset q,ff,i of the locked leg and the position of the center of the U-joint (respectively the S-joint) of this leg along the axis of its prismatic motorized joint. Thus, placing the center of the locked joint along its leg direction will satisfy the locking constraint (cf. figure 3). That is why we have a non identifiable parameter more. This situation has not been discovered in reference [ 111, but it has been shown that two different joints must be locked to get good results. Zhuang [9] has presented autonomous methods based on the use of extra sensors on some passive U-joints. Knowing a set of e random configuration Q and the real (measured) values of 81,~ and 82,i of U-joint i for each configuration, the following linear differential system can be written from (1 8): I J where (y&, ) is the vector of the values measured for the ith U-joint and y t , is computed from the generalized DKM" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002980_ja00054a001-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002980_ja00054a001-Figure1-1.png", + "caption": "Figure 1. Glucose oxidase catalyzed electrochemical oxidation of j3-Dglucose mediated by ferroccnemethanol. Dashed lines are cyclic voltammograms of ferroccnemethanol (0.1 mM) in the absence or presence of glucose (0.5 M). Full lines are voltammograms obtained upon addition of glucosc oxidase (2.7 pM). Scan rate = 0.08 V s-I; temperature = 25 'C; ionic strength = 0.1 M. (a) acetate buffer, pH = 4.5. (b) phosphate buffer, pH = 6.5.", + "texts": [ + " SOC., Vol. 115, No. 1, 1993 will also serve as a base for a discussion of the factors that control the reactivity of the flavin site toward one-electron cosubstrates. Concerning the question of the steric accessibility of the flavin center, we have compared the kinetics observed with the native A . niger enzyme to that observed with a recombinant glucose oxidase in which the periphery of the enzyme has been extensively glycosylated through N-linkages (350 000-400 000 molecular weight) .3J3 RHultS Figure 1 shows two typical examples of catalytic currents observed with one of the ferrocenes we have investigated (ferrocenemethanol, h\" = 0.19 V vs SCE) a t two pHs where catalysis is weak (pH = 4.5) and strong (pH = 6.5), respectively. In the latter case, the voltammogram exhibits a characteristic polarogram-like shape and the reverse trace is almost superimposable on the forward trace. This behavior indicates that the rate-determining step of the overall catalytic process is fast as compared to diffusion and that the consumption of the substrate in the diffusion-reaction layer is negligible", + " 1990,68, 1837. (e) Regel, M. J.; Dunn, E. J.; Buncel, E. Cun. J. Chem. 1990,68,1846. (f) Regel, M. J.; Buncel, E. J . Am. Chem. Soc. 1991, 113, 3545. (g) Pregel, M. J.; Buncel, E. J. Chem. Soc., Perkin Tram. 2 1991, 307. (h) Pregel, M. J.; Buncel, E. J . Org. Chem. 1991, 56, 5583. 0002-7863/93/ 151 5-10$04.00/0 esters, including the p-trifluoromethylphenyl ester (2). 1 2 R\u20acSultS Kinetic data for the reaction of pnitrophenyl methanesulfonate (1) with various alkali-metal ethoxide species are shown in Figure 1 and Table I. The observed rate constants increase in the order LiOEt < NaOEt < CsOEt = KOEt = KOEt + 18C6 < KOEt + 2.2.2. A striking result in this system is the fact that potassium ethoxide in the presence of excess 2.2.2 cryptand is more reactive than either potassium ethoxide alone or potassium ethoxide in the presence of excess 18-crown-6 (Figure 1). If the data for KOEt + 18C6 are taken to represent free ethoxide ion, as will be argued. below, it follows that the potassium cryptate catalyzes the reaction which is inhibited by some uncomplexed alkali-metal ions (Li+, Na+) and relatively unaffected by others (K+, Cs'). As seen in Figure 1, the plot of kob vs [MOEt], for KOEt + 2.2.2 shows marked upward curvature, while plots for other ethoxide species are only slightly w e d . In our previouS treatment of ester ethanolysis reactions, curvature in plots of kh vs [MOEt], Q 1993 American Chemical Society" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003667_1.4000646-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003667_1.4000646-Figure1-1.png", + "caption": "Fig. 1 Indexing motion of face-hobbing", + "texts": [ + "org/ on 01/28/201 Papers dealing with the correction technique for the facehobbing process using computer numerical controlled CNC hypoid generators have not been found. This paper presents an approach to the correction of the tooth surface errors for facehobbed spiral bevel and hypoid gears using the universal motions. 2 Kinematics of Face-Hobbing Process Unlike the face-milling process, face-hobbing is a continuous indexing process in which the concave and convex tooth surfaces are generated simultaneously under a single set of machine tool settings. During the hobbing process, two sets of independent motions are provided. As shown in Fig. 1, the first set of related motion is called indexing, which is the relative rotation between the cutter head and the virtual generating gear under the following relationship: c t = Nt Nc 1 Here, t and c denote the angular velocity of the tool and the generating gear; Nt and Nc denote the numbers of the blade groups and of the teeth of the generating gears, respectively. The indexing motion generates the lengthwise trace of the teeth, which is called the extended epicycloid. The second set of related motion is the relative rotation between the virtual generating gear and the work, which is called rolling or generating motion, and is represented as w c = Nc Nw = Ra 2 Here, w denotes the angular velocity of the work, Nw denotes the number of teeth of the work, and Ra is called the ratio of roll" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000477_lra.2021.3068115-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000477_lra.2021.3068115-Figure1-1.png", + "caption": "Fig. 1. Robotic system. (a) The manipulator; (b) The close-up view of one wire rope and tube configuration; (c) The driver system; (d) The close-up view of a single driving unit.", + "texts": [ + " For the manipulator, the kinematics, workspace, and stiffness are analyzed. Tests in terms of the grasping force and variable stiffness are conducted. The manipulator\u2019s performance toward the basic operation procedures is demonstrated in the ex vivo test. The rest of this letter is organized as follows. In Section II, the system, including the manipulator and the driving system, is introduced in detail. Section III presents the workspace and stiffness analysis. Performance tests are introduced in Section IV. The conclusions are summarized in Section VI. As shown in Fig. 1, the robotic system consists of a miniature manipulator with variable stiffness (1(a)) and a detachable driver system (1(c)). The close-up view of one wire rope and tube configuration is shown in 1(b). The close-up view of a single driving unit is shown in 1(d). The manipulator and the driver system are connected by flexible tubes. The manipulator consists of forceps, modules (modules 1 to 4), and wire ropes with flexible tubes. The manipulator\u2019s diameter is 4 mm, which is compact enough for dexterous surgical operation" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure10.6-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure10.6-1.png", + "caption": "Fig. 10.6 2D micro actuator and mechanical elements", + "texts": [ + " Lu Ru T LL Vu01 T LL Vu10 Since the voltage\u2019s displacement derivative is output from the output neuron of the neural network, as previously mentioned, the voltage\u2019s time derivative is calculated by multiplying the time derivative of the displacement by it. In addition, 113 after integration, the voltage is applied to the piezoelectric element and fed to the input layer through the feedback loop. The parallel two-axial actuator is comprised of two bimorph type piezoelectric elements, two small links, and three joints (Fig.10.6). The piezoelectric element (31 mm long, 2.0 mm wide, 0.50 mm thick) was disassembled from a Braille cell SC9 developed for the visually handicapped by KGS Ltd. Small 