Abstract
The aim of this paper is to compute of the generalized aspects, i.e. the maximal singularity-free domains in the Cartesian product of the joint space and workspace, for a planar parallel mechanism in using quadtree model and interval analysis based method. The parallel mechanisms can admit several solutions to the inverses and the direct kinematic models. These singular configurations divide the joint space and the workspace in several not connected domains. To compute this domains, the quadtree model can be made by using a discretization of the space. Unfortunately, with this method, some singular configurations cannot be detected as a single point in the joint space. The interval analysis based method allow us to assure that all the singularities are found and to reduce the computing times. This approach is tested on a simple planar parallel mechanism with two degrees of freedom.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Merlet, J-P., “Workspace-Oriented Methodology for Designing a Parallel Manipulator,” Proc. IEEE Int. Conf. on Robotics and Automation, pp. 3726–3731,1996.
Clavel, R., “DELTA, a Fast Robot with Parallel Geometry,” Proc. 18th Int. Symposium of Industrial Robots, pp. 91–100, 1988.
Gosselin, C. and Angeles, J., “A Global Performance Index for the Kinematic Optimization of Robotic Manipulators,” Journal of Mechanical Design, vol. 113, pp. 220–226, 1991.
Wenger Ph., and Chablat D., “Definition Sets for the Direct Kinematics of Parallel Manipulators,” Proc. 8th International Conference in Advanced Robotics, pp. 859–864, 1997.
Chablat D., and Wenger Ph., “Working Modes and Aspects in Fully-Parallel Manipulator,” Proc. IEEE International Conference on Robotics and Automation, pp. 1964–1969, May 1998.
Borrel, P., “A study of manipulator inverse kinematic solutions with application to trajectory planning and workspace determination,” Proc. IEEE International Conference on Robotic And Automation, pp. 1180–1185, 1986.
Merlet, J-P., “ALIAS: an interval analysis based library for solving and analyzing system of equations,” Pro. Séminaire Systèmes et équations algébriques, SEA, June, pp. 1964–1969, 2000.
Chablat D., Wenger P., Majou F., and Merlet J.P., ”An Interval Analysis Based Study for the Design and the Comparison of 3-DOF Parallel Kinematic Machine”, International Journal of Robotics Research, pp. 615–624, vol. 23(6), June 2004.
Meagher, D., “Geometric Modelling using Octree Encoding”, Technical Report IPL-TR-81-005, Image Processing Laboratory, Rensselaer Polytechnic Institute, Troy, 1981, New York 12181.
Faverjon B., “Obstacle avoidance using an octree in the configuration space of a manipulator”, Proc. IEEE International Conference on Robotics And Autaumation, pp. 504–510, 1984.
Garcia G., Wenger P., Chedmail P., “Computing moveability areas of a robot among obstacles using octrees”, Proc. International Conference on Advanced Robotics, Columbus, Ohio, USA, June 1989.
Figielski, A., Bonev, I.A., and Bigras, P., “Towards Development of a 2-DOF Planar Parallel Robot with Optimal Workspace Use”, IEEE International Conference on Systems, Man, and Cybernetics (SMC 2007), Montréal, QC, Canada, 7–10 October 2007.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 CISM, Udine
About this paper
Cite this paper
Chablat, D. (2010). Joint space and workspace analysis of a two-DOF closed-chain manipulator. In: Parenti Castelli, V., Schiehlen, W. (eds) ROMANSY 18 Robot Design, Dynamics and Control. CISM International Centre for Mechanical Sciences, vol 524. Springer, Vienna. https://doi.org/10.1007/978-3-7091-0277-0_9
Download citation
DOI: https://doi.org/10.1007/978-3-7091-0277-0_9
Publisher Name: Springer, Vienna
Print ISBN: 978-3-7091-0276-3
Online ISBN: 978-3-7091-0277-0
eBook Packages: EngineeringEngineering (R0)