Abstract
Determination of the safe working zone (SWZ) of a parallel manipulator is a one-time computational task with several permanent benefits. As this subspace of the workspace of the manipulator is free of both the loss- and gain-type singularities, link interference, as well as physical joint limits, the manipulator can move freely in this space. Moreover, if the natural choice of a convex-shaped SWZ is adhered to, then point-to-point path planning inside the SWZ always has a trivial solution, namely, a segment joining the two points, which is guaranteed to be inside the workspace. In this paper, the SWZ of the 3-RRS existing in the İzmir Institute of Technology has been computed. Starting with the geometry of the manipulator, the loop-closure constraint equations have been derived. The singularity conditions are obtained based on the singularity of certain Jacobian matrices associated with the constraint functions. The interference between the links are detected by first encapsulating the links in rectangular parallelepipeds, which are then discretized into triangles, and subjected to collision tests between the relevant pairs of triangles. Using these theoretical developments, the SWZ is computed. The numerical results are depicted graphically.
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 subscriptionsNotes
- 1.
Over-constrained and redundant manipulators are not considered here.
- 2.
Packing efficiency can be defined as the ratio of the volume of the link to the volume of its bounding box.
- 3.
This code is available for free download at https://github.com/benardp/contours/tree/master/freestyle/view_map/triangle_triangle_intersection.c.
- 4.
All the linear dimensions are in metres and all angles are in radians, unless mentioned otherwise explicitly.
References
Devillers, O., Guigue, P.: Faster triangle-triangle intersection tests. Tech. Rep. RR-4488, INRIA (2002). https://hal.inria.fr/inria-00072100
Itul, T., Pisla, D.: 446. On the kinematics and dynamics of 3-dof parallel robots with triangle platform. J. Vibroeng. 11(1) (2009)
Perrin, N., Stasse, O., Lamiraux, F., Kim, Y.J., Manocha, D.: Real-time footstep planning for humanoid robots among 3d obstacles using a hybrid bounding box. In: 2012 IEEE International Conference on Robotics and Automation (ICRA), pp. 977–982. IEEE (2012)
Srivatsan, R.A., Bandyopadhyay, S.: Computational Kinematics: Proceedings of the 6th International Workshop on Computational Kinematics (CK2013), Chap. Determination of the Safe Working Zone of a Parallel Manipulator, pp. 201–208. Springer, Netherlands, Dordrecht (2014)
Tetik, H., Kalla, R., Kiper, G., Bandyopadhyay, S.: Position Kinematics of a 3-\(\underline{{\rm {R}}}\)RS Parallel Manipulator. Accepted for Presentation at the 21st CISM-IFToMM Symposium on Robot Design, Dynamics, and Control, ROMANSY (2016)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing Switzerland
About this paper
Cite this paper
Patel, D., Kalla, R., Tetik, H., Kiper, G., Bandyopadhyay, S. (2017). Computing the Safe Working Zone of a 3-RRS Parallel Manipulator. In: Wenger, P., Flores, P. (eds) New Trends in Mechanism and Machine Science. Mechanisms and Machine Science, vol 43. Springer, Cham. https://doi.org/10.1007/978-3-319-44156-6_12
Download citation
DOI: https://doi.org/10.1007/978-3-319-44156-6_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-44155-9
Online ISBN: 978-3-319-44156-6
eBook Packages: EngineeringEngineering (R0)