Title

A Singularity Theory Approach to Swept Volumes

Abstract

An approach to the study of the topology and geometry of swept volumes is developed based on the theory of singularities of sweep mappings. It is shown how the computation of the critical point and bifurcation sets of a certain (sweep) mapping yields important information about both the local and global structure of swept volumes. For example, it is proved under mild restrictions that a swept volume can be arbitrary closely approximated by a product manifold. a computer program - incorporating singularity calculations - for the approximate analysis and representation of swept volumes is developed and applied to several examples in order to demonstrate its usefulness.

Department(s)

Mechanical and Aerospace Engineering

Keywords and Phrases

Computer-Aided Geometric Design; Envelopes; Singularity Theory; Sweep Differential Equations; Swept Volume

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2000 World Scientific Publishing, All rights reserved.


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