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Research Papers

A Design System for Six-Bar Linkages Integrated With a Solid Modeler

[+] Author and Article Information
Kaustubh H. Sonawale

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

J. Michael McCarthy

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

Contributed by the Computers and Information Division of ASME for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received May 6, 2015; final manuscript received May 29, 2015; published online August 3, 2015. Assoc. Editor: Bahram Ravani.

J. Comput. Inf. Sci. Eng 15(4), 041002 (Aug 03, 2015) (9 pages) Paper No: JCISE-15-1161; doi: 10.1115/1.4030940 History: Received May 06, 2015

This paper presents a design system for planar and spherical six-bar linkages, which is integrated with a solid modeler. The user specifies a backbone 3R chain in five task configurations in the sketch mode of the solid modeler and executes the design system. Two RR constraints are computed, which constrain the 3R chain to a single degree-of-freedom six-bar linkage. There are six ways that these constraints can be added to the 3R serial chain to yield as many as 63 different linkages in case of planar six-bar linkages and 165 in case of spherical six-bar linkages. The performance of each candidate is analyzed, and those that meet the required task are presented to the designer for selection. The design algorithm is run iteratively with random variations applied to the task configurations within user-specified tolerance zones, to increase the number of candidate designs. The output is a solid model of the six-bar linkage. Examples are presented, which demonstrate the effectiveness of this strategy for both planar and spherical linkages.

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Copyright © 2015 by ASME
Topics: Linkages , Chain , Design
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References

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Soh, G. S. , Perez-Gracia, 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. , 2008, “The Synthesis of Six-Bar Linkages as Constrained Planar 3R Chains,” Mech. Mach. Theory, 43(2), pp. 160–170. [CrossRef]
Freudenstein, F. , and Sandor, G. N. , 1959, “Synthesis of Path Generating Mechanisms by Means of a Programmed Digital Computer,” ASME J. Eng. Ind., 81, pp. 159–168.
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Rubel, A. J. , and Kaufman, R. E. , 1977, “KINSYN III: A New Human-Engineered System for Interactive Computer-Aided Design of Planar Linkages,” ASME J. Eng. Ind., 99(2), pp. 440–448. [CrossRef]
Burmester, L. , 1888, Lehrbuch der Kinematik, Vol. 1, Die ebene Bewegung, Leipzig, Germany.
Erdman, A. G. , and Gustafson, J. , 1977, “LINCAGES: A Linkage Interactive Computer Analysis and Graphically Enhanced Synthesis Package,” ASME Paper No. 77-DTC-5.
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Ruth, D. A. , and McCarthy, J. M. , 1997, “SphinxPC: An Implementation of Four Position Synthesis for Planar and Spherical Linkages,” ASME Design Engineering Technical Conferences, Sacramento, CA, Sept. 14–17.
Furlong, T. J. , Vance, J. M. , and Larochelle, P. M. , 1999, “Spherical Mechanism Synthesis in Virtual Reality,” ASME J. Mech. Des., 121(4), pp. 515–520. [CrossRef]
Collins, C. L. , McCarthy, J. M. , Perez, A. , and Su, H. , 2002, “The Structure of an Extensible Java Applet for Spatial Linkage Synthesis,” ASME J. Comput. Inf. Sci. Eng., 2(1), pp. 45–49. [CrossRef]
Perez, A. , Su, H.-J. , and McCarthy, J. M. , 2004, “SYNTHETICA 2.0: Software for the Synthesis of Constrained Serial Chains,” ASME Paper No. DETC2004-57524.
Sonawale, K. H. , Arredondo, A. , and McCarthy, J. M. , 2013, “Computer Aided Design of Useful Spherical Watt I Six-Bar Linkages,” ASME Paper No. DETC2013-13454.
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Figures

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Fig. 1

A planar and spherical 3R serial chain with joints C1,…, C3. Body one is the ground link and body four is the end-effector. Both chains have the same linkage graph.

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Fig. 2

RR constraints that form substructures: (a) the linkage graph L(13)(35) includes triangular substructure {3, 5, 6} and (b) the linkage graph L(13)(25) has a constrained quadrilateral {1, 2, 3, 5, 6} that forms a structure

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Fig. 3

The input consists of five task positions and a 3R serial chain defined in the first task position for both planar and spherical six-bar linkage design systems

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Fig. 4

The elbow C2 configuration for the chain is defined as (a) positive for θ3j < ωj, and (b) negative for ωj < θ3j

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Fig. 5

The joint angles for the spherical 3R serial chain are defined relative to the previous link

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Fig. 6

Two different six-bar linkage graphs (ij)(kl) are obtained using two independent RR dyad constraints, such that i, j, k, l ∈ {1, 2, 3, 4}: (a) Watt Ib and (b) Stephenson IIb

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Fig. 7

Four different six-bar linkage graphs (ij)(kl) are obtained by connecting the second RR dyad, to the link of the first RR dyad, such that i, j, k ∈ {1, 2, 3, 4} and l ∈ {5}: (a) Watt Ia, (b) Stephenson I, (c) Stephenson IIa, and (d) Watt Ib

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Fig. 8

The spherical Watt I six-bar linkage can be analyzed as an assembly of two spherical four-bar linkages

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Fig. 9

The rectilinear motion task positions and user-defined 3R planar serial chains are drawn in the sketch environment

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Fig. 10

The design system reads the sketch and computes candidate linkage designs for review by the designer

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Fig. 11

For a selected planar six-bar linkage design, the system exports part and assembly files readable by the solid modeler, in this case, solidworks

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Fig. 12

The task positions selected along a great circle and the user-defined 3R spherical chains are drawn in the sketch environment of the solid modeler, in this case, solidworks

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Fig. 13

For a selected spherical six-bar linkage design, the system exports part and assembly files readable by the solid modeler, in this case, solidworks

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