Algebraic Algorithm for the kinematic analysis of slider-crank/rocker mechanisms

This paper deals with the formulation and validation of a comprehensive algebraic algorithm for the kinematic analysis of slider-crank/rocker mechanisms, which is based on the use of geometric loci, as the fixed and moving centrodes, along with their evolutes, the cubic of stationary curvature and the inflection circle. In particular, both centrodes are formulated in implicit and explicit algebraic forms by using the complex algebra. Moreover, the algebraic curves representing the moving centrodes are recognized and proven to be Jerˇa´bek’s curves for the first time. Then, the cubic of stationary curvature along with the inflection circle are expressed in algebraic form by using the instantaneous geometric invariants. Finally, the proposed algorithm has been implemented in a MATLAB code and significant numerical and graphical results are shown, along with the particular cases in which these geometric loci degenerate in lines and circles or give cycloidal positions.