雅可比矩阵对并联机器人的速度、精度、刚度等性能分析有重要意义。通常雅可比分析需要计算与驱动关节运动螺旋不互易而与支链其他运动螺旋均互易的力螺旋,分析过程复杂,计算量大。为此,针对一类常见的特殊支链结构,提出正则支链的概念,研究了正则支链的结构特征。分析了转动副和移动副的做功驱动力螺旋,提出含正则支链的并联机器人雅可比简化分析方法,克服了现有方法中计算驱动关节产生的支链约束螺旋的复杂过程。这种方法不必计算支链约束螺旋就能获得并联机器人的部分雅可比矩阵,进而结合支链约束螺旋获得并联机器人的整体雅可比矩阵,实现驱动关节与动平台之间运动和力的双向映射。方法不仅适用于常见的6自由度并联机器人,也适用于具有正则支链的少自由度并联机器人。
Jacobian is significant to the analysis of kinematics, precision and stiffness of parallel manipulators. Usually the wrench, which is reciprocal to all the twists in a limb except the twist of the actuated joint, is needed for Jacobian analysis. The procedure to calculate this wrench, however, is quite complex. Hence, for the particular limb structures commonly used in parallel robots, a novel concept about the regular limbs is presented, and the limb structural characteristics are summarized. The actuating wrenches of the revolute and prismatic joints are studied, and the approach to simplify the Jacobian analysis of parallel robots is proposed based on the actuating wrenches, which overcomes the complex procedure in existing methods to calculate the limb constraint wrench produced by the actuated joint. The partial Jacobian matrix can be obtained without the calculation of the limb constraint wrenches, and the overall Jacobian matrix can be derived with these limb constraint wrenches to perform the kinematic and static bijection between actuated joints and the moving platform. The proposed method can not only apply to the common 6 DOF parallel robots, but also apply to the lower mobility parallel robots with regular limbs.
[1] 熊有伦,丁汉,刘恩沧. 机器人学[M]. 北京：机械工业出版社,1993.
XIONG Youlun,DING Han,LIU Encang. Robotics [M]. Beijing：China Machine Press,1993.
[2] MURRAY R M,LI Z,SASTRY S S. A mathematical introduction of robotic manipulation [M]. USA：CRC,1994.
[3] BU Wanghui,LIU Zhenyu,TAN Jianrong,et al. Detachment avoidance of joint elements of a robotic manipulator with clearances based on trajectory planning [J]. Mechanism and Machine Theory,2010,45：925-940.
[4] 卜王辉,刘振宇,谭建荣. 基于切断点自由度解耦的手腕偏置型6R机器人位置反解[J]. 机械工程学报,2010, 46(21)：1-5.
BU Wanghui, LIU Zhenyu, TAN Jianrong. Inverse displacement analysis of 6R robots with offset wrists based on decoupling degrees of freedom at the cutoff points [J]. Journal of Mechanical Engineering,2010,46(21)：1-5.
[5] 李玉航,梅江平,刘松涛,等. 一种新型4自由度高速并联机械手动力尺度综合[J]. 机械工程学报,2014,50(19)：32-40.
LI Yuhang,MEI Jiangping,LIU Songtao, et al. Dynamic dimensional synthesis of a 4-DOF high-speed parallel manipulator [J]. Journal of Mechanical Engineering,2014,50(19)：32-40.
[6] 任子武,王振华,孙立宁. 基于改进人工蜂群算法的并联机器人正运动学解[J]. 机械工程学报,2013,49(13)：48-55.
REN Ziwu,WANG Zhenhua,SUN Lining. Forward kinematics solution for parallel manipulators based on improved artificial bee colony algorithm [J]. Journal of Mechanical Engineering,2013,49(13)：48-55.
[7] JOSHI A S,TSAI L. Jacobian analysis of limited-DOF parallel manipulators [J]. ASME Journal of Mechanical Design,2002,124(6)：254-258.
[8] HUANG Zhen. The kinematics and type synthesis of lower-mobility parallel robot manipulator [C]// Proceedings of the 11th World Congress in Mechanism and Machine Science,April 1-4,2004,Tianjin,China.2004：65-76.
[9] ZHU S J,HUANG Z,DING H F. Forward/Reverse velocity and acceleration analysis for a class of lower-mobility parallel mechanisms [J]. ASME Journal of Mechanical Design,2007,129(4)：390-396.
[10] LU Yi,HU Bo. Unified solving Jacobian/Hessian matrices of some parallel manipulators with n SPS active legs and a passive constrained leg [J]. ASME Journal of Mechanical Design,2007,129(11)：1161-1169.
[11] HUANG T,LIU H T,CHETWYND D G. Generalized Jacobian analysis of lower mobility manipulators [J]. Mechanism and Machine Theory,2011,46(6)：831-844.
[12] HONG M B,CHOI Y J. Formulation of unique form of screw based Jacobian for lower mobility parallel manipulators [J]. ASME Journal of Mechanisms and Robotics,2011,3(1)：011002.
[13] 黄真,赵永生,赵铁石. 高等空间机构学[M]. 北京：高等教育出版社,2006.
HUANG Zhen,ZHAO Yongsheng,ZHAO Tieshi. Advanced spatial mechanism [M]. Beijing：Higher Education Press,2006.
[14] 戴建生. 机构学与机器人学的几何基础与旋量代数[M]. 北京：高等教育出版社,2014.
DAI Jiansheng. Geometrical foundations and screw algebra for mechanisms and robotics [M]. Beijing：Higher Education Press,2014.
[15] KONG X,GOSSELIN C. Type synthesis of parallel mechanisms [M].Berlin：Springer,2007.
