中文摘要：

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。

英文摘要：

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.