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Research Papers

Workspace Analysis of Multibody Cable-Driven Mechanisms

[+] Author and Article Information
Siavash Rezazadeh

Department of Mechanical Engineering, University of Alberta, Edmonton, AB, T6G 2G8, Canadasiavash.rezazadeh@ualberta.ca

Saeed Behzadipour

Department of Mechanical Engineering, University of Alberta, Edmonton, AB, T6G 2G8, Canadasaeed.behzadipour@ualberta.ca

The expression can be provided upon request.

Compared with {1,2} design, the extra cable of this case has been attached to link 2, and compared with {0,3} design, the extra cable has been attached to link 1.

J. Mechanisms Robotics 3(2), 021005 (Mar 10, 2011) (10 pages) doi:10.1115/1.4003581 History: Received August 12, 2010; Revised January 12, 2011; Published March 10, 2011; Online March 10, 2011

A systematic approach is proposed to determine the tensionable workspace of multibody cable-driven mechanisms. The method is also capable of finding analytical descriptions for the boundaries of the tensionable regions for any number of redundant cables used. The presented approach builds upon the available methods for conventional (rigid body) cable-driven mechanisms, i.e., null space analysis and supporting/separating hyperplanes. It extends these methods to the case of a multibody driven by cables. For this purpose, the notion of generalized forces and Lagrange’s method is used to eliminate the constraint forces/moments from the equilibrium equations. This has resulted in a more compact equation form with fewer unknowns. The method is then applied to several one- and two-DOF mechanisms with various cable distributions. Analytical descriptions for the boundaries of their workspaces are found. These boundaries and the resulting regions are then used to improve the design for larger tensionable workspaces.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematics of a rigid body cable-driven mechanism

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Figure 2

A typical cable-driven serial multibody system

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Figure 3

Schematic of a 1DOF rigid body driven by two cables

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Figure 4

Schematic of a 2DOF two-link multibody system driven by three cables having {1,2} distribution

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Figure 5

The angular positions of the winches of the system of Fig. 4

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Figure 6

Regions of configuration space for a two-link mechanism with {1,2} cable distribution: curve set 1: – – – –, curve set 2: …….., curve set 3: ——..——, and curve set 4: ———

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Figure 7

The {1,2}-distribution system with the third winch relocated

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Figure 8

Regions of configuration space for the {1,2} cable distribution and relocated winch 3: curve set 1: – – –, curve set 2: ………, curve set 3: ——..——, and curve set 4: ———

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Figure 9

Schematic of a 2DOF two-link multibody system driven by three cables having the distribution {0,3}

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Figure 10

Workspace analysis of a two-link mechanism driven by three cables attached to the second link: curve set 1: ———, curve set 2: – – – –, and curve set 3: ………

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Figure 11

The modified design for {0,3} cable distribution

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Figure 12

Schematic of a 2DOF two-link multibody system driven by four cables having the distribution {1,3}

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Figure 13

Workspace analysis of a two-link mechanism driven by the distribution {1,3}: curve set 1: ———, curve set 2: – – – –, and curve set 3: ………

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