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Research Papers

On the Design of Adaptive Cable-Driven Systems

[+] Author and Article Information
Giulio Rosati1

Department of Innovation in Mechanics and Management (DIMEG), University of Padua-Faculty of Engineering, Via Venezia 1, 35131 Padova, Italygiulio.rosati@unipd.it

Damiano Zanotto

Department of Innovation in Mechanics and Management (DIMEG), University of Padua-Faculty of Engineering, Via Venezia 1, 35131 Padova, Italy

Sunil K. Agrawal

Mechanical Systems Laboratory, Department of Mechanical Engineering, University of Delaware, Newark, DE 19716agrawal@udel.edu

This index had already been introduced by Gallina et al.  in Ref. 21.

That is, the $(mod(i,3)+1)th$ cable vector.

Theoretically, this is true also for the first design solution, if we do not impose the orthogonality constraint between each cable and the corresponding guide. In practice, however, the straight-line arrangement limits the motion of each trolley to a single guide.

Actually, this is true as far as the center of the circumference lies above the line segment $P2P3¯$.

The simplest cable-based device capable of controlling 3DOF employs four cables.

This is clear since the direction of each cable would be parallel to the straight line connecting the center of the end-effector to the center of the corresponding pulley.

From a geometrical point of view, each pair of normalized matrices $A¯$ corresponding to points that are symmetrical with respect to the $x$ axis (or to the $y$ axis) can always be rewritten in terms of two rotated frames with mutually symmetrical $x′$ and $y′$ axes (the remaining axes $z′$ being opposite). The new representations of those matrices are the same (column permutations excepted), thus ensuring that the corresponding $A¯A¯T$ are similar and, therefore, yield the same eigenvalues. With the same reasoning, it can be proved that the matrices $A¯A¯T$ are similar even in the case of points being symmetric with respect to the bisectors.

1

Corresponding author.

J. Mechanisms Robotics 3(2), 021004 (Mar 10, 2011) (13 pages) doi:10.1115/1.4003580 History: Received December 03, 2009; Revised January 29, 2011; Published March 10, 2011; Online March 10, 2011

Abstract

Several systematic approaches have been developed for the optimal design of cable-based systems. Global indices are usually employed to quantify the effectiveness of a specific design inside a reference region of the workspace. The performances at the moving platform are strictly related to cable configuration, which, in turn, depends on the pose of the moving platform. As a result, traditional designs are characterized by the high variability of performances within the workspace and are often badly tailored to the design goals. The motivation behind this paper is to formalize a new design methodology for cable-driven devices. Based on a total or partial decoupling between cable disposition and end-effector pose, this methodology allows us to achieve well-tailored design solutions for a given design requirement. The resulting systems are here defined as adaptive cable-driven systems. Two simple design problems are presented and solved with both the traditional and the novel approaches, and the advantages of the latter are emphasized by comparing the resulting design solutions.

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Figures

Figure 1

Figure 2

Normalized force index for a three-cable, 2DOF design (38)

Figure 3

Three-cable, 2DOF device: operational polytope

Figure 4

Correlation between layout geometry and force performances for the traditional design (solid line), the semi-adaptive design (dashed lines), the adaptive triangular design (asterisk), and the adaptive circular design (circle)

Figure 5

Fully adaptive designs with linear guides

Figure 6

Fully adaptive designs with circular guides

Figure 7

Semi-adaptive device: derivation of the optimal design for given k

Figure 8

Normalized force index for a three-cable, 2DOF semi-adaptive design (38)

Figure 9

Correlation between (Aus/Atot)opt and force performances for the traditional design (solid line), the semi-adaptive design (dashed line), the adaptive triangular design (asterisk), and the adaptive circular design (circle)

Figure 10

Four-cable, 3DOF device: traditional design (38)

Figure 11

Dexterity index κ(A¯)−1 for the device portrayed in Fig. 1

Figure 14

Figure 13

Figure 12

Correlation of κ(A¯)min−1 (a) with (rREQ/L)opt and (b) with (Aus/Atot)opt. The corresponding data for the adaptive designs are represented by the asterisk (squarelike design) and by the circle (circular design).

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