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Research Papers

Dynamic and Oscillatory Motions of Cable-Driven Parallel Robots Based on a Nonlinear Cable Tension Model

[+] Author and Article Information
Sana Baklouti

Université Bretagne-Loire,
INSA de Rennes,
Laboratoire de Génie Civil et Génie Mécanique
(LGCGM) - EA 3913,
20, avenue des Buttes de Cöesmes,
Rennes Cedex 35043, France
e-mail: sana.baklouti@insa-rennes.fr

Eric Courteille

Université Bretagne-Loire,
INSA de Rennes,
Laboratoire de Génie Civil et Génie Mécanique
(LGCGM) - EA 3913,
20, avenue des Buttes de Cöesmes,
Rennes Cedex 35043, France
e-mail: eric.courteille@insa-rennes.fr

Stéphane Caro

CNRS,
Laboratoire des Sciences du
Numérique de Nantes,
UMR CNRS n6004,
1, rue de la Noë,
Nantes Cedex 03 44321, France
e-mail: stephane.caro@ls2n.fr

Mohamed Dkhil

Université Bretagne-Loire,
INSA de Rennes,
Laboratoire de Génie Civil et Génie Mécanique
(LGCGM) - EA 3913,
20, avenue des Buttes de Cöesmes,
Rennes Cedex 35043, France
e-mail: mohamed.dkhil@insa-rennes.fr

1Corresponding author.

Manuscript received February 3, 2016; final manuscript received September 22, 2017; published online October 12, 2017. Assoc. Editor: K. H. Low.

J. Mechanisms Robotics 9(6), 061014 (Oct 12, 2017) (14 pages) Paper No: JMR-17-1029; doi: 10.1115/1.4038068 History: Received February 03, 2016; Revised September 22, 2017

In this paper, dynamic modeling of cable-driven parallel robots (CDPRs) is addressed where each cable length is subjected to variations during operation. It is focusing on an original formulation of cable tension, which reveals a softening behavior when strains become large. The dynamic modulus of cable elasticity is experimentally identified through dynamic mechanical analysis (DMA). Numerical investigations carried out on suspended CDPRs with different sizes show the effect of the proposed tension formulation on the dynamic response of the end-effector.

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Figures

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Fig. 1

Schematic diagram of the studied CDPR (3DOF CDPR suspended by three cables)

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Fig. 2

Experimental setup: (a) cross section of a rotation-resistant steel wire cable, Carl Stahl Technocables Ref 1692; (b) Thema Concept cyclic loading test bench

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Fig. 3

Load–elongation diagram of a steel wire cable measured in steady-state conditions at the rate of 0.05 mm/s

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Fig. 4

Hysteresis loops for a 4 mm steel wire cable preloaded at 1500 N with force-controlled sine waves applied at 0.1, 1, 2, 5, 10, and 20 Hz

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Fig. 5

Circular helical trajectory: (a) end-effector trajectory and (b) end-effector Cartesian velocities

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Fig. 6

Cable linear velocity profiles

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Fig. 7

Comparison between linear and nonlinear tension formulations: tension, elongation, and strain for the three cables. Time history of tension T1 (a), of elongation r1 (b), of strain of cable 1 (c), of tension T2 (d), of elongation r2 (e), of strain of cable 2 (f), of tension T3 (g), of elongation r3 (h), and of strain of cable 3 (i).

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Fig. 8

Comparison between linear and nonlinear tension formulations: time history of positioning error of the end-effector along (a) x-axis, (b) y-axis, and (c) z-axis

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Fig. 9

Schematics of the (a) CAROCA and (b) FAST CDPR

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Fig. 10

Comparison between linear and nonlinear tension formulations: time history of tension T2: CAROCA (a), of elongation r2: CAROCA (b), of strain of cable 2: CAROCA (c), of tension T2: FAST (d), of elongation r2: FAST (e), and of strain of cable 2: FAST (f)

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Fig. 11

Positioning errors of the CDPR end-effector calculated with a linear and a nonlinear cable tension model, respectively: (a) CAROCA and (b) FAST

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Fig. 12

Trapezoidal-velocity trajectory: (a) trapezoidal actuation velocities; (b) trajectory of the end-effector

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Fig. 13

Comparison between nonlinear constitutive formulations using static or dynamic modulus: tension, elongation, and strain for the three cables. Time history of tension T1 (a), of elongation r1 (b), of strain of cable 1 (c), of tension T2 (d), of elongation r2 (e), of strain of cable 2 (f), of tension T3 (g), of elongation r3 (h), and of strain of cable 3 (i).

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Fig. 14

Comparison between nonlinear constitutive formulations using static or dynamic modulus: time history of positioning error of the end-effector along (a) x-axis, (b) y-axis, and (c) z-axis

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Fig. 15

Comparison between nonlinear constitutive formulations using static or dynamic modulus (2 Hz)—natural frequency: time history of f1 (a), of f2 (b), and of f3 (c)

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Fig. 16

Comparison between dynamic responses of the CAROCA while using quasi-static or dynamic modulus (10 Hz): time history of tension T2: CAROCA (a), of elongation r2: CAROCA (b), of strain of cable 2: CAROCA (c), of f1: CAROCA (g), of f2: CAROCA (h), and of f3: CAROCA (i); positioning error along x-axis: CAROCA (d), along y-axis: CAROCA (e), and along z-axis: CAROCA (f)

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Fig. 17

Comparison between nonlinear constitutive formulations with and without damping: tension, elongation, and strain for the three cables. Time history of tension T1 (a), of elongation r1 (b), of strain of cable 1 (c), of tension T2 (d), of elongation r2 (e), of strain of cable 2 (f), of tension T3 (g), of elongation r3 (h), and of strain of cable 3 (i).

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Fig. 18

Comparison between nonlinear constitutive formulations with and without damping: time history of positioning error of the end-effector along (a) x-axis, (b) y-axis, and (c) z-axis

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