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Topological and dimensional synthesis of planar linkages for multiple kinematic tasks

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Abstract

This paper presents the combined use of two systematic methods for the synthesis of planar linkage mechanisms satisfying multiple kinematic tasks. First, a Graph Theory-based method is used to exhaustively enumerate the topological alternatives for a given problem. Then each feasible alternative is automatically dimensioned using the Precision Position Method; this computation includes space and design constraints. The existing methods to synthesize multiple tasks solve, in sequence, a decomposition of the problem into single kinematic tasks. The task decomposition and the topology selection for each task are usually performed by hand. This process leads to topologies with a repeated pattern and could lead to ignoring potentially desirable topologies. This paper analyzes a design strategy for the simultaneous solution of multiple kinematic tasks. This strategy has two advantages: (i) it eliminates the need for task decomposition, and (ii) it allows the exhaustive exploration of all non-isomorphic topologies up to a defined number of links. An example of simultaneous synthesis for a double rigid-body guidance task with application to a flap-tab mechanism is shown to illustrate the methodology.

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Notes

  1. 1.

    Hereafter, the term “type” embraces both the type and the number synthesis stages of design.

  2. 2.

    Genetic algorithms are suitable for problems where neither domain nor goal function and restrictions are known; or they are so complicated that gradient computation becomes difficult or impossible [18]. Note that in this sizing problem, the system of (10) may not have a solution and it is difficult to compute the gradient of the space constraints.

References

  1. 1.

    Acharyya, S., Mandal, M.: Performance of eas for four-bar linkage synthesis. Mech. Mach. Theory 44(9), 1784–1794 (2009)

    MATH  Article  Google Scholar 

  2. 2.

    Avilés, R., Vallejo, J., Fernández de Bustos, I., Aguirrebeitia, J., Ajuria, G.: Optimum synthesis of planar linkages using a strain-energy error function under geometric constraints. Mech. Mach. Theory 45(1), 65–79 (2010)

    MATH  Article  Google Scholar 

  3. 3.

    Cabrera, J., Ortiz, A., Nadal, F., Castillo, J.: An evolutionary algorithm for path synthesis of mechanisms. Mech. Mach. Theory 46(2), 127–141 (2011)

    MATH  Article  Google Scholar 

  4. 4.

    Campanile, L.F.: Chapter 4: Lightweight shape-adaptable airfoils: A new challenge for an old dream. In: Wagg, D., Bond, I., Weaver, P., Friswell, M. (eds.) Adaptive Structures: Engineering Applications, pp. 89–135. Wiley, New York (2007)

    Google Scholar 

  5. 5.

    Chen, C., Angeles, J.: A novel family of linkages for advanced motion synthesis. Mech. Mach. Theory 43(7), 882–890 (2008)

    MATH  Article  Google Scholar 

  6. 6.

    Collard, J.F., Duysinx, P., Fisette, P.: Optimal synthesis of planar mechanisms via an extensible-link approach. Struct. Multidiscip. Optim. 42, 403–415 (2010)

    Article  Google Scholar 

  7. 7.

    Cugnon, F., Cardona, A., Selvi, A., Paleczny, C., Pucheta, M.: Chapter: Synthesis and optimization of flexible mechanisms. In: Bottasso, C.L. (ed.) Multibody Dynamics, Computational Methods and Applications. Comp. Meth. in App. Sci., vol. 12, pp. 81–93. Springer, Amsterdam (2008)

    Google Scholar 

  8. 8.

    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)

    MathSciNet  MATH  Article  Google Scholar 

  9. 9.

    Diab, N., Smaili, A.: Optimum exact/approximate point synthesis of planar mechanisms. Mech. Mach. Theory 43(12), 1610–1624 (2008)

    MATH  Article  Google Scholar 

  10. 10.

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

    Google Scholar 

  11. 11.

    Fang, W.E.: Simultaneous type and dimensional synthesis of mechanisms by genetic algorithms. In: Proc. of the 23rd Biennial Mechanisms Conference. Mechanism Synthesis and Analysis, vol. 70, pp. 35–41. ASME Design Engineering Division (1994)

  12. 12.

    Hansen, J.M.: Synthesis of mechanisms using time-varying dimensions. Multibody Syst. Dyn. 7(1), 127–144 (2002)

    MATH  Article  Google Scholar 

  13. 13.

    Hartenberg, R.S., Denavit, J.: Kinematic Synthesis of Linkages. McGraw-Hill, New York (1964)

    Google Scholar 

  14. 14.

    Jensen, O., Hansen, J.: Dimensional synthesis of spatial mechanisms and the problem of non-assembly. Multibody Syst. Dyn. 15(2), 107–133 (2006)

    MathSciNet  MATH  Article  Google Scholar 

  15. 15.

    Liu, Y., McPhee, J.: Automated kinematic synthesis of planar mechanisms with revolute joints. Mech. Based Des. Struct. Mach. 35(4), 405–445 (2007)

    Article  Google Scholar 

  16. 16.

    Luo, Z., Dai, J.: Chapter: Searching for undiscovered planar straight-line linkages. In: Lenarčič, J., Roth, B. (eds.) Advances in Robot Kinematics, Mechanisms and Motion, Part 2, pp. 113–122. Springer, Berlin (2006)

    Google Scholar 

  17. 17.

    McCarthy, J.M., Soh, G.S.: Geometric Design of Linkages, 2 edn. Springer, Berlin (2010)

    Google Scholar 

  18. 18.

