This article presents an application of symmetry group theory in kinematic identification of parallel mechanisms of nlegs legs -- Kinematic Identification implies the estimation of the actual geometrical parameters (as opposed to nominal ones) of a physical mechanism -- For a symmetric mechanism, KI requires configuring sets of leg positions with symmetrical observability – This article presents as main contributions: (i) a conjecture that allows mapping the symmetries of the mechanism into the active-joint workspace, (ii) a set of necessary conditions to express leg parameters in coordinate systems which allow symmetrical observability, and (iii) a procedure for exploiting symmetries in pose selection for kinematic identification of symmetrical parallel mechanisms -- For the kinematic identification itself, we adopt a divide-and-conquer (DC) identification protocol -discussed by us in another publication- in which each leg of the mechanism is independently identified by using the inverse calibration method -- In this article we emphasize how to exploit the symmetries existent in (nlegs − 1) legs of the parallel mechanism allowing to apply to other legs the symmetry-transformed sample protocol used for the kinematic identification of a reference leg -- The symmetrical observability of sets of leg parameters allows to reduce the costs of the pose selection procedure by a factor of (1/nlegs) compared to a complete DC procedure in which the poses of each leg are selected independently -- The pose selection is carried out only for the reference leg -- For the (nlegs−1) remaining legs the poses are dictated by symmetry operations performed onto the poses of the reference leg -- An application of the symmetrical observability is presented through the simulated kinematic identification of a 3RRR symmetrical parallel mechanism
展开▼
