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An automated method for type synthesis of planar linkages based on a constrained subgraph isomorphism detection

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Abstract

We present a method to enumerate and codify all non-isomorphic solutions, for the problem of synthesizing the type of single-DOF linkage mechanisms that satisfy structural requirements for a given kinematic problem. The method is based on the construction of an “initial graph” taking into account prescribed parts (such as fixations, moving bodies, joints and their interconnections) and the kinematic constraints imposed on them. This initial graph containing structural characteristics of the problem is used as a pattern to search inside a selected atlas of one-DOF mechanism also represented by graphs. A new graph-matrix representation of mechanisms and a mechanism identifier based on the degree code concept was developed to avoid isomorphic occurrences of the initial graph inside each mechanism of the atlas. The same tools were used to enumerate various atlases specialized in a non-isomorphic way from basic kinematic chains. This enumeration takes into account different types of links (rigid, flexible) and joints (revolute, prismatic, flexible, clamped), and proper restrictions were designed to avoid kinematically invalid topologies. The methodology is illustrated with examples for several kinematic tasks.

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References

  1. Olson, D.G., Erdman, A.G., Riley, D.R.: A systematic procedure for type synthesis of mechanisms with literature review. Mech. Mach. Theory 20, 285–295 (1985)

    Article  Google Scholar 

  2. Yan, H.S., Hwang, Y.W.: The specialization of mechanisms. Mech. Mach. Theory 26, 541–551 (1991)

    Article  Google Scholar 

  3. Tsai, L.W.: Mechanism Design: Enumeration of Kinematic Structures According to Function. CRC Press, Boca Raton (2001)

    Google Scholar 

  4. Sandor, G.N., Erdman, A.G.: Advanced Mechanism Design: Analysis and Synthesis, vol. 2. Prentice-Hall, New Jersey (1984)

    Google Scholar 

  5. Lin, C.S., Erdman, A.G., Jia, B.P.: Use of compatibility linkages and solution structures in the dimensional synthesis of mechanism components. Mech. Mach. Theory 31, 619–635 (1996)

    Article  Google Scholar 

  6. Erdman, A.G., Sandor, G.N.: Mechanism Design: Analysis and Synthesis, vol. 1, 3rd edn. Prentice-Hall, New Jersey (1997)

    Google Scholar 

  7. Sardain, P.: Linkage synthesis: Topology selection fixed by dimensional constraints, study of an example. Mech. Mach. Theory 32, 91–102 (1997)

    Article  MATH  Google Scholar 

  8. McCarthy, J.M.: Geometric Design of Linkages. Springer, Berlin (2000)

    MATH  Google Scholar 

  9. Mruthyunjaya, T.S.: Kinematic structure of mechanisms revisited. Mech. Mech. Theory 38(4), 279–320 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  10. Murphy, M.D., Midha, A., Howell, L.L.: The topological synthesis of compliant mechanisms. Mech. Mach. Theory 31, 185–199 (1996)

    Article  Google Scholar 

  11. Howell, L.L.: Compliant Mechanisms. Wiley, New York (2001)

    Google Scholar 

  12. Freudenstein, F., Maki, E.R.: Creation of mechanisms according to kinematic structure and function. J. Environ. Plan. B 6, 375–391 (1979)

    Article  Google Scholar 

  13. Tsai, L.W.: Systematic enumeration of parallel manipulators. Technical report, Institute for Systems Research, College Park, MD, USA (1998)

  14. Chen, D.Z., Pai, W.M.: A methodology for conceptual design of mechanisms by parsing design specifications. ASME J. Mech. Des. 127(6), 1039–1044 (2005)

    Article  Google Scholar 

  15. Tang, C.S., Liu, T.: The degree code—a new mechanism identifier. ASME J. Mech. Des. 115, 627–630 (1993)

    Article  MathSciNet  Google Scholar 

  16. Yan, H.S.: Creative Design of Mechanical Devices. Springer, Singapore (1998)

    Google Scholar 

  17. Hwang, W.M., Hwang, Y.W.: Computer-aided structural synthesis of planar kinematic chains with simple joints. Mech. Mach. Theory 27, 189–199 (1992)

    Article  Google Scholar 

  18. Hsieh, H.I.: Sistematic methodologies for the automatic enumeration of topological structures of mechanisms. Master’s thesis, University of Maryland, USA (1992)

  19. Tuttle, E.R.: Generation of planar kinematic chains. Mech. Mach. Theory 31(6), 729–748 (1996)

    Article  Google Scholar 

  20. Nieto Nieto, J.: Síntesis de Mecanismos. Editorial AC, Madrid (1977)

    Google Scholar 

  21. Geradin, M., Cardona, A.: Flexible Multi-Body Dynamics. A Finite Element Approach. Wiley, New York (2001)

    Google Scholar 

  22. Cardona, A.: Computational methods for synthesis of mechanisms. Technical report, CIMEC-INTEC (2002)

  23. Pucheta, M.A., Cardona, A.: Type synthesis and initial sizing of planar linkages using graph theory and classic genetic algorithms starting from parts prescribed by user. In: Multibody Dynamics 2005, ECCOMAS Thematic Conference, Madrid, Spain (2005)

    Google Scholar 

  24. Jiménez, J.M., Álvarez, G., Cardenal, J., Cuadrado, J.: A simple and general method for kinematic synthesis of spatial mechanisms. Mech. Mach. Theory 32(4), 323–341 (1997)

    Article  Google Scholar 

  25. Da Lio, M., Cossalter, V., Lot, R.: On the use of natural coordinates in optimal synthesis of mechanisms. Mech. Mach. Theory 35(10), 1367–1389 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  26. Pucheta, M.A., Cardona, A.: A decomposition method for modular dimensional synthesis of planar multi-loop linkage mechanisms. In: Mecánica Computacional, XV Congreso sobre Métodos Numéricos y sus Aplicaciones, ENIEF 2006, vol. XXVII, pp. 351–373, Santa Fe, Argentina, November 2006

  27. Cugnon, F., Cardona, A., Selvi, A., Paleczny, C.: Synthesis and optimization of flexible mechanisms. In: Bottasso, C.L., Masarati, P., Trainelli, L. (eds.) Multibody Dynamics 2007, ECCOMAS Thematic Conference on Multibody Dynamics, Milan, Italy (2007)

  28. Pucheta, M.A., Cardona, A.: Kinematics synthesis of compliant mechanisms using rigid-body replacement. In: Bottasso, C.L., Masarati, P., Trainelli, L. (eds.) Multibody Dynamics 2007, ECCOMAS Thematic Conference on Multibody Dynamics, Milan, Italy (2007)

  29. SAMTECH S.A. SAMCEF, http://www.samcef.com

  30. Open Engineering S.A. OOFELIE: oriented object finite elements led by interactive executor. http://www.open-engineering.com. University of Liège, Belgium and INTEC, Argentina

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Authors and Affiliations

  1. Centro Internacional de Métodos Computacionales en Ingeniería, CIMEC-INTEC, Universidad Nacional del Litoral-CONICET, Güemes 3450, S3000GLN, Santa Fe, Argentina

    Martín Pucheta & Alberto Cardona

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  1. Martín Pucheta
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  2. Alberto Cardona
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Correspondence to Alberto Cardona.

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Pucheta, M., Cardona, A. An automated method for type synthesis of planar linkages based on a constrained subgraph isomorphism detection. Multibody Syst Dyn 18, 233–258 (2007). https://doi.org/10.1007/s11044-007-9087-x

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