REVERSIBLE GEOMETRIC CONSTRAINT PROGRAMMING ON KINEMATIC ANALYSIS AND SYNTHESIS OF PLANAR LINKAGES

This paper proposes a novel reversible approach to do the kinematic analysis and synthesis for higher-order motion. The method plots the traditional velocity and acceleration polygon in the sketch mode of commercial computer aid design (CAD) software. Based on the geometric constraint and the aid of similar triangles, the approach can synthesize the linkages with prescribed velocity and acceleration at the specified positions. The approach shows the analysis results at the same time when the synthesis process is finished, it is conceptually intuitive and does not require Euler-Savary equation and advanced computational techniques. The approach can be used as an ideal tool to teach undergraduate students about the graphical method of kinematic analysis. With a similar setting, the synthesis process can be introduced by reversible programming. This paper demonstrates the procedure by synthesizing a four-bar linkage with the prescribed velocity and acceleration of its coupler point, and extends the method to synthesize a Stephenson six-bar linkage. It is a simpler and more intuitive approach of order synthesis for planar linkages, and it may have the potential to make the analysis and synthesis of spatial linkages easier.