机械臂运动轨迹规划研究【物联网开题报告外文翻译说明书论文】.zip
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Science in China Series E: Technological Sciences 2009 SCIENCE IN CHINA PRESSCitation: Li Y B, Jin Z L, J S M. Design of a novel 3-DOF hybrid mechanical arm. Sci China Ser E-Tech Sci, 2009, 52(12): 35923600, doi: 10.1007/s11431-009-0293-zDesign of a novel 3-DOF hybrid mechanical armLI YanBiao1,2, JIN ZhenLin1 & JI ShiMing21 College of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, China2 Key Laboratory of Mechanical Manufacture and Automation, Zhejiang University of Technology, Hangzhou 310014, China;Parameter optimization for a novel 3-DOF hybrid mechanical arm was presented by using a statisticsmethod called the statistics parameters optimization method based on index atlases. Several kinematics and mechanics performance evaluation indices were proposed and discussed, according to the kinematics and mechanics analyses of the mechanical arm. Considering the assembly technique, a prototype of the 3-DOF hybrid mechanical arm was developed, which provided a basis for applications of the 3-DOF hybrid mechanical arm. The novel 3-DOF hybrid mechanical arm can be applied to the modern industrial fields requiring high stiffness, lower inertia and good technological efficiency.A novel 6-DOF hybrid humanoidmechanical arm was built,in which the present mechanical arm was connected with a spherical 3-DOF parallelmanipulator.Key word: 3-DOF hybrid mechanical arm;kinematics analyses; performance evaluation index; parameter optimization;1 IntroductionMechanical arms include serial, parallel and hybrid structures. The serial mechanical arm has advantages of flexible moving, big workspace, etc. Zhao1 developed TH1 arm, Morita2 the Wendy arm, and ABB3 the IRB series of mechanical arms. The parallel mechanical arm owns advantages of simple structure, lower inertia and high payload capacity4,5. SIG Company in Switzerland developed SIG XR22 parallel manipulator of high speed, Huang6 built a 2-DOF parallel manipulator which can move at high speed and Jin7 proposed the 4-DOF parallel mechanical arm. Hybrid structure such as the 7-DOF hybrid mechanical arm proposed by Gao8 owns all the above advantages. Parameters optimization is the basis for design of the mechanical arm911, and the proper parameters which can achieve good performance of the mechanical arm are very difficult to select. Therefore, parameters optimization by intuition and experience will be far from enough. Currently, there are two main ways including single-objective parameter optimization and multi-objective parameter optimization. The former aims at design with single performance. Su12 optimized the Stewart platform by using sensitivity as the objective function; Li13 adopted the workspace as the objective function to optimize a three-leg virtual machine tool. These methods do not consider other performance. The multiobjective parameter optimization uses several performance indices as the objective function to optimize the parameters of the manipulator. Stoughton optimized the improved Stewart platform by choosing the workspace and sensitivity as the objective function; Merlet proposed an optimization method which considered workspace and regarded other design objectives14. Lu15 optimized parameters of the Stewart platform by using the genetic algorithm. Based on the structural characteristics of human body, a novel 