含柔性运动副欠驱动机构运动学和动力学求解的数值迭代算法

doi:10.3901/JME.2018.13.066

机械工程学报 ›› 2018, Vol. 54 ›› Issue (13): 66-72.doi: 10.3901/JME.2018.13.066

• 特邀专栏：柔性机构及机器人 • 上一篇下一篇

含柔性运动副欠驱动机构运动学和动力学求解的数值迭代算法

张建军, 杜春翠, 杨高炜, 李为民

河北工业大学机械工程学院天津 300130

收稿日期:2017-07-25 修回日期:2017-12-22 出版日期:2018-07-05 发布日期:2018-07-05
作者简介:张建军,男,1971年出生,博士,教授,博士研究生导师。主要研究方向为机器人机构学。E-mail:zhjjun96@139.com;杜春翠,女,1990年出生,硕士研究生。主要研究方向为机器人机构学。E-mail:1351716146@qq.com;杨高炜,男,1984年出生,博士研究生。主要研究方向为机器人机构学。E-mail:ygw19841127@163.com;李为民,男,1964年出生,博士,教授,博士研究生导师。主要研究方向为数控并联装备设计理论。E-mail:vmin@163.com
基金资助:
国家自然科学基金资助项目（51175144）。

Numerical Iterative Algorithm for Solving Kinematics and Dynamics of Under-actuated Mechanisms with Flexible Joints

ZHANG Jianjun, DU Chuncui, YANG Gaowei, LI Weimin

School of Mechanical Engineering, Hebei University of Technology, Tianjin 300130

Received:2017-07-25 Revised:2017-12-22 Online:2018-07-05 Published:2018-07-05

摘要/Abstract

摘要： 欠驱动机构运动学和动力学约束不完整，机构运动具有不确定性，欠驱动机构引入柔性运动副后可利用其弹性反力一定程度上弥补动力学约束的不完整，但机构的运动学和动力学求解依然困难。针对该问题，以含有柔性移动副的平面2自由度欠驱动机构为研究对象，提出一种运动学动力学求解的数值迭代算法。在运动学、动力学建模的基础上，给定各构件的初始运动条件及原动件的运动规律，基于时间无限细分时两个时刻区间内速度和加速度不变的原理进行迭代和求解，能够得到各构件的运动规律及原动件的驱动力（力矩）。利用Matlab对该机构进行了求解，并分析了柔性移动副刚度对方程求解的影响。所提出的数值迭代算法在一定程度上突破了这类机构深入研究的瓶颈。

关键词: 欠驱动机构, 柔性运动副, 数值迭代算法, 运动学及动力学

Abstract: The kinematic and dynamic constraints of under-actuated mechanism are incomplete and its movement is uncertain. The elastic reaction of flexible joints involved in an under-actuated mechanism can make up for the incompleteness of dynamic constraints in a way, but the kinematics and dynamics equations are still unsolvable. To solve this problem, a planar 2-DOF under-actuated mechanism with a flexible joint, as an example, is analyzed. A numerical iterative algorithm is proposed to solve the kinematics and dynamics. Based on the kinematics model and dynamics model, the initial conditions of all the components and the motion law of the active joint are given. In the course of numerical iteration, considered the theory that velocity and acceleration is the same in an extremely brief period, the motion laws of all the components and the driving force/torque of the active joint can be obtained. Based on Matlab programming, the kinematics and dynamics equation is solved, and the relationship between the flexible joint stiffness of the flexible joint and the driving torque is analyzed. Also, the equations solution influenced by the flexible joint stiffness is analyzed. This numerical iterative algorithm will break through the bottleneck of the further study of this kind of mechanisms to a certain extent.

Key words: flexible joint, iterative algorithm, kinematics and dynamics, under-actuated mechanism

中图分类号:

TH112

张建军, 杜春翠, 杨高炜, 李为民. 含柔性运动副欠驱动机构运动学和动力学求解的数值迭代算法[J]. 机械工程学报, 2018, 54(13): 66-72.

ZHANG Jianjun, DU Chuncui, YANG Gaowei, LI Weimin. Numerical Iterative Algorithm for Solving Kinematics and Dynamics of Under-actuated Mechanisms with Flexible Joints[J]. Journal of Mechanical Engineering, 2018, 54(13): 66-72.

