Novel Plücker Operators and a Dual Rodrigues Formula Applied to the IKP of General 3R Chains

Abstract

Based on new concepts for three -matrix operators for Plücker vectors, the paper presents a novel adjoint formulation of the Rodrigues equation for spatial displacements in the trigonometric form. Due to the structural similarity of this dualized equation to its spherical pendant, the principle of transference is applicable to lift the analytic solution to the inverse kinematics problem (IKP) of generic spherical 3R chains yielding a simple analytic solution for generic spatial 3R chains based on the geometry of lines and screws.