A Planar Quaternion Approach to the Kinematic Synthesis of a Parallel Manipulator
Document Type
Article
Publication Date
7-1997
Publication Source
Robotica
Abstract
In this paper we present a technique for designing planar parallel manipulators with platforms capable of reaching any number of desired poses. The manipulator consists of a platform connected to ground by RPR chains. The set of positions and orientations available to the end-effector of a general RPR chain is mapped into the space of planar quaternions to obtain a quadratic manifold. The coefficients of this constraint manifold are functions of the locations of the base and platform R joints and the distance between them. Evaluating the constraint manifold at each desired pose and defining the limits on the extension of the P joint yields a set of equations.
Solutions of these equations determine chains that contain the desired poses as part of their workspaces. Parallel manipulators that can reach the prescribed workspace are assembled from these chains. An example shows the determination of three RPR chains that form a manipulator able to reach a prescribed workspace.
Inclusive pages
361-365
ISBN/ISSN
0263-5747
Copyright
Copyright © 1997, Cambridge University Press
Publisher
Cambridge University Press
Volume
15
Issue
4
Peer Reviewed
yes
eCommons Citation
Murray, Andrew P.; Pierrot, François; Dauchez, Pierre; and McCarthy, J. Michael, "A Planar Quaternion Approach to the Kinematic Synthesis of a Parallel Manipulator" (1997). Mechanical and Aerospace Engineering Faculty Publications. 189.
https://ecommons.udayton.edu/mee_fac_pub/189
COinS
Comments
Permission documentation is on file.