Abstract

Ordinary differential equations of motion for a broad spectrum of parallel manipulators are derived and implemented in manipulator input coordinates for system simulation and controller design. Equations of motion are systematically embedded in singularity free domains of manipulator configuration space, assuring controllability and existence of a unique solution of the equations of motion. The kinematic foundation for the formulation is a mechanics-based model of the underlying mechanism with forward and inverse kinematic mappings that are evaluated on singularity free domains of manipulator configuration space. The kinetic foundation is d’Alembert’s variational formulation of multibody dynamics that, with forward kinematic mappings, yields explicit ordinary differential equations of motion. No ad-hoc derivations of Lagrange’s equations, Newton–Euler equations, or Lagrange multiplier-based differential-algebraic equations are required. Differential equations of motion for a planar front-end loader and a spatial Stewart platform manipulator are implemented to illustrate the formulation.

摘要

在用于系统仿真和控制器设计的机械臂输入坐标中推导并实现了广泛的并行机械臂的常微分运动方程。运动方程系统地嵌入在机械手配置空间的无奇点域中，确保运动方程的唯一解的可控性和存在性。该公式的运动学基础是基于力学的基础机制模型，具有正向和逆向运动学映射，这些映射在操纵器配置空间的无奇点域上进行评估。动力学基础是 d'Alembert 的多体动力学变分公式，通过正向运动映射，产生显式的常微分运动方程。拉格朗日方程没有特别的推导，需要牛顿-欧拉方程或基于拉格朗日乘子的微分代数方程。实施平面前端装载机和空间 Stewart 平台机械手的微分运动方程来说明公式。