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Research Papers

A Design System for Eight-Bar Linkages as Constrained 4R Serial Chains

[+] Author and Article Information
Kaustubh H. Sonawale

Robotics and Automation Laboratory,
Department of Mechanical and
Aerospace Engineering,
University of California, Irvine,
Irvine, CA 92697
e-mail: ksonawal@uci.edu

J. Michael McCarthy

Professor
Fellow ASME
Robotics and Automation Laboratory,
Department of Mechanical and
Aerospace Engineering,
University of California, Irvine,
Irvine, CA 92697
e-mail: jmmccart@uci.edu

Manuscript received March 9, 2015; final manuscript received July 2, 2015; published online August 18, 2015. Assoc. Editor: Andreas Mueller.

J. Mechanisms Robotics 8(1), 011016 (Aug 18, 2015) (10 pages) Paper No: JMR-15-1054; doi: 10.1115/1.4031026 History: Received March 09, 2015

This paper presents a design system for planar eight-bar linkages that adds three RR constraints to a user-specified 4R serial chain. R denotes a revolute, or hinged, joint. There are 100 ways in which these constraints can be added to yield as many as 3951 different linkages. An analysis routine based on the Dixon determinant evaluates the performance of each linkage candidate and determines the feasible designs that reach the task positions in a single assembly. A random search within the user-specified tolerance zones around the task specifications is iterated in order to increase the number of linkage candidates and feasible designs. The methodology is demonstrated with the design of rectilinear eight-bar linkages that guide an end-effector through five parallel positions along a straight line.

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Copyright © 2016 by ASME
Topics: Linkages , Chain , Design
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References

Soh, G. S. , Perez, A. , and McCarthy, J. M. , 2006, “The Kinematic Synthesis of Mechanically Constrained Planar 3R Chains,” First European Conference on Mechanism Science (EuCoMeS), Obergurgl, Austria, Feb. 21–26.
Soh, G. S. , and McCarthy, J. M. , 2007, “Synthesis of Eight-Bar Linkages as Mechanically Constrained Parallel Robots,” 12th IFToMM World Congress, Besancon, France, June 18–21.
Burmester, L. , 1888, Lehrbuch der Kinematik, Vol. 1, Die ebene Bewegung, Arthur Felix Verlag, Leipzig, Germany.
Koetsier, T. , 1989, “The Centenary of Ludwig Burmester's Lehrbuch der Kinematik,” Mech. Mach. Theory, 24(1), pp. 37–38. [CrossRef]
Sandor, G. N. , and Erdman, A. G. , 1984, Advanced Mechanism Design: Analysis and Synthesis, Vol. 2, Prentice-Hall, Englewood Cliffs, NJ.
Burdick, J. W. , 1989, “On the Inverse Kinematics of Redundant Manipulators: Characterization of the Self-Motion Manifolds,” IEEE International Conference on Robotics and Automation (ICRA), Scottsdale, AZ, May 14–19, pp. 264–270.
Murray, R. M. , Li, Z. , and Sastry, S. S. , 1994, A Mathematical Introduction to Robotics Manipulators, CRC Press, Boca Raton, FL, p. 456.
McCarthy, J. M. , and Soh, G. S. , 2010, Geometric Design of Linkages, 2nd ed., Springer-Verlag, New York.
Tsai, L. W. , 2000, Mechanism Design: Enumeration of Kinematic Structures According to Function, CRC Press, Boca Raton, FL.
Parrish, B. E. , McCarthy, J. M. , and Eppstein, D. , 2015, “Automated Generation of Linkage Loop Equations for Planar 1-DoF Linkages Demonstrated up to 8-Bar,” ASME J. Mech. Rob., 7(1), p. 011006. [CrossRef]
Parrish, B. E. , 2014, “Automated Configuration Analysis of Planar Eight-Bar Linkages,” Ph.D. dissertation, University of California, Irvine, CA.
Mueller, J. , 1954, “Design Procedures for the Determination of Dimensions of Eight-Bar and Ten-Bar Linkages,” Ph.D. dissertation, Technische Universitat Dresden, Dresden, Germany.
Hain, K. , 1967, “The Simultaneous Production of Two Rectilinear Translations by Means of Eight-Link Mechanisms,” J. Mech., 2(2), pp. 185–191. [CrossRef]
Hamid, S. , and Soni, A. H. , 1973, “Synthesis of an Eight-Link Mechanism for Varieties of Motion Programs,” J. Eng. Ind., 95(3), pp. 744–750. [CrossRef]
Chen, C. , and Angeles, J. , 2008, “A Novel Family of Linkages for Advanced Motion Synthesis,” Mech. Mach. Theory, 43(7), pp. 882–890. [CrossRef]
Sonawale, K. H. , and McCarthy, J. M. , 2014, “Synthesis of Useful Eight-Bar Linkages as Constrained 6R Loops,” ASME Paper No. DET2014-35523.
Kempe, A. B. , 1877, How to Draw a Straight Line: A Lecture on Linkages, Macmillan, London, p. 47.
Artobolevskii, I. I. , 1964, Mechanisms for the Generation of Plane Curves translated by R. D. Wills, Pergamon Press, Oxford, UK.
Dijksman, E. A. , 1994, “True Straight-Line Linkages Having a Rectilinear Translating Bar,” Advances in Robot Kinematics and Computational Geometry, A. J. Lenarcic and B. B. Ravani , eds., Kluwer Academic Publishers, Dordrecht, pp. 411–420.
McCarthy, J. M. , and Choe, J. , 2010, “Difficulty of Kinematic Synthesis of Usable Constrained Planar 6R Robots,” 12th International Symposium on Advances in Robot Kinematics, Portoroz, Slovenia, June 28–July 1, pp. 455–464.
Sonawale, K. H. , Arredondo, A. , and McCarthy, J. M. , 2013, “Computer Aided Design of Useful Spherical Watt I Six-Bar Linkages,” ASME Paper No. DET2013-13454.
Plecnik, M. M. , and McCarthy, J. M. , 2013, “Numerical Synthesis of Six-Bar Linkages for Mechanical Computation,” ASME J. Mech. Rob., 6(3), p. 031012. [CrossRef]

