刚弹耦合的机器人机构动力学方程及其解

本文给出了一般开链弹性机器人机构动力学方程。该方程是由关节广义坐标和杆件模态坐标联立的非线性微分方程组。对方程的刚性性质作了讨论,根据Rosenbrock的二级二阶半隐式Runge—Kutta公械,导出了一种求解弹性机器人机构动力学方程的算法。对一平面二杆操作手机构作了计算。对该例同时也用Gill方法作了计算,验证了上述算法的精度和效率。

Dynamic Equations and Their Solution of Manipulators Concerning Coupling of Gross-Motion and Elastic Deformation

In this paper the governing equations of flexible manipulators are derived, which are nonlinear simultaneous differential equations of joint variables and link elastic modal coordinates. With cussion on the stiff equations, an algorithm for solving them is deduced according to Rosenbrock's Half Implicit Rung-Kutta formula. A numerical example of a two-link manipulator system is given, which is also calculated with Gill's method in order to examine the efficiency of above algorithm.