Articles | Volume 13, issue 1
https://doi.org/10.5194/ms-13-585-2022
https://doi.org/10.5194/ms-13-585-2022
Research article
 | 
27 Jun 2022
Research article |  | 27 Jun 2022

A novel compound topological invariant for isomorphism detection of planar kinematic chains

Yingxian Wang, Rongjiang Cui, and Jinxi Chen

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Cited articles

Ambekar, A. G. and Agrawal, V. P.: Canonical numbeloop of kinematic chains and isomorphism problem: min code, Mech. Mach. Theory, 22, 453–461, https://doi.org/10.1016/0094-114X(87)90062-0, 1987. 
Ding, H. and Huang, Z.: Isomorphism identification of graphs: Especially for the graphs of kinematic chains, Mech. Mach. Theory, 44, 122–139, https://doi.org/10.1016/j.mechmachtheory.2008.02.008, 2009. 
Ding, H., Hou, F., Andrés, K., and Huang, Z.: Synthesis of a complete set of contracted graphs for planar non-fractionated simple-jointed kinematic chains with all possible DOFs, Mech. Mach. Theory, 46, 1588–1600, https://doi.org/10.1016/j.mechmachtheory.2011.07.012, 2011. 
Ding, H., Huang, P., Yang, W., and Andrés, K.: Automatic generation of the complete set of planar kinematic chains with up to six independent loops and up to 19 links, Mech. Mach. Theory, 96, 75–93, https://doi.org/10.1016/j.mechmachtheory.2015.09.006, 2016a. 
Ding, H., Yang, W., Zi, B., and Andrés, K.: The family of planar kinematic chains with two multiple joints, Mech. Mach. Theory, 99, 103–116, https://doi.org/10.1016/j.mechmachtheory.2016.01.003, 2016b. 
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Short summary
This paper use the topological characteristic constants for isomorphism identification, such as the power value sequence (PVS), least distance matrix sequence (LDMS), and loop number (LN). The fourth PVS, the LDMS, and the LN are compared and arranged in descending order, forming a strong complementary chain. Our results show that solving the problem of the isomorphism identification of the kinematic chain (KC) based on graph theory definition has no advantage in efficiency.