Simplification and Abstraction of Kinematic Behaviors

Abstract

Efficient problem-solving in any physical domain requires: (1) the ability to ignore irrelevant information by incorporating constraints and assumptions (simplification), and (2) the ability to ignore detail by reasoning at different levels of resolution (abstraction). Existing analysis methods for mechanical devices derive qualitative descriptions of a mechanism's kinematic behavior from the shapes and positions of its parts. Although qualitative, these descriptions provide a single level of abstraction which is exceedingly complex and detailed to automate common analysis and design tasks. This paper presents a set of operators to simplify and abstract kinematic descriptions derived from configuration spaces. The description hierarchy defined by these operators provides a basis for many reasoning tasks, such as mechanism comparison – determining when two mechanisms are kinematically equivalent.