Detection of isomorphism in planar and geared kinematic chains (GKCs) is an interesting area since many years. Enumeration of planar and geared kinematic chains becomes easy only when isomorphism problem is resolved effectively. Many researchers proposed algorithms based on topological characteristics or some coding which need lot of computations and comparisons. In this paper, a novel and simple algorithm is proposed based on graph theory by which elimination of isomorphic chains can be done very easily without any tedious calculations or comparisons. A new concept “Net distance” is proposed based on the graph theory to be a quantitative measure to assess isomorphism in planar kinematic chains (PKCs) as well as GKCs. The proposed algorithm is applied on nine-link two-degrees-of-freedom (DOF) distinct kinematic chains completely and the results are presented. Algorithm is tested on examples from eight-link 1-DOF, ten-link 1-DOF, 12-link 1-DOF, and 15link 4-DOF PKCs. The algorithm is also tested on four-, six-link 1-DOF GKCs to detect isomorphism. All the results are in agreement with the existing literature.
An Innovative Approach to Detect Isomorphism in Planar and Geared Kinematic Chains Using Graph Theory
Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received February 7, 2017; final manuscript received August 3, 2017; published online October 3, 2017. Assoc. Editor: Massimo Callegari.
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Venkata Kamesh, V., Mallikarjuna Rao, K., and Balaji Srinivasa Rao, A. (October 3, 2017). "An Innovative Approach to Detect Isomorphism in Planar and Geared Kinematic Chains Using Graph Theory." ASME. J. Mech. Des. December 2017; 139(12): 122301. https://doi.org/10.1115/1.4037628
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