3-DOF hybrid mechanical arm and its statistics parameters optimization based on index atlases are proposed. Firstly, several kinematics and mechanics performance evaluation indices and its global performance evaluation indices are proposed based on the kinematics and mechanics analyses and the distributions of the evaluation indices in workspace and the index atlases are presented. Then considering the assembly technique, a prototype of the 3-DOF hybrid mechanical arm is developed by using the statistics parameters optimization based on the index atlases. It can provide a basis for applications of the 3-DOF hybrid mechanical arm. Compared with previous serial mechanical arms, the present arm uses 2-DOF parallel structure as the upper arm, as shown in Figure 1, in which two motors are connected with the fixed part in order to reduce the moving mass. Therefore, the mechanical arm owns advantages of high payload capacity and lower inertia and is suitable for humanoid robot, precision polishing, aviation, shipbuilding and automotive.Received November 12, 2008; accepted May 7, 2009 doi: 10.1007/s11431-009-0293-zCorresponding author (email: lyb781003) Supported by the National Natural Science Foundation of China (Grant No. 50575208), the Open Fund of Prime Important Discipline of Mechanical and Mechatronics Engineering (Grant No. 2009EP004), and the Fund of Yanshan University2 Description of the novel 3-DOF hybrid mechanical armThe novel mechanical arm is a planar 3-DOF hybrid manipulator, as shown in Figure 1. The detailed structure is described as follows: (1) The straight-line prismatic pair P1 is parallel with the straight-line prismatic pair P2, which connect with the fixed basement, and the vertical distance between P1 and P2 is a; (2) the straight-line prismatic pair P3 is parallel with O1O2 and its distance to O1O2 is m; (3) when O2G is perpendicular to P3 and is parallel with prismatic pair P1 and the input displacement of the 3-DOF hybrid mechanical arm is zero, the mechanical arm is on the initial assembly position. Li0 (i=1, 2, 3) is the initial length of the prismatic pair Pi (i=1, 2, 3). A novel 6-DOF hybrid humanoid mechanical arm16 was constituted, in which the present mechanical arm was connected to a spherical 3-DOF parallel mechanism.3 Inverse kinematicAs shown in Figure 1, three coordinate systems are set up: P-Oxy, fixed to the basement, is the absolute coordinate system; Q-O1x1y1 is the following coordinate system; R-O2x2y2 is the movable coordinate system, O2 expressed as (xy)T is the reference point of the mechanical arm, (xy)T is the rotational angle of the reference point O2, and the axis y2 is along O2G. The position vectors of A, B and O1 in P can be described asWhere l1 and l2 are the input displacements of P1 and P2, respectively.The position vectors of C, D, E, F and O2 in Q can be described asWhere l3 is the input displacement of P3, and d is the length of O1D.The position vector of G in R is According to the structure of the mechanical arm, its inverse kinematic equations can be described aswhere 1 is the rotational angle of Q about O1, 2 is the rotational angle of R about O2, 1 is the rotational angle of BC about B, 2 is the rotational angle of FG about F, as shown in Figure 2. The solutions of the inverse kinematic eq. (4) are given as Where3.1 Rotational constraints1 and 2 are the angles between BC and CO1, FG and GO2, respectively. So 