广义坐标的选择在Lagrange动力学分析中的作用

Impact of selection of different generalized coordinates in lagrange dynamics analysis

基于拉格朗日方程的并联机器人动力学概念清晰,推导过程简单明白,能够得到输入力与承载力的显式表达式。但由于机器人结构的复杂性和参数的多样性,使得矩阵运算量很大,尤其是当以输入量为广义坐标时,其雅可比矩阵更难计算。以3-2-1正交结构的6-PSS型的并联机器人为研究对象,以末端位姿为广义坐标推导广义力方程,同时,由于并联机器人"反解易求"的优点,所求反向雅可比矩阵(即由输出确定输入)非常容易得出。当分别以输入输出参数为广义坐标时,其各自对应的广义力表达式具有一定的对偶关系。

Parallel robot’s dynamics based on Lagrange’s equation has the merits of plain concepts and simple deducing process and can obtain explicit expressions between input forces and payload forces. But because of robot’s complex structure and multiple parameters,matrix’s computation is cumbersome,especially when generalized coordinates are input variables,solving Jacobian matrix will be more difficult. Take 6-PSS parallel robot with 3-2-1 orthogonal structure as investigated subject and end-effector’s pose as generalized coordinates to derive generalize forces,at the same time,because parallel robot’s inverse solution is easy to solve,the inverse Jacobian matrix （namely determine input ones according to output ones）to be obtained is very easy to acquired. When take input parameters and out parameters as generalize coordinates respectively, their corresponding generalized forces’expressions have some kind of duality relations.