On Shaping With Motion

Abstract

Mechanical parts are modeled as (predominantly rigid) solid shapes that may move in space in order to function, be manufactured (for example, machine or be machined), and be assembled or disassembled. While it is clear that such mechanical shapes are greatly influenced by collision, interference, containment, and contact constraints through prescribed motions, the motion itself is usually not part of these shape models. This in turn leads to proliferation of computational methods for modeling and analysis of various motion-related constraints. We show that all motion-related constraints can be formulated and applied within the same computational framework that treats motion as an integral part of the model. Our approach relies on two computational utilities. The first one is the unsweep operation which, given an arbitrary n-dimensional subset of Euclidean space E and a general motion M, returns the largest subset of E that remains inside E under M. The second modeling utility is a disjoint decomposition of space induced by the operations of unsweep and the standard set operations. The proposed approach subsumes and unifies the traditional sweep-based modeling of moving parts, and provides improved computational support for mechanical shape design. [S1050-0472(00)02404-1]