5-mm links made of aluminum alloy were used in this actuator. Since the two links or the link and the piezoelectric element end are connected with an aluminum alloy joint, they can be rotated mutually. The center of the three joints functions as the manipulatable joint. In these joints, micro-sliding bearings are used to remove the gap between the shaft and the bearing, which is about the same size as a grain of rice (Fig.10.6). We used an OLYMPUS, IX71, inverted research microscope to measure the displacements of the three joints. A 1.25-power PlanApo\u00d71.25 for the objective lens and 0.35-power U-TV0.35\u00d7C-2 for the camera adaptor were used. The movement trajectories of joints A, B, and C were measured by image data processing of the image retrieved by a CCD camera mounted in the microscope. The centroid coordinates of these joints were obtained with noise reduction and circular regression. The above operation was executed in each stepwise voltage variation to measure the trajectories of the three joints" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure3.18-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure3.18-1.png", + "caption": "Fig. 3.18. Definition of object motion", + "texts": [ + "17). Let it be stressed that when we talk about the gripper we understand the whole segment Un\" of the chain. Let us first discuss the prescribed motion of the object to which the 186 gripper is connected (nonstationary constraint). Let us define the lin * ear motion of the object (i.e., of its point A shown in Figs. 3.17 and 3.18) by * * * xA = f 1 (t) , YA = f 2 (t) , zA = f3 (t) (3.4.84 ) and the angular motion of the object by * * * e f4 (t) , 4J = f 5 (t) , ljJ = f6 (t) (3.4.85) * * * (see Fig. 3.18). The angles e , 4J , ljJ are defined for the moving object but in a way analogous to the definition of gripper angles e, 4J, ljJ in Para. 2.4. 187 * * * * Let us define an orientation coordinate system 0sxsYszs corresponding to the moving object, in a way analogous to the definition of gripper * orientation system (0 x y z in Para. 2.4). The origin 0 coincides * * s s s~s * ~* * s~* ~* ~* with A . Axis x is along h*, z is along s , and Ys along ~ = s xh \u2022 s s If we connect the gripper to the moving object, as shown in Fig" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure6.2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure6.2-1.png", + "caption": "Fig. 6.2 (a) Working principle of the bimorph stacked piezo actuator. (b) Working principle of parallelogram mechanism", + "texts": [ + " A novel parallelogram mechanism for the stage with six degrees of freedom is designed, and the actuator is integrated into the parallelogram mechanism. This integration allows a high symmetric structure in the design. Fig.6.1 shows the schematic figure of the stage design and the parallelogram mechanism. Four arms with parallelogram mechanism support the center stage and the double-layered piezostack actuator is integrated in each center of the arm. The double-layered piezo-stack actuator, as the cross section is shown in the top of Fig.6.2(a), consists of two stacked piezoactuators, and the stacked piezoactuators can be individually driven by applying an appreciate voltage. The doublelayered piezo-stack actuators can elongate to drive the stage in XY-plane, and can bend to move into out-of-plane. Individual operation of the four-parallelogram arms can drive the stage with six degrees of freedom in X, Y, Z, x, y and z directions, as the typical motions are illustrated in Fig.6.3. The enlarging ratio KXY for XY displacement of the built-in parallelogram mechanism is given by: L XKXY " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003907_978-1-84882-991-6-Figure24.8-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003907_978-1-84882-991-6-Figure24.8-1.png", + "caption": "Fig. 24.8 Rotor and Stator", + "texts": [ + " The developed motor showed some good performances, but the output torque is still too small to drive a robot\u2019s joint. I will increase the output torque by using iron cored back yoked armature coils. Figure 24.7 (a) shows a picture of the developed hexahedron-octahedron based spherical stepping motor (6-8 spherical stepping motor) and Fig.24.7 (b) shows the structure of it. Both the rotor and the stator are sphere shaped. The rotor is supported by six spherical bearings. Compressed air is supplied for the three bearings positioned on the bottom to reduce the friction of the balls. Figure 24.8 (a) shows the structure of the rotor and Fig.24.8 (b) shows the structure of the stator. Eight NdFeB permanent magnets are attached on the spherical shell at the vertexes of the virtual hexahedron inscribed in the rotor so that the North and the South poles are located alternately. Six iron cores are also attached on the spherical shell at the center of the faces of the virtual hexahedron inscribed in the rotor. The spherical shell is made of iron, the inner diameter is 52mm and the thickness is 5mm. The rotor is covered with an acrylic spherical shell to make the rotor surface sphere" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003619_s0263574708004268-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003619_s0263574708004268-Figure2-1.png", + "caption": "Fig. 2. Static force model.", + "texts": [ + "\u201d The equation of motion of the three link model can be written as follows:[ Hf Hf l HT f l H l ] [ \u03bd\u0307 \u03b8\u0308 ] + [ cf cl ] + [ gf gl ] = [ 0 \u03c4 ] + [ JT fp JT ] [ f n ] (8) where \u03b8 \u2208 2 Joint angle vector \u03bd \u2208 3 Foot velocity (angular speed incl.) H l \u2208 2\u00d72 Leg and upper body inertia matrix Hf \u2208 3\u00d73 Foot inertia matrix Hf l \u2208 3\u00d72 Inertia coupling matrix cl \u2208 2 Velocity dependent nonlinear joint torque cf \u2208 3 Velocity dependent nonlinear wrench at the foot gl \u2208 2 Gravity joint torque gf \u2208 3 Gravity wrench at the foot \u03c4 \u2208 2 Joint torque vector. Assume that an external wrench [ f T n]T is applied at the upper body link at a point displaced by a units from the CoM of this link outward. Figure 2 illustrates the static forces on the model. The imposed wrench at the foot [ f T f nf ]T and the static joint torque \u03c4 \u2032 = [\u03c4 \u2032 1 \u03c4 \u2032 2]T , appearing in the right- hand-side of Eq. (8), are: \u23a1 \u23a2\u23a3 f f nf \u03c4 \u2032 \u23a4 \u23a5\u23a6 = [ JT fp JT ][ f n ] , (9) http://journals.cambridge.org Downloaded: 18 Jul 2014 IP address: 134.153.184.170 where JT fp = [ I2\u00d72 0 [rfp\u00d7] 1 ] = \u23a1 \u23a3 1 0 0 0 1 0 \u2212rfpz rfpx 1 \u23a4 \u23a6 , (10) rfp = [ xb + l1C1 + (lg2 + a)C12 l1S1 + (lg2 + a)S12 ] (11) and the Jacobian matrix for the point where the wrench is applied, is: J = \u23a1 \u23a2\u23a3 \u2212l1S1 \u2212 (lg2 + a)S12 \u2212(lg2 + a)S12 l1C1 + (lg2 + a)C12 (lg2 + a)C12 1 1 \u23a4 \u23a5\u23a6 ", + " Indeed, the inertia coupling matrix Hf l is 3 \u00d7 2, and we have an underactuated system at hand. We can make use of the selective Reaction Null-Space, though, to control particular component(s) of the reaction. Consider the model shown in Fig. 3. This is the same threelink model as already described, but now attached to the ground. With this model, balance will be ensured by always keeping the total CoM on the vertical. In other words, we will ignore the imposed force component in the z direction and the moment component nf (cf. Fig. 2). Hence, the selective Reaction Null-Space will be applied to control the imposed force component in the x direction only. Denote by r the position of the CoM, with components: rx = m1lg1S1 + m2(l1S1 + lg2S12) m1 + m2 rz = m1lg1C1 + m2(l1C1 + lg2C12) m1 + m2 . (15) The initial condition rx = 0 will be maintained to ensure that the speed r\u0307x is zero throughout the motion. The velocity of http://journals.cambridge.org Downloaded: 18 Jul 2014 IP address: 134.153.184.170 the CoM is: [ r\u0307x r\u0307z ] = \u23a1 \u23a2\u23a2\u23a3 rz m2lg2C12 m1 + m2 \u2212rx \u2212m2lg2S12 m1 + m2 \u23a4 \u23a5\u23a5\u23a6 [ \u03b8\u03071 \u03b8\u03072 ] " + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003097_j.fss.2004.07.007-Figure3-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003097_j.fss.2004.07.007-Figure3-1.png", + "caption": "Fig. 3. Newly created MF.", + "texts": [ + " , n as illustrated in Fig. 2. Step 2: Create 2n fuzzy rules which combine the generated MFs in Step 1 as follows. R1,1,...,1 : IF x1 is A1 1 \u00b7 \u00b7 \u00b7 and xn is An 1,THEN h\u0302 is C1,1,...,1 R1,1,...,2 : IFs x1 is A1 1 \u00b7 \u00b7 \u00b7 and xn is An 2,THEN h\u0302 is C1,1,...,2 ... R2,2,...,2 : IF x1 is A1 2 \u00b7 \u00b7 \u00b7 and xn is An 2,THEN h\u0302 is C2,2,...,2. (13) with this FLS, controlling begins. Step 3: While controlling, if a state variable xi moves into the outside of [pi 1 pi 2], create a new MF Ai 3 as illustrated in Fig. 3. Step 4: Assume that all the other current state variables xj (t) \u2032s, j = i are in the ranges of [pj 1 p j 2 ]. Then, 2n\u22121 fuzzy rules are newly added in the FLS using the MF just created in step 3. R1,...,3,...,1 : IF x1 is A1 1 \u00b7 \u00b7 \u00b7 xi is Ai 3 \u00b7 \u00b7 \u00b7 and xn is An 1,THEN h\u0302 is C1,...,3,...,1, R1,...,3,...,2 : IF x1 is A1 1 \u00b7 \u00b7 \u00b7 xi is Ai 3 \u00b7 \u00b7 \u00b7 and xn is An 2,THEN h\u0302 is C1,...,3,...,2, ... R2,...,3,...,2 : IF x1 is A1 2 \u00b7 \u00b7 \u00b7 xi is Ai 3 \u00b7 \u00b7 \u00b7 and xn is An 2,THEN h\u0302 is C2,...,3,...,2. (14) Step 5: In general, assume that the centers of the left- and right-most MF of xi arepi l andpi r , respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003723_978-3-540-73956-2-Figure9-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003723_978-3-540-73956-2-Figure9-1.png", + "caption": "Fig. 9. The stability condition for speed controller", + "texts": [ + " 6 To follow object a) with use markers, b)without use markers 235Computer\u00a0gait\u00a0diagnostics\u00a0for\u00a0people\u00a0with\u00a0hips\u00a0implants - The dynamic Investigations \u2013 in case of dynamic investigations it consists of Electromyography EMG - Measurement of muscles electrical activity, measurement of reaction force to foot \u2013 Ground reaction force vector In order to define / state and measure the range of motion of implanted limbs the series of simple tests were conducted - lifting the operated leg forward / lifting the leg with implanted hip joint - lifting the operated leg backward - lifting the operated leg out to the side Fig. 7. Lifting the leg forward Fig. 8 Lifting the leg backward Fig 9 Lifting the leg out to the side These exercises should be done under the physical therapist\u2019s control in order to prevent the dislocation of a joint. At the beginning of the rehabilitation process the patient lifted the operated leg / the leg with implanted hip joint/ forward maximum 40 degrees. It is extremely satisfactory because in case of a healthy person the same value reaches ca. 30 degrees. An identical situation occurred when the patient lifted the leg backwards and the result was between 20 and 30 degrees", + " Selected measured characteristics of joints resistance R as function of board curvature c are shown of Fig. 7. lr c \u03b121 == l h\u03b1\u03b5 = 296 Z.\u00a0Drozd,\u00a0M.\u00a0Szwech,\u00a0R.\u00a0Kisiel 0 0,01 0,02 0,03 0,04 0,05 -5 -4 -3 -2 -1 0 1 2 3 4 5C[1/m] R [Ohm] N=1 N=10 N=20 N=30 N=40 The cracks after thermal and mechanical cycling are shown on Fig. 8 Fig. 7. Selected characteristics R(c) Fig8. Selected cracks after thermal (top) and mechanical (bottom) cycling Selected results of thermal and mechanical cycling test are shown as Weibull plots on Fig.9 and 10. It can be seen that general results of thermal and mechanical; tests are comparable. Fig.9 Weibull plots for thermal cycling Fig. 10 Weibull plots for mechanical cycling [1] Drozd Z., Szwech M.: Failure Modes and Fatigue Testing Characteristics of SMT Solder Joints. Proc. 1st Electronics Systemintegration Technology Conference ESTC 2006 Dresden 5 \u2013 6.09.2006, pp.1187 \u2013 1193 1206 SAC 1206 PbSn 0805PbSn 0805 SAC 0805 PbSn 1206 SAC 1206 PbSn 0805 SAC 297Accelerated\u00a0fatigue\u00a0tests\u00a0of\u00a0lead\u00a0\u2013\u00a0free\u00a0soldered\u00a0SMT\u00a0Joints Early Failure Detection in Fatigue Tests of BGA Packages R", + " The controlled active damping with additional force link inside the structure is in Fig. 5. The new solution by active drive mounting by additional actuator is in Fig. 6 and the new solution by mechatronic stiffness, where the auxiliary structure provides flexible support for exerting additional force, is in Fig. 7. The control methods of particular proposed variants of mechatronic solution for controlled vibration suppression have been synthetized and simulated. The results of frequency response are in Fig. 8-11 for variants in Fig. 3-6. Fig. 8 Controlled dynamic absorber from Fig. 9 Controlled vibrocompensation Fig. 3 from Fig. 4 Controlled Controlled Without Without Passive Passive 461Variants\u00a0of\u00a0mechatronic\u00a0vibration\u00a0suppression\u00a0of\u00a0machine\u00a0tools The mechatronic stiffness solution from Fig. 7 is characterized by frequency dependence of dynamic stiffness in Fig. 12. The comparison is done between cases without modification, with passive modification of the structure and with controlled modifications. All results have demonstrated the large potential of mechatronic solutions of controlled vibration suppression" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003307_1.330653-FigureI-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003307_1.330653-FigureI-1.png", + "caption": "FIG. I. Cross-sectional side view of the left-hand portion of a multilayer strip cut by plane A-A.", + "texts": [], + "surrounding_texts": [ + "Simple stress formula for multilayered thin films on a thick substrate J. Vilms and D. Kerps Citation: J. Appl. Phys. 53, 1536 (1982); doi: 10.1063/1.330653 View online: http://dx.doi.org/10.1063/1.330653 View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v53/i3 Published by the American Institute of Physics. 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Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions", + "Simple stress formula for multilayered thin films on a thick substrate J. Vilms and D. Kerps Hewlett-Packard Laboratories. Palo Alto. California 94304\n(Received 8 June 1981; accepted for publication 10 November 1981)\nA simple formula for stress produced by differential thermal contraction in a multilayered structure composed of thin layers on a thick substrate is derived. Formulas for bending radius and substrate stress are also given. Numerical results agree with more complicated calculations of prior work.\nPACS numbers: 68.60. + q, 46.30.Cn, 81.40.Jj, 85.30.De\nStress calculations for multilayered structures have been presented before by numerous authors,I-7 but the re sults are in fairly complicated form and not convenient to evaluate numerically without considerable calculation. In typical applications, the deposited multilayered film is often appreciably thinner than the substrate, and our intention here is to derive a truly simple multilayer stress formula ap plicable for this particular case.\nFollowing Olsen and Ettenberg,4.5 we consider a struc ture in the shape of a long, narrow strip amenable to one dimensional stress analysis. If the experimental specimen it self does not have nearly this shape but has comparable length and width, stress is isotropic in the plane of the layers, with deformation approximately spherical away from edges,2 and thus a similar long, narrow strip in which the transverse stresses balance to zero may be cut along a merid ian line of the specimen. In this case, the results are the same but E I( I - v) must be used everywhere in place of E in what follows, E being the elasticity modulus and v, Poisson's ra tio. As an example, Fig. 1 shows the cross-sectional side view (greatly expanded in the vertical direction) of a strip com posed of two different thin layers on a substrate. There are two sources of stress in this strip, bending and differential (thermal) contraction. Stress (1 is related to strain \u20ac by (1 = E\u20ac { or by (1 = [E I( 1 - v)k l, and strain is found from geometrical considerations, by comparing the actual size and shape of each layer to what it would be if the layer were unconstrained by the substrate and other layers. We use the middle atomic sheet of the substrate (dashed line in Fig. 1) as a reference in calculating strain. Because of bending, each atomic sheet of the strip has an extra strain, compared to the reference sheet, which varies linearly with its vertical dis tance from that reference sheet, with proportionality con stant 1/ R. R is the radius of bending, the substrate and layer thicknesses are t\" (I' (2' . .