The Motion of Compliantly-Connected Rigid Bodies in Contact, Part I: The Motion Prediction Problem

摘要

Consider the problem of planning and predicting the motion of a flexible object amidst obstacles in the plane by modelling the flexible object as a rigid root body, attached to compliant members of torsional springs. The root's position may be controlled, but the compliant members move in response to forces from contact with the environment. Such a model encompasses several important and complicated mechanisms in mechanical design and automated assembly: snap-fasteners, latches, ratchet and pawl mechanisms, and escapements. The problem is to predict the motion of such a mechanism amidst fixed obstacles. For example, our algorithm could be used to determine whether a snap-fastener design can be assembled with a certain plan. This paper analyzes the physics of these flexible devices, and develop the first combinatorially precise algorithm for predicting their movement under a motion plan. This algorithm determines when and where the motion will terminate, and also computes the time-history of contacts. In addition to providing the first known exact algorithm that addresses flexibility in motion planning, we also note that our approach to compliance permits an exact algorithm for predicting motions under rotational compliance, which was not possible in earlier work. (JHD)