Heuristic Algorithm for Velocity Scheduling with a Schönflies-Motion Generator

  • Bruno BelzileEmail author
  • Jorge Angeles
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)


The authors propose a trajectory-planning algorithm to minimize the maximum torque required to produce a prescribed trajectory with a pick-and place robot. This is done with a scheduling of the velocity of the moving plate, while following the Adept path. Simulation tests are conducted with the dynamics model of an isostatic Schönflies-motion generator, but the proposed algorithm can be applied to any architecture capable of producing Schönflies motions. Results show a reduction of more than 40 % of the maximum torque required from the actuators, regardless of the cycle time, when traversing the path at 1 Hz and higher.


Kinematics dynamics pick-and-place Schönflies-motion generators 


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  1. 1.
    Nabat, V., Rodriguez, M., Company, O., Krut, S., Pierrot, F.: Par4: Very high speed parallel robot for pick-and-place. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems. Edmonton, Canada (2005)Google Scholar
  2. 2.
    Makino, H., Kato, A., Yamazaki, Y.: Research and commercialization of SCARA robot-the case of industry-university joint research and development. International Journal of Automation Technology. 1, 61-67 (2007)Google Scholar
  3. 3.
    Brogårdh, T.: Device for Relative Movement of Two Elements. U.S. Patent No. 6,301,988(2001)Google Scholar
  4. 4.
    Angeles, J., Morozov, A.: Four-Degree-of-Freedom Parallel Manipulator for Producing Schönflies Motions. U.S. Patent No. 7,127,962 (2006)Google Scholar
  5. 5.
    Gallardo-Alvarado, J., Abedinnasab, M.H.,Lichtblau, D.: Simplified Kinematics for a Parallel Manipulator Generator of the Schönflies Motion. Journal of Mechanisms and Robotics. 8(6), 061020 (2016)Google Scholar
  6. 6.
    Corbel, D., Gouttefarde, M., Pierrot, F.: Actuation redundancy as a way to improve the acceleration capabilities of 3T and 3T1R pick-and-place parallel manipulators. Journal of Mechanisms and Robotics. 2(4), 041002 (2010)Google Scholar
  7. 7.
    Altuzarra, O., Zubizarreta, A., Cabanes, I., Pinto, C.: Dynamics of a four degrees-of-freedom parallel manipulator with parallelogram joints. Mechatronics, 19(8), 1269-1279 (2009)Google Scholar
  8. 8.
    Zhang, N., Shang,W. Dynamic trajectory planning of a 3-DOF under-constrained cable-driven parallel robot. Mechanism and Machine Theory. 98, 21-35 (2016)Google Scholar
  9. 9.
    Gosselin, C., Foucault, S.: Dynamic point-to-point trajectory planning of a two-DOF cablesuspended parallel robot. IEEE Transactions on Robotics. 30(3), 728-736 (2014)Google Scholar
  10. 10.
    Jiang, X., Gosselin, C.: Dynamic point-to-point trajectory planning of a three-DOF cablesuspended parallel robot. IEEE Transactions on Robotics. 32(6), 1550-1557 (2016)Google Scholar
  11. 11.
    Park, J.S.: Motion profile planning of repetitive point-to-point control for maximum energy conversion efficiency under acceleration conditions. Mechatronics. 6(6), 649-663 (1996)Google Scholar
  12. 12.
    Pellicciari, M., Berselli, G., Leali, F., Vergnano, A.: A method for reducing the energy consumption of pick-and-place industrial robots. Mechatronics. 23, 326-334 (2013)Google Scholar
  13. 13.
    Wigström, O., Lennartson, B., Vergnano, A.: High-Level Scheduling of Energy Optimal Trajectories.IEEE Transactions on Automation Science and Engineering. 10(1), 57-64 (2013)Google Scholar
  14. 14.
    Bobrow, J.E., Dubowsky, S., Gibson, J.S.: Time-optimal control of robotic manipulators along specified paths. The International Journal of Robotics Research. 4(3), 3-17 (1985)Google Scholar
  15. 15.
    Karimi Eskandary, P., Belzile, B., Angeles, J.: Trajectory-Planning and Normalized-Variable Control for Parallel Pick-and-Place Robots. ASME Journal of Mechanisms and Robotics. Inpress, 1-15 (2018)Google Scholar
  16. 16.
    Karimi Eskandary, P., Angeles, J.: The dynamics of a parallel Sch¨oflies-motion generator. Mechanism and Machine Theory. 119, 119-129 (2018)Google Scholar
  17. 17.
    Karimi Eskandary, P., Angeles, J.: The translating Π-joint: Design and applications. Mechanism and Machine Theory. 122, 361370 (2018)Google Scholar
  18. 18.
    Angeles, J., Lee, S.:The formulation of dynamical equations of holonomic mechanical systems using a natural orthogonal complement. ASME J. of Applied Mechanics, 55(1), 243-244 (1988)Google Scholar
  19. 19.
    Gauthier, J.F., Angeles, J., Nokleby, S.B.: Optimization of a test trajectory for SCARA systems. In: Lenarčič, Thomas, F. (eds.) On Advances in Robot Kinematics. pp. 225-234. Springer, Amsterdam (2008)Google Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringCentre for Intelligent Machines, McGill UniversityMontrealCanada

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