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Optimal free-defect synthesis of four-bar linkage with joint clearance using PSO algorithm

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Abstract

This paper presents the design of planar four-bar linkages free of order, branch and circuit defects, for the purpose of path generation, having clearances at one, two, three or all of its joints. Joint clearance is treated as a massless virtual link and its direction is known by the direction of the joint force. A Particle Swarm Optimization based algorithm is given here to solve this highly nonlinear optimization problem with some constraints, namely; the Grashof’s and free of the foregoing defects conditions. An example is included in which the optimal problem is solved for different cases; namely planar four-bar linkage having clearances at one, two, three, all of the joints and without clearance. For all the designs, the generated paths, the errors and the directions of the virtual links are plotted and are compared. Finally, we compare the optimal designs with reality.

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Abbreviations

a i :

Length of ith link

K i :

Position of center of ith link gravity

r i :

Length of ith VJCL joint

α i :

Direction of ith VJCL joint

β :

Structural angle at joint A of the coupler link

P x :

x-coordinate of point P

P y :

y-coordinate of point P

θ i :

Angle of ith link

\(x_{G_{i}}\) :

x-coordinate of the mass center of ith link

\(y_{G_{i}}\) :

y-coordinate of the mass center of ith link

m i :

Mass of ith link

\(I_{G_{3}}\) :

Central moment of inertia of the coupler

\(I_{B_{0}}\) :

Moment of inertia of follower around the axis passing through B 0

F xij :

The x-coordinate of the Joint force acting from ith link to jth link

F yij :

The y-coordinate of the Joint force acting from ith link to jth link

T in :

Input torque

References

  1. Venanzi S, Castelli VP (2005) A new technique for clearance influence analysis in spatial mechanisms. Trans ASME, J Mech Des 127(3):446–455

    Article  Google Scholar 

  2. Feng B, Morita N, Torii T (2002) A new optimization method for dynamic design of planar linkage with clearances at joints. Trans ASME, J Mech Des 124:68–73

    Article  Google Scholar 

  3. Frisoli A, Solazzi M, Pellegrinetti D, Bergamasco M (2011) A new screw theory method for the estimation of position accuracy in spatial parallel manipulators with revolute joint clearances. Mech Mach Theory 46:1929–1949

    Article  Google Scholar 

  4. Chunmei J, Yang Q, Ling F, Ling Z (2002) The non-linear dynamic behavior of an elastic linkage mechanism with clearances. J Sound Vib 249(2):213–226

    Article  ADS  Google Scholar 

  5. Tian Q, Zhang Y, Chen L, Flores P (2009) Dynamics of spatial flexible multibody systems with clearance and lubricated spherical joints. Comput Struct 87:913–929

    Article  Google Scholar 

  6. Erkaya S, Uzmay I (2009) Investigation on effect of joint clearance on dynamics of four-bar mechanism. Nonlinear Dyn 58:179–198

    Article  MATH  Google Scholar 

  7. Lu JW, Gu J, Liu MJ (2010) Modeling of the vehicle shimmy system with consideration of clearance of the steering linkage mechanism. Meccanica 45:53–61

    Article  MATH  Google Scholar 

  8. Li Z, Bai S (1991) Amendments to a criterion of contact loss between pairing elements in planar linkages with clearances. Mech Mach Theory 26(7):669–676

    Article  Google Scholar 

  9. Farahanchi F, Shaw SW (1994) Chaotic and periodic dynamics of a slider-crank mechanism with slider clearance. J Sound Vib 177(3):307–324

    Article  ADS  MATH  Google Scholar 

  10. Seneviratne LD, Earles SWE (1992) Chaotic behavior exhibited during contact loss in a clearance joint of a four-bar mechanism. Mech Mach Theory 27(3):307–321

    Article  Google Scholar 

  11. Flores P, Ambrosio J (2004) Revolute joints with clearance in multibody systems. Comput Struct 82:1359–1369

    Article  Google Scholar 

  12. Rhee J, Akay A (1996) Dynamic response of a revolute joint with clearance. Mech Mach Theory 31:121–134

    Article  Google Scholar 

  13. Schwab AL, Meijaard JP, Meijers P (2002) A comparison of revolute joint clearance models in the dynamic analysis of rigid and elastic mechanical systems. Mech Mach Theory 37:895–913

    Article  MATH  Google Scholar 

  14. Bai ZF, Zhao Y (2013) A hybrid contact force model of revolute joint with clearance for planar mechanical systems. Int J Non-Linear Mech 48:15–36

    Article  Google Scholar 

  15. Flores P, Ambrosio J, Claro JCP, Lankarani HM, Koshy CS (2006) A study on dynamics of mechanical systems including joints with clearance and lubrication. Mech Mach Theory 41:247–261

    Article  MATH  Google Scholar 

  16. Zhang LX, Bai ZF, Zhao Y, Cao XB (2012) Dynamic response of solar panel deployment on spacecraft system considering joint clearance. Acta Astronaut 81:174–185

    Article  ADS  Google Scholar 

  17. Olyaei AA, Ghazavi MR (2012) Stabilizing slider-crank mechanism with clearance joints. Mech Mach Theory 53:17–29

    Article  Google Scholar 

  18. Ting KL, Zhu J, Watkins D (2000) The effects of joint clearance on position and orientation deviation of linkages and manipulators. Mech Mach Theory 35:391–401

    Article  MATH  Google Scholar 

  19. Tsai MJ, Lai TH (2004) Kinematic sensitivity analysis of linkage with joint clearance based on transmission quality. Mech Mach Theory 39:1189–1206

