A New Assessment of Singularities of Parallel Kinematic Chains

This paper presents a novel assessment of singularities of general parallel kinematic chains. Hierarchical levels in which different critical phenomena originate are recognized. At each level, the causes of singular events are identified and interpreted, and on their basis, a comprehensive taxonomy is proposed. First, the unactuated kinematic chain is studied. The concepts of leg and passive-constraint singularities are described, and stationary and increased instantaneous mobility configurations are identified. Then, a set of motorized joints is chosen. The effects of first-level singularities on the actuated chain are investigated, and further phenomena are identified, such as redundancy singularities and active-constraint singularities. The notions of reaction and action spaces are originally discussed. The consequences on the ability of the actuated chain to effectively govern its local and global freedoms are analyzed, and the complex interactions between the various singular events are studied. The instantaneous redundancy of actuators, which occur when these work either against each other or against joint constraints, is also evaluated. Finally, when the input-output mechanism is considered, the events described at the previous stages are interpreted within the perspective of the machine's desired use.