ON THE ABILITY OF A CABLE-DRIVEN ROBOT TO GENERATE A PRESCRIBED SET OF WRENCHES (DETC2008-49518) Samuel Bouchard, Clément Gosselin, Brian Moore [email_address] [email_address] [email_address] ASME IDETC-CIE August 6th 2008, New York City

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

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

Different wrenches for different tasks Skycam Photo: jamd.com Tokyo University Wire Haptic Interface Photo: Prof. Takeda, Tokyo Institute of Technology

General Concept

Plan of the presentation Nature of A. Representations and method to define A . Relationship between A and T .

Nature of A.

Representations and method to define A .

Relationship between A and T .

Nature of A

Nature of A

Wrench equation Solve considering the constraint:

Solve

considering the constraint:

Nature of A

Zonotope, definition 1

Zonotope, definition 2

Zonotope, definition 3 A

Examples [Animations]

[Animations]

A in the litterature [Pham et al., 2005] [Bosscher et al.,2004]

How to obtain A ?

How to obtain A ?

Representations V-Representation H-Representation

Algorithms No H Hyperplane shifting Yes H or V Convex hull Iterative? Representations Method

Convex Hull

Convex Hull where

where

Hyperplane shifting

Relation between A and T

Relation between A and T

Set of inequalities T is a single wrench:

T is a single wrench:

Set of inequalities T is a single wrench: T is a set with many wrenches:

T is a single wrench:

T is a set with many wrenches:

Future work Improve hyperplane shifting method Optimal tension distribution

Improve hyperplane shifting method

Optimal tension distribution