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Research Papers

Trajectory Generation for Three-Degree-of-Freedom Cable-Suspended Parallel Robots Based on Analytical Integration of the Dynamic Equations

[+] Author and Article Information
Xiaoling Jiang

Département de génie mécanique,
Université Laval,
1065 Avenue de la Médecine,
Québec, QC G1V0A6, Canada
e-mail: xiaoling.jiang.1@ulaval.ca

Clément Gosselin

Département de génie mécanique,
Université Laval,
1065 Avenue de la Médecine,
Québec, QC G1V0A6, Canada
e-mail: gosselin@gmc.ulaval.ca

1Corresponding author.

Manuscript received May 18, 2015; final manuscript received August 20, 2015; published online March 7, 2016. Assoc. Editor: Venkat Krovi.

J. Mechanisms Robotics 8(4), 041001 (Mar 07, 2016) (7 pages) Paper No: JMR-15-1117; doi: 10.1115/1.4031501 History: Received May 18, 2015; Revised August 20, 2015

This paper proposes a trajectory generation technique for three degree-of-freedom (3-dof) planar cable-suspended parallel robots. Based on the kinematic and dynamic modeling of the robot, positive constant ratios between cable tensions and cable lengths are assumed. This assumption allows the transformation of the dynamic equations into linear differential equations with constant coefficients for the positioning part, while the orientation equation becomes a pendulum-like differential equation for which accurate solutions can be found in the literature. The integration of the differential equations is shown to yield families of translational trajectories and associated special frequencies. This result generalizes the special cases previously identified in the literature. Combining the results obtained with translational trajectories and rotational trajectories, more general combined motions are analyzed. Examples are given in order to demonstrate the results. Because of the initial assumption on which the proposed method is based, the ratio between cable forces and cable lengths is constant and hence always positive, which ensures that all cables remain under tension. Therefore, the acceleration vector remains in the column space of the Jacobian matrix, which means that the mechanism can smoothly pass through kinematic singularities. The proposed trajectory planning approach can be used to plan dynamic trajectories that extend beyond the static workspace of the mechanism.

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Figures

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Fig. 1

Schematic diagram of a general planar 3-dof cable-suspended robot

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Fig. 2

Schematic diagram of a specific planar 3-dof cable-suspended robot

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Fig. 3

Amplitude θ0 as a function of L/L1 for different values of L/L2

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Fig. 4

Amplitude θ0 as a function of L/L2 for different values of L/L1

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Fig. 5

Cable tensions for the pure rotation

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Fig. 6

Horizontal oscillations with combined rotations

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Fig. 7

Cable tensions for the horizontal oscillations with combined rotations

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Fig. 8

Circular motion with combined rotations

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Fig. 9

Cable tensions for the circular motion with combined rotations

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