Symmetrical Observability of Kinematic Parameters in Symmetrical Parallel Mechanisms
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2014-05
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Editora Edgard Blücher Ltda.
Resumen
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
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@InProceedings{Durango_Restrepo_Ruiz_Achiche_2012,
author = {Durango, S. and Restrepo, D. and Ruiz, O. and Restrepo-Giraldo, J. and Achiche, S.},
title = {Symetrical Observability of Kinematic Parameters in Symmetrical Parallel Mechanisms},
booktitle = {10th World Congress on Computational Mechanics},
pages = {16714},
year = {2012},
editor = {Pimenta, P.M. and Campello, E.M.B.},
address = {Sao Paulo, Brazil},
month = {08-13 July},
OPTpublisher = {ABMEC},
note = {ISBN 978-85-86686-70-2},
abstract={This article presents an application of symmetry groups in symmetrical observability of the kinematic parameters of a mechanism. We use the devised concepts in the particular domain of Kinematic Identification of symmetric parallel mechanisms. KI implies the estimation of the actual geometrical parameters (as opposed to nominal ones) of a physical mechanism and, for a symmetric mechanism it allows configuring sets of leg positions with symmetrical observability. Our investigation takes advantage of this situation and presents the following contributions: (\textit{i}) a conjecture that allows mapping the symmetries of the mechanism into the active-joint workspace, (\textit{ii}) a set of necessary conditions to express leg parameters in coordinate systems which allow symmetrical observability, and (\textit{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 ($n_{legs} - 1$) legs of the parallel mechanism allowing to apply to other legs the symmetry-transformed sample protocol used for the kinematic identification of a \textit{reference} leg. The symmetrical observability of sets of leg parameters allows to reduce the costs of the pose selection procedure by a factor of $(1/n_{legs})$ 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 ($n_{legs} - 1$) 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 3$\underline{R}RR$ symmetrical parallel mechanism. }
}