Abstract
This paper presents a novel geometric solution to the problem of finding singularity-free paths joining two arbitrary points in the constant orientation workspace of a semi-regular Stewart platform manipulator. The formulation builds upon the known closed-form expression for the gain-type singularity surface of the manipulator. Using a rational parametrisation of the surface, it computes the geodesic curve on this surface, connecting the projections of the two given points on this surface. A sequence of spheres is then constructed in such a manner that each sphere is tangential to a previous one as well as the singularity surface, at a point on the said geodesic curve. Thus the geodesic curve acts as a guide, over which the singularity-free sphere is rolled, till it reaches its destination. Multiple methods for computing such sequences of spheres are presented and compared with the help of a numerical example. Finally, a sequence of line segments connecting the centres of the spheres is constructed, which connects the two given points via a provably singularity-free path.
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
Similar content being viewed by others
Notes
- 1.
Flowcharts for the other methods could not be included for the want of space.
References
Dasgupta B, Mruthyunjaya T (1998) Singularity-free path planning for the Stewart platform manipulator. Mech Mach Theory 33(6):711–725
Dash AK, Chen IM, Yeo SH, Yang G (2003) Singularity-free path planning of parallel manipulators using clustering algorithm and line geometry. In: 2003 IEEE international conference on robotics and automation (Cat. No.03CH37422), vol 1, pp 761–766
Sen S, Dasgupta B, Mallik AK (2003) Variational approach for singularity-free path-planning of parallel manipulators. Mech Mach Theory 38:1165–1183
Bandyopadhyay S, Ghosal A (2004) Analysis of configuration space singularities of closed-loop mechanisms and parallel manipulators. Mech Mach Theory 39:519–544
Coste M, Moussa S (2015) On the rationality of the singularity locus of a Gough-Stewart platform biplanar case. Mech Mach Theory 87:82–92
Nag A, Reddy V, Agarwal S, Bandyopadhyay S (2018) Identifying singularity-free spheres in the position workspace of Semi-regular Stewart Platform Manipulators. In: Lenarčič J, Merlet JB (eds.) Advances in Robot Kinematics 2016, Cham, pp 421–430. Springer International Publishing
Bandyopadhyay S, Ghosal A (2006) Geometric characterization and parametric representation of the singularity manifold of a 6–6 Stewart platform manipulator. Mech Mach Theory 41(11):1377–1400
Srivatsan RA, Bandyopadhyay S (2014) Determination of the safe working zone of a parallel manipulator. In: Thomas F, Perez Gracia A (eds) Computational kinematics: proceedings of the 6th international workshop on computational kinematics (CK2013), Dordrecht, pp 201–208. Springer Netherlands
Ghosal A (2006) Robotics: fundamental concept and analysis. Oxford University Press, India, New-Delhi
Somasundaram D (2010) Differential geometry: a first course. Alpha Science International Limited, New-Delhi
Wolfram Research Inc (2016) Mathematica, Version 11.0. Champaign, IL
Acknowledgements
The authors would like to thank Mr. Anirban Nag, Doctoral scholar and Ms. Shivani Guptasarma, Dual Degree student, both in the Department of Engineering Design, Indian Institute of Technology Madras, for reading this paper thoroughly and suggesting improvements. The first author would also like to thank Council of Scientific & Industrial Research (CSIR) for the scholarship provided under the grant number: 09/084(0697)/2017-EMR-I.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Prasad, P.K., Bandyopadhyay, S. (2021). A Geometric Method for Non-singular Path-planning in the Constant Orientation Workspace of a Stewart Platform Manipulator. In: Sen, D., Mohan, S., Ananthasuresh, G. (eds) Mechanism and Machine Science. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-15-4477-4_6
Download citation
DOI: https://doi.org/10.1007/978-981-15-4477-4_6
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-4476-7
Online ISBN: 978-981-15-4477-4
eBook Packages: EngineeringEngineering (R0)