In this paper, we present an algorithm that automatically creates the linkage loop equations for planar one degree of freedom, 1DOF, linkages of any topology with revolute joints, demonstrated up to 8 bar. The algorithm derives the linkage loop equations from the linkage adjacency graph by establishing a rooted cycle basis through a single common edge. Divergent and convergent loops are identified and used to establish the fixed angles of the ternary and higher links. Results demonstrate the automated generation of the linkage loop equations for the nine unique 6-bar linkages with ground-connected inputs that can be constructed from the five distinct 6-bar mechanisms, Watt I–II and Stephenson I–III. Results also automatically produced the loop equations for all 153 unique linkages with a ground-connected input that can be constructed from the 71 distinct 8-bar mechanisms. The resulting loop equations enable the automatic derivation of the Dixon determinant for linkage kinematic analysis of the position of every possible assembly configuration. The loop equations also enable the automatic derivation of the Jacobian for singularity evaluation and tracking of a particular assembly configuration over the desired range of input angles. The methodology provides the foundation for the automated configuration analysis of every topology and every assembly configuration of 1DOF linkages with revolute joints up to 8 bar. The methodology also provides a foundation for automated configuration analysis of 10-bar and higher linkages.
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February 2015
Research-Article
Automated Generation of Linkage Loop Equations for Planar One Degree-of-Freedom Linkages, Demonstrated up to 8-Bar
Brian E. Parrish,
Brian E. Parrish
1
Robotics and Automation Laboratory,
Department of Mechanical and
Aerospace Engineering,
e-mail: bparrish@uci.edu
Department of Mechanical and
Aerospace Engineering,
University of California
,Irvine, CA 92697
e-mail: bparrish@uci.edu
1Corresponding author.
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J. Michael McCarthy,
J. Michael McCarthy
Robotics and Automation Laboratory,
Department of Mechanical and
Aerospace Engineering,
e-mail: jmmccart@uci.edu
Department of Mechanical and
Aerospace Engineering,
University of California
,Irvine, CA 92697
e-mail: jmmccart@uci.edu
Search for other works by this author on:
David Eppstein
David Eppstein
Information and Computer Sciences,
Department of Computer Science,
e-mail: eppstein@ics.uci.edu
Department of Computer Science,
University of California
,Irvine, CA 92697
e-mail: eppstein@ics.uci.edu
Search for other works by this author on:
Brian E. Parrish
Robotics and Automation Laboratory,
Department of Mechanical and
Aerospace Engineering,
e-mail: bparrish@uci.edu
Department of Mechanical and
Aerospace Engineering,
University of California
,Irvine, CA 92697
e-mail: bparrish@uci.edu
J. Michael McCarthy
Robotics and Automation Laboratory,
Department of Mechanical and
Aerospace Engineering,
e-mail: jmmccart@uci.edu
Department of Mechanical and
Aerospace Engineering,
University of California
,Irvine, CA 92697
e-mail: jmmccart@uci.edu
David Eppstein
Information and Computer Sciences,
Department of Computer Science,
e-mail: eppstein@ics.uci.edu
Department of Computer Science,
University of California
,Irvine, CA 92697
e-mail: eppstein@ics.uci.edu
1Corresponding author.
Manuscript received September 26, 2014; final manuscript received November 24, 2014; published online December 31, 2014. Assoc. Editor: Thomas Sugar.
J. Mechanisms Robotics. Feb 2015, 7(1): 011006 (8 pages)
Published Online: February 1, 2015
Article history
Received:
September 26, 2014
Revision Received:
November 24, 2014
Online:
December 31, 2014
Citation
Parrish, B. E., Michael McCarthy, J., and Eppstein, D. (February 1, 2015). "Automated Generation of Linkage Loop Equations for Planar One Degree-of-Freedom Linkages, Demonstrated up to 8-Bar." ASME. J. Mechanisms Robotics. February 2015; 7(1): 011006. https://doi.org/10.1115/1.4029306
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