On the Terminology and Geometric Aspects of Redundant Parallel Manipulators

TL;DR

This paper clarifies the terminology and geometric understanding of actuation and kinematic redundancy in parallel kinematic machines, introducing a new classification based on control system dynamics and configuration space geometry.

Contribution

It proposes a consistent terminology for redundant PKM, introduces a nonlinear control system model on the configuration space, and classifies PKM based on actuation redundancy and control vector fields.

Findings

Input singularities can be avoided with redundant actuation schemes.

The degree of actuation (DOA) is defined as the number of independent control vector fields.

PKM are classified as full-actuated or underactuated based on DOA relative to DOF.

Abstract

Parallel kinematics machines (PKM) can exhibit kinematic as well as actuation redundancy. While the meaning of kinematic redundancy has been clarified already for serial manipulators, actuation redundancy, that is only possible in PKM, is differently classified in the literature. In this paper a consistent terminology for general redundant PKM is proposed. A kinematic model is introduced with the configuration space (c-space) as central part. The notion of kinematic redundancy is recalled for PKM. C-space, output, and input singularities are distinguished. The significance of the c-space geometry is emphasized, and it is pointed out geometrically that input singularities can be avoided by redundant actuation schemes. In order to distinguish different actuation schemes of PKM a non-linear control system is introduced whose dynamics evolves on the c-space. The degree of actuation (DOA) is introduced as the number of independent control vector fields, and PKM are classified as full-actuated and underactuated. Relating this DOA to the degree of freedom (DOF) allows to classify the actuation redundancy.