1 and 2 can be obtained aswhere 1, 2, 1 and 2 are the unit vectors along the directions of BC, FG, CO1 and GO2, respectively, and 1 = (C B P P ) / , b 2 = (G F h P P ) / , 1 1 = (O C P P ) / , c 2 2 = (O G P P ) / e . The minimum angles of 1 and 2 are 1min and 2min, respectively, the maximum angles are 1max and 2max, respectively, then rotational angle constraints are obtained as3.2 Translation constraints of input prismatic pairsThe maximum and minimum input displacements of P1, P2 and P3 are Limax and Limin (i=1, 2, 3), respectively. Then input displacement constraints of the input prismatic pairs are given as4 Balance equations of kinematic transmissionV= (VxVyb) tdenotes the velocity vector of O2 inP which is supported by the end effecter of the mechanical arm, V= (V1V23)t denotes the input velocity vector, where vi is the value of the input velocity of Pi (i = 3,2,1) . With the driving of P1 and P2, the linear velocity vector of O1 isAfter differentiating the third and fourth equations in eq. (4) with respect to time, the angular velocity 1 of Q about O1 in P is obtained as1 = (v2 v1) / c cos (-1) - c sin (-1 )tan 1) (11)ThenwhereO1P and O2P are the position vectors of O1 and O2 in P, respectively.After differentiating the seventh and eighth equations in eq. (4) with respect to time, the rotational angular velocity of R about O2 is2=v3/(ecos2+esin2tan2). (13)Then with driving of P3, there is only the angular velocity vector for O2, which isB2= 2. (14)According to eqs. (10)(14), the linear and angular velocity vectors of O3 can be obtained aswhere VB = (VxVy )T . According to eqs. (10)(15), the transmission relationship between the input velocity and output velocity isV=JBv (16)where JBR33 is the velocity Jacobian matrix of the mechanical arm which can be described as5 Balance equations of force transmissionThe basement and parts are assumed to be rigid bodies and frictionless. F = (Fx Fy Mb)T denotes the output force vector, f = (f1 f2 f3)T denotes the driving force, where fi=(i=3,2,1) is the driving force along the direction of Pi =(i=3,2,1) . The relationship between f and F can be obtained by using the principle of virtual power. Let the end effecter endure the force F and lead to virtual displacement tB; then the virtual displacement of the input driver should be pB . Therefore, the total virtual work by f is6 Definition of performance evaluation indicesWhen the mechanical arm is not at the singular position, considering difference between the linear velocity and rotational velocity, eq. (16) can be rewritten asWhere JV and J are the first two row vectors and last row vector of JB , respectively. When the arm is at the non-singular position, J B is the auxiliary matrix, so JV can be decomposed by the auxiliary matrixes 22 RA BV and BV RB 33 , i.e.,Where 1V and 2V are the singular values of JV and 1V2V . Thus, in order to kinematics analyses, the input matrix is defined as a unit matrix, namelyEq. (27) denotes an ellipse17, whose axes lengths are the reciprocals of 1V and 2V . The ellipse is called the linear velocity transmission ellipse. When the input velocity is a unit vector, output linear velocity VB is located on the ellipse. When 1V equals 2V , the output velocity is located on a circle. Since JB is changed with the posture of moving platform, a quantitative index is needed to evaluate the velocity transmission performance of the