Isomorphism Identification of Compound Kinematic Chain and Their Mechanism

Ali Hasan*, R.A. Khan**, ***
*-** Department of Mechanical Engineering, Jamia Millia Islamia, Delhi, India.
*** M.Tech Student, Department of Mechanical Engineering, Jamia Millia Islamia, Delhi, India.
Periodicity:November - January'2012


Isomorphism is an imperative topic in the field of mechanism. Isomorphism identification is a difficult problem in kinematic chains. There are number of method given by many researchers. This paper presents  the application of the [JJ] matrix proposed by Hasan A[1] for the identification of the distinct mechanisms (DM) from a given kinematic chain (KC). The method is based on the Joint —Joint matrix. The process  is fully computational and easy to apply for the purpose. With the help of this method, we can determine easily their distinct mechanism and identify the isomorphism of kinematic chains.


kinematic chains ,distinct mechanisms, and isomorphism

How to Cite this Article?

Ali Hasan, R. A. Khan and Mubina (2012). Isomorphism Identification Of Compound Kinematic Chain And Their Mechanism. i-manager’s Journal on Mechanical Engineering, 2(1), 7-15.


[1]. Hasan A. (2007). A un-published Ph.D.thesis “Some Studies on Characterization and Identification of Kinematic Chains and Mechanisms”
[2]. Uicher J.J. & Raicu A. (1975). “A method for identification and recognition of equivalence of kinematic chains,” Mech. Mach. Theory, 10, pp 375-383.
[3]. Yan, H.S., & Hall, A.S. (1981). “Linkage characteristic polynomials: definition, coefficients by inspection,” ASME, Journal of Mechanical Design, 103, pp.578.
[4]. Mruthyunjaya, T.S. & Balasubramanium, H.R. (1987). “In Quest of a Reliable and Efficient Computational Test for Detection of Isomorphism in KC,” Mechanism and Machine Theory, 22(2), pp131-139.
[5]. W.J. Sohn, F. Freudenstein. (1986). An application of dual graphs to the automatic generation of the kinematic structures of mechanisms, ASME J. Mech. Des. 108 392–398.
[6]. Zongyu Chang, Ce Zhang, Yuhu Yang & Yuxin Wang. (2002). “A new method to mechanism kinematic chain isomorphism identification,” Mechanism and Machine Theory, 37, pp 411.
[7]. Chu, Jin-Kui & Cao Wei-Qing, (1992). “Identification of isomorphism of KC and Inversions using Link's adjacent-chain- table,” Mech Mach Theory, 29(1), pp 53-58.
[8]. A. G. Ambekar† & D V. P. Agrawal. (1987). Identification of kinematic chains, mechanisms, path generators and function generators using min codes Identification des chaînes cinématiques, des mecanismes, des generateurs de trajectores et de fonctions en utilisant des codes minimums. “Mechanism and Machine Theory, 22(5), pp. 463-471.
[9]. Rao. A.C. (1988). “Kinematic chains, Isomorphism, inversions and type of freedom using the concept of Hamming distance,” Indian J. of Tech, 26, pp,105-109.
[10]. A.C. Rao, (1997). Hamming number technique-2, generation of planar kinematic chains, Mech. Mach. Theory, 32 (4), 489–499.
[11]. A.C. Rao, P. B. Deshmukh. (2001). Computer aided structural synthesis of planar kinematic chains obviating the test for isomorphism, Mech. Mach. Theory, 36 (4), 489–506.
[12]. A.C. Rao,(2000). Genetic algorithm for topological characteristics of kinematic chains, ASME J. Mech. Des. 122 (2), pp 228–231.
[13]. Kong, F.G., Q. Li, & Zhang, W. J. (1999). “An artificial neural network approach to mechanism kinematic chain isomorphism identification”, Mechanism and Machine Theory, 34 (2), pp 271-283.
[14]. E.A. Butcher, C. Hartman, (2005). Efficient enumeration and hierarchical classification of planar simple-jointed kinematic chains: Application to 12- and 14-bar 1 DOF chains, in: Mech-mach. Theory, 40, 1030- 1050.
[15]. M. Huang, A.H. Soni. (1973). Application of linear and nonlinear graphs in structural synthesis of kinematic chains, J. Eng. Ind. ASME Trans., Ser. B 95, 525–532.
[16]. N.L. Biggs, E. Keyth Lloyd, R.J. Wilson. (1976). Graph Theory, Clarendon Press, Oxford.
[17]. F.R.E. Crossley. (1964). A contribution to Cruebler's theory in the number synthesis of planar mechanisms, J. Mech. Des., ASME Trans. 86, 1–8.
[18]. H.S. Yan, A.S. Hall. (1982). Linkage characteristic polynomials: assembly, theorems, uniqueness, ASME J. Mech. Des. 104 (1), 11–20.
[19]. T.S. Mruthyunjaya. (2003). Kinematic structure of mechanisms revisited, Mech. Mach. Theory, 38(4) 279–320.
