A Derivation of a Minimal Set of Multilinear Loop Equations for Spatial Mechanisms

Abstract

The relationship between skew-symmetric and rotation matrices due to Cayley is associated with the quaternion representation of finite rotations. Novel rotation parameters yield three real (dual) equations of simple form for spherical (spatial) polygons which are multilinear in half-tangents. This new form of the equations implies that all mechanisms (with the exception of geared linkages) are multilinear systems. Solution strategies for these equations are discussed for simple spatial structures.