mechanical arm. Therefore, the evaluation index of the linear velocity transmission performance index KV and the rotational velocity transmission performance index K are defined asFrom Figures 3 and 4, it is seen that when the mechanical arm is in the middle of workspace, values of evaluation indices of the linear velocity transmission performance index and force transmission performance index are quite small, and when the arm is near the edges, the values are large; when the mechanical arm is in the middle of workspace, values of evaluation indices of rotational velocity transmission performance indexand torque transmission performance index are large, and when the arm is near the edges, the values are small. Figure 3 Distributions of KV and K in workspace. (a) Distribution of KV (m/s) when =90; (b) Distribution of Kv (rad/s) when =907 Parameter optimization7.1 Performance evaluation index atlasesThe physical model technique is a useful tool for design of mechanisms. By using the physical model technique and performance index, the performance index atlases of mechanisms which are used to analyze the relationships between the performance index and geometric parameters of mechanisms18 are constructed. The mechanical arm includes an upper arm and forearm, with a length ratio of the upper arm and forearm being 1.3. As shown in Figure 1, a, b, c and are the parameters of the upper arm and d, h and e are the parameters of the forearm. The relationship between c and isThe parameters of the upper arm and forearm are independent. In order to analyze conveniently, models of solutions for the upper arm and forearm are built respectively. DefineRegard r 1 , r2 , r3 and r 1 , r2 , r3 as coordinate axes. By eq. (36), the solutions of the models for the upper arm and forearm can be constructed as isosceles trapezoids H K R and H K R as shown in Figure 5(a), respectively. Within the model, the relationships between the index and parameters of the mechanical arm can be investigated. For convenience, the isosceles trapezoids H K R and H K R in the r 1 , r2 , r3 and r 1 , r2 , r3 coordinate system can be changed into the isosceles trapezoids H K R and H K R in the x-y coordinate system as shown in Figure 5(b) by using the following equations:Using eqs. (29), (32) and (33)(38), the atlases of the global evaluation index of the linear velocity transmission performance index, rotational velocity transmission performance index, force transmission performance index and torque transmission performance index are plotted on the solution space model of the mechanical arm as shown in Figures 6 and 7.Figure 5 Solutions of models for upper arm and forearm of 3-DOF hybrid mechanical arm.Figure6 Global velocity index atlases. (a) Atlases of global linear velocity transmission performance indexes of upper arm (m/s); (b) atlases of global rotational velocity transmission performance indexes of upper arm (rad/s); (c) atlases of global rotational velocity transmission performance indexes of forearm (rad/s).Figure 7 Global force index atlases. (a) Atlases of global force transmission performance indexes of upper arm (N); (b) atlases of global torque transmission performance indexes of upper arm (N.m); (c) atlases of global force transmission performance indexes of forearm (N); (d) atlases of global torque transmission performance indexes of forearm (N.m).7.2 Design of the novel 3-DOF hybrid