Figures

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Fig. 1

A 4R serial chain robot together with its linkage graph. Link 1 is the ground link, and link 5 is the end-effector link.

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Fig. 7

When the end-effector of the 4R chain is in each task positions, the remaining bars form a quadrilateral loop with the free parameter θ2. For each value of θ2 there are two configurations of the 4R chain: (a) elbow up and (b) elbow down.

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Fig. 8

An eight-bar linkage with the graph L(13)(24)(25) that has three independent RR constraints

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Fig. 9

An eight-bar linkage with the graph L(15)(46)(27) with the second-level dependent RR constraint, C27

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Fig. 10

Analysis of each eight-bar linkage determines if the five task positions lie on a single linkage assembly. Only linkages that satisfy this condition are feasible.

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Fig. 11

Line drawing of the example rectilinear eight-bar linkage obtained from the design procedure

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Fig. 12

The topology and linkage graph L(24)(35)(17) for the example rectilinear eight-bar linkage design

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Fig. 13

A solid model of the rectilinear eight-bar linkage showing the rectilinear movement of the end-effector

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Fig. 14

The 12 eight-bar linkages obtained from three independent RR constraints, with i,j,k,l,m,n ∈ {1,2,3,4,5}

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Fig. 15

Eight-bar linkages 1–16 of 48 with level one constraints, which are those with i,j,k,l ∈ {1,2,3,4,5},m ∈ {1,2,3,4,5,6}, and n ∈ {6,7}

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Fig. 16

Eight-bar linkages 17–32 of 48 with level one constraints, which are those with i,j,k,l ∈ {1,2,3,4,5},m ∈ {1,2,3,4,5,6}, and n ∈ {6,7}

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Fig. 17

Eight-bar linkages 33–48 of 48 with level one constraints, which are those with i,j,k,l ∈ {1,2,3,4,5},m ∈ {1,2,3,4,5,6}, and n ∈ {6,7}

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Fig. 18

Eight-bar linkages 1–20 of 40 with level two constraints, which are those with i,j,k,m ∈ {1,2,3,4,5},l ∈ {6}, and n ∈ {6,7}

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Fig. 19

Eight-bar linkages 21–40 of 40 with level two constraints, which are those with i,j,k,m ∈ {1,2,3,4,5},l ∈ {6}, and n ∈ {6,7}

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