Abstract: Kinematics of a kind of [N] degrees of freedom robot driven by [N+1] steel cables is researched and analyzed in this paper. The kinematic analysis can be accomplished by two steps which is derivation of a kinematic relationship between joint space and Cartesian space of open-loop chain robot, and a kinematic relationship between joint space and motor-driven space. Branch analysis method using branch matrix and equivalent radius matrix representation for kinematics of steel cable-driven robot is put forward on the basis of kinematic analysis with fundamental circuit, coaxiality condition and transmission lines. Branch matrix and effect radius matrix in motor-driven space can be written and the mapping relationship can be got by observation method according to the schematic of steel cable transmission, which realizes the motion decoupling existing joints of steel cable-driven robot. The full kinematic mapping relationships among motor actuator space, joint space, and Cartesian space are accomplished, which speeds up and simplifies the kinematic modeling and analysis process of steel cable-driven robot. Finally, the kinematic analysis of the Stanford/JPL finger validates that branch analysis method using branch matrix and equivalent radius matrix representation for kinematics of steel cable-driven robot. The analysis method lays the foundation for design, kinematic analysis and motion control of cable-driven mechanism.

Key words: steel cable-driven, kinematics, branch matrix, equivalent radius matrix, branch analysis method

摘要： 通过研究分析一类[N+1]条钢丝绳驱动[N]个自由度机器人的运动学，其运动学可通过推导移去钢丝绳后开环链机器人关节空间与笛卡尔空间之间的运动学关系和关节空间与驱动空间之间的运动学关系来完成。在基本回路、共轴条件和传动线运动学分析的基础上，提出了用支路矩阵和等效半径矩阵描述钢丝绳传动机器人运动学的支路分析方法。根据钢丝绳传动原理，通过观察法可直接列写支路矩阵和驱动空间等效半径矩阵，从而得到了驱动空间与关节空间之间的运动学映射关系，解耦了由于钢丝绳传动导致机器人关节间的运动耦合。结合传统机器人运动学，实现了驱动空间、关节空间和笛卡尔空间完整运动学映射关系，加快和简化了钢丝绳传动机器人运动学建模和分析过程。以Stanford/JPL手指为例进行了运动学分析和仿真，验证了用支路矩阵和等效半径矩阵描述钢丝绳传动机器人运动学支路分析方法的正确性，为钢丝绳传动机构的设计、运动学分析与控制奠定了基础。

关键词: 钢丝绳传动, 运动学, 支路矩阵, 等效半径矩阵, 支路分析方法