Gough-Stewart并联机器人刚体动力学模型

Rigid dynamic model of Gough-Stewart parellel robot

综合采用拉格朗日方程和牛顿-欧拉公式推导了Gough-Stewart并联机器人机构逆动力学模型的封闭解形式.通过选择合适的分支广义坐标,简化了拉格朗日函数对广义坐标的偏导求解,得到了求导矩阵的解析表达式.分析了分支角速度、角加速度轴向分量对机构动力学的影响,仿真结果表明:当机构运动加速度及分支轴向惯量较小时,可以忽略该分量的影响;但当机构运动加速度或者分支轴向惯量较大时,应对传统模型进行修正以满足机构运动高速性和定位精确性的要求.

Closed-form solutions to the inverse dynamics of Gough-Stewart parellel robots were derived based on Lagrange equation and Newton-Euler formulation.Derivatives of Lagrange functions were simplified through appropriate selection of branch generalized coordinates and analytical form of derivative matrices could be obtained.Self-rotation velocity and acceleration of branches were taken into consideration.Simulation results show that the self-rotation effects can be omitted when robot moves in a low acceleration and the branches have small axial inertia.However,when the robot moves in a high acceleration or the branches have a large axial inertia,the traditional model should be modified to satisfy the moving velocity and the positioning accuracy requirement.