An algebraic version of the input-output equation of planar four-bar mechanisms

Abstract

This paper uses a formulation of the motion of the planar four-bar mechanism in the projective three-space of planar kinematic mapping and an algebraic version of the input-output relation is derived. This fourth order algebraic curve describes a new convenient form of the Freudenstein equation. Different geometric properties of the curve, independent of the design parameters, are carried out and their impact on the topology of the mechanism is shown. Furthermore the coefficients of this algebraic input-output curve are interpreted geometrically in the design parameter space which yields regions of parameter sets to the different topologies of four-bar mechanisms.