\" and we assume R).ts + tl + t2\n+ ., .. The reference sheet has a strain \u20aco representing the adjustment of the entire structure in order to make the net force zero. Following these considerations, the substrate and ith layer strains for an arbitrary number oflayers are given by\nand\nrs - (s12 \u20acs =\u20aco+--~-\nR (I)\n(J2+(I+(2+ ... +t;l2 r-t./2 \u20acj = \u20acO + R - \u20acci + ' R' ,(2)\nwhere tj is layer thickness, rj is internal vertical distance measured from rj = 0 at the lower face of each layer, and \u20acci is the difference of elastic contraction between the ith layer and the substrate produced during cooldown from deposi tion to room temperature. Expansion (tension) is taken to be positive and contraction (compression) negative; \u20accj is posi tive if the unconstrained layer would be longer than the sub strate. In Eqs. (I) and (2), we have separated the strain into components so that the integrated stress over the cross sec tion of each layer at A-A is resolved into a net force F j\n= Ej\u20acjwt j acting at the midpoint of the layer, and a pure bending couple M; = Ejw( :/12R, arising from the term in volving r;. Here, E; is the elasticity modulus of the layer, and w is the width of the strip perpendicular to the plane of the paper. The unknown parameters 60 and R are found from stat ic equilibrium conditions, considering Fig. 1 as a free-body diagramS ofthe left-hand portion of the strip, cut atA-A. Because there are no external forces applied, the only forces present are stresses at cross-section A -A, indicated by arrows in the figure. Forces in the long direction of the strip and their moments about point 0, sum to zero. We thus obtain\n< [ TI(ts/2 + t/2) + T2(tJ2 + (1 + t2/2) + ... ] \u20ac)TC R\n\u20aco = -----=---------=------------ ts + T\n1536 J. Appl. Phys. 53(3), March 1982 0021-8979/82/031536-02$02.40 \u00a9 1982 American Institute of PhySiCS 1536\nDownloaded 06 Jun 2012 to 132.236.27.111. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions", + "and\nF (~+~) 1 2 2\n( ts t2) + F2 \"2 + tl +\"2 + ... + Ms + MI + M2 + ... = O. (4)\nT; = t; (E;I Es) are effective layer thicknesses, T = TI + T2 + '\" is the total effective deposited layer thickness and\n(Eo) = Eel TI + Ec2 T2 + ... TI + T2 + ...\n(5)\nis an average differential contraction strain. Let t = t 1 + t2 + ... denote the total deposited layer thickness. We make three approximations allowed by ts >t. First, we approximate the term in brackets in Eq. (3) by [(fs + t)T 1(2R )], which is exact in case of equal elastic mo duli. Second, we replace the first group of terms in Eq. (4), which comprise the moment of force about 0 produced by the forces F;, by (FI + F2 + ... )(ts + f )/2, which is an ap proximate moment produced by the sum of the F; acting at the midpoint of the total deposited layer. Third, MI + M2 + ... is neglected in comparison to Ms. Using the relationships FI + F2 + ... = - Fs' Fs = EsEowfs' and in troducing dimensionless thickness ratios.J = Tlfs' 8 = flf\" and 8; = f;lt\" we obtain\nR (6)\nand\n(Ec ).J Eo = -----=-----\n1 +.J + 3.J (1 + 8)2 (7)\nThe ith layer stress is\n= E; [(Ec).J {I + 3~1 +:)[1 + 2(81 + 8~ + ... + t 8;)]} E ci ],\n+ + 3.J (1 + 8)\nand the substrate stress is\nu, ~/6k,)il (tl1+6)~ + ~ f)\\ \\ - 1 +.J + 3.J (1 + 8)2 )\nwhere t = r;lf; is an internal vertical position parameter within each layer or the substrate, varying from 0 to 1.\n(8)\n(9)\nThe key parameters in the stress formulas for our spe cial case of thin multilayers on a thick substrate are the aver age differential contraction (Ec) and the effective deposited layer-to-substrate thickness ratio .J. There is no restriction to equal elastic moduli. The stress within each thin layer is almost uniform because the t8; term is small. Our results are very similar to the linear approximation case for a single thin film on a thick substrate discussed by Roll. 3 By considering the deposited multilayer to be a single layer having an average applied stress (ac) = - (EIEc1 f. + E2Ec2 t2 + ... )It = - Es (Ec).J 18 owing to differential contraction, and dropping the second order.J and 8 terms, Eq. (6) reduces to Eq. (18) of Roll. In a less rigorous approxi mation neglecting.J, 8, and 8; in comparison to unity, our\n1537 J. Appl. Phys., Vol. 53, No.3, March 1982\nEq. (8) reduces to a j ;:::,E j (4(E<).J - Eci ), which is essentially the same as Eq. (2) of Roll. In this same less rigorous approxi mation, Eq. (9) reduces to as ;:::,6Es (Ec)..1 (t - II3), showing that the neutral plane is at t = II3-in other words, (2/3)fs away from the substrate-first layer interface.\nThe simple formulas (8) and (9) are perfectly adequate to describe the results of prior work. For example, using Eq. (8) and t = 1, the active-region stress of the GaAIAs double heterostructure laser described in Fig. 5 of Oslen and Etten berg4 is expressible by one formula\naa = 1.l4X108(xc -1O.94xa)' (10)\nusing their parameter values-l X 1012dyn/cm2 for elastic moduli, all assumed equal, and 1.26 X 1O- 3x; for differential thermal contraction, xiIi = a, c) being the fractional AlAs composition of the layer in question. In Eq. (10), Xc and Xa are the compositions of the confining and the active layers of the laser structure. The zero stress points given by Eq. (10) arexa = 0.023 and 0.046 for Xc = 0.25 and 0.5, respectively, which are very close to the values given in the referenced figure, viz. Xa = 0.022 and 0.045; and other points are simi larly close. As another example, stress in a Burrus diode structure consisting of lO,um of X 1 = 0.3,0.5,um of an unde termined composition X 2, l,um of X3 = 0.3, and l,um of X 4 = 0.16 of GaAIAs material grown sequentially on a 104- ,urn thick GaAs substrate, was found by machine calcula tion9 using the formulas of Olsen and Ettenberg.4 That cal culation gave X 2 = 0.112 for the zero-stress composition of the 0.5-,um-thick layer, while Eq. (8) gives almost the same value, X 2 = 0.114. A third example concerns the location of the neutral, unstressed atomic plane in the substrate. Rein hart and Logan2 observe as well as calculate the neutral plane at 45 ,urn from the interface of a 33-,um thick single layer on a 70.2-,um thick substrate, both before and after etching the layer to a thickness of 4.4 ,urn. The values of 43 and 46,um found from Eq. (9), before and after etching, are in good agreement with their result.\nIn conclusion, a simple formula for stress in thin multi ple layers on a thick substrate was derived and shown to agree well with prior work. Substrate stress and the location of the neutral plane were also determined.\nThe authors wish to thank R. W. H. Engelmann for encouragement and a critical reading of the manuscript.\nJR. H. Saul, J. Appl. Phys. 40, 3273 (1969). 2F. K. Reinhart and R. A. Logan, J. Appl. Phys. 44, 3171 (1973). 3K. Roll, J. Appl. Phys. 47, 3224 (1976). 'G. H. Olsen and M. Ettenberg, J. Appl. Phys. 48, 2543 (1977). 'G. H. Olsen and M. Ettenberg, in Crystal Growth, Theory, and Techniques, Vol. 2, edited by C. H. L. Goodman (Plenum, New York, 1978), pp. 9-17, 49-54. 6W. A. Brantley, J. Appl. Phys. 44,535 (1973). 7H. Shimizu, K. Itoh, M. Wada, T. Sugino, and I. Teramoto, IEEEJ. Quan tum Electron. QE-17, 763 (1981). 8E. P. Popov, Mechanics of Materials (Prentice Hall, New Jersey, 1952), p. 3. 9John A. Herb, 1977 (unpublished).\nJ. Vilms and D. Kerps 1537\nDownloaded 06 Jun 2012 to 132.236.27.111. