Research Papers

A Linear Relaxation Method for Computing Workspace Slices of the Stewart Platform

[+] Author and Article Information
Oriol Bohigas

e-mail: obohigas@iri.upc.edu

Montserrat Manubens

e-mail: mmanuben@iri.upc.edu

Lluís Ros

e-mail: llros@iri.upc.edu
Institut de Robòtica i Informàtica
Industrial (CSIC-UPC),
Barcelona 08028, Catalonia

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the Journal of Mechanisms and Robotics. Manuscript received July 28, 2011; final manuscript received May 18, 2012; published online October 19, 2012. Assoc. Editor: Kazem Kazerounian.

J. Mechanisms Robotics 5(1), 011005 (Oct 19, 2012) (9 pages) Paper No: JMR-11-1085; doi: 10.1115/1.4007706 History: Received July 28, 2011; Revised May 18, 2012

The workspace of a Stewart platform is a complex six-dimensional volume embedded in the Cartesian space defined by six pose parameters. Because of its large dimension and complex shape, this volume is difficult to compute and represent, and comprehension on its structure is being gained by studying its three-dimensional slices. While successful methods have been given to determine the constant-orientation slice, the computation and appropriate visualization of the constant-position slice (also known as the orientation workspace) has proved to be a challenging task. This paper presents a unified method for computing both of such slices, and any other ones defined by fixing three pose parameters, on general Stewart platforms possibly involving mechanical limits on the active and passive joints. Advantages over existing methods include, in addition to the previous, the ability to determine all connected components of the workspace, and any motion barriers present in its interior.

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Fig. 1

A Stewart platform. The base and platform joints are meant to be universal and spherical, respectively.

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Fig. 2

Circle constraint of an active-joint limit

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Fig. 3

Elements of a passive joint-limit constraint

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Fig. 5

Boundaries of the constant-position workspace of the standard platform, without taking passive-joint limits into account

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Fig. 6

Only one component in Fig. 5 (left) is partially achievable after taking passive-joint limits into account (right)

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Fig. 7

Boundaries of the constant-orientation workspace of the standard platform for z > 0

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Fig. 8

Boundaries of the planar-mode workspace of the standard platform before and after the consideration of passive-joint limits

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Fig. 9

A 3-UPS/S platform (figure adapted from Ref. [25])

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Fig. 10

Degenerate boundaries of the constant-position workspace of the special platform




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