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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

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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