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions" + ] + }, + { + "image_filename": "designv10_6_0003030_j.snb.2004.09.033-Figure4-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003030_j.snb.2004.09.033-Figure4-1.png", + "caption": "Fig. 4. (A) Cyclic voltammogram of a bare glassy carbon electrode in the supporting electrolyte (scan a) and upon addition of sulfite to a final concentration of 3.0 mM (scan b). (B) Cyclic voltammogram of a FeHCF modified glassy carbon electrode in the supporting electrolyte solution (scan c) and upon addition of sulfite to a final concentration of 3.0 mM (scan d). Scan rate 50 mV s\u22121.", + "texts": [ + " The surface coverage remains almost constant during the first 15 min and after this time a linear decay of the surface coverage with the cycling time, corresponding to a diminution of 1.57 \u00d7 10\u221211 mol cm\u22122 per minute, is observed. The loss of electroactivity after 1 h of continuous cycling (about 60 cycles) could be estimated in a 15% of the initial charge. On the basis of these results the FeHCF modi p 3 h a O b c r s e a r t i r t v o B t e i t f g b fied electrode is quite stable and therefore it can be used as otential sensor. .2. Electrocatalytic oxidation of sulfite at iron exacyanoferrate modified electrodes Curve a in Fig. 4A, depicts the cyclic voltammogram of bare glassy carbon electrode placed in 0.1 M KCl solution. ver the potential range of \u22120.3 to +1.2 V, only a featureless ackground is observed. Upon the addition of sulfite to a final oncentration of 3.0 mM an enhancement of the anodic curent at about +1.15 V is observed (curve b in Fig. 4A). Fig. 4B hows cyclic voltammograms in 0.1 M KCl of a glassy carbon lectrode modified with a FeHCF film in the absence (curve c) nd presence (curve d) of sulfite. In the absence of sulfite the esponse is that previously described for the modified elecrode, ascribed to the reversible oxidation/reduction of the ron(II) hexacyanoferrate(III)/iron(III) hexacyanoferrate(III) edox couple with a formal potential at +0.82 V. Upon addiion of sulfite to a final concentration of 3.0 mM, the cyclic oltammogram exhibits a dramatic enhancement in the andic peak current with a decrease in the cathodic peak current" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002845_s100510050424-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002845_s100510050424-Figure1-1.png", + "caption": "Fig. 1. Problem statement.", + "texts": [ + " One of these simulations [35] considers finite duration of a collision and uses ad hoc interaction laws whereas the other one [36] is based on series of binary collisions for a column of hard spheres, i.e., for which the collisions are considered as instantaneous. However, until now no experimental work has been done and the behaviors observed numerically rely on unrealistic interaction laws [36] or are without clear interpretation [35]. In this paper, we analyse the dynamics of the collision of a column of N beads with a fixed wall. Initially, the beads are at rest with no separation between them, and they are dropped from a height h above the wall. The problem statement is shown in Figure 1. This system is well adapted to study, in a simple manner, the detachment effect observed in 1\u2013D simulations [35] with a linear or nonlinear dissipative interaction law. This effect is discussed in Section 8 while the experimental and numerical observations are presented respectively in Sections 3.5 and 6.6. More generally, the low dimensionality of the experiment and the fact that there is no injected energy during the collision allows a good understanding of elementary mechanisms which play a role in vibrated granular media (see Sect" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000562_j.mechmachtheory.2021.104380-Figure8-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000562_j.mechmachtheory.2021.104380-Figure8-1.png", + "caption": "Fig. 8. The parameters identification of the PR drives.", + "texts": [ + " In addition, the SoftBUS communication protocol is employed to connect the controller of the servo motors (Maxon RE40) and the software of the OptiTrack system, together. Hence, the validation experiments can run automatically once the measuring configurations are prescribed in advance. To reduce the influence of the actuation errors on the prediction accuracy of the proposed analysis method, the actual parameters of the compound PR drives are identified before the validation experiments. As shown in Fig. 8 , the active PR joint is realized via a differential belt-driven mechanism, which transforms two rotational inputs into a pair of perpendicular translational and rotational outputs. Specifically, when the two active pulleys rotate in the same direction at the same rate, only the rotation occurs in the compound PR drive. On the contrary, when they rotate at the same rate but in opposite directions, the drive only translates along the vertical direction. In general, a combination of translation and rotation can be generated via the two motors", + " Due to manufacturing/assembling errors, the axes of translation and rotation of the PR drives are not perfectly located. This will influence the geometric constraints to the kinetostatics problems of the studied PCMs, so does the positioning accuracy of the developed prototype. Therefore, the actual assembling configurations of these PR drives in the developed prototype are identified individually before the validation experiments. For each PR drive, a grid of poses are generated for the parameter identification by means of discretizing the translation and rotation, respectively. As illustrated in Fig. 8 , 10 positions (each 10 mm from 0 to 90 mm ) are generated equally along the translational axis. And for each position, 9 orientations are further discretized in an even way (each 20 \u25e6 from \u221280 \u25e6 to 80 \u25e6). As a result, totally 10 \u00d7 9 = 90 different poses can be collected to specify the kinematic parameters of these compound drives in the developed prototype. As shown in the figure, for each limb, a local frame (termed { D j } ) is defined on the mounting plate of the flexible link. In this section, it is assumed that the axes of translation and rotation of the corresponding PR drive are coincident with the w j -axis and u j -axis of { D j } , respectively" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003542_28.2871-Figure11-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003542_28.2871-Figure11-1.png", + "caption": "Fig. 11. Rotor-bar currents in period 0-50 ms of starting to - nsynchr.", + "texts": [], + "surrounding_texts": [ + "3 12 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 24, NO. 2 . MARCH/APRIL 1988\nconstant in space. After an initial 1-2 periods the dc component vanishes and the rotor tooth induction forms a wave with decreasing speed, which is due to the decrease of the slip. At the end of the transient the magnitude of rotortooth fluxes suddenly rises near the synchronous speed. This behavior is explained in the previous section.\nUnsymmetrical Stator Connection To illustrate what is going on in a three-phase machine in which one phase is oppositely connected, forming a pulsating air-gap field, the computer run illustrated with the next set of figures was carried out. Fig. 16 shows the torque, whose average is equal to zero during this transient. One can see pulsations with the double mains frequency.\nThe reason why the rotor does not move constantly in any direction is obvious from Fig. 17, which represents the air-gap\nfield for this transient. Simply, there is no defined direction in which the rotor should move because the stator air-gap field is pulsating in space.