Abstract:For the redundantly actuated parallel robot with both translational and rotational degrees of freedom (DOFs), anoptimal design method is proposed. Firstly, a parallel robot bio-inspired by human jaw is introduced, with a 6-PUS (prismaticuniversal-spherical) parallel mechanism imitating 6 main masticatory muscles and 2 passive HKPs (higher kinematic pairs) imitating mandibular joints. As characteristics of the mechanism with passive HKPs are considered, the dimensionallyhomogeneous Jacobian matrix of the robot is established by using the pose description method based on the three points onthe end-effector. Then, an optimization method of the redundantly actuated parallel robot is given, based on analyses on howthe velocity error transmission performance is effected by the structure and dimension of the robot. Finally, the performanceindex is set to perform the dimension optimization of the redundantly actuated parallel robot. The global error standarddeviation decreases by 39.83% compared with that of the robot configuration before optimization. The results show that theproposed optimal design method improves the velocity transmission performance of the parallel mechanism, and it can beextended and applied to the optimal design of other robots.
[1] Yoshikawa T. Manipulability of robotic mechanisms[J]. International Journal of Robotics Research, 1985, 4(2):3-9. [2] Tsai L W, Joshi S. Kinematics and optimization of a spatial 3-UPU parallel manipulator[J]. Journal of Mechanical Design, 2000, 122(4):439-446. [3] Badescu M, Mavroidis C. Workspace optimization of 3-legged UPU and UPS parallel platforms with joint constraints[J]. Journal of Mechanical Design, 2004, 126(2):291-300. [4] Gosselin C M. The optimum design of robotic manipulators using dexterity indices[J]. Robotics and Autonomous Systems, 1992, 9(4):213-226. [5] Kim S G, Ryu J. New dimensionally homogeneous Jacobian matrix formulation by three end-effector points for optimal design of parallel manipulators[J]. IEEE Transactions on Robotics and Automation, 2003, 19(4):731-736. [6] Pond G, Carretero J A. Formulating Jacobian matrices for the dexterity analysis of parallel manipulators[J]. Mechanism and Machine Theory, 2006, 41(12):1505-1519. [7] Fattah A, Ghasemi A M H. Isotropic design of spatial parallel manipulators[J]. International Journal of Robotics Research, 2002, 21(9):811-824. [8] Xu L M, Chen Q H, He L Y, et al. Kinematic analysis and design of a novel 3T1R 2-(PRR)2RH hybrid manipulator[J]. Mechanism and Machine Theory, 2017, 112:105-122. [9] Liu H, Huang T, Chetwynd D G. A method to formulate a dimensionally homogeneous Jacobian of parallel manipulators[J]. IEEE Transactions on Robotics, 2011, 27(1):150-156. [10] Chen C, Angeles J. Generalized transmission index and transmission quality for spatial linkages[J]. Mechanism and Machine Theory, 2007, 42(9):1225-1237. [11] Marlow K, Isaksson M, Nahavandi S. Motion/force transmission analysis of planar parallel mechanisms with closed-loop subchains[J]. Journal of Mechanisms and Robotics, 2016, 8(4). DOI:10.1115/1.4033158. [12] Wang J S, Wu C, Liu X J. Performance evaluation of parallel manipulators:Motion/force transmissibility and its index[J]. Mechanism and Machine Theory, 2010, 45(10):1462-1476. [13] 陈学生,陈在礼,孔民秀. 并联机器人研究的进展与现状[J].机器人,2002,24(5):464-470.Chen X S, Chen Z L, Kong M X. Recent development and current status of Stewart platform research[J]. Robot, 2002, 24(5):464-470. [14] 李晓成,高涛,代小林. 重载冗余六自由度并联机构优化设计[J].机器人,2013,35(6):731-735.Li X C, Gao T, Dai X L. Optimal design for redundant 6-DOF parallel mechanism with heavy load[J]. Robot, 2013, 35(6):731-735. [15] Zhu Z S, Dou R L. Optimum design of 2-DOF parallel manipulators with actuation redundancy[J]. Mechatronics, 2009, 19(5):761-766. [16] Liang D, Song Y M, Sun T, et al. Optimum design of a novel redundantly actuated parallel manipulator with multiple actuation modes for high kinematic and dynamic performance[J]. Nonlinear Dynamics, 2016, 83:631-658. [17] Shin H, Lee S, In W, et al. Kinematic optimization of a redundantly actuated parallel mechanism for maximizing active stiffness and workspace using Taguchi method[C]//ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering. New York, USA:ASME, 2009:607-617. [18] Li Q C, Zhang N B, Wang F B. New indices for optimal design of redundantly actuated parallel manipulators[J]. Journal of Mechanisms and Robotics, 2017, 9(1). DOI:10.1115/1. 4035126. [19] Xie F G, Liu X J, Wang J S. Performance evaluation of redundant parallel manipulators assimilating motion/force transmissibility[J]. International Journal of Advanced Robotic Systems, 2011, 8(5). DOI:10.5772/50904. [20] Xie F G, Liu X J, Zhou Y H. Optimization of a redundantly actuated parallel kinematic mechanism for a 5-degree-of-freedom hybrid machine tool[J]. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 2014, 228(12):1630-1641. [21] 温海营,丛明,王贵飞,等. 冗余驱动仿下颌运动机器人工作空间分析及试验验证[J].机器人,2015,37(3):286-297.Wen H Y, Cong M, Wang G F, et al. Workspace analysis and experimental verification of redundant actuated mandible motion robot[J]. Robot, 2015, 37(3):286-297. [22] Merlet J P. Jacobian, manipulability, condition number, and accuracy of parallel robots[M]//Springer Tracts in Advanced Robotics, Vol.28. Berlin, Germany:Springer, 2006:175-184.