skip to main content
10.1145/1998196.1998273acmconferencesArticle/Chapter ViewAbstractPublication PagessocgConference Proceedingsconference-collections
research-article

Extremal reaches in polynomial time

Published: 13 June 2011 Publication History

Abstract

Given a 3D polygonal chain with fixed edge lengths and fixed angles between consecutive edges (shortly, a revolute-jointed chain or robot arm), the Extremal Reaches Problem asks for those configurations where the distance between the endpoints attains a global maximum or minimum value. In this paper, we solve it with a polynomial time algorithm.

References

[1]
Karim Abdel-Malek, Jingzhou Yang, and Yunqing Zhang. On the workspace boundary determination of serial manipulators with non-unilateral constraints. Robotics and Computer-Integrated Manufacturing, 24:60--76, 2008.
[2]
Greg Aloupis, Erik D. Demaine, Vida Dujmovic, Jeffrey Gordon Erickson, Stefan Langerman, Henk Meijer, Joseph O'Rourke, Mark Overmars, Michael A. Soss, Ileana Streinu, and Godfried T. Toussaint. Flat state connectivity of linkages under dihedral motions. In Proc. 13th Annual Internat. Symp. Algorithms and Computation (ISAAC'02), pages 369--380, November 2002.
[3]
Greg Aloupis, Erik D. Demaine, Henk Meijer, Joseph O'Rourke, Ileana Streinu, and Godfried T. Toussaint. Flat-state connectivity of chains with fixed acute angles. In Proceedings of the 14th Canadian Conference on Computational Geometry (CCCG 2002), pages 27--30, Lethbridge, Alberta, Canada, 2002.
[4]
Ciprian Borcea and Ileana Streinu. Exact workspace boundary by extremal reaches. In these proceedings, SoCG, 2011.
[5]
Ciprian S. Borcea and Ileana Streinu. Extremal configurations of manipulators with revolute joints. In Reconfigurable Mechanisms and Robots, Proc. ASME/IFToMM International Conference (ReMAR'09), Jian S. Dai, Matteo Zoppi and Xianwen Kong (eds.), King's College, London, UK, pages 279--284. KC Edizioni, June 2009. arXiv:0812.1375.
[6]
Ciprian S. Borcea and Ileana Streinu. How far can you reach? In Proc. ACM-SIAM Symposium on Discrete Algorithms (SODA10), pages 928--937, January 2010.
[7]
John F. Canny and David Parsons. Geometric problems in molecular biology and robotics. In Proceedings of the Second International Conference on Intelligent Systems for Molecular Biology, Stanford, CA. August 1994.
[8]
Erik D. Demaine and Joseph O'Rourke. Geometric Folding Algorithms: Linkages, Origami, and Polyhedra. Cambridge University Press, 2007.
[9]
Stephen Derby. The maximum reach of revolute jointed manipulators. Mechanism and Machine Theory, 16(3):255--261, 1981.
[10]
James Urey Korein. A geometric investigation of reach. MIT Press, Cambridge, MA, June 1985.
[11]
A. Kumar and K. J. Waldron. The workspaces of a mechanical manipulator. Journal of Mechanical Design, 103(3):665--672, 1981.
[12]
Scott B. Nokleby. Singularity analysis of the Canadarm2. Mechanism and Machine Theory, 42(4):442--454, April 2007.
[13]
Andres Oberhauser and Mariano Carrion-Vazquez. Mechanical biochemistry of proteins one molecule at a time. Journal of Biological Chemistry, 283(11):6617--6621, March 2008.
[14]
Robert J. Schilling. Fundamentals of Robotics. Prentice Hall, 1990.
[15]
R. G. Selfridge. The reachable volume of a robot arm. In Proceedings of the 20th Annual Southeast Regional Conference, 1982, pages 110--114. ACM, April 1982.
[16]
R. G. Selfridge. The reachable workarea of a manipulator. Mechanism and Machine Theory, 18(2):131--137, 1983.
[17]
Michael A. Soss. Geometric and computational aspects of molecular reconfiguration. Phd thesis, School Comput. Science, McGill University, 2001.
[18]
Michael A. Soss and Godfried T. Toussaint. Geometric and computational aspects of polymer reconfiguration. Journal of Mathematical Chemistry, 27(4):303--318, 2000.
[19]
K. Sugimoto and Joseph Duffy. Determination of extreme distances of a robot hand - Part 1 : A general theory. Journal of Mechanical Design, 103(3):631--636, 1981.
[20]
H van den Bedem, Itay Lotan, Jean-Claude Latombe, and A. M. Deacon. Real-space protein-model completion: an inverse kinematics approach. Acta Crystallographica Section D, D61:2--13, 2005.

Cited By

View all
  • (2011)Exact workspace boundary by extremal reachesProceedings of the twenty-seventh annual symposium on Computational geometry10.1145/1998196.1998274(481-490)Online publication date: 13-Jun-2011

Recommendations

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences
SoCG '11: Proceedings of the twenty-seventh annual symposium on Computational geometry
June 2011
532 pages
ISBN:9781450306829
DOI:10.1145/1998196
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Sponsors

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 13 June 2011

Permissions

Request permissions for this article.

Check for updates

Author Tags

  1. reach problem
  2. robot arm

Qualifiers

  • Research-article

Conference

SoCG '11
SoCG '11: Symposium on Computational Geometry
June 13 - 15, 2011
Paris, France

Acceptance Rates

Overall Acceptance Rate 625 of 1,685 submissions, 37%

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)1
  • Downloads (Last 6 weeks)0
Reflects downloads up to 22 Feb 2025

Other Metrics

Citations

Cited By

View all
  • (2011)Exact workspace boundary by extremal reachesProceedings of the twenty-seventh annual symposium on Computational geometry10.1145/1998196.1998274(481-490)Online publication date: 13-Jun-2011

View Options

Login options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Figures

Tables

Media

Share

Share

Share this Publication link

Share on social media