A comparative study of the configuration-space and actuator-space formulations of the Lagrangian dynamics of parallel manipulators and the effects of kinematic singularities on these

This paper studies the configuration-space and the actuator-space variants of the Lagrangian formulation of dynamics of parallel manipulators. In particular, the effects of the gain-type singularity and the configuration-space singularity on the forward and inverse dynamic analyses using these formulations are studied in detail. A condition for kinematic consistency at a gain-type singularity is established. The formulations are implemented on a planar five-bar manipulator and a bi-planar Stewart platform manipulator. Extensive numerical simulations augment the analytical developments in the understanding of the dynamic behaviour of the manipulators, in both the singular and the non-singular cases.