A simple numerical approach for optimum synthesis of a class of planar mechanisms

Abstract In this study a numerical method for optimum synthesis of planar mechanisms, generators of functions, paths and rigid motions, is presented. Design parameters have wide variability ranges, inside which first guesses, demanded by the iterative minimization procedure, can be chosen at random. Kinematic analysis is carried out by decomposition of the mechanism into Assur groups; mechanism assembly is managed by the construction of a proper penalty function. Optimization is carried out by using a non-derivative and a quasi-Newton method in series. Some optimum design examples are presented to illustrate the power of the method.

[1]  G. R. Wray,et al.  The use of optimization techniques with precision synthesis for producing a planar linkage giving parallel motion , 1979 .

[2]  S. N. Kramer,et al.  Detection and elimination of mechanism defects in the selective precision synthesis of planar mechanisms , 1985 .

[3]  Singiresu S Rao,et al.  Mechanism design by chance constrained programming techniques , 1979 .

[4]  S. N. Kramer,et al.  Selective precision synthesis of planar mechanisms satisfying position and velocity constraints , 1979 .

[5]  G. N. Sandor,et al.  Selective Precision Synthesis—A General Method of Optimization for Planar Mechanisms , 1975 .

[6]  N. I. Levitskii,et al.  On the special properties of Lagrange's multipliers in the least-square synthesis of mechanisms , 1968 .

[7]  G. H. Sutherland,et al.  Ten-design-parameter 4-bar synthesis with tolerance considerations , 1978 .

[8]  A. C. Rao,et al.  Synthesizing linkages with minimal structural and mechanical error based upon tolerance allocation , 1982 .

[9]  C. H. Suh,et al.  Kinematics and mechanisms design , 1978 .

[10]  N. I. Levitskii,et al.  Synthesis of four-element spatial mechanisms with lower pairs☆☆☆ , 1960 .

[11]  A. C. Rao.  Synthesis of 4-bar function-generators using geometric programming , 1979 .

[12]  G. H. Sutherland,et al.  An Improved Least-Squares Method for Designing Function-Generating Mechanisms , 1975 .

[13]  G. N. Sandor,et al.  Optimum Synthesis of Four-Bar and Offset Slider-Crank Planar and Spatial Mechanisms Using the Penalty Function Approach With Inequality and Equality Constraints , 1975 .

[14]  Edward J. Haug,et al.  Design Sensitivity Analysis of Planar Mechanism and Machine Dynamics , 1981 .