Stiffness of Cable-based Parallel Manipulators With Application to Stability Analysis

[+] Author and Article Information
Saeed Behzadipour

 University of Waterloo, Department of Mechanical Engineering, Waterloo, Ontario N2L 3G1, Canada

Amir Khajepour1

 University of Waterloo, Department of Mechanical Engineering, Waterloo, Ontario N2L 3G1, Canadaakhajepour@uwaterloo.ca


Corresponding author.

J. Mech. Des 128(1), 303-310 (Apr 28, 2005) (8 pages) doi:10.1115/1.2114890 History: Received August 12, 2004; Revised April 28, 2005

The stiffness of cable-based robots is studied in this paper. Since antagonistic forces are essential for the operation of cable-based manipulators, their effects on the stiffness should be considered in the design, control, and trajectory planning of these manipulators. This paper studies this issue and derives the conditions under which a cable-based manipulator may become unstable because of the antagonistic forces. For this purpose, a new approach is introduced to calculate the total stiffness matrix. This approach shows that, for a cable-based manipulator with all cables in tension, the root of instability is a rotational stiffness caused by the internal cable forces. A set of sufficient conditions are derived to ensure the manipulator is stabilizable meaning that it never becomes unstable upon increasing the antagonistic forces. Stabilizability of a planar cable-based manipulator is studied as an example to illustrate this approach.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

General model of a cable-based fully parallel manipulator

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Figure 2

A single cable with some internal force

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Figure 3

An equivalent stiffness model for a single cable with pretension: (a) a single cable, (b) an equivalent four-spring

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Figure 4

The equivalent stiffness model of the manipulator shown in Fig. 1. (a) The cables’ stiffness and (b) the stiffness caused by the force distribution on the end-effector.

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Figure 5

The stabilizability of a plannar cable-based manipulator in four different orientations of the end-effector: (a) 0 deg, (b) 10 deg, (c ) 20 deg, (d) 30 deg

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Figure 6

The effect of change of the cable configuration on the stabilizability. Orientations of the end-effector are (a) 0 deg, (b) 10 deg, (c) 20 deg, (d) 30 deg.

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Figure 7

A plannar cable-based manipulator which is unstabilizable everywhere and beomces unstable for relatively small antagonistic forces



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