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.
M. Leu and D. Blackmore, "A Differential Equation Approach to Swept Volumes," Proceedings of Rensselaer's Second International Conference on Computer Integrated Manufacturing, 1990, Institute of Electrical and Electronics Engineers (IEEE), Jan 1990.
The definitive version is available at http://dx.doi.org/10.1109/CIM.1990.128088
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
Article - Conference proceedings
© 1990 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.