凯恩方法中弹性元件广义主动力计算新方法

A New Method for Calculating Spring Element Generalized Active Force in Kane Equation

为了解决传统的凯恩方法中弹簧、阻尼器等弹性元件所产生的广义主动力用偏微分方程描述不便于数值计算的问题。本文采用矢量变换的方法把偏微分方程简化为矢量方程。文中对弹簧两接点用相对于参考系中固定点的位置矢量进行表示,并代入原来的偏微分方程并展开,进行矢量变换后,引入偏速度的定义,得到了一个用弹簧两接点的偏速度与单位矢量的点积表示的矢量方程,实现了将偏微分方程简化为矢量方程的目的,便于编写计算机程序求解凯恩方程。

In the Kane method, the generalized active force that is produced by the spring and the attenuator is generally described in partial differential form, and it results in difficulty of numerical calculation. For solving this problem, we transform the partial differential equation to a vector equation by using vector transformation method. We first discribe the positions of two joints of the spring in vector form, and then substitutes them into the original partial differential equation. After vector transformation, we introduce the definition of partial speed, and obtain a vector equation that is expressed by the scarlar product equation of the spring endpoint＇s partial speed and unit vec- tor. Therefore, the differential equation is reduced to a vector equation.