Optimum Path Synthesis of a Geared Five-Bar Mechanism

Most studies on path synthesis problems are to trace simple or smooth trajectories. In this work, an optimum synthesis for several special trajectories generated by a geared five-bar mechanism is studied using the one-phase synthesis method. The synthesis problem for the special trajectories, which is originally studied using the two-phase synthesis method discussed in the literature, is a real challenge due to very few dimensionally proportioned mechanisms that can generate the special trajectories. The challenging special trajectories with up to 41 discrete points include a self-overlapping curve, nonsmooth curves with straight segments and vertices, and sophisticated shapes. The error function of the square deviation of positions is used as the objective function and the GA-DE evolutionary algorithm is used to solve the optimization problems. Findings show that the proposed method can obtain approximately matched trajectories at the cost of a tremendous number of evaluations of the objective function. Therefore, the challenging problems may serve as the benchmark problems to test the effectiveness and efficiency of synthesis methods and/or optimization algorithms. All the synthesized solutions have been validated using the animation of the SolidWorks assembly so that the obtained mechanisms are sound and usable.

[1]  R. Venkata Rao,et al.  Teaching-learning-based optimization: A novel method for constrained mechanical design optimization problems , 2011, Comput. Aided Des..

[2]  H. Zhou,et al.  Optimal synthesis of crank–rocker linkages for path generation using the orientation structural error of the fixed link , 2001 .

[3]  Duc Truong Pham,et al.  The Bees Algorithm: Modelling foraging behaviour to solve continuous optimization problems , 2009 .

[4]  Ahmad Smaili,et al.  A new approach to shape optimization for closed path synthesis of planar mechanisms , 2007 .

[5]  Ferdinand Freudenstein,et al.  Closure to “Discussions of ‘Synthesis of Path-Generating Mechanisms by Numerical Methods’” (1963, ASME J. Eng. Ind., 85, pp. 305–306) , 1963 .

[6]  Gerald P. Roston,et al.  Genetic algorithm synthesis of four-bar mechanisms , 1996, Artificial Intelligence for Engineering Design, Analysis and Manufacturing.

[7]  Bernard Yannou,et al.  Dimensional synthesis of planar mechanisms using neural networks: application to path generator linkages , 2001 .

[8]  Tang Dewei,et al.  Study on a new computer path synthesis method of a four-bar linkage , 2007 .

[9]  Sanjib Kumar Acharyya,et al.  Performance of EAs for four-bar linkage synthesis , 2009 .

[10]  Panos S. Shiakolas,et al.  On the Optimum Synthesis of Four-bar Linkages Using Differential Evolution and the Geometric Centroid of Precision Positions , 2002 .

[11]  Wen Yi Lin,et al.  A GA–DE hybrid evolutionary algorithm for path synthesis of four-bar linkage , 2010 .

[12]  G. R. Gogate,et al.  Optimum synthesis of path generating four-bar mechanisms using differential evolution and a modified error function , 2012 .

[13]  Jacek Buśkiewicz,et al.  Use of shape invariants in optimal synthesis of geared five-bar linkage , 2010 .

[14]  Panos S. Shiakolas,et al.  On the Optimum Synthesis of Six-Bar Linkages Using Differential Evolution and the Geometric Centroid of Precision Positions Technique , 2005 .

[15]  B. Roth,et al.  Synthesis of Path-Generating Mechanisms by Numerical Methods , 1963 .

[16]  Scott B. Nokleby,et al.  Optimization-Based Synthesis of Grashof Geared Five-Bar Mechanisms , 2001 .

[17]  S. Kota,et al.  Optimal Synthesis of Mechanisms for Path Generation Using Fourier Descriptors and Global Search Methods , 1997 .

[18]  Donald R. Flugrad,et al.  Five-Bar Path Generation Synthesis by Continuation Methods , 1993 .

[19]  J. A. Cabrera,et al.  Optimal synthesis of mechanisms with genetic algorithms , 2002 .

[20]  Bin Wang.  Shape retrieval using combined Fourier features , 2011 .

[21]  F. J. Alonso,et al.  Shape optimization for path synthesis of crank-rocker mechanisms using a wavelet-based neural network , 2009 .

[22]  Ahmad Smaili,et al.  Optimum synthesis of hybrid-task mechanisms using ant-gradient search method , 2007 .

[23]  J. Buśkiewicz,et al.  On the application of the curve curvature in path synthesis , 2009 .

[24]  Ahmad Smaili,et al.  Optimum exact/approximate point synthesis of planar mechanisms , 2008 .

[25]  L. Romdhane,et al.  A combined genetic algorithm-fuzzy logic method (GA-FL) in mechanisms synthesis , 2004 .

[26]  Wen Yi Lin.  Optimum path synthesis of a four-link mechanism with rolling contacts , 2012 .

[27]  Antonio Moreno Ortiz,et al.  An evolutionary algorithm for path synthesis of mechanisms , 2011 .

[28]  D. E. Goldberg,et al.  Genetic Algorithms in Search , 1989 .

[30]  Sundar Krishnamurty,et al.  A generalized exact gradient method for mechanism synthesis , 1996 .

[31]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[32]  T. Mruthyunjaya,et al.  Synthesis of workspaces of planar manipulators with arbitrary topology using shape representation and simulated annealing , 1999 .

[33]  F. Peñuñuri,et al.  Synthesis of mechanisms for single and hybrid tasks using differential evolution , 2011 .

[34]  Josu Aguirrebeitia,et al.  Kinematical synthesis of 1-dof mechanisms using finite elements and genetic algorithms , 2005 .

[35]  Radovan R. Bulatović,et al.  On the optimum synthesis of a four-bar linkage using differential evolution and method of variable controlled deviations , 2009 .

[36]  C Zhang,et al.  Optimization of parameters for specified path generation using an atlas of coupler curves of geared five-bar linkages , 1984 .

[37]  T. Subbian,et al.  Six and Seven Position Triad Synthesis Using Continuation Methods , 1994 .

[38]  J. McGarva.  Rapid search and selection of path generating mechanisms from a library , 1994 .

[39]  Ramon Sancibrian,et al.  Hybrid Optimization Approach for the Design of Mechanisms Using a New Error Estimator , 2012 .