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Research Papers: Design of Mechanisms and Robotic Systems

Split Hamming String as an Isomorphism Test for One Degree-of-Freedom Planar Simple-Jointed Kinematic Chains Containing Sliders

[+] Author and Article Information
Varadaraju Dharanipragada

Professor
Department of Mechanical Engineering,
Gayatri Vidya Parishad College of Engineering (A),
Madhurawada, Visakhapatnam,
Andhra Pradesh 530 048, India
e-mail: d_varada_raju@gvpce.ac.in

Mohankumar Chintada

Department of Mechanical Engineering,
Gayatri Vidya Parishad College of Engineering (A),
Madhurawada, Visakhapatnam,
Andhra Pradesh 530 048, India
e-mail: mohankumar.chintada@gmail.com

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received November 23, 2015; final manuscript received April 27, 2016; published online June 29, 2016. Assoc. Editor: Dar-Zen Chen.

J. Mech. Des 138(8), 082301 (Jun 29, 2016) (8 pages) Paper No: MD-15-1778; doi: 10.1115/1.4033611 History: Received November 23, 2015; Revised April 27, 2016

Over the last six decades, kinematicians have devised many tests for the identification of isomorphism among kinematic chains (KCs) with revolute pairs. But when it comes to KCs with prismatic pairs, tests are woefully absent and the age-old method of visual inspection is being resorted to even today. This void is all the more conspicuous because sliders are present in all kinds of machinery like quick-return motion mechanism, Davis steering gear, trench hoe, etc. The reason for this unfortunate avoidance is the difficulty in discriminating between sliding and revolute pairs in the link–link adjacency matrix, a popular starting point for many methods. This paper attempts to overcome this obstacle by (i) using joint–joint adjacency, (ii) labeling the revolute pairs first, followed by the sliding pairs, and (iii) observing whether an element of the adjacency matrix belongs to revolute–revolute (RR), revolute–prismatic (RP) (or PR), or prismatic–prismatic (PP) zone, where R and P stand for revolute and prismatic joints, respectively. A procedure similar to hamming number technique is applied on the adjacency matrix but each hamming number is now split into three components, so as to yield the split hamming string (SHS). It is proposed in this paper that the SHS is a reliable and simple test for isomorphism among KCs with prismatic pairs. Using a computer program in python, this method has been applied successfully on a single degree-of-freedom (DOF) simple-jointed planar six-bar chains (up to all possible seven prismatic pairs) and eight-bar KCs (up to all ten prismatic pairs). For six-bar chains, the total number of distinct chains obtained was 94 with 47 each for Watt and Stephenson lineages. For eight-bar chains, the total number is 7167 with the distinct chain count and the corresponding link assortment in parenthesis as 3780(0-4-4), 3037(1-2-5), and 350(2-0-6). Placing all these distinct KCs in a descending order based on SHS can substantially simplify communication during referencing, storing, and retrieving.

Copyright © 2016 by ASME
Topics: String , Chain
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Figures

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Fig. 1

Watt chain with all revolute pairs

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Fig. 2

Eight-bar 1DOF KC with four prismatic pairs

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Fig. 3

Watt chains with one prismatic joint

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Fig. 4

Watt chains with two prismatic joints

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Fig. 5

Watt chains with three prismatic joints (Note: Seventh KC above belongs to Davis Steering gear)

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Fig. 6

Watt chains with four prismatic joints

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Fig. 7

Watt chains with five prismatic joints

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Fig. 8

Watt chains with six prismatic joints

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Fig. 9

Watt chains with seven prismatic joints

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Fig. 10

Stephenson chains with one prismatic joint

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Fig. 11

Stephenson chains with two prismatic joints

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Fig. 12

Stephenson chains with three prismatic joints

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Fig. 13

Stephenson chains with four prismatic joints

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Fig. 14

Stephenson chains with five prismatic joints

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Fig. 15

Stephenson chains with six prismatic joints

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Fig. 16

Stephenson chains with seven prismatic joints

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