Abstract
It has been shown elsewhere that the solution of the direct kinematic problem of spherical three-degree-of-freedom parallel manipulators leads to a maximum of 8 solutions. Moreover, a polynomial of degree 8 can be obtained, whose roots will lead to all the solutions of the problem. In this paper, a particular geometry of spherical parallel manipulator is studied. This geometry arises from kinematic optimization which has been performed in previous work. The direct kinematic problem associated with this special architecture is studied here and it is shown that a simple closed-form solution can be obtained for this manipulator, which contrasts with the very complex polynomial solution obtained for the general case. This work is mainly motivated by the real-time trajectory planning and control of a prototype of parallel manipulator which is based on the simplified geometry studied here.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
H.Asada and J.A. Cro Granito, ‘Kinematic and static characterization of wristjoints and their optimal design’, Proceedings of the IEEE InternationalConference on Robotics and Automation, pp. 244–250, 1985.
D.J.Cox and D. Tesar,The dynamic model of a three-degree-of-freedom parallelrobotic shoulder module5, Proceedings of the Fourth InternationalConferenceon Advanced Robotics, Columbus,June 13–15, 1989.
W.M.Craver, ‘Structural analysis and design of a three-degree-of-freedom roboticshoulder module’, Master Thesis, The University of Texas at Austin, 1989.
C. Gosselin and J. Angeles, ‘The optimum kinematic design of a sphericalthree-degree-of-freedom parallel manipulator’, ASME Journal of Mechanisms,Transmissions, and Automation in Design, Vol. 111, No. 2, pp. 202–207, 1989.
C.Gosselin and E. Lavoie, ‘On the kinematic design of sphericalthree-degree-of-freedom parallel manipulators’, The International Journal ofRobotics Research, Vol. 12, No. 4, pp. 394–402, 1993.
C.Gosselin and J.-F. Hamel, ‘The agile eye: a high-performancethree-degree-of-freedom camera-orienting device’, Proceedings of the IEEEInternational Conference on Robotics and Automation, San Diego, May, pp.781–786, 1994.
C.Innocenti and V. Parenti-Castelli, ‘Echelon form solution of direct kinematicsfor the general fully-parallel spherical wrist’, Mechanism and MachineTheory, Vol. 28, No. 4, pp. 553 561, 1993.
C.Gosselin, J. Sefrioui and M.J. Richard, ‘On the direct kinematics of sphericalthree-degree-of-freedom parallel manipulators with a coplanar platform’, ASMEJournal of Mechanical Design, Vol. 116, No. 2, pp. 587–593, 1994.
C.Gosselin, J. Sefrioui and M.J. Richard, ‘On the direct kinematics of sphericalthree-degree-of-freedom parallel manipulators of general architecture’, ASMEJournal of Mechanical Design, Vol. 116, No. 2, pp. 594–598, 1994.
K.Wohlhart,‘Displacementanalysis of the general spherical Stewart platform’, Mechanism and MachineTheory, Vol. 29, No. 4, pp. 581–589, 1994.
H.R.M.Daniali, P.J. Zsombor-Murray and J. Angeles, ‘Isotropic design of sphericalparallel manipulators’, Proceedings of the ASME Design AutomationConference, Minneapolis, September 11–14, Volume 2, 1994.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Gosselin, C.M., Gagné, M. (1995). A Closed-Form Solution for the Direct Kinematics of a Special Class of Spherical Three-Degree-of-Freedom Parallel Manipulators. In: Merlet, JP., Ravani, B. (eds) Computational Kinematics ’95. Solid Mechanics and Its Applications, vol 40. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0333-6_24
Download citation
DOI: https://doi.org/10.1007/978-94-011-0333-6_24
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4147-8
Online ISBN: 978-94-011-0333-6
eBook Packages: Springer Book Archive