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本文根据Lagrange运动方程建立了受约束机械系统的运动方程。由于系统是受约束的,这类运动方程通常是一组代数-微分方程。对于含有弹簧-阻尼器-动作缸组件,或者扭簧-阻尼器-动作缸组件的系统,文中载有这些组件合力的表达式。此外,本文还以铰链副为例说明了Lagrange乘子的物理意义及运动副约束反力的求取方法。最后给出了用程序DAP进行分析的实例。
In this paper, the equations of motion of a constrained mechanical system are established according to Lagrange’s equations of motion. Because the system is constrained, such equations of motion are usually a set of algebraic-differential equations. For systems with spring-damper-operating cylinder components, or torsion spring-damper-actuating cylinder components, the expressions for resultant force of these components are given. In addition, the hinge pair is taken as an example to illustrate the physical meaning of Lagrange multiplier and the method of calculating the reaction force of secondary constraint. Finally, an example of program DAP analysis is given.