Resolving the Inconsistency of Rigid Body Frictional Mechanics $-L\ddot{o}tstedt$'s Sliding Rod

마찰력이 개재된 강체역학에서 불일치의 해소 $-L\ddot{o}tstedt$의 미끄러지는 막대

The problem of a rigid rod sliding on a rough horizontal surface in the plane is analyzed, which is commonly cited as an example of the inconsistency of rigid body frictional mechanics. The inconsistency is demonstrated by analyzing the normal reaction force at the contact point with the surface, and the concept of tangential collision is derived to resolve the inconsistency. Using the Poisson's hypothesis for the coefficient of restitution and Coulomb's law for the friction, the general methodology for solving the tangential collision is presented. The problem of the inconsistency generated in the sliding rod is completely resolved, building the concept of the tangential collision and adopting the theory of frictional impact. The result presented in this paper will obviate a generic obstacle to the development of simulation packages for planar rigid body mechanical systems with temporary contacts, and planning efficient motion strategies for robot manipulators.