Abstract: The impulsive dynamics of planar multi-rigid-body systems with friction is studied. When impact applies on a planar multi-rigid-body system in which one of the constraints is a constant constraint with coulomb friction, the phenomenon of slip-stick and slip-reversal at the frictional applied point can cause the change of frictional force and make it impossible to integrate the frictional force over the impact interval according to the traditional impulsive dynamics of multi-rigid-body systems. Under considering slip-stick and slip-reversal phenomena and keeping the traditional approximate assumptions of impact, the method of piecewise analysis during the finite region of impulse is used and the theoretical solution of the impact problem of planar multi-rigid-body systems with friction is obtained, i.e., the dynamic response after the impact can be obtained according to initial conditions before the impact and geometry properties of the system by using the formulation provided. The example here validates the rationality of the expressions.

Key words: friction, planar multi-rigid-body system, impact, piecewise analysis

摘要： 由于经典的多体系统冲击动力学的方法无法在冲击的瞬间计算摩擦力的积分，所以在考虑滑动粘滞、反向及保留经典的近似冲击假定的情况下，通过采用分段分析的方法，得到含摩擦的平面多刚体系统的冲击问题的理论解，即根据冲击的初始条件及几何特性，以及作者提供的公式，可以直接得到冲击后的动力学响应。

关键词: 摩擦, 平面多刚体系统, 冲击, 分段分析