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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.
The Lagrangian equation and Newton-Euler formula are used to derive the closed form of the inverse dynamics model of the Gough-Stewart parallel robot mechanism. By selecting the appropriate generalized branch of the branch, the Lagrange’s function is simplified The analytical expression of the derivation matrix is obtained.The influence of the branch angular velocity and the axial component of the angular acceleration on the mechanism dynamics is analyzed.The simulation results show that this component can be ignored when the acceleration of the mechanism and the axial inertia of the branch are small However, when the acceleration of the mechanism or the axial inertia of the branch is large, the traditional model should be modified to meet the requirements of high-speed mechanism and positioning accuracy.