Uncertainty configurations of parallel manipulators

Abstract Uncertainty configurations of three-branch parallel manipulators are investigated. Considered is a broad class which includes all three-branch manipulators where each branch is comprised of a serial arrangement of three main-arm joints supporting a common payload platform through a passive spherical branch-end joint-group. The investigation is based on examining potential degeneracies of the screw systems formed by actuated-joint associated wrenches, identifying all potential uncertainties for the class. The characteristics of the unconstrained instantaneous degrees of freedom corresponding to each uncertainty configuration are discussed. Joint actuation layouts that eliminate the uncertainty configurations are determined through the consideration of all feasible cases of main-arm joint actuation (non-redundant and redundant). Furthermore, example configurations which result in the corresponding dependency case for an example three-branch parallel manipulator are identified. All potential uncertainty cases are shown to be eliminated by redundant actuation of all main-arm joints (3-3-3 actuation). The screw system spanned by the wrenches associated with the actuated joints of the branches and also by the screws reciprocal to all the joints of degenerate branch configurations can be concluded to always have an order of six for redundant actuation of all main-arm joints. In addition, 3-3-2 main-arm joint actuation is demonstrated to eliminate all except for one case of pottential uncertainty configuration types, and 3-2-2 is shown to be an advantageous seven actuator configuration in comparison to 3-3-1.