\nCONCLUSION\nThe magnetic equivalent-circuit method, being essentially a kind of finite-element analysis, can be made as accurate as necessary. Keeping in mind the fact that, from the engineering point of view, accuracies of more than 0.5 percent are unnecessary, conclusions about the number of elements that are needed to represent a part of machine, e.g., tooth, are easily derived. For most applications the level of flux density will be low enough, so the assumption that a complete tooth is just one finite element is accurate enough. Increase of flux density imposes the need of more subtle representation of the machine magnetic circuit, including more divisions of teeth", + "OSTOVIC: MAGNETIC EQUIVALENT-CIRCUIT MODELING 313", + "3 14\nIEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 24, NO. 2. MARCHlAPRlL 1988" + ] + }, + { + "image_filename": "designv10_6_0002787_978-94-011-4120-8_29-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002787_978-94-011-4120-8_29-Figure1-1.png", + "caption": "Figure 1. Sketch of a Tendon-based Stewart Platform", + "texts": [ + " The set of postures where this is possible is called \"controllable workspace\" (CWS); it depends on the external forces and torques acting on the platform. The equilibrium conditions for force and torque at the end-effector are m L I~ + Ip = 0 and ~=1 m L P~ x I J.l + Tp = 0 , J.l=1 (1) where IJ.l are the tendon forces, PJ.l are the vectors pointing from the plat form coordinate frame to the platform connection points, and Ip, Tp are any other forces and torques acting on the platform, including gravity, in ertia, contact forces etc. (see Fig. 1). As the tendon forces I J.l act parallel to the tendon lengthes IJ.l' this can be rewritten as (2) Now the CWS for a given pair Ip, Tp is the set of postures where Eq. (2) can be satisfied with positive tendqn forces fw 2. Concentrating on the Force Equilibrium The goal of this paper is to describe in an exhaustive way that region in space where just the force equilibrium can be obtained. This supplies a superset of the CWS as a first step towards a complete description of the CWS itself. It turns out that the analysis of the force equilibrium can be performed in a general way, valid for any number of dimensions and tendons, with or without external forces Ip. Fig. 1 shows that lp. = bp. - Pp. - r =: bpp. - r, thus we have to solve f {p. (bpp. - r) + fp = 0 with Ip. > a for all J-L. (3) p.=1 p. The vector bpp. denotes that position of the platform where the J-Lth tendon has zero length (for a given orientation R). Now the problem is equivalent to determining the CWS of a manipulator with translational DOFs only, where the tendons join all in one point and the winches are located at the points bpw If fp = 0, the CWS is the convex hull of these points. Otherwise, fp can be modeled as the force of an additional tendon fixed at infinite distance, and the concept of convex hull can be extended to this case" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002831_3477.558842-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002831_3477.558842-Figure1-1.png", + "caption": "Fig. 1. The 6-DOF PUMA manipulator [18].", + "texts": [ + " Thus, det(J11) = 0 determines the conditions for forearm singularities. By the same token, from (11), J22 relates the wrist joint rates, _ l, to the task space angular velocities. Therefore, det(J22) = 0 determines the condition for wrist singularity. In order to further understand the properties of the manipulator singularities, the well-known PUMA manipulator is selected as an example. Also, its various singularities will be fully analyzed in the following subsection. The 6-DOF PUMA manipulator is shown in Fig. 1 and the D-H parameters are given in Table I [18]. In order to simplify the analysis, the velocity reference point will be selected at the Wrist (origin of the coordinate 4). Then, 0 JW is the Jacobian matrix expressed in coordinate 0 with the Wrist as the velocity reference point and can be represented as 0 JW = 0 J11 03 3 0 J21 0 J22 (14) with (15)\u2013(17) (shown at the bottom of the page). Here Ci; Si; Cij , and Sij represent cos( i); sin( i); cos( i + j), and sin( i + j), respectively. Thus, the singularities can be identified by checking the determinants of the two 3 3 matrices 0 J11 and 0 J22 as follows: Forearm Singularities: The forearm singularities can be identified by checking the determinant of the matrix 0 J11 in (15) as det(0J11) = a2(d4C3 a3S3)(d4S23 + a2C2 + a3C23): (18) There are two conditions, denoted as b and i, for forearm singularities", + " The PI, SRI, or SICQP methods are applied as the motion resolution schemes when singularity occurs. For the nonredundant case, the PI method is equivalent to the direct\u2013inverse method. Therefore, the motion resolution scheme of the PI method is simply _ = J 1 _r: (62) As for the SRI method, _ is expressed in (32). The motion resolution scheme using the SICQP method is shown in Fig. 5 together with (56)\u2013(58). In the following, Example 1 will be presented. Example 1: Forearm Interior Singularity: PUMA manipulator and its corresponding D-H parameters have been shown in Fig. 1 and Table I, respectively. The translational motion planning is defined in Fig. 7 with motion in x direction of base coordinate, xB , only. The initial settings are chosen as (0) = [152:09 38:06 77:60 0:15 39:67 0:10 ]T deg and _ (0) = [0 0 0 0 0 0 ]T rad/s: The orientation of the end-effector is planned to be fixed through the whole trajectory. It is noted that it takes 10 s to finish the whole motion and the desired trajectory passes through the forearm interior singular point at t = 8 s. In this example, k0 = 10; \"i = 0:06, and \"w = 0:28", + " This load distribution approach uses optimization schemes that degenerate to a linear search algorithm for the case of two robots manipulating a common load, and this results in significant reduction of computation time. The load distribution scheme not only enables us to reduce the computation time, but also gives us the possibility of applying this method in real-time planning and control of CMMS. Further, we show that for certain object trajectories the load distribution scheme yields truly time-optimal trajectories. I. INTRODUCTION A cooperative multi-manipulator system (CMMS) is defined as the system of multiple robots handling a common object, forming closed kinematic chains, as shown in Fig. 1. In many robotic applications, CMMS is needed for handling an object due to the inherent nature of the task itself or the desire to enhance the flexibility. For example, in a flexible assembly system one may use multiple robots to assemble two or more parts into a final product. If an object is so big that it cannot be handled by a single robot, the use of multi-robots may be required. Research on time-optimal trajectory planning for CMMS has to consider many issues which may not be important in the single robot Manuscript received February 8, 1993; revised September 14, 1995" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0000133_j.wear.2021.203616-Figure2-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0000133_j.wear.2021.203616-Figure2-1.png", + "caption": "Fig. 2. Schematic and photographic representation of the sliding bearing test rig.", + "texts": [ + " The feasibility of AE to detect mixed friction conditions was examined at a planet speed of 20 min\u2212 1 which results in a sliding velocity of 0.1 m/s. The nominal load acting on the bearing was 88 kN, which is a specific pressure of 8 MPa. The tilting moment which is resulting from the helical gears in this operating point is 1482 Nm. The tilting moment can be obtained with Mt = Fa\u22c5dpc by multiplying the axial force Fa and the pitch circle diameter dpc. To study running-in wear, experiments were conducted on the test rig depicted in Fig. 2. Experiments with 30,000 and 360,000 shaft revolutions were conducted with a stationary load and speed of 2250 N and 250 min\u2212 1, respectively. Consequently, the duration of the short experiments was 2 h, whereas the bearing was operated for 24 h in the long experiments. A new shaft sleeve and a bearing were used for each experimental set up. The radial load was applied to the housing of the bearing using a flexible load unit with low friction ball bearings. The full radial load was applied after reaching the stationary drive speed to reduce wear caused by mixed lubrication conditions during the start-up procedure" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0002602_ip-cta:20030398-Figure1-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0002602_ip-cta:20030398-Figure1-1.png", + "caption": "Fig. 1 Dead-zone model", + "texts": [], + "surrounding_texts": [ + "1 Introduction\nA dead-zone, which can severely limit system performance, is one of the most important nonsmooth nonlinearitics that arise in actuators such as, servo valves and DC servo motors. In most practical motion systems, the dead-zone parameters are only poorly known, and robust adaptive control techniques are required. Proportional-derivative (PD) controllers have been observed to result in limit cycles, Due to the nonanalytic nature ofthe dead-zone in actuators and the fact that the exact parameters (e.g. the width of the dead-zonc) are unknown, systems with dead-zones present a challenge for control design engineers.