mechanical armA statistics parameter optimization method is presented for multi-objective function of the mechanical arm. The method aims at multiple parameters which have uniformly distributed characteristics, and regards the values of multiple evaluation indices as objectives. Then it selects proper parameters according to the model calculation and distribution regulation of the values of the statistical sampling. According to Figures 6 and 7, the maximums and minimums of RV, R, RFB and RMB are 0.8115 m/s, 0.2135 rad/s, 2.1231 N, 0.4521 Nm and 0.1052 m/s, 0.0412 rad/s, 0.4988 N, and 0.1032 Nm, respectively. Considering the mechanical arm structure characteristics,ranges of the parameters are supposed to be as follows: minimums of a, b, c, d, h, e are 80, 100, 80, 210, 80, 80 mm, respectively, and maximums of a, b, c, d, h, e are 200, 300, 150, 450, 200, 200 mm, respectively. From eqs. (33)(38), the relationship between the parameters and space model parameters are as follows: 26.67 a 66.67, 33.33 300.00, b 26.67 c 50.00, 70.00 150.00, d 26.67 66.67 h and 26.67 e 66.67. Consider the middle values of the performance indices as the design target, that is, RV=0.3531 m/s, R=0.0861 rad/s, RFB=0.8121 N, and RMB=0.1744 Nm. When RV0.3531 m/s, R0.0861 rad/s, RFB0.8121 N, and RMB0.1744 Nm, the performance indices are better for the samples according to the uniform distribution within range of the parameters. Figure 8 shows distributions for the parameters optimization when the performance indices are better. The horizontal coordinate axis in Figure 8 represents the dimensions of a, b, c, d, h, e, respectively. f (a), f (b), f (c), f (d), f (h) and f (e) represent probabilities of being better than design targets. When one parameter is constant, other parameters change within their ranges, so the evaluation indices of the multidimensions are available. Then, ratios of number of groups of parameters which are better than design targets to number of total groups of parameters are counted. According to Figure 8, when parameters of the mechanical arm are a=130, b=150, c=135, d=300, h=180 and e=90, the values of f (a), f (b), f (c), f (d), f (h) and f (e) are quite high. Considering the assembly technique,Figure 8 Histograms of parameter design of arm structure.a 3-DOF mechanical arm is designed, and the mechanical arm is fixed to the moving platform of the shoulder joint; the forearm is assembled at the side of the upper arm in order to make the center of gravity of grasped object and rotational center of the shoulder joint are on the same plane. Figures 9 and 10 show the design scheme and the prototype of the 3-DOF hybrid mechanical arm.Figure 9 Design scheme of the 3-DOF mechanical arm. 1, Basement of upper arm; 2, 3 and 5, motors; 4 and 15, guides of upper arm; 11 and 14, slides of upper arm; 6, basement of forearm; 7, slide; 8, guide; 9, wrist pushing rod; 10, wrist connecting part; 12, elbow connecting part; 13, elbow pushing rod.8 ConclusionA novel 3-DOF hybrid humanoid mechanical arm and its statistics parameters optimization method based on index atlases were presented. Several kinematics and mechanics performance evaluation indices and its global performance evaluation indices were proposed basedupon kinematics and mechanics analyses of the mechanical arm, the distributions of the evaluation indices in workspace and index atlases were also plotted. Considering