    Article  MATH  Google Scholar 

  20. Flores P (2010) A parametric study on the dynamic response of planar multibody systems with multiple clearance joints. Nonlinear Dyn 61:633–653

    Article  MATH  Google Scholar 

  21. Cabrera JA, Simon A, Prado M (2002) Optimal synthesis of mechanisms with genetic algorithms. Mech Mach Theory 37:1165–1177

    Article  MATH  Google Scholar 

  22. Erkaya S, Uzmay I (2009) Determining link parameters using genetic algorithm in mechanisms with joint clearance. Mech Mach Theory 44:222–234

    Article  MATH  Google Scholar 

  23. Pramanik N, Naskar TK (2009) Synthesis of kinematics chains with and without clearance using GA. In: 14th National Conference on Machines and Mechanisms, pp 7–14

    Google Scholar 

  24. Balli SS, Chand S (2002) Defects in link mechanisms and solution rectification. Mech Mach Theory 37:851–876

    Article  MathSciNet  MATH  Google Scholar 

  25. Balli S, Chand S (2004) Synthesis of a five-bar mechanism of variable topology type with transmission angle control. Trans ASME, J Mech Des 126:128–134

    Article  Google Scholar 

  26. Bawab S, Li H (1997) A new circuit identification method in 4-bar linkages. Trans ASME, J Mech Des 119:417–419

    Article  Google Scholar 

  27. Chase TR, Mirth JA (1993) Circuit and branches of single degree-of-freedom planar linkages. Trans ASME, J Mech Des 115:223–230

    Article  Google Scholar 

  28. Rao SS (2009) Engineering optimization theory and practice, 4th edn.

    Google Scholar 

  29. Toffolo A, Benini E (2003) Genetic diversity as an objective in multi-objective evolutionary algorithms. Evol Comput 11(2):151–167

    Article  Google Scholar 

  30. Coello Coello CA, Becerra RL (2003) Evolutionary multi objective optimization using a cultural algorithm. In: Proceedings of the IEEE Swarm Intelligence Symposium, pp 6–13

    Google Scholar 

  31. Ghashochi Bargh H, Sadr MH (2012) Stacking sequence optimization of composite plates for maximum fundamental frequency using particle swarm optimization algorithm. Meccanica 47:719–730

    Article  MathSciNet  Google Scholar 

  32. Deb K, Agrawal S, Pratap A, Meyarivan T (2002) A fast and elitist multi-objective genetic algorithm. NSGA-II. IEEE Trans Evol Comput 6(2):182–197

    Article  Google Scholar 

  33. Panigrahi SK, Chakraverty S, Mishra BK (2009) Vibration based damage detection in a uniform strength beam using genetic algorithm. Meccanica 44:697–710

    Article  MathSciNet  MATH  Google Scholar 

  34. Shiakolas PS, Koladiya D, Kebrle J (2002) On the optimum synthesis of four-bar linkages using differential evolution and the geometric centroid of precision positions. Inverse Probl Sci Eng 10(6):485–502

    Article  Google Scholar 

  35. Zhou H, Cheung EHM (2004) Adjustable four-bar linkages for multi-phase motion generation. Mech Mach Theory 39:261–270

    Article  MATH  Google Scholar 

  36. Bulatovic RR, Djordlevic SR (2004) Optimal synthesis of a four-bar linkage method of controlled deviation. Theor Appl Mech 31(3–4):265–280

    Article  MATH  Google Scholar 

  37. Fang WE (1994) Simultaneous type and dimensional synthesis of mechanisms by genetic algorithms. Mechanism Synthesis Analysis DE-70:35–41

    Google Scholar 

  38. Laribi MA, Mlike A, Romdhane L, Zeghloul S (2004) A combined genetic algorithm-fuzzy logic method (GA-FL) in mechanism synthesis. Mech Mach Theory 39:265–280

    Article  Google Scholar 

  39. Kanarachos A, Koulocheris D (2003) Evolutionary algorithm with deterministic mutation operators used for the optimization of the trajectory of a four-bar mechanism. Math Comput Simul 63:483–492

    Article  MathSciNet  MATH  Google Scholar 

  40. Roston GD, Sturgs RH (1996) Genetic algorithm synthesis of four-bar mechanisms. Artif Intell Eng Des Anal Manuf 10:371–390

    Article  Google Scholar 

  41. Kunjur A, Krishnamurty S (1997) Genetic algorithms in mechanical synthesis. J Appl Mech Robot 4(2):18–24

    Google Scholar 

  42. Zhou H, Cheung EHM (2002) Analysis and optimal synthesis of adjustable linkages for path generation. Mechatronics 12:949–961

    Article  Google Scholar 

  43. Gupta A, Swarnkar KK, Wadhwani K (2012) Combined economic emission dispatch problem using particle swarm optimization. Int J Comput Appl 49(6):1–6

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Babol University of Technology, Babol, P.O. Box 47148-71167, Iran

    Arash Sardashti, H. M. Daniali & S. M. Varedi

Authors
  1. Arash Sardashti
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  2. H. M. Daniali
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  3. S. M. Varedi
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Corresponding author

Correspondence to H. M. Daniali.

Appendices

Appendix A

(A.1)
(A.2)
(A.3)
(A.4)
(A.5)
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Appendix B

(B.1)
(B.2)
(B.3)

Appendix C

(C.1)
(C.2)

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Sardashti, A., Daniali, H.M. & Varedi, S.M. Optimal free-defect synthesis of four-bar linkage with joint clearance using PSO algorithm. Meccanica 48, 1681–1693 (2013). https://doi.org/10.1007/s11012-013-9699-6

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  • DOI: https://doi.org/10.1007/s11012-013-9699-6

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