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Four-bar Mechanism Synthesis for n Desired Path Points Using Simulated Annealing

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Advances in Metaheuristics for Hard Optimization

Part of the book series: Natural Computing Series ((NCS))

Abstract

This chapter presents an alternative method of linkage synthesis (finding link lengths and its initial position) using a computational intelligence technique: Simulated Annealing. The technique allows one to define n desired path points to be followed by a four-bar linkage (path generation problem). The synthesis problem is transformed into an optimization problem in order to use the Simulated Annealing algorithm. With this approach, a path can be better specified since the user will be able to provide more “samples” than the usual limited number of five allowed by the classical methods. Several examples are shown to demonstrate the advantages of this alternative synthesis technique.

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References

  1. I. Bohachevsky, M.E. Johnson, and M.L. Stein. Generalized simulated annealing for function optimization. Technometrics, 28:209–217, 1986

    Article  MATH  Google Scholar 

  2. R.E. Burkard and F. Rendl. A thermodynamically motivated simulation procedure for combinatorial optimization problems. European Journal of Operational Research, 17:169–174, 1984

    Article  MATH  Google Scholar 

  3. A. Casotto, F. Romeo, and A.L. Sangiovanni-Vincentelli. A parallel simulated annealing algorithm for the placement of macro-cells. In Proceedings IEEE International Conference on Computer-Aided Design, pp. 30–33, Santa Clara, November 1986

    Google Scholar 

  4. T. Elperin. Monte carlo structural optimization in discrete variables with annealing algorithm. Internatrional Journal for Numerical Methods in Engineering, 26:815–821, 1988

    Article  MATH  Google Scholar 

  5. A.G. Erdman. Three and four precision point kinematic synthesis of planar synthesis. Journal of Mechanism and Machine Theory, 16:227–245, 1981

    Article  Google Scholar 

  6. A.G. Erdman. Improved centerpoint curve generation technique for four-precision position synthesis using the complex number approach. Journal of Mechanisms, Transmisions, and Automation in Design, 107:370–376, 1985

    Article  Google Scholar 

  7. A.G. Erdman and W.E. Sandor. Mechanism Design: Analysis and Synthesis. Prentice-Hall, New Jersey, 1987

    Google Scholar 

  8. U. Faigle and W. Kern. Note on the convergence of simulated annealing algorithms. SIAM Journal on Control and Optimization, 29:153–9, January 1991

    Google Scholar 

  9. T.L. Friesz, H.-J. Cho, and N.J. Mehta. A simulated annealing approach to the network design problem with variational inequality constraints. Transportation Science, 26:18–26, February 1992

    Google Scholar 

  10. S. B. Gelfand and S. K. Mitter. Analysis of simulated annealing for optimization. In Proceedings of 24th Conference on Decision and Control, pp. 779–786, Ft Lauderdale, December 1985

    Google Scholar 

  11. G.G.E. Gielen, Herman C.C. Walscharts, and W.M.C. Sansen. Analog circuit design optimization based on symbolic simulation and simulated annealing. IEEE Journal of Solid-State Circuits, 25:707–713, June 1990

    Google Scholar 

  12. S. Kirkpatrick, C.D. Gelatt, and M.P. Vecchi. Optimization by simulated annealing. Science, 220(4598):671–680, 1983

    Article  MathSciNet  Google Scholar 

  13. S. Kirkpatrick and G. Toulouse. Configuration space analysis of travelling salesman problems. Journal Physique, 46:1277–1292, 1985

    Article  MathSciNet  Google Scholar 

  14. P. J. M. van Laarhoven and E. H. L. Aarts. Simulated Annealing: Theory and Applications. D. Reidel, Dordrecht, Holland, 1987

    MATH  Google Scholar 

  15. A. Malhotra, J. H. Oliver, and W. Tu. Synthesis of spatially and intrinsically constrained curves using simulated annealing. ASME Advances in Design Automation, DE-32:145–155, 1991

    Google Scholar 

  16. H. Martínez-Alfaro and D.R. Flugrad. Collision-free path planning of an object using B-splines and simulated annealing. In IEEE Internactional Conference on Systems, Man, & Cybernetics, 1994

    Google Scholar 

  17. H. Martínez-Alfaro and D.R. Flugrad. Collision-free path planning of robots and/or AGVs using B-splines and simulated annealing. In ASME DTEC/Mechanisms Conference, 1994

    Google Scholar 

  18. H. Martínez-Alfaro and A. Ulloa-Pérez. Computing near optimal paths in C-space using simulated annealing. In ASME Design Engineering Technical Conference/Mechanisms Conference, Irvine, CA, 1996

    Google Scholar 

  19. H. Martínez-Alfaro, H. Valdez, and J. Ortega. Linkage synthesis of a four-bar mechanism for n precision points using simulated annealing. In ASME Design Engineering Technical Conferences/Mechanisms Conference, 1998

    Google Scholar 

  20. N. Metropolis, A. Rosenbluth, M. Rosenbluth, and A. Teller. Equations of state calculations by fast computing machines. Journal of Chemical Physics, 21:1087–1091, 1953

    Article  Google Scholar 

  21. R.L. Norton. Design of Machinery. An Introduction to the Synthesis and Analysis of Mechanisms. McGraw-Hill, New York, 1992

    Google Scholar 

  22. R.A. Rutenbar. Simulated annealing algorithms: An overview. IEEE Circuits and Devices, Vol. 5, January:19–26, 1989

    Google Scholar 

  23. G.N. Sandor, D. Kohli, C.F. Reinholtz, and A. Ghosal. Closed-form analytic synthesis of a five-link spatial mmotion generator. Journal of Mechanism and Machine Theory, (1):97–105, 1984

    Article  Google Scholar 

  24. T. Subbian. Use of continuation methods for kinematic synthesis and analysis. PhD thesis, Iowa State University, Ames, IA, 1990

    Google Scholar 

  25. T. Subbian and D.R. Flugrad. Four-bar path generation synthesis by a continuation method. In ASME Advances in Design Automation, ASME DE-19-3:425–432, 1989

    Google Scholar 

  26. C. H. Suh and C. W. Radcliffe. Kinematics and Mechanism Design. John Wiley & Sons, Inc., New York, 1978

    Google Scholar 

  27. D. Vanderbilt and S.G. Louie. A Monte Carlo simulated annealing approach to optimization over continuous variables. Journal of Computational Physics, 36:259–271, 1984

    Article  MathSciNet  Google Scholar 

  28. C. W. Wampler, A. P. Morgan, and A. J. Sommese. Complete solution of nine-point path synthesis problem for four-bar linkage. In ASME Advances in Design Automation, ASME DE-25:361–368, 1990

    Google Scholar 

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Martínez-Alfaro, H. (2007). Four-bar Mechanism Synthesis for n Desired Path Points Using Simulated Annealing. In: Siarry, P., Michalewicz, Z. (eds) Advances in Metaheuristics for Hard Optimization. Natural Computing Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72960-0_2

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  • DOI: https://doi.org/10.1007/978-3-540-72960-0_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72959-4

  • Online ISBN: 978-3-540-72960-0

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