Motion of Objects in Contact

Abstract

The use of computers in the design, manufacture, and ma nipulation of physical objects is increasing. An important aspect of reasoning about such actions concerns the motion of objects in contact. The study of problems of this nature requires not only the ability to represent physical objects but also the development of a framework or theory in which to reason about them. In this paper such a development is in vestigated and a fundamental theorem concerning the motion of objects in contact is proved. The simplest form of this theorem states that if two objects in contact can be moved to another configuration in which they are in contact, then there is a way to move them from the first configuration to the second configuration such that the objects remain in contact throughout the motion. This result is proved when translation and rotation of objects are allowed. The problem of more generalized types of motion is also discussed. This study has obvious applications in compliant motion and in motion planning.