Design of Stephenson Linkages that Guide a Point Along a Specified Trajectory.

Abstract This paper presents a design procedure for Stephenson I-III six-bar linkages that guide a point along a specified trajectory. The first step is to identify an RR serial chain with a point on its end-link that traces the required trajectory. Eleven configurations of this chain are selected to provide accuracy points for the synthesis of Stephenson II and III function generators that coordinate the two joint angles of the RR chain. These function generators can be attached to the RR chain four different ways to obtain four kinds of Stephenson path generators. (1) A Stephenson I path generator and (2) a Stephenson II path generator are obtained by attaching a Stephenson III function generator. (3) Another kind of Stephenson II path generator and (4) a Stephenson III path generator are obtained by attaching a Stephenson II function generator. An example of this synthesis procedure finds six-bar leg designs that produce a desired foot trajectory for each of these cases.

[1]  A. H. Soni,et al.  Synthesis of six-link mechanisms for point path generation , 1971 .

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

[3]  J. Michael McCarthy,et al.  Computational Design of Stephenson II Six-Bar Function Generators for 11 Accuracy Points , 2016 .

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

[5]  Cemil Bagci,et al.  Minimum Error Synthesis of Multiloop Plane Mechanisms for Rigid Body Guidance , 1974 .

[6]  Ferdinand Freudenstein,et al.  Synthesis of Path-Generating Mechanisms by Means of a Programmed Digital Computer , 1959 .

[7]  Ferdinand Freudenstein,et al.  On the Burmester Points of a Plane , 1961 .

[8]  John McPhee,et al.  Automated Kinematic Synthesis of Planar Mechanisms with Revolute Joints , 2007 .

[9]  R. Bulatovic,et al.  Optimal synthesis of a path generator six-bar linkage , 2012 .

[10]  Mark M. Plecnik,et al.  Dimensional Synthesis of Six-Bar Linkage as a Constrained RPR Chain , 2013 .

[11]  Cemil Bagci,et al.  Optimum Synthesis of Multiloop Planar Mechanisms for the Generation of Paths and Rigid-Body Positions by the Linear Partition of Design Equations , 1977 .

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

[13]  Kurt Hain Applied kinematics / Kurt Hain , 1967 .

[14]  Gim Song Soh,et al.  The synthesis of six-bar linkages as constrained planar 3R chains , 2008 .

[15]  J. Michael McCarthy,et al.  Kinematic synthesis of Stephenson III six-bar function generators , 2016 .

[16]  Jonathan D. Hauenstein,et al.  Numerically Solving Polynomial Systems with Bertini , 2013, Software, environments, tools.

[17]  A. Morgan,et al.  Complete Solution of the Nine-Point Path Synthesis Problem for Four-Bar Linkages , 1992 .