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RESEARCH PAPERS

# Workspaces of Cable-Actuated Parallel Manipulators

[+] Author and Article Information
Ethan Stump

GRASP Laboratory, Department of Mechanical Engineering, University of Pensylvania, Philadelphia, Pennsylvania 19104estump@grasp.upenn.edu

Vijay Kumar

GRASP Laboratory, Department of Mechanical Engineering, University of Pensylvania, Philadelphia, Pennsylvania 19104kumar@cis.upenn.edu

Excerpts from this manuscript appeared in the ASME DETC 2004 conference. The conference paper (10) developed results for the planar case.

J. Mech. Des 128(1), 159-167 (Jul 25, 2005) (9 pages) doi:10.1115/1.2121741 History: Received May 10, 2005; Revised July 25, 2005

## Abstract

This paper develops analytical techniques to delineate the workspace boundaries for parallel mechanisms with cables. In such mechanisms, it is not only necessary to solve the closure equations but it is also essential to verify that equilibrium can be achieved with non-negative actuator (cable) forces. We use tools from convex analysis and linear algebra to derive closed-form expressions for the workspace boundaries and illustrate the applications using planar and spatial examples.

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## Figures

Figure 1

General planar platform geometry

Figure 2

Plots showing (x,y) regions that satisfiy the individual inequalities in Eq. 13. Platform angle is fixed at u=0.015.

Figure 3

Plot showing (x,y) region that satisfies all of the inequalities in Eq. 13. Platform angle is fixed at u=0.015.

Figure 4

Plot showing (x,y) Region that satisfies all of the inequalities in Eq. 13. Platform angle is fixed at u=0.

Figure 5

Plot showing (x,y) region that is reachable for a random spatial platform with no rotation (dimensions given in the Appendix, z=0.8)

Figure 6

Array of plots showing (x,y) regions that are reachable for random spatial platforms with no rotation. Columns correspond with increasing z values from left to right; rows correspond to different random platform geometries.

Figure 7

Diagram of an octahedral manipulator

Figure 8

Plot showing (x,y) region that is reachable for the octahedral manipulator with R1 equal to 4 and no platform rotation

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