Research Papers

Synthesis of Spatial RPRP Closed Linkages for a Given Screw System

[+] Author and Article Information
Alba Perez-Gracia

 Institut de Robòtica i Informàtica Industrial (CSIC-UPC), Llorens i Artigas, 4-6, 08028 Barcelona, Spain; College of Science and Engineering, Idaho State University, 921 South 8th Avenue, Pocatello, ID 83209aperez@iri.upc.edu

J. Mechanisms Robotics 3(2), 021009 (Apr 11, 2011) (8 pages) doi:10.1115/1.4003846 History: Received May 11, 2010; Revised February 15, 2011; Published April 11, 2011; Online April 11, 2011

The dimensional synthesis of spatial chains for a prescribed set of positions can be applied to the design of parallel robots by joining the solutions of each serial chain at the end-effector. This design method does not provide with the knowledge about the trajectory between task positions and, in some cases, may yield a system with negative mobility. These problems can be avoided for some overconstrained but movable linkages if the finite-screw system associated with the motion of the linkage is known. The finite-screw system defining the motion of the robot is generated by a set of screws, which can be related to the set of finite task positions traditionally used in the synthesis theory. The interest of this paper lies in presenting a method to define the whole workspace of the linkage as the input task for the exact dimensional synthesis problem. This method is applied to the spatial RPRP closed linkage, for which one solution exists.

Copyright © 2011 by American Society of Mechanical Engineers
Topics: Screws , Linkages , Chain , Equations
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Figure 1

The RP serial chain

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Figure 2

The RPRP closed linkage

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Figure 3

Screw system generated by the RPRP linkage, above; corresponding absolute displacements, below

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Figure 4

Above, screw system generated by S12 and S13 (shown as first and last screws); below, corresponding absolute displacements with reference displacement being the identity

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Figure 5

RPRP linkage reaching three positions of the trajectory

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Figure 6

Screw system generated by S12 and S13 (first and last screws)

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Figure 7

The RPRP end-effector task trajectory

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Figure 8

The RPRP linkage reaching three positions along the trajectory




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