[20]. Eric A. Butcher, Chris Hartman. (2005). Efficient enumeration and hierarchical classification of planar simple-jointed kinematic chain: application to 12- and 14-bar single degree-of freedom chains, Mech. Mach. Theory 40 (12), 1030–1050.
[21]. Z.Y. Chang, C. Zhang, Y.H. Yang, et al. (2002). A new method to mechanism kinematic chain isomorphism identification, Mech. Mach. Theory, 37 (4), 411–417.
[22]. J.P. Cubillo, J.B. Wan. (2005). Comments on mechanism kinematic chain isomorphism identification using adjacent matrices, Mech. Mach. Theory, 40(2), 31-139.
[23]. J.K. Shin, S. Krishnamurty. (1992). Development of a standard code for colored graphs and its application to kinematic chains, ASME J. Mech. Des. 114 (1), 89-196.
[24]. J.K. Shin, S. Krishnamurty, (1994). On identification and canonical numbering of pin jointed kinematic chains, ASME J. Mech. Des. 116, pp 182–188.
[25]. D.G. Olson, T.R. Thompson, D.R. Riley, et al, (1985). An algorithm for automatic sketching of planar kinematic chains, ASME J. Mech. 107, pp 106–111.
[26]. W. Chieng, D.A. Hoeltzel, (1990). A combinatorial approach for the automatic sketching of planar kinematic chains and epicyclic gear trains, ASME J. Mech. Des. 112. 6–15.
[27]. N.P. Belfiore, E. Pennestri, (1994). Automatic sketching of planar kinematic chains, Mech. Mach. Theory, 9(1), 177–193.
[28]. S. Mauskar, S. Krishnamurty. (1996). A loop configuration approach to automatic sketching of mechanisms, Mech. Mach. Theory, 31(4), 423–437.
[29]. H.F. Ding, Z. Huang. (2007). A unique representation of the kinematic chain and the atlas database, in: Mech-mach. Theory, 42, 637-651.
[30]. H.F. Ding, Z. Huang, (2007). A unique matrix representation for kinematic chain, in:12th IFToMM World Congress, Besancon (France), June 18-21.
[31]. H.F. Ding, Z. Huang. (2007). A new theory for the topological structure analysis of kinematic chains and its applications, in: Mech-mach. Theory, 42, 1264-1279.
[32]. H.F. Ding, Z. Huang. (2009). Isomorphism identification of graphs: Especially for the graphs of kinematic chains, in: Mech-mach. Theory, 44, 122-139.
[33]. H.F. Ding, Z. Huang. (2007). The establishment of the Canonical Perimeter Topological graph of kinematic chains and isomorphism identification, in: Journal of Mechanical Design, Sep. Vol. 129/915.
[34]. H.F. Ding, Z. Huang, (2004). A new topological description method of kinematic chain, in: The 14th National Conference on Mechanisms in Chongqing, pp. 161–164.
[35]. H.F. Ding, Z. Huang, (2005). The novel characteristic representations of kinematic chains and their applications, in: ASME Conference, MECH-84282, September 24–28, 2005, Long Beach, CA, USA.
[36]. H.F. Ding, Z. Huang, (2005). A Software For Creating The Atlas Database Of Kinematic Chains, Authorized Number: SR04487.
[37]. Hasan A., (2006). “Identification of Multiple Jointed Kinematic Chains”, Journal of Analysis and Computation', Vol.2 No.2, pp.175-182.
[38]. Hasan A., (2006). “Identification of Kinematic Chains and Distinct Mechanisms” International Journal of Applied Engineering Research, Vol.1, No.2, pp.251-264.
[39]. Hasan A., (2007). “Structural synthesis of planar Kinematic chains using [JJ] matrix”, Journal of Intelligent System Research (JISR), Vol.1, No-1, pp.11-23.
[40]. Hasan A., (2007). “Systematic Development of Kinematic Chains and Mechanisms from a given Assortment of Links”, Journal of Institution of Engineers (India), Vol. 88,pp.15-19.
[41]. Hasan A., (2007). “Isomorphism in Kinematic Chains Using Path Matrix”, Journal of Institution of Professional Engineers (IPENZ), New Zealand.
[42]. Hasan A., (2008). “Isomorphism and Inversions of Kinematic Chains Up to 10 Links Using Degrees of Freedom of Kinematic Pairs”, International Journal of Computational Methods (IJCM) , Vol. 5, No. 2 ,pp. 329-339, June.
[43]. Hasan A., (2009). “Isomorphism and Inversions of Kinematic Chains up to 10 Links”, Journal of 'Institution of Engineers (India), Vol. 90, pp.10-14.

Purchase Instant Access

Single Article

North Americas,UK,
Middle East,Europe
India Rest of world
Pdf 35 35 200 20
Online 35 35 200 15
Pdf & Online 35 35 400 25

If you have access to this article please login to view the article or kindly login to purchase the article
Options for accessing this content:
  • If you would like institutional access to this content, please recommend the title to your librarian.
    Library Recommendation Form
  • If you already have i-manager's user account: Login above and proceed to purchase the article.
  • New Users: Please register, then proceed to purchase the article.