the assembly technique, the prototype of the 3-DOF hybrid mechanical arm was designed by using the statistics parameters optimization method based on index atlases, it provides a basis for applications of the 3-DOF hybrid mechanical arm. Due to flexible movement, high payload capacity, lower inertia, good technological efficiency, etc. the mechanical arm is suitable for humanoid robot, precision polishing, aviation, shipbuilding and automotive.Reference documentation:1 Zhao D B, Yi J Q, Zhang W Z, et al. Arms kinematics on a humanoid robot TH-1 (in Chinese). Robot, 2002, 24(6): 5025072 Morita T, Iwata H, Sugano S. Human symbiotic robot design based on division and unification of functional requirements. IEEE Inter Con ference Robotics Automation. San Francisco: IEEE, 2000, 3: 2229 22343 Ostring M, Gunnarsson S, Norrlof M. Closed-loop identification of an industrial robot containing flexibilities. Control Eng Pract, 2003, 11(3): 2913004 Huang Z, Zhao Y S, Zhao T S. Advanced Spatial Mechanism (in Chinese). Beijing: Higher Education Press, 2006. 3263855 Kim D, Chung W K. Kinematic condition analysis of three-DOF pure translational parallel manipulators. ASME J Mech Des, 2003, 125(7): 3233316 Zhao Y J. Dynamic Design Theory and Methodology of the High speed and Light-weight Parallel Robot (in Chinese). Dissertation of the Doctoral Degree. Tianjin: Tianjin University, 2006. 110 7 Jin Z L, Li Y B. 4-DOF parallel mechanical arm (in Chinese). China Patent, CN200610012824.68 Liu X J, Wang J S, Gao F, et al. Design of a serial-parallel 7-DOF redundant anthropomorphic arm (in Chinese). China Mech Eng, 2002, 13(2): 1021049 Rao N M, Rao K M. Dimensional synthesis of a spatial 3-RPS parallel manipulator for a prescribed range of motion of spherical joints. Mech Mach Theor, 2009, 44(2): 47748610 Huang T, Li Y, Li S W, et al. Error modeling, sensitivity analysis andassembly process of a class of 3-DOF parallel kinematic machines with parallelogram struts. Sci China Ser E-Tech Sci, 2002, 32(5):62863511 Liu H T, Mei J P, Zhao X M, et al. Inverse dynamics and servomotor parameter estimation of a 2-DOF spherical parallel mechanism. Sci China Ser E-Tech Sci, 2008, 51(3): 28830112 Su Y X, Duan B Y. Optimization design of structural parameters on Stewart platform based on genetic algorithm. Mach Des, 2000, 17(9): 101213 Li B, Cai G Q. Parameter design of the virtual axis machine tool based on workspace and genetic algorithm. Mech Sci Tech, 2000, 19(2): 24624814 Lu Q. Research on Designing Theory and Method of Stewart-Platform Based Machine Tool (in Chinese). Dissertation of the Doctoral Degree. Nanjing: Nanjing University of Technology and Engineering, 2001. 355215 Hao F, Merlet J P. Multi-criteria optimal design of parallel manipulators based on interval analysis. Mech Mach Theor, 2005, 40(2): 15717116 Jin Z L, Li Y B, Wang Y L. A 6-DOF hybrid mechanical arm (in Chinese). China Patent, 200620025075.617 Xiong Y L. Robotics (in Chinese). Beijing: Machinery Industry Press, 1993. 10711318 Gao F. The relationships between the shapes of the workspaces and the link lengths of 3-DOF symmetrical parallel manipulators. Mech Mach Theor, 2001, 36(2): 205220 中国科学E辑：技术科学2009中国科学出版社引用：Li Y B, Jin Z L, J S M的一种新型3-DOF混联机械臂设计。中国科学：易达科技，2009，52（12）：35923600，DOI: 10.1007/s11431-009-0293-z 一种新型3-DOF的混联机械臂李彦彪1,2， 金振林1和纪世明21大学燕山大学机械学院，秦皇岛0660042机械制造与自动化重点实验室，浙江工业大学，杭州310014摘要： 一种新型三维混合机械臂参数优化是通过一种称为统计参数优化方法来介绍指标，根据机械臂的运动学和力学分析，提出并讨论了力学性能评价指标，考虑装配技术，对一个原型三自由度混合机械臂的开发，来为三自由度混合机械手臂应用提供依据。