Analysis of Crank-Rocker Inflection Circle Behavior at Singularity Poses

Inflection Circle is one of the major concepts in the Path Curvature Theory and it was first identified more than three centuries ago. Since then it has been explored intermittently. At certain poses of crank its’ diameter is prohibitive for graphic analysis using the ‘drawing board’ technique. The complex analytical treatment is not very user friendly and limited to the domain of mathematical analysis. During last six decades data based modeling is being explored for using Inflection Circle as a potent concept for development of approximate straight line linkages. While generating the database, and application of numerical methods to it, few positions of crank are encountered where tracing of Inflection Circle requires a logic which is different than the accepted theory. In this study such crank locations are identified and alternate geometric constructions are demonstrated to overcome the limitations of commonly used methods. Two positions of the crank where theoretically Inflection Circle cannot exist are also identified as absolute singularity poses.