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). It will be presented that uncertainty configurations of three-branch parallel manipulators with spherical branch-end joints can 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. Furthermore, 3-3-2 main-arm joint actuation is demonstrated to eliminate all except for one case of potential uncertainty configuration, and 3-2-2 and 2-2-2 actuations are shown to be advantageous seven and six actuator configurations in comparison to 3-3-1 and 3-2-1, respectively.
