A qualitative approach to rigid body mechanics

Abstract

In order for a program to interact with the world as well as people do, we must provide it with a great deal of commonsense about the way things work. Reasoning about the geometric interactions and motions of objects is an important part of that commonsense. Some of the most complex problems we solve involve reasoning about mechanical devices, such as gears, cams, and clocks. Qualitative mechanics is the symbolic analysis of the motions and the geometric interactions of physical objects. This thesis describes a theory for analysis of rigid body mechanisms, an important subset of qualitative mechanics problems. This theory has been implemented and tested on several mechanisms including a mechanical clock. Beginning with drawings of the parts involved we compute a discrete symbolic description showing changes in position and motion of the parts of the mechanism as well as its global behavior.