    Michalewicz, Z.: Genetic Algorithms + Data Structures = Evolution Programs. Springer, New Jersey (1997)

  19. 19.

    Murray, A., Schmiedeler, J., Korte, B.: Synthesis of planar, shape-changing rigid-body mechanisms. J. Mech. Des. 130(3), 1–10 (2008)

    Article  Google Scholar 

  20. 20.

    Oliva, J.C., Goodman, E.D.: Simultaneous type and dimensional synthesis of planar 1DOF mechanisms using evolutionary search and convertible agents. ASME J. Mech. Robotics 2(3), 1–9 (2010)

    Google Scholar 

  21. 21.

    Persinger, J., Schmiedeler, J., Murray, A.: Synthesis of planar rigid-body mechanisms approximating shape changes defined by closed curves. J. Mech. Des. 131(7), 1–7 (2009)

    Article  Google Scholar 

  22. 22.

    Peñuñuri, F., Peón-Escalante, R., Villanueva, C., Pech-Oy, D.: Synthesis of mechanisms for single and hybrid tasks using differential evolution. Mech. Mach. Theory 46(10), 1335–1349 (2011)

    MATH  Article  Google Scholar 

  23. 23.

    Pucheta, M.: Computational methods for design and synthesis of planar mechanisms. Ph.D. thesis, Universidad Nacional del Litoral, Santa Fe, Argentina (2008)

  24. 24.

    Pucheta, M., Cardona, A.: An automated method for type synthesis of planar linkages based on a constrained subgraph isomorphism detection. Multibody Syst. Dyn. 18(2), 233–258 (2007)

    MATH  Article  Google Scholar 

  25. 25.

    Pucheta, M., Cardona, A.: Synthesis of planar multi-loop linkages starting from existing parts or mechanisms: Enumeration and initial sizing. Mech. Based Des. Struct. Mach. 36(4), 364–391 (2008)

    Article  Google Scholar 

  26. 26.

    Pucheta, M.A., Cardona, A.: Automated type and modular dimensional synthesis of planar linkages. In: Proc. of ASME IDETC/CIE Conferences. Montreal, Quebec, Canada (2010). Paper DETC-28540

    Google Scholar 

  27. 27.

    Pucheta, M.A., Cardona, A.: Design of bistable compliant mechanisms using precision-position and rigid-body replacement methods. Mech. Mach. Theory 45(2), 304–326 (2010)

    MATH  Article  Google Scholar 

  28. 28.

    Raghavan, M.: Number and dimensional synthesis of independent suspension mechanisms. Mech. Mach. Theory 31(8), 1141–1153 (1996)

    Article  Google Scholar 

  29. 29.

    Sancibrian, R.: Improved GRG method for the optimal synthesis of linkages in function generation problems. Mech. Mach. Theory 46(10), 1350–1375 (2011)

    MATH  Article  Google Scholar 

  30. 30.

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

    Google Scholar 

  31. 31.

    Sardain, P.: Linkage synthesis: Topology selection fixed by dimensional constraints, study of an example. Mech. Mach. Theory 32(1), 91–102 (1997)

    MATH  Article  Google Scholar 

  32. 32.

    Schreiber, H., Meer, K., Schmitt, B.J.: Dimensional synthesis of planar Stephenson mechanisms for motion generation using circlepoint search and homotopy methods. Mech. Mach. Theory 37(7), 717–737 (2002)

    MathSciNet  MATH  Article  Google Scholar 

  33. 33.

    Shen, Q., Al-Smadi, Y.M., Martin, P., Russell, K., Sodhi, R.: An extension of mechanism design optimization for motion generation. Mech. Mach. Theory 44(9), 1759–1767 (2009)

    MATH  Article  Google Scholar 

  34. 34.

    Smaili, A., Diab, N.: Optimum synthesis of hybrid-task mechanisms using ant-gradient search method. Mech. Mach. Theory 42(1), 115–130 (2007)

    MathSciNet  MATH  Article  Google Scholar 

  35. 35.

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

    Google Scholar 

  36. 36.

    Vucina, D., Freudenstein, F.: An application of graph theory and nonlinear programming to the kinematic synthesis of mechanisms. Mech. Mach. Theory 26, 553–563 (1991)

    Article  Google Scholar 

  37. 37.

    Wu, L.C., Carbone, G., Ceccarelli, M.: Designing an underactuated mechanism for a 1 active DOF finger operation. Mech. Mach. Theory 44(2), 336–348 (2009)

    MATH  Article  Google Scholar 

Download references

Acknowledgements

This work has received financial support from the following Argentinean institutions: Consejo Nacional de Investigaciones Científicas y Técnicas PIP2009 112-200801-02473, Agencia Nacional de Promoción Científica y Tecnológica PICT-2010-1240, and Universidad Nacional del Litoral CAI+D 2009 PI65-330.

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Correspondence to Alberto Cardona.

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Pucheta, M.A., Cardona, A. Topological and dimensional synthesis of planar linkages for multiple kinematic tasks. Multibody Syst Dyn 29, 189–211 (2013). https://doi.org/10.1007/s11044-011-9294-3

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Keywords

  • Planar linkage mechanisms
  • Graph theory
  • Number synthesis
  • Modular dimensional synthesis
  • Multiple kinematic tasks
  • Synthesis strategies