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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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References

Lim, W. B. , Yang, G. , Yeo, S. H. , Mustafa, S. K. , and Chen, I.-M. , 2009, “ A Generic Tension-Closure Analysis Method for Fully-Constrained Cable-Driven Parallel Manipulators,” IEEE International Conference on Robotics and Automation (ICRA '09), Kobe, Japan, May 12–17, pp. 2187–2192.
Gouttefarde, M. , Krut, S. , Company, O. , Pierrot, F. , and Ramdani, N. , 2008, “ On the Design of Fully Constrained Parallel Cable-Driven Robots,” Advances in Robot Kinematics: Analysis and Design, Springer, Dordrecht, pp. 71–78.
Gosselin, C. , 2014, “ Cable-Driven Parallel Mechanisms: State of the Art and Perspectives,” Bull. Jpn. Soc. Mech. Eng.: Mech. Eng. Rev., 1(1), pp. 1–17.
Bosscher, P. , Riechel, A. T. , and Ebert-Uphoff, I. , 2006, “ Wrench-Feasible Workspace Generation for Cable-Driven Robots,” IEEE Trans. Rob., 22(5), pp. 890–902. [CrossRef]
Alp, A. B. , and Agrawal, S. U. , 2002, “ Cable Suspended Robots: Design, Planning and Control,” IEEE International Conference on Robotics and Automation (ICRA '02), Washington, DC, May 11–15, pp. 4275–4280.
Pusey, J. , Fattah, A. , Agrawal, S. , and Messina, E. , 2004, “ Design and Workspace Analysis of a 6-6 Cable-Suspended Parallel Robot,” Mech. Mach. Theory, 39(7), pp. 761–778. [CrossRef]
Fattah, A. , and Agrawal, S. K. , 2002, “ Workspace and Design Analysis of Cable-Suspended Planar Parallel Robots,” ASME Paper No. DETC2002/MECH-34330.
Barrette, G. , and Gosselin, C. M. , 2005, “ Determination of the Dynamic Workspace of Cable-Driven Planar Parallel Mechanisms,” ASME J. Mech. Des., 127(2), pp. 242–248. [CrossRef]
Cunningham, D. , and Asada, H. H. , 2009, “ The Winch-Bot: A Cable-Suspended, Under-Actuated Robot Utilizing Parametric Self-Excitation,” IEEE International Conference on Robotics and Automation (ICRA '09), Kobe, Japan, May 12–17, pp. 1844–1850.
Lefrançois, S. , and Gosselin, C. , 2010, “ Point-to-Point Motion Control of a Pendulum-Like 3-Dof Underactuated Cable-Driven Robot,” IEEE International Conference on Robotics and Automation (ICRA), Anchorage, AK, May 3–7, pp. 5187–5193.
Zanotto, D. , Rosati, G. , and Agrawal, S. K. , 2011, “ Modeling and Control of a 3-Dof Pendulum-Like Manipulator,” IEEE International Conference on Robotics and Automation (ICRA), Shanghai, China, May 9–13, pp. 3964–3969.
Zoso, N. , and Gosselin, C. , 2012, “ Point-to-Point Motion Planning of a Parallel 3-Dof Underactuated Cable-Suspended Robot,” IEEE International Conference on Robotics and Automation (ICRA), St Paul, MN, May 14–18, pp. 2325–2330.
Fantoni, I. , and Lozano, R. , 2001, Non Linear Control for Underactuated Mechanical Systems, Springer, London.
Gosselin, C. , Ren, P. , and Foucault, S. , 2012, “ Dynamic Trajectory Planning of a Two-Dof Cable-Suspended Parallel Robot,” IEEE International Conference on Robotics and Automation (ICRA), St Paul, MN, May 14–18, pp. 1476–1481.
Gosselin, C. , 2012, “ Global Planning of Dynamically Feasible Trajectories for Three-DoF Spatial Cable-Suspended Parallel Robots,” First International Conference on Cable-Driven Parallel Robots, Stuttgart, Germany, Sept. 2–4, pp. 3–22.
Jiang, X. , and Gosselin, C. , 2014, “ Dynamically Feasible Trajectories for Three-DoF Planar Cable-Suspended Parallel Robots,” ASME Paper No. DETC2014-34419.
Davis, H. T. , 1962, Introduction to Nonlinear Differential and Integral Equations, Dover Publications, New York.
Beléndez, A. , Pascal, C. , Méndez, D. I. , Beléndez, T. , and Neipp, C. , 2007, “ Exact Solution for the Nonlinear Pendulum,” Rev. Bras. Ensino Fís., 29(4), pp. 645–648. [CrossRef]
Marion, J. B. , 1970, Classical Dynamics of Particles and Systems, Academic Press, New York.

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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