参考文献

[1] 于靖军,郝广波,陈贵敏,等. 柔性机构及其应用研究进展[J]. 机械工程学报, 2015, 51(13):53-68. YU Jingjun, HAO Guangbo, CHEN Guimin, et al. State-of-art of compliant mechanisms and their applications[J]. Journal of Mechanical Engineering,2015, 51(13):53-68.
[2] KATAKE A B, MAHINDRAKAR A D, BANAVAR R N. Study of underactuated mechanisms in the presence of holonomic constraints:The constrained Acrobot[C]//Proceedings of IEEE International Conference on Industrial Technology, 2000:703-706.
[3] 熊培银,赖旭芝,吴敏. 一类二阶非完整平面欠驱动机械系统位姿控制[J]. 东南大学学报, 2015, 45(4):690-695. XIONG Peiyin, LAI Xuzhi, WU Min. Position and attitude control for a class of planar underactuated mechanical system with second order non-holonomic constraints[J]. Journal of Southeast University, 2015, 45(4):690-695.
[4] AMOOZGAR M R, SHAHVERDI H. Analysis of nonlinear fully intrinsic equations of geometrically exact beams using generalized differential quadrature method[J]. Acta Mechanica, 2016, 227(5):1265-1277.
[5] 刘善增,余跃庆,杨建新,等. 3-RRC并联柔性机器人的动力学分析[J]. 振动与冲击, 2008, 27(2):157-161. LIU Shanzeng, YU Yueqing, YANG Jianxin, et al. Dynamic analysis of a 3-RRC parallel flexible manipulator[J]. Journal of Vibration and Shock, 2008, 27(2):157-161.
[6] FAZEL M R, MOGHADDAM M M, POSHTAN J. Application of GDQ method in nonlinear analysis of a flexible manipulator undergoing large deformation[J]. Proceedings of the Institution of Mechanical Engineers, Part C:Journal of Mechanical Engineering Science,2013, 227(12):2671-2685.
[7] 李美之,钟伟芳,吴国荣,等. 一种求解柔性操纵器动力学方程的数值方法[J]. 华中科技大学学报, 2004, 32(8):25-27. LI Meizhi, ZHONG Weifang, WU Guorong, et al, A numerical method for solving the dynamic equations of the flexible manipulator[J]. Journal of Huazhong University of Science and Technology, 2004, 32(8):25-27.
[8] METTIN U, LA H P X, FREIDOVICH L B, et al. Parallel elastic actuators as control tool for preplanned trajectories of underactuated mechanical systems[J]. The International Journal of Robotics Research, 2009, 29(9):1186-1198.
[9] LORIA A. Observers are unnecessary for output-feedback control of lagrangian systems[J]. IEEE Transactions on Automatic Control, 2016, 61(4):905-920.
[10] MUJUMDAR A, TAMHANE B, KURODS,. Observer-based sliding mode control for a class of noncommensurate fractional-order systems[J]. Mechatronics, IEEE/ASME Transactions on Mechatronics, 2015, 20(5):2504-2512.
[11] BAUER F, ROMER U, FIDLIN A, et al. Optimization of energy efficiency of walking bipedal robots by use of elastic couplings in the form of mechanical springs[J]. Nonlinear Dynamics, 2016, 83(3):1275-1301.
[12] ATEN Q T, ZIRBEL S A, JENSEN B D, et al. A numerical method for position analysis of compliant mechanisms with more degrees of freedom than inputs[J]. Journal of Mechanical Design, 2010, 133(6):491-502.
[13] 陈炜,余跃庆,张绪平,等. 欠驱动柔性机器人的动力学建模与耦合特性[J]. 机械工程学报, 2006, 42(6):16-23. CHEN Wei, YU Yueqing, ZHANG Xuping, et al. Dynamic modeling and coupling of underactuated flexible robot[J]. Chinese Journal of Mechanical Engineering, 2006, 42(6):16-23.
[14] 田富洋,吴洪涛,赵大旭,等. 柔性多体系统混合递推动力学建模及实时仿真研究[J]. 中国机械工程, 2010, 21(1):6-12. TIAN Fuyang, WU Hongtao, ZHAO Daxu, et al. Hybrid dynamics of flexible multibody system and real time simulation[J]. China Mechanical Engineering, 2010, 21(1):6-12.

含柔性运动副欠驱动机构运动学和动力学求解的数值迭代算法

Numerical Iterative Algorithm for Solving Kinematics and Dynamics of Under-actuated Mechanisms with Flexible Joints

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