An approach to the analysis of swept volumes is introduced. It is shown that every smooth Euclidean motion or sweep, can be identified with a first-order, linear, ordinary differential equation. This sweep differential equation provides useful insights into the topological and geometrical nature of the swept volume of an object. A certain class, autonomous sweeps, is identified by the form of the associated differential equation, and several properties of the swept volumes of the members of this class are analyzed. The results are applied to generate swept volumes for a number of objects. Implementation of the sweep differential equation approach with computer-based numerical and graphical methods is also discussed.

Meeting Name

Rensselaer's Second International Conference on Computer Integrated Manufacturing, 1990


Mechanical and Aerospace Engineering

Keywords and Phrases

Autonomous Sweeps; Computational Geometry; Differential Equations; Graphical Methods; Linear Algebra; Numerical Methods; Smooth Euclidean Motion; Swept Volumes

Document Type

Article - Conference proceedings

Document Version

Final Version

File Type





© 1990 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 Jan 1990