索牵引并联机器人静态平衡位置的正解研究

研究了一种大跨度但运动缓慢的索牵引并联机器人的位置正解问题,此时可认为系统处于静平衡状态,但必须考虑柔索垂度的影响。索牵引并联机器人的静态平衡位置的正解就是确定机器人末端执行器的位置和姿态,使得系统能在给定的柔索长度下处于静平衡状态。这涉及到系统的非线性力学分析而不仅仅是一个几何问题。本文采用悬链线方程描述柔索的力学特性,结合索端位移与机器人末端执行器位移之间的关系推导出机器人的末端执行器位移与索长变化之间的增量关系,据此提出一种迭代策略完成正解计算。数值算例验证了本文方法的有效性。

Forward equilibrium position analysis of cable-driven parallel robot

The forward position problem of a long-span, slowly moving cable-driven parallel robot is investigated in the paper. The robot can be considered as in an equilibrium state due to its slow motion. However, the effects of cable sag need to be taken into account because of its long span. Forward equilibrium problem of such a cable-driven parallel robot is determining the position and orientation of the end-effector when the cable lengths are known, and the position and orientation can keep the robot in an equilibrium state. This involves the nonlinear mechanics solution of a cable-driven robot instead of only a geometrical problem involved. In the paper, characteristics of a sagged cable are described by catenary equation. The incremental relation between the displacement of the end-effector and the change of cable length is deduced when the relation between the displacement of end-effector and that of cable end achieved. According to the relation, an iterative method to obtain the forward solution is presented. Numerical examples validate the method proposed.