Further analytical investigation into centrodes of the planar FBL: Symbolic representations, double points, tacnodes, degenerate forms

This paper presents a conclusive analytical investigation into the centrodes of the planar four bar linkage (FBL), treating various aspects. First, symbolic formulations including implicit Cartesian and explicit polar representations are presented and the existing asymptotes are determined. Double points of the centrodes are classified and conditions and positions of occurrence are derived with rules developed to determine feasibility within a circuit. Tacnodes are proved to occur only on fixed pivots subject to conditions derived. Loci are also provided to construct mechanisms with instant center passing through double points and tacnodes with respective assumptions. Degenerate forms and change point mechanisms are also studied.