Algebraic Algorithm for the Kinematic Analisys of the Slider-Crank/Rocker Mechanisms

This paper deals with the formulation of an 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, 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 also recognized and proven to be Jeřábek'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 geometric invariants. Finally, the proposed algorithm has been implemented in a Matlab code and interesting numerical and graphical results are shown along with some particular cases in which the geometric loci degenerate in lines and circles.