Solving the Kinematics of Planar Mechanisms by Dixon Determinant and a Complex-Plane Formulation

This paper presents a general method for the analysis of any planar mechanism consisting of rigid links connected by revolute and slider joints. The method combines the complex plane formulation of Wampler (1999) with the Dixon determinant procedure of Nielsen and Roth (1999). The result is simple to derive and implement, so in addition to providing numerical solutions, the approach facilitates analytical explorations. The procedure leads to a generalized eigenvalue problem of minimal size. Both input/output problems and the derivation of tracing curve equations are addessed. NOMENCLATURE � Number of kinematic loops. θj e iΘj ,w here Θ j is an angle, in radians. z ∗ Complex conjugate of z.