on the ability of a cable-driven robot to generate a prescribed set of wrenches

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ON THE ABILITY OF A CABLE-DRIVEN ROBOT TO GENERATE A PRESCRIBED

SET OF WRENCHES(DETC2008-49518)

Samuel Bouchard, Clément Gosselin, Brian Mooresamuel@robotiq.ca

gosselin@gmc.ulaval.cabrian.moore@ricam.oeaw.ac.at

ASME IDETC-CIEAugust 6th 2008, New York City

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Objective

Ability to generate a set of wrenches at the platform considering:

• Minimum and maximum tension

• n cables, d degrees of freedom, n>=d

• Suspended or fully constrained

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Different wrenches for different tasks

Skycam

Photo: jamd.com

Tokyo University Wire Haptic Interface

Photo: Prof. Takeda, Tokyo Institute of Technology

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General Concept

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Plan of the presentation

1. Nature of A.

2. Representations and method to define A.

3. Relationship between A and T.

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Nature of A

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Wrench equation

Solve

considering the constraint:

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Nature of A

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Zonotope, definition 1

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Zonotope, definition 2

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Zonotope, definition 3

A

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Examples

[Animations]

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A in the litterature

[Pham et al., 2005][Bosscher et al.,2004]

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How to obtain A?

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Representations

V-Representation H-Representation

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Algorithms

Method Representations Iterative?

Convex hull H or V Yes

Hyperplane shifting H No

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Convex Hull

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Convex Hull

where

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Hyperplane shifting

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Relation between A and T

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Set of inequalities

• T is a single wrench:

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Set of inequalities

• T is a single wrench:

• T is a set with many wrenches:

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Future work

• Improve hyperplane shifting method

• Optimal tension distribution