On the Terminology and Geometric Aspects of Redundant Parallel Manipulators
2026-04-10 • Robotics
Robotics
AI summaryⓘ
The authors explain different types of redundancy in parallel kinematics machines (PKM), focusing on how they move and how they are controlled. They clarify confusing terms around actuation redundancy, which is unique to PKM, by introducing a clear way to describe these systems using a concept called the configuration space (c-space). They also define a new measure called the degree of actuation to help classify whether a PKM has full or partial control over its movements. This helps understand how redundancy can prevent control problems called singularities. Overall, the paper offers a structured way to talk about and analyze redundant PKM systems.
Parallel kinematics machinesKinematic redundancyActuation redundancyConfiguration spaceSingularityDegree of actuationDegree of freedomNon-linear control systemFull-actuatedUnderactuated
Authors
Andreas Mueller
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.