Geometric loci for the kinematic analysis of planar mechanisms via the instantaneous geometric invariants

Abstract

This paper deals with the formulation of a general algorithm to determine and visualize several geometric loci for the kinematic analysis and synthesis of planar mechanisms, as the inflection and stationary circles (Bresse’s circles), the zero-normal and zero-tangential jerk circles, the cubic of stationary curvature and the Burmester curve, via the instantaneous geometric invariants. Consequently, the instant center of rotation, the acceleration and jerk centers, the Ball and Javot points, are also determined. Therefore, this algorithm is validated on a slider-crank mechanism obtaining significant graphical and numerical results of the abovementioned geometric loci.