Analysis of Constraint Equations and Their Singularities

The identification of singularities is an important aspect of research in parallel manipulators, which has received a great deal of attention in the past few decades. Yet, even in many well-studied manipulators, very few reported results are of complete or analytical nature. This chapter tries to address this issue from a slightly different perspective than the standard method of Jacobian analysis. Using the condition for existence of repeated roots of the univariate equation representing the forward kinematic problem of the manipulator, it shows that it is possible to gain some more analytical insight into such problems. The proposed notions are illustrated by means of applications to a spatial \(3\)-RPS manipulator, leading to the closed-form expressions for the singularity manifold of the \(3\)-RPS in the actuator space.