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Research Papers

Kinematics and Dynamics of a Self-Stressed Cartesian Cable-Driven Mechanism

[+] Author and Article Information
Saeed Behzadipour

Mechanical Engineering, University of Alberta, Edmonton, AB, T6G 2G8, Canadasaeedb@ualberta.ca

J. Mech. Des 131(6), 061005 (May 19, 2009) (10 pages) doi:10.1115/1.3125206 History: Received June 11, 2008; Revised March 12, 2009; Published May 19, 2009

A novel hybrid cable-driven mechanism with Cartesian motion is introduced. It consists of a rigid-link Cartesian mechanism and a cable drive system with stationary actuators to provide the motion. The cable drive system is self-stressed meaning that the tension in the cables required to keep them taut is provided internally and hence does not depend on either actuation redundancy or external sources such as gravity. This keeps the number of actuators at minimum and also eliminates the static loading of actuators as well as redundant work. The kinematic analysis of the mechanism is presented. The forward and inverse kinematic solutions are found and shown to be linear and pose independent. Also the stiffness of the mechanism induced by the compliance of the cable is analyzed to find the weakest stiffness. For this purpose, a parameter called “compliance length” is defined and used. Compliance length presents the stiffness of the mechanism by the length of the cable with the same stiffness. It makes the analysis independent from the design and the properties of the cable and can be quite useful in the design process. Finally, two dynamic models are given for the mechanism depending on whether or not the cable is stretchable and the properties of each model are discussed.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic of the Cartesian cable-driven mechanism

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Figure 2

The Cartesian mechanism and the sample storage trays

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Figure 3

Geometrical parameters of the Cartesian cable-driven mechanism (note that inertia frame OXYZ is not body-fixed to the end-effector)

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Figure 4

The notation used for the static and stiffness analysis

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Figure 5

The free body diagram of the H-shape frame

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Figure 6

The free body diagrams of two sections of the mechanisms

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Figure 7

Compliance length of the mechanism in its workspace at z=0

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Figure 8

Compliance length of the mechanism in its workspace at z=0

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Figure 9

Physical model for the dynamics of the mechanism: a) un-stretchable cable, b) stretchable cable

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Figure 10

The free body diagrams of the of the system shown in Fig. 9

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Figure 11

The compliance length calculated in the workspace

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Figure 12

The sample trajectory simulated for three cable sizes such that the unit length stiffness of the cables are (a)1/100, (b)1/10, and (c) equal to the stiffness found in Eq. 42

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