Synthesis of Quasi-Constant Transmission Ratio Planar Linkages

The present paper deals with the formulation of novel closed-form algorithms for the kinematic synthesis of quasi-constant transmission ratio planar four-bar and slider–crank linkages. The algorithms are specific for both infinitesimal and finite displacements. In the first case, the approach is based on the use of kinematic loci, such as centrodes, inflection circle, and cubic of stationary curvature, as well as Euler–Savary equation. In the second case, the design equations follow from the application of Chebyshev min–max optimality criterion. These algorithms are aimed to obtain, within a given range of motion, a quasi-constant transmission ratio between the driving and driven links. The numerical examples discussed allow a direct comparison of structural errors for mechanisms designed with different methodologies, such as infinitesimal Burmester theory and the Chebyshev optimality criterion. [DOI: 10.1115/1.4031058]

[1]  C. H. Suh.  Design of spatial linkages to replace gears , 1970 .

[2]  Kurt Hain,et al.  How to Replace Gears by Mechanisms (Linkages) , 1959 .

[3]  D. C. Tao,et al.  Applied linkage synthesis , 1964 .

[4]  Ettore Pennestrì,et al.  On a technique for higher order synthesis of four-bar function generators , 1989 .

[5]  Delun Wang,et al.  Distribution of coupler curves for crank-rocker linkages , 1993 .

[6]  T. P. Goodman,et al.  Kinematics and Linkage Design , 1986 .

[7]  Giorgio Figliolini,et al.  Algebraic Algorithm for the Kinematic Analysis of Slider-Crank/Rocker Mechanisms , 2010 .

[8]  Alexander H. Slocum,et al.  Transmission ratio based analysis and robust design of mechanisms , 2010 .

[9]  Xiong Zhang,et al.  Optimal mechanism design using interior-point methods , 2000 .

[10]  Ferdinand Freudenstein,et al.  Kinematic Synthesis of Linkages , 1965 .

[11]  Yi Liu,et al.  Automated Type Synthesis of Planar Mechanisms Using Numeric Optimization With Genetic Algorithms , 2005 .

[12]  McCarthy,et al.  Geometric Design of Linkages , 2000 .

[13]  Pier Luigi Magnani,et al.  Meccanismi per macchine automatiche , 1986 .

[14]  A. Smaili,et al.  Optimum Synthesis of Mechanisms Using Tabu-Gradient Search Algorithm , 2005 .

[15]  Yong Liu,et al.  Optimal Synthesis of Mechanisms for Path Generation Using Refined Numerical Representation Based Model and AIS Based Searching Method , 2005 .

[16]  K. H. Hunt,et al.  Kinematic geometry of mechanisms , 1978 .

[17]  Ramon Sancibrian,et al.  Gradient-based optimization of path synthesis problems in planar mechanisms , 2004 .

[18]  Ea Evert Dijksman.  Motion Geometry of Mechanisms , 1976 .

[19]  Kenneth J. Waldron,et al.  Kinematics, dynamics, and design of machinery , 1998 .

[20]  Jian S. Dai,et al.  Patterned Bootstrap: A New Method That Gives Efficiency for Some Precision Position Synthesis Problems , 2007 .

[21]  Ettore Pennestrì,et al.  Introduzione alla Cinematica dei Meccanismi , 2001 .

[22]  Ferdinand Freudenstein,et al.  Structural Error Analysis in Plane Kinematic Synthesis , 1959 .

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

[24]  Arthur G. Erdman,et al.  Mechanism Design : Analysis and Synthesis , 1984 .

[25]  K. Watanabe,et al.  Application of natural equations to the synthesis of curve generating mechanisms , 1992 .