Abstract
A semigraphical method is presented for computing all real direct kinematic solutions of platform-type parallel manipulators with general geometries. The direct kinematic problem is reduced to basically two bivariate equations in the sines and cosines of two unknown angles. One equation is derived by solving an overdetermnined system of equations that can be perturbed by different multiples of the least-square error involved in the solutions. Upon perturbing this equation by two different multiples, two distinct equations are obtained. The first bivariate equation and each of these two equations define three contours in the plane of the two angles involved, the intersections of these contours providing all real solutions. The method is uscd to finnd all rcal dircct kincmatic soluticr.s of a general parallel manipulator of the platform type.
Key words
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Angeles, J., Ranjbaran, F., and Patel, R. V.: 1992, ‘On the Design of the Kinemmatic Structure of Seven-Axis Redundant Manipulators for Maximum Conditioning’, Proc. IEEE Int. Conf. on Robotics and Automation, Nice, May 12–14, pp. 494–499.
Angeles, J. and Zanganeh, K. E.: 1992, ‘The Semigraphical Solution of the Direct Kinematics of General Platform Manipulators’, Proc. 4th Int. Symp. on Robotics and Manufacturing, Santa Fe, Nov. 11–13, pp. 45–52.
Golub, G. H. and Van Loan, C.: 1989, Matrix Computations, Johns Hopkins: Baltimore.
Innocenti, C., and Parenti-Castelli, V.: 1993, ‘Forward Kinematics of the general 6–6 FullyParallel Mechanism: An Exhaustive Numerical Approach Via a Mono-Dimensional-Search Algorithm’, to appear in ASME, J. Mechanical Design.
Lazard, D.: 1992, ‘Stewart Platforms and Gröbner Basis’, Proc. 3rd Int. Workshop on
Advances in Robot Kinematics, Ferrara, Sept. 7–9, pp. 136–142.
Parenti-Castelli, V.: 1992, ‘Recent Techniques for Direct Position Analysis of the Generalized Stewart Platform Mechanism’, Proc. 3rd Int. Workshop on Advances in Robot Kinematics, Ferrara, Sept. 7–9, pp. 129–135.
Raghavan, M.: 1991, ‘The Stewart Platform of General Geometry Has 40 Configurations’ in Gabriele, G. A., ed., Advances in Design Automation, ASME Press: New York, pp. 397–402.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Zanganeh, K.E., Angeles, J. (1993). The Semigraphical Solution of the Direct Kinematics of General Platform-Type Parallel Manipulators. In: Angeles, J., Hommel, G., Kovács, P. (eds) Computational Kinematics. Solid Mechanics and Its Applications, vol 28. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8192-9_15
Download citation
DOI: https://doi.org/10.1007/978-94-015-8192-9_15
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4342-9
Online ISBN: 978-94-015-8192-9
eBook Packages: Springer Book Archive