Abstract
This paper proposes a novel approach to obtain the maximal singularity-free regions of planar parallel mechanisms which is based on a constructive geometric reasoning. The proposed approach consists of two algorithms. First, the borders of the singularity-free region corresponding to an arbitrary start point of the moving platform is obtained. Then, the second algorithm aims to find the center of the maximal singularity-free circle which is obtained using the so-called offset curve algorithm. As a case study, the procedure is applied to a 3-PRR planar parallel mechanism and results are given in order to graphically illustrate the effectiveness of the proposed algorithm. The proposed approach can be directly applied to obtain the maximal singularity-free circle of similar parallel mechanisms, which is not the case for other approaches proposed in the literature which is limited to a given parallel mechanism, namely, 3-RPR. Moreover, as the main feature of the proposed approach, it can be implemented both in a CAD system or in a computer algebra system where non-convex and re-entrant curves can be considered.
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 subscriptionsReferences
Aichholzer, O., Aigner, W., Aurenhammer, F., Hackl, T., Jüttler, B., Pilgerstorfer, E., Rabl, M.: Divide-and-conquer for voronoi diagrams revisited. Comput. Geom. 43(8), 688–699 (2010)
Bonev, I.A.: Geometric analysis of parallel mechanisms. Ph.D. thesis, Laval University, Quebec, QC, Canada (2002)
Davidson, J., Hunt, K., Pennock, G.: Robots and Screw Theory: Applications of Kinematics and Statics to Robotics. Oxford University Press, New York (2004)
Elber, G., Lee, I., Kim, M.: Comparing offset curve approximation methods. IEEE Comput. Graphics Appl. 17(3), 62–71 (1997)
Gosselin, C.: Determination of the workspace of 6-DOF parallel manipulators. ASME J. Mech. Des. 112(3), 331–336 (1990)
Jiang, L.: Singularity-free workspace analysis and geometric optimization of parallel mechanisms. Ph.D. thesis, Laval University, Quebec (2008)
Li, H., Gosselin, C., Richard, M.: Determination of maximal singularity-free zones in the workspace of planar three-degree-of-freedom parallel mechanisms. Mech. mach. theory 41(10), 1157–1167 (2006)
Merlet, J.P.: Parallel Robots. Springer, Dordrecht (2006)
Rao, S.: Engineering optimization: theory and practice. Wiley, New York (2009)
Yang, Y., O’Brien, J.: A case study of planar 3-RPR parallel robot singularity free workspace design. In: International Conference on Mechatronics and Automation (ICMA), pp. 1834–1838. IEEE (2007)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Kaloorazi, M.H.F., Masouleh, M.T., Caro, S., Gholamali, B.M. (2014). Determination of Maximal Singularity-Free Workspace of Parallel Mechanisms Using Constructive Geometric Approach. In: Thomas, F., Perez Gracia, A. (eds) Computational Kinematics. Mechanisms and Machine Science, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7214-4_34
Download citation
DOI: https://doi.org/10.1007/978-94-007-7214-4_34
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-7213-7
Online ISBN: 978-94-007-7214-4
eBook Packages: EngineeringEngineering (R0)