新型三自由度混合机械臂可以应用于现代工业刚度方面，惯性小、工艺性好，最后建立了新型六自由度的机械臂，并与目前的机械臂和球形铝三自由度进行并联组合。关键词：三自由度；机械臂；运动学分析；参数优化；1引言机械臂结构包括串行，并行和混合。串行机械臂具有移动灵活，工作空间大等优点，赵 1 推进了机械臂的发展，森田 2 中温迪的机械臂，和ABB 3 中机械臂的IRB系列。并联得机械手具有结构简单、惯性小、载荷力高。随着瑞士SIG公司的大步发展，高速信号xr22并联机械手，黄 6 建立了一个二自由度并联机器人，它可以高速运行。金 7 提出了机械臂。7-DOF混合机械臂采用高 8 提出的混合结构，它拥有以上所有的优点。参数优化是在机械臂 11 设计的基础上，用适当的参数可实现机对性能好的械臂的选择，虽然比较困难。因此，凭直觉和经验想实现参数优化，将远远不够。目前，主要有2种方式实现对单目标和多目标的参数优化。前者的目的在于设计单性能。苏 12 斯图尔特平台采用灵敏度优化，以TY为目标函数；李 13 采用工作空间来优化目标函数，得到虚拟机床。是在不考虑其他性能的基础上。多目标的参数优化是使用多个性能指标来实现。在斯托顿优化改进后的斯图尔特平台上，最后选择以ACE和灵敏度为目标函数；提出一个优化的方法，考虑空间及其他设计目标 14 。斯图尔特利用遗传算法的价值来优化参数鲁 15 。基于人体结构的特点，一种新型的三自由度混合机械臂，及其基于指数图谱提出的统计参数优化。首先，在运动学和力学分析的基础上，提出了若干运动学和力学性能评价指标及其全局性能评价指标，也提出了在工作区评价指标的模型和指标图谱。然后在考虑装配技术后，基于指数图谱统计参数的优化后，实现对三自由度混联机械臂的机制应用。它为三自由度混联机械臂的应用提供了基础。与以前的串行机械臂相比，本RM采用上臂并联结构，如图1所示，其中两电机用固定部分相连接，减少移动惯性。因此，机械手臂拥有高负载能力和较低的惯性，才很适用于仿真机器人，应用于精密抛光、航空、造船和汽车。 接收于2008年11月12日；在2009年5月7日通过，DOI：10.1007/s11431-009-0293-z通讯作者（电子邮件：lyb781003）由中国国家自然科学基金资助（GRANT 50575208号），由机械和机电工程学科开放基金（批准号：2009ep004），和燕山大学基金。 2等级三自由度机械臂的描述混合新的机械臂是一种平面三自由度混联机械手，如图1所示。体结构如下：（1）战略飞行线移动副P1与P2的平行直线移动副，连接与固定基底，P1和P2之间的垂直距离是一个；（2）直线棱镜对P3与O1O2，O1O2距离十分米的平行；（3）当O2g垂直移动副P3与P1和三自由度机械臂并联混合输入位移是零，机械臂在初始装配位置。（i = 1，2 Li0，3）是棱镜对PI的初始长度（i = 1，2，3）。一种新型6-DOF拟人机械臂 16 构成，在目前的机械臂被连接到一个球面并联机构。3反向运动如图1所示，三套坐标系： p Oxy，固定到地下室，是绝对坐标系统；问 - o1x1y1如下坐标系；R - o2x2y2是动坐标系，O2表示为（XY）T是机械臂的参考点，（XY）T是R的旋转角度参考点O2，和轴Y2沿着O2g。一位向量，B和O1 P在 可以描述为分别在L1和L2是P1和P2输入位移。丙，丁，氟和氧在Q的位置矢量可以被描述为在L3是P3的输入位移，和D是老的长度。G在R的位置矢量根据机械臂的结构，其逆运动学方程可以描述为在1是重置关于O1的旋转角度，2是Q对O2的旋转角度，1是约公元前B的旋转角度，2 FG关于F的旋转角度，如图2所示的解决方案给出逆运动学方程（4）得到3.1 转动约束1和2 BC和CO1之间的角度，FG和GO2，分别。因此，可以得到2和1的在1，2、1和2是单位向量沿BC，FG的方向，分别为CO1和CO2，和1 =（C P P），B2 =（G F H P）/ 1 = 1，（O C P P）/ 2 = 2，C（O G P P）/电子。1和2 最小角1min和2min，分别最大角度1和2max，分别，然后得到了旋转角度的限制3.2输入棱镜对平移约束最大和最小输入位移的P1，P2和P3是Limax and Limin (i=1, 2, 3)，分别为。然后输入的输入棱镜对的输入位移约束4运动传动的平衡方程V =（vxvyB）在 P O2的速度矢量是由机械臂末端执行器的支持，。V =（V1V23）T为输入矢量，其中VI是PI的输入速度值（i= 3,2,1）,与P1和P=的驱动，O1的线速度矢量在区分第三和第四方程Eq.（4）相对于时间，角速度Q对O1 P得到1 = (v2 v1) / c cos (-1) - c sin (-1 )tan 1) (11)然后分别是o1p和O2p是O1和O2在 p 的位置向量。在区分第七和第八方程Eq.（4）相对于时间的R，对O2的旋转角速度2=v3/(ecos2+esin2tan2). (13)然后用驱动P3，只有角速度矢量为O2，这是B2= 2. (14)根据方程（10）（14），线性和角速度矢量可以得到O3其中VB =（vxvy）T。根据方程。（10）（15），输入速度和输出速度之间的传导关系V=JBv (16)在JBR33是机械臂，可谓速度可比矩阵5力传递的平衡方程地下室部分被假定为刚体和摩擦。F =（fx fy MB）T表示输出力矢量，F =（F1 F2 F3）T为驱动力，其中fi =（I = 3,2,1）是驱动力的方向沿着Pi（i = 3,2,1）。利用虚功率原理，可以得到与之相关的关系。让末端执行器的忍受力F和导致虚拟位移；然后输入驱动的虚拟位移应铅。因此，总的虚拟工作由6绩效评估指标的定义当机械臂不在奇异点的位置，考虑到线性速度和旋转速度的差异，公式（16）可以改写为分别在JV和J是前两行向量和JB最后一行向量。当手臂在非奇异位置，即JB是辅助矩阵，所以企业可以通过辅助矩阵22RA BV及BVRB33分解在1V 2V和是JV和1V 2V奇异值。因此，为了进行运动学分析，输入矩阵被定义为一个单元矩阵，即Eq表示一个椭圆 17 ，其轴的长度是1V和2V的倒数。椭圆称为线速传输椭圆。当输入速度是单位向量，输出线性速度VB位于椭圆。当1V等于2V，输出速度位于圆。因为JB与动平台位姿变化，定量指标评估需要机械臂的速度传输性能。因此，评价指标的线性速度传输性能指标千伏和旋转速度传输性能指数的定义为从图3和图4中看到，当机械臂处于工作空间中时，线性速度传递性能指标和力传递性能指标的评价指标均较小，当手臂靠近边缘时，值是大的；当机械臂在工作空间中的旋转速度，传输性能和扭矩传输性能指标评价指标值大，当T他手臂在边缘附近，值很小。图3：当=90时的传输性能描述7参数优化7.1绩效评价指标图谱物理模型技术是一种有用的工具，设计机制。利用物理模型技术和性能指标，这是用来分析的性能指标和机制 18 几何参数之间的关系机制的性能指标图谱的构建。机械臂包括上臂和前臂，上臂和前臂的长度比为1.3。如图1，所示，B，C和是上臂的参数和D、H、E是前臂的参数。C、之间的关系上臂和前臂的参数是独立的。为了便于分析，分别建立了上肢和前臂的解的模型。定义为以1，R2 R3，和R 1”，R2 “R3”，作为坐标轴。由式（36），该解决方案的模型的上臂和前臂可以构造等腰梯形H K R和H “K “R”如图5（a）。在模型中，机械臂的指数和参数之间的关系可以被调查。为方便起见，等腰梯形H K R和H K R在R 1，R2 R3，和R 1” ”，R2，R3坐标系统可以转化为等腰梯形H K R” ” ”H K R” ” ”在X-Y坐标系如图5（b）利用下列方程：使用均衡器。（29）、（32）和（33）（38），对线性速度传输
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