A differential equation approach to swept volumes

D. Blackmore; M. C. Leu

A differential equation approach to swept volumes

D. Blackmore, M. C. Leu

Mathematical Sciences

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

23 Scopus citations

Abstract

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.

Original language	English (US)
Title of host publication	Proc Rensselaer 2 Int Conf Comput Integr Manuf
Publisher	Publ by IEEE
Pages	143-149
Number of pages	7
ISBN (Print)	081861966X
State	Published - 1990
Event	Proceedings of the Rensselaer's 2nd International Conference on Computer Integrated Manufacturing - Troy, NY, USA Duration: May 21 1990 → May 23 1990

Publication series

Name	Proc Rensselaer 2 Int Conf Comput Integr Manuf

Other

Other	Proceedings of the Rensselaer's 2nd International Conference on Computer Integrated Manufacturing
City	Troy, NY, USA
Period	5/21/90 → 5/23/90

All Science Journal Classification (ASJC) codes

General Engineering

Cite this

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title = "A differential equation approach to swept volumes",

abstract = "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.",

author = "D. Blackmore and Leu, {M. C.}",

year = "1990",

language = "English (US)",

isbn = "081861966X",

series = "Proc Rensselaer 2 Int Conf Comput Integr Manuf",

publisher = "Publ by IEEE",

pages = "143--149",

booktitle = "Proc Rensselaer 2 Int Conf Comput Integr Manuf",

note = "Proceedings of the Rensselaer's 2nd International Conference on Computer Integrated Manufacturing ; Conference date: 21-05-1990 Through 23-05-1990",

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TY - GEN

T1 - A differential equation approach to swept volumes

AU - Blackmore, D.

AU - Leu, M. C.

PY - 1990

Y1 - 1990

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0025623055&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0025623055&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0025623055

SN - 081861966X

T3 - Proc Rensselaer 2 Int Conf Comput Integr Manuf

SP - 143

EP - 149

BT - Proc Rensselaer 2 Int Conf Comput Integr Manuf

PB - Publ by IEEE

T2 - Proceedings of the Rensselaer's 2nd International Conference on Computer Integrated Manufacturing

Y2 - 21 May 1990 through 23 May 1990

ER -

A differential equation approach to swept volumes

Abstract

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All Science Journal Classification (ASJC) codes

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