Abstract The kinematics and design for “quasi-isotropy” of a class of 6R serial manipulators, with joint axes intersecting pairwise, are investigated. This is a subset of manipulators with reduced wrists, offering higher load-carrying capacity and maneuverability when compared with their spherical counterparts. A concise symbolic expression for the inverse of the Jacobian matrix is derived, the terms involved bearing a clear geometric meaning. This expression is shown to bring about high robustness to the kinematic analysis even when the robot finds itself close to a singularity. Moreover, a concise singularity expression is derived while incorporating simplifications due to the special geometry. Furthermore, the meaningful expressions are also useful for design optimization, based on which the design for isotropy and quasi-isotropy is investigated; the complete set of “quasi-isotropic” designs is identified and characterized by symbolic expressions. These results can also be used as a module for the inverse kinematics of 7R robots with a kinematic subchain of the special class under study, or directly extended to the analysis and design for isotropy and quasi-isotropy of six-dof parallel manipulators whose six actuator-wrenches intersect pairwise.

中文翻译：

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3U系列减腕机械手准各向同性运动学及设计

摘要 研究了一类关节轴成对相交的6R系列机械手的“准各向同性”运动学和设计。这是手腕减少的机械手的一个子集，与球形机械手相比，具有更高的承载能力和可操作性。推导出雅可比矩阵逆的简明符号表达式，所涉及的术语具有明确的几何意义。即使当机器人发现自己接近奇点时，该表达式也可以为运动学分析带来高鲁棒性。此外，由于特殊的几何形状，在合并简化的同时导出了简洁的奇点表达式。此外，有意义的表达式对于设计优化也很有用，在此基础上研究了各向同性和准各向同性的设计；整套“准各向同性”设计通过符号表达进行识别和表征。这些结果也可以作为7R机器人逆运动学的模块，用于研究特殊类运动学子链，或直接扩展到六自由度并联机械臂的各向同性和准各向同性的分析和设计，其六个执行器-扳手成对相交。