\nAn immediate method for the control of the dead-zone is to construct an adaptive dead-zone inverse. This approach was pioneered by Tan and Kokotovic [ I , 21. Continuoustime and discrete-time adaptive dead-zone inverses for linear systems were built in [ I ] and [2], respectively. Simulations indicated that the tracking performance is significantly improved by using a dead-zone inverse. This works was extended in [3] and [4] and a perfect asymptotical adaptive cancellation of an unknown dead-zone was achieved with the condition that the output of a dead-zone is measurable.\nAlternative methods to produce an approximate deadzone inversc include trying Fuzzy logic or neural network prccompensators. Kim et ai. [ 5 ] , Jang [6] and Lewis et d. [7] have proposed h z z y prccompensators in nonlinear industrial motion systems and Selinic and Lewis [8] employed neural networks to construct a dead-zone precompensator. Corradini and Orlando [9] separated an unknown dead-zone into a known part and a bounded '\nICE, 2003\nIEE P,nceedingr online no. 20030398\nPaprr first received 24th April 2002 and in revised form 7th February 2003\nX.-S. Wang is with the Department of Mechanical Engineering, Southeast University, Nanjing 2100Y6. China\nH. Hong and C:Y. Su are with the Department of Mechanical Engineering. Cancardia University. Montreal, Quebec, Canada H3G IM8\n/\u20acE Pmc.-Conrml Theon. Appl., Yo1 150, ,Yo. 3. ,!4q 201J3\nDO/: 10. I O ~ Y ~ ~ ~ - ~ W : ~ O O ~ ~ ~ Y X\nunknown part, and used direct compensation of the known part and a variable structure controller for the whole system to overcome the effect of the unknown part.\nWe now extend the approach of constructing an adaptive dead-zone inverse in transfer function fomi by considering systems in a state space form. By given a matching condition to the reference model, an adaptive controller with an adaptive dead-zone inverse can be introduced. Benefiting from the matching condition of the reference model, the global convergence is guaranteed even when the dead-zone slopes are unequal and the output of the dead-zone is not measurable as needed in [ I ] and [4], which may he a valuable choice for a number of practical problems that can he simplified in the proposed system Structures.\nAs stated in [ l ] , this dead-zone model is a static simplification of diverse physical phenomena with negligible fast dynamics. Equation (I) is a good model for a hydraulic servo valve or a servo motor.\nThe key features of the dead-zone in the control problems currently investigated are:\n(AI) The dead-zone output w(t) is not available for measurement. (A2) The dead-zone parameters h,, b,, in,, mI are unknown, but their signs are known as: b, > 0, bl c 0, m, 0, ml > 0. (A3) The dead-zone parameters b,, bl, m,, ml are hounded i.e. there exist known constants b, mill1 h, lnjlX, b, ,\"in, bl mr ,,,ill, nl,,,,,, nll,i,,,ml,,,,,suchtbatb,~ [b,,,i,, br,,laxl,~~~[b~,ni,l,\n\"Ir m,l. mi E tnaxl, and m, E [w min, mi ,nrnl Assumptions (AI) and (A2) are common in practical systems, such as servo motors and servo valves. If w(t) is\n261", + "4 Adaptive controller design\nIn presenting the adaptive control law, we define the state difference (error) between the plant and the refcrence model as:\nE = X , -X,\" (7)\n( 8 )\nTo design the controller, we simplify the vector equation to a scalar error form by introducing the following lemma as used and proved in [IO].\nLemma I : Let\nBy using (3) , (4) and ( 6 ) , we have\nE = A,E + B(w(I) - r - a'X,)\nX = A X + bv a(s) = det(s1 - A ) = (s + k)R(s) (9) where A is asymptotically stable with a charactcristic polynomial a(.?), k > 0 and (A, h) is controllable. Then\n1. There exist h, such that\nmeasurable, the control of the dead-zone will be relatively easy. Assumption (A3) is also common for linear systems with dead-zones, which is reasonable in real systems.\n2 . if x=h'X, then: (i) X E L \" + X E L ~ ; and (ii) if lim,,,x(f)=O, then Iim,+\" X(t)=O\nBased on lemma 1, it is obviously from ( I O ) that there exist a /I, so that:\n3 Statement of the problem\nA dead-zone nonlinearity can be denoted as an operator\nW(t) = O(v(0) (2)\nwith v(t) being the input and w ( f ) the output. The operator D(v(t)) has been discussed in detail in the preceding Section. The dynamic system in a state spacc preceded by the above dead-zone can he described in canonical form as:\nX,,(t) = A,X,(t) + B 4 f ) (3)\nThe control objective is to let X,,(t) in (3) follow a reference signal X,,(t) defined as:\nXm(f) =A,X,(f) +Br(t ) (4)\nin which, r(t) is a specified desired trajectory input and A,,, is an asymptotically stable matrix in R\"\"\" with\ndet(s1 - A , ) = R,,,(r) = (s + k)R(s) k > 0 ( 5 )\nand R(s) being a Hunvitz polynomial. We have the following assumptions about system (3) and the reference modal (4):\n(A4) A , E R \" ~ \" is unknown, B ER\" is known, while (Ap, B ) is controllable with:\nA , + B ~ = A , (6)\nfor some unknown vector a E R \" .\nAssumption (A4) confines the type of systems to he considered to those that represent a number of systems of practical interest. An example system is discussed in Section 5.\n262\nThen, a scalar error IS defined as:\ne, = hTE (12) Form the Laplace transform of ( X ) , we have:\nE(s) = (SI - A,)- 'B(MJ(s) - T(S) - aX, (s ) )\nMultiply both sides with h'and applying (1 1) and (12), we have:\n1 s + k e, (s) = -(>*(A) - ~(s) - olx,(s))\nThus (8) is changed to:\ne, = -kec + ( ~ ( t ) - r - a'x,)\n4.1 In this case, v(t)= w(/), in (13), if we let: A known system without a dead-zone\nv( t ) = ~ ( t ) = r + arx, then we have\nc; =-Xe\nbecause k > O , which implies that et:+ 0 as f i w . According to lemma I , we have E + 0, that is to say that as f + 00, we have X , + X , .\n4.2 A known system with a known dead-zone We define the desired output of dead-zone wd(t) as:\nWd(f) = r + arx, It is obvious from (l4), that this wd(t) will lead X, + X,,,. Therefore, the task is to find v(t) so that the output of the\n/ \u20ac E Plac.-Conwl Theon Appl.. Vol. 150, No. 2. M q 2003", + "dead-zone satisfies W ( I ) = wd(f). For this purpose, we let the input of the known dead-zone be\n~ . -\nwhich will lead w(l) = ilid(f) To demonstrate the point, we introduce xr. xl and N as:\nI for wd( f ) b,\n0 otherwise\nI for wd(t) 5 b, 1 0 otherwise\nxr =\n%I =\nN = [%,2 &I And define\nH = [Or. HI]' = [m,b,, m,b,]'\nm = [m,. nil]\n(16) T\nThus the dead-zone of ( I ) can be written as:\nw(t) = D(v(t)) = Nmv(t) ~ N O (17)\nAnd we can rewrite (15) as\n' 0, if Bi = Bi,,, and ye, < 0\nif [L, < 6 < kn,l --..e ,, , or [ H i = O,,,, and ye, ? 01\nor [Hi = Himin and ye, 5 01 (26)\n. 0. if Oi = Oimin and ye, > 0 Substituting (15) into' (17) clearly shows w ( f ) = v v d ( f ) . Thus, the effect of the known dead-zone can be completely compensated and the same tracking performance as the preceding Section will he achieved.\n- 4.3 Unknown system with an unknown dead-zone As stated in assumption (A4), A , E R \" ~ \" is unknown, B E R \" is known, while (AP. E ) is controllable. What we do not know, is the unknown vector 01 ER\" in the matching condition (6).\nIn this case, we will use an adaptive controller to control the unknown system with the task of compensating the effect of the unknown dead-zone.\nBy defining the estimated value of Q as dr , we have the estimate error of 01\n(19) -~ O1=a-a\nAssume i)= [a,, 8,1T is the estimated valne of 8, and the estimate error is:\na - - 1 - \" 8 = 8 - 0 = [Or, 011\n= [m,b,, mIb,lr ~ [m,b,, m,b11' (20)\nDefine a slope ratio as\n0. if q5i = b,,,, and qe,n,. < 0\n-ilecn<,, or [Ji = 4i,,,ax and rle,n, ? 01 (27) if Mimi, < 4, < 4 i , \" , X l\nor [di = q$,,,in and iI&nv 5 01\nif 9; = 4imjn and q e p , > 0 . 0,\nAnd the estimated slope ratio is defined as\nwe have the estimate error of the slope ratio as\nFrom (17), the estimated dead-zone can be expressed as:\nW(f) = \"v ( t ) - N 6\nBased on the given plant and reference model as well as the dead-zone model subjecting to the assumptions descnhed above, the following control and adaptation laws are presented:" + ] + }, + { + "image_filename": "designv10_6_0003788_978-1-4020-5967-4-Figure7-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003788_978-1-4020-5967-4-Figure7-1.png", + "caption": "FIGURE 7. The compound pulley (Mechanics 2.12). Drachmann\u2019s drawing from Ms L is on the left (The Mechanical Technology, p. 70); the figure from Heronis Alexandrini opera, vol. II, p. 124, is on the right.", + "texts": [ + " If the weight is divided into two equal parts, each one will balance the other, just like the two weights suspended on the circumference of the larger circles in 2.7. This result is then generalized to cover multiple pulleys and ropes, yielding a precise quantitative relationship: the ratio of the known weight (t iql) to the force (quwwa) that moves it is as the ratio of the taut ropes that carry the weight to the ropes that the moving force (al-quwwat al-muh. arrikat ) moves.35 For example, in Fig. 7, each of the four lengths of rope stretched between the weight Z and the two pulleys on A carries \u00bc the total weight. If we imagine detaching the rightmost section of the weight Z from the sections G\u030cBT. , it will hold those sections in equilibrium. Thus a force equal to \u00bc the total weight of Z, applied at K, balances \u00be the total weight (G\u030cBT. ), and a slightly larger force will move it.36 In the case of the wedge and screw the similarity to the concentric circles is much less clear. Since Heron claims that the screw is simply a twisted wedge (2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure3.7-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure3.7-1.png", + "caption": "Fig. 3.7. Virtual displacement of coordinate q2", + "texts": [ + " We find the expression for the virtual work OAi of all active forces over that displacement. By definition, the coefficient of 8qi in the expression for the work represents the generalized force Qi. Let us note that the active forces are the drives and the gravity forces. We consider the mechanism shown in Figs. 3.4, 3.6. If q1 has a displacement oq1 then the work is done only by the driving torque P1. Thus, oA = P 1 oq1 and (3.3.15) Let now q2 have a displacement 8q2 while all other generalized coordi nates remain constant (Fig. 3.7). The virtual work is and the generalized force a Y2 + r'-m-2-.. -g~(-;;-2-X-r;-2-.. -:')-+-m-2-,-'i'-(-;;-2-X-(-r;-2-\"---1-2-.. -+-r;-2-'-) ..... ) (3.3.17) (3.3.18) 160 where Y~ is the component holding for the direct chain which can be computed from (2.3.57). Let now q3 have a virtual displacement oQ3 while other generalized co ordinates remain constant (Fig. 3.8). 161 (3.3.19 ) -+ -+ We conclude that e 2 = e 3 and thus (3.3.20) The generalized force is (3.3.21 ) (3.3.22) d where Y3 is the component holding for the direct chain which can be computed from (2" + ], + "surrounding_texts": [] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure1.16-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure1.16-1.png", + "caption": "Fig. 1.16. Workspace of RPR - structure", + "texts": [], + "surrounding_texts": [ + "12\n1 ~1 .13. Comparison of the workspaces of\ndifferent minimal configurations\nTo this end we will make the following assumptions:\npermissible rotation of each rotational connection is 3600 ,\n- translation of each prismatic connection equals L,\nthe \"principal\" (greatest) dimension of each segment of the manipu lation robot equals L.\nThe workspaces illustrated suppose some arbitrary wrist, the center of which, 0, is the reference pOint.\n(a) PPP structure\n(b) RPP - structure (or PRP)\nWorkspace is a cube of side L\nv\nWorkspace is a thorus of square cross-section of mean radius Land external radius 2L", + "13\nWorkspace is a hollow sphere of interior radius L and external ra dius 2L\nWorkspace is a cylinder of radius 2L and height L", + "14\nThis comparison demonstrates the evident superiority of the RRP and RRR structures, possessing a workspace approximatelly 30 times greater than the PPP - structure. The RPP and RPR - structures, with workspaces approximatelly 10 times greater, thus offer medium sized workspaces.\n1.2. General Remarks on Up-To-Date Methods for Design of Machines\n1.2.1. Task specification and starting data\nWe witness today a considerable growth of the complexity of problems that should be solved in the process of designing constructions and machines. Realization of machines of a qualitatively new level assumes the use of important achievements of fundamental sciences, design and technology, protection of servicing personnel against vibration, noise and injuries. The task of improving the quality of machines should be solved in the stage of design when it is necessary and possible to thoroughly consider a construction, i.e., take into account a large number of, frequently, contradictory requirements, such as a minimum mass providing a sufficient rigidity and a sufficient reliability, high-speed operation with a lower dynamic load, a low price and a long lifecycle, etc. In the design of machines and mechanisms it is neces sary to achieve an optimal choice of their parameters (structural, kinematic, dynamic, exploitative) which are best suited to the imposed, often numerous, requirements. In the present design practice this task is solved by studying a number of alternative variants and performing appropriate calculations. Elaboration of a large number of alternative variants, based on conventional approaches, connot, in principle, give to a designer the idea about machine capabilities. To illustrate this, let us say that, e.g., if ten different values are assigned to each of ten parameters, it follows that 10 10 variants-tasks should be solved, and this exceeds even the performances of contemporary computers.\nThe costs associated with solving such tasks by classical methods con stantly increase, and the negative effects of accepting nonoptimal so lutions become more and more serious. A further aggravating circum stance is the fact that these are multicriteria tasks with conflicting objective functions. It is therefore difficult for a designer to se lect a compromise solution applying the classical methods for finding the extremum, and most new optimization procedures are predetermined" + ] + }, + { + "image_filename": "designv10_6_0003726_978-3-642-82204-9-Figure3.23-1.png", + "original_path": "designv10-6/openalex_figure/designv10_6_0003726_978-3-642-82204-9-Figure3.23-1.png", + "caption": "Fig. 3.23. Gripper subject to a rotational joint constraint", + "texts": [ + " If friction is strong enough then there will be no sliding in points A1 and A;. In such case rolling or jamming will appear. Also, there can be a rolling with sliding. These problems are rather complex and they 194 will not be considered here. 3.4.8. Rotational joint constraint We consider a manipulator having the gripper connected to the ground, or to an object which moves according to a given lew, by means of a ->- joint permitting one rotation only. Let h be the unit vector of rotation axis (Fig. 3.23). Let us first discuss the prescribed motion of the object to which the gripper is connected. Let this motion be defined by (3.4.113) * * e = f4 (t) , (jJ = fS (t) , (3.4.114) * as was done in the previous Para. 3.4.7. Note that A = A here, and, * * * accordingly, xA = xA ' YA = YA' zA = zA. Thus we use A only. The joint * * connection also produces: e = e and (jJ = (jJ \u2022 The parameter * u 1); - 1); (3.4.11S) defines the relative position of the gripper with respect to the moving object. If a six d" + ], + "surrounding_texts": [] + } +] \ No newline at end of file