Approximate the swept volume of revolutions along curved trajectories

Abstract

Swept volume has been applied to many applications areas such as NC machining simulation and verification, robot workspace analysis, collision detection, and CAD. The numerical computation of swept volume remains to be a very challenging problem in terms of simplicity, efficiency and accuracy. The paper presents a novel swept volume approximation method for revolution generator solids sweeping along curved trajectories. This algorithms consists of the following main steps: (1) Discretization of the trajectory curve and establishments of reference frames; (2) Extraction and approximation of envelop profile at each discretized position based on the velocity vector calculated; and (3) Generation of envelop surfaces from the extracted envelop profile curves, and attachment of the ingress and egress surfaces to the envelop surface to form the SV Solid. Examples show that our